bishop_1990b#
D. M. Bishop, J. Pipin and M. Rérat, “Nonlinear optical properties of H2 and D2”, J. Chem. Phys. 92, 1902 (1990)
Source record · Catalogue · Review register
DOI: 10.1063/1.458072
Source kind: theory
Recorded technique: Sum-over-states (Orr-Ward, Eq. 12) evaluation of the electronic gamma components of H2 with explicitly correlated James-Coolidge-type wave functions (r12-dependent, elliptical coordinates; Sigma_g+, Sigma_u+, Pi_u, Pi_g and Delta_g states, Eqs. 13-20, the Pi and Delta basis sets enlarged over Bishop and Lam 1988) at seven internuclear distances R = 0.4-3.0 a0; combined to laboratory-frame gamma_par and gamma_perp, averaged over the rovibrational wave functions of the ground vibrational state and over a Maxwell-Boltzmann rotational distribution at 295 K; the pure vibrational contribution evaluated as in Bishop and Lam 1988. Also the dynamic field-gradient polarizabilities B and C (Eqs. 29-32) (pp. 1902-1906).
Materials in structured entries: D2, H2, He
Dataset quantities: hyperpolarizability, hyperpolarizability_ratio
Contents: 67 datasets; 7 formulas.
Curation notes#
Identity checked against the first page (J. Chem. Phys. 92, 1902 (1990), received 15 September 1989). Page numbers are the journal’s: pdf page 1 is the publisher’s cover, so p. = pdf page + 1900. The paper that bishop_1991 takes its pure vibrational values from ‘unchanged’ (bishop_1991, p. 4847) and that bishop_1990, shelton_1990, sekino_1993, tammer_1990 and tammer_1992 cite as ‘Bishop, Pipin and Rerat, J. Chem. Phys. 92, 1902 (1990)’. SUPERSEDED for the electronic part by bishop_1991 (extended Delta basis; its electronic values are 1.3-1.8 % higher, bishop_1991 p. 4851); the vibrational part is the one bishop_1991 reprints.
DEFINITIONS (pp. 1902-1903). mu_a = alpha_ab F_b + (1/6) gamma_abgd F_b F_g F_d + ... (Eq. 1): the Taylor-series (T) convention of Buckingham, the same as bishop_1989 and bishop_1991. dc Kerr gamma_par = gamma_ZZZZ(-w; w, 0, 0), gamma_perp = gamma_XXZZ(-w; w, 0, 0) (Eq. 4); ESHG gamma_par = gamma_ZZZZ(-2w; 0, w, w), gamma_perp = gamma_ZZXX(-2w; 0, w, w) (Eq. 6); THG gamma_par = gamma_ZZZZ(-3w; w, w, w) (Eq. 8), gamma_perp^THG = gamma_par^THG/3 exactly (not listed); ‘par’ and ‘perp’ refer to the static field parallel and perpendicular to the laser field; ‘total’ includes vibration, rotational contributions are excluded (‘either insignificant or have been eliminated, by a temperature analysis, from the experimental data’). dc Kerr gamma^K = (3/2)[gamma_par - gamma_perp] (Eq. 9). Atomic units, ‘gamma = e^4 a0^4 E_h^-3 = 6.23538 x 10^-65 C^4 m^4 J^-3’ (p. 1903). The vibrational contribution is resonant where omega = omega_01 (Kerr), omega or 2 omega = omega_01 (ESHG) and 2 omega = omega_01 (THG), omega_01 = 0.01897 a.u. the first vibrational transition (p. 1904).
DATASETS: Tables II-VII (p. 1904-1906), per gas, process, component and part, split by the tables’ two abscissae (hbar omega 0.00-0.05 a.u.; the lasers 10 640, 6943, 6328, 5900, 5145, 4880 A: 60 datasets of 6 points); Table IX ratios S and T (theory, and the experimental values of Mizrahi and Shelton 1985, reproduced); Table X gamma^K; text: the experimental gamma^K of H2 (reproduced). The laser wavelengths are given without saying vacuum or air (the nominal lines; stored as vacuum; the difference, 3e-4 in lambda, is negligible for gamma). All theory values are use = check; no uncertainty is given for gamma, but the ratios carry estimated errors (R +-0.04, S +-0.01, T +-0.2, gamma^K +-10, Tables VIII-X).
