christiansen_1998

O. Christiansen, C. Hattig and J. Gauss, “Polarizabilities of CO, N2, HF, Ne, BH, and CH+ from ab initio calculations: Systematic studies of electron correlation, basis set errors, and vibrational contributions”, J. Chem. Phys. 109, 4745 (1998)

Source record · Catalogue · Review register

DOI: 10.1063/1.477086

Source kind: theory

Recorded technique: Coupled-cluster linear response (CCS, CC2, CCSD, CC3, CCSDT; orbital-relaxed and unrelaxed; CCSD(T) static polarizabilities analytically, CC3 and CCSDT by finite field) with correlation-consistent basis sets up to d-aug-cc-pV5Z (326 functions), DALTON and ACES II. Correlation benchmark at aug-cc-pVTZ against CCSDT (Table III); basis-set study at the unrelaxed CCSD level (Table IV); fixed bond lengths R_CO = 2.132 a.u., R_NN = 2.068 a.u. Vibrational averaging over v = 0 and the pure vibrational polarizability from CC potential and property curves (aug-cc-pVQZ; nuclear Schrodinger equation by the ‘renormalized Numerov-Cooley approach’, spline interpolation of the property curves, sum over vibrational states), Tables V, VI, VIII (pp. 4746-4748). The isotropic polarizability is (alpha_xx + alpha_yy + alpha_zz)/3 (p. 4748).

Materials in structured entries: CO, N2, Ne

Dataset quantities: polarizability, polarizability_anisotropy

Contents: 16 datasets; 3 formulas.

Curation notes

The library identity is VALIDATED (DOI 10.1063/1.477086); first page checked (pdf page 2: J. Chem. Phys. 109, No. 12, 22 September 1998, p. 4745; pdf page 1 is the publisher’s cover). Page numbers here are journal pages (pdf page + 4743). Only CO, N2 and Ne are curated; HF, BH and CH+ are skipped.

WHAT IS COMPUTED. ‘Electronic’ polarizabilities are the static or dynamic responses of the electrons at fixed nuclei; ‘vibrationally averaged’ ones are averaged over the ground vibrational state (v = 0); the ‘pure vibrational’ polarizability is the response through the infrared transitions (Eq. 8, oscillators of Table VIII). Rotation is not treated (no orientation term). All values are in atomic units.

FINAL STATIC ELECTRONIC VALUES (Table IX, p. 4754), tensor components at the fixed R_e. Estimate 1 = CCSD(T)/aug-cc-pVQZ + basis-set correction (unrelaxed CCSD d-aug-cc-pV5Z minus aug-cc-pVQZ) + CCSDT(r) - CCSD(T) correlation correction; estimate 2 = CCSD(u)/d-aug-cc-pV5Z + CCSDT(u) - CCSD(u). Final estimate (their average): CO alpha_xx 11.83, alpha_zz 15.41; N2 10.15, 14.70; Ne 2.66 (every sum and average checked, 2026-09-25). ‘The polarizability components are accurate within a few hundredth of an a.u.’ (p. 4754). Vibrationally averaged, estimate 1: CO 11.85, 15.49; N2 10.20, 14.88; with the pure vibrational term: CO 11.85, 15.86 (N2 unchanged). The isotropic means of these (2 alpha_xx + alpha_zz)/3 are printed in Table X and extracted from there. Basis-set limits (Table IV, CCSD(u)): the aug-cc-pVQZ values lie within 0.05 a.u. of d-aug-cc-pV5Z for CO and N2 and 0.07 a.u. for Ne (p. 4750); d-aug-cc-pV5Z: CO 11.790, 15.569; N2 10.085, 14.516; Ne 2.668 (the benchmark tables III and IV, method by method and basis by basis, are not extracted). Also in Table IX: previous calculations (MCSCF, SOPPA, MP2, CCSD(T) of Refs. 40-48; the MP2 and CCSD(T) rows are printed shifted one pair of columns to the left, image checked: MP2 is CO 11.97, 15.60 and N2 10.12, 14.29) and Kumar and Meath’s DOSD values (Refs. 50, 51: CO 11.89, 15.46; N2 10.21, 14.80), not extracted. BH’s printed estimate 2, 20.090, is not 21.042 - 0.133 = 20.909 (a misprint; BH is not curated).

