hohm_1994
=========

U\. Hohm, "Dispersion of polarizability anisotropy of H2, O2, N2O, CO2, NH3, C2H6, and cyclo\-C3H6 and evaluation of isotropic and anisotropic dispersion\-interaction energy coefficients", Chem\. Phys\. 179, 533 \(1994\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/hohm_1994.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1016/0301\-0104\(94\)87028\-4 <https://doi.org/10.1016/0301-0104%2894%2987028-4>`__

**Source kind:** fit

**Recorded technique:** A two\-term sum\-over\-states model of the parallel and perpendicular polarizabilities \(Eqs\. 4\-5, four parameters f\_par, f\_perp, omega\_par^2, omega\_perp^2\) fitted by least squares \(Eq\. 13, relative residuals\) to N = 4\-5 mean polarizabilities measured in the author's laboratory by refractometry at 632\.99\-325\.13 nm and M = 1\-5 Rayleigh depolarization ratios from the literature at 647\.1\-457\.9 nm \(p\. 536\)\.

**Materials in structured entries:** CO2, H2, N2O, O2

**Dataset quantities:** polarizability

**Contents:** 9 datasets; 5 formulas.

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

Page numbers are the journal's \(533\-541; pdf page 1 = p\. 533\)\. Atomic units throughout \(p\. 535\)\: 1 au of polarizability = 1\.648778e\-41 C^2 m^2 J^\-1\.

Mean polarizabilities \(Table 2, input rows\)\: 'whose frequency dependence is determined in our laboratory with very high precision \(Delta alpha\(omega\)/alpha\(omega\) ~ 10^\-5 with respect to a reference value alpha\(omega\_1\)\) in the frequency range between omega = 0\.07198 au \(632\.99 nm\) and omega = 0\.1401 au \(325\.13 nm\)' \(p\. 536\); from the free\-molecule limit of the Lorentz\-Lorenz function \(Eq\. 6\)\. The absolute accuracy of the reference value alpha\(omega\_1\) is not stated here; the same laboratory's apparatus gives \|Delta alpha/alpha\| \< 1e\-3 \(hohm\_1990, p\. 809\), used as the datasets' scale uncertainty\. The column wavelengths are those of the table's note a\), vacuum \(632\.990 nm with 0\.0719812 au\)\. The measurement temperature is not stated \(room temperature presumably\)\.

Sources of the inputs \(note b\-d\)\: H2, ref\. \[33\] 'U\. Hohm, unpublished results', so this paper is their first publication \(primary here\); O2, N2O and CO2, ref\. \[29\] 'U\. Hohm, Mol\. Phys\. \(1993\); in press', published as U\. Hohm, Mol\. Phys\. 81, 157 \(1994\) \(hohm\_1994b\), whose Table 1 rows \(b, this work\) these inputs are, digit for digit \(checked 2026\-09\-26\)\: reproductions, not fitted beside the original\. The original prints an absolute uncertainty of the last digits \(O2 0\.0013, N2O 0\.0015, CO2 0\.0013 au, level not stated, the same at every wavelength\) and the gas temperatures \(292\.06, 295\.05, 293\.80 K\), which this paper omits; the 1e\-5 relative figure quoted below is this paper's statement of the dispersion's precision\.

Accuracy of the fit \(p\. 537\)\: 'the mean dipole polarizabilities alpha\(omega\) are correct to 0\.5% in the range between omega = 0 and omega = 0\.2 au' \(by comparison with Meath's DOSD values\); kappa\(omega\) to 3 %\. Table 1's caption\: Delta f/f ~ 0\.05 %, Delta omega^2/omega^2 ~ 0\.1 %, 'more figures are given in order to reproduce the input data correctly'\. The two\-term form 'cannot account correctly for the Schumann\-Runge band of O2' \(p\. 540\), which makes its C6 10\-20 % low\.

Not extracted\: the depolarization ratios \(100 rho, Table 2; for the anisotropies later\), the kappa\(omega\) dispersion \(Figs\. 2\-3\), the C6, C6', C6'' coefficients \(Tables 3\-5\), and NH3, C2H6, cyclo\-C3H6 \(not curated species\)\.

