shelton_1994#

D. P. Shelton and J. E. Rice, Chem. Rev. 94, 3 (1994)

Source record · Catalogue · Review register

Source kind: compilation

Recorded technique: Review of gas-phase measurements (dc Kerr, ESHG, THG, ac Kerr, CARS, DFWM) and ab initio calculations of the first and second hyperpolarizabilities beta and gamma of atoms and small molecules, with the authors’ recommended dispersion fits and a few calculations of their own (Table VIII notes h, i: vibrational and rotational gamma in the full quantum and classical limits). Experimental values calibrated against He are rescaled by the authors to Bishop & Pipin’s ab initio He (ref 100 = bishop_1989).

Materials in structured entries: Ar, CH4, CO, CO2, D2, H2, He, Kr, N2, Ne, O2, SF6, Xe

Dataset quantities: hyperpolarizability

Contents: 77 datasets; 20 formulas.

Curation notes#

Almost every value here is reproduced from an original paper (named per dataset); only the Table VIII values under notes h and i are the review’s own. Page numbers are the journal’s (the PDF page plus 2).

DEFINITIONS (Section II.A, pp. 3-5), the Taylor-series (‘T’) convention. Eqs 1-3 (p. 3): mu_a(nu_s) = alpha_ab(-nu_s; nu_1) E_b(nu_1) + (1/2) K^(2) beta_abc(-nu_s; nu_1, nu_2) E_b(nu_1) E_c(nu_2) + (1/6) K^(3) gamma_abcd(-nu_s; nu_1, nu_2, nu_3) E_b(nu_1) E_c(nu_2) E_d(nu_3), ‘the terms of the Taylor series for the molecular dipole mu ... linear, quadratic, and cubic in the amplitudes of the monochromatic components of the applied field’; each term is ‘an induced dipole fluctuating at the sum frequency nu_s = sum_i nu_i’. ‘The factors K^(n) are required in order that all hyperpolarizabilities of the same order have the same static limit.’ The field is written E = E_o + E_omega cos(omega t) (p. 6), so the amplitudes are those of cos(omega t) and the factors K^(n) ‘are essentially the combinatoric and trigonometric factors in the multinomial expansion of the n-th power of the sum of applied fields’ (Table I note a). Table I (p. 4), third order, (-nu_s; nu_1, nu_2, nu_3) and K^(3): static (0; 0, 0, 0), 1; dc Kerr (-nu; 0, 0, nu), 3; ac Kerr (-nu_2; nu_1, -nu_1, nu_2), 3/2; CARS (-2nu_1 + nu_2; nu_1, nu_1, -nu_2), 3/4; DFWM (-nu; nu, nu, -nu), 3/4 (‘also called nonlinear refractive index or intensity dependent refractive index’); ESHG (-2nu; nu, nu, 0), 3/2; THG (-3nu; nu, nu, nu), 1/4. In the static limit all these gamma coincide. Measured gas quantities (p. 4): gamma_par = (1/15) sum_{xi,eta} {gamma_xixietaeta + gamma_xietaetaxi + gamma_xietaxieta} (eq 5, <gamma>_zzzz, all fields parallel); gamma_perp = (1/15) sum {2 gamma_xietaetaxi - gamma_xixietaeta} (eq 7, <gamma>_zxxz); dc Kerr measures gamma_K = (3/2)(gamma_par - gamma_perp); statically gamma_par = 3 gamma_perp and gamma_K = gamma_par (= gamma_o). ‘gamma’ in the tables is gamma_par, or gamma_K for dc Kerr. ESHG measures {gamma + mu beta/3kT} (eq 8, p. 5). dc Kerr measures the molar Kerr constant A_K = (N_A/81 eps_o) {gamma + 2 mu beta/3kT + (3/10)[(sum alpha_xieta alpha^(0)_xieta - alpha alpha^(0))/kT] + [mu^2 (alpha_zz - alpha)/(kT)^2]} (eq 9), for a homonuclear diatomic {gamma + Delta alpha Delta alpha^(0)/5kT}. The paper gives no relation to chi(3) or n2.

UNITS (Table II, p. 5; 1986 CODATA): gamma, 1 au = 1 e^4 a_o^4 E_h^-3 = 6.235 377 x 10^-65 C^4 m^4 J^-3 (SI) = 7.042 3 x 10^-54 m^5 V^-2 (‘SI alternative’, ‘obtained when the right-hand sides of eqs 1-3 are multiplied by eps_o’) = 5.036 7 x 10^-40 cm^5 statvolt^-2 (esu = cm^6 erg^-1). omega = 1 au is nu = 219 474.630 7 cm^-1, ‘where nu is the reciprocal of the vacuum wavelength ... (note that experimental wavelengths differ slightly from 1/nu since they are measured in air)’: the nm column headings (632.8, 694.3, 514.5, 1055, 532, 458) are laser lines in air (standard_air here).

DISPERSION (p. 11): below the first electronic resonance gamma_par(-nu_s; nu_1, nu_2, nu_3) = gamma_par(0; 0, 0, 0) [1 + A nu_L^2 + B nu_L^4 + C nu_L^6 ...] (eq 18), nu_L^2 = nu_s^2 + nu_1^2 + nu_2^2 + nu_3^2 (eq 19), ‘where the coefficient A is independent of nu_s, nu_1, nu_2, nu_3, but B, C, etc. are not’; nu_L^2 = 2 nu^2, 4 nu^2, 6 nu^2, 12 nu^2 for dc Kerr, DFWM, ESHG, THG. gamma_par/gamma_perp = 3 [1 + A’ nu_L^2 + ...] (eq 20), A’ = r (1 - 6a) (eq 21), a = (nu_s nu_3 - nu_1 nu_2)/nu_L^2 (eq 22): A’ in the ratios -1:2:1:0 for dc Kerr, DFWM, ESHG, THG. The relations ‘are in fact also valid for the electronic hyperpolarizabilities of molecules’ but not for gamma^v and gamma^R (pp. 11, 14). For H, ‘at nu_L^2 = 20 x 10^8 cm^-2 ... the dispersion curves for dc Kerr, DFWM, ESHG, and THG ... differ by no more than 0.7%’ (p. 11-12). Table VII and Table X give the fits (formulas below); they are fitted up to nu_L^2 = 6 nu^2 = 30 x 10^8 cm^-2, and ‘The fitted value of B so obtained will be somewhat sensitive to the frequency range of the data used in the fit, but the fitted value of A should be reliable’ (p. 12).

PARTS (pp. 6-7, 14-17). gamma = gamma^e + gamma^v + gamma^R (Born-Oppenheimer). ‘The contribution due to vibrational and rotational terms tends to increase in the order THG < ESHG < DFWM, ac Kerr, CARS, dc Kerr’ (p. 4). For ESHG and THG gamma^R ‘will be reduced by a typical factor (omega_R/omega)^2 ~ 10^-5 and will be negligible’; for dc Kerr, ac Kerr and DFWM ‘gamma^R at optical frequencies will be comparable to the static value’; in the high-frequency limit gamma_par^R for ac Kerr and DFWM are 2/3 and 8/9 of gamma_K^R for dc Kerr, and the static gamma_K^R is 4/3 of its optical value; M-sublevel redistribution ‘accounts for about 1/4 of gamma^R for the dc Kerr effect’ (eqs 31-32, p. 14). The experimental gamma^e of H2, D2, N2, O2 (Tables IX, X) are ESHG values with calculated gamma^vR subtracted, then extrapolated to the static limit; for H2 the subtracted gamma^v may be uncertain by up to +-6 % (+-1 au) in the infrared, ‘although the actual error is thought to be much smaller’ (pp. 16-17). The polyatomic experimental values are gamma^ev (Table XII), except CARS with ‘vibrational contributions of alpha^2 type subtracted’. For CO2 (ESHG) the vibrational contribution is ‘about 6%’ (p. 20).

ACCURACY. ‘The reported accuracy of gas-phase hyperpolarizability measurements ...: dc Kerr (0.5-100%), ESHG (0.1-20%), THG (3-20%), ac Kerr, CARS and DFWM (5-100%)’; ‘local field corrections are usually much smaller than 1%’ (p. 4). The He calculation of Bishop & Pipin ‘is thought to be better than 0.1%’ (p. 11). Reduced-mass corrections ‘increase the calculated static values of gamma [by] 0.382%, 0.191%, 0.096%, and 0.019%’ for H, D, He and Ne (p. 10); Table IV is without, Tables VI, VII with them (He: 43.104 against 43.145). Relativistic corrections reduce gamma by less than 1 % for Kr and Xe (p. 10). Intermolecular (pair) effects in the H2 ESHG measurements ‘are at the 0.1% level’ (p. 16, ref 35 = donley_1993). For polyatomics: ‘For the five molecules where there is a pair of independent ESHG measurements at the same wavelength ... the average experimental error bar is +-1.3% and the independent measurements tend to agree to within their joint uncertainty (reduced chi^2 = 1.3)’ (p. 20). Measurements of Ne by Shelton & Lu (ref 37) ‘have been shown to be invalid’ (Fig. 3 caption): the anomalous Ne dispersion is ‘now discredited’ (see shelton_1992).

