hattig_1998b#

C. Hättig, O. Christiansen and P. Jørgensen, “Coupled cluster response calculations of two-photon transition probability rate constants for helium, neon and argon”, J. Chem. Phys. 108, 8355-8359 (1998)

Source record · Catalogue · Review register

DOI: 10.1063/1.476262

Source kind: theory

Recorded technique: Coupled cluster response theory (the preceding paper, J. Chem. Phys. 108, 8331 (1998)): the left and right two-photon transition moments M^ab_{0<-f} and M^ab_{f<-0} as second derivatives of variational transition-moment Lagrangians (Eqs. 7-14), and the transition strength as their symmetrised product, S^0f_{ab,cd} = (1/2){M^ab_{0<-f} (-w) M^cd_{f<-0}(w) + c.c.} (Eq. 5), at the CCS, CC2 and CCSD levels. Basis (p. 8357): t-aug-cc-pV5Z (Woon and Dunning 1995), He (11s7p6d5f4g)/[8s7p6d5f4g], Ne (17s11p7d6f5g4h)/[9s8p7d6f5g4h], Ar (23s15p7d6f5g4h)/[10s9p7d6f5g4h]; ‘In the calculations for neon and argon only the eight valence electrons were correlated.’ Non-relativistic, LS coupling: ‘For argon, the neglect of the spin-orbit interaction leads to additional errors’ (p. 8357). Frequencies: omega_1 = omega_2 = omega_f0/2, and omega_2 = 10.49 eV = 0.3855 a.u. with omega_1 = omega_f - omega_2 (p. 8358), omega_f0 the method’s own excitation energy (Table I; established by the checks).

Materials in structured entries: Ar, He, Ne

Dataset quantities: oscillator_strength, two_photon_transition_strength

Contents: 27 datasets; 0 formulas.

Curation notes#

Journal pp. 8355-8359 = PDF pages 2-6 (PDF page 1 is the AIP download cover); journal page = PDF page + 8353. Identity checked on the first page (PDF p. 2: ‘JOURNAL OF CHEMICAL PHYSICS VOLUME 108, NUMBER 20 22 MAY 1998’, ‘0021-9606/98/108(20)/8355/5’, Christof Hättig, Ove Christiansen and Poul Jørgensen, Aarhus; received 12 November 1997, accepted 19 February 1998) on 2026-10-08. The id hattig_1998b: hattig_1998 is another paper by Hättig of 1998.

THE QUANTITY (p. 8356). ‘The two-photon transition probability rate constant is given by: K_{0-f} = a0^4 t0 (2 pi)^2 alpha^2 omega_1 omega_2 delta^TP’ (Eq. 15), ‘delta^TP is a rotationally averaged two-photon transition strength (in a.u.) defined as: delta^TP = F delta_F + G delta_G + H delta_H’ (Eq. 16), with delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 17-19): ‘For parallel linearly polarized laser beams the appropriate values are F = G = H = 2’ (after Moccia and Rizzo 1985). Tables III-V print, for each level and method, a column headed S^0f/a.u. and one headed K_{0-f}/cm4 s. Every K of the tables (36 cells, 1Se and 1De, both pairs of frequencies, the CC rows and the reproduced SCF/MCSCF rows) is reproduced from its S^0f within its printing (worst 0.26 %, Ar 1De CCS at 10.49 eV, printed to 0.4 %) by 2 pi times Eq. (15), with omega_f0 the method’s own Table I excitation energy, and with delta^TP = S^0f for the 1Se levels and (4/15) S^0f for the 1De levels (tools/extract/hattig_1998b.py). So: (a) Eq. (15) as printed gives every tabulated K 2 pi too small; the tables follow (2 pi)^3 (equivalently t0 taken as h/E_h, 1.52e-16 s). The K are not data here (no quantity holds a rate constant in cm4 s), and the values taken are the strengths. (b) For a 1Se level S^0f is delta^TP (with F = G = H = 2 the rotational average of an isotropic tensor S_ab = s delta_ab is s^2 = S_zz^2): taken. (c) For a 1De level S^0f is not delta^TP: it is the square of the one tensor element S_xy of the level’s xy component (the SCF and MCSCF entries of argon, 90.23 and 108.66, are the squares of the S_xy = 9.499 and 10.424 a.u. of Sundholm et al. 1994, and neon’s SCF entry 8.799 the square of Hettema et al.’s 2.9663 a.u., as henriksson_2005 quotes them, to 4-5 figures). The rotational average of that component (F = G = H = 2) is (4/15) S^0f, which reproduces the 1De K; summed over the level’s five components it is (4/3) S^0f, henriksson_2005’s convention (its TDHF 11.060 and 113.40 a.u. for Ne and Ar 1D2 are (4/3) of the squares of its quoted S_xy). The 1De K of Tables IV-V are thus those of one of the level’s five components. NOT TAKEN: the 1De rows (CCS, CC2, CCSD, and the SCF/MCSCF of Refs. 6 and 12), which no quantity holds as printed; their S^0f times 4/3 would be the level’s delta^TP in the convention of henriksson_2005.

