bermejo_1977
============

D\. Bermejo, R\. Escribano and J\. M\. Orza, "Absolute Raman intensities of CH4, CH3D, CH2D2, CHD3, and CD4", J\. Mol\. Spectrosc\. 65, 345 \(1977\)

`Source record <https://github.com/LupoLab/optmat/blob/main/src/optmat/data/sources/bermejo_1977.toml>`__ · :doc:`Catalogue </the-data/sources>` · :doc:`Review register </register>`

DOI: `10\.1016/0022\-2852\(77\)90274\-0 <https://doi.org/10.1016/0022-2852%2877%2990274-0>`__

**Source kind:** measurement

**Recorded technique:** Spontaneous vibrational Raman scattering of the gases at room temperature, Ar\+ laser at 488\.0 nm \(0\.5 W\), 90\-degree scattering with the electric vector of the incident light perpendicular to the direction of observation, f/0\.95 collection, a Polaroid analyzer and a scrambler, Jarrell\-Ash 25\-300 spectrophotometer with photon counting; spectral sensitivity from calibrated tungsten and halogen lamps; collection angle and convergence corrections \(pp\. 347\-348\)\. Relative band intensities in a glass cell at about 1\.5 atm; every compound referred to the nu1 band of CH4 in a steel cell \(five sequences\); the absolute nu1 intensity of CH4 measured against the Rayleigh line of CH4 at about 0\.1 atm, 20 alternating recordings \(pp\. 348\-349\)\. The alpha^S tensors \(derivatives with respect to Mills's symmetry coordinates\) from a weighted least\-squares fit to the 36 intensities and depolarization ratios of the five isotopologues, with Mills's L matrix \(p\. 352\)\.

**Materials in structured entries:** CH4

**Dataset quantities:** polarizability\_derivative, raman\_scattering\_activity, raman\_shift

**Contents:** 9 datasets; 0 formulas.

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

Journal pages 345\-353 = PDF pages 1\-9 \(page n of the PDF is p\. 344 \+ n\)\. The citation first requested, 'J\. Raman Spectrosc\. 6', is wrong\: the paper is J\. Mol\. Spectrosc\. 65, 345 \(1977\) \(checked against the first page\)\.

SCOPE AND ISOTOPOLOGUES\. Only CH4 \(12CH4, natural methane, purity \>= 99\.9 %\) is a curated material\. The deuterated isotopologues CH3D \(~98 %\), CH2D2 \(~94 %\), CHD3 \(~85 %\) and CD4 \(~89 %, with air and CHD3\) \(p\. 347\) fill the rest of Tables I and II and are not extracted\: for review, CD4 nu1 \(2108\.6 cm\-1\) I = 71\.9 and 115 \+\- 8 with 2nu2, nu2 \+ nu4 and 2nu4 added \(Table II\); CD4 nu3 \(2258\.5 cm\-1\) 70\.5 \+\- 5\.

WHAT THE INTENSITY IS\. Table I footnote b\: 'I = g\_i \(45 alpha'^2 \+ 7 gamma'^2\) \. N \. 10^\-32 cm^4 gr^\-1 \(Where N is the Avogadro Number\)'\: the scattering activity, as in Murphy et al\. 1969 \(murphy\_1969\), so a printed number is in angstrom^4/amu exactly\. It is absolute\: 'we measured the absolute intensity of the nu1\(a1\) band of methane with reference to the Rayleigh line' of CH4 \(p\. 348; the reduction from the Rayleigh line, through CH4's polarizability and anisotropy, is not given\), and every other band was referred to CH4's nu1 \(p\. 348\)\. 'We found \(45 alpha'^2 \+ 7 gamma'^2\) = 223 \. N \. 10^\-32 g^\-1 cm^4; comparable, for instance, with 237 and 223, calculated from data published in Refs\. \(10\) and \(11\)' \(p\. 349\)\: the two reproduced values are the inline dataset intensity\_CH4\_nu1\_others\. The excitation wavelength does not enter the activity; it is 488\.0 nm \(air\) for every datum\.

TABLE I \(p\. 348\)\: band positions \('a\: Our measurement'; nu4's 1310 cm\-1 carries no mark and is excluded from shift\_CH4\), intensities and depolarization ratios\. Every CH4 depolarization ratio is 'd\: Expected values, not measured' \(0 for nu1, 3/4 for the others\)\: none is extracted\. Footnote c defines rho = 3 gamma'^2/\(45 alpha'^2 \+ 4 gamma'^2\), the ratio for linearly polarized incident light\. nu4's intensity is an upper limit, '\<= 0\.05^Q' \(Q branch only\), not extracted\. No uncertainty is printed in Table I; Table II gives the adopted values with their \+\-\.

