hohm_1993
=========

U\. Hohm, "Experimental determination of the dispersion in the mean linear dipole polarizability alpha\(omega\) of small hydrocarbons and evaluation of Cauchy moments between 325 nm and 633 nm", Mol\. Phys\. 78, 929 \(1993\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/hohm_1993.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1080/00268979300100621 <https://doi.org/10.1080/00268979300100621>`__

**Source kind:** measurement

**Recorded technique:** Michelson twin interferometer, gas cell of length l/2 about 0\.5 m, pressure below 3e5 Pa, illuminated simultaneously by four He\-Ne lasers \(vacuum wavelengths 632\.990, 611\.971, 594\.096 and 543\.516 nm, from Rowley and Gill's frequencies\) and a He\-Cd laser \(325\.130 nm\)\. The cell is evacuated in about 20 isothermal steps \(pressure to 50 Pa, temperature to 10 mK\) while a monochromatic \(632\.99 nm\) and the polychromatic interferogram are recorded; the polychromatic one is Fourier transformed over the density, and each peak position gives alpha\(omega\_j\) \(Eq\. 5; peak centre to \<= 5e\-6, of the order of the lasers' relative wavelength accuracy\)\. Gas purity of CH4 99\.995 % \(pp\. 931\-932\)\.

**Materials in structured entries:** CH4

**Dataset quantities:** cauchy\_moment, polarizability

**Contents:** 5 datasets; 1 formula.

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

Page numbers are the journal's \(929\-941\); pdf page 1 is the publisher's cover, so p\. = pdf page \+ 927\. Only CH4 is a curated species\: C2H6, C3H8, n\-C4H10, neopentane, C2H4, C3H6 and cyclo\-C3H6 are not transcribed\.

Reduction \(Eq\. 1, p\. 930\)\: \(n^2 \- 1\)/\(n^2 \+ 2\) = 4 pi N\_A \[a0^3 alpha\(omega, T\)\] rho\_0 \[1 \+ sum\_k B\_k\* rho\_0^k\]/3, rho\_0 = p/RT the ideal\-gas molar density; alpha is the polarizability of the free molecule \(zero density\), in atomic units, so it needs no state\. The wavelengths are vacuum wavelengths \(p\. 931 and Table 1 note a\)\. The text prints omega\_2 = '0\.7445345 a\.u\.' \(p\. 931\), a misprint for Table 1's 0\.07445345 \(the value of 611\.971 nm\); no dataset uses it\.

Uncertainty\: the paper does not say what the parenthesised digits of Table 1 are \(level not stated; the same 0\.0017 au at all five wavelengths, 1e\-4 of alpha\)\. 'The uncertainty in the relative dispersion \.\.\. is mostly determined by the uncertainty in the frequency of the radiation sources used' \(p\. 929\); the fit parameters of Table 2 carry their 'r\.m\.s\. error' \(p\. 936\)\.

Table 1 \(p\. 935\)\: CH4 at 294\.47\(1\) K, this work \(b\) and alpha from Thomas and Meath's DOSD Cauchy moments \(c \[26\], S\(\-2\) \.\.\. S\(\-16\), p\. 936\)\. 'Very good agreement', and the relative dispersion Delta alpha/Delta omega is 15\.14 \(this work\) against 15\.02 \[26\] \(p\. 936\)\. The 'latest experimental value' alpha\(omega\_1\) = 17\.5922\(54\) au at 323 K is Achtermann et al\.'s \(\[41\], achtermann\_1991; p\. 936\)\. Reprinted as hohm\_1994b/alpha\_CH4 \(Table 1 row h there\)\.

Table 2 \(p\. 937\)\: a\_0\-a\_2 of the quadratic fit in omega^2 \(Eq\. 13\), recorded as the formula cauchy\_CH4, and the Cauchy moments\: S\(\-2k\) of this work, obtained from a\_k by the iteration of Eqs\. \(12\) and \(17\) \(M = 7, about 200 steps, p\. 936\), with Thomas and Meath's \(b \[26\]\) and Spackman's TDHF \(e \[13\]\) values\. The moments are refraction\-derived over 325\-633 nm\: 'S\(\-2\) only reflects the electronic part of the static polarizability, excluding polarization effects resulting from vibrations' \(p\. 939\), and S\(\-6\), S\(\-8\) rest on the estimate \(17\) of the higher moments; use = 'check'\. The mean deviations Delta\_1, Delta\_2 from Meath's moments over six hydrocarbons \(Table 2's last rows\: S\(\-2\) 0\.10\(0\.24\) %, S\(\-4\) \-0\.7\(1\.0\) %, S\(\-6\) \-1\.4\(4\.8\) %, S\(\-8\) 9\.4\(9\.1\) % for Delta\_1\) are not extracted\. Spackman's row mixes his two basis sets\: S\(\-2\) = 15\.895 is his ELP value \(Spackman 1991 Table I; 6\-31G\(\+sd\+sp\) 15\.771\), S\(\-4\) = 50\.07 and S\(\-6\) = 199\.11 his 6\-31G\(\+sd\+sp\) values \(ELP 50\.68, 204\.05\)\.

Table 3 \(p\. 939\)\: B\_2\*\(omega, T\) = b\_R\(omega, T\) \- B\(T\) in cm^3/mol, a fit parameter that is not a vocabulary quantity \(it contains the thermodynamic virial B\)\: CH4 48\.58\(1\.20\) at omega\_1, 49\.17 and 49\.00 at omega\_4 and omega\_5, 'uncertainty \.\.\. about 0\.15 \[omega\_3, omega\_4\], \.\.\. 0\.1 cm^3 mol^\-1 \[omega\_5\] relative to B\_2\*\(omega\_1, T\)'\. hohm\_1994b turns them into B\_R with Burns et al\.'s reference \(hohm\_1994b/B\_R\_CH4\)\.