EXTRACTED (tools/extract/hattig_1998b.py), from the library’s cells (the tables have merged two-row headers), every cell checked against the table images (2026-10-08): - Tables III (He, p. 8358), IV (Ne, p. 8358), V (Ar, p. 8359): the CCS, CC2 and CCSD S^0f of the 1Se level, one dataset per gas, method and pair of frequencies (18), the row named by the method and x by the level as printed (He: Table III prints no level; its caption’s ‘the 1Se state in He’ is the 1s1 2s1 level of Table I). Table V prints argon’s levels as ‘2p5 3p1’ (neon’s shells), corrected by errata to 3p5 4p1. - Table II (p. 8357): the CCS, CC2 and CCSD oscillator strengths of the ground state to the lowest 1P level, the paper’s own calculations, one dataset per gas and method (9). Its heading prints the level as 1Pe; corrected by errata to 1Po (the text: ‘the ground state to 1Po transitions’). For Ne and Ar the authors compare them with the sum of the experimental P1/2 and P3/2 (J = 1) strengths: ‘For all three atoms we obtain at the CCSD level oscillator strengths ... within the experimental uncertainities’ (checked: He 0.2766 vs 0.280 +- 0.007, Ne 0.1650 vs 0.171 +- 0.008, Ar 0.3219 vs 0.331 +- 0.016). All use = check (computed values; no model of this quantity is fitted). The paper states no numerical uncertainty: ‘The CCSD results are close to the best available MCSCF results’; correlation changes the Ne and the argon 10.49 eV strengths by about 50 % from CCS to CCSD, and ‘CC2 overshoot the CCSD value considerably by 10%-25%’ there (p. 8358); for He the remaining errors of the excitation energies are ‘due to basis set defects’ (p. 8357).

THE TEXT’S COMPARISONS (p. 8358). ‘For argon we can compare with the experimental transition probability rate constant for the transition to the 1De state, derived as the sum of the transition probability rates to the spin-orbit mixed states 3p5 4p[3/2]_{J=2} (1De), 3p5 4p[5/2]_{J=2} (3De) and 3p5 4p[3/2]_{J=2} (3Pe). The resulting experimental value of 2.05 x 10^-51 cm4 s agrees well with the CCSD result of 1.83 x 10^-51 cm4 s’ (Table V, omega_2 = 10.49 eV, footnote b: Refs. 12, 21-23: Sundholm, Rizzo and Jørgensen, J. Chem. Phys. 101, 4931 (1994); M. G. Payne, C. H. Chen, G. S. Hurst and G. W. Foltz, Adv. At. Mol. Phys. 17, 229-274 (1981); M. P. McCann, C. H. Chen and M. G. Payne, J. Chem. Phys. 89, 5429 (1989); M. G. Payne, C. H. Chen, G. S. Hurst, S. D. Kramer, W. R. Garrett and M. Pindzola, Chem. Phys. Lett. 79, 142 (1981)). NOT TAKEN: it is a rate constant in cm4 s (and, by (c), the computed K it is compared with is one component’s), not this quantity, and its primary sources are not in the library.

MISPRINTS. Table V’s K of the SCF row at 10.49 eV is printed ‘1.19 x 20^-51’ (the PDF’s text and the rendered table agree: a misprint, not an extraction artefact); it is 1.19 x 10^-51 (reproduced 1.1875e-51 from S^0f = 418.90 and Table I’s SCF energy 13.485 eV). Not an erratum entry: the K are not held. The argon level labels and the Table II heading are corrected by the errata below.