VIBRATIONAL CONTRIBUTIONS (Table VI, aug-cc-pVQZ, p. 4752). Vibrational averaging raises CO by 0.02 (xx) and 0.11 (zz, CCSD(T)), N2 by 0.03 and 0.09. The pure vibrational static polarizability of CO is alpha_zz = 0.37 (CCSD(T); 0.36 CCSD, 0.68 CCS, 0.07 CC2: ‘rather dramatic variations’, p. 4752), i.e. 0.12 a.u. in the mean (0.1246 from Table VIII’s CCSD(T) oscillators, computed here), against Bishop and Cheung’s 0.1213 a.u. (bishop_1982, Table 1: 0.020 x 10^-40 C^2 m^2 J^-1). N2 has none. At optical frequencies the pure vibrational term is small and negative (Table X ‘Vibrational’, mean alpha of CO -0.001, -0.001, -0.002, -0.002 a.u. at 457.9, 488.0, 514.8, 632.8 nm; not extracted: a contribution, not a polarizability). ‘Such extrapolations [of optical data to zero frequency] do not - or only partially - include the vibrational contribution’ (p. 4754).

TABLE X (p. 4755), the extracted values: isotropic alpha (a.u.). ‘Electronic’ static = the vibrationally averaged estimate 1; its frequency dependence from the Cauchy moments of Table VII (k > 0, CCSD/aug-cc-pVQZ); the pure vibrational term from Table VIII (CCSD(T)). All checked: estimate 1’s mean (CO 13.066, N2 11.762) plus the moment series reproduces every dynamic value to 0.005 a.u. (N2 at 488.0 nm: 12.016 against 12.01), with the wavelengths as vacuum wavelengths. The CO ‘Electronic+Vibrational’ static 13.18 is 0.01 below 13.066 + 0.1246 = 13.191 (rounding in the paper; its anisotropy 4.01 checks). Wavelengths are the argon-ion and He-Ne lines as printed (nm); the medium is not stated. The theory rows are recorded as vacuum wavelengths (the calculation is at the frequency; the 0.03 % air-vacuum difference changes alpha by < 1e-4 of itself); the experimental rows as standard air, as alms_1975 records these lines. The anisotropies Delta alpha (CO 3.64 static electronic, 4.01 with the vibrational term, 3.65 at 457.9-632.8 nm; experiment 3.59 at 632.8 nm, Bridge and Buckingham) are not extracted (later phase).

EXPERIMENTAL VALUES IN TABLE X, reproduced: b ‘Extrapolated from refractive index in Ref. 36’ (Werner and Meyer 1976, a theory paper quoting it); c Ref. 58 (Bridge and Buckingham 1966); d Ref. 55 (Alms et al. 1975 = alms_1975); f Ref. 57 (Muenter 1972, the HF Stark-effect paper: implausible as the source of neon’s 2.669, see the dataset); g Ref. 49 (Kumar and Meath 1985) on N2’s anisotropy 4.69, which the text attributes to Ref. 56 (Buckingham et al. 1970; footnote h is printed but not used in the table): the footnote letters are inconsistent. The paper’s accuracy statement for the comparison: ‘For the isotropic part the values obtained in this way agrees within 0.05 a.u. with the given estimates for the electronic contributions’ (p. 4755).

FORMULAS. Table VII’s Cauchy moments (components) are recorded as the formulas co_cauchy and n2_cauchy; Table VIII’s vibrational oscillators of CO as co_vibrational. Printed misprints: Table VII’s headers S_zz(6) and S_zz(8) lack the minus signs of S_zz(-6), S_zz(-8) (image checked; the sums require k < 0); Table VIII’s CCSD(T) CO omega_1 is printed 0.09785 for 0.009785 (see co_vibrational).

