shelton_1988 ============ D\. P\. Shelton and L\. Ulivi, J\. Chem\. Phys\. 89, 149 \(1988\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1063/1\.455497 `__ **Source kind:** theory **Recorded technique:** Perturbation\-theory expressions \(from Orr & Ward's sum over states, Eq\. 1\) for the vibrational second hyperpolarizability of a spherical\-top \(Td or Oh\) molecule in the static limit and for the dc Kerr effect, ESHG and THG \(Eqs\. 5\-8\), evaluated for SF6 with infrared transition dipoles from the literature \(Kim, McDowell & King 1980; Person & Overend 1977\), Raman transition polarizabilities from the authors' own Raman cross\-section measurements \(514\.5 nm, 1 W, 22 C, 2\-10 atm, calibrated on H2 rotational lines\), and an estimated hyper\-Raman beta for nu\_3 \(pp\. 149\-153\)\. **Materials in structured entries:** SF6 **Dataset quantities:** hyperpolarizability **Contents:** 8 datasets; 0 formulas. Curation notes -------------- Shelton & Rice 1994 cite this paper as ref 130 \(Shelton, D\. P\.; Ulivi, L\.\)\. Definitions\: gamma\(\-omega\_s; omega\_1, omega\_2, omega\_3\) of Orr & Ward \(Eq\. 1\); the observables are the isotropic averages \\_XXXX = \(1/15\)\(gamma\_aabb \+ gamma\_abab \+ gamma\_abba\) and, for the dc Kerr effect, \(3/2\)\(\\_XXXX \- \\_XYYX\), \\_XYYX = \(1/30\)\(\-gamma\_aabb \- gamma\_abab \+ 4 gamma\_abba\) \(Eqs\. 4a, 4b\), the same gamma as Shelton's ESHG papers \(Taylor\-series convention, SI units C^4 m^4 J^\-3\)\. The vibrational part is 'the sum of all those terms for which at least one of the intermediate states is a vibrationally excited state in the ground electronic manifold' \(p\. 149\)\. The expressions correct the earlier CF4 treatment \(lu\_1987\)\: 'That work is in agreement with the present work except for Eqs\. \(18\) and \(23\), which are incorrect by factors of 2 and 3' \(p\. 150\); CF4's beta is 2x the value reported there\. Rough experimental check \(p\. 155, rounded values quoted from the literature, not extracted\)\: gamma\_Kerr = 15e\-62 C^4 m^4 J^\-3 at 632\.8 nm \(Buckingham & Dunmur 1968 = buckingham\_1968\), gamma\_ESHG = 10e\-62 at 632\.8 nm \(shelton\_1985\_sf6; Ward & Miller 1979\), gamma\_THG = 11e\-62 at 694\.3 nm \(Ward & Elliott 1984\); observed gamma\_Kerr \- gamma\_ESHG = 5e\-62 against the calculated gamma^v difference 5\.6e\-62, and gamma\_THG \- gamma\_ESHG = 1e\-62 against 2\.4e\-62 \('about as good as can be expected', accuracy \+\-1e\-62\)\. The Table III caption gives the measured ESHG gamma = gamma^e \+ gamma^v at nu = 20000 cm^\-1 as 11e\-62\. Not extracted \(no matching quantity; kept here for the record\)\: Table I, Raman scattering cross sections of 15 SF6 bands \(and Holzer & Ouillon's\), hot\-band factors F and {\(a\_gm\)^2 \+ 7/45 \(Delta alpha\_gm\)^2}^\(1/2\); Table II, transition dipoles and polarizability matrix elements \(e\.g\. nu\_3 948 cm^\-1, \|mu^x\| = 146e\-32 C m; nu\_4 615 cm^\-1, 42e\-32 C m; nu\_1 775 cm^\-1, \|a\| = 11\.6e\-42 C^2 m^2 J^\-1; nu\_2 643 cm^\-1, \|alpha^xx \- alpha^yy\| = 14\.0e\-42; nu\_5 524 cm^\-1, \|alpha^xy\| = 4\.60e\-42\) and the ground\-state a\_gg = 500e\-42 C^2 m^2 J^\-1 with nu\_eg = 167 000 cm^\-1 'derived from refractive index data' \(Bogaard & Orr; Landolt\-Bornstein; reproduced\)\. The H2 rotational transition anisotropies used for calibration, \(alpha\_par \- alpha\_perp\)\_J,J\+2 = 35\.19 and 35\.46e\-42 C^2 m^2 J^\-1 for S\(0\) and S\(1\) at 514\.5 nm \(p\. 152\), are values 'deduced by considering' three ab initio calculations\: not extracted \(the H2 anisotropies are in shelton\_1993\)\. The library notes two unmatched figure captions \(the publisher's cover page\); the table cells agree with the images\. Figure 1 \(gamma^v against frequency\) is not digitised\. **Recorded bibliographic identity status:** VALIDATED\_WITH\_WARNINGS. This concerns identification of the source; it does not establish the scientific correctness of its contents. Datasets -------- shelton\_1988/gammav\_static ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gammav_static", "material": "SF6", "file": "SF6/shelton_1988__gammav_static.csv", "table": "tbl_5ed5e11e4508", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "nm", "use": "primary", "uncertainty": { "level": "not stated" }, "parameters": { "process": "static", "convention": "T", "part": "vibrational" } } Table III \(p\. 