NOT TAKEN. Table I, the excitation energies (SCF, CCS, CC2, CCSD, MCSCF, and Moore’s experimental ones): computed energies of a non-relativistic model, not the levels of the atom that level_energy holds (they are used by the checks). Table II’s experimental rows (Chan et al. 1991, 1992: chan_1991, chan_1992_neon, chan_1992) and argon’s SCF and CAS rows (Sundholm et al. 1994). The K columns and the experimental K (above). The 1De rows (above). Table IV’s SCF and MCSCF 1De rows are Hettema et al.’s (Ref. 6: H. Hettema, H. J. Aa. Jensen, P. Jørgensen and J. Olsen, J. Chem. Phys. 97, 1174 (1992)), whose K the authors computed ‘assuming omega_1 = omega_2 = 0.3425 a.u.’ (footnote b); the MCSCF entry 11.289 is not the square of the SD RAS S_xy = 3.3450 (11.189) that henriksson_2005 quotes from the same paper (at 19.170 eV, where Table I’s MCSCF of Ref. 6 is at 18.874 eV): a different calculation of Ref. 6, not resolvable here.

COMPARISON. henriksson_2005’s TDHF strength of He 1s2s 1S0 (10.426 a.u., qaug-cc-pVTZ, 21.125 eV) against CCS here (10.824 a.u., 21.137 eV): different methods (TDHF is the random phase approximation, CCS is not) and bases, same convention for a 1S level.

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

Datasets#

hattig_1998b/S_He_CCS_degenerate#

{
  "id": "S_He_CCS_degenerate",
  "material": "He",
  "file": "He/hattig_1998b__S_He_CCS_degenerate.csv",
  "table": "tbl_1bfdadd98b52",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "degenerate",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCS (coupled cluster singles) response, t-aug-cc-pV5Z, (11s7p6d5f4g)/[8s7p6d5f4g]"
  }
}

Table III, column S^0f/a.u., omega_1 = omega_2 = omega_f0/2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_He_CCS_w2_10p49eV#

{
  "id": "S_He_CCS_w2_10p49eV",
  "material": "He",
  "file": "He/hattig_1998b__S_He_CCS_w2_10p49eV.csv",
  "table": "tbl_1bfdadd98b52",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "10.49 eV",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCS (coupled cluster singles) response, t-aug-cc-pV5Z, (11s7p6d5f4g)/[8s7p6d5f4g]"
  }
}

Table III, column S^0f/a.u., omega_2 = 10.49 eV = 0.3855 au (the experimental laser of argon, Refs. 21-23), omega_1 = omega_f0 - omega_2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_He_CC2_degenerate#

{
  "id": "S_He_CC2_degenerate",
  "material": "He",
  "file": "He/hattig_1998b__S_He_CC2_degenerate.csv",
  "table": "tbl_1bfdadd98b52",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "degenerate",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CC2 (approximate coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (11s7p6d5f4g)/[8s7p6d5f4g]"
  }
}

Table III, column S^0f/a.u., omega_1 = omega_2 = omega_f0/2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_He_CC2_w2_10p49eV#

{
  "id": "S_He_CC2_w2_10p49eV",
  "material": "He",
  "file": "He/hattig_1998b__S_He_CC2_w2_10p49eV.csv",
  "table": "tbl_1bfdadd98b52",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "10.49 eV",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CC2 (approximate coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (11s7p6d5f4g)/[8s7p6d5f4g]"
  }
}

hattig_1998b/S_He_CCSD_degenerate#

{
  "id": "S_He_CCSD_degenerate",
  "material": "He",
  "file": "He/hattig_1998b__S_He_CCSD_degenerate.csv",
  "table": "tbl_1bfdadd98b52",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "degenerate",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCSD (coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (11s7p6d5f4g)/[8s7p6d5f4g]"
  }
}

Table III, column S^0f/a.u., omega_1 = omega_2 = omega_f0/2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_He_CCSD_w2_10p49eV#

