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 <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/bishop_1990b.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1063/1\.458072 <https://doi.org/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 SUPERSEDED for the electronic part by bishop\_1991 \(extended Delta basis; its electronic values are 1\.3\-1\.8 % higher, bishop\_1991 p\. 4851\); the vibrational part is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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. 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"
     ],
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "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
-----------

.. code-block:: text

   [
     {
       "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 :doc:`review register </register>` for the checks and decisions.