bishop_1991#
D. M. Bishop, J. Pipin and S. M. Cybulski, “Theoretical investigation of the nonlinear optical properties of H2 and D2: Extended basis set”, Phys. Rev. A 43, 4845 (1991)
Source record · Catalogue · Review register
Source kind: theory
Recorded technique: Sum-over-states (Orr-Ward) evaluation of the electronic gamma components of H2 with explicitly correlated (r12-dependent, elliptical-coordinate) wave functions for the Sigma, Pi and Delta intermediate states, with new ‘primed’ Delta geminals that pass closure tests; 14 internuclear distances R = 0.6-3.0 a0, averaged over the rovibrational levels of the ground vibrational state with a Maxwell-Boltzmann rotational population at 295 K; the pure vibrational contributions taken unchanged from Bishop, Pipin and Rerat, J. Chem. Phys. 92, 1902 (1990) (pp. 4845-4847, 4851).
Materials in structured entries: D2, H2, He
Dataset quantities: hyperpolarizability, hyperpolarizability_ratio
Contents: 44 datasets; 5 formulas.
Curation notes#
Identity: journal pages 4845-4853 = pdf pages 1-9 (page = pdf page + 4844). H2 and D2 only.
DEFINITIONS (p. 4846, Eq. 1): gamma_abgd(-w_s; w1, w2, w3) = hbar^-3 sum over the 24 permutations of (mu_a, -w_s), (mu_b, w1), (mu_g, w2), (mu_d, w3) of the Orr-Ward terms (Buckingham’s and Bogaard and Orr’s definitions): the Taylor-series (T) convention, the same as bishop_1989 (whose He values these papers use as the reference; T = H2/He below). Processes (p. 4850): dc Kerr w1 = w, w2 = w3 = 0; ESHG w1 = 0, w2 = w3 = w; THG all w. The laboratory-frame gamma_par and gamma_perp are the isotropic averages ‘for radiation transmitted parallel and perpendicular to the applied electric field’ (p. 4851), Shelton’s gamma_par and gamma_perp; the dc Kerr gamma^K = (3/2)[gamma_par^Kerr - gamma_perp^Kerr] (Eq. 19). ‘We do not list the gamma_perp^THG values since they are exactly one-third of gamma_par^THG.’ Atomic units: ‘gamma = e^4 a0^4 E_h^-3 = 6.23538 x 10^-65 C^4 m^4 J^-3’ (p. 4845), the standard unit (the Born-Oppenheimer calculation has no reduced-mass rescaling).
PARTS. elec: the electronic gamma, rovibrationally averaged (v = 0) over a 295 K rotational population (overline gamma), recorded as part ‘electronic’ with parameters.temperature_k = 295. vib: the pure vibrational contribution of Bishop, Pipin and Rerat (1990), part ‘vibrational’; near omega = 0.01-0.02 a.u. it passes the vibrational resonance (H2 fundamental about 0.019 a.u.), where the values are large and of either sign. total = elec + vib (‘electronic_vibrational’); no rotational (orientational) term is included (p. 4847). ‘The values of gamma_par^ESHG(vib) are very similar to the values of gamma^vR reported in Table III(a) of Ref. 4’ (Shelton 1990; p. 4851).
DATASETS: Tables VI-XI (H2 dc Kerr, ESHG, THG; D2 the same), 30 datasets x 13 omegas; Table XIV ratios S (H2/D2) and T (H2/He), theory, experiment (reproduced) and ‘fitted experiment’; Table XVI gamma^K(total) of H2 and D2 at seven wavelengths. Checks: gamma^K(H2, 6328 A) = 1.5 (786.6 - 302.5) = 726.15 (printed 726); T(13 190 A) = 661.1 / 43.788 = 15.098 (15.10); T(6943 A) = 798.1 / 45.647 (bishop_1989 Table II) = 17.484 (17.48); S(13 190 A) = 661.1 / 669.1 = 0.988 (checked 2026-09-26). The wavelengths of Table II pair omega and lambda as vacuum values (0.03454 a.u. = 13 190 A).