{
  "id": "S_He_CCSD_w2_10p49eV",
  "material": "He",
  "file": "He/hattig_1998b__S_He_CCSD_w2_10p49eV.csv",
  "table": "tbl_1bfdadd98b52",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "10.49 eV",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCSD (coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (11s7p6d5f4g)/[8s7p6d5f4g]"
  }
}

hattig_1998b/S_Ne_CCS_degenerate#

{
  "id": "S_Ne_CCS_degenerate",
  "material": "Ne",
  "file": "Ne/hattig_1998b__S_Ne_CCS_degenerate.csv",
  "table": "tbl_821a4b276e0b",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "degenerate",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCS (coupled cluster singles) response, t-aug-cc-pV5Z, (17s11p7d6f5g4h)/[9s8p7d6f5g4h], the eight valence electrons correlated"
  }
}

Table IV, column S^0f/a.u., omega_1 = omega_2 = omega_f0/2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_Ne_CCS_w2_10p49eV#

{
  "id": "S_Ne_CCS_w2_10p49eV",
  "material": "Ne",
  "file": "Ne/hattig_1998b__S_Ne_CCS_w2_10p49eV.csv",
  "table": "tbl_821a4b276e0b",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "10.49 eV",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCS (coupled cluster singles) response, t-aug-cc-pV5Z, (17s11p7d6f5g4h)/[9s8p7d6f5g4h], the eight valence electrons correlated"
  }
}

Table IV, column S^0f/a.u., omega_2 = 10.49 eV = 0.3855 au (the experimental laser of argon, Refs. 21-23), omega_1 = omega_f0 - omega_2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_Ne_CC2_degenerate#

{
  "id": "S_Ne_CC2_degenerate",
  "material": "Ne",
  "file": "Ne/hattig_1998b__S_Ne_CC2_degenerate.csv",
  "table": "tbl_821a4b276e0b",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "degenerate",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CC2 (approximate coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (17s11p7d6f5g4h)/[9s8p7d6f5g4h], the eight valence electrons correlated"
  }
}

Table IV, column S^0f/a.u., omega_1 = omega_2 = omega_f0/2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_Ne_CC2_w2_10p49eV#

{
  "id": "S_Ne_CC2_w2_10p49eV",
  "material": "Ne",
  "file": "Ne/hattig_1998b__S_Ne_CC2_w2_10p49eV.csv",
  "table": "tbl_821a4b276e0b",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "10.49 eV",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CC2 (approximate coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (17s11p7d6f5g4h)/[9s8p7d6f5g4h], the eight valence electrons correlated"
  }
}

hattig_1998b/S_Ne_CCSD_degenerate#

{
  "id": "S_Ne_CCSD_degenerate",
  "material": "Ne",
  "file": "Ne/hattig_1998b__S_Ne_CCSD_degenerate.csv",
  "table": "tbl_821a4b276e0b",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "degenerate",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCSD (coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (17s11p7d6f5g4h)/[9s8p7d6f5g4h], the eight valence electrons correlated"
  }
}

Table IV, column S^0f/a.u., omega_1 = omega_2 = omega_f0/2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_Ne_CCSD_w2_10p49eV#

{
  "id": "S_Ne_CCSD_w2_10p49eV",
  "material": "Ne",
  "file": "Ne/hattig_1998b__S_Ne_CCSD_w2_10p49eV.csv",
  "table": "tbl_821a4b276e0b",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "10.49 eV",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCSD (coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (17s11p7d6f5g4h)/[9s8p7d6f5g4h], the eight valence electrons correlated"
  }
}

hattig_1998b/S_Ar_CCS_degenerate#

{
  "id": "S_Ar_CCS_degenerate",
  "material": "Ar",
  "file": "Ar/hattig_1998b__S_Ar_CCS_degenerate.csv",
  "table": "tbl_75eb5ba0dfd3",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "degenerate",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCS (coupled cluster singles) response, t-aug-cc-pV5Z, (23s15p7d6f5g4h)/[10s9p7d6f5g4h], the eight valence electrons correlated"
  }
}

Table V, column S^0f/a.u., omega_1 = omega_2 = omega_f0/2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_Ar_CCS_w2_10p49eV#

{
  "id": "S_Ar_CCS_w2_10p49eV",
  "material": "Ar",
  "file": "Ar/hattig_1998b__S_Ar_CCS_w2_10p49eV.csv",
  "table": "tbl_75eb5ba0dfd3",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "10.49 eV",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCS (coupled cluster singles) response, t-aug-cc-pV5Z, (23s15p7d6f5g4h)/[10s9p7d6f5g4h], the eight valence electrons correlated"
  }
}

