shelton_1993 ============ D\. P\. Shelton and B\. Rugar, Chem\. Phys\. Lett\. 201, 364 \(1993\) `Source record `__ · :doc:`Catalogue ` · :doc:`Review register ` DOI: `10\.1016/0009\-2614\(93\)85084\-2 `__ **Source kind:** measurement **Recorded technique:** Absolute dc Kerr effect of H2 gas at 632\.8 nm \(He\-Ne laser\)\: a gas Kerr cell and a calibrated liquid Kerr cell between crossed polarizers, ac and dc voltages, lock\-in detection of the modulated retardation \(0\.1\-0\.7 urad\); stainless\-steel electrodes 456\.7 mm long, effective separation \^\-1/2 = 3\.195 \+\- 0\.007 mm; 99\.999 % H2 at 1300\-9900 Torr and 25\.1\-25\.4 C, all results adjusted to 25\.2 C with gamma\_eff^\-1 d gamma\_eff/dT ~ \-0\.11 %/C; density from pressure \(\+\-1 Torr\) and temperature \(\+\-0\.1 C\) with the virial equation of state; extrapolation to zero density \(pp\. 1\-3\)\. **Materials in structured entries:** H2 **Dataset quantities:** hyperpolarizability, polarizability\_anisotropy **Contents:** 11 datasets; 0 formulas. Curation notes -------------- Definitions \(p\. 2\)\: 'The quantity derived from the experimental measurements is gamma\_eff = 3 eps0 lambda\_0 phi / \(pi rho integral F^2 dz\)' \(Eq\. 1\), lambda\_0 the vacuum wavelength, phi the induced retardation, rho the number density, F the transverse static field along the beam; its zero\-density limit is gamma^evR = gamma^ev \+ gamma^R, with gamma^R = \(Delta alpha\_eff\)^2/5kT in the simple form \(p\. 1\) and Eq\. \(2\) in full \(Delta J = 0 M\-sublevel redistribution plus Delta J = \+\-2 virtual Raman terms, with centrifugal distortion, a resonance factor 1 \+ Delta \(Eq\. 5\) and the dispersion factor Q \(Eq\. 6\)\)\. This is the dc Kerr gamma\_K of Shelton & Rice's Taylor\-series convention \(shelton\_1994 reproduces 697 au as gamma^R for dc Kerr at 632\.8 nm, Table VIII\)\. The paper gives no Kerr constant B or K\: gamma\_eff is the reported quantity\. Units\: 1 au of gamma = 6\.235377e\-65 C^4 m^4 J^\-3, of alpha = 1\.648778e\-41 C^2 m^2 J^\-1, E/hc\: 1 au = 219474\.63 cm^\-1 \(Table 2 caption\); rotational constants B\_0 = 59\.3392 cm^\-1, D\_0 = 0\.04599 cm^\-1 \(ref\. \[17\], Weber 1979, curated as weber\_1979\: Table 3\.2 from Stoicheff 1957, where the H2 B\_0 is misprinted \[56\.3392\]; the erratum there cites this quotation\)\. Part separation\: by calculation, not by temperature dependence\: 'it should be sufficient to measure the Kerr effect for H2 at a single temperature and subtract the calculated value of gamma^R' \(p\. 1\), justified by Tammer & Huttner's temperature study\. The result depends on the gamma^R expression\: 718\.5 au with Eq\. \(2\), 730\.3 au with Tammer & Huttner's \(both recorded\)\. 'Either choice of gamma^R results in an experimental value of gamma^ev within 1% of the ab initio value, which indicates that the previously observed discrepancies between theory and experiment for the dc Kerr effect in H2 were due to systematic errors in the experiments' \(p\. 5\)\. Uncertainties \(pp\. 2\-3\)\: LKC calibration scatter \+\-0\.16 %, systematic \+\-0\.05 %; ac voltage \+\-0\.1 %; GKC/LKC signal ratio \+\-0\.2\-0\.5 % \(statistical\); geometrical calibration constant of the GKC \+\-0\.46 % \(the largest\); total systematic 0\.48 %, overall \+\-0\.51 % on gamma^evR\. The text writes the minimum electrode separation as '3\.171 nm' \(p\. 