ERRATA (the tables’ own arithmetic, total = elec + vib, which every other entry obeys to +-0.1): (1) Table V, D2 dc Kerr gamma_perp(total) at 10 640 A printed 227.6, the sum 222.0 + 55.7 = 277.7; Table X’s gamma^K(D2, 10 640 A) = 655 = 1.5 (714.6 - 277.7) confirms it (227.6 would give 730). (2) Table III, H2 ESHG gamma_par(elec) at 5145 A printed 931.9, where total - vib = 923.8 + 7.5 = 931.3: the total is confirmed by Table VIII (R = 923.8/322.0 = 2.869, printed 2.869) and Table IX (T = 923.8/47.888 = 19.29, printed; 924.4 would give 19.30), the vib by bishop_1991’s reprint (-7.5). (3) Table IV, H2 THG gamma_par(elec) at 10 640 A printed 774.4, where total - vib = 767.5 + 9.9 = 777.4: the vib is bishop_1991’s reprint (-9.9), and 777.4 is what the smooth omega dependence requires (Table XI’s fit, extrapolated from omega < 0.03 to 0.04282 a.u., gives 777.0; the table’s own 0.04 and 0.05 a.u. values interpolate to about 777.5), and makes bishop_1991’s improved 790.3 1.7 % higher, within its stated 1.3-1.8 % (774.4 would be 2.1 %). Checked 2026-09-27.
OTHER CHECKS (2026-09-27). Table XI’s fits (formulas) reproduce the elec columns at omega = 0.01-0.03 a.u. to within 0.05 a.u.; gamma^K of Table X = 1.5 (gamma_par - gamma_perp)(total) of Tables II and V to within 0.5 (rounding) except D2 at 10 640 A (erratum 1); T of Table IX = gamma_par^ESHG(total, H2)/[43.104 (1 + 2.189 w_L^2 + 3.602 w_L^4)] (Eq. 25, w_L^2 = 6 w^2) to the last digit at all four wavelengths; S = H2/D2 totals to the last digit.
REPRODUCTIONS ELSEWHERE (to be re-pointed; none of these records is from this extraction): bishop_1991’s pure vibrational datasets (*_vib_*, 13 frequencies each) reprint Tables II-VII’s vib columns digit for digit at the six laser wavelengths and at omega = 0.00, 0.03-0.05, but differ by 0.1 at five near-resonant entries: H2 dc Kerr gamma_par at 0.02 (-929.1 here, -929.0 there), D2 dc Kerr gamma_par at 0.01 (316.5, 316.6) and 0.02 (-43.4, -43.3), D2 ESHG gamma_par at 0.01 (206.0, 206.1), D2 THG at 0.01 (-153.7, -153.6); bishop_1991’s 13 190 A row has no counterpart here. bishop_1990’s Table X rows from ‘Bishop, Pipin and Rerat 1990’ (854.5 total static, and the 4880 A dc Kerr and ESHG values), shelton_1990, sekino_1993, tammer_1990 cite this paper by citation. tammer_1992’s ‘ref 5’ gamma^K = 4.45 x 10^-62 C^4 m^4 J^-3 at 632.8 nm is this paper’s Table X 714 au x 6.23538e-65 = 4.452e-62 (checked; re-pointed there).
NOT EXTRACTED: Table I (the molecular-frame gamma components at R = 1.4 a0 before averaging; its ESHG and THG blocks print a column ‘gamma_xzzz’ that the text calls gamma_xxzz); Table VIII, R = gamma_par^ESHG/gamma_perp^ESHG (total), theory (estimated error +-0.04) H2 2.880, 2.908, 2.901, 2.893, 2.869, 2.857 and D2 2.934, 2.925, 2.915, 2.905, 2.878, 2.865 at 10 640-4880 A, against Mizrahi and Shelton’s and Shelton and Lu’s H2 2.891(7), 2.890(4), 2.867(2), 2.858(3) and D2 2.909(6), 2.881(3), 2.872(4) (the ratio of two components of one gas: no quantity); Tables XII-XIII, the field-gradient polarizabilities B_par, C_par (and the R = 1.4 a0 components) of H2 and D2 at 295 K (no quantity); Table XIV, the static R = 1.4 a0 components against Berns and Wormer, Diercksen and Sadlej, Maroulis and Bishop, Augspurger and Dykstra (alpha_zz 6.3875, alpha_xx 4.5786 a.u., gamma_zzzz 682.5, gamma_xxxx 558.4, gamma_xxzz 211.9). Vibrational averaging raises gamma_par(elec) and gamma_perp(elec) by about 11 % (p. 1908).