Table V, column S^0f/a.u., omega_2 = 10.49 eV = 0.3855 au (the experimental laser of argon, Refs. 21-23), omega_1 = omega_f0 - omega_2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_Ar_CC2_degenerate#

{
  "id": "S_Ar_CC2_degenerate",
  "material": "Ar",
  "file": "Ar/hattig_1998b__S_Ar_CC2_degenerate.csv",
  "table": "tbl_75eb5ba0dfd3",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "degenerate",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CC2 (approximate coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (23s15p7d6f5g4h)/[10s9p7d6f5g4h], the eight valence electrons correlated"
  }
}

Table V, column S^0f/a.u., omega_1 = omega_2 = omega_f0/2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_Ar_CC2_w2_10p49eV#

{
  "id": "S_Ar_CC2_w2_10p49eV",
  "material": "Ar",
  "file": "Ar/hattig_1998b__S_Ar_CC2_w2_10p49eV.csv",
  "table": "tbl_75eb5ba0dfd3",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "10.49 eV",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CC2 (approximate coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (23s15p7d6f5g4h)/[10s9p7d6f5g4h], the eight valence electrons correlated"
  }
}

hattig_1998b/S_Ar_CCSD_degenerate#

{
  "id": "S_Ar_CCSD_degenerate",
  "material": "Ar",
  "file": "Ar/hattig_1998b__S_Ar_CCSD_degenerate.csv",
  "table": "tbl_75eb5ba0dfd3",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "degenerate",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCSD (coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (23s15p7d6f5g4h)/[10s9p7d6f5g4h], the eight valence electrons correlated"
  }
}

Table V, column S^0f/a.u., omega_1 = omega_2 = omega_f0/2, omega_f0 the method’s own excitation energy (Table I). Row: the method; x: the 1Se level.

hattig_1998b/S_Ar_CCSD_w2_10p49eV#

{
  "id": "S_Ar_CCSD_w2_10p49eV",
  "material": "Ar",
  "file": "Ar/hattig_1998b__S_Ar_CCSD_w2_10p49eV.csv",
  "table": "tbl_75eb5ba0dfd3",
  "quantity": "two_photon_transition_strength",
  "unit": "au",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "polarization": "linear_parallel",
    "frequencies": "10.49 eV",
    "rotational_average": "delta^TP = F delta_F + G delta_G + H delta_H, delta_F = (1/30) sum_ab S^0f_aabb, delta_G = (1/30) sum_ab S^0f_abab, delta_H = (1/30) sum_ab S^0f_abba (Eqs. 16-19), F = G = H = 2 for parallel linearly polarised beams; for this 1Se level delta^TP = S^0f",
    "method": "CCSD (coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (23s15p7d6f5g4h)/[10s9p7d6f5g4h], the eight valence electrons correlated"
  }
}

hattig_1998b/f_He_CCS#

{
  "id": "f_He_CCS",
  "material": "He",
  "file": "He/hattig_1998b__f_He_CCS.csv",
  "table": "tbl_ee7b52d10a52",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "method": "CCS (coupled cluster singles) response, t-aug-cc-pV5Z, (11s7p6d5f4g)/[8s7p6d5f4g]"
  }
}

Table II, the dipole oscillator strength of the ground state to the lowest 1Po level (LS coupling, no spin-orbit), computed. Row: the method; x: the column heading as printed (corrected by an erratum).

hattig_1998b/f_He_CC2#

{
  "id": "f_He_CC2",
  "material": "He",
  "file": "He/hattig_1998b__f_He_CC2.csv",
  "table": "tbl_ee7b52d10a52",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "method": "CC2 (approximate coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (11s7p6d5f4g)/[8s7p6d5f4g]"
  }
}

hattig_1998b/f_He_CCSD#

{
  "id": "f_He_CCSD",
  "material": "He",
  "file": "He/hattig_1998b__f_He_CCSD.csv",
  "table": "tbl_ee7b52d10a52",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "method": "CCSD (coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (11s7p6d5f4g)/[8s7p6d5f4g]"
  }
}

hattig_1998b/f_Ne_CCS#

{
  "id": "f_Ne_CCS",
  "material": "Ne",
  "file": "Ne/hattig_1998b__f_Ne_CCS.csv",
  "table": "tbl_ee7b52d10a52",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "method": "CCS (coupled cluster singles) response, t-aug-cc-pV5Z, (17s11p7d6f5g4h)/[9s8p7d6f5g4h], the eight valence electrons correlated"
  }
}