NOT TABULATED, from the text: local-density static gamma_0 of He, Ne, Ar, Kr, Xe, 88, 211, 1860, 3950 and 9160 au, and with partial self-interaction corrections 35, 86, 1330, 3200 and 8350 au (ref 105a,b; p. 9-10), ‘values which differ markedly from the CCSD(T) results and from experiment’: not extracted (inadequate method, per the authors). Two-electron scaling gamma_o = 2420 x (Z - 0.5)^-10 au (He to Ne8+, +-3 %, p. 10). Figures 1-7 (dispersion plots) are not digitised.

ERRATA IN REFERENCES (not values). Table VII note d attributes the static CCSD(T) Ne value to ref 171 and notes k and m the Ar, Kr, Xe values to ref 170; Table IV, Table V note a and the Figure 3 and 4 captions give the opposite (170 = Rice et al. 1992, ‘Connected triple excitations ... neon’, 171 = Rice et al. 1991, the heavier noble gases). The records follow Table IV. Table IX prints O2’s static gamma^e as 962 +- 6 and Table X as 963 for the same fit (shelton_1990: 60.03e-63 / 6.235377e-65 = 962.7 au). The library’s text of this paper omits references 34 and 35 and 128 and 131 (column breaks); read from the PDF page images: (34) Shelton, D. P. Phys. Rev. A 1990, 42, 2578 (= shelton_1990); (35) Donley, E. A.; Shelton, D. P. Chem. Phys. Lett. 1993, 215, 156 (= donley_1993); (128) Malik, D. J. J. Chem. Phys. 1988, 88, 2624; (131) Bishop, D. M.; Lam, B. Chem. Phys. Lett. 1988, 143, 515.

SPECIES. Only curated species are extracted: He, Ne, Ar, Kr, Xe, H2, D2, N2, O2, CO, CO2, CH4, SF6. Skipped: H, H-, the two- to twelve-electron ions and Li to F, Mg, Ca (Table IV); H2+, HF (Table VIII); Li2, F2, Cl2, Br2, LiH, BH, CH+, OH+/-, NeH+, HF, HCl, NO (Table IX); NH3, H2O (Table XI); CF4, CCl4, C(CH3)4, the halomethanes, HCN, C2H2, C4H2, CS2, NH3, CH3CN, C3H6, C6H6 and the other hydrocarbons, H2O, H2S, SO2, CH3OH, (CH3)2O (Table XII); all beta values (Tables VIII, IX, XII(a), XIII: first hyperpolarizabilities). N2O and O3 do not appear.

DUPLICATE. The library’s second copy (Shelton_1994_MeasurementsCalculationsHyperpolarizabilities_058fee, same DOI, a different PDF file) has the same fourteen tables; every number in every table agrees with this copy’s (compared 2026-09-26). This copy is used.

Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets#

shelton_1994/table4_He#

{
  "id": "table4_He",
  "material": "He",
  "file": "He/shelton_1994__table4_He.csv",
  "table": "tbl_fbf8e009a36f",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1989",
    "T. Voegel, J. Hinze and F. Tobin, J. Chem. Phys. 70, 1107 (1979)"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

shelton_1994/table4_Ne#

{
  "id": "table4_Ne",
  "material": "Ne",
  "file": "Ne/shelton_1994__table4_Ne.csv",
  "table": "tbl_fbf8e009a36f",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "J. E. Rice, G. E. Scuseria, T. J. Lee, P. R. Taylor and J. Almlof, Chem. Phys. Lett. 191, 23 (1992)",
    "T. Voegel, J. Hinze and F. Tobin, J. Chem. Phys. 70, 1107 (1979)"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table IV (p. 9): static gamma_0 = gamma_par(0;0,0,0) of the atom, ab initio with electron correlation (first row) and at the SCF level (second row). ‘The ab initio results in this table are reported without reduced mass corrections’ (note a); # marks a calculation that also gives a dispersion curve. Note k: ref 170 (Rice et al. 1992, CCSD(T), static; MP2 dispersion curve in ref 122 = rice_1992). Note e: ref 108 numerical SCF. Table V’s CCSD(T)/I value from the same ref 170 is 111.2: Table IV prints the rounded 110 (Table V note a: ‘best theoretical estimate 110 +- 3 au’).

shelton_1994/table4_Ar#

{
  "id": "table4_Ar",
  "material": "Ar",
  "file": "Ar/shelton_1994__table4_Ar.csv",
  "table": "tbl_fbf8e009a36f",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "rice_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table IV (p. 9): static gamma_0 = gamma_par(0;0,0,0) of the atom, ab initio with electron correlation (first row) and at the SCF level (second row). ‘The ab initio results in this table are reported without reduced mass corrections’ (note a); # marks a calculation that also gives a dispersion curve. Note n: ref 171 (Rice, Taylor, Lee & Almlof, J. Chem. Phys. 94, 4972 (1991) = rice_1991), CCSD(T) and SCF, static; MP2 dispersion curves in ref 122 (rice_1992).

shelton_1994/table4_Kr#

{
  "id": "table4_Kr",
  "material": "Kr",
  "file": "Kr/shelton_1994__table4_Kr.csv",
  "table": "tbl_fbf8e009a36f",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "rice_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

shelton_1994/table4_Xe#

{
  "id": "table4_Xe",
  "material": "Xe",
  "file": "Xe/shelton_1994__table4_Xe.csv",
  "table": "tbl_fbf8e009a36f",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "rice_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table IV (p. 9): static gamma_0 = gamma_par(0;0,0,0) of the atom, ab initio with electron correlation (first row) and at the SCF level (second row). ‘The ab initio results in this table are reported without reduced mass corrections’ (note a); # marks a calculation that also gives a dispersion curve. Note n: ref 171 (rice_1991), CCSD(T) and SCF, static (no # mark: no dispersion curve). ‘The relativistic corrections reduce gamma by less than 1% for Kr and Xe’ (p. 10).

shelton_1994/table5_Ne#

{
  "id": "table5_Ne",
  "material": "Ne",
  "file": "Ne/shelton_1994__table5_Ne.csv",
  "table": "tbl_38363e48379b",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "J. E. Rice, G. E. Scuseria, T. J. Lee, P. R. Taylor and J. Almlof, Chem. Phys. Lett. 191, 23 (1992)",
    "rice_1992",
    "H. J. A. Jensen, P. Jorgensen, H. Hettema and J. Olsen, Chem. Phys. Lett. 187, 387 (1991)",
    "D. P. Chong and S. R. Langhoff, J. Chem. Phys. 93, 570 (1990)",
    "G. Maroulis and A. J. Thakkar, Chem. Phys. Lett. 156, 87 (1989)",
    "M. Jaszunski and D. L. Yeager, Phys. Rev. A 40, 1651 (1989)",
    "I. Cernusak, G. H. F. Diercksen and A. J. Sadlej, Phys. Rev. A 33, 814 (1986)",
    "P. D. Dacre, Can. J. Phys. 60, 963 (1982)",
    "T. Voegel, J. Hinze and F. Tobin, J. Chem. Phys. 70, 1107 (1979)",
    "P. R. Taylor, T. J. Lee, J. E. Rice and J. Almlof, Chem. Phys. Lett. 163, 359 (1989); erratum 189, 197 (1992)",
    "G. Maroulis and D. M. Bishop, Chem. Phys. Lett. 114, 182 (1985)",
    "R. Klingbeil, Phys. Rev. A 7, 376 (1973)",
    "E. Leuliette-Devin and R. Locqueneux, Chem. Phys. Lett. 19, 497 (1973)",
    "R. E. Sitter and R. P. Hurst, Phys. Rev. A 5, 5 (1972)",
    "H. D. Cohen, J. Chem. Phys. 45, 10 (1966)"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table V (p. 10): ab initio static gamma_0 of Ne by method and basis set, rows ‘method basis (ref n)’ as printed (two side-by-side lists, left then right). Basis sets (note b): I [4+1+1s 3+1+1p 2+1+1d 1+1f]+(3s 3p 2d 3f 2g) or [9s 8p 6d 5f 2g]; II [4+1s 3+1p 2+1d 1+1f]+(3s 3p 2d 3f) or [8s 7p 5d 5f]; III [4s 3p 2d 1f]+(4s 3p 4d 5f) or [8s 7p 6d 6f]; IV [10s 8p 6d 4f], (a) spherical, (b) Cartesian polarization functions; V [9s 6p 5d 3f]; VI [7s 4p 3d]. ‘An asterisk (*) indicates that gamma was determined assuming mu(E) = alpha + gamma E^3/6 with field strengths of 0.001 and 0.01 au’ (note a): rows ‘CISD VI (ref 177)’ (116*) and ‘SCF VI (ref 177)’ (84*). The VPT cell prints two values, ‘8, 65’ (ref 179): rows ‘VPT (ref 179) a’ and ‘b’. Note a: ‘The present best experimental estimate of gamma_0 is 108 +- 2 au (ref 33 = shelton_1992), as compared with the best theoretical estimate 110 +- 3 au (ref 170), and the Hartree-Fock limit 70 au (ref 108).’ Refs: 170 Rice et al. 1992; 122 rice_1992; 104 Jensen et al. 1991; 173 Chong & Langhoff 1990; 174 Maroulis & Thakkar 1989; 103 Jaszunski & Yeager 1989; 175 Cernusak et al. 1986; 177 Dacre 1982; 108 Voegel et al. 1979 (NHF = numerical Hartree-Fock); 110 Taylor et al. 1989; 176 Maroulis & Bishop 1985; 178 Klingbeil 1973; 179 Leuliette-Devin & Locqueneux 1973; 156 Sitter & Hurst 1972; 181 Cohen 1966.