TABLE II \(p\. 350\)\: 'Observed and Calculated Intensities and Depolarization Ratios'\. Footnote a\: 'Intensities of overtones and combinations assumed to be in interaction with fundamentals have been added to that of the fundamental', so CH4 nu1's 230 \+\- 12 is Table I's 223 \+ 7 \(2nu2\); nu2 7\.0 \+\- 0\.4 and nu3 128 \+\- 7 are Table I's\. 'We have thus adopted as experimental intensities, I\_exp, those given in Table II' \(p\. 352\)\. The \+\- level is not stated\. I\_calc is recomputed from the fitted alpha^S tensors \(use = "check"\); the fit's 'standard deviation of the calculated values of the data is sigma = 0\.94' \(p\. 352\)\. nu4\: calculated 0\.22, experimental '\<= 0\.24' \(not extracted\)\.

THE alpha^S INVARIANTS \(p\. 352\)\: 'From a weighted least\-squares adjustment of the 36 experimental measurements, using the L matrix derived from Mills \(6\), we find\: \|c\(S1\)\| = 2\.260 \+\- 0\.042 A^2; \|c\(S2\)\| = 0\.139 \+\- 0\.015 A^2; c\(S3\) = 1\.366 \+\- 0\.077 A^2; c\(S4\) = 0\.00 \+\- 0\.10 A^2 \(signs of c\(S3\) and c\(S4\) may be simultaneously changed\)'\: the derivatives of the polarizability tensor with respect to Mills's symmetry coordinates, the one parameter of each tensor \(theory, pp\. 345\-346\: for S1, alpha\_xx' = alpha\_yy' = alpha\_zz' = c, the mean\-polarizability derivative; S2, S3, S4 traceless\)\. They are isotope invariant, so they hold for CH4 and every deuterated form\. Datasets dS1\_CH4 \(component mean\) and dS\_aniso\_CH4 \(component anisotropy\: the tensor element c, not the invariant gamma'\)\. Check \(2026\-09\-26\)\: for CH4, I\(nu1\) = 45 alpha\_1'^2 with alpha\_1' = l\_11 c\(S1\) and l\_11 = m\_H^\(\-1/2\) \(S1 the symmetric sum of the four C\-H stretches with coefficient 1/2\); 230 gives c\(S1\) = \(230/45\)^\(1/2\) 1\.008^\(1/2\) = 2\.270, 223 gives 2\.235\: the fitted 2\.260 lies between \(the fit uses all five molecules\)\.

ELECTRO\-OPTICAL PARAMETERS \(p\. 352\), from Eqs\. \(3\)\-\(6\) in the first\-order bond polarizability approximation\: '\|alpha'\_C\-H\| = 1\.130 \+\- 0\.021 A^2; \|gamma\_C\-H\| = 0\.279 \+\- 0\.030 A^3; \|gamma'\_C\-H\| = 2\.05 \+\- 0\.16 A^2; \|gamma'^\(alpha\)\_C\-H\| = 0\.18 \+\- 0\.13 A^2, which agree fairly well with those found by Yoshino and Bernstein'\. Eq\. \(3\)\: alpha'\_C\-H = \(1/3\)\|alpha\_l' \+ 2 alpha\_p'\| = \(1/2\)\(dalpha/dS1\)\_xx, the derivative of the mean bond polarizability with respect to the C\-H bond length \(1\.130 = 2\.260/2, checked\); Eq\. \(5\)\: gamma'\_C\-H = \|alpha\_l' \- alpha\_p'\| = \(3/2\)\(dalpha/dS3\)\_yz \(1\.366 x 3/2 = 2\.049, checked\)\. The datasets dalpha\_CH\_CH4 \(component mean\) and dgamma\_CH\_CH4 \(component anisotropy\) hold them per bond\. gamma\_C\-H \(a bond polarizability anisotropy, not per molecule\) and gamma'^\(alpha\) \(a derivative with respect to the bond angle; its sign is argued negative, p\. 352\) have no quantity\: notes only\. Sign\: 'alpha'\_C\-H must be positive' \(Yoshino and Bernstein\); no reason is found to choose the sign of gamma'\_C\-H \(p\. 352\)\.