hattig_1998b/f_Ne_CC2#

{
  "id": "f_Ne_CC2",
  "material": "Ne",
  "file": "Ne/hattig_1998b__f_Ne_CC2.csv",
  "table": "tbl_ee7b52d10a52",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "method": "CC2 (approximate coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (17s11p7d6f5g4h)/[9s8p7d6f5g4h], the eight valence electrons correlated"
  }
}

hattig_1998b/f_Ne_CCSD#

{
  "id": "f_Ne_CCSD",
  "material": "Ne",
  "file": "Ne/hattig_1998b__f_Ne_CCSD.csv",
  "table": "tbl_ee7b52d10a52",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "method": "CCSD (coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (17s11p7d6f5g4h)/[9s8p7d6f5g4h], the eight valence electrons correlated"
  }
}

hattig_1998b/f_Ar_CCS#

{
  "id": "f_Ar_CCS",
  "material": "Ar",
  "file": "Ar/hattig_1998b__f_Ar_CCS.csv",
  "table": "tbl_ee7b52d10a52",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "method": "CCS (coupled cluster singles) response, t-aug-cc-pV5Z, (23s15p7d6f5g4h)/[10s9p7d6f5g4h], the eight valence electrons correlated"
  }
}

hattig_1998b/f_Ar_CC2#

{
  "id": "f_Ar_CC2",
  "material": "Ar",
  "file": "Ar/hattig_1998b__f_Ar_CC2.csv",
  "table": "tbl_ee7b52d10a52",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "method": "CC2 (approximate coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (23s15p7d6f5g4h)/[10s9p7d6f5g4h], the eight valence electrons correlated"
  }
}

hattig_1998b/f_Ar_CCSD#

{
  "id": "f_Ar_CCSD",
  "material": "Ar",
  "file": "Ar/hattig_1998b__f_Ar_CCSD.csv",
  "table": "tbl_ee7b52d10a52",
  "quantity": "oscillator_strength",
  "abscissa": "label",
  "use": "check",
  "parameters": {
    "method": "CCSD (coupled cluster singles and doubles) response, t-aug-cc-pV5Z, (23s15p7d6f5g4h)/[10s9p7d6f5g4h], the eight valence electrons correlated"
  }
}

Formulas#

No formulas are recorded.