154\)\: vibrational contributions to the isotropically averaged gamma of SF6 'in the static limit and for the dc Kerr effect, ESHG, and THG, evaluated at the optical frequency nu = 20000 cm^\-1 using Eqs\. \(5\)\-\(8\)', in 1e\-62 C^4 m^4 J^\-3 \(unit SI, scale 1e\-62\), for molecules in the ground vibrational state \('we will assume for simplicity that all the molecules are in the ground vibrational state, even though this is not the case at room temperature'; the room\-temperature gamma^v 'may be substantially larger', p\. 152\)\. dc Kerr\: the observable \(3/2\)\(\\_XXXX \- \\_XYYX\); the others \\_XXXX\. Row 'total'\. 'The expected uncertainty ranges from a few percent at best to perhaps a factor of 2 at worst' \(mu^4 and alpha^2 terms accurate, mu^2 alpha \+ mu alpha mu less reliable, mu beta possibly poor\: beta of the nu\_3 transition is an educated guess, 3e\-52 C^3 m^3 J^\-2\) \(p\. 154\)\. 'gamma^v\_static is more than 20x the estimated value of gamma^e\_static' \(p\. 154\), dominated by the mu^4 terms; in the molecular frame gamma^v\_xyyx ~ 10 gamma^v\_xxxx in the static limit\. The printed total 239\.4 against the sum of the printed terms 239\.3 \(rounding\)\. shelton\_1988/gammav\_dc\_kerr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gammav_dc_kerr", "material": "SF6", "file": "SF6/shelton_1988__gammav_dc_kerr.csv", "table": "tbl_5ed5e11e4508", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "cm-1", "use": "primary", "uncertainty": { "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "vibrational" } } Table III \(p\. 154\)\: vibrational contributions to the isotropically averaged gamma of SF6 'in the static limit and for the dc Kerr effect, ESHG, and THG, evaluated at the optical frequency nu = 20000 cm^\-1 using Eqs\. \(5\)\-\(8\)', in 1e\-62 C^4 m^4 J^\-3 \(unit SI, scale 1e\-62\), for molecules in the ground vibrational state \('we will assume for simplicity that all the molecules are in the ground vibrational state, even though this is not the case at room temperature'; the room\-temperature gamma^v 'may be substantially larger', p\. 152\)\. dc Kerr\: the observable \(3/2\)\(\\_XXXX \- \\_XYYX\); the others \\_XXXX\. Row 'total'\. 'The expected uncertainty ranges from a few percent at best to perhaps a factor of 2 at worst' \(mu^4 and alpha^2 terms accurate, mu^2 alpha \+ mu alpha mu less reliable, mu beta possibly poor\: beta of the nu\_3 transition is an educated guess, 3e\-52 C^3 m^3 J^\-2\) \(p\. 154\)\. The four terms cancel\: 3\.6 \- 10\.4 \+ 5\.6 \+ 1\.5 = 0\.3\. gamma^v\_Kerr depends strongly on frequency \(Fig\. 1, not digitised\)\. shelton\_1988/gammav\_eshg ~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gammav_eshg", "material": "SF6", "file": "SF6/shelton_1988__gammav_eshg.csv", "table": "tbl_5ed5e11e4508", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "cm-1", "use": "primary", "uncertainty": { "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "vibrational" } } Table III \(p\. 154\)\: vibrational contributions to the isotropically averaged gamma of SF6 'in the static limit and for the dc Kerr effect, ESHG, and THG, evaluated at the optical frequency nu = 20000 cm^\-1 using Eqs\. \(5\)\-\(8\)', in 1e\-62 C^4 m^4 J^\-3 \(unit SI, scale 1e\-62\), for molecules in the ground vibrational state \('we will assume for simplicity that all the molecules are in the ground vibrational state, even though this is not the case at room temperature'; the room\-temperature gamma^v 'may be substantially larger', p\. 