shelton_1994/table6_He_dc_kerr_expt#

{
  "id": "table6_He_dc_kerr_expt",
  "material": "He",
  "file": "He/shelton_1994__table6_He_dc_kerr_expt.csv",
  "table": "tbl_678f6d31104f",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "tammer_1992",
    "carusotto_1985",
    "buckingham_1968",
    "boyle_1966"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "electronic"
  }
}

Table VI (p. 11): He, ‘ab initio values of gamma(He) from the CI-Hylleraas calculation of Bishop and Pipin (ref 100) compared with the results of absolute experimental determinations’. Note a: ‘Theory and experiment agree to within the stated experimental uncertainty except for one dc Kerr measurement. The best test is at the 2% level of accuracy. The values of gamma_calc include the reduced mass correction.’ The dc Kerr gamma is gamma_K = (3/2)(gamma_par - gamma_perp) (p. 4), equal to gamma_par in the Kleinman (static) limit. Wavelengths are laser lines as printed, in air (Table II note a). Rows by the reference: 11 Tammer et al. 1992; 19 Carusotto, Iacopini & Polacco 1985; 30 Buckingham & Dunmur 1968 (buckingham_1968, as converted to gamma by Shelton & Rice); 31 Boyle et al. 1966. Re-pointed 2026-09-26 (the dataset averages several sources and is not split): row ‘ref 11’ (44.3 +- 0.8 au) is Tammer et al.’s (tammer_1992/table3_gamma_He: 27.6(5) x 10^-64 C^4 m^4 J^-3 / 6.2354e-65 = 44.26 au, digit-identical; its error contains a 1.3 % systematic part); row ‘ref 19’ (47.3 +- 3 au at 514.5 nm) is Shelton & Rice’s conversion to gamma of carusotto_1985’s K(He) = 0.134 +- 0.009 x 10^-17 cm^2 statV^-2 amagat^-1 (no gamma is printed there). Re-pointed 2026-09-27: row ‘ref 31’ (51.6 +- 8 au) is Boyle et al.’s (boyle_1966: (2.6 +- 0.4) x 10^-38 esu / 5.0367e-40 = 51.62, 0.4e-38 -> 7.9; checked).

shelton_1994/table6_He_thg_expt#

{
  "id": "table6_He_thg_expt",
  "material": "He",
  "file": "He/shelton_1994__table6_He_thg_expt.csv",
  "table": "tbl_678f6d31104f",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "lehmeier_1985"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "electronic"
  }
}

shelton_1994/table6_He_dc_kerr_calc#

{
  "id": "table6_He_dc_kerr_calc",
  "material": "He",
  "file": "He/shelton_1994__table6_He_dc_kerr_calc.csv",
  "table": "tbl_678f6d31104f",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1989"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "electronic"
  }
}

shelton_1994/table6_He_thg_calc#

{
  "id": "table6_He_thg_calc",
  "material": "He",
  "file": "He/shelton_1994__table6_He_thg_calc.csv",
  "table": "tbl_678f6d31104f",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1989"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "electronic"
  }
}

shelton_1994/table8_H2_gammav_static#

{
  "id": "table8_H2_gammav_static",
  "material": "H2",
  "file": "H2/shelton_1994__table8_H2_gammav_static.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note e: ref 197 (Bishop, Pipin & Cybulski 1991 = bishop_1991).

shelton_1994/table8_H2_gammav_dc_kerr#

{
  "id": "table8_H2_gammav_dc_kerr",
  "material": "H2",
  "file": "H2/shelton_1994__table8_H2_gammav_dc_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table8_H2_gammav_kerr#

{
  "id": "table8_H2_gammav_kerr",
  "material": "H2",
  "file": "H2/shelton_1994__table8_H2_gammav_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "kerr",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): DFWM 0.759 x 10^-62 C^4 m^4 J^-3 of shelton_1987 Table 4 = 121.7 au (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_H2_gammav_eshg#

{
  "id": "table8_H2_gammav_eshg",
  "material": "H2",
  "file": "H2/shelton_1994__table8_H2_gammav_eshg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table8_H2_gammav_thg#

{
  "id": "table8_H2_gammav_thg",
  "material": "H2",
  "file": "H2/shelton_1994__table8_H2_gammav_thg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table8_D2_gammav_static#

{
  "id": "table8_D2_gammav_static",
  "material": "D2",
  "file": "D2/shelton_1994__table8_D2_gammav_static.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table8_D2_gammav_dc_kerr#

{
  "id": "table8_D2_gammav_dc_kerr",
  "material": "D2",
  "file": "D2/shelton_1994__table8_D2_gammav_dc_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table8_D2_gammav_kerr#

{
  "id": "table8_D2_gammav_kerr",
  "material": "D2",
  "file": "D2/shelton_1994__table8_D2_gammav_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "kerr",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): DFWM 0.737 x 10^-62 (unchanged by the correction) = 118.2 au (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_D2_gammav_eshg#

{
  "id": "table8_D2_gammav_eshg",
  "material": "D2",
  "file": "D2/shelton_1994__table8_D2_gammav_eshg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table8_D2_gammav_thg#

{
  "id": "table8_D2_gammav_thg",
  "material": "D2",
  "file": "D2/shelton_1994__table8_D2_gammav_thg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table8_N2_gammav_static#

{
  "id": "table8_N2_gammav_static",
  "material": "N2",
  "file": "N2/shelton_1994__table8_N2_gammav_static.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): static 0.506 x 10^-62 (Table 3) = 81.1 au (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_N2_gammav_dc_kerr#

{
  "id": "table8_N2_gammav_dc_kerr",
  "material": "N2",
  "file": "N2/shelton_1994__table8_N2_gammav_dc_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): dc Kerr +0.003 x 10^-62 (Table 4 and its Eq. (17) note) = 0.5 au (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_N2_gammav_kerr#

{
  "id": "table8_N2_gammav_kerr",
  "material": "N2",
  "file": "N2/shelton_1994__table8_N2_gammav_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "kerr",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): DFWM 0.336 x 10^-62 = 53.9 au (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_N2_gammav_eshg#

{
  "id": "table8_N2_gammav_eshg",
  "material": "N2",
  "file": "N2/shelton_1994__table8_N2_gammav_eshg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): not a printed value: Eq. (22) at 694.3 nm gives -1.63 au (shelton_1987 gives ESHG only at 633 nm, -0.008 x 10^-62 corrected) (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_N2_gammav_thg#

{
  "id": "table8_N2_gammav_thg",
  "material": "N2",
  "file": "N2/shelton_1994__table8_N2_gammav_thg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): not a printed value: Eq. (22) at 694.3 nm gives -0.54 au, printed -0.6 (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_O2_gammav_static#

{
  "id": "table8_O2_gammav_static",
  "material": "O2",
  "file": "O2/shelton_1994__table8_O2_gammav_static.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): static 0.734 x 10^-62 (Table 3) = 117.7 au (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_O2_gammav_dc_kerr#

{
  "id": "table8_O2_gammav_dc_kerr",
  "material": "O2",
  "file": "O2/shelton_1994__table8_O2_gammav_dc_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): dc Kerr +0.038 x 10^-62 (Table 4 and its Eq. (17) note) = 6.1 au (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_O2_gammav_kerr#

{
  "id": "table8_O2_gammav_kerr",
  "material": "O2",
  "file": "O2/shelton_1994__table8_O2_gammav_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "kerr",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): DFWM 0.489 x 10^-62 = 78.4 au (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_O2_gammav_eshg#

{
  "id": "table8_O2_gammav_eshg",
  "material": "O2",
  "file": "O2/shelton_1994__table8_O2_gammav_eshg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): not a printed value: Eq. (22) at 694.3 nm gives -1.04 au (shelton_1987 gives ESHG only at 633 nm, -0.005 x 10^-62 corrected) (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_O2_gammav_thg#

{
  "id": "table8_O2_gammav_thg",
  "material": "O2",
  "file": "O2/shelton_1994__table8_O2_gammav_thg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1987",
    "shelton_1987b"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note f: ref 134 (Shelton, Mol. Phys. 60, 65 (1987)), ‘with corrections given in ref 133’ (Shelton, Phys. Rev. A 36, 3461 (1987)). Re-pointed to the originals now in the library (shelton_1987, with the corrections of shelton_1987b ref. 10): not a printed value: Eq. (22) at 694.3 nm gives -0.34 au, printed -0.4 (1 au = 6.2354e-65 C^4 m^4 J^-3; computed here, 2026-09-26).

shelton_1994/table8_H2_gammaR_static#

{
  "id": "table8_H2_gammaR_static",
  "material": "H2",
  "file": "H2/shelton_1994__table8_H2_gammaR_static.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "D. M. Bishop and B. Lam, Chem. Phys. Lett. 143, 515 (1988)"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "rotational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note c: ref 131 (Bishop & Lam, Chem. Phys. Lett. 143, 515 (1988)), ‘quantum expression applied for the v = 0 state (results up to v = 5 are given)’; ‘the classical orientational average for the v = 0 state gives ... gamma^v = 184 au and gamma^R = 1169 au for H2’.