NOT EXTRACTED: Table IV (the molecular-frame components gamma_xxxx ... gamma_zzzz of H2 at R = 1.4 a0, before averaging; the ESHG and THG blocks print a column ‘gamma_xzzz’, evidently gamma_xxzz), Table III (alpha), Tables V and XII (B, C), Table XIII (the ratio R = gamma_par/gamma_perp of ESHG, theory against Mizrahi and Shelton 1985 and Shelton and Lu 1988, e.g. H2 at 5145 A 2.873 against 2.867(2)). The electronic values rose by 1.3-1.8 % from Bishop, Pipin and Rerat (1990) (p. 4851).
TEXT VALUES (datasets below): He ESHG gamma_par ‘calculated expressly for this work’ at 13 190, 10 640 and 5900 A (p. 4851); experimental dc Kerr gamma^K of H2 and D2 (p. 4852); the ac Kerr estimate and experiment (p. 4853); Shelton’s static electronic H2 686 +- 4 and D2 669 (pp. 4845, 4852).
Recorded bibliographic identity status: VALIDATED_WITH_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.
Datasets#
bishop_1991/dc_kerr_par_elec_H2#
{
"id": "dc_kerr_par_elec_H2",
"material": "H2",
"file": "H2/bishop_1991__dc_kerr_par_elec_H2.csv",
"table": "tbl_7138422de0e9",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table VI, gamma_par of the dc Kerr gamma(-w; w, 0, 0): the electronic gamma averaged over the v = 0 rovibrational states at 295 K; hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_par_vib_H2#
{
"id": "dc_kerr_par_vib_H2",
"material": "H2",
"file": "H2/bishop_1991__dc_kerr_par_vib_H2.csv",
"table": "tbl_7138422de0e9",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"bishop_1990b"
],
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VI, gamma_par of the dc Kerr gamma(-w; w, 0, 0): the pure vibrational contribution (from Bishop, Pipin and Rerat 1990; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_par_total_H2#
{
"id": "dc_kerr_par_total_H2",
"material": "H2",
"file": "H2/bishop_1991__dc_kerr_par_total_H2.csv",
"table": "tbl_7138422de0e9",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VI, gamma_par of the dc Kerr gamma(-w; w, 0, 0): electronic plus pure vibrational (no rotational term; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_perp_elec_H2#
{
"id": "dc_kerr_perp_elec_H2",
"material": "H2",
"file": "H2/bishop_1991__dc_kerr_perp_elec_H2.csv",
"table": "tbl_7138422de0e9",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VI, gamma_perp of the dc Kerr gamma(-w; w, 0, 0): the electronic gamma averaged over the v = 0 rovibrational states at 295 K; hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_perp_vib_H2#
{
"id": "dc_kerr_perp_vib_H2",
"material": "H2",
"file": "H2/bishop_1991__dc_kerr_perp_vib_H2.csv",
"table": "tbl_7138422de0e9",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"bishop_1990b"
],
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VI, gamma_perp of the dc Kerr gamma(-w; w, 0, 0): the pure vibrational contribution (from Bishop, Pipin and Rerat 1990; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_perp_total_H2#
{
"id": "dc_kerr_perp_total_H2",
"material": "H2",
"file": "H2/bishop_1991__dc_kerr_perp_total_H2.csv",
"table": "tbl_7138422de0e9",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VI, gamma_perp of the dc Kerr gamma(-w; w, 0, 0): electronic plus pure vibrational (no rotational term; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_par_elec_H2#
{
"id": "eshg_par_elec_H2",
"material": "H2",
"file": "H2/bishop_1991__eshg_par_elec_H2.csv",
"table": "tbl_a26e8934041a",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table VII, gamma_par of the ESHG gamma(-2w; 0, w, w): the electronic gamma averaged over the v = 0 rovibrational states at 295 K; hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_par_vib_H2#
{
"id": "eshg_par_vib_H2",
"material": "H2",
"file": "H2/bishop_1991__eshg_par_vib_H2.csv",
"table": "tbl_a26e8934041a",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"bishop_1990b"
],
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VII, gamma_par of the ESHG gamma(-2w; 0, w, w): the pure vibrational contribution (from Bishop, Pipin and Rerat 1990; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_par_total_H2#
{
"id": "eshg_par_total_H2",
"material": "H2",
"file": "H2/bishop_1991__eshg_par_total_H2.csv",