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

Datasets
--------

hohm\_1994/input\_H2
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "input_H2",
     "material": "H2",
     "file": "H2/hohm_1994__input_H2.csv",
     "table": "tbl_14b1cb679065",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "relative": 1e-05,
       "level": "not stated",
       "systematic_relative": 0.001
     }
   }

Table 2 \(p\. 537\), H2 input row \(ref\. \[33\], unpublished results of the author\)\: 632\.990\-325\.130 nm\.

hohm\_1994/input\_O2
~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "input_O2",
     "material": "O2",
     "file": "O2/hohm_1994__input_O2.csv",
     "table": "tbl_14b1cb679065",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "hohm_1994b"
     ],
     "uncertainty": {
       "relative": 1e-05,
       "level": "not stated",
       "systematic_relative": 0.001
     }
   }

Table 2, O2 input row\: ref\. \[29\] 'U\. Hohm, Mol\. Phys\. \(1993\); in press', published as hohm\_1994b; digit\-identical to hohm\_1994b/alpha\_O2 \(Table 1 there, which also gives the temperature and an absolute uncertainty of the last digits\)\. A reproduction\: not fitted beside the original\.

hohm\_1994/input\_N2O
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "input_N2O",
     "material": "N2O",
     "file": "N2O/hohm_1994__input_N2O.csv",
     "table": "tbl_14b1cb679065",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "hohm_1994b"
     ],
     "uncertainty": {
       "relative": 1e-05,
       "level": "not stated",
       "systematic_relative": 0.001
     }
   }

Table 2, N2O input row \(no value at 611\.971 nm\)\: ref\. \[29\] 'U\. Hohm, Mol\. Phys\. \(1993\); in press', published as hohm\_1994b; digit\-identical to hohm\_1994b/alpha\_N2O \(Table 1 there, which also gives the temperature and an absolute uncertainty of the last digits\)\. A reproduction\: not fitted beside the original\.

hohm\_1994/input\_CO2
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "input_CO2",
     "material": "CO2",
     "file": "CO2/hohm_1994__input_CO2.csv",
     "table": "tbl_14b1cb679065",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "hohm_1994b"
     ],
     "uncertainty": {
       "relative": 1e-05,
       "level": "not stated",
       "systematic_relative": 0.001
     }
   }

Table 2, CO2 input row\: ref\. \[29\] 'U\. Hohm, Mol\. Phys\. \(1993\); in press', published as hohm\_1994b; digit\-identical to hohm\_1994b/alpha\_CO2 \(Table 1 there, which also gives the temperature and an absolute uncertainty of the last digits\)\. A reproduction\: not fitted beside the original\.

hohm\_1994/fit\_H2\_a
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "fit_H2_a",
     "material": "H2",
     "file": "H2/hohm_1994__fit_H2_a.csv",
     "table": "tbl_14b1cb679065",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 2, the calculated row of set a \(two anisotropies fitted\)\.

hohm\_1994/fit\_H2\_b
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "fit_H2_b",
     "material": "H2",
     "file": "H2/hohm_1994__fit_H2_b.csv",
     "table": "tbl_14b1cb679065",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 2, the calculated row of set b \(one anisotropy fitted\)\.

hohm\_1994/fit\_O2
~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "fit_O2",
     "material": "O2",
     "file": "O2/hohm_1994__fit_O2.csv",
     "table": "tbl_14b1cb679065",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 2, calculated row\.

hohm\_1994/fit\_N2O
~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "fit_N2O",
     "material": "N2O",
     "file": "N2O/hohm_1994__fit_N2O.csv",
     "table": "tbl_14b1cb679065",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 2, calculated row\.

hohm\_1994/fit\_CO2
~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "fit_CO2",
     "material": "CO2",
     "file": "CO2/hohm_1994__fit_CO2.csv",
     "table": "tbl_14b1cb679065",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "check"
   }

Table 2, calculated row\.

Formulas
--------

hohm\_1994/two\_term\_H2\_a
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "two_term_H2_a",
     "material": "H2",
     "equation": "Eq. (4) with Table 1, p. 536",
     "printed": "alpha(omega) = (1/3)(f_par/(omega_par^2 - omega^2) + 2 f_perp/(omega_perp^2 - omega^2)); H2 (a): f_par = 1.62632, f_perp = 1.40105, omega_par^2 = 0.23940245 au, omega_perp^2 = 0.29486069 au",
     "variable": "omega: photon energy in hartree; alpha in au",
     "range": "0-0.2 au (to 228 nm), 'correct to 0.5%' (p. 537); fitted 325-633 nm",
     "coefficients": {
       "f_par": "1.62632",
       "f_perp": "1.40105",
       "omega_par2": "0.23940245",
       "omega_perp2": "0.29486069"
     },
     "check": "Reproduces Table 2's calculated row to 1e-5 au (5.53888, 5.54649, 5.55364, 5.57795, 5.86052 against 5.53887 ... 5.86051); static limit 5.4321 au. Checked 2026-09-25."
   }