shelton_1994/table8_H2_gammaR_dc_kerr#

{
  "id": "table8_H2_gammaR_dc_kerr",
  "material": "H2",
  "file": "H2/shelton_1994__table8_H2_gammaR_dc_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "rotational",
    "temperature_k": 295.0
  }
}

shelton_1994/table8_H2_gammaR_kerr#

{
  "id": "table8_H2_gammaR_kerr",
  "material": "H2",
  "file": "H2/shelton_1994__table8_H2_gammaR_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "kerr",
    "convention": "T",
    "part": "rotational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note h: ‘Full quantum expressions’ (eqs 33-39): the review’s own calculation.

shelton_1994/table8_H2_gammaR_eshg#

{
  "id": "table8_H2_gammaR_eshg",
  "material": "H2",
  "file": "H2/shelton_1994__table8_H2_gammaR_eshg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "rotational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note h: ‘Full quantum expressions’ (eqs 33-39): the review’s own calculation.

shelton_1994/table8_H2_gammaR_thg#

{
  "id": "table8_H2_gammaR_thg",
  "material": "H2",
  "file": "H2/shelton_1994__table8_H2_gammaR_thg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "rotational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note h: ‘Full quantum expressions’ (eqs 33-39): the review’s own calculation.

shelton_1994/table8_N2_gammaR_static#

{
  "id": "table8_N2_gammaR_static",
  "material": "N2",
  "file": "N2/shelton_1994__table8_N2_gammaR_static.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "primary",
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "rotational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note i: ‘Classical limit’ (eqs 31-32 type): the review’s own calculation.

shelton_1994/table8_N2_gammaR_dc_kerr#

{
  "id": "table8_N2_gammaR_dc_kerr",
  "material": "N2",
  "file": "N2/shelton_1994__table8_N2_gammaR_dc_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "rotational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note i: ‘Classical limit’ (eqs 31-32 type): the review’s own calculation.

shelton_1994/table8_N2_gammaR_kerr#

{
  "id": "table8_N2_gammaR_kerr",
  "material": "N2",
  "file": "N2/shelton_1994__table8_N2_gammaR_kerr.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "kerr",
    "convention": "T",
    "part": "rotational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note i: ‘Classical limit’ (eqs 31-32 type): the review’s own calculation.

shelton_1994/table8_N2_gammaR_eshg#

{
  "id": "table8_N2_gammaR_eshg",
  "material": "N2",
  "file": "N2/shelton_1994__table8_N2_gammaR_eshg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "rotational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note i: ‘Classical limit’ (eqs 31-32 type): the review’s own calculation.

shelton_1994/table8_N2_gammaR_thg#

{
  "id": "table8_N2_gammaR_thg",
  "material": "N2",
  "file": "N2/shelton_1994__table8_N2_gammaR_thg.csv",
  "table": "tbl_a56d72648e32",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "primary",
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "rotational",
    "temperature_k": 295.0
  }
}

Table VIII (p. 15): ‘Vibrational and rotational hyperpolarizabilities calculated for diatomic molecules, at T = 295 K, including only the fundamental vibrational transition’, in atomic units. Columns: static; dc Kerr 632.8 nm (gamma_K = (3/2)(gamma_par - gamma_perp)); DFWM 632.8 nm (gamma(-w; w, w, -w), process ‘kerr’); ESHG 694.3 nm; THG 694.3 nm (air wavelengths). Note a: ‘The gamma^v results for dc Kerr tend to be anomalously small because of the cancellation of terms that occurs when evaluating gamma_K = (3/2)(gamma_par - gamma_perp). Quantum effects are significant for gamma^R of H2. The classical limit of eqs 34-39 gives gamma_K^R = 909 au for dc Kerr and gamma_par^R = 834 au for DFWM at lambda = 632.8 nm, which are 30% larger than the results given by the full quantum calculation for H2.’ Note i: ‘Classical limit’ (eqs 31-32 type): the review’s own calculation.

shelton_1994/table9_H2_calc#

{
  "id": "table9_H2_calc",
  "material": "H2",
  "file": "H2/shelton_1994__table9_H2_calc.csv",
  "table": "tbl_a4a5bfa3d452",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table IX (p. 16): ‘Comparison of ab initio calculations and experimental measurements of hyperpolarizabilities for diatomic molecules’. Note a: ‘The results of ESHG measurements at lambda = 1319-457.9 nm for H2, D2, N2, and O2 have been extrapolated to the static limit after subtracting calculated values of gamma^v. However, only ESHG measurements at lambda = 694.3 nm (nu = 14399 cm-1) are available for HF, HCl, CO, and NO, so the calculated and measured results are compared for ESHG at this wavelength for these four molecules (gamma^v has not been subtracted from these experimental measurements).’ Calculations in parentheses are vibrationally averaged; # marks values determined at more than one frequency. Printed (682.7): vibrationally averaged gamma^e, ref 197 (bishop_1991), static.

shelton_1994/table9_D2_calc#

{
  "id": "table9_D2_calc",
  "material": "D2",
  "file": "D2/shelton_1994__table9_D2_calc.csv",
  "table": "tbl_a4a5bfa3d452",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1991"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table IX (p. 16): ‘Comparison of ab initio calculations and experimental measurements of hyperpolarizabilities for diatomic molecules’. Note a: ‘The results of ESHG measurements at lambda = 1319-457.9 nm for H2, D2, N2, and O2 have been extrapolated to the static limit after subtracting calculated values of gamma^v. However, only ESHG measurements at lambda = 694.3 nm (nu = 14399 cm-1) are available for HF, HCl, CO, and NO, so the calculated and measured results are compared for ESHG at this wavelength for these four molecules (gamma^v has not been subtracted from these experimental measurements).’ Calculations in parentheses are vibrationally averaged; # marks values determined at more than one frequency. Printed (663.1): vibrationally averaged gamma^e, ref 197 (bishop_1991), static.

shelton_1994/table9_N2_calc#

{
  "id": "table9_N2_calc",
  "material": "N2",
  "file": "N2/shelton_1994__table9_N2_calc.csv",
  "table": "tbl_a4a5bfa3d452",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "sekino_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table IX (p. 16): ‘Comparison of ab initio calculations and experimental measurements of hyperpolarizabilities for diatomic molecules’. Note a: ‘The results of ESHG measurements at lambda = 1319-457.9 nm for H2, D2, N2, and O2 have been extrapolated to the static limit after subtracting calculated values of gamma^v. However, only ESHG measurements at lambda = 694.3 nm (nu = 14399 cm-1) are available for HF, HCl, CO, and NO, so the calculated and measured results are compared for ESHG at this wavelength for these four molecules (gamma^v has not been subtracted from these experimental measurements).’ Calculations in parentheses are vibrationally averaged; # marks values determined at more than one frequency. Note f: ref 123 (Sekino & Bartlett 1993 = sekino_1993), static CCSD(T) (not vibrationally averaged).

shelton_1994/table9_H2_expt#

{
  "id": "table9_H2_expt",
  "material": "H2",
  "file": "H2/shelton_1994__table9_H2_expt.csv",
  "table": "tbl_a4a5bfa3d452",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1990"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table IX (p. 16): ‘Comparison of ab initio calculations and experimental measurements of hyperpolarizabilities for diatomic molecules’. Note a: ‘The results of ESHG measurements at lambda = 1319-457.9 nm for H2, D2, N2, and O2 have been extrapolated to the static limit after subtracting calculated values of gamma^v. However, only ESHG measurements at lambda = 694.3 nm (nu = 14399 cm-1) are available for HF, HCl, CO, and NO, so the calculated and measured results are compared for ESHG at this wavelength for these four molecules (gamma^v has not been subtracted from these experimental measurements).’ Calculations in parentheses are vibrationally averaged; # marks values determined at more than one frequency. Note d: ref 34 (shelton_1990), ‘experimental static gamma^e’: shelton_1990’s Table IV gamma_0 converted to au (1 au = 6.235377e-65 C^4 m^4 J^-3). shelton_1990 states an uncertainty only for H2 (686 +- 4 au, p. 14); the D2, N2 and O2 uncertainties first appear here.

shelton_1994/table9_D2_expt#

{
  "id": "table9_D2_expt",
  "material": "D2",
  "file": "D2/shelton_1994__table9_D2_expt.csv",
  "table": "tbl_a4a5bfa3d452",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1990"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table IX (p. 16): ‘Comparison of ab initio calculations and experimental measurements of hyperpolarizabilities for diatomic molecules’. Note a: ‘The results of ESHG measurements at lambda = 1319-457.9 nm for H2, D2, N2, and O2 have been extrapolated to the static limit after subtracting calculated values of gamma^v. However, only ESHG measurements at lambda = 694.3 nm (nu = 14399 cm-1) are available for HF, HCl, CO, and NO, so the calculated and measured results are compared for ESHG at this wavelength for these four molecules (gamma^v has not been subtracted from these experimental measurements).’ Calculations in parentheses are vibrationally averaged; # marks values determined at more than one frequency. Note d: ref 34 (shelton_1990), ‘experimental static gamma^e’: shelton_1990’s Table IV gamma_0 converted to au (1 au = 6.235377e-65 C^4 m^4 J^-3). shelton_1990 states an uncertainty only for H2 (686 +- 4 au, p. 14); the D2, N2 and O2 uncertainties first appear here.

