On the proper use of the Bigeleisen-Mayer equation and corrections to it in the calculation of isotopic fractionation equilibrium constants

Geochimica et Cosmochimica Acta

Volumn 74, Issue 24, 2010, Pages 6965-6983

  Liu, Qi ^a   Tossell, John A ^b,c   Liu, Yun ^a  

^a INSTITUTE OF GEOCHEMISTRY   (China)

^b GEORGE WASHINGTON UNIVERSITY   (United States)

^c University of Maryland   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EQUATION; ERROR ANALYSIS; GEOCHEMISTRY; ISOTOPIC FRACTIONATION; STABLE ISOTOPE;

EID: 78650173594     PISSN: 00167037     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.gca.2010.09.014     Document Type: Article

References (91)

1. Anbar A.D., Jarzecki A.A., Spiro T.G. Theoretical investigation of iron isotope fractionation between Fe(H2O)63+ and Fe(H2O)62+: implications for iron stable isotope geochemistry. Geochim. Cosmochim. Acta 2005, 69:825-837.
2. Barone V. Vibrational zero-point energies and thermodynamic functions beyond the harmonic approximation. J. Chem. Phys. 2004, 120:3059-3065.
3. Barone V. Anharmonic vibrational properties by a fully automated second-order perturbative approach. J. Chem. Phys. 2005, 122:014108.
4. Benedict W.S., Gailar N., Plyler E.K. Rotation-vibration spectra of deuterated water vapor. J. Chem. Phys. 1956, 24:1139-1165.
5. Bigeleisen J. Chemistry of isotopes. Science 1965, 147:463-471.
6. Bigeleisen J. Nuclear size and shape effects in chemical reactions. Isotope chemistry of the heavy elements. J. Am. Chem. Soc. 1996, 118:3676-3680.
7. Bigeleisen J., Mayer M.G. Calculation of equilibrium constants for isotopic exchange reactions. J. Chem. Phys. 1947, 15:261-267.
8. 3. Z. Naturforsch. 1973, 28a:129-136.
9. Carbonniere P., Barone V. Performances of different density functionals in the computation of vibrational spectra beyond the harmonic approximation. Chem. Phys. Lett. 2004, 399:226-229.
10. Chacko T., Cole D.R., Horita J. Equilibrium oxygen, hydrogen and carbon isotope fractionation factors applicable to geologic systems. Rev. Mineral. Geochem. 2001, 43:1-81.
11. Cramer C.J. Essentials of Computational Chemistry: Theories and Models 2002, Wiley, New York.
12. Criss R.E. Temperature dependence of isotopic fractionation factors. Stable Isotope Geochemistry: A Tribute to Samuel Epstein 1991, vol. 3:11-16. Geochem. Soc. Spec. Pub., San Antonio, Texas.
13. Criss R.E. Principles of Stable Isotope Distribution 1999, Oxford University Press, New York.
14. Darling B.T., Dennison D.M. The water vapor molecule. Phys. Rev. 1940, 57:128-139.
15. Domagal-Goldman S.D., Kubicki J.D. Density functional theory predictions of equilibrium isotope fractionation of iron due to redox changes and organic complexation. Geochim. Cosmochim. Acta 2008, 72:5201-5216.
16. Domagal-Goldman S.D., Paul K.W., Sparks D.L., Kubicki J.D. Quantum chemical study of the Fe(III)-desferrioxamine B siderophore complex - electronic structure, vibrational frequencies, and equilibrium Fe-isotope fractionation. Geochim. Cosmochim. Acta 2009, 73:1-12.
17. Driesner T., Seward T.M. Experimental and simulation study of salt effects and pressure/density effects on oxygen and hydrogen stable isotope liquid-vapor fractionation for 4-5 molal aqueous NaCl and KCl solutions to 400°C. Geochim. Cosmochim. Acta 2000, 64:1773-1784.
18. Ellingson B.A., Lynch V.A., Mielke S.L., Truhlar D.G. Statistical thermodynamics of bond torsional modes: tests of separable, almost-separable, and improved Pitzer-Gwinn approximations. J. Chem. Phys. 2006, 125:084305.
19. 13C kinetic isotope effect with emphasis on the effects of coordinate system and torsional treatment. J. Phys. Chem. A 2007, 111:11706-11717.
20. Friedman L., Shiner V.J. Experimental determination of disproportionation of hydrogen isotopes in water. J. Chem. Phys. 1966, 44:4639-4640.