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_1990b/dc_kerr_par_elec_H2#
{
"id": "dc_kerr_par_elec_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_par_elec_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table II, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of H2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_par_elec_lasers_H2#
{
"id": "dc_kerr_par_elec_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_par_elec_lasers_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table II, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of H2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_par_vib_H2#
{
"id": "dc_kerr_par_vib_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_par_vib_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table II, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of H2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_par_vib_lasers_H2#
{
"id": "dc_kerr_par_vib_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_par_vib_lasers_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table II, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of H2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_par_total_H2#
{
"id": "dc_kerr_par_total_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_par_total_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table II, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of H2: electronic plus pure vibrational (no rotational term); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_par_total_lasers_H2#
{
"id": "dc_kerr_par_total_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_par_total_lasers_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table II, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of H2: electronic plus pure vibrational (no rotational term); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_perp_elec_H2#
{
"id": "dc_kerr_perp_elec_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_perp_elec_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table II, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of H2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_perp_elec_lasers_H2#
{
"id": "dc_kerr_perp_elec_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_perp_elec_lasers_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table II, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of H2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_perp_vib_H2#
{
"id": "dc_kerr_perp_vib_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_perp_vib_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table II, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of H2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_perp_vib_lasers_H2#
{
"id": "dc_kerr_perp_vib_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_perp_vib_lasers_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table II, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of H2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_perp_total_H2#
{
"id": "dc_kerr_perp_total_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_perp_total_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table II, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of H2: electronic plus pure vibrational (no rotational term); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_perp_total_lasers_H2#
{
"id": "dc_kerr_perp_total_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__dc_kerr_perp_total_lasers_H2.csv",
"table": "tbl_3542c447427e",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table II, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of H2: electronic plus pure vibrational (no rotational term); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_par_elec_H2#
{
"id": "eshg_par_elec_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_par_elec_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table III, gamma_par of the ESHG gamma(-2w; 0, w, w) of H2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_par_elec_lasers_H2#
{
"id": "eshg_par_elec_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_par_elec_lasers_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table III, gamma_par of the ESHG gamma(-2w; 0, w, w) of H2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_par_vib_H2#
{
"id": "eshg_par_vib_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_par_vib_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table III, gamma_par of the ESHG gamma(-2w; 0, w, w) of H2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_par_vib_lasers_H2#
{
"id": "eshg_par_vib_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_par_vib_lasers_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table III, gamma_par of the ESHG gamma(-2w; 0, w, w) of H2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_par_total_H2#
{
"id": "eshg_par_total_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_par_total_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table III, gamma_par of the ESHG gamma(-2w; 0, w, w) of H2: electronic plus pure vibrational (no rotational term); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_par_total_lasers_H2#
{
"id": "eshg_par_total_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_par_total_lasers_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table III, gamma_par of the ESHG gamma(-2w; 0, w, w) of H2: electronic plus pure vibrational (no rotational term); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_perp_elec_H2#
{
"id": "eshg_perp_elec_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_perp_elec_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table III, gamma_perp of the ESHG gamma(-2w; 0, w, w) of H2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_perp_elec_lasers_H2#
{
"id": "eshg_perp_elec_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_perp_elec_lasers_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table III, gamma_perp of the ESHG gamma(-2w; 0, w, w) of H2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_perp_vib_H2#
{
"id": "eshg_perp_vib_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_perp_vib_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table III, gamma_perp of the ESHG gamma(-2w; 0, w, w) of H2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_perp_vib_lasers_H2#
{
"id": "eshg_perp_vib_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_perp_vib_lasers_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table III, gamma_perp of the ESHG gamma(-2w; 0, w, w) of H2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_perp_total_H2#
{
"id": "eshg_perp_total_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_perp_total_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table III, gamma_perp of the ESHG gamma(-2w; 0, w, w) of H2: electronic plus pure vibrational (no rotational term); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_perp_total_lasers_H2#
{