2\), evidently mm \(the average is 3\.195 mm\); not a value used here\. Table 2's anisotropies are reproduced ab initio values \(with the authors' interpolations\), recorded as polarizability\_anisotropy per rotational level\. **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\_1993/gamma\_evR ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_evR", "material": "H2", "file": "H2/shelton_1993__gamma_evR.csv", "table": "tbl_c405d96f0062", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "total", "temperature_k": 298.35 } } Table 1 row 'a\)' \(p\. 3\)\: the zero\-density limit of gamma\_eff, 'Extrapolated value from least\-squares fit in fig\. 1'\: gamma^evR = \(8\.827 \+\- 0\.045\) x 10^\-62 C^4 m^4 J^\-3 \(1415\.6 \+\- 7\.2 au\), at 25\.2 C and 632\.8 nm\. The uncertainty 'also includes the 0\.48% systematic uncertainty added in quadrature' \(caption\); '\+\-0\.51%' overall \(p\. 3\)\. This is the total dc Kerr hyperpolarizability, including the orientational gamma^R \(697\.1 au\) and the vibrational part\. shelton\_1993/gamma\_eff ~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_eff", "material": "H2", "file": "H2/shelton_1993__gamma_eff.csv", "table": "tbl_c405d96f0062", "quantity": "hyperpolarizability", "unit": "SI", "scale": 1e-62, "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "total", "temperature_k": 298.35 } } Table 1 \(p\. 3\)\: gamma\_eff = 3 eps0 lambda\_0 phi / \(pi rho integral F^2 dz\) \(Eq\. 1\) at finite density \(row\: rho in mol/m^3\), 25\.2 C, 632\.8 nm; 'The tabulated error bars include only the statistical uncertainties' \(the 0\.48 % systematic part excluded\)\. The weighted fit gamma\_eff = gamma^evR \(1 \+ A rho\) gives A = \(1\.2 \+\- 0\.4\) x 10^\-5 m^3/mol \(Fig\. 1 caption; 1\.4 \+\- 0\.1 from Tammer and Huttner's data\)\: 'The dielectric, refractive and Kerr virial coefficients all contribute to the coefficient A\.' Finite\-density values \(local field and pair effects included\)\: the zero\-density gamma\_evR is the molecular value\. shelton\_1993/gamma\_R ~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_R", "material": "H2", "table": "text", "quantity": "hyperpolarizability", "unit": "au", "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "rotational", "temperature_k": 298.35 } } 1 inline points in the source record. p\. 4\: 'The result obtained using eq\. \(2\) is gamma^R = 4\.347 x 10^\-62 C^4 m^4 J^\-3 \(697\.1 au\) at 25\.2 C' \(the orientational contribution for a gas of quantum rotors, Eqs 2\-6, with Table 2's anisotropies and B\_0 = 59\.3392, D\_0 = 0\.04599 cm^\-1, nuclear\-spin weights n\_J = 1, 3 for even, odd J\)\. 'The largest contributions \.\.\. are from the J = 0 and J = 1 rotational levels \(16% and 70%\), and there are about equal contributions to the total from the Delta J = 0 and Delta J = \+\-2 terms \(42% and 58%\); the rotational resonance term Delta is negligible, contributing only 0\.03%\.' Reproduced by shelton\_1994 Table VIII \(697\)\. shelton\_1993/gamma\_R\_tammer ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_R_tammer", "material": "H2", "table": "text", "quantity": "hyperpolarizability", "unit": "au", "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "check", "reproduced_from": [ "tammer_1990" ], "uncertainty": { "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "rotational", "temperature_k": 298.35 } } 1 inline points in the source record. p\. 4\: 'The result for gamma^R obtained using eq\. \(6\) of ref\. \[2\] instead is significantly different\: gamma^R = 685\.3 au\. This result for gamma^R is 2% smaller because the rotational transition frequencies are overestimated by 1% and because Delta alpha\_J,J is 1% smaller than Delta alpha\_J,J\+2 \(for J = 1\)\.' The authors' evaluation of the alternative expression \(Tammer and Huttner, Chem\. Phys\. 146, 155 \(1990\) = tammer\_1990, now in the library\)\: tammer\_1990 prints no gamma^R, only its orientation\-term expression \(Eqs\. 