"table": "tbl_a26e8934041a",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VII, gamma_par of the ESHG gamma(-2w; 0, w, w): electronic plus pure vibrational (no rotational term; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_perp_elec_H2#
{
"id": "eshg_perp_elec_H2",
"material": "H2",
"file": "H2/bishop_1991__eshg_perp_elec_H2.csv",
"table": "tbl_a26e8934041a",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VII, gamma_perp of the ESHG gamma(-2w; 0, w, w): the electronic gamma averaged over the v = 0 rovibrational states at 295 K; hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_perp_vib_H2#
{
"id": "eshg_perp_vib_H2",
"material": "H2",
"file": "H2/bishop_1991__eshg_perp_vib_H2.csv",
"table": "tbl_a26e8934041a",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"bishop_1990b"
],
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VII, gamma_perp of the ESHG gamma(-2w; 0, w, w): the pure vibrational contribution (from Bishop, Pipin and Rerat 1990; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_perp_total_H2#
{
"id": "eshg_perp_total_H2",
"material": "H2",
"file": "H2/bishop_1991__eshg_perp_total_H2.csv",
"table": "tbl_a26e8934041a",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VII, gamma_perp of the ESHG gamma(-2w; 0, w, w): electronic plus pure vibrational (no rotational term; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/thg_par_elec_H2#
{
"id": "thg_par_elec_H2",
"material": "H2",
"file": "H2/bishop_1991__thg_par_elec_H2.csv",
"table": "tbl_4827aae9526c",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table VIII, gamma_par of the THG gamma(-3w; w, w, w): the electronic gamma averaged over the v = 0 rovibrational states at 295 K; hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/thg_par_vib_H2#
{
"id": "thg_par_vib_H2",
"material": "H2",
"file": "H2/bishop_1991__thg_par_vib_H2.csv",
"table": "tbl_4827aae9526c",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"bishop_1990b"
],
"parameters": {
"process": "thg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VIII, gamma_par of the THG gamma(-3w; w, w, w): the pure vibrational contribution (from Bishop, Pipin and Rerat 1990; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/thg_par_total_H2#
{
"id": "thg_par_total_H2",
"material": "H2",
"file": "H2/bishop_1991__thg_par_total_H2.csv",
"table": "tbl_4827aae9526c",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VIII, gamma_par of the THG gamma(-3w; w, w, w): electronic plus pure vibrational (no rotational term; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_par_elec_D2#
{
"id": "dc_kerr_par_elec_D2",
"material": "D2",
"file": "D2/bishop_1991__dc_kerr_par_elec_D2.csv",
"table": "tbl_25f1365d9669",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table IX, gamma_par of the dc Kerr gamma(-w; w, 0, 0): the electronic gamma averaged over the v = 0 rovibrational states at 295 K; hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_par_vib_D2#
{
"id": "dc_kerr_par_vib_D2",
"material": "D2",
"file": "D2/bishop_1991__dc_kerr_par_vib_D2.csv",
"table": "tbl_25f1365d9669",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"bishop_1990b"
],
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table IX, gamma_par of the dc Kerr gamma(-w; w, 0, 0): the pure vibrational contribution (from Bishop, Pipin and Rerat 1990; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_par_total_D2#
{
"id": "dc_kerr_par_total_D2",
"material": "D2",
"file": "D2/bishop_1991__dc_kerr_par_total_D2.csv",
"table": "tbl_25f1365d9669",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table IX, gamma_par of the dc Kerr gamma(-w; w, 0, 0): electronic plus pure vibrational (no rotational term; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_perp_elec_D2#
{
"id": "dc_kerr_perp_elec_D2",
"material": "D2",
"file": "D2/bishop_1991__dc_kerr_perp_elec_D2.csv",
"table": "tbl_25f1365d9669",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table IX, gamma_perp of the dc Kerr gamma(-w; w, 0, 0): the electronic gamma averaged over the v = 0 rovibrational states at 295 K; hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_perp_vib_D2#
{
"id": "dc_kerr_perp_vib_D2",
"material": "D2",
"file": "D2/bishop_1991__dc_kerr_perp_vib_D2.csv",
"table": "tbl_25f1365d9669",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"bishop_1990b"
