henriksson_2005#
J. Henriksson, P. Norman and H. J. Aa. Jensen, “Two-photon absorption in the relativistic four-component Hartree-Fock approximation”, J. Chem. Phys. 122, 114106 (2005)
Source record · Catalogue · Review register
DOI: 10.1063/1.1869469
Source kind: theory
Recorded technique: The single residue of the quadratic response function, which gives the two-photon matrix element S^{0->f}_ab(omega) (Eqs. 4, 5, 10), in the time-dependent Hartree-Fock approximation: non-relativistic (TDHF) and relativistic four-component, Kramers restricted (TDDHF; all LL, LS and SS integrals and the e->e and e->p orbital rotations), in the DIRAC program (p. 114106-3). Uncontracted spherical Gaussian bases (p. 114106-3): He, Ne, Ar with the exponents of qaug-cc-pVTZ; Kr, Xe, Rn the well-tempered sets of Huzinaga and Klobukowski with f functions added and quadruply augmented (Eq. 12); small components by restricted kinetic balance. No electron correlation. Monochromatic two-photon absorption, both photons at omega_f/2 (Eqs. 5, 6).
Materials in structured entries: Ar, He, Kr, Ne, Xe
Dataset quantities: oscillator_strength, two_photon_transition_strength
Contents: 21 datasets; 0 formulas.
Curation notes#
Pages 114106-1 to -9 = PDF pages 2-10 (PDF page 1 is the AIP download cover); page 114106-n = PDF page n + 1. Identity checked on the first page (PDF p. 2: ‘THE JOURNAL OF CHEMICAL PHYSICS 122, 114106 (2005)’, ‘0021-9606/2005/122(11)/114106/9’, Johan Henriksson and Patrick Norman (Linköping), Hans Jørgen Aa. Jensen (Odense); received 21 December 2004, accepted 19 January 2005, published online 21 March 2005) on 2026-10-08.
THE QUANTITIES (p. 114106-2). One-photon: ‘we adopt the custom to present results for the oscillator strength, delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2’ (Eq. 2): taken as oscillator_strength. Two-photon: ‘the relevant orientationally averaged two-photon absorption cross section is determined from the expression delta_TPA = (1/15) sum_ab {F S_aa (S_bb)* + G S_ab (S_ab)* + H S_ab (S_ba)*}’ at omega_f/2 (Eq. 6, after McClain 1971), ‘where F, G, and H are factors that depend on the polarization of the incident light’; their values and the polarisation are not stated. ‘Our results presented below for one- and two-photon absorption cross sections correspond to the summed absorption to the degenerate M_J components of the excited states’ (p. 114106-3). Each table’s delta is delta_OPA or delta_TPA, ‘clear from the atomic selections rules’ (footnote b): the even configurations’ rows are two-photon, the odd ones’ one-photon (the parity of each configuration checked against the terms’ ‘o’ marks). THE POLARISATION, inferred (tools/extract/henriksson_2005.py): (i) the J = 0 strengths are non-zero, which circular polarisation (F, G, H = -2, 3, 3 in the 1/30 normalisation) forbids; (ii) the text’s tensor elements of the 1D2 levels (p. 114106-8: Ne TDHF S_xy = 2.8801 a.u., TDDHF 2.0510, Ar TDHF 9.222) give the tables’ 11.060, 5.6086 and 113.40 as (4/3) S_xy^2 to 2e-4, which is the rotational average with F = G = H = 1 in Eq. 6’s normalisation (F = G = H = 2 with 1/30, parallel linear: hattig_1998b’s convention), summed over the level’s five components; circular would give 2 S_xy^2. So polarization = linear_parallel, recorded as inferred.