5\-7\) and the gamma it leaves \(Table 1\); reproduced\_from marks the expression's origin, not a copied number\. tammer\_1990's calibration was superseded by tammer\_1992 \(K, mK, A\_K x 1\.0637\), which does not change the orientation term\. shelton\_1993/gamma\_ev ~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_ev", "material": "H2", "table": "text", "quantity": "hyperpolarizability", "unit": "au", "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "primary", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic_vibrational", "temperature_k": 298.35 } } 1 inline points in the source record. p\. 4\: 'Subtracting gamma^R = 697\.1 au, calculated using eq\. \(2\), from the experimentally determined value for gamma^evR, gives gamma^ev = 718\.5 \+\- 7\.2 au'; abstract\: gamma^ev = \(4\.48 \+\- 0\.05\) x 10^\-62 C^4 m^4 J^\-3 \(719 \+\- 7 au\)\. Electronic plus vibrational dc Kerr gamma of H2 at 632\.8 nm and 25\.2 C \(the vibrational part is not separated here; shelton\_1994 Table VIII gives gamma^v\(dc Kerr, 632\.8 nm\) = \-7\.2 au from bishop\_1991\)\. 'The present best experimental estimate of gamma^ev, obtained using eq\. \(2\) for gamma^R, is significantly below the ab initio result' \(p\. 5\)\. shelton\_1993/gamma\_ev\_tammer ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_ev_tammer", "material": "H2", "table": "text", "quantity": "hyperpolarizability", "unit": "au", "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "check", "uncertainty": { "column": true, "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic_vibrational", "temperature_k": 298.35 } } 1 inline points in the source record. p\. 4\: 'If instead one subtracts gamma^R = 685\.3 au calculated using the expression in ref\. \[2\], one obtains gamma^ev = 730\.3 \+\- 7\.2 au, in somewhat better agreement with the ab initio result\.' shelton\_1993/gamma\_ev\_abinitio ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "gamma_ev_abinitio", "material": "H2", "table": "text", "quantity": "hyperpolarizability", "unit": "au", "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "bishop_1991" ], "uncertainty": { "level": "not stated" }, "parameters": { "process": "dc_kerr", "convention": "T", "part": "electronic_vibrational", "temperature_k": 298.35 } } 1 inline points in the source record. p\. 4\: 'the ab initio value gamma^ev = 726\.2 au from Bishop et al\. \[1\] \.\.\. thought to be accurate to better than 1%' \(bishop\_1991\), dc Kerr at 632\.8 nm\. shelton\_1993/anisotropy\_JJ\_static ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "anisotropy_JJ_static", "material": "H2", "file": "H2/shelton_1993__anisotropy_JJ_static.csv", "table": "tbl_84bb0efc5489", "quantity": "polarizability_anisotropy", "unit": "au", "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "R. J. LeRoy and C. Schwartz, U. Waterloo Chemical Physics Research Report CP-301R (1987)" ], "uncertainty": { "relative": 0.0001, "level": "not stated" }, "parameters": { "vibrational_state_v": 0, "transition": "J,J" } } Table 2 \(p\. 4\)\: 'ab initio values of Delta alpha\_JJ'^\(omega\) for H2, in the static limit and for lambda = 632\.8 nm \.\.