],
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table IX, gamma_perp of the dc Kerr gamma(-w; w, 0, 0): the pure vibrational contribution (from Bishop, Pipin and Rerat 1990; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/dc_kerr_perp_total_D2#
{
"id": "dc_kerr_perp_total_D2",
"material": "D2",
"file": "D2/bishop_1991__dc_kerr_perp_total_D2.csv",
"table": "tbl_25f1365d9669",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table IX, gamma_perp of the dc Kerr gamma(-w; w, 0, 0): electronic plus pure vibrational (no rotational term; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_par_elec_D2#
{
"id": "eshg_par_elec_D2",
"material": "D2",
"file": "D2/bishop_1991__eshg_par_elec_D2.csv",
"table": "tbl_cdf929a9c5ce",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table X, gamma_par of the ESHG gamma(-2w; 0, w, w): the electronic gamma averaged over the v = 0 rovibrational states at 295 K; hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_par_vib_D2#
{
"id": "eshg_par_vib_D2",
"material": "D2",
"file": "D2/bishop_1991__eshg_par_vib_D2.csv",
"table": "tbl_cdf929a9c5ce",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"bishop_1990b"
],
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table X, gamma_par of the ESHG gamma(-2w; 0, w, w): the pure vibrational contribution (from Bishop, Pipin and Rerat 1990; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_par_total_D2#
{
"id": "eshg_par_total_D2",
"material": "D2",
"file": "D2/bishop_1991__eshg_par_total_D2.csv",
"table": "tbl_cdf929a9c5ce",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table X, gamma_par of the ESHG gamma(-2w; 0, w, w): electronic plus pure vibrational (no rotational term; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_perp_elec_D2#
{
"id": "eshg_perp_elec_D2",
"material": "D2",
"file": "D2/bishop_1991__eshg_perp_elec_D2.csv",
"table": "tbl_cdf929a9c5ce",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table X, gamma_perp of the ESHG gamma(-2w; 0, w, w): the electronic gamma averaged over the v = 0 rovibrational states at 295 K; hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_perp_vib_D2#
{
"id": "eshg_perp_vib_D2",
"material": "D2",
"file": "D2/bishop_1991__eshg_perp_vib_D2.csv",
"table": "tbl_cdf929a9c5ce",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"bishop_1990b"
],
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table X, gamma_perp of the ESHG gamma(-2w; 0, w, w): the pure vibrational contribution (from Bishop, Pipin and Rerat 1990; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/eshg_perp_total_D2#
{
"id": "eshg_perp_total_D2",
"material": "D2",
"file": "D2/bishop_1991__eshg_perp_total_D2.csv",
"table": "tbl_cdf929a9c5ce",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table X, gamma_perp of the ESHG gamma(-2w; 0, w, w): electronic plus pure vibrational (no rotational term; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/thg_par_elec_D2#
{
"id": "thg_par_elec_D2",
"material": "D2",
"file": "D2/bishop_1991__thg_par_elec_D2.csv",
"table": "tbl_b3b2cb2c1406",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table XI, gamma_par of the THG gamma(-3w; w, w, w): the electronic gamma averaged over the v = 0 rovibrational states at 295 K; hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/thg_par_vib_D2#
{
"id": "thg_par_vib_D2",
"material": "D2",
"file": "D2/bishop_1991__thg_par_vib_D2.csv",
"table": "tbl_b3b2cb2c1406",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "reproduced",
"reproduced_from": [
"bishop_1990b"
],
"parameters": {
"process": "thg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table XI, gamma_par of the THG gamma(-3w; w, w, w): the pure vibrational contribution (from Bishop, Pipin and Rerat 1990; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/thg_par_total_D2#
{
"id": "thg_par_total_D2",
"material": "D2",
"file": "D2/bishop_1991__thg_par_total_D2.csv",
"table": "tbl_b3b2cb2c1406",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table XI, gamma_par of the THG gamma(-3w; w, w, w): electronic plus pure vibrational (no rotational term; resonant near omega = 0.01-0.02 a.u.); hbar omega = 0-0.05 a.u. and seven laser frequencies (Table II).