THIRD-ORDER DATA (2026-09-26). The paper has no hyperpolarizability (gamma) values: nothing of that kind is added. The polarizability ANISOTROPIES of Table X (the columns Delta alpha = alpha_zz - alpha_xx, p. 4755), needed to separate the rotational (orientational) Kerr and Raman responses, are now extracted for CO and N2 (anisotropy_* datasets, quantity polarizability_anisotropy, a.u.): electronic (vibrationally averaged, static and 457.9-632.8 nm; CO 3.64 static, 3.65 optical; N2 4.68, 4.83-4.75), CO electronic + pure vibrational static 4.01 (N2’s equals its electronic value and is not written again), and the experimental values as reproduced: N2 footnote d (Alms et al. 1975 = alms_1975: 4.45 static, 4.89, 4.85, 4.82, 4.69 at 457.9-632.8 nm), N2 footnote g (4.69 static; see the footnote inconsistency above: Ref. 49 Kumar and Meath 1985, or Ref. 56 Buckingham et al. 1970 per the text), and footnote c (Bridge and Buckingham 1966, 632.8 nm: CO 3.59, N2 4.70). The pure vibrational anisotropy of CO at optical frequencies (-0.004 to -0.007) is a contribution, not extracted. Accuracy: ‘a few hundredth of an a.u.’ for the components (p. 4754).

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

Datasets

christiansen_1998/electronic_CO

{
  "id": "electronic_CO",
  "material": "CO",
  "file": "CO/christiansen_1998__electronic_CO.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check",
  "uncertainty": {
    "absolute": 0.03,
    "level": "not stated"
  }
}

Table X ‘Electronic’: the vibrationally averaged (v = 0) electronic mean polarizability, static (estimate 1, CCSD(T)/aug-cc-pVQZ with basis-set and CCSDT corrections) and at 457.9, 488.0, 514.8, 632.8 nm (the static value plus the CCSD/aug-cc-pVQZ Cauchy series, co_cauchy). No pure vibrational term (static: +0.12 a.u.; optical: -0.001 to -0.002 a.u.) and no orientation term. Accuracy ‘a few hundredth of an a.u.’ in the components (p. 4754); level not stated.

christiansen_1998/total_static_CO

{
  "id": "total_static_CO",
  "material": "CO",
  "file": "CO/christiansen_1998__total_static_CO.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check",
  "uncertainty": {
    "absolute": 0.03,
    "level": "not stated"
  }
}

Table X ‘Electronic+Vibrational’, static: electronic_CO’s 13.06 plus the pure vibrational polarizability of the infrared band (CCSD(T), Table VIII; 0.12 a.u. in the mean), the value a dielectric measurement would see without the orientation term. Not the refractive (electronic) static limit. 13.066 + 0.1246 = 13.191 would round to 13.19 (printed 13.18).

christiansen_1998/werner_meyer_CO

{
  "id": "werner_meyer_CO",
  "material": "CO",
  "file": "CO/christiansen_1998__werner_meyer_CO.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "H. J. Werner and W. Meyer, Mol. Phys. 31, 855 (1976) (Table X footnote b: 'Extrapolated from refractive index in Ref. 36'; the refractive-index source behind it is not named)"
  ]
}

Table X ‘Experiment’, static, footnote b: an optical extrapolation to zero frequency, so electronic (vibrationally averaged) only, 0.02 a.u. above electronic_CO. Uncertainty not stated.

christiansen_1998/bridge_buckingham_CO

{
  "id": "bridge_buckingham_CO",
  "material": "CO",
  "file": "CO/christiansen_1998__bridge_buckingham_CO.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "N. J. Bridge and A. D. Buckingham, Proc. R. Soc. London, Ser. A 295, 344 (1966) (Table X footnote c, Ref. 58; sneep_2005 cites it as 295, 334)"
  ]
}

Table X ‘Experiment’, 632.8 nm, footnote c: the He-Ne value used with Bridge and Buckingham’s depolarization measurement; 0.02 a.u. above electronic_CO at 632.8 nm. Whether the mean polarizability is Bridge and Buckingham’s own measurement or a refractive index they quote is not said here. Uncertainty not stated.

christiansen_1998/electronic_N2

{
  "id": "electronic_N2",
  "material": "N2",
  "file": "N2/christiansen_1998__electronic_N2.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check",
  "uncertainty": {
    "absolute": 0.03,
    "level": "not stated"
  }
}

Table X ‘Electronic’: vibrationally averaged electronic mean polarizability, static (estimate 1) and at 457.9-632.8 nm (plus the CCSD Cauchy series, n2_cauchy). N2 has no pure vibrational polarizability, so Table X’s ‘Electronic+Vibrational’ row repeats the static value (not written twice). The authors expect ‘a slightly too small dispersion’ from CCSD (p. 4755).

christiansen_1998/alms_N2

{
  "id": "alms_N2",
  "material": "N2",
  "file": "N2/christiansen_1998__alms_N2.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "alms_1975"
  ]
}

