Theoretical Study of Isotope Fractionation Effects in Different Systems Based on First Principles
Keywords:
isotope fractionation, theoretical calculations, B3LYP/6-311 G(d, p), HF/3-21G
Abstract
The study of theoretical calculation work of isotope fractionation effect provides a good theoretical basis for the research of geochemistry and other related disciplines. Numerous scholars use different calculation methods which may lead to the deviation of the calculation results. In this work, we calculated some gases, liquids, and minerals systems by Gaussian software with two different methods, B3LYP/6-311+G(d, p) and HF/3-21G. Theoretical calculation results could be compared with the previous experimental and natural sample measurements in this field. The comparison between theoretical calculation and experimental results could come up with which theoretical method is closer to the results of many kinds of research, and provide a direction for future researchers when choosing to apply the theoretical methods. This study draws some preliminary conclusions as follows: 1. The isotope fractionation effect of isotopologue with light atoms is greater than that with heavy atoms. 2. The isotope fractionation factors are a function of temperature, and these parameters decrease with the temperature increase. 3. The calculations with the HF/3-21G method are not very accurate. The calculations with the B3LYP/6-311+G(d, p) method are closer to the results of many research works than those of the HF/3-21G method.
References
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[42] Boschetti, T. (2013). Oxygen isotope equilibrium in sulfate–water systems: A revision of geothermometric applications in low-enthalpy systems. Journal of Geochemical Exploration, 124, 92–100. https://doi.org/10.1016/j.gexplo.2012.08.013
[43] Chiba, H., & Sakai, H. (1985). Oxygen isotope exchange rate between dissolved sulfate and water at hydrothermal temperatures. Geochimica et Cosmochimica Acta, 49(4), 993–1000. https://doi.org/10.1016/0016-7037(85)90317-1
[44] Zeebe, R. E. (2010). A new value for the stable oxygen isotope fractionation between dissolved sulfate ion and water. Geochimica et Cosmochimica Acta, 74(3), 818–828. https://doi.org/10.1016/j.gca.2009.10.033
[45] Beck, W. C., Grossman, E. L., & Morse, J. W. (2005). Experimental studies of oxygen isotope fractionation in the carbonic acid system at 15, 25, and 40 °C. Geochimica et Cosmochimica Acta, 69(14), 3493–3503. https://doi.org/10.1016/j.gca.2005.02.003
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[50] Zheng, Y.-F. (1999). Oxygen isotope fractionation in carbonate and sulfate minerals. Geochemical Journal, 33(2), 109–126. https://doi.org/10.2343/geochemj.33.109
[2] Schauble, E. A. (2004). Applying stable isotope fractionation theory to new systems. Reviews in Mineralogy and Geochemistry, 55(1), 65–111. https://doi.org/10.2138/gsrmg.55.1.65
[3] Young, E. D., Manning, C. E., Schauble, E. A., et al. (2015). High-temperature equilibrium isotope fractionation of non-traditional stable isotopes: Experiments, theory, and applications. Chemical Geology, 395, 176–195. https://doi.org/10.1016/j.chemgeo.2014.12.013
[4] Lindemann, F. A., & Aston, F. W. (1919). XLVIII. The possibility of separating isotopes. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 37(221), 523–534. https://doi.org/10.1080/14786440508635914
[5] Urey, H. C., & Greiff, L. J. (1935). Isotopic exchange equilibria. Journal of the American Chemical Society, 57(2), 321–327. https://doi.org/10.1021/ja01305a021
[6] Urey, H. C. (1947). The thermodynamic properties of isotopic substances. Journal of the Chemical Society (Resumed), 562–581. https://doi.org/10.1039/JR9470000562
[7] Bigeleisen, J., & Mayer, M. G. (1947). Calculation of equilibrium constants for isotopic exchange reactions. The Journal of Chemical Physics, 15(5), 261–267. https://doi.org/10.1063/1.1746492
[8] Richet, P., Bottinga, Y., & Javoy, M. (1977). A review of hydrogen, carbon, nitrogen, oxygen, sulphur, and chlorine stable isotope fractionation among gaseous molecules. Annual Review of Earth and Planetary Sciences, 5(1), 65–110. https://doi.org/10.1146/annurev.ea.05.050177.000433
[9] Adnew, G. A., Workman, E., Janssen, C., et al. (2022). Temperature dependence of isotopic fractionation in the CO2-O2 isotope exchange reaction. Rapid Communications in Mass Spectrometry, 36(12), e9301. https://doi.org/10.1002/rcm.9301
[10] Bigeleisen, J. (1961). Statistical mechanics of isotope effects on the thermodynamic properties of condensed systems. The Journal of Chemical Physics, 34(5), 1485–1493. https://doi.org/10.1063/1.1701034
[11] Jakli, G., Chan, T. C., & Van Hook, W. A. (1975). Equilibrium isotope effects in aqueous systems. IV. The vapor pressures of NaBr, NaI, KF, Na2SO4, and CaCl2 solutions in H2O and D2O (0 to 90°C). Vapor pressures of Na2SO4·10H2O, ·10D2O and CaCl2·2H2O, ·2D2O. Journal of Solution Chemistry, 4(1), 71–90. https://doi.org/10.1007/BF00649751
[12] Bottinga, Y. (1968). Calculation of fractionation factors for carbon and oxygen isotopic exchange in the system calcite-carbon dioxide-water. The Journal of Physical Chemistry, 72(3), 800–808. https://doi.org/10.1021/j100849a008
[13] Zheng, Y.-F. (1991). Calculation of oxygen isotope fractionation in metal oxides. Geochimica et Cosmochimica Acta, 55(8), 2299–2307. https://doi.org/10.1016/0016-7037(91)90105-W
[14] Xiao, Z. C., Zhou, C., Kang, J. T., et al. (2022). The factors controlling equilibrium inter-mineral Ca isotope fractionation: Insights from first-principles calculations. Geochimica et Cosmochimica Acta, 333, 373–389. https://doi.org/10.1016/j.gca.2022.07.013
[15] Ferrari, C., Méheut, M., Resongles, E., et al. (2022). Equilibrium mass-dependent isotope fractionation of antimony between stibnite and Sb secondary minerals: A first-principles study. Chemical Geology, 611, 121115. https://doi.org/10.1016/j.chemgeo.2022.121115
[16] Duan, H., Yang, B., & Huang, F. (2023). Site-specific isotope effect: Insights from equilibrium magnesium isotope fractionation in mantle minerals. Geochimica et Cosmochimica Acta, 357, 13–25. https://doi.org/10.1016/j.gca.2023.07.008
[17] Criss, R. E. (1999). Principles of stable isotope distribution. Oxford University Press.