152\)\. dc Kerr\: the observable \(3/2\)\(\\_XXXX \- \\_XYYX\); the others \\_XXXX\. Row 'total'\. 'The expected uncertainty ranges from a few percent at best to perhaps a factor of 2 at worst' \(mu^4 and alpha^2 terms accurate, mu^2 alpha \+ mu alpha mu less reliable, mu beta possibly poor\: beta of the nu\_3 transition is an educated guess, 3e\-52 C^3 m^3 J^\-2\) \(p\. 154\)\. shelton\_1988/gammav\_thg ~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gammav_thg", "material": "SF6", "file": "SF6/shelton_1988__gammav_thg.csv", "table": "tbl_5ed5e11e4508", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "cm-1", "use": "primary", "uncertainty": { "level": "not stated" }, "parameters": { "process": "thg", "convention": "T", "part": "vibrational" } } Table III \(p\. 154\)\: vibrational contributions to the isotropically averaged gamma of SF6 'in the static limit and for the dc Kerr effect, ESHG, and THG, evaluated at the optical frequency nu = 20000 cm^\-1 using Eqs\. \(5\)\-\(8\)', in 1e\-62 C^4 m^4 J^\-3 \(unit SI, scale 1e\-62\), for molecules in the ground vibrational state \('we will assume for simplicity that all the molecules are in the ground vibrational state, even though this is not the case at room temperature'; the room\-temperature gamma^v 'may be substantially larger', p\. 152\)\. dc Kerr\: the observable \(3/2\)\(\\_XXXX \- \\_XYYX\); the others \\_XXXX\. Row 'total'\. 'The expected uncertainty ranges from a few percent at best to perhaps a factor of 2 at worst' \(mu^4 and alpha^2 terms accurate, mu^2 alpha \+ mu alpha mu less reliable, mu beta possibly poor\: beta of the nu\_3 transition is an educated guess, 3e\-52 C^3 m^3 J^\-2\) \(p\. 154\)\. shelton\_1988/gammav\_terms\_static ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gammav_terms_static", "material": "SF6", "file": "SF6/shelton_1988__gammav_terms_static.csv", "table": "tbl_5ed5e11e4508", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "nm", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "process": "static", "convention": "T", "part": "vibrational" } } Table III \(p\. 154\)\: vibrational contributions to the isotropically averaged gamma of SF6 'in the static limit and for the dc Kerr effect, ESHG, and THG, evaluated at the optical frequency nu = 20000 cm^\-1 using Eqs\. \(5\)\-\(8\)', in 1e\-62 C^4 m^4 J^\-3 \(unit SI, scale 1e\-62\), for molecules in the ground vibrational state \('we will assume for simplicity that all the molecules are in the ground vibrational state, even though this is not the case at room temperature'; the room\-temperature gamma^v 'may be substantially larger', p\. 152\)\. dc Kerr\: the observable \(3/2\)\(\\_XXXX \- \\_XYYX\); the others \\_XXXX\. The four terms \(parts a\-d of Eqs\. 5\-8\), rows mu^4, mu^2 alpha \+ mu alpha mu, mu beta, alpha^2; they sum to gammav\_static \(not independent values\)\. Cells printed with their own power of ten are kept in E notation\. 'The expected uncertainty ranges from a few percent at best to perhaps a factor of 2 at worst' \(mu^4 and alpha^2 terms accurate, mu^2 alpha \+ mu alpha mu less reliable, mu beta possibly poor\: beta of the nu\_3 transition is an educated guess, 3e\-52 C^3 m^3 J^\-2\) \(p\. 154\)\. shelton\_1988/gammav\_terms\_dc\_kerr ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gammav_terms_dc_kerr", "material": "SF6", "file": "SF6/shelton_1988__gammav_terms_dc_kerr.csv", "table": "tbl_5ed5e11e4508", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "cm-1", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "vibrational" } } Table III \(p\. 154\)\: vibrational contributions to the isotropically averaged gamma of SF6 'in the static limit and for the dc Kerr effect, ESHG, and THG, evaluated at the optical frequency nu = 20000 cm^\-1 using Eqs\. \(5\)\-\(8\)', in 1e\-62 C^4 m^4 J^\-3 \(unit SI, scale 1e\-62\), for molecules in the ground vibrational state \('we will assume for simplicity that all the molecules are in the ground vibrational state, even though this is not the case at room temperature'; the room\-temperature gamma^v 'may be substantially larger', p\. 