Table X ‘Experiment’, footnote d (Ref. 55, Alms et al. 1975): static 11.74 and 457.9-632.8 nm. alms_1975’s Table I (angstrom^3, itself Landolt-Bornstein’s) gives, over 0.1481847 angstrom^3/a.u., 12.06, 12.03, 12.00, 11.92 and 11.76 (inf): the 632.8 nm and static values here, 11.88 and 11.74, do not match (checked 2026-09-25; the conversion Christiansen et al. used is not stated). Take alms_1975 itself.

christiansen_1998/bridge_buckingham_N2

{
  "id": "bridge_buckingham_N2",
  "material": "N2",
  "file": "N2/christiansen_1998__bridge_buckingham_N2.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "N. J. Bridge and A. D. Buckingham, Proc. R. Soc. London, Ser. A 295, 344 (1966) (Table X footnote c, Ref. 58)"
  ]
}

Table X ‘Experiment’, 632.8 nm, footnote c. Equal to alms_1975’s 1.766 angstrom^3 in a.u. (11.92), which Alms et al. used with Bridge and Buckingham’s depolarization ratio.

christiansen_1998/electronic_Ne

{
  "id": "electronic_Ne",
  "material": "Ne",
  "file": "Ne/christiansen_1998__electronic_Ne.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check",
  "uncertainty": {
    "absolute": 0.03,
    "level": "not stated"
  }
}

Table X ‘Electronic’, static: the final estimate of Table IX (estimate 1 2.661, estimate 2 2.658). Basis-set limit at CCSD(u), d-aug-cc-pV5Z: 2.668 (Table IV); aug-cc-pVQZ is 0.07 a.u. lower. No dynamic values for Ne (the authors refer to their earlier Cauchy-moment paper, Ref. 35).

christiansen_1998/experiment_Ne

{
  "id": "experiment_Ne",
  "material": "Ne",
  "file": "Ne/christiansen_1998__experiment_Ne.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "As printed: Table X footnote f, 'From Ref. 57', J. S. Muenter, J. Chem. Phys. 56, 5490 (1972), an HF Stark-effect paper: the true source of the neon value is doubtful"
  ]
}

Table X ‘Experiment’, static, 2.669 a.u., footnote f. The footnote points to Muenter’s HF paper, which cannot be the source of a neon polarizability; the footnotes of Table X are inconsistent (source notes). Kept as a reproduction of unknown origin; the curated neon static values (gaiser_2018, lesiuk_2020) supersede it.

christiansen_1998/anisotropy_electronic_CO

{
  "id": "anisotropy_electronic_CO",
  "material": "CO",
  "file": "CO/christiansen_1998__anisotropy_electronic_CO.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability_anisotropy",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check"
}

Table X ‘Electronic’ Delta alpha = alpha_zz - alpha_xx of CO: static (estimate 1, vibrationally averaged) and 457.9-632.8 nm (with the CCSD Cauchy series). Electronic only; accuracy ‘a few hundredth of an a.u.’ in the components.

christiansen_1998/anisotropy_total_static_CO

{
  "id": "anisotropy_total_static_CO",
  "material": "CO",
  "file": "CO/christiansen_1998__anisotropy_total_static_CO.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability_anisotropy",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check"
}

Table X ‘Electronic+Vibrational’, static Delta alpha of CO including the pure vibrational (infrared) term: 4.01 (electronic 3.64).

christiansen_1998/anisotropy_electronic_N2

{
  "id": "anisotropy_electronic_N2",
  "material": "N2",
  "file": "N2/christiansen_1998__anisotropy_electronic_N2.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability_anisotropy",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "vacuum",
  "use": "check"
}

Table X ‘Electronic’ Delta alpha of N2: static and 457.9-632.8 nm (vibrationally averaged). N2 has no pure vibrational term.

christiansen_1998/anisotropy_alms_N2

{
  "id": "anisotropy_alms_N2",
  "material": "N2",
  "file": "N2/christiansen_1998__anisotropy_alms_N2.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability_anisotropy",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "alms_1975"
  ]
}

Table X ‘Experiment’, footnote d (Alms et al. 1975): N2 Delta alpha static (4.45) and at 457.9, 488.0, 514.8, 632.8 nm.