EXTRACTED (tools/extract/henriksson_2005.py), Tables I-V (He p. 114106-4, Ne -4, Ar -5, Kr -5, Xe -6), from the library’s cells: per gas, TDHF and TDDHF, the two-photon strengths (two_photon_transition_strength, a.u.) and the one-photon oscillator strengths, 20 datasets, all rows including the selection-rule zeros. TDHF rows are named by configuration and LS term (‘3p5 4p 1D_2’; ‘*’ marks an odd term). The TDDHF columns carry their own J and are sorted by the computed energy within each configuration’s block of rows (one inversion: argon’s J = 0 at 13.575 eV is printed before J = 1 at 13.567 eV); they do not line up row by row with the LS terms, so each TDDHF row is named by what it prints, ‘J = 2, 20.090 eV’. For He to Kr each block’s TDDHF J are those of its LS terms; for Xe they are not (5p5 6p: LS J 0011112223, TDDHF 0111122233; 5p5 7p: 011223 against 001122): the table does not say which configuration each TDDHF level belongs to. Also taken, from the text (p. 114106-3), the TDDHF strength of He’s second 1S0 level with the qaug-cc-pV5Z basis, 1.4737 a.u. (1.6002 with qaug-cc-pVTZ, Table I). All use = check (uncorrelated theory). THE NEON TABLE. The library’s extraction of Table II merged each configuration’s rows into one cell per column (e.g. TDHF delta ‘000011.060000012.850’). Its 18 rows were read from the table image cell by cell and are written in the script (NEON); the script checks that each column’s cells, joined, are exactly the merged cell, and, as for every table, that each row’s six numbers stand in order in the PDF’s text layer (78 of 78 rows found, all five tables). ACCURACY (p. 114106-3): with qaug-cc-pV5Z the He 1 1S0 strength is within 1 %, the 2 1S0 changes from 1.6002 to 1.4737 a.u., Ne and Ar within 4 % and 1 %: ‘apart from the single transition in helium, the results presented here for helium, neon, and argon should be within 5% of the Hartree-Fock limiting values.’ Nothing stated for Kr and Xe. Electron correlation is not included: ‘electron correlation does play a significant role in calculations of the two-photon spectrum of neon’ (p. 114106-8).
CHECKS (the script fails if one is missed): every row of Tables I-V in the PDF text; parity against the ‘o’ marks; the (4/3) S_xy^2 relation above; the text’s He 2 1S0 1.6002; Ne’s quoted oscillator strengths (TDDHF 3P1 0.0043 and 1P1 0.1608, TDHF 0.1645); argon’s leakage ‘amounts to 9%’ (3P1/1P1 = 0.089); the integrated TDDHF strength of each J against TDHF, ‘virtually the same’ (Ne J = 2: +0.7 %, J = 0: +0.4 %; Ar J = 2: +1.4 %, J = 0: +0.6 %).
FINDING: THE TEXT’S QUOTATION OF HÄTTIG ET AL. (p. 114106-8; hattig_1998b, the paper’s Ref. 4). Quoted: Ne 1D2 ‘DE = 18.532 eV and delta_TPA = 19.915 a.u.’, Ne 1S0 ‘DE = 18.855 eV and delta_TPA = 12.559 a.u.’. The energies are Hättig’s CCSD 1De and 1Se energies, but 19.915 is Hättig’s CCSD strength of the 1Se level and 12.559 its CCS strength of the 1Se level; Hättig’s CCSD 1De strength is 12.024 (Table IV there). So ‘the TPA cross section of the 1D2 state in neon is underestimated by almost 50% at the Hartree-Fock level’ (11.060 against 19.915) and the ‘close agreement ... for the 1S0 state ... regarded as fortuitous’ (12.850 against 12.559) rest on the misquotation: against the CCSD values the TDHF 1S0 is 35 % below (12.850 against 19.915). For the 1D2 level the two papers’ numbers are also in different conventions: Hättig’s 1De S^0f is S_xy^2 of one component, this paper’s (4/3) S_xy^2 summed over M_J (hattig_1998b notes), so Hättig’s CCSD 12.024 is 16.03 here (TDHF 31 % below), and the argon comparison (‘good agreement’, TDHF 113.40 against CCSD 104.59) is 113.40 against 139.45. The He (20.615 eV, 12.306) and Ar 1S0 (13.487 eV, 197.71) quotations are Hättig’s CCSD values as printed. He: TDHF 1s2s 1S0 10.426 a.u. (21.125 eV) against Hättig’s CCS 10.824 (21.137 eV), a different method (TDHF is the random phase approximation, CCS the singles-only coupled cluster) and basis in the same convention for a J = 0 level.
The text also quotes, from Hettema et al. (J. Chem. Phys. 97, 1174 (1992)) and Sundholm et al. (J. Chem. Phys. 101, 4931 (1994)), tensor elements S_xy of the Ne and Ar 1D2 levels (Ne HF 2.9663 and SD RAS 3.3450 a.u. at 20.106 and 19.170 eV, one photon fixed at 9.320 eV; Ar HF 9.499 and CAS 10.424 a.u. at 13.485 and 13.185 eV): not taken (no quantity holds one tensor element; secondary).