FOR REVIEW \(solprop's CH4 1\.04e\-20 m^2, Murphy et al\.'s Table I, ref\. 17\)\: the same per\-bond mean derivative here is 1\.130 \+\- 0\.021 A^2 = 1\.130e\-20 m^2 \(8\.7 % higher\), from a laser measurement against the Rayleigh line; Murphy et al\.'s own four values are 1\.03 to 1\.08\.

ISOTOPE RULES \(Table III, p\. 351, printed as an equation block garbled in the library text\)\: the sum rules hold to 0\.96\-1\.05\. Not extracted\.

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

Datasets
--------

bermejo\_1977/shift\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "shift_CH4",
     "material": "CH4",
     "file": "CH4/bermejo_1977__shift_CH4.csv",
     "table": "tbl_602282e66a5e",
     "quantity": "raman_shift",
     "unit": "cm-1",
     "abscissa": "label",
     "use": "check",
     "excluded_rows": {
       "nu4 (f2)": "1310 cm-1 is not marked 'a: Our measurement' and its source is not stated"
     },
     "parameters": {
       "transition": "per row: the band of the row label (Raman band maximum)"
     }
   }

Table I \(p\. 348\), nu/cm\-1 of CH4's bands, measured here \(footnote a\)\: band maxima of room\-temperature gas spectra, not band origins\. nu3 is printed as two braced maxima \(3016\.7, 3021\.3\), both kept; 2nu2 is printed '~3071' \(approximate\)\.

bermejo\_1977/intensity\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "intensity_CH4",
     "material": "CH4",
     "file": "CH4/bermejo_1977__intensity_CH4.csv",
     "table": "tbl_602282e66a5e",
     "quantity": "raman_scattering_activity",
     "unit": "angstrom4/amu",
     "abscissa": "label",
     "use": "primary",
     "parameters": {
       "mode": "per row: nu1 (a1) C-H symmetric stretch, the 2nu2 overtone, nu2 (e), nu3 (f2)"
     }
   }

Table I \(p\. 348\), I = g\(45 alpha'^2 \+ 7 gamma'^2\) in N x 10^\-32 cm^4 g^\-1 \(N Avogadro's number\), exactly angstrom^4/amu; absolute, through CH4's nu1 against the Rayleigh line of CH4 \(p\. 348\), 488\.0 nm\. Each band on its own \(nu1 without 2nu2\)\. No uncertainty in Table I\: Table II's adopted values carry \+\- 12 \(nu1 with 2nu2\), 0\.4 \(nu2\) and 7 \(nu3\), about 5 %, level not stated\.

bermejo\_1977/intensity\_exp\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "intensity_exp_CH4",
     "material": "CH4",
     "file": "CH4/bermejo_1977__intensity_exp_CH4.csv",
     "table": "tbl_29036d066e28",
     "quantity": "raman_scattering_activity",
     "unit": "angstrom4/amu",
     "abscissa": "label",
     "use": "check",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "mode": "per row: nu1 (a1) with 2nu2 added, nu2 (e), nu3 (f2)"
     }
   }

Table II \(p\. 350\), I\_exp\: the adopted experimental intensities, the same measurement as Table I \(intensity\_CH4\) regrouped\: nu1's 230 includes the 2nu2 overtone's 7 \(footnote a\)\. The \+\- \(the sigma column\) has no stated level\.

bermejo\_1977/intensity\_calc\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "intensity_calc_CH4",
     "material": "CH4",
     "file": "CH4/bermejo_1977__intensity_calc_CH4.csv",
     "table": "tbl_29036d066e28",
     "quantity": "raman_scattering_activity",
     "unit": "angstrom4/amu",
     "abscissa": "label",
     "use": "check",
     "parameters": {
       "mode": "per row: nu1 (a1), nu2 (e), nu3 (f2)"
     }
   }

Table II \(p\. 350\), I\_calc\: recomputed from the four fitted alpha^S parameters \(a fit to all five isotopologues\), to compare with I\_exp\.

bermejo\_1977/intensity\_CH4\_nu1\_others
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "intensity_CH4_nu1_others",
     "material": "CH4",
     "table": "text",
     "quantity": "raman_scattering_activity",
     "unit": "angstrom4/amu",
     "abscissa": "label",
     "use": "reproduced",
     "reproduced_from": [
       "C. M. Penney, L. M. Goldman and M. Lapp, Nature (London) 235, 110 (1972)",
       "D. G. Fouche and P. K. Chang, Appl. Phys. Lett. 20, 7 (1972)"
     ],
     "parameters": {
       "mode": "nu1 (a1), the C-H symmetric stretch"
     }
   }

2 inline points in the source record.