"id": "eshg_perp_total_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__eshg_perp_total_lasers_H2.csv",
"table": "tbl_998201c95e2d",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table III, gamma_perp of the ESHG gamma(-2w; 0, w, w) of H2: electronic plus pure vibrational (no rotational term); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/thg_par_elec_H2#
{
"id": "thg_par_elec_H2",
"material": "H2",
"file": "H2/bishop_1990b__thg_par_elec_H2.csv",
"table": "tbl_147e4bcd04b8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table IV, gamma_par of the THG gamma(-3w; w, w, w) of H2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/thg_par_elec_lasers_H2#
{
"id": "thg_par_elec_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__thg_par_elec_lasers_H2.csv",
"table": "tbl_147e4bcd04b8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table IV, gamma_par of the THG gamma(-3w; w, w, w) of H2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/thg_par_vib_H2#
{
"id": "thg_par_vib_H2",
"material": "H2",
"file": "H2/bishop_1990b__thg_par_vib_H2.csv",
"table": "tbl_147e4bcd04b8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table IV, gamma_par of the THG gamma(-3w; w, w, w) of H2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/thg_par_vib_lasers_H2#
{
"id": "thg_par_vib_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__thg_par_vib_lasers_H2.csv",
"table": "tbl_147e4bcd04b8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table IV, gamma_par of the THG gamma(-3w; w, w, w) of H2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/thg_par_total_H2#
{
"id": "thg_par_total_H2",
"material": "H2",
"file": "H2/bishop_1990b__thg_par_total_H2.csv",
"table": "tbl_147e4bcd04b8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table IV, gamma_par of the THG gamma(-3w; w, w, w) of H2: electronic plus pure vibrational (no rotational term); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/thg_par_total_lasers_H2#
{
"id": "thg_par_total_lasers_H2",
"material": "H2",
"file": "H2/bishop_1990b__thg_par_total_lasers_H2.csv",
"table": "tbl_147e4bcd04b8",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table IV, gamma_par of the THG gamma(-3w; w, w, w) of H2: electronic plus pure vibrational (no rotational term); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_par_elec_D2#
{
"id": "dc_kerr_par_elec_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_par_elec_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table V, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of D2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_par_elec_lasers_D2#
{
"id": "dc_kerr_par_elec_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_par_elec_lasers_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table V, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of D2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_par_vib_D2#
{
"id": "dc_kerr_par_vib_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_par_vib_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table V, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of D2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_par_vib_lasers_D2#
{
"id": "dc_kerr_par_vib_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_par_vib_lasers_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table V, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of D2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_par_total_D2#
{
"id": "dc_kerr_par_total_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_par_total_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table V, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of D2: electronic plus pure vibrational (no rotational term); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_par_total_lasers_D2#
{
"id": "dc_kerr_par_total_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_par_total_lasers_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table V, gamma_par of the dc Kerr gamma(-w; w, 0, 0) of D2: electronic plus pure vibrational (no rotational term); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_perp_elec_D2#
{
"id": "dc_kerr_perp_elec_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_perp_elec_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table V, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of D2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_perp_elec_lasers_D2#
{
"id": "dc_kerr_perp_elec_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_perp_elec_lasers_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table V, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of D2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_perp_vib_D2#
{
"id": "dc_kerr_perp_vib_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_perp_vib_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table V, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of D2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_perp_vib_lasers_D2#
{
"id": "dc_kerr_perp_vib_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_perp_vib_lasers_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table V, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of D2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/dc_kerr_perp_total_D2#
{
"id": "dc_kerr_perp_total_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_perp_total_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table V, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of D2: electronic plus pure vibrational (no rotational term); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/dc_kerr_perp_total_lasers_D2#
{
"id": "dc_kerr_perp_total_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__dc_kerr_perp_total_lasers_D2.csv",
"table": "tbl_50515faab394",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table V, gamma_perp of the dc Kerr gamma(-w; w, 0, 0) of D2: electronic plus pure vibrational (no rotational term); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_par_elec_D2#
{
"id": "eshg_par_elec_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_par_elec_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table VI, gamma_par of the ESHG gamma(-2w; 0, w, w) of D2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_par_elec_lasers_D2#
{
"id": "eshg_par_elec_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_par_elec_lasers_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table VI, gamma_par of the ESHG gamma(-2w; 0, w, w) of D2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_par_vib_D2#
{
"id": "eshg_par_vib_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_par_vib_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VI, gamma_par of the ESHG gamma(-2w; 0, w, w) of D2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_par_vib_lasers_D2#
{
"id": "eshg_par_vib_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_par_vib_lasers_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VI, gamma_par of the ESHG gamma(-2w; 0, w, w) of D2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_par_total_D2#
