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 `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1103/physreva\.43\.4845 `__ **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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "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 :doc:`review register ` for the checks and decisions.