Corrections#

[
  {
    "dataset": "S_Ar_CCS_degenerate",
    "row": "CCS",
    "column": "x",
    "printed": "2p5 3p1 (1Se)",
    "corrected": "3p5 4p1 (1Se)",
    "reason": "Table V (argon) labels its levels with neon's shells, 2p5 3p1, as Table IV does.",
    "evidence": "Table V's caption: 'states in Ar'; Table I's argon levels 3p5 4p1 (1De, 1Pe, 1Se) at 13.218-13.487 eV (CCSD), whose CCS, CC2 and CCSD energies reproduce Table V's K (checks); argon's ground configuration is 3p6."
  },
  {
    "dataset": "S_Ar_CCS_w2_10p49eV",
    "row": "CCS",
    "column": "x",
    "printed": "2p5 3p1 (1Se)",
    "corrected": "3p5 4p1 (1Se)",
    "reason": "Table V (argon) labels its levels with neon's shells, 2p5 3p1, as Table IV does.",
    "evidence": "Table V's caption: 'states in Ar'; Table I's argon levels 3p5 4p1 (1De, 1Pe, 1Se) at 13.218-13.487 eV (CCSD), whose CCS, CC2 and CCSD energies reproduce Table V's K (checks); argon's ground configuration is 3p6."
  },
  {
    "dataset": "S_Ar_CC2_degenerate",
    "row": "CC2",
    "column": "x",
    "printed": "2p5 3p1 (1Se)",
    "corrected": "3p5 4p1 (1Se)",
    "reason": "Table V (argon) labels its levels with neon's shells, 2p5 3p1, as Table IV does.",
    "evidence": "Table V's caption: 'states in Ar'; Table I's argon levels 3p5 4p1 (1De, 1Pe, 1Se) at 13.218-13.487 eV (CCSD), whose CCS, CC2 and CCSD energies reproduce Table V's K (checks); argon's ground configuration is 3p6."
  },
  {
    "dataset": "S_Ar_CC2_w2_10p49eV",
    "row": "CC2",
    "column": "x",
    "printed": "2p5 3p1 (1Se)",
    "corrected": "3p5 4p1 (1Se)",
    "reason": "Table V (argon) labels its levels with neon's shells, 2p5 3p1, as Table IV does.",
    "evidence": "Table V's caption: 'states in Ar'; Table I's argon levels 3p5 4p1 (1De, 1Pe, 1Se) at 13.218-13.487 eV (CCSD), whose CCS, CC2 and CCSD energies reproduce Table V's K (checks); argon's ground configuration is 3p6."
  },
  {
    "dataset": "S_Ar_CCSD_degenerate",
    "row": "CCSD",
    "column": "x",
    "printed": "2p5 3p1 (1Se)",
    "corrected": "3p5 4p1 (1Se)",
    "reason": "Table V (argon) labels its levels with neon's shells, 2p5 3p1, as Table IV does.",
    "evidence": "Table V's caption: 'states in Ar'; Table I's argon levels 3p5 4p1 (1De, 1Pe, 1Se) at 13.218-13.487 eV (CCSD), whose CCS, CC2 and CCSD energies reproduce Table V's K (checks); argon's ground configuration is 3p6."
  },
  {
    "dataset": "S_Ar_CCSD_w2_10p49eV",
    "row": "CCSD",
    "column": "x",
    "printed": "2p5 3p1 (1Se)",
    "corrected": "3p5 4p1 (1Se)",
    "reason": "Table V (argon) labels its levels with neon's shells, 2p5 3p1, as Table IV does.",
    "evidence": "Table V's caption: 'states in Ar'; Table I's argon levels 3p5 4p1 (1De, 1Pe, 1Se) at 13.218-13.487 eV (CCSD), whose CCS, CC2 and CCSD energies reproduce Table V's K (checks); argon's ground configuration is 3p6."
  },
  {
    "dataset": "f_He_CCS",
    "row": "CCS",
    "column": "x",
    "printed": "X 1Se - 1Pe",
    "corrected": "X 1Se - 1Po",
    "reason": "A dipole transition from the even ground state reaches an odd level: the lowest 1Po, not a 1Pe level (Table I lists both; the 1Pe level of Ne and Ar is 2p5 3p / 3p5 4p, the 1Po level 2p5 3s / 3p5 4s).",
    "evidence": "p. 8358: 'we computed the dipole transition strengths for the ground state to 1Po transitions in He, Ne, and Ar' and 'the dominating contributions originate from the lowest 1Po states'; Table I's lowest 1Po levels. The caption and one sentence of the text also print 1Pe."
  },
  {
    "dataset": "f_He_CC2",
    "row": "CC2",
    "column": "x",
    "printed": "X 1Se - 1Pe",
    "corrected": "X 1Se - 1Po",
    "reason": "A dipole transition from the even ground state reaches an odd level: the lowest 1Po, not a 1Pe level (Table I lists both; the 1Pe level of Ne and Ar is 2p5 3p / 3p5 4p, the 1Po level 2p5 3s / 3p5 4s).",
    "evidence": "p. 8358: 'we computed the dipole transition strengths for the ground state to 1Po transitions in He, Ne, and Ar' and 'the dominating contributions originate from the lowest 1Po states'; Table I's lowest 1Po levels. The caption and one sentence of the text also print 1Pe."
  },
  {
    "dataset": "f_He_CCSD",
    "row": "CCSD",
    "column": "x",
    "printed": "X 1Se - 1Pe",
    "corrected": "X 1Se - 1Po",