shelton_1994/table9_N2_expt#

{
  "id": "table9_N2_expt",
  "material": "N2",
  "file": "N2/shelton_1994__table9_N2_expt.csv",
  "table": "tbl_a4a5bfa3d452",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1990"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table IX (p. 16): ‘Comparison of ab initio calculations and experimental measurements of hyperpolarizabilities for diatomic molecules’. Note a: ‘The results of ESHG measurements at lambda = 1319-457.9 nm for H2, D2, N2, and O2 have been extrapolated to the static limit after subtracting calculated values of gamma^v. However, only ESHG measurements at lambda = 694.3 nm (nu = 14399 cm-1) are available for HF, HCl, CO, and NO, so the calculated and measured results are compared for ESHG at this wavelength for these four molecules (gamma^v has not been subtracted from these experimental measurements).’ Calculations in parentheses are vibrationally averaged; # marks values determined at more than one frequency. Note d: ref 34 (shelton_1990), ‘experimental static gamma^e’: shelton_1990’s Table IV gamma_0 converted to au (1 au = 6.235377e-65 C^4 m^4 J^-3). shelton_1990 states an uncertainty only for H2 (686 +- 4 au, p. 14); the D2, N2 and O2 uncertainties first appear here.

shelton_1994/table9_O2_expt#

{
  "id": "table9_O2_expt",
  "material": "O2",
  "file": "O2/shelton_1994__table9_O2_expt.csv",
  "table": "tbl_a4a5bfa3d452",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1990"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table IX (p. 16): ‘Comparison of ab initio calculations and experimental measurements of hyperpolarizabilities for diatomic molecules’. Note a: ‘The results of ESHG measurements at lambda = 1319-457.9 nm for H2, D2, N2, and O2 have been extrapolated to the static limit after subtracting calculated values of gamma^v. However, only ESHG measurements at lambda = 694.3 nm (nu = 14399 cm-1) are available for HF, HCl, CO, and NO, so the calculated and measured results are compared for ESHG at this wavelength for these four molecules (gamma^v has not been subtracted from these experimental measurements).’ Calculations in parentheses are vibrationally averaged; # marks values determined at more than one frequency. Note d: ref 34 (shelton_1990), ‘experimental static gamma^e’: shelton_1990’s Table IV gamma_0 converted to au (1 au = 6.235377e-65 C^4 m^4 J^-3). shelton_1990 states an uncertainty only for H2 (686 +- 4 au, p. 14); the D2, N2 and O2 uncertainties first appear here. Table X prints 963 for the same fit (60.03e-63 / 6.235377e-65 = 962.7).

shelton_1994/table9_CO_calc#

{
  "id": "table9_CO_calc",
  "material": "CO",
  "file": "CO/shelton_1994__table9_CO_calc.csv",
  "table": "tbl_a4a5bfa3d452",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "cm-1",
  "use": "reproduced",
  "reproduced_from": [
    "sekino_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic"
  }
}

Table IX (p. 16): ‘Comparison of ab initio calculations and experimental measurements of hyperpolarizabilities for diatomic molecules’. Note a: ‘The results of ESHG measurements at lambda = 1319-457.9 nm for H2, D2, N2, and O2 have been extrapolated to the static limit after subtracting calculated values of gamma^v. However, only ESHG measurements at lambda = 694.3 nm (nu = 14399 cm-1) are available for HF, HCl, CO, and NO, so the calculated and measured results are compared for ESHG at this wavelength for these four molecules (gamma^v has not been subtracted from these experimental measurements).’ Calculations in parentheses are vibrationally averaged; # marks values determined at more than one frequency. Note p: ref 123 (sekino_1993), ‘ESHG beta^e and gamma^e at 694.3 nm from static CCSD(T) with SCF percentage dispersion’. The abscissa is the printed vacuum wavenumber of the ruby line.

shelton_1994/table9_CO_expt#

{
  "id": "table9_CO_expt",
  "material": "CO",
  "file": "CO/shelton_1994__table9_CO_expt.csv",
  "table": "tbl_a4a5bfa3d452",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "cm-1",
  "use": "reproduced",
  "reproduced_from": [
    "ward_1979"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table IX (p. 16): ‘Comparison of ab initio calculations and experimental measurements of hyperpolarizabilities for diatomic molecules’. Note a: ‘The results of ESHG measurements at lambda = 1319-457.9 nm for H2, D2, N2, and O2 have been extrapolated to the static limit after subtracting calculated values of gamma^v. However, only ESHG measurements at lambda = 694.3 nm (nu = 14399 cm-1) are available for HF, HCl, CO, and NO, so the calculated and measured results are compared for ESHG at this wavelength for these four molecules (gamma^v has not been subtracted from these experimental measurements).’ Calculations in parentheses are vibrationally averaged; # marks values determined at more than one frequency. Note q: ref 53 (Ward & Miller 1979 = ward_1979), ‘experimental ESHG beta^ev and gamma^ev at 694.3 nm rescaled to new gamma(He) of ref 100’ (reproduced and rescaled). CO is polar: the ESHG signal measures gamma + mu beta/3kT (eq 8); the table gives gamma and beta separately. Vibration not subtracted.

shelton_1994/table9_N2_static_theory_note#

{
  "id": "table9_N2_static_theory_note",
  "material": "N2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "sekino_1993",
    "G. Maroulis and A. J. Thakkar, J. Chem. Phys. 88, 7623 (1988)",
    "G. Maroulis and D. M. Bishop, Mol. Phys. 58, 273 (1986)",
    "C. J. Jameson and P. W. Fowler, J. Chem. Phys. 85, 3432 (1986)"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

7 inline points in the source record.

Table IX note f (p. 16), N2 static gamma^e besides the tabulated CCSD(T) 1010: ‘also, static MP2, gamma^e = 930; static SCF, gamma^e = 730 using [5s 3p 2d] basis’ (ref 123); ‘Reference 209, static SDQ-MP4, gamma^e = 830; static MP2, gamma^e = 860; static SCF, gamma^e = 665* using [6s 4p 3d 1f] basis (more complete than ref 123). Reference 210, static SCF, gamma^e = 766*. Reference 208, static SCF, gamma^e = 700*.’ (* = without electron correlation.)

shelton_1994/table9_N2_eshg_calc_note#

{
  "id": "table9_N2_eshg_calc_note",
  "material": "N2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "sekino_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic"
  }
}

1 inline points in the source record.

Table IX note f (p. 16): ‘ESHG at 694.3 nm from static CCSD(T) with SCF percentage dispersion gives gamma^e = 1100’.

shelton_1994/table9_N2_eshg_fit_note#

{
  "id": "table9_N2_eshg_fit_note",
  "material": "N2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "check",
  "reproduced_from": [
    "shelton_1990"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic"
  }
}

1 inline points in the source record.

Table IX note f (p. 16): ‘1058 from the experimental dispersion curve of Table X’ (gamma^e of shelton_1990’s fit evaluated by Shelton & Rice at 694.3 nm). Check: 917 [1 + 1.003e-10 x 6 x 14399^2 + 1.85e-20 x (6 x 14399^2)^2] = 1057.7 au (checked 2026-09-26).

shelton_1994/table9_N2_eshg_ward_note#

{
  "id": "table9_N2_eshg_ward_note",
  "material": "N2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "ward_1979"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

1 inline points in the source record.

Table IX note f (p. 16): ‘1042 +- 12 from the experiment of ref 53 scaled to new gamma(He) of ref 100’ (Ward & Miller 1979, reproduced and rescaled to Bishop & Pipin’s He). ESHG total (gamma^v not subtracted).

shelton_1994/table9_CO_static_note#

{
  "id": "table9_CO_static_note",
  "material": "CO",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "sekino_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

3 inline points in the source record.

Table IX note p (p. 16), CO: ‘also, static CCSD(T), beta^e = 23.5, gamma^e = 1590; static MP2, beta^e = 22.6, gamma^e = 1500; static SCF, beta^e = 21.1*, gamma^e = 1020*’ (ref 123 = sekino_1993). The beta values are first hyperpolarizabilities, not extracted.

shelton_1994/table11_CO2_gammav_static#

{
  "id": "table11_CO2_gammav_static",
  "material": "CO2",
  "file": "CO2/shelton_1994__table11_CO2_gammav_static.csv",
  "table": "tbl_c6b7f0da4741",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

Table XI (p. 20): ‘Vibrational hyperpolarizabilities calculated at the MP2 level for polyatomic molecules (from ref 124)’ = Bishop, Kirtman, Kurtz & Rice 1993 (bishop_1993). Note a: ‘All values of beta^v and gamma^v are for omega = 0.07 au (nu = 15363 cm-1) and T = 295 K, and are given in atomic units.’ The abscissa is that vacuum wavenumber (the static column: inf). Columns: static, dc Kerr, DFWM (process ‘kerr’), ESHG, THG. The text (p. 20): ‘the vibrational contribution to gamma is about 6% for CO2’ for ESHG.

shelton_1994/table11_CO2_gammav_dc_kerr#

{
  "id": "table11_CO2_gammav_dc_kerr",
  "material": "CO2",
  "file": "CO2/shelton_1994__table11_CO2_gammav_dc_kerr.csv",
  "table": "tbl_c6b7f0da4741",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "cm-1",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table11_CO2_gammav_kerr#

{
  "id": "table11_CO2_gammav_kerr",
  "material": "CO2",
  "file": "CO2/shelton_1994__table11_CO2_gammav_kerr.csv",
  "table": "tbl_c6b7f0da4741",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "cm-1",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "kerr",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table11_CO2_gammav_eshg#

{
  "id": "table11_CO2_gammav_eshg",
  "material": "CO2",
  "file": "CO2/shelton_1994__table11_CO2_gammav_eshg.csv",
  "table": "tbl_c6b7f0da4741",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "cm-1",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table11_CO2_gammav_thg#