p\. 349\: CH4 nu1's 223 is 'comparable, for instance, with 237 and 223, calculated from data published in Refs\. \(10\) and \(11\)' \(Penney et al\.; Fouche and Chang\)\: these authors' reductions of the cited laser cross sections to the scattering activity \(N x 10^\-32 cm^4 g^\-1 = angstrom^4/amu\)\.

bermejo\_1977/dS1\_CH4
~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dS1_CH4",
     "material": "CH4",
     "table": "text",
     "quantity": "polarizability_derivative",
     "unit": "angstrom2",
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "component": "mean",
       "mode": "nu1 (A1): the symmetry coordinate S1 (Mills 1960)",
       "coordinate": "S1, Mills's symmetry coordinate (the symmetric sum of the C-H stretches)"
     }
   }

1 inline points in the source record.

p\. 352\: \|c\(S1\)\| = 2\.260 \+\- 0\.042 A^2, the element alpha\_xx' = alpha\_yy' = alpha\_zz' of the derivative of the polarizability tensor \(volume, A^3\) with respect to Mills's symmetric\-stretch symmetry coordinate S1 \(A\)\: the mean\-polarizability derivative\. Isotope invariant, fitted to the 36 data of the five isotopologues; the sign is not determined by the fit \(positive by Yoshino and Bernstein's argument, p\. 352\)\. The \+\- level is not stated\. Excitation 488\.0 nm \(air\)\.

bermejo\_1977/dS\_aniso\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dS_aniso_CH4",
     "material": "CH4",
     "table": "text",
     "quantity": "polarizability_derivative",
     "unit": "angstrom2",
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "component": "anisotropy",
       "mode": "per row: S2 (E), S3 and S4 (F2) symmetry coordinates (Mills 1960)",
       "coordinate": "the symmetry coordinate of the row (Mills 1960)"
     }
   }

3 inline points in the source record.

p\. 352\: \|c\(S2\)\| = 0\.139 \+\- 0\.015, c\(S3\) = 1\.366 \+\- 0\.077, c\(S4\) = 0\.00 \+\- 0\.10 A^2, the one parameter of each traceless derivative tensor with respect to Mills's symmetry coordinates S2 \(E\), S3 and S4 \(F2\) \(the tensor forms, pp\. 345\-346\)\: anisotropic derivatives, tensor elements rather than the invariant gamma'\. 'Signs of c\(S3\) and c\(S4\) may be simultaneously changed'\. The \+\- level is not stated\.

bermejo\_1977/dalpha\_CH\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dalpha_CH_CH4",
     "material": "CH4",
     "table": "text",
     "quantity": "polarizability_derivative",
     "unit": "angstrom2",
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "component": "mean",
       "mode": "nu1 (A1), C-H stretch",
       "coordinate": "r_CH, the bond length (per bond)"
     }
   }

1 inline points in the source record.

p\. 352\: \|alpha'\_C\-H\| = 1\.130 \+\- 0\.021 A^2, the derivative of the mean C\-H bond polarizability with respect to the bond length, Eq\. \(3\), alpha'\_C\-H = \(1/3\)\|alpha\_l' \+ 2 alpha\_p'\| = \(1/2\)\(dalpha/dS1\)\_xx \(1\.130 = 2\.260/2\)\. The quantity Murphy et al\. tabulate as dalpha/dr \(murphy\_1969 dadr\_CH4\_nu1\: 1\.03\-1\.08\)\. The \+\- level is not stated\.

bermejo\_1977/dgamma\_CH\_CH4
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

.. code-block:: text

   {
     "id": "dgamma_CH_CH4",
     "material": "CH4",
     "table": "text",
     "quantity": "polarizability_derivative",
     "unit": "angstrom2",
     "abscissa_unit": "nm",
     "wavelength_medium": "standard_air",
     "use": "primary",
     "uncertainty": {
       "column": true,
       "level": "not stated"
     },
     "parameters": {
       "component": "anisotropy",
       "mode": "C-H stretch (from nu3, F2)",
       "coordinate": "r_CH, the bond length (per bond)"
     }
   }

1 inline points in the source record.

p\. 352\: \|gamma'\_C\-H\| = 2\.05 \+\- 0\.16 A^2, the derivative of the C\-H bond polarizability anisotropy \|alpha\_l' \- alpha\_p'\| with respect to the bond length, Eq\. \(5\) = \(3/2\)\(dalpha/dS3\)\_yz \(1\.366 x 1\.5 = 2\.049\)\. Sign not determined \(p\. 352\)\. The \+\- level is not stated\.

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.