NOT TAKEN. The experimental excitation energies (Moore’s tables, Refs. 20-22); Table II prints 2p5 4s 3P0 as 16.761 eV, out of sequence with its neighbours (19.664-19.780 eV), not corrected here. The TDHF and TDDHF excitation energies (they name the TDDHF rows and stand in the printed cells; computed, not the atom’s levels). Table VI (Rn; optmat has no radon). Figs. 1-4 (the tables’ values and their sums over J).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
henriksson_2005/tdhf_tpa_He#
{
"id": "tdhf_tpa_He",
"material": "He",
"file": "He/henriksson_2005__tdhf_tpa_He.csv",
"table": "tbl_930ae06840e1",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDHF, non-relativistic time-dependent Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table I (p. 114106-4), column TDHF delta (a.u.), the rows of even configurations (delta_TPA); rows named by configuration and LS term as printed. Zeros are the selection rules (spin in TDHF, Delta J = 0, +-2 in TDDHF), printed.
henriksson_2005/tdhf_opa_He#
{
"id": "tdhf_opa_He",
"material": "He",
"file": "He/henriksson_2005__tdhf_opa_He.csv",
"table": "tbl_930ae06840e1",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "TDHF, non-relativistic time-dependent Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table I (p. 114106-4), column TDHF delta, the rows of odd configurations: delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2 (Eq. 2), the oscillator strength, summed over M_J; rows named by configuration and LS term as printed. Zeros printed as such.
henriksson_2005/tddhf_tpa_He#
{
"id": "tddhf_tpa_He",
"material": "He",
"file": "He/henriksson_2005__tddhf_tpa_He.csv",
"table": "tbl_930ae06840e1",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table I (p. 114106-4), column TDDHF delta (a.u.), the rows of even configurations (delta_TPA); rows named by ‘J = <J>, <TDDHF dE> eV’ as printed (the TDDHF columns are sorted by the computed energy and do not line up with the LS terms). Zeros are the selection rules (spin in TDHF, Delta J = 0, +-2 in TDDHF), printed.
henriksson_2005/tddhf_opa_He#
{
"id": "tddhf_opa_He",
"material": "He",
"file": "He/henriksson_2005__tddhf_opa_He.csv",
"table": "tbl_930ae06840e1",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table I (p. 114106-4), column TDDHF delta, the rows of odd configurations: delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2 (Eq. 2), the oscillator strength, summed over M_J; rows named by ‘J = <J>, <TDDHF dE> eV’ as printed (the TDDHF columns are sorted by the computed energy and do not line up with the LS terms). Zeros printed as such.
henriksson_2005/tdhf_tpa_Ne#
{
"id": "tdhf_tpa_Ne",
"material": "Ne",
"file": "Ne/henriksson_2005__tdhf_tpa_Ne.csv",
"table": "tbl_1fcee34b02cc",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDHF, non-relativistic time-dependent Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table II (p. 114106-4), column TDHF delta (a.u.), the rows of even configurations (delta_TPA); rows named by configuration and LS term as printed. Zeros are the selection rules (spin in TDHF, Delta J = 0, +-2 in TDDHF), printed.
henriksson_2005/tdhf_opa_Ne#
{
"id": "tdhf_opa_Ne",
"material": "Ne",
"file": "Ne/henriksson_2005__tdhf_opa_Ne.csv",
"table": "tbl_1fcee34b02cc",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "TDHF, non-relativistic time-dependent Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table II (p. 114106-4), column TDHF delta, the rows of odd configurations: delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2 (Eq. 2), the oscillator strength, summed over M_J; rows named by configuration and LS term as printed. Zeros printed as such.
henriksson_2005/tddhf_tpa_Ne#
{
"id": "tddhf_tpa_Ne",
"material": "Ne",
"file": "Ne/henriksson_2005__tddhf_tpa_Ne.csv",
"table": "tbl_1fcee34b02cc",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table II (p. 114106-4), column TDDHF delta (a.u.), the rows of even configurations (delta_TPA); rows named by ‘J = <J>, <TDDHF dE> eV’ as printed (the TDDHF columns are sorted by the computed energy and do not line up with the LS terms). Zeros are the selection rules (spin in TDHF, Delta J = 0, +-2 in TDDHF), printed.
henriksson_2005/tddhf_opa_Ne#
{
"id": "tddhf_opa_Ne",
"material": "Ne",
"file": "Ne/henriksson_2005__tddhf_opa_Ne.csv",
"table": "tbl_1fcee34b02cc",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table II (p. 114106-4), column TDDHF delta, the rows of odd configurations: delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2 (Eq. 2), the oscillator strength, summed over M_J; rows named by ‘J = <J>, <TDDHF dE> eV’ as printed (the TDDHF columns are sorted by the computed energy and do not line up with the LS terms). Zeros printed as such.