{
  "id": "table11_CO2_gammav_thg",
  "material": "CO2",
  "file": "CO2/shelton_1994__table11_CO2_gammav_thg.csv",
  "table": "tbl_c6b7f0da4741",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "cm-1",
  "use": "reproduced",
  "reproduced_from": [
    "bishop_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "vibrational",
    "temperature_k": 295.0
  }
}

shelton_1994/table12_CH4_calc_static#

{
  "id": "table12_CH4_calc_static",
  "material": "CH4",
  "file": "CH4/shelton_1994__table12_CH4_calc_static.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "G. Maroulis, Chem. Phys. Lett. 195, 85 (1992)"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note w: ref 227 (Maroulis, Chem. Phys. Lett. 195, 85 (1992)), static SCF gamma (* = without electron correlation). Fig. 7 caption: ‘The static SCF result ... gamma^e = 1870 au falls off scale’.

shelton_1994/table12_CH4_dc_kerr#

{
  "id": "table12_CH4_dc_kerr",
  "material": "CH4",
  "file": "CH4/shelton_1994__table12_CH4_dc_kerr.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "buckingham_1969",
    "dunmur_1979b"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Row ‘ref 28’: Buckingham & Orr 1969 (buckingham_1969), dc Kerr (note h): 2887 +- 140 au = its 0.180 +- 0.009 x 10^-60 C^4 m^4 J^-3 / 6.2354e-65 (digit-identical; the error is its 5 % absolute accuracy). Row ‘ref 22’: Dunmur, Hunt & Jessup 1979, ‘dc Kerr at 633 nm except CH4 at 458 nm’ (note aa; @ = other wavelength; the row’s wavelength is that 458 nm) = dunmur_1979b (re-pointed 2026-09-27): its gamma-bar(CH4) = 19.2 +- 1.0 x 10^-62 C^4 m^4 J^-3 / 6.23538e-65 = 3079 +- 160 au, digit for digit (checked).

shelton_1994/table12_CH4_eshg#

{
  "id": "table12_CH4_eshg",
  "material": "CH4",
  "file": "CH4/shelton_1994__table12_CH4_eshg.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1990",
    "C. K. Miller and J. F. Ward, Phys. Rev. A 16, 1179 (1977)"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note x: ref 34 (shelton_1990), ‘ESHG gamma at 694.3 nm from ESHG dispersion curves with measurements over 1319-457.9 nm’ (Shelton & Rice’s evaluation of shelton_1990’s fit). Row ‘ref 55’: Miller & Ward 1977, ‘ESHG rescaled’ (note m).

shelton_1994/table12_CH4_thg#

{
  "id": "table12_CH4_thg",
  "material": "CH4",
  "file": "CH4/shelton_1994__table12_CH4_thg.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "ward_1984"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

shelton_1994/table12_CH4_cars#

{
  "id": "table12_CH4_cars",
  "material": "CH4",
  "file": "CH4/shelton_1994__table12_CH4_cars.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "lundeen_1983"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "cars",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note z: ref 73 (Lundeen, Hou & Nibler 1983 = lundeen_1983), ‘CARS with vibrational contributions of alpha^2 type subtracted’.

shelton_1994/table12_SF6_dc_kerr#

{
  "id": "table12_SF6_dc_kerr",
  "material": "SF6",
  "file": "SF6/shelton_1994__table12_SF6_dc_kerr.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "buckingham_1968",
    "dunmur_1979b"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Row ‘ref 30’: Buckingham & Dunmur 1968 (buckingham_1968), dc Kerr (note bb). Row ‘ref 22’: Dunmur, Hunt & Jessup 1979, dc Kerr at 633 nm (note aa) = dunmur_1979b (re-pointed 2026-09-27): its gamma-bar(SF6) = 11.9 +- 0.8 x 10^-62 C^4 m^4 J^-3 = 1908 au (checked; the error 0.8 converts to 128, printed 133). The original’s SF6 A_K, from which that gamma comes, was ‘measured at a wavelength of 458 nm’ (its Table 4, 297 K row), not 633 nm as note aa says; the row is kept at 632.8 nm as Shelton and Rice print it.

shelton_1994/table12_SF6_eshg#

{
  "id": "table12_SF6_eshg",
  "material": "SF6",
  "file": "SF6/shelton_1994__table12_SF6_eshg.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1990",
    "ward_1979"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note x: ref 34 (shelton_1990), ‘ESHG gamma at 694.3 nm from ESHG dispersion curves with measurements over 1319-457.9 nm’ (Shelton & Rice’s evaluation of shelton_1990’s fit). Row ‘ref 53’: Ward & Miller 1979 (ward_1979), ‘ESHG rescaled’ (note d).

shelton_1994/table12_SF6_thg#

{
  "id": "table12_SF6_thg",
  "material": "SF6",
  "file": "SF6/shelton_1994__table12_SF6_thg.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "ward_1984"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note y: ref 62 (ward_1984), ‘THG rescaled’ (the note reads ‘Fluoromethanes’ but marks SF6’s value too; ward_1984 measured SF6).

shelton_1994/table12_SF6_cars#

{
  "id": "table12_SF6_cars",
  "material": "SF6",
  "file": "SF6/shelton_1994__table12_SF6_cars.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "lundeen_1983"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "cars",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note z: ref 73 (lundeen_1983), ‘CARS with vibrational contributions of alpha^2 type subtracted’.

shelton_1994/table12_CO2_calc_static#

{
  "id": "table12_CO2_calc_static",
  "material": "CO2",
  "file": "CO2/shelton_1994__table12_CO2_calc_static.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "sekino_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note ff: ref 123 (Sekino & Bartlett 1993 = sekino_1993), ‘static CCSD(T) gamma, ESHG at 694.3 nm from CCSD(T) static with SCF percentage dispersion’.

shelton_1994/table12_CO2_calc_eshg#

{
  "id": "table12_CO2_calc_eshg",
  "material": "CO2",
  "file": "CO2/shelton_1994__table12_CO2_calc_eshg.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "sekino_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note ff: ref 123 (Sekino & Bartlett 1993 = sekino_1993), ‘static CCSD(T) gamma, ESHG at 694.3 nm from CCSD(T) static with SCF percentage dispersion’.

shelton_1994/table12_CO2_dc_kerr#

{
  "id": "table12_CO2_dc_kerr",
  "material": "CO2",
  "file": "CO2/shelton_1994__table12_CO2_dc_kerr.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "gentle_1989"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "dc_kerr",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note gg: ref 18 (Gentle, Laver & Ritchie, J. Phys. Chem. 93, 3035 (1989) = gentle_1989), dc Kerr. Digit-identical with gentle_1989’s gamma^K = (0.125 +- 0.032) x 10^-60 C m^4 V^-3 (1.25e-61 / 6.2354e-65 = 2005 au; 0.032 -> 513 au), measured at 632.8 nm; that error is the scaled fit error only (gentle_1989 notes).

shelton_1994/table12_CO2_eshg#

{
  "id": "table12_CO2_eshg",
  "material": "CO2",
  "file": "CO2/shelton_1994__table12_CO2_eshg.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "shelton_1990",
    "ward_1979"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note x: ref 34 (shelton_1990), ‘ESHG gamma at 694.3 nm from ESHG dispersion curves with measurements over 1319-457.9 nm’ (Shelton & Rice’s evaluation of shelton_1990’s fit). Row ‘ref 53’: Ward & Miller 1979 (ward_1979), ‘ESHG rescaled’ (note d).

shelton_1994/table12_CO2_thg#

{
  "id": "table12_CO2_thg",
  "material": "CO2",
  "file": "CO2/shelton_1994__table12_CO2_thg.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "ward_1969"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

shelton_1994/table12_CO2_cars#

{
  "id": "table12_CO2_cars",
  "material": "CO2",
  "file": "CO2/shelton_1994__table12_CO2_cars.csv",
  "table": "tbl_f5d00dad6453",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "lundeen_1983"
  ],
  "uncertainty": {
    "column": true,
    "level": "not stated"
  },
  "parameters": {
    "process": "cars",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

Table XII(b) (pp. 22-23): ‘Measured and calculated values of gamma for small polyatomic molecules’. Note a: ‘The calculated values are beta^e and gamma^e, while the experimental values are beta^ev and gamma^ev at optical frequencies. None of the calculations includes vibrational averaging. Where an experimental dispersion curve has been measured, this is indicated by #. The calculations include electron correlation, except those marked with *. Results at a wavelength different [from] that stated in the column heading are indicated by @. The experimental values calibrated against He have been rescaled using the calculated gamma(He) values from Bishop and Pipin (ref 100).’ Columns: calc static, calc ESHG 694.3 nm, expt dc Kerr 632.8 nm, expt ESHG 694.3 nm, expt THG 694.3 nm, expt CARS 532 nm (air wavelengths; CARS: the pump; the Stokes frequency is not stated). The dc Kerr gamma is gamma_K with the orientational terms of eq 9 separated. Note z: ref 73 (lundeen_1983), ‘CARS with vibrational contributions of alpha^2 type subtracted’.

shelton_1994/table12_CO2_static_theory_note#

{
  "id": "table12_CO2_static_theory_note",
  "material": "CO2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "use": "reproduced",
  "reproduced_from": [
    "sekino_1993",
    "G. Maroulis and A. J. Thakkar, J. Chem. Phys. 93, 4164 (1990)"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "static",
    "convention": "T",
    "part": "electronic"
  }
}

5 inline points in the source record.