\. either transcribed or interpolated from tabulated values in refs\. \[14,16\] which have an estimated accuracy of 0\.01%' \(1 au = 1\.648778e\-41 C^2 m^2 J^\-1\)\. Row = the rotational level J of the ground vibrational state\. Delta alpha\_JJ^\(0\), static, 'From ref\. \[14\]' \(LeRoy & Schwartz 1987\) \(note a\)\. v = 0 matrix elements \; each row is a different rotational level \(not a dispersion series\)\. shelton\_1993/anisotropy\_JJ\_632nm ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "anisotropy_JJ_632nm", "material": "H2", "file": "H2/shelton_1993__anisotropy_JJ_632nm.csv", "table": "tbl_84bb0efc5489", "quantity": "polarizability_anisotropy", "unit": "au", "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "R. J. LeRoy and C. Schwartz, U. Waterloo Chemical Physics Research Report CP-301R (1987)", "D. M. Bishop and L. M. Cheung, J. Chem. Phys. 72, 5125 (1980)" ], "uncertainty": { "relative": 0.0001, "level": "not stated" }, "parameters": { "vibrational_state_v": 0, "transition": "J,J" } } Table 2 \(p\. 4\)\: 'ab initio values of Delta alpha\_JJ'^\(omega\) for H2, in the static limit and for lambda = 632\.8 nm \.\.\. either transcribed or interpolated from tabulated values in refs\. \[14,16\] which have an estimated accuracy of 0\.01%' \(1 au = 1\.648778e\-41 C^2 m^2 J^\-1\)\. Row = the rotational level J of the ground vibrational state\. Delta alpha\_JJ^\(omega\) at 632\.8 nm\: 'Interpolation of results in ref\. \[14\] using dispersion function from results in table VI of ref\. \[15\]' \(note b; Bishop & Cheung 1980\); J = 5, 6 marked e\) 'Interpolation of results in ref\. \[14\]'\. v = 0 matrix elements \; each row is a different rotational level \(not a dispersion series\)\. shelton\_1993/anisotropy\_JJ2\_static ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "anisotropy_JJ2_static", "material": "H2", "file": "H2/shelton_1993__anisotropy_JJ2_static.csv", "table": "tbl_84bb0efc5489", "quantity": "polarizability_anisotropy", "unit": "au", "abscissa_unit": "nm", "use": "reproduced", "reproduced_from": [ "D. M. Bishop and J. Pipin, J. Chem. Phys. 94, 6073 (1991)" ], "uncertainty": { "relative": 0.0001, "level": "not stated" }, "parameters": { "vibrational_state_v": 0, "transition": "J,J+2" } } Table 2 \(p\. 4\)\: 'ab initio values of Delta alpha\_JJ'^\(omega\) for H2, in the static limit and for lambda = 632\.8 nm \.\.\. either transcribed or interpolated from tabulated values in refs\. \[14,16\] which have an estimated accuracy of 0\.01%' \(1 au = 1\.648778e\-41 C^2 m^2 J^\-1\)\. Row = the rotational level J of the ground vibrational state\. Delta alpha\_J,J\+2^\(0\), static transition anisotropy for J \-\> J\+2\: 'From table X of ref\. \[16\]' \(Bishop & Pipin, J\. Chem\. Phys\. 94, 6073 \(1991\)\) \(note c\)\. v = 0 matrix elements \; each row is a different rotational level \(not a dispersion series\)\. shelton\_1993/anisotropy\_JJ2\_632nm ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. code-block:: text { "id": "anisotropy_JJ2_632nm", "material": "H2", "file": "H2/shelton_1993__anisotropy_JJ2_632nm.csv", "table": "tbl_84bb0efc5489", "quantity": "polarizability_anisotropy", "unit": "au", "abscissa_unit": "nm", "wavelength_medium": "standard_air", "use": "reproduced", "reproduced_from": [ "D. M. Bishop and J. Pipin, J. Chem. Phys. 94, 6073 (1991)" ], "uncertainty": { "relative": 0.0001, "level": "not stated" }, "parameters": { "vibrational_state_v": 0, "transition": "J,J+2" } } Table 2 \(p\. 4\)\: 'ab initio values of Delta alpha\_JJ'^\(omega\) for H2, in the static limit and for lambda = 632\.8 nm \.\.\. either transcribed or interpolated from tabulated values in refs\. \[14,16\] which have an estimated accuracy of 0\.01%' \(1 au = 1\.648778e\-41 C^2 m^2 J^\-1\)\. Row = the rotational level J of the ground vibrational state\. Delta alpha\_J,J\+2^\(omega\) at 632\.8 nm\: 'Interpolation of results in table X of ref\. \[16\]' \(note d\)\. v = 0 matrix elements \; each row is a different rotational level \(not a dispersion series\)\. 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.