Set a\: two of Kumar and Meath's anisotropies used as depolarization inputs; its kappa\(omega\) is within 1\.34 % of theirs at 0\.3 au \(set b\: 40 %, p\. 536\)\.

hohm\_1994/two\_term\_H2\_b
~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "two_term_H2_b",
     "material": "H2",
     "equation": "Eq. (4) with Table 1, p. 536",
     "printed": "as two_term_H2_a; H2 (b): f_par = 1.36603, f_perp = 1.70361, omega_par^2 = 0.20191405 au, omega_perp^2 = 0.35741442 au",
     "variable": "omega: photon energy in hartree; alpha in au",
     "range": "as two_term_H2_a",
     "coefficients": {
       "f_par": "1.36603",
       "f_perp": "1.70361",
       "omega_par2": "0.20191405",
       "omega_perp2": "0.35741442"
     },
     "check": "Reproduces Table 2's calculated row to 1e-5 au (5.53893, 5.54651, 5.55362, 5.57784, 5.86052); static limit 5.4328 au. Checked 2026-09-25."
   }

Set b\: one anisotropy input; its anisotropy dispersion is poor \(40 % at 0\.3 au\), its mean polarizability as good as set a's\.

hohm\_1994/two\_term\_O2
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "two_term_O2",
     "material": "O2",
     "equation": "Eq. (4) with Table 1, p. 536",
     "printed": "as two_term_H2_a; O2: f_par = 2.74876, f_perp = 4.86007, omega_par^2 = 0.18095751 au, omega_perp^2 = 0.58545449 au",
     "variable": "omega: photon energy in hartree; alpha in au",
     "range": "0-0.2 au, 0.5 % (p. 537); fitted 325-633 nm; cannot represent the Schumann-Runge band (p. 540)",
     "coefficients": {
       "f_par": "2.74876",
       "f_perp": "4.86007",
       "omega_par2": "0.18095751",
       "omega_perp2": "0.58545449"
     },
     "check": "Reproduces Table 2's calculated row to 1e-5 au (10.79627 ... 11.40610 against 10.7963 ... 11.4061); static limit 10.5976 au. Checked 2026-09-25."
   }

hohm\_1994/two\_term\_N2O
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "two_term_N2O",
     "material": "N2O",
     "equation": "Eq. (4) with Table 1, p. 536",
     "printed": "as two_term_H2_a; N2O: f_par = 5.65126, f_perp = 9.72095, omega_par^2 = 0.17424213 au, omega_perp^2 = 0.72904985 au",
     "variable": "omega: photon energy in hartree; alpha in au",
     "range": "0-0.2 au, 0.5 % (p. 537); fitted 325-633 nm",
     "coefficients": {
       "f_par": "5.65126",
       "f_perp": "9.72095",
       "omega_par2": "0.17424213",
       "omega_perp2": "0.72904985"
     },
     "check": "Reproduces Table 2's calculated row to 1e-4 au (20.09523, 20.12363, 20.15028, 20.24116, 21.31967 against 20.0952, 20.1236, 20.1503, 20.2412, 21.3197); static limit 19.7003 au (electronic only). Checked 2026-09-25."
   }

hohm\_1994/two\_term\_CO2
~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "two_term_CO2",
     "material": "CO2",
     "equation": "Eq. (4) with Table 1, p. 536",
     "printed": "as two_term_H2_a; CO2: f_par = 6.00332, f_perp = 8.54433, omega_par^2 = 0.22525399 au, omega_perp^2 = 0.66083749 au",
     "variable": "omega: photon energy in hartree; alpha in au",
     "range": "0-0.2 au, 0.5 % (p. 537); fitted 325-633 nm",
     "coefficients": {
       "f_par": "6.00332",
       "f_perp": "8.54433",
       "omega_par2": "0.22525399",
       "omega_perp2": "0.66083749"
     },
     "check": "Reproduces Table 2's calculated row to 1e-4 au (17.78075, 17.80053, 17.81908, 17.88221, 18.61600 against 17.7808, 17.8005, 17.8191, 17.8822, 18.6160); static limit 17.5035 au (electronic only). Checked 2026-09-25."
   }

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.