Table XII note ff (p. 23; read on the page image, the library’s text drops ‘1f’): ‘also, static MP2, gamma = 1170; static SCF, gamma = 800*, using [5s 3p 2d] basis ... See also the following: reference 224, static SDQ-MP4, gamma = 1197; static MP2, gamma = 1251; static SCF, gamma = 844*; using [6s 4p 3d 1f] basis (more complete than in ref 123).’ Ref 224: Maroulis & Thakkar, J. Chem. Phys. 93, 4164 (1990).

shelton_1994/table12_CO2_thg_calc_note#

{
  "id": "table12_CO2_thg_calc_note",
  "material": "CO2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "sekino_1993"
  ],
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "thg",
    "convention": "T",
    "part": "electronic"
  }
}

1 inline points in the source record.

Table XII note ff (p. 23): ‘THG at 694.3 nm from CCSD(T) static with SCF percentage dispersion; THG, gamma = 1500’.

shelton_1994/text_CO2_eshg_best_estimate#

{
  "id": "text_CO2_eshg_best_estimate",
  "material": "CO2",
  "table": "text",
  "quantity": "hyperpolarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "check",
  "uncertainty": {
    "level": "not stated"
  },
  "parameters": {
    "process": "eshg",
    "convention": "T",
    "part": "electronic_vibrational"
  }
}

1 inline points in the source record.

Text p. 24: for NH3, H2O and CO2, ‘where the vibrational hyperpolarizability has also been calculated (ref 124), the best estimates of 5580, 2190, and 1220 au are still in good agreement with the experimental values (ref 53) of 6147 +- 110, 2311 +- 120, and 1346 +- 15 au’. Shelton & Rice’s own sum for ESHG at 694.3 nm: the calculated gamma^e (1300, Table XII) plus gamma^v (-81, Table XI, omega = 0.07 au).

Formulas#

shelton_1994/table7_He_calc#

{
  "id": "table7_He_calc",
  "material": "He",
  "equation": "Eqs 18-19, p. 11; Table VII, p. 12",
  "printed": "gamma_par(-nu_s; nu_1, nu_2, nu_3) = gamma_par(0; 0, 0, 0) [1 + A nu_L^2 + B nu_L^4 + C nu_L^6 ...]; Table VII: gamma_o,calc = 43.145 au, A_calc = 0.455 0 x 10^-10 cm^2, B_calc = 0.145 8 x 10^-20 cm^4, C_calc = 0.060 4 x 10^-30 cm^6",
  "variable": "nu_L^2 = nu_s^2 + nu_1^2 + nu_2^2 + nu_3^2, the vacuum wavenumbers in cm^-1; for ESHG nu_L^2 = 6 nu^2 (nu of the fundamental)",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 6 nu^2 = 30 x 10^8 cm^-2 (Table VII note a)",
  "coefficients": {
    "gamma0": "43.145",
    "A": "0.4550",
    "B": "0.1458",
    "C": "0.0604"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4",
    "C": "1e-30 cm^6"
  },
  "reproduced_from": [
    "bishop_1989"
  ],
  "check": "The same coefficients as shelton_1990 Table II in SI (4.550e-11 cm^2, 1.458e-21 cm^4, and C = 6.043e-32 cm^6 once that table's misprinted 10^-31 is corrected), where gamma_0 = 43.104 au without the reduced-mass factor; 43.104 x 1.00096 = 43.145 (the 0.096 % correction, p. 10). Evaluated for THG at 1055 nm (air; nu = 9476 cm^-1, nu_L^2 = 12 nu^2) it gives 45.34 au against Table VI's 45.338, and for dc Kerr at 632.8 nm (nu_L^2 = 2 nu^2) 44.14 against 44.211 (B, C differ by process). Checked 2026-09-26."
}

Note c: ‘Reference 100, CI-Hylleraas (this dispersion curve is used for calibration of the ESHG experiments; note the misprint for C in SI units in Table II of ref 34)’: shelton_1990 Table II prints C = 6.043e-31 cm^6 where 0.0604e-30 = 6.04e-32 is right (shelton_1992: ‘10^-31 in the last line should be 10^-32’; 6.748 au / 219444.5^6 = 6.043e-32). ‘The coefficients given for H and He are estimates of the leading coefficients of the infinite order power series expansion based on the limited ab initio results’ (p. 12). Includes the reduced-mass correction (note a). Used by Shelton and co-workers to calibrate every ESHG ratio.

shelton_1994/table7_Ne_calc_mp2_ccsdt#

{
  "id": "table7_Ne_calc_mp2_ccsdt",
  "material": "Ne",
  "equation": "Eqs 18-19, p. 11; Table VII, p. 12",
  "printed": "gamma_o,calc = 110 au, A_calc = 0.498 x 10^-10 cm^2, B_calc = 0.230 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "110",
    "A": "0.498",
    "B": "0.230"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "rice_1992",
    "J. E. Rice, G. E. Scuseria, T. J. Lee, P. R. Taylor and J. Almlof, Chem. Phys. Lett. 191, 23 (1992)"
  ],
  "check": "Not checked against the originals (the theory records)."
}

Note d: ‘MP2 dispersion curve of ref 122 with multiplicative correction using static CCSD(T) of ref 171’ (eq 11). Ref 122 = rice_1992; the Ne CCSD(T) static value is ref 170 by Table IV and Table V note a (the note’s ‘171’ is a reference slip, see the record notes). ‘The best theoretical estimate of gamma is the curve marked CCSD(T)’ (Fig. 3 caption). Includes the reduced-mass correction.

shelton_1994/table7_Ne_calc_casscf#

{
  "id": "table7_Ne_calc_casscf",
  "material": "Ne",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,calc = 99 au, A_calc = 0.529 x 10^-10 cm^2, B_calc = 0.256 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "99",
    "A": "0.529",
    "B": "0.256"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "H. J. A. Jensen, P. Jorgensen, H. Hettema and J. Olsen, Chem. Phys. Lett. 187, 387 (1991)"
  ],
  "check": "Not checked (original not in the library)."
}

Note f: ‘Reference 104, CASSCF’. Table V lists this reference’s static CASSCF value as 94.6 (basis IVb); Table VII’s gamma_0 is 99. shelton_1992 explains it: Jensen et al.’s ‘best static value’ is 99 +- 6 au (RASSCF, adjusted for more correlating orbitals), while the static intercept of their CASSCF dispersion curve is 94.6; shelton_1992 Table 2 fits that curve as gamma_0 = 94.6, A = 2.55, B = 5.94 (omega_L^2 in au), i.e. A = 0.5294e-10 cm^2 and B = 0.2562e-20 cm^4 with 1 au = 219469 cm^-1: Table VII combines the adjusted static value with the curve’s A and B.

shelton_1994/table7_Ne_calc_mctdhf#

{
  "id": "table7_Ne_calc_mctdhf",
  "material": "Ne",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,calc = 86.5 au, A_calc = 0.478 x 10^-10 cm^2, B_calc = 0.22 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "86.5",
    "A": "0.478",
    "B": "0.22"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "M. Jaszunski and D. L. Yeager, Phys. Rev. A 40, 1651 (1989)"
  ],
  "check": "Not checked (original not in the library)."
}

Note g: ‘Reference 103, MCTDHF’.

shelton_1994/table7_Ne_calc_scf_rice#

{
  "id": "table7_Ne_calc_scf_rice",
  "material": "Ne",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,calc = 68.7 au, A_calc = 0.473 x 10^-10 cm^2, B_calc = 0.203 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "68.7",
    "A": "0.473",
    "B": "0.203"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "rice_1992"
  ],
  "check": "Not checked against rice_1992 (its own record)."
}

Note h: ‘Reference 122, SCF’ (uncorrelated).

shelton_1994/table7_Ne_calc_scf_jensen#

{
  "id": "table7_Ne_calc_scf_jensen",
  "material": "Ne",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,calc = 68.8 au, A_calc = 0.472 x 10^-10 cm^2, B_calc = 0.200 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "68.8",
    "A": "0.472",
    "B": "0.200"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "H. J. A. Jensen, P. Jorgensen, H. Hettema and J. Olsen, Chem. Phys. Lett. 187, 387 (1991)"
  ],
  "check": "Not checked (original not in the library)."
}

Note i: ‘Reference 104, SCF’ (uncorrelated).

shelton_1994/table7_Ne_calc_scf_klingbeil#

{
  "id": "table7_Ne_calc_scf_klingbeil",
  "material": "Ne",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,calc = 54 au, A_calc = 0.466 x 10^-10 cm^2, B_calc = 0.19 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "54",
    "A": "0.466",
    "B": "0.19"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "R. Klingbeil, Phys. Rev. A 7, 376 (1973)"
  ],
  "check": "Not checked (original not in the library)."
}

Note j: ‘Reference 178, SCF’ (uncorrelated, small basis).

shelton_1994/table7_Ne_expt#

{
  "id": "table7_Ne_expt",
  "material": "Ne",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,expt = 108 au, A_expt = 0.513 x 10^-10 cm^2, B_expt = 0.237 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "108",
    "A": "0.513",
    "B": "0.237"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "calibration": "He: Bishop & Pipin's ab initio curve (Table VII note a)",
  "reproduced_from": [
    "shelton_1992"
  ],
  "check": "See shelton_1992 (the original fit)."
}