christiansen_1998/anisotropy_experiment_g_N2

{
  "id": "anisotropy_experiment_g_N2",
  "material": "N2",
  "file": "N2/christiansen_1998__anisotropy_experiment_g_N2.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability_anisotropy",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "As printed: Table X footnote g, Ref. 49 (A. Kumar and W. J. Meath, 1985) or Ref. 56 (Buckingham et al., 1970)"
  ]
}

Table X ‘Experiment’, footnote g: N2 static Delta alpha 4.69 (the footnote points to Ref. 49, Kumar and Meath 1985, the text to Ref. 56, Buckingham et al. 1970; see the source notes).

christiansen_1998/anisotropy_bridge_buckingham_CO

{
  "id": "anisotropy_bridge_buckingham_CO",
  "material": "CO",
  "file": "CO/christiansen_1998__anisotropy_bridge_buckingham_CO.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability_anisotropy",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "N. J. Bridge and A. D. Buckingham, Proc. R. Soc. London, Ser. A 295, 344 (1966) (Table X footnote c, Ref. 58)"
  ]
}

Table X ‘Experiment’, 632.8 nm, footnote c: Bridge and Buckingham’s CO anisotropy 3.59 (from depolarisation of scattered light).

christiansen_1998/anisotropy_bridge_buckingham_N2

{
  "id": "anisotropy_bridge_buckingham_N2",
  "material": "N2",
  "file": "N2/christiansen_1998__anisotropy_bridge_buckingham_N2.csv",
  "table": "tbl_08a3d26f2c43",
  "quantity": "polarizability_anisotropy",
  "unit": "au",
  "abscissa_unit": "nm",
  "wavelength_medium": "standard_air",
  "use": "reproduced",
  "reproduced_from": [
    "N. J. Bridge and A. D. Buckingham, Proc. R. Soc. London, Ser. A 295, 344 (1966) (Table X footnote c, Ref. 58)"
  ]
}

Table X ‘Experiment’, 632.8 nm, footnote c: Bridge and Buckingham’s N2 anisotropy 4.70.

Formulas

christiansen_1998/co_cauchy

{
  "id": "co_cauchy",
  "material": "CO",
  "equation": "Eq. (7), p. 4752, with Table VII, p. 4753",
  "printed": "alpha_XY(-omega, omega) = sum_{k>=0} S_XY(-2k-2) omega^(2k); CO: S_xx(-2) 11.837, S_zz(-2) 15.666, S_xx(-4) 46.4, S_zz(-4) 49.2, S_xx(-6) 315, S_zz(6) 194, S_xx(-8) 0.3x10^4, S_zz(8) 0.8x10^3",
  "variable": "omega: photon energy in hartree (atomic units); alpha in atomic units, per component; the mean is (2 alpha_xx + alpha_zz)/3",
  "state": "none (per molecule)",
  "density": "none",
  "range": "'accuracy of 0.01 a.u. for omega < 0.02 a.u.' for N2 and HF 'and < 0.01 a.u. for CO' (p. 4752, as printed; the text is garbled, and Table X uses the series up to 457.9 nm, omega = 0.0995)",
  "coefficients": {
    "Sxx_m2": "11.837",
    "Szz_m2": "15.666",
    "Sxx_m4": "46.4",
    "Szz_m4": "49.2",
    "Sxx_m6": "315",
    "Szz_m6": "194",
    "Sxx_m8": "0.3e4",
    "Szz_m8": "0.8e3"
  },
  "check": "The k > 0 moments added to the estimate 1 static mean (13.066) reproduce Table X's electronic CO values at 457.9, 488.0, 514.8 and 632.8 nm (as vacuum wavelengths) to within 0.004 a.u.: 13.5638, 13.5010, 13.4547, 13.3191 against 13.56, 13.50, 13.45, 13.32. Mean moments: S(-4) 47.33, S(-6) 274.7, S(-8) 2267 (computed; zhao_2026 quotes Kumar and Meath's 48.26, 292.9, 2308). Checked 2026-09-25."
}

Unrelaxed CCSD/aug-cc-pVQZ, fitted to vibrationally averaged polarizabilities at several frequencies (a fit, not an analytic moment calculation). Printed headers S_zz(6) and S_zz(8) are S_zz(-6) and S_zz(-8) (lost minus signs; image checked). S(-2) here is CCSD/aug-cc-pVQZ, not the final estimate; Table X combines the final static value with these k > 0 moments.