    "reason": "A dipole transition from the even ground state reaches an odd level: the lowest 1Po, not a 1Pe level (Table I lists both; the 1Pe level of Ne and Ar is 2p5 3p / 3p5 4p, the 1Po level 2p5 3s / 3p5 4s).",
    "evidence": "p. 8358: 'we computed the dipole transition strengths for the ground state to 1Po transitions in He, Ne, and Ar' and 'the dominating contributions originate from the lowest 1Po states'; Table I's lowest 1Po levels. The caption and one sentence of the text also print 1Pe."
  },
  {
    "dataset": "f_Ne_CCS",
    "row": "CCS",
    "column": "x",
    "printed": "X 1Se - 1Pe",
    "corrected": "X 1Se - 1Po",
    "reason": "A dipole transition from the even ground state reaches an odd level: the lowest 1Po, not a 1Pe level (Table I lists both; the 1Pe level of Ne and Ar is 2p5 3p / 3p5 4p, the 1Po level 2p5 3s / 3p5 4s).",
    "evidence": "p. 8358: 'we computed the dipole transition strengths for the ground state to 1Po transitions in He, Ne, and Ar' and 'the dominating contributions originate from the lowest 1Po states'; Table I's lowest 1Po levels. The caption and one sentence of the text also print 1Pe."
  },
  {
    "dataset": "f_Ne_CC2",
    "row": "CC2",
    "column": "x",
    "printed": "X 1Se - 1Pe",
    "corrected": "X 1Se - 1Po",
    "reason": "A dipole transition from the even ground state reaches an odd level: the lowest 1Po, not a 1Pe level (Table I lists both; the 1Pe level of Ne and Ar is 2p5 3p / 3p5 4p, the 1Po level 2p5 3s / 3p5 4s).",
    "evidence": "p. 8358: 'we computed the dipole transition strengths for the ground state to 1Po transitions in He, Ne, and Ar' and 'the dominating contributions originate from the lowest 1Po states'; Table I's lowest 1Po levels. The caption and one sentence of the text also print 1Pe."
  },
  {
    "dataset": "f_Ne_CCSD",
    "row": "CCSD",
    "column": "x",
    "printed": "X 1Se - 1Pe",
    "corrected": "X 1Se - 1Po",
    "reason": "A dipole transition from the even ground state reaches an odd level: the lowest 1Po, not a 1Pe level (Table I lists both; the 1Pe level of Ne and Ar is 2p5 3p / 3p5 4p, the 1Po level 2p5 3s / 3p5 4s).",
    "evidence": "p. 8358: 'we computed the dipole transition strengths for the ground state to 1Po transitions in He, Ne, and Ar' and 'the dominating contributions originate from the lowest 1Po states'; Table I's lowest 1Po levels. The caption and one sentence of the text also print 1Pe."
  },
  {
    "dataset": "f_Ar_CCS",
    "row": "CCS",
    "column": "x",
    "printed": "X 1Se - 1Pe",
    "corrected": "X 1Se - 1Po",
    "reason": "A dipole transition from the even ground state reaches an odd level: the lowest 1Po, not a 1Pe level (Table I lists both; the 1Pe level of Ne and Ar is 2p5 3p / 3p5 4p, the 1Po level 2p5 3s / 3p5 4s).",
    "evidence": "p. 8358: 'we computed the dipole transition strengths for the ground state to 1Po transitions in He, Ne, and Ar' and 'the dominating contributions originate from the lowest 1Po states'; Table I's lowest 1Po levels. The caption and one sentence of the text also print 1Pe."
  },
  {
    "dataset": "f_Ar_CC2",
    "row": "CC2",
    "column": "x",
    "printed": "X 1Se - 1Pe",
    "corrected": "X 1Se - 1Po",
    "reason": "A dipole transition from the even ground state reaches an odd level: the lowest 1Po, not a 1Pe level (Table I lists both; the 1Pe level of Ne and Ar is 2p5 3p / 3p5 4p, the 1Po level 2p5 3s / 3p5 4s).",
    "evidence": "p. 8358: 'we computed the dipole transition strengths for the ground state to 1Po transitions in He, Ne, and Ar' and 'the dominating contributions originate from the lowest 1Po states'; Table I's lowest 1Po levels. The caption and one sentence of the text also print 1Pe."
  },
  {
    "dataset": "f_Ar_CCSD",
    "row": "CCSD",
    "column": "x",
    "printed": "X 1Se - 1Pe",
    "corrected": "X 1Se - 1Po",
    "reason": "A dipole transition from the even ground state reaches an odd level: the lowest 1Po, not a 1Pe level (Table I lists both; the 1Pe level of Ne and Ar is 2p5 3p / 3p5 4p, the 1Po level 2p5 3s / 3p5 4s).",
    "evidence": "p. 8358: 'we computed the dipole transition strengths for the ground state to 1Po transitions in He, Ne, and Ar' and 'the dominating contributions originate from the lowest 1Po states'; Table I's lowest 1Po levels. The caption and one sentence of the text also print 1Pe."
  }
]

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.