Note e: ref 33 (Shelton & Donley 1992 = shelton_1992), the corrected Ne dispersion; supersedes shelton_1990’s anomalous Ne fit (A < 0). Table V note a: ‘The present best experimental estimate of gamma_0 is 108 +- 2 au’.

shelton_1994/table7_Ar_calc#

{
  "id": "table7_Ar_calc",
  "material": "Ar",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,calc = 1 220 au, A_calc = 1.076 x 10^-10 cm^2, B_calc = 1.373 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "1220",
    "A": "1.076",
    "B": "1.373"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "rice_1992",
    "rice_1991"
  ],
  "check": "Not checked against the originals (the theory records)."
}

Note k: ‘MP2 dispersion curve of ref 122 with multiplicative correction using static CCSD(T) of ref 170’; the Ar and Kr CCSD(T) static values are ref 171 (rice_1991) by Table IV (reference slip, record notes). ‘The theoretical dispersion curve for Ar ... lies slightly above and rises less steeply than the experimental dispersion curve’ (p. 13).

shelton_1994/table7_Kr_calc#

{
  "id": "table7_Kr_calc",
  "material": "Kr",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,calc = 2 810 au, A_calc = 1.354 x 10^-10 cm^2, B_calc = 4.684 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "2810",
    "A": "1.354",
    "B": "4.684"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "rice_1992",
    "rice_1991"
  ],
  "check": "Not checked against the originals (the theory records)."
}

Note k, as for Ar. Xe: Table VII prints only gamma_o,calc = 7 020 (note m, CCSD(T), static; no dispersion), recorded in table4_Xe.

shelton_1994/table7_Ar_expt#

{
  "id": "table7_Ar_expt",
  "material": "Ar",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,expt = 1 167 au, A_expt = 1.066 x 10^-10 cm^2, B_expt = 2.033 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2 (the data: 1319-457.9 nm)",
  "coefficients": {
    "gamma0": "1167",
    "A": "1.066",
    "B": "2.033"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "calibration": "He: Bishop & Pipin's ab initio curve",
  "reproduced_from": [
    "shelton_1990"
  ],
  "check": "shelton_1990 Table IV: gamma_0 = 72.75e-63 C^4 m^4 J^-3 = 1166.7 au (1 au = 6.235377e-65), A and B identical. Checked 2026-09-26."
}

Note l: ref 34 (shelton_1990).

shelton_1994/table7_Kr_expt#

{
  "id": "table7_Kr_expt",
  "material": "Kr",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,expt = 2 600 au, A_expt = 1.389 x 10^-10 cm^2, B_expt = 3.465 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "2600",
    "A": "1.389",
    "B": "3.465"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "calibration": "Ar: shelton_1990's fitted Ar curve (itself calibrated on He)",
  "reproduced_from": [
    "shelton_1990"
  ],
  "check": "shelton_1990 Table IV: 162.1e-63 = 2599.7 au, A and B identical. Checked 2026-09-26."
}

Note l: ref 34 (shelton_1990). ‘the hyperpolarizabilities of Kr and Xe are measured relative to gamma of argon’ (p. 12).

shelton_1994/table7_Xe_expt#

{
  "id": "table7_Xe_expt",
  "material": "Xe",
  "equation": "Table VII, p. 12",
  "printed": "gamma_o,expt = 6 888 au, A_expt = 1.499 x 10^-10 cm^2, B_expt = 8.048 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "6888",
    "A": "1.499",
    "B": "8.048"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "calibration": "Ar: shelton_1990's fitted Ar curve",
  "reproduced_from": [
    "shelton_1990"
  ],
  "check": "shelton_1990 Table IV: 429.5e-63 = 6888.1 au, A and B identical. Checked 2026-09-26."
}

Note l: ref 34 (shelton_1990).

shelton_1994/table10_H2_calc#

{
  "id": "table10_H2_calc",
  "material": "H2",
  "equation": "Eqs 18-19; Table X, p. 17",
  "printed": "gamma_o,calc = 683 au, A_calc = 1.286 x 10^-10 cm^2, B_calc = 1.81 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2 (Table X note a)",
  "coefficients": {
    "gamma0": "683",
    "A": "1.286",
    "B": "1.81"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "bishop_1991"
  ],
  "check": "Not checked against bishop_1991 (its own record). gamma_0 = 683 against Table IX's 682.7."
}

Note b: ref 197 (Bishop, Pipin & Cybulski 1991), fitted by Shelton & Rice to the calculated gamma^e ‘truncated at the B nu_L^4 term’.

shelton_1994/table10_D2_calc#

{
  "id": "table10_D2_calc",
  "material": "D2",
  "equation": "Table X, p. 17",
  "printed": "gamma_o,calc = 664 au, A_calc = 1.268 x 10^-10 cm^2, B_calc = 1.73 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "664",
    "A": "1.268",
    "B": "1.73"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "bishop_1991"
  ],
  "check": "Not checked against bishop_1991. gamma_0 = 664 against Table IX's 663.1."
}

Note b: ref 197 (bishop_1991).

shelton_1994/table10_N2_calc#

{
  "id": "table10_N2_calc",
  "material": "N2",
  "equation": "Table X, p. 17",
  "printed": "gamma_o,calc = 1010 au, A_calc = 0.974 x 10^-10 cm^2, B_calc = 0.87 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "1010",
    "A": "0.974",
    "B": "0.87"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "reproduced_from": [
    "sekino_1993",
    "H. Sekino and R. J. Bartlett, J. Chem. Phys. 94, 3665 (1991)"
  ],
  "check": "Not checked against the originals."
}

Note d: ‘From static CCSD(T) of ref 123 and SCF dispersion curve of ref 95’ (ref 123 = sekino_1993; ref 95 = Sekino & Bartlett, J. Chem. Phys. 94, 3665 (1991)): a composite, not a single calculation.

shelton_1994/table10_H2_expt#

{
  "id": "table10_H2_expt",
  "material": "H2",
  "equation": "Table X, p. 17",
  "printed": "gamma_o,expt = 686 au, A_expt = 1.200 x 10^-10 cm^2, B_expt = 2.25 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2 (data 1319-457.9 nm)",
  "coefficients": {
    "gamma0": "686",
    "A": "1.200",
    "B": "2.25"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "calibration": "He: Bishop & Pipin",
  "reproduced_from": [
    "shelton_1990"
  ],
  "check": "shelton_1990 Table IV: 42.80e-63 = 686.4 au, A = 1.200, B = 2.254 (rounded here to 2.25). Checked 2026-09-26."
}

Note c: ref 34 (shelton_1990); fitted to the measured gamma minus the calculated gamma^vR (‘Calculated values of gamma^v were subtracted from the measured values of gamma to obtain the experimental values of gamma^e’, note a).

shelton_1994/table10_D2_expt#

{
  "id": "table10_D2_expt",
  "material": "D2",
  "equation": "Table X, p. 17",
  "printed": "gamma_o,expt = 669 au, A_expt = 1.184 x 10^-10 cm^2, B_expt = 2.10 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "669",
    "A": "1.184",
    "B": "2.10"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "calibration": "H2: shelton_1990's fitted H2 curve",
  "reproduced_from": [
    "shelton_1990"
  ],
  "check": "shelton_1990 Table IV: 41.71e-63 = 668.9 au, A = 1.184, B = 2.104. Checked 2026-09-26."
}

Note c: ref 34 (shelton_1990); gamma^vR subtracted.

shelton_1994/table10_N2_expt#

{
  "id": "table10_N2_expt",
  "material": "N2",
  "equation": "Table X, p. 17",
  "printed": "gamma_o,expt = 917 au, A_expt = 1.003 x 10^-10 cm^2, B_expt = 1.85 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "917",
    "A": "1.003",
    "B": "1.85"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "calibration": "He: Bishop & Pipin",
  "reproduced_from": [
    "shelton_1990"
  ],
  "check": "shelton_1990 Table IV: 57.20e-63 = 917.3 au, A = 1.003, B = 1.852. At 694.3 nm it gives 1057.7 au, the '1058' of Table IX note f. Checked 2026-09-26."
}

Note c: ref 34 (shelton_1990); gamma^vR subtracted.

shelton_1994/table10_O2_expt#

{
  "id": "table10_O2_expt",
  "material": "O2",
  "equation": "Table X, p. 17",
  "printed": "gamma_o,expt = 963 au, A_expt = 1.112 x 10^-10 cm^2, B_expt = 4.60 x 10^-20 cm^4",
  "variable": "nu_L^2 in cm^-2 (vacuum wavenumbers); ESHG: nu_L^2 = 6 nu^2",
  "process": "eshg",
  "convention": "T",
  "part": "electronic",
  "range": "nu_L^2 up to 30 x 10^8 cm^-2",
  "coefficients": {
    "gamma0": "963",
    "A": "1.112",
    "B": "4.60"
  },
  "coefficient_units": {
    "gamma0": "au",
    "A": "1e-10 cm^2",
    "B": "1e-20 cm^4"
  },
  "calibration": "N2: shelton_1990's fitted N2 curve",
  "reproduced_from": [
    "shelton_1990"
  ],
  "check": "shelton_1990 Table IV: 60.03e-63 = 962.7 au, A = 1.112, B = 4.603. Table IX prints 962 +- 6 for the same value. Checked 2026-09-26."
}

Note c: ref 34 (shelton_1990); gamma^vR subtracted.

Corrections#

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the review register for the checks and decisions.