bishop_1991/ratio_s_theory#
{
"id": "ratio_s_theory",
"material": "H2",
"file": "H2/bishop_1991__ratio_s_theory_H2.csv",
"table": "tbl_fad13f7ef088",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"reference_material": "D2",
"process": "eshg",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table XIV ‘S Theory’: gamma_par^ESHG(total, H2) / gamma_par^ESHG(total, D2) (Eq. 17), electronic plus pure vibrational at 295 K; lambda in angstrom (vacuum).
bishop_1991/ratio_s_expt#
{
"id": "ratio_s_expt",
"material": "H2",
"file": "H2/bishop_1991__ratio_s_expt_H2.csv",
"table": "tbl_fad13f7ef088",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "angstrom",
"use": "reproduced",
"reproduced_from": [
"shelton_1990",
"mizrahi_1985_h2d2"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"reference_material": "D2",
"process": "eshg",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table XIV ‘S Expt.’ (Refs. 4, 12: Shelton 1990; Mizrahi and Shelton, Phys. Rev. A 32, 3454 (1985)), with the printed uncertainty on the last digits. Measured ratio of the total ESHG gammas.
bishop_1991/ratio_t_theory#
{
"id": "ratio_t_theory",
"material": "H2",
"file": "H2/bishop_1991__ratio_t_theory_H2.csv",
"table": "tbl_fad13f7ef088",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"reference_material": "He",
"process": "eshg",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table XIV ‘T Theory’: gamma_par^ESHG(total, H2) / gamma_par^ESHG(He) (Eq. 18), with Bishop and Pipin’s He (bishop_1989 and the three values of dataset he_eshg).
bishop_1991/ratio_t_expt#
{
"id": "ratio_t_expt",
"material": "H2",
"file": "H2/bishop_1991__ratio_t_expt_H2.csv",
"table": "tbl_fad13f7ef088",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "angstrom",
"use": "reproduced",
"reproduced_from": [
"shelton_1990"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"reference_material": "He",
"process": "eshg",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table XIV ‘T Expt.’ (Shelton 1990, Ref. 4), with the printed uncertainty on the last digits. Measured ratio of the total ESHG gammas (He calibration).
bishop_1991/ratio_t_fitted#
{
"id": "ratio_t_fitted",
"material": "H2",
"file": "H2/bishop_1991__ratio_t_fitted_H2.csv",
"table": "tbl_fad13f7ef088",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "angstrom",
"use": "reproduced",
"reproduced_from": [
"shelton_1990"
],
"parameters": {
"reference_material": "He",
"process": "eshg",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table XIV ‘Fitted Expt.’ (footnote a, ‘See text’): T reconstructed from the fit of Eq. (20) to Shelton’s ‘experimental’ gamma_par(elec) (Table XV) plus the theoretical vibrational part, which ‘smooths out’ experimental noise (p. 4852). Derived from shelton_1990’s data.
bishop_1991/gamma_k_total_H2#
{
"id": "gamma_k_total_H2",
"material": "H2",
"file": "H2/bishop_1991__gamma_k_total_H2.csv",
"table": "tbl_60de52729ff9",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "K",
"temperature_k": 295
}
}
Table XVI: gamma^K = (3/2)[gamma_par^Kerr(total) - gamma_perp^Kerr(total)] (Eq. 19) from Tables VI, electronic plus pure vibrational at 295 K; lambda in angstrom (vacuum). No orientational (Delta alpha) term.
bishop_1991/gamma_k_total_D2#
{
"id": "gamma_k_total_D2",
"material": "D2",
"file": "D2/bishop_1991__gamma_k_total_D2.csv",
"table": "tbl_60de52729ff9",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "K",
"temperature_k": 295
}
}
Table XVI: gamma^K = (3/2)[gamma_par^Kerr(total) - gamma_perp^Kerr(total)] (Eq. 19) from Tables IX, electronic plus pure vibrational at 295 K; lambda in angstrom (vacuum). No orientational (Delta alpha) term.
bishop_1991/he_eshg#
{
"id": "he_eshg",
"material": "He",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "zzzz"
}
}
3 inline points in the source record.