{
"id": "eshg_par_total_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_par_total_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VI, gamma_par of the ESHG gamma(-2w; 0, w, w) of D2: electronic plus pure vibrational (no rotational term); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_par_total_lasers_D2#
{
"id": "eshg_par_total_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_par_total_lasers_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VI, gamma_par of the ESHG gamma(-2w; 0, w, w) of D2: electronic plus pure vibrational (no rotational term); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_perp_elec_D2#
{
"id": "eshg_perp_elec_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_perp_elec_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VI, gamma_perp of the ESHG gamma(-2w; 0, w, w) of D2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_perp_elec_lasers_D2#
{
"id": "eshg_perp_elec_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_perp_elec_lasers_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VI, gamma_perp of the ESHG gamma(-2w; 0, w, w) of D2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_perp_vib_D2#
{
"id": "eshg_perp_vib_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_perp_vib_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VI, gamma_perp of the ESHG gamma(-2w; 0, w, w) of D2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_perp_vib_lasers_D2#
{
"id": "eshg_perp_vib_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_perp_vib_lasers_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VI, gamma_perp of the ESHG gamma(-2w; 0, w, w) of D2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/eshg_perp_total_D2#
{
"id": "eshg_perp_total_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_perp_total_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VI, gamma_perp of the ESHG gamma(-2w; 0, w, w) of D2: electronic plus pure vibrational (no rotational term); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/eshg_perp_total_lasers_D2#
{
"id": "eshg_perp_total_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__eshg_perp_total_lasers_D2.csv",
"table": "tbl_76a1d5aaa9d0",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "eshg",
"convention": "T",
"part": "electronic_vibrational",
"component": "perpendicular",
"temperature_k": 295
}
}
Table VI, gamma_perp of the ESHG gamma(-2w; 0, w, w) of D2: electronic plus pure vibrational (no rotational term); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/thg_par_elec_D2#
{
"id": "thg_par_elec_D2",
"material": "D2",
"file": "D2/bishop_1990b__thg_par_elec_D2.csv",
"table": "tbl_13d5a3420da6",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table VII, gamma_par of the THG gamma(-3w; w, w, w) of D2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/thg_par_elec_lasers_D2#
{
"id": "thg_par_elec_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__thg_par_elec_lasers_D2.csv",
"table": "tbl_13d5a3420da6",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic",
"component": "parallel",
"temperature_k": 295
}
}
Table VII, gamma_par of the THG gamma(-3w; w, w, w) of D2: the electronic gamma averaged over the v = 0 rovibrational states with a 295 K Maxwell-Boltzmann rotational population; the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/thg_par_vib_D2#
{
"id": "thg_par_vib_D2",
"material": "D2",
"file": "D2/bishop_1990b__thg_par_vib_D2.csv",
"table": "tbl_13d5a3420da6",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VII, gamma_par of the THG gamma(-3w; w, w, w) of D2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/thg_par_vib_lasers_D2#
{
"id": "thg_par_vib_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__thg_par_vib_lasers_D2.csv",
"table": "tbl_13d5a3420da6",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VII, gamma_par of the THG gamma(-3w; w, w, w) of D2: the pure vibrational contribution (resonant where omega or 2 omega is the vibrational frequency 0.01897 a.u., hence the large values of either sign near omega = 0.01-0.02 a.u.); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/thg_par_total_D2#
{
"id": "thg_par_total_D2",
"material": "D2",
"file": "D2/bishop_1990b__thg_par_total_D2.csv",
"table": "tbl_13d5a3420da6",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "hartree",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VII, gamma_par of the THG gamma(-3w; w, w, w) of D2: electronic plus pure vibrational (no rotational term); hbar omega = 0.00-0.05 a.u. (hartree).
bishop_1990b/thg_par_total_lasers_D2#
{
"id": "thg_par_total_lasers_D2",
"material": "D2",
"file": "D2/bishop_1990b__thg_par_total_lasers_D2.csv",
"table": "tbl_13d5a3420da6",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"parameters": {
"process": "thg",
"convention": "T",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table VII, gamma_par of the THG gamma(-3w; w, w, w) of D2: electronic plus pure vibrational (no rotational term); the six laser wavelengths 10 640-4880 A (vacuum or air not stated).
bishop_1990b/ratio_s_theory#
{
"id": "ratio_s_theory",
"material": "H2",
"file": "H2/bishop_1990b__ratio_s_theory_H2.csv",
"table": "tbl_cf07a9edd99b",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "angstrom",
"use": "check",
"uncertainty": {
"absolute": 0.01,
"level": "not stated"
},
"parameters": {
"reference_material": "D2",
"process": "eshg",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table IX (p. 1907) ‘S Theory’: gamma_par^ESHG(total, H2)/gamma_par^ESHG(total, D2) (Eq. 21), electronic plus pure vibrational at 295 K (‘estimated error +-0.01’); lambda in angstrom. The ratio of Tables III and VI’s totals (checked).
bishop_1990b/ratio_s_expt#
{
"id": "ratio_s_expt",
"material": "H2",
"file": "H2/bishop_1990b__ratio_s_expt_H2.csv",
"table": "tbl_cf07a9edd99b",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "angstrom",
"use": "reproduced",
"reproduced_from": [
"mizrahi_1985_h2d2"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"reference_material": "D2",
"process": "eshg",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table IX ‘S Expt.’ (note b, Ref. 10: Mizrahi and Shelton, Phys. Rev. A 32, 3454 (1985) = mizrahi_1985_h2d2), with the printed uncertainty on the last digits (level not stated). Measured ratio of the total ESHG gammas.
bishop_1990b/ratio_t_theory#
{
"id": "ratio_t_theory",
"material": "H2",
"file": "H2/bishop_1990b__ratio_t_theory_H2.csv",
"table": "tbl_cf07a9edd99b",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "angstrom",
"use": "check",
"uncertainty": {
"absolute": 0.2,
"level": "not stated"
},
"parameters": {
"reference_material": "He",
"process": "eshg",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table IX ‘T Theory’ (printed ‘Thoery’): gamma_par^ESHG(total, H2)/gamma_par^ESHG(He) (Eq. 22), with Bishop and Pipin’s He of Eq. (25) (formula he_eshg_bishop_1989); ‘estimated error +-0.2’. No value at 5900 A (’—’).