henriksson_2005/tdhf_tpa_Ar#
{
"id": "tdhf_tpa_Ar",
"material": "Ar",
"file": "Ar/henriksson_2005__tdhf_tpa_Ar.csv",
"table": "tbl_37bc1a24b4ae",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDHF, non-relativistic time-dependent Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table III (p. 114106-5), column TDHF delta (a.u.), the rows of even configurations (delta_TPA); rows named by configuration and LS term as printed. Zeros are the selection rules (spin in TDHF, Delta J = 0, +-2 in TDDHF), printed.
henriksson_2005/tdhf_opa_Ar#
{
"id": "tdhf_opa_Ar",
"material": "Ar",
"file": "Ar/henriksson_2005__tdhf_opa_Ar.csv",
"table": "tbl_37bc1a24b4ae",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "TDHF, non-relativistic time-dependent Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table III (p. 114106-5), column TDHF delta, the rows of odd configurations: delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2 (Eq. 2), the oscillator strength, summed over M_J; rows named by configuration and LS term as printed. Zeros printed as such.
henriksson_2005/tddhf_tpa_Ar#
{
"id": "tddhf_tpa_Ar",
"material": "Ar",
"file": "Ar/henriksson_2005__tddhf_tpa_Ar.csv",
"table": "tbl_37bc1a24b4ae",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table III (p. 114106-5), column TDDHF delta (a.u.), the rows of even configurations (delta_TPA); rows named by ‘J = <J>, <TDDHF dE> eV’ as printed (the TDDHF columns are sorted by the computed energy and do not line up with the LS terms). Zeros are the selection rules (spin in TDHF, Delta J = 0, +-2 in TDDHF), printed.
henriksson_2005/tddhf_opa_Ar#
{
"id": "tddhf_opa_Ar",
"material": "Ar",
"file": "Ar/henriksson_2005__tddhf_opa_Ar.csv",
"table": "tbl_37bc1a24b4ae",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pVTZ"
}
}
Table III (p. 114106-5), column TDDHF delta, the rows of odd configurations: delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2 (Eq. 2), the oscillator strength, summed over M_J; rows named by ‘J = <J>, <TDDHF dE> eV’ as printed (the TDDHF columns are sorted by the computed energy and do not line up with the LS terms). Zeros printed as such.
henriksson_2005/tdhf_tpa_Kr#
{
"id": "tdhf_tpa_Kr",
"material": "Kr",
"file": "Kr/henriksson_2005__tdhf_tpa_Kr.csv",
"table": "tbl_42d892cee858",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDHF, non-relativistic time-dependent Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted well-tempered basis of Huzinaga and Klobukowski with added f functions, quadruply augmented (Eq. 12)"
}
}
Table IV (p. 114106-5), column TDHF delta (a.u.), the rows of even configurations (delta_TPA); rows named by configuration and LS term as printed. Zeros are the selection rules (spin in TDHF, Delta J = 0, +-2 in TDDHF), printed.
henriksson_2005/tdhf_opa_Kr#
{
"id": "tdhf_opa_Kr",
"material": "Kr",
"file": "Kr/henriksson_2005__tdhf_opa_Kr.csv",
"table": "tbl_42d892cee858",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "TDHF, non-relativistic time-dependent Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted well-tempered basis of Huzinaga and Klobukowski with added f functions, quadruply augmented (Eq. 12)"
}
}
Table IV (p. 114106-5), column TDHF delta, the rows of odd configurations: delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2 (Eq. 2), the oscillator strength, summed over M_J; rows named by configuration and LS term as printed. Zeros printed as such.
henriksson_2005/tddhf_tpa_Kr#
{
"id": "tddhf_tpa_Kr",
"material": "Kr",
"file": "Kr/henriksson_2005__tddhf_tpa_Kr.csv",
"table": "tbl_42d892cee858",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted well-tempered basis of Huzinaga and Klobukowski with added f functions, quadruply augmented (Eq. 12)"
}
}
Table IV (p. 114106-5), column TDDHF delta (a.u.), the rows of even configurations (delta_TPA); rows named by ‘J = <J>, <TDDHF dE> eV’ as printed (the TDDHF columns are sorted by the computed energy and do not line up with the LS terms). Zeros are the selection rules (spin in TDHF, Delta J = 0, +-2 in TDDHF), printed.
henriksson_2005/tddhf_opa_Kr#
{
"id": "tddhf_opa_Kr",
"material": "Kr",
"file": "Kr/henriksson_2005__tddhf_opa_Kr.csv",
"table": "tbl_42d892cee858",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted well-tempered basis of Huzinaga and Klobukowski with added f functions, quadruply augmented (Eq. 12)"
}
}
Table IV (p. 114106-5), column TDDHF delta, the rows of odd configurations: delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2 (Eq. 2), the oscillator strength, summed over M_J; rows named by ‘J = <J>, <TDDHF dE> eV’ as printed (the TDDHF columns are sorted by the computed energy and do not line up with the LS terms). Zeros printed as such.