p. 4851: ‘For T, we have used the values of gamma_par^ESHG(He) that we reported in Ref. 13 [bishop_1989], as well as further ones calculated expressly for this work, namely 43.788, 44.161, and 46.684 e^4 a0^4 E_h^-3 for lambda = 13 190, 10 640, and 5900 A’: the bishop_1989 method (infinite-mass atomic units, see bishop_1989), ESHG gamma_zzzz of He at three more wavelengths.
bishop_1991/expt_dc_kerr_H2#
{
"id": "expt_dc_kerr_H2",
"material": "H2",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "reproduced",
"reproduced_from": [
"buckingham_1968b",
"carusotto_1985",
"tammer_1990"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "total",
"component": "K"
}
}
3 inline points in the source record.
pp. 4852-4853: experimental gamma^K of H2, ‘A rather old experimental value for H2 at lambda = 6328 A is 550 +- 60’ (Ref. 14), ‘a more recent value at lambda = 5145 A is 820 +- 49’ (Ref. 15), and Tammer and Huttner’s ‘666(19)’ at 6328 A (Ref. 16), against the theory’s 726 (Table XVI). Level of the uncertainties not stated. Re-pointed to the originals now in the library (2026-09-26): row buckingham_orr_1968 = buckingham_1968b’s gamma = 0.277 (+-0.03, a bound) x 10^-36 esu = 550 au; row carusotto_1985 is Bishop’s conversion to gamma^K of carusotto_1985’s K(H2) = 4.32 +- 0.14 x 10^-17 cm^2 statV^-2 amagat^-1 at 514.5 nm (no gamma is printed there); row tammer_huttner_1990 = tammer_1990’s 4.15(12) x 10^-62 C^4 m^4 J^-3 = 666 au. That last value rests on a field integral that tammer_1992 found wrong: every K, mK and A_K of tammer_1990 is to be multiplied by 1.0637 +- 0.0031, and the recalibrated gamma is 4.68(14) x 10^-62 = 751 +- 22 au (tammer_1992/table2_gamma_H2), above the theory’s 726 rather than below it.
bishop_1991/expt_dc_kerr_D2#
{
"id": "expt_dc_kerr_D2",
"material": "D2",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "reproduced",
"reproduced_from": [
"tammer_1990"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "total",
"component": "K"
}
}
1 inline points in the source record.
p. 4852: Tammer and Huttner’s D2 gamma^K ‘669(26)’ at 6328 A, against the theory’s 712. = tammer_1990’s 4.17(16) x 10^-62 C^4 m^4 J^-3 (re-pointed 2026-09-26). Superseded calibration: tammer_1992 multiplies every K, mK and A_K of tammer_1990 by 1.0637 +- 0.0031 but did not re-evaluate D2; with that factor alone the D2 gamma would be about 4.73 x 10^-62 = 758 au (computed, not a published value; see tammer_1990’s notes).
bishop_1991/ac_kerr_estimate#
{
"id": "ac_kerr_estimate",
"material": "H2",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "other",
"convention": "T",
"part": "electronic",
"component": "K"
}
}
2 inline points in the source record.
p. 4853: the ac (optical) Kerr gamma^K for ‘w1 = 14797, w2 = 17751 cm^-1, and w_L^2 = 0.02215 a.u.’, gamma(-w_s; w1, w2, -w2), estimated from the dc Kerr fits (Eqs. 20, 22) with the vibrational part ignored: 796.7 (H2); experiment (Ref. 18, Rosasco and Hurst, J. Opt. Soc. Am. B 3, 1251 (1986) = rosasco_1986) 789 +- 38 (row rosasco_hurst, a reproduction). Process ‘other’ (two-frequency optical Kerr); the wavelength column is the w1 beam, 1/14797 cm^-1 = 6758 A (computed here); the w2 beam is 5633 A.
bishop_1991/ac_kerr_estimate_D2#
{
"id": "ac_kerr_estimate_D2",
"material": "D2",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "other",
"convention": "T",
"part": "electronic",
"component": "K"
}
}
2 inline points in the source record.
p. 4853: as ac_kerr_estimate, D2: 771.9 (theory), 774 +- 39 (Rosasco and Hurst 1986, row rosasco_hurst, a reproduction).