christiansen_1998/n2_cauchy

{
  "id": "n2_cauchy",
  "material": "N2",
  "equation": "Eq. (7), p. 4752, with Table VII, p. 4753",
  "printed": "alpha_XY(-omega, omega) = sum_{k>=0} S_XY(-2k-2) omega^(2k); N2: S_xx(-2) 10.147, S_zz(-2) 14.612, S_xx(-4) 23.6, S_zz(-4) 37.8, S_xx(-6) 74, S_zz(6) 121, S_xx(-8) 0.3x10^3, S_zz(8) 0.5x10^3",
  "variable": "omega: photon energy in hartree; alpha in atomic units, per component; the mean is (2 alpha_xx + alpha_zz)/3",
  "state": "none (per molecule)",
  "density": "none",
  "range": "'accuracy of 0.01 a.u. for omega < 0.02 a.u.' (p. 4752, as printed)",
  "coefficients": {
    "Sxx_m2": "10.147",
    "Szz_m2": "14.612",
    "Sxx_m4": "23.6",
    "Szz_m4": "37.8",
    "Sxx_m6": "74",
    "Szz_m6": "121",
    "Sxx_m8": "0.3e3",
    "Szz_m8": "0.5e3"
  },
  "check": "The k > 0 moments added to the estimate 1 static mean (11.762) give 12.052, 12.016, 11.990, 11.912 at 457.9, 488.0, 514.8, 632.8 nm against Table X's 12.05, 12.01, 11.99, 11.91 (488.0 nm 0.006 off, the rest within rounding). Checked 2026-09-25."
}

As co_cauchy. The authors note CCSD places N2’s first dipole-allowed transition slightly too high, so the dispersion is expected slightly too small (p. 4755).

christiansen_1998/co_vibrational

{
  "id": "co_vibrational",
  "material": "CO",
  "equation": "Eq. (8), p. 4753, with Table VIII (CCSD(T) row), p. 4754",
  "printed": "<<X,Y>>^v_omega = sum_k f_k^XY/(omega^2 - omega_k^2); CO, CCSD(T): omega_1 0.09785, f_1 0.3572x10^-4, omega_2 0.01954, f_2 0.299x10^-6, omega_3 0.02917, f_3 0.50x10^-8, omega_4 0.03868, f_4 0.1x10^-11",
  "variable": "omega: photon energy in hartree; the pure vibrational alpha_zz = -<<z,z>> = sum_k f_k/(omega_k^2 - omega^2) in atomic units (alpha_xx has none); the mean is alpha_zz/3",
  "state": "none (per molecule)",
  "density": "none",
  "range": "static to optical; the poles are the fundamental and overtones of CO's ground state (v = 0 -> k)",
  "coefficients": {
    "omega1": "0.09785",
    "f1": "0.3572e-4",
    "omega2": "0.01954",
    "f2": "0.299e-6",
    "omega3": "0.02917",
    "f3": "0.50e-8",
    "omega4": "0.03868",
    "f4": "0.1e-11"
  },
  "check": "omega_1 is misprinted (image checked: 0.09785): with it the static alpha_zz^v is 0.0045, not Table VI's 0.37, and the optical values change sign. With omega_1 = 0.009785 (half of omega_2 less anharmonicity, and the CCSD omega_1 is 0.01006) the static alpha_zz^v is 0.3739 (Table VI: 0.37) and alpha_zz^v at 457.9, 488.0, 514.8, 632.8 nm is -0.0037, -0.0042, -0.0047, -0.0071, the mean -0.0012, -0.0014, -0.0016, -0.0024: Table X's 'Vibrational' Delta alpha -0.004, -0.004, -0.005, -0.007 and alpha -0.001, -0.001, -0.002, -0.002. Read omega_1 = 0.009785 (2147.6 cm^-1). The CCSD row (omega_1 0.01006, f_1 0.3623e-4, ...) gives a static 0.3585 (Table VI: 0.36). Checked 2026-09-25."
}

The pure vibrational polarizability of CO at aug-cc-pVQZ; the static mean 0.1246 a.u. compares with Bishop and Cheung’s 0.1213 a.u. (bishop_1982). The CCSD row: omega 0.01006, 0.02000, 0.02984, 0.03957; f 0.3623e-4, 0.218e-6, 0.12e-8, 0.5e-11 (image checked).

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.