21. Frisch M.J., Trucks G.W., Schlegel H.B., Scuseria G.E., Robb M.A., Cheeseman J.R., Montgomery J.A., Vreven T., Kudin K.N., Burant J.C., Millam J.M., Iyengar S.S., Tomasi J., Barone V., Mennucci B., Cossi M., Scalmani G., Rega N., Petersson G.A., Nakatsuji H., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Klene M., Li X., Knox J.E., Hratchian H.P., Cross J.B., Adamo C., Jaramillo J., Gomperts R., Stratmann R.E., Yazyev O., Austin A.J., Cammi R., Pomelli C., Ochterski J.W., Ayala P.Y., Morokuma K., Voth G.A., Salvador P., Dannenberg J.J., Zakrzewski V.G., Dapprich S., Daniels A.D., Strain M.C., Farkas O., Malick D.K., Rabuck A.D., Raghavachari K., Foresman J.B., Ortiz J.V., Cui Q., Baboul A.G., Clifford S., Cioslowski J., Stefanov B.B., Liu G., Liashenko A., Piskorz P., Komaromi I., Martin R.L., Fox D.J., Keith T., Al-Laham M.A., Peng C.Y., Nanayakkara A., Challacombe M., Gill P.M.W., Johnson B., Chen W., Wong M.W., Gonzalez C., Pople J.A. Gaussian 03 (Revision E.01) 2004, Gaussian, Inc., Wallingford, CT.
22. Goodson D.Z., Sarpal S.K., Bopp P., Wolfsberg M. Influence on isotope effect calculations of the method of obtaining force constants from vibrational data. J. Phys. Chem. 1982, 86:659-663.
23. Grev R.S., Janssen C.L., Schaefer H.F. Concerning zero-point vibrational energy corrections to electronic energies. J. Chem. Phys. 1991, 95:5128-5132.
24. Harris N.J. A systematic theoretical-study of harmonic vibrational frequencies and deuterium-isotope fractionation factors for small molecules. J. Phys. Chem. 1995, 99:14689-14699.
25. 2O⇔2 HDO isotopic equilibrium. J. Chem. Phys. 1969, 50:1483-1484.
26. Jarzecki A.A., Anbar A.D., Spiro T.G. DFT analysis of Fe(H2O)63+ and Fe(H2O)62+ structure and vibrations; implications for isotope fractionation. J. Phys. Chem. A 2004, 108:2726-2732.
27. Khachkuruzov G.A. Vibration constants for isotopic varieties of molecular water. Trudy Gosudart. Inst. Priklad. Khim. 1959, 42:109-130.
28. Kivelson D., Wilson E.B. Approximate treatment of the effect of centrifugal distortion on the rotational energy levels of asymmetric-rotor molecules. J. Chem. Phys. 1952, 20:1575-1579.
29. Klochko K., Kaufman A.J., Yao W.S., Byrne R.H., Tossell J.A. Experimental measurement of boron isotope fractionation in seawater. Earth Planet. Sci. Lett. 2006, 248:276-285.
30. Knyazev V.D. Density of states of one-dimensional hindered internal rotors and separability of rotational degrees of freedom. J. Phys. Chem. A 1998, 102:3916-3922.
31. Knyazev V.D. Comment on " Hindered rotor density-of-states interpolation function" [J. Chem. Phys. 106, 6675 (1997)] and " The hindered rotor density-of-states" [J. Chem. Phys. 108, 1748 (1998)]. J. Chem. Phys. 1999, 111:7161-7162.
32. Koput J., Carter S., Handy N.C. Ab initio prediction of the vibrational-rotational energy levels of hydrogen peroxide and its isotopomers. J. Chem. Phys. 2001, 115:8345-8350.
33. Li X., Zhao H., Tang M., Liu Y. Theoretical prediction for several important equilibrium Ge isotope fractionation factors and geological implications. Earth Planet. Sci. Lett. 2009, 287:1-11.
34. Lindemann F.A. Note on the vapour pressure and affinity of isotopes. Philos. Mag. 1919, 38:173-181.
35. Lindemann F.A., Aston F.W. The possibility of separating isotopes. Philos. Mag. 1919, 37:523-534.
36. Liu Y., Tossell J.A. Ab initio molecular orbital calculations for boron isotope fractionations on boric acids and borates. Geochim. Cosmochim. Acta 2005, 69:3995-4006.
37. Lynch V.A., Mielke S.L., Truhlar D.G. High-precision quantum thermochemistry on nonquasiharmonic potentials: converged path-integral free energies and a systematically convergent family of generalized Pitzer-Gwinn approximations. J. Phys. Chem. A 2005, 109:10092-10099.
38. Møller C., Plesset M.S. Note on an approximation treatment for many-electron systems. Phys. Rev. 1934, 46:618-622.
39. McClurg R.B., Flagan R.C., Goddard W.A. The hindered rotor density-of-states interpolation function. J. Chem. Phys. 1997, 106:6675-6680.
40. McQuarrie D.A., Simon J.D. Molecular Thermodynamics 1999, University Science Books Press, Sausalito, California.