bishop_1991/shelton_static_H2#
{
"id": "shelton_static_H2",
"material": "H2",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "reproduced",
"reproduced_from": [
"shelton_1990"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "static",
"convention": "T",
"part": "electronic"
}
}
1 inline points in the source record.
pp. 4845, 4852: ‘the experimentally derived static, averaged, gamma_par (electronic) for H2 is 686 +- 4’, from Shelton’s ESHG data with the theoretical vibrational-rotational part removed (21-point weighted fit, Table XV); the theory’s static value is 682.7 (683).
bishop_1991/shelton_static_D2#
{
"id": "shelton_static_D2",
"material": "D2",
"table": "text",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "reproduced",
"reproduced_from": [
"shelton_1990"
],
"parameters": {
"process": "static",
"convention": "T",
"part": "electronic"
}
}
1 inline points in the source record.
p. 4852: ‘the corresponding values for D2 are 669 and 663.1’ (Shelton’s experimental static electronic value and the theory’s).
Formulas#
bishop_1991/fit_theory#
{
"id": "fit_theory",
"material": "H2",
"equation": "Eq. (20), p. 4852, with Table XV (tbl_b2bf2e0b7efa), row 'Theory, 7 points (unweighted)'",
"printed": "gamma_par(elec) = gamma_0 (1 + A w_L^2 + B w_L^4); Theory, 7 points (unweighted): gamma_0 684.4, A 6.034, B 44.27",
"variable": "w_L^2 = w_s^2 + w1^2 + w2^2 + w3^2 = 6 w^2 for ESHG, w in atomic units (hartree); gamma in atomic units. Process eshg (fitted), convention T, part electronic (rovibrationally averaged, 295 K), component parallel.",
"state": "none (per molecule)",
"density": "none",
"range": "the seven laser wavelengths 13 190-4880 A (footnote a)",
"coefficients": {
"gamma_0": "684.4",
"A": "6.034",
"B": "44.27"
},
"check": "Reproduces Table VII's elec column: 715.5 against 715.3 at 0.03454 a.u. and 983.3 against 983.6 at 0.09337 a.u. (checked 2026-09-26)."
}
The authors’ fit to their own gamma_par^ESHG(elec) of H2 (Table VII) at the seven laser frequencies (footnote a); ‘Our actual theoretical value (unfitted) is 682.7’ (footnote b). Same form as Shelton’s gamma_0 [1 + A nu_L^2 + B nu_L^4] with the frequency in hartree instead of cm^-1 (A_cm2 = A / 219474.63^2, B_cm4 = B / 219474.63^4).
bishop_1991/fit_expt_7u#
{
"id": "fit_expt_7u",
"material": "H2",
"equation": "Eq. (20), p. 4852, with Table XV (tbl_b2bf2e0b7efa), row 'Expt., 7 points (unweighted)'",
"printed": "gamma_par(elec) = gamma_0 (1 + A w_L^2 + B w_L^4); Expt., 7 points (unweighted): gamma_0 685.7, A 5.953, B 48.84",
"variable": "w_L^2 = w_s^2 + w1^2 + w2^2 + w3^2 = 6 w^2 for ESHG, w in atomic units (hartree); gamma in atomic units. Process eshg (fitted), convention T, part electronic (rovibrationally averaged, 295 K), component parallel.",
"state": "none (per molecule)",
"density": "none",
"range": "the seven laser wavelengths 13 190-4880 A (footnote a)",
"coefficients": {
"gamma_0": "685.7",
"A": "5.953",
"B": "48.84"
},
"check": "Not checked against data (the experimental points are not tabulated here)."