bishop_1990b/ratio_t_expt#
{
"id": "ratio_t_expt",
"material": "H2",
"file": "H2/bishop_1990b__ratio_t_expt_H2.csv",
"table": "tbl_cf07a9edd99b",
"quantity": "hyperpolarizability_ratio",
"abscissa_unit": "angstrom",
"use": "reproduced",
"reproduced_from": [
"mizrahi_1985_h2d2"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"reference_material": "He",
"process": "eshg",
"part": "electronic_vibrational",
"component": "parallel",
"temperature_k": 295
}
}
Table IX ‘T Expt.’ (note b, Ref. 10: Mizrahi and Shelton 1985 = mizrahi_1985_h2d2), with the printed uncertainty on the last digits (level not stated). Theory lies 1-3 % below: ‘these discrepancies ... do not systematically increase or decrease with frequency’ (p. 1904).
bishop_1990b/gamma_k_total_H2#
{
"id": "gamma_k_total_H2",
"material": "H2",
"file": "H2/bishop_1990b__gamma_k_total_H2.csv",
"table": "tbl_ba8c25793416",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"uncertainty": {
"absolute": 10,
"level": "not stated"
},
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "K",
"temperature_k": 295
}
}
Table X (p. 1907): gamma^K = (3/2)[gamma_par^Kerr(total) - gamma_perp^Kerr(total)] (Eq. 9) from Table II, electronic plus pure vibrational at 295 K (‘estimated error +-10’); lambda in angstrom. No orientational (Delta alpha) term. Superseded by bishop_1991’s Table XVI (about 1.5 % higher).
bishop_1990b/gamma_k_total_D2#
{
"id": "gamma_k_total_D2",
"material": "D2",
"file": "D2/bishop_1990b__gamma_k_total_D2.csv",
"table": "tbl_ba8c25793416",
"quantity": "hyperpolarizability",
"unit": "au",
"abscissa_unit": "angstrom",
"use": "check",
"uncertainty": {
"absolute": 10,
"level": "not stated"
},
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "electronic_vibrational",
"component": "K",
"temperature_k": 295
}
}
Table X (p. 1907): gamma^K of D2 from Table V, as gamma_k_total_H2 (‘estimated error +-10’). Its 10 640 A value, 655, is what confirms erratum (1) of Table V.
bishop_1990b/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"
],
"uncertainty": {
"column": true,
"level": "not stated"
},
"parameters": {
"process": "dc_kerr",
"convention": "T",
"part": "total",
"component": "K"
}
}
2 inline points in the source record.
p. 1905: ‘An early pioneering measurement [Ref. 12, Buckingham and Orr 1968 = buckingham_1968b] for H2 at lambda = 6328 A gave 550 +- 60 a.u. which is very different from our result. A more recent experiment [Ref. 13, Carusotto et al. 1985 = carusotto_1985] at 5145 A, together with Eq. (9) of Ref. 12, leads to a value of gamma^K = (820 +- 49) a.u. which can be compared with our value of 747 a.u.’ The second is Bishop et al.’s reduction of Carusotto’s Kerr constant, not a number Carusotto prints. The same two values as bishop_1991’s expt_dc_kerr_H2. Level of the uncertainties not stated.
Formulas#
bishop_1990b/table11_H2_kerr#
{
"id": "table11_H2_kerr",
"material": "H2",
"equation": "Eqs. (27)-(28), p. 1905, with Table XI (tbl_630e3b7a8ddd), H2 Kerr",
"printed": "gamma_par^w/gamma_par^0 = 1 + A w_L^2 + A' w_L^4; gamma_perp^w/gamma_perp^0 = 1 + B w_L^2 + B' w_L^4; H2 (note a: gamma_par^0 = 670.77 a.u., gamma_perp^0 = 223.59 a.u.), Kerr: A 6.504, A' 30.47, B 5.753, B' 24.82",
"variable": "w_L^2 = w_s^2 + w1^2 + w2^2 + w3^2 in atomic units (hartree^2) (Eq. 26): here 2 w^2, w the laser photon energy in hartree. Electronic part only (295 K average), convention T; process dc_kerr.",
"range": "0 < w < 0.03 a.u. (the fitted data)",
"coefficients": {
"A": "6.504",
"A_prime": "30.47",
"B": "5.753",
"B_prime": "24.82",
"gamma_par_0": "670.77",
"gamma_perp_0": "223.59"
},
"check": "Reproduces Table II's elec columns at w = 0.01, 0.02, 0.03 a.u. to within 0.05 a.u. (e.g. gamma_par 674.27 against 674.3 at 0.02). Checked 2026-09-27."