41. Merrick J.P., Moran D., Radom L. An evaluation of harmonic vibrational frequency scale factors. J. Phys. Chem. A 2007, 111:11683-11700.
42. Nielsen H.H. The vibration-rotation energies of molecules. Rev. Mod. Phys. 1951, 23:90-136.
43. O'Neil J.R. Theoretical and experimental aspects of isotopic fractionation. Rev. Mineral. 1986, 16:1-40.
44. Oi T. Ab initio molecular orbital calculations of reduced partition function ratios of polyboric acids and polyborate anions. Z. Naturforsch. 2000, 55a:623-628.
45. Oi T., Yanase S. Calculations of reduced partition function ratios of hydrated monoborate anion by the ab initio molecular orbital theory. J. Nucl. Sci. Technol. 2001, 38:429-432.
46. Otake T., Lasaga A.C., Ohmoto H. Ab initio calculations for equilibrium fractionations in multiple sulfur isotope systems. Chem. Geol. 2008, 249:357-376.
47. Pennington R.E., Kobe K.A. Contributions of vibrational anharmonicity and rotation-vibration interaction to thermodynamic functions. J. Chem. Phys. 1954, 22:1442-1447.
48. Pitzer K.S., Gwinn W.D. Energy levels and thermodynamic functions for molecules with internal rotation. I: Rigid frame with attached tops. J. Chem. Phys. 1942, 10:428-440.
49. Polyakov V.B. On anharmonic and pressure corrections to the equilibrium isotopic constants for minerals. Geochim. Cosmochim. Acta 1998, 62:3077-3085.
50. Polyakov V.B., Kharlashina N.N. Effect of pressure on equilibrium isotopic fractionation. Geochim. Cosmochim. Acta 1994, 58:4739-4750.
51. Pyper J.W., Christensen L.D. Equilibrium constants of hydrogen-deuterium-tritium self-exchange reactions in water vapor as studied with a pulsed molecular-beam quadrupole mass filter. J. Chem. Phys. 1975, 62:2596-2599.
52. Pyper J.W., Newbury R.S. Hydrogen-deuterium self-exchange in hydrogen sulfide and hydrogen selenide as studied with a pulsed-molecular-beam quadrupole mass filter. J. Chem. Phys. 1970, 52:1966-1971.
53. Pyper J.W., Newbury R.S., Barton G.W. Study of isotopic disproportionation reaction between light and heavy water using a pulsed-molecular-beam mass spectrometer. J. Chem. Phys. 1967, 46:2253-2257.
54. Redlich O. Eine allgemeine beziehung zwischen den schwingungsfrequenzen isotoper molekeln. Z. Phys. Chem. B 1935, 28:371-382.
55. Richet P., Bottinga Y., Javoy M. A review of hydrogen, carbon, nitrogen, oxygen, sulphur, and chlorine stable isotope fractionation among gaseous molecules. Ann. Rev. Earth Planet. Sci. 1977, 5:65-110.
56. 3(aq) and B(OH)4-(aq). J. Am. Chem. Soc. 2007, 129:2222-2223.
57. Rustad J.R., Zarzycki P. Calculation of site-specific carbon-isotope fractionation in pedogenic oxide minerals. Proc. Natl. Acad. Sci. USA 2008, 105:10297-10301.
58. 2(g), aqueous carbonate species, and carbonate minerals. J. Phys. Chem. A 2008, 112:542-555.
59. Schaad L.J., Bytautas L., Houk K.N. Ab initio test of the usefulness of the Redlich-Teller product rule in computing kinetic isotope effects. Can. J. Chem. 1999, 77:875-878.
60. Schauble E.A. Applying stable isotope fractionation theory to new systems. Rev. Mineral. Geochem. 2004, 55:65-111.
61. Schauble E.A. Role of nuclear volume in driving equilibrium stable isotope fractionation of mercury, thallium, and other very heavy elements. Geochim. Cosmochim. Acta 2007, 71:2170-2189.
62. Schauble E.A., Ghosh P., Eiler J.M. Preferential formation of 13C-18O bonds in carbonate minerals, estimated using first-principles lattice dynamics. Geochim. Cosmochim. Acta 2006, 70:2510-2529.
63. Schauble E.A., Rossman G.R., Taylor H.P. Theoretical estimates of equilibrium chlorine-isotope fractionations. Geochim. Cosmochim. Acta 2003, 67:3267-3281.
64. Schmidt M.W., Baldridge K.K., Boatz J.A., Elbert S.T., Gordon M.S., Jensen J.H., Koseki S., Matsunaga N., Nguyen K.A., Su S.J., Windus T.L., Dupuis M., Montgomery J.A. General atomic and molecular electronic-structure system. J. Comput. Chem. 1993, 14:1347-1363.