}
Fit to ‘experimental’ gamma_par^ESHG(elec, H2) = T(expt) x gamma(He, theory) minus the theoretical vibrational-rotational part (p. 4852) at the seven frequencies. Same form as Shelton’s gamma_0 [1 + A nu_L^2 + B nu_L^4] with the frequency in hartree instead of cm^-1 (A_cm2 = A / 219474.63^2, B_cm4 = B / 219474.63^4).
bishop_1991/fit_expt_7w#
{
"id": "fit_expt_7w",
"material": "H2",
"equation": "Eq. (20), p. 4852, with Table XV (tbl_b2bf2e0b7efa), row 'Expt., 7 points (weighted)'",
"printed": "gamma_par(elec) = gamma_0 (1 + A w_L^2 + B w_L^4); Expt., 7 points (weighted): gamma_0 686.6, A 5.746, B 53.27",
"variable": "w_L^2 = w_s^2 + w1^2 + w2^2 + w3^2 = 6 w^2 for ESHG, w in atomic units (hartree); gamma in atomic units. Process eshg (fitted), convention T, part electronic (rovibrationally averaged, 295 K), component parallel.",
"state": "none (per molecule)",
"density": "none",
"range": "the seven laser wavelengths 13 190-4880 A (footnote a)",
"coefficients": {
"gamma_0": "686.6",
"A": "5.746",
"B": "53.27"
},
"check": "Not checked against data (the experimental points are not tabulated here)."
}
As fit_expt_7u, ‘Values at lambda = 13 190 and 10 640 A weighted by a factor of 4’ (footnote c). Same form as Shelton’s gamma_0 [1 + A nu_L^2 + B nu_L^4] with the frequency in hartree instead of cm^-1 (A_cm2 = A / 219474.63^2, B_cm4 = B / 219474.63^4).
bishop_1991/fit_expt_21u#
{
"id": "fit_expt_21u",
"material": "H2",
"equation": "Eq. (20), p. 4852, with Table XV (tbl_b2bf2e0b7efa), row 'Expt., 21 points (unweighted)'",
"printed": "gamma_par(elec) = gamma_0 (1 + A w_L^2 + B w_L^4); Expt., 21 points (unweighted): gamma_0 685.2, A 6.026, B 47.57",
"variable": "w_L^2 = w_s^2 + w1^2 + w2^2 + w3^2 = 6 w^2 for ESHG, w in atomic units (hartree); gamma in atomic units. Process eshg (fitted), convention T, part electronic (rovibrationally averaged, 295 K), component parallel.",
"state": "none (per molecule)",
"density": "none",
"range": "the seven laser wavelengths 13 190-4880 A (footnote a) or Sheltons 21 frequencies",
"coefficients": {
"gamma_0": "685.2",
"A": "6.026",
"B": "47.57"
},
"check": "Not checked against data (the experimental points are not tabulated here)."
}
As fit_expt_7u with ‘All the frequencies used in Ref. 4’ (Shelton 1990). Same form as Shelton’s gamma_0 [1 + A nu_L^2 + B nu_L^4] with the frequency in hartree instead of cm^-1 (A_cm2 = A / 219474.63^2, B_cm4 = B / 219474.63^4).
bishop_1991/fit_expt_21w#
{
"id": "fit_expt_21w",
"material": "H2",
"equation": "Eq. (20), p. 4852, with Table XV (tbl_b2bf2e0b7efa), row 'Expt., 21 points (weighted)'",
"printed": "gamma_par(elec) = gamma_0 (1 + A w_L^2 + B w_L^4); Expt., 21 points (weighted): gamma_0 686.4, A 5.780, B 52.30",
"variable": "w_L^2 = w_s^2 + w1^2 + w2^2 + w3^2 = 6 w^2 for ESHG, w in atomic units (hartree); gamma in atomic units. Process eshg (fitted), convention T, part electronic (rovibrationally averaged, 295 K), component parallel.",
"state": "none (per molecule)",
"density": "none",
"range": "the seven laser wavelengths 13 190-4880 A (footnote a) or Sheltons 21 frequencies",
"coefficients": {
"gamma_0": "686.4",
"A": "5.780",
"B": "52.30"
},
"check": "Not checked against data (the experimental points are not tabulated here)."
}
‘This was the fit published in Ref. 4’ (footnote e): Shelton’s H2 fit, reproduced; in Shelton’s units A = 5.780 / 219474.63^2 = 1.200e-10 cm^2 and B = 52.30 / 219474.63^4 = 2.254e-20 cm^4 (computed here). Same form as Shelton’s gamma_0 [1 + A nu_L^2 + B nu_L^4] with the frequency in hartree instead of cm^-1 (A_cm2 = A / 219474.63^2, B_cm4 = B / 219474.63^4).
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.