}
Bishop’s naming: A, A’ for gamma_par, B, B’ for gamma_perp (Shelton’s A = Bishop’s A / 219474.63^2 cm^2, B = A’ / 219474.63^4 cm^4, for w_L in cm^-1). ‘A is indeed constant for all processes’, and B meets the ratios 1 : (1 + k/3) : (1 + k/6) for Kerr : ESHG : THG with k/6 = 0.13, or 1 : (4 + delta)/3 : (7 + delta)/6 with delta = -0.22 (p. 1905). Superseded by bishop_1991’s electronic values.
bishop_1990b/table11_H2_eshg#
{
"id": "table11_H2_eshg",
"material": "H2",
"equation": "Eqs. (27)-(28), p. 1905, with Table XI, H2 ESHG",
"printed": "as table11_H2_kerr; H2 (gamma_par^0 = 670.77, gamma_perp^0 = 223.59 a.u.), ESHG: A 6.502, A' 31.13, B 7.252, B' 38.33",
"variable": "as table11_H2_kerr, with w_L^2 = 6 w^2; process eshg",
"range": "0 < w < 0.03 a.u.",
"coefficients": {
"A": "6.502",
"A_prime": "31.13",
"B": "7.252",
"B_prime": "38.33",
"gamma_par_0": "670.77",
"gamma_perp_0": "223.59"
},
"check": "Reproduces Table III's elec columns at w = 0.01-0.03 a.u. to within 0.04 a.u. Checked 2026-09-27."
}
As table11_H2_kerr.
bishop_1990b/table11_H2_thg#
{
"id": "table11_H2_thg",
"material": "H2",
"equation": "Eqs. (27)-(28), p. 1905, with Table XI, H2 THG",
"printed": "as table11_H2_kerr; H2 (gamma_par^0 = 670.77 a.u.), THG: A 6.497, A' 31.95, B (6.497), B' (31.95) (note c: necessarily A = B and A' = B' for THG)",
"variable": "as table11_H2_kerr, with w_L^2 = 12 w^2; process thg",
"range": "0 < w < 0.03 a.u.",
"coefficients": {
"A": "6.497",
"A_prime": "31.95",
"gamma_par_0": "670.77"
},
"check": "Reproduces Table IV's elec column at w = 0.01-0.03 a.u. to within 0.04 a.u.; extrapolated to 0.04282 a.u. (10 640 A) it gives 777.0 (see erratum 3). Checked 2026-09-27."
}
As table11_H2_kerr.
bishop_1990b/table11_D2_kerr#
{
"id": "table11_D2_kerr",
"material": "D2",
"equation": "Eqs. (27)-(28), p. 1905, with Table XI, D2 Kerr",
"printed": "as table11_H2_kerr; D2 (note b: gamma_par^0 = 652.17 a.u., gamma_perp^0 = 217.39 a.u.), Kerr: A 6.399, A' 29.40, B 5.658, B' 23.93",
"variable": "as table11_H2_kerr, with w_L^2 = 2 w^2; process dc_kerr",
"range": "0 < w < 0.03 a.u.",
"coefficients": {
"A": "6.399",
"A_prime": "29.40",
"B": "5.658",
"B_prime": "23.93",
"gamma_par_0": "652.17",
"gamma_perp_0": "217.39"
},
"check": "Reproduces Table V's elec columns at w = 0.01-0.03 a.u. to within 0.04 a.u. Checked 2026-09-27."
}
As table11_H2_kerr.
bishop_1990b/table11_D2_eshg#
{
"id": "table11_D2_eshg",
"material": "D2",
"equation": "Eqs. (27)-(28), p. 1905, with Table XI, D2 ESHG",
"printed": "as table11_H2_kerr; D2 (gamma_par^0 = 652.17, gamma_perp^0 = 217.39 a.u.), ESHG: A 6.398, A' 30.03, B 7.138, B' 37.01",
"variable": "as table11_H2_kerr, with w_L^2 = 6 w^2; process eshg",
"range": "0 < w < 0.03 a.u.",
"coefficients": {
"A": "6.398",
"A_prime": "30.03",
"B": "7.138",
"B_prime": "37.01",
"gamma_par_0": "652.17",
"gamma_perp_0": "217.39"
},
"check": "Reproduces Table VI's elec columns at w = 0.01-0.03 a.u. to within 0.04 a.u. Checked 2026-09-27."