[18] Yang, J., Li, Y., Liu, S., et al. (2015). Theoretical calculations of Cd isotope fractionation in hydrothermal fluids. Chemical Geology, 391, 74–82. https://doi.org/10.1016/j.chemgeo.2014.10.028
[19] Young, E. D., Manning, C. E., Schauble, E. A., et al. (2015). High-temperature equilibrium isotope fractionation of non-traditional stable isotopes: Experiments, theory, and applications. Chemical Geology, 395, 176–195. https://doi.org/10.1016/j.chemgeo.2014.12.013
[20] Zhao, Y., Li, Y., Wiggenhauser, M., et al. (2021). Theoretical isotope fractionation of cadmium during complexation with organic ligands. Chemical Geology, 571, 120178. https://doi.org/10.1016/j.chemgeo.2021.120178
[21] Ratié, G., Chrastný, V., Guinoiseau, D., et al. (2021). Cadmium isotope fractionation during complexation with humic acid. Environmental Science & Technology, 55(11), 7430–7444. https://doi.org/10.1021/acs.est.0c07824
[22] Yamaji, K., Makita, Y., Watanabe, H., et al. (2001). Theoretical estimation of lithium isotopic reduced partition function ratio for lithium ions in aqueous solution. The Journal of Physical Chemistry A, 105(3), 602–613. https://doi.org/10.1021/jp002868q
[23] Schauble, E. A., Méheut, M., & Hill, P. S. (2009). Combining metal stable isotope fractionation theory with experiments. Elements, 5(6), 369–374. https://doi.org/10.2113/gselements.5.6.369
[24] Mavromatis, V., Gautier, Q., Bosc, O., et al. (2013). Kinetics of Mg partition and Mg stable isotope fractionation during its incorporation in calcite. Geochimica et Cosmochimica Acta, 114, 188–203. https://doi.org/10.1016/j.gca.2013.03.024
[25] Brazier, J. M., Blanchard, M., Méheut, M., et al. (2023). Experimental and theoretical investigations of stable Sr isotope fractionation during its incorporation in aragonite. Geochimica et Cosmochimica Acta, 358, 134–147. https://doi.org/10.1016/j.gca.2023.08.011
[26] Fujii, T., Kato, C., Wada, N., et al. (2023). Theoretical and experimental study on vanadium isotope fractionation among species relevant to geochemistry. ACS Earth and Space Chemistry, 7(4), 912–925. https://doi.org/10.1021/acsearthspacechem.2c00387
[27] Bartlett, R. J. (Ed.). (1997). Recent advances in coupled-cluster methods. World Scientific Publishing.
[28] Del Bene, J. E. (Ed.). (2002). Recent advances in density functional methods. World Scientific Publishing.
[29] Koch, W., & Holthausen, M. C. (2015). A chemist’s guide to density functional theory (2nd ed.). Wiley-VCH.
[30] Giannozzi, P., Baroni, S., Bonini, N., et al. (2009). QUANTUM ESPRESSO: A modular and open-source software project for quantum simulations of materials. Journal of Physics: Condensed Matter, 21(39), 395502. https://doi.org/10.1088/0953-8984/21/39/395502
[31] Giannozzi, P., Andreussi, O., Brumme, T., et al. (2017). Advanced capabilities for materials modelling with Quantum ESPRESSO. Journal of Physics: Condensed Matter, 29(46), 465901. https://doi.org/10.1088/1361-648X/aa8f79
[32] Frisch, M. J. (2004). Gaussian 03, Revision E.01 [Computer software]. Gaussian, Inc. http://www.gaussian.com/
[33] Gao, T., Gillispie, G. J., Copus, J. S., et al. (2018). Optimization of gelatin–alginate composite bioink printability using rheological parameters: A systematic approach. Biofabrication, 10(3), 034106. https://doi.org/10.1088/1758-5090/aacdc7
[34] He, C., Liu, L., Chu, