spackman_1991
=============

M\. A\. Spackman, "Time\-dependent Hartree\-Fock second\-order molecular properties with a moderately sized basis set\. I\. The frequency dependence of the dipole polarizability", J\. Chem\. Phys\. 94, 1288 \(1991\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/spackman_1991.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1063/1\.460038 <https://doi.org/10.1063/1.460038>`__

**Source kind:** theory

**Recorded technique:** Time\-dependent coupled Hartree\-Fock \(RPA\) calculations with CADPAC of the frequency\-dependent mean polarizability and its anisotropy for 25 molecules, with the 6\-31G\(\+sd\+sp\) basis and, for ten small molecules, Liu and Dykstra's larger 'electrical properties' \(ELP\) basis; Cauchy moments from the RPA solution or, for butane, pentane and SF6, from a quartic fit of alpha\(omega\) in omega^2 \(pp\. 1288\-1289\)\. Compared with the DOSD moments of Meath and co\-workers \(Table I\) and with Bogaard et al\.'s and Alms et al\.'s anisotropy dispersion \(Table III\)\.

**Materials in structured entries:** CH4, CO, CO2, H2, N2, N2O, SF6

**Dataset quantities:** cauchy\_moment

**Contents:** 7 datasets; 0 formulas.

Curation notes
--------------

Page numbers are the journal's \(1288\-1294\); pdf page 1 is the publisher's cover, so p\. = pdf page \+ 1286\.

The TDHF moments are not used\: they are theory that underestimates the dispersion systematically, 'S\(\-2\) and S\(\-4\) \.\.\. are systematically underestimated by 20% and 40%' \(abstract, p\. 1288\); the rms deviation from the DOSD values is 27\.6 % for S\(\-4\) and 50\.3 % for S\(\-6\) with the small basis, and HF limit calculations 'will typically underestimate the true values by more than 20%' \(pp\. 1290\-1291\)\. For the curated species \(6\-31G\(\+sd\+sp\), ELP in parentheses; au\)\: H2 alpha\(0\) 5\.116 \(5\.091\), S\(\-4\) 16\.84 \(18\.03\), S\(\-6\) 58\.79 \(68\.55\); CH4 15\.771 \(15\.895\), 50\.07 \(50\.68\), 199\.11 \(204\.05\); N2 10\.773 \(11\.435\), 24\.73 \(27\.53\), 69\.48 \(83\.56\); CO 11\.357 \(12\.226\), 36\.78 \(41\.85\), 213\.23 \(234\.18\); N2O 17\.624, 50\.80, 200\.80; CO2 15\.043 \(15\.731\), 34\.23 \(37\.49\), 100\.95 \(118\.85\); SF6 26\.041, 42\.82, 110\.39 \(S\(\-4\) 52 % and S\(\-6\) 89 % below the DOSD, pp\. 1290\-1291\)\. hohm\_1993's 'Spackman \[13\]' CH4 row mixes the two bases \(ELP alpha\(0\), 6\-31G S\(\-4\), S\(\-6\)\)\.

Table I's 'Experiment' columns \(p\. 1290, note b\: 'Experimental DOSD alpha\(0\), S\(\-4\), and S\(\-6\) from Meath et al\. \(Refs\. 47\-60\)'\) are reproductions and are extracted for the curated species \(datasets meath\_\<gas\>\)\. The paper does not say which of Refs\. 47\-60 gives which molecule; the attributions are\: H2, N2 and N2O equal zeiss\_1977's moments \(5\.428, 19\.96, 82\.94; 11\.74, 30\.11, 101\.8; 19\.70, 72\.11, 410\.7\: checked\); CH4 equals Thomas and Meath's \(Ref\. 48; thomas\_1977, curated since\); CO and CO2 equal Jhanwar and Meath 1982's \(jhanwar\_1982; CO 13\.08, 48\.27, 296\.5 match it and not Kumar and Meath 1994's 48\.26, 292\.9\); SF6 equals Kumar, Fairley and Meath 1985's electronic sums \(kumar\_1985b\) \(checked 2026\-09\-27\)\. O2 is not treated \(open shell, p\. 1289\)\.

Table II \(p\. 1291\)\: other theory for H2, HF, H2O and N2 \(CI, RPA, SOPPA, MCTDHF\), with the DOSD S\(\-4\), S\(\-6\) repeated\: not extracted\. Table III \(p\. 1292\)\: the dispersion delta\[alpha\] and delta\[Delta alpha\] between 632\.8 and 488\.0 nm and 100 rho\_0 at 488\.0 nm, experiment from Bogaard et al\. \(Ref\. 63; not in the library\) and, for N2, Alms et al\. \(alms\_1975\)\: N2 1\.07, 0\.10, 0\.16; CO 0\.52, 0\.19, 0\.21; CO2 4\.12, 0\.19, 0\.29; N2O 6\.12, 0\.29, 0\.58 \(au\); differences of polarizabilities between two wavelengths, which no quantity holds\: not extracted\. The paper argues that the measured anisotropy dispersion is overestimated for molecules with rho\_0 \< 1e\-2, from a frequency\-dependent vibrational Raman contribution \(p\. 1293\)\.

**Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents.

Datasets
--------

spackman\_1991/meath\_H2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "meath_H2",
     "material": "H2",
     "file": "H2/spackman_1991__meath_H2.csv",
     "table": "tbl_6f890f395ef6",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "zeiss_1977"
     ]
   }

Table I \(p\. 1290\), 'Experiment'\: S\(\-2\) = alpha\(0\), S\(\-4\), S\(\-6\) of Meath's DOSD; equal to zeiss\_1977/moments\_H2\.

spackman\_1991/meath\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "meath_CH4",
     "material": "CH4",
     "file": "CH4/spackman_1991__meath_CH4.csv",
     "table": "tbl_6f890f395ef6",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "thomas_1977"
     ]
   }

Table I, 'Experiment'\: Thomas and Meath's moments \(Ref\. 48; the same values as hohm\_1993/moments\_thomas\_1977\_CH4\)\: equal to thomas\_1977's S\(\-2\) = 17\.27, S\(\-4\) = 62\.41 \(Table 2\) and S\(\-6\) = 298\.3 \(p\. 121\) \(checked 2026\-09\-27\)\.

spackman\_1991/meath\_N2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "meath_N2",
     "material": "N2",
     "file": "N2/spackman_1991__meath_N2.csv",
     "table": "tbl_6f890f395ef6",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "zeiss_1977"
     ]
   }

Table I, 'Experiment'\: equal to zeiss\_1977/moments\_N2\.

spackman\_1991/meath\_CO
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "meath_CO",
     "material": "CO",
     "file": "CO/spackman_1991__meath_CO.csv",
     "table": "tbl_6f890f395ef6",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "jhanwar_1982"
     ]
   }

Table I, 'Experiment'\: 13\.08, 48\.27, 296\.5 au\. Spackman does not name the paper among Refs\. 47\-60; the values equal jhanwar\_1982's CO sums \(13\.08, 48\.27, 29\.65\(1\)\) and not Kumar and Meath 1994's later 48\.26 and 292\.9 \(kumar\_1994\), which Spackman \(1991\) predates \(checked 2026\-09\-27\)\.

spackman\_1991/meath\_N2O
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "meath_N2O",
     "material": "N2O",
     "file": "N2O/spackman_1991__meath_N2O.csv",
     "table": "tbl_6f890f395ef6",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "zeiss_1977"
     ]
   }

Table I, 'Experiment'\: equal to zeiss\_1977/moments\_N2O\.

spackman\_1991/meath\_CO2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "meath_CO2",
     "material": "CO2",
     "file": "CO2/spackman_1991__meath_CO2.csv",
     "table": "tbl_6f890f395ef6",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "jhanwar_1982"
     ]
   }

Table I, 'Experiment'\: 17\.51, 50\.99, 211\.4 au, equal to jhanwar\_1982's electronic \(UV\) CO2 sums S\(\-2\), S\(\-4\), S\(\-6\) = 17\.51, 50\.99, 21\.14\(1\) \(checked 2026\-09\-27\); Spackman does not name the paper \(Ref\. 52 by the attribution through hohm\_1994b's row j\)\.

spackman\_1991/meath\_SF6
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "meath_SF6",
     "material": "SF6",
     "file": "SF6/spackman_1991__meath_SF6.csv",
     "table": "tbl_6f890f395ef6",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "kumar_1985b"
     ]
   }

Table I, 'Experiment'\: 30\.04, 88\.59, 982\.1 au \(the electronic DOSD; SF6's large vibrational polarizability is not in it\)\. Spackman does not name the paper; the values equal kumar\_1985b's electronic S\(\-2\) = 3\.004\(1\), S\(\-4\) = 8\.859\(1\) \(Table II\) and S\(\-6\) = 982\.1 \(p\. 73\) \(checked 2026\-09\-27\)\.

Formulas
--------

No formulas are recorded.

Corrections
-----------

No dataset errata are recorded in this source record.

Formula corrections, where recorded, appear with their formulas above. Curation notes may also discuss corrections or unresolved interpretation. Consult the :doc:`review register </register>` for the checks and decisions.