}
As table11_H2_kerr.
bishop_1990b/table11_D2_thg#
{
"id": "table11_D2_thg",
"material": "D2",
"equation": "Eqs. (27)-(28), p. 1905, with Table XI, D2 THG",
"printed": "as table11_H2_kerr; D2 (gamma_par^0 = 652.17 a.u.), THG: A 6.393, A' 30.79, B (6.393), B' (30.79)",
"variable": "as table11_H2_kerr, with w_L^2 = 12 w^2; process thg",
"range": "0 < w < 0.03 a.u.",
"coefficients": {
"A": "6.393",
"A_prime": "30.79",
"gamma_par_0": "652.17"
},
"check": "Reproduces Table VII's elec column at w = 0.01-0.03 a.u. to within 0.05 a.u. Checked 2026-09-27."
}
As table11_H2_kerr.
bishop_1990b/he_eshg_bishop_1989#
{
"id": "he_eshg_bishop_1989",
"material": "He",
"equation": "Eqs. (25)-(26), p. 1904",
"printed": "gamma_par^ESHG(He) = 43.104 (1 + 2.189 w_L^2 + 3.602 w_L^4), w_L^2 = w_s^2 + w1^2 + w2^2 + w3^2",
"variable": "w_L^2 = 6 w^2 for ESHG, w in atomic units (hartree); gamma in atomic units; electronic, convention T",
"range": "the frequencies of Table IX (6943-4880 A)",
"coefficients": {
"gamma_0": "43.104",
"A": "2.189",
"A_prime": "3.602"
},
"reproduced_from": [
"bishop_1989"
],
"check": "With Table III's totals it gives Table IX's T to the last digit: 17.198, 17.701, 19.291, 19.854 against 17.20, 17.70, 19.29, 19.85 (checked 2026-09-27). The coefficients are bishop_1989's ESHG fit (its Table V: A 2.189, A' 3.602)."
}
Ref. 11, Bishop and Pipin 1989 (bishop_1989): the helium reference used for T.
Corrections#
[
{
"dataset": "dc_kerr_perp_total_lasers_D2",
"row": "10640",
"column": "value",
"printed": "227.6",
"corrected": "277.7",
"reason": "Table V defines the total as the electronic plus the vibrational gamma, and the row's gamma_perp(elec) + gamma_perp(vib) = 222.0 + 55.7 = 277.7 (every other entry of Tables II-VII obeys total = elec + vib to +-0.1). Table X's gamma^K(D2, 10 640 A) = 655 = 1.5 (714.6 - 277.7) = 655.4 confirms the sum; the printed 227.6 would give 730.",
"evidence": "Table V image (tbl_50515faab394.jpg) prints 227.6 (not a mis-extraction); Table X (tbl_ba8c25793416) prints 655 (checked 2026-09-27)."
},
{
"dataset": "eshg_par_elec_lasers_H2",
"row": "5145",
"column": "value",
"printed": "931.9",
"corrected": "931.3",
"reason": "Table III's total at 5145 A, 923.8, minus the vibrational -7.5 is 931.3, not the printed electronic 931.9. The total is confirmed by Table VIII (R = 923.8/322.0 = 2.869, printed) and Table IX (T = 923.8/47.888 = 19.29, printed; 931.9 - 7.5 = 924.4 would give 19.30); the vibrational -7.5 by bishop_1991's reprint of it. So the electronic entry is misprinted.",
"evidence": "Table III image (tbl_998201c95e2d.jpg) prints 931.9, -7.5, 923.8 (not a mis-extraction); Tables VIII and IX, and bishop_1991/eshg_par_vib_H2 at 0.08856 a.u. (checked 2026-09-27)."
},
{
"dataset": "thg_par_elec_lasers_H2",
"row": "10640",
"column": "value",
"printed": "774.4",
"corrected": "777.4",
"reason": "Table IV's total at 10 640 A, 767.5, minus the vibrational -9.9 is 777.4, not the printed electronic 774.4. The vibrational -9.9 is confirmed by bishop_1991's reprint; 777.4 is what the electronic column's smooth frequency dependence requires (Table XI's THG fit gives 777.0 at 0.04282 a.u. from omega < 0.03, and the table's 762.6 at 0.04 and 822.2 at 0.05 a.u. interpolate in omega^2 to about 777.5), and it puts bishop_1991's improved electronic value 790.3 1.7 % above this paper's, within the 1.3-1.8 % that paper states (774.4 would give 2.1 %).",
"evidence": "Table IV image (tbl_147e4bcd04b8.jpg) prints 774.4, -9.9, 767.5 (not a mis-extraction); Table XI, bishop_1991/thg_par_vib_H2 and thg_par_elec_H2 at 0.04282 a.u. (checked 2026-09-27)."
}
]
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.