152\)\. dc Kerr\: the observable \(3/2\)\(\\_XXXX \- \\_XYYX\); the others \\_XXXX\. The four terms \(parts a\-d of Eqs\. 5\-8\), rows mu^4, mu^2 alpha \+ mu alpha mu, mu beta, alpha^2; they sum to gammav\_dc\_kerr \(not independent values\)\. Cells printed with their own power of ten are kept in E notation\. 'The expected uncertainty ranges from a few percent at best to perhaps a factor of 2 at worst' \(mu^4 and alpha^2 terms accurate, mu^2 alpha \+ mu alpha mu less reliable, mu beta possibly poor\: beta of the nu\_3 transition is an educated guess, 3e\-52 C^3 m^3 J^\-2\) \(p\. 154\)\. shelton\_1988/gammav\_terms\_eshg ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gammav_terms_eshg", "material": "SF6", "file": "SF6/shelton_1988__gammav_terms_eshg.csv", "table": "tbl_5ed5e11e4508", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "cm-1", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "process": "eshg", "convention": "T", "part": "vibrational" } } Table III \(p\. 154\)\: vibrational contributions to the isotropically averaged gamma of SF6 'in the static limit and for the dc Kerr effect, ESHG, and THG, evaluated at the optical frequency nu = 20000 cm^\-1 using Eqs\. \(5\)\-\(8\)', in 1e\-62 C^4 m^4 J^\-3 \(unit SI, scale 1e\-62\), for molecules in the ground vibrational state \('we will assume for simplicity that all the molecules are in the ground vibrational state, even though this is not the case at room temperature'; the room\-temperature gamma^v 'may be substantially larger', p\. 152\)\. dc Kerr\: the observable \(3/2\)\(\\_XXXX \- \\_XYYX\); the others \\_XXXX\. The four terms \(parts a\-d of Eqs\. 5\-8\), rows mu^4, mu^2 alpha \+ mu alpha mu, mu beta, alpha^2; they sum to gammav\_eshg \(not independent values\)\. Cells printed with their own power of ten are kept in E notation\. 'The expected uncertainty ranges from a few percent at best to perhaps a factor of 2 at worst' \(mu^4 and alpha^2 terms accurate, mu^2 alpha \+ mu alpha mu less reliable, mu beta possibly poor\: beta of the nu\_3 transition is an educated guess, 3e\-52 C^3 m^3 J^\-2\) \(p\. 154\)\. shelton\_1988/gammav\_terms\_thg ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gammav_terms_thg", "material": "SF6", "file": "SF6/shelton_1988__gammav_terms_thg.csv", "table": "tbl_5ed5e11e4508", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "cm-1", "use": "check", "uncertainty": { "level": "not stated" }, "parameters": { "process": "thg", "convention": "T", "part": "vibrational" } } Table III \(p\. 154\)\: vibrational contributions to the isotropically averaged gamma of SF6 'in the static limit and for the dc Kerr effect, ESHG, and THG, evaluated at the optical frequency nu = 20000 cm^\-1 using Eqs\. \(5\)\-\(8\)', in 1e\-62 C^4 m^4 J^\-3 \(unit SI, scale 1e\-62\), for molecules in the ground vibrational state \('we will assume for simplicity that all the molecules are in the ground vibrational state, even though this is not the case at room temperature'; the room\-temperature gamma^v 'may be substantially larger', p\. 152\)\. dc Kerr\: the observable \(3/2\)\(\\_XXXX \- \\_XYYX\); the others \\_XXXX\. The four terms \(parts a\-d of Eqs\. 5\-8\), rows mu^4, mu^2 alpha \+ mu alpha mu, mu beta, alpha^2; they sum to gammav\_thg \(not independent values\)\. Cells printed with their own power of ten are kept in E notation\. 'The expected uncertainty ranges from a few percent at best to perhaps a factor of 2 at worst' \(mu^4 and alpha^2 terms accurate, mu^2 alpha \+ mu alpha mu less reliable, mu beta possibly poor\: beta of the nu\_3 transition is an educated guess, 3e\-52 C^3 m^3 J^\-2\) \(p\. 154\)\. 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 ` for the checks and decisions.