65. Scott A.P., Radom L. Harmonic vibrational frequencies: an evaluation of Hartree-Fock, Møller-Plesset, quadratic configuration interaction, density functional theory, and semiempirical scale factors. J. Phys. Chem. 1996, 100:16502-16513.
66. Seo J.H., Lee S.K., Lee I. Quantum chemical calculations of equilibrium copper(I) isotope fractions in ore-forming fluids. Chem. Geol. 2007, 243:225-237.
67. Shaffer W.H., Schuman R.P. The Infra-Red spectra of bent XYZ molecules. Part I: Vibration-rotation energies. J. Chem. Phys. 1944, 12:504-513.
68. Shimanouchi T. (1972) Tables of Molecular Vibrational Frequencies, Consolidated Volume I. Natl. Stand. Ref. Data Ser., Natl. Bur. Stand Press, Washington, DC. pp. 1-160.
69. Shimanouchi T. Tables of molecular vibrational frequencies, consolidated volume II. J. Phys. Chem. Ref. Data 1977, 6:993-1102.
70. 2 O = 2HDO at temperatures to 673 K and at pressures to 40 MPa. J. Chem. Thermodyn. 1990, 22:739-749.
71. Singh G., Wolfsberg M. The calculation of isotopic partition function ratios by a perturbation theory technique. J. Chem. Phys. 1975, 62:4165-4180.
72. Sinha P., Boesch S.E., Gu C.M., Wheeler R.A., Wilson A.K. Harmonic vibrational frequencies: scaling factors for HF, B3LYP, and MP2 methods in combination with correlation consistent basis sets. J. Phys. Chem. A 2004, 108:9213-9217.
73. Stockmayer W.H., Kavanagh G.M., Mickley H.S. The thermodynamic properties of gaseous sulfur trioxide. J. Chem. Phys. 1944, 12:408-412.
74. Stripp K.F., Kirkwood J.G. Asymptotic expansion of the partition function of the asymmetric top. J. Chem. Phys. 1951, 19:1131-1133.
75. Tossell J.A. Calculating the partitioning of the isotopes of Mo between oxidic and sulfidic species in aqueous solution. Geochim. Cosmochim. Acta 2005, 69:2981-2993.
76. Truhlar D.G. A simple approximation for the vibrational partition function of a hindered internal rotation. J. Comput. Chem. 1991, 12:266-270.
77. Urey H.C. The thermodynamic properties of isotopic substances. J. Chem. Soc. (Lond.) 1947, 562-581.
78. Urey H.C., Greiff L.J. Isotopic exchange equilibria. J. Am. Chem. Soc. 1935, 57:321-327.
79. 2 atom. J. Chem. Phys. 1933, 1:137-143.
80. Urey H.C., Lowenstam H.A., Epstein S., McKinney C.R. Measurement of paleotemperatures and temperatures of the upper cretaceous of England, Denmark, and the Southeastern United-States. Bull. Geol. Soc. Am. 1951, 62:399-416.
81. Vojta G. Grundlagen der statistischen thermodynamik von isotopensystemen mit chemischen reactionen. Kernenergie 1960, 3:917-927.
82. Vojta G. Berechnung der schwingungszustandssumme entarteter anharmonischer oszillatoren mit hilfe der mellinschen integraltransformation. Ann. Phys. 1961, 462:397-402.
83. Vojta G., Zylka C. Hindered internal rotation in molecular systems: quantum statistics of equilibrium and rate constants in the Wigner function formalism. Theor. Chim. Acta 1993, 86:439-449.
84. Wilson E.B. The effect of rotational distortion on the thermodynamic properties of water and other polyatomic molecules. J. Chem. Phys. 1936, 4:526-528.
85. Wilson E.B., Decius J.C., Cross P.C. Molecular Vibrations: The Theory of Infrared and Raman Vibrational Spectra 1955, McGraw-Hill Book Co. Press, New York.
86. Wolfsberg M. Correction to the effect of anharmonicity on isotopic exchange equilibria - application to polyatomic molecules. J. Chem. Phys. 1969, 50:1484-1486.
87. 2X=2HDX. J. Chem. Phys. 1970, 12:408-412.
88. 3 and B(OH)4- Geochim. Cosmochim. Acta 2005, 69:2753-2766.
89. Zeebe R.E. Hydration in solution is critical for stable oxygen isotope fractionation between carbonate ion and water. Geochim. Cosmochim. Acta 2009, 73:5283-5291.
90. Zhang Q., Day P.N., Truhlar D.G. The accuracy of second order perturbation theory for multiply excited vibrational energy levels and partition functions for a symmetrical top molecular ion. J. Chem. Phys. 1993, 98:4948-4958.
91. Zhao Y., Truhlar D.G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 2008, 120:215-241.