henriksson_2005/tdhf_tpa_Xe#
{
"id": "tdhf_tpa_Xe",
"material": "Xe",
"file": "Xe/henriksson_2005__tdhf_tpa_Xe.csv",
"table": "tbl_e64a945b01a8",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDHF, non-relativistic time-dependent Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted well-tempered basis of Huzinaga and Klobukowski with added f functions, quadruply augmented (Eq. 12)"
}
}
Table V (p. 114106-6), column TDHF delta (a.u.), the rows of even configurations (delta_TPA); rows named by configuration and LS term as printed. Zeros are the selection rules (spin in TDHF, Delta J = 0, +-2 in TDDHF), printed.
henriksson_2005/tdhf_opa_Xe#
{
"id": "tdhf_opa_Xe",
"material": "Xe",
"file": "Xe/henriksson_2005__tdhf_opa_Xe.csv",
"table": "tbl_e64a945b01a8",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "TDHF, non-relativistic time-dependent Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted well-tempered basis of Huzinaga and Klobukowski with added f functions, quadruply augmented (Eq. 12)"
}
}
Table V (p. 114106-6), column TDHF delta, the rows of odd configurations: delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2 (Eq. 2), the oscillator strength, summed over M_J; rows named by configuration and LS term as printed. Zeros printed as such.
henriksson_2005/tddhf_tpa_Xe#
{
"id": "tddhf_tpa_Xe",
"material": "Xe",
"file": "Xe/henriksson_2005__tddhf_tpa_Xe.csv",
"table": "tbl_e64a945b01a8",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted well-tempered basis of Huzinaga and Klobukowski with added f functions, quadruply augmented (Eq. 12)"
}
}
Table V (p. 114106-6), column TDDHF delta (a.u.), the rows of even configurations (delta_TPA); rows named by ‘J = <J>, <TDDHF dE> eV’ as printed (the TDDHF columns are sorted by the computed energy and do not line up with the LS terms). Zeros are the selection rules (spin in TDHF, Delta J = 0, +-2 in TDDHF), printed.
henriksson_2005/tddhf_opa_Xe#
{
"id": "tddhf_opa_Xe",
"material": "Xe",
"file": "Xe/henriksson_2005__tddhf_opa_Xe.csv",
"table": "tbl_e64a945b01a8",
"quantity": "oscillator_strength",
"abscissa": "label",
"use": "check",
"parameters": {
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted well-tempered basis of Huzinaga and Klobukowski with added f functions, quadruply augmented (Eq. 12)"
}
}
Table V (p. 114106-6), column TDDHF delta, the rows of odd configurations: delta_OPA = (2 omega_f/3) sum_a |<0|mu_a|f>|^2 (Eq. 2), the oscillator strength, summed over M_J; rows named by ‘J = <J>, <TDDHF dE> eV’ as printed (the TDDHF columns are sorted by the computed energy and do not line up with the LS terms). Zeros printed as such.
henriksson_2005/tddhf_tpa_He_pv5z#
{
"id": "tddhf_tpa_He_pv5z",
"material": "He",
"table": "text",
"quantity": "two_photon_transition_strength",
"unit": "au",
"abscissa": "label",
"use": "check",
"parameters": {
"polarization": "linear_parallel",
"frequencies": "degenerate",
"rotational_average": "delta_TPA = (1/15) sum_ab {F S_aa S_bb* + G S_ab S_ab* + H S_ab S_ba*}, S at omega_f/2 (Eq. 6, after McClain 1971); F, G, H not given numerically; summed over the final level's M_J components (p. 114106-3); the values follow F = G = H = 1 in this normalisation (= F = G = H = 2 with 1/30, parallel linear; inferred, see the notes)",
"method": "TDDHF, relativistic time-dependent four-component Kramers-restricted Dirac-Hartree-Fock (residue of the quadratic response function), DIRAC; uncontracted basis with the exponents of qaug-cc-pV5Z"
}
}
1 inline points in the source record.
p. 114106-3, the basis-set study: ‘for the X 1S0 -> 2 1S0 transition, the value changes from delta = 1.6002 a.u. (see Table I) to delta = 1.4737 a.u. using qaug-cc-pV5Z’ (the second 1S0 level, 1s3s; TDDHF, the calculations of the basis study). Its energy is not given.
Formulas#
No formulas are recorded.
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.