Elsewhere\: he\_2021's O2 formula \(O2\_table1\) lists 'Hohm \(1993\)' among its sources; this paper has no O2 \(the O2 dispersion is hohm\_1994b's\)\.

**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\_1993/alpha\_CH4
~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "alpha_CH4",
     "material": "CH4",
     "file": "CH4/hohm_1993__alpha_CH4.csv",
     "table": "tbl_90f137181bd7",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "temperature_k": 294.47
     }
   }

Table 1 \(p\. 935\), CH4 this work \(b\), 294\.47\(1\) K; the parenthesised last digits in the sigma column, level not stated\.

hohm\_1993/thomas\_1977\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "thomas_1977_CH4",
     "material": "CH4",
     "file": "CH4/hohm_1993__thomas_1977_CH4.csv",
     "table": "tbl_90f137181bd7",
     "quantity": "polarizability",
     "unit": "au",
     "abscissa_unit": "nm",
     "wavelength_medium": "vacuum",
     "use": "reproduced",
     "reproduced_from": [
       "thomas_1977"
     ]
   }

Table 1 row c \(\[26\], 'calculated using DOSD'\)\: alpha from Thomas and Meath's moments S\(\-2\) \.\.\. S\(\-16\) \(p\. 936\)\. Their S\(\-2\) \.\.\. S\(\-8\) \(moments\_thomas\_1977\_CH4\) reproduce it to 4e\-5 au at 544\-633 nm and 2e\-3 au at 325 nm \(the higher moments\)\.

hohm\_1993/moments\_CH4
~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "moments_CH4",
     "material": "CH4",
     "file": "CH4/hohm_1993__moments_CH4.csv",
     "table": "tbl_efe74204a8d8",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "check"
   }

Table 2 \(p\. 937\), CH4, this work\: S\(\-2\), S\(\-4\), S\(\-6\), S\(\-8\) iterated from the fit parameters \(the first of three stacked values in each merged cell, split against the image\)\. Electronic only \(refraction at 325\-633 nm\); no uncertainty printed \(Delta\_1 of the table's last row is a mean over six hydrocarbons\)\. The four moments reproduce Table 1 to 6e\-4 au at 544\-633 nm and 1\.5e\-3 au at 325 nm\.

hohm\_1993/moments\_thomas\_1977\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "moments_thomas_1977_CH4",
     "material": "CH4",
     "file": "CH4/hohm_1993__moments_thomas_1977_CH4.csv",
     "table": "tbl_efe74204a8d8",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "thomas_1977"
     ]
   }

Table 2, CH4 row b \(\[26\]\)\: Thomas and Meath's recommended DOSD moments S\(\-2\) \.\.\. S\(\-8\) \(the second stacked value\)\. Spackman 1991 prints the same S\(\-2\), S\(\-4\), S\(\-6\) \(spackman\_1991/meath\_CH4\)\.

hohm\_1993/moments\_spackman\_1991\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "moments_spackman_1991_CH4",
     "material": "CH4",
     "file": "CH4/hohm_1993__moments_spackman_1991_CH4.csv",
     "table": "tbl_efe74204a8d8",
     "quantity": "cauchy_moment",
     "unit": "au",
     "abscissa": "order",
     "abscissa_unit": "1",
     "use": "reproduced",
     "reproduced_from": [
       "spackman_1991"
     ]
   }

Table 2, CH4 row e \(\[13\]\)\: Spackman's TDHF moments S\(\-2\), S\(\-4\), S\(\-6\) \(theory; 8\-28 % below the DOSD\)\. S\(\-2\) = 15\.895 is Spackman's ELP\-basis value, S\(\-4\) and S\(\-6\) his 6\-31G\(\+sd\+sp\) values\: Hohm mixes the two basis sets \(Spackman 1991 Table I\)\.

Formulas
--------

hohm\_1993/cauchy\_CH4
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "cauchy_CH4",
     "material": "CH4",
     "equation": "Eq. (13) with Table 2, pp. 934 and 937",
     "printed": "alpha(omega) = a_0^(2) + a_1^(2) omega^2 + a_2^(2) omega^4; CH4: a_0^(2) = 17.2585(21), a_1^(2) = 62.72(47), a_2^(2) = 349(19)",
     "variable": "omega: photon energy in hartree; alpha in au (vacuum wavelengths 325.13-632.99 nm)",
     "range": "325.130-632.990 nm (the data fitted), 294.47 K",
     "coefficients": {
       "a0": "17.2585",
       "a1": "62.72",
       "a2": "349",
       "a0_rms": "0.0021",
       "a1_rms": "0.47",
       "a2_rms": "19"
     },
     "check": "Reproduces Table 1's CH4 row to 4e-4 au (-0.00006, +0.00030, -0.00041, +0.00001, +0.00006 at 633 ... 325 nm), within its printed 0.0017 au. Checked 2026-09-26."
   }

The Gaussian least\-squares parameters with their 'r\.m\.s\. error' \(p\. 936\); a\_k is not S\(\-2k\-2\) \(Eq\. 10\), the moments of moments\_CH4 are its iterated correction\. A formula of the free molecule's electronic polarizability at 294\.47 K; not to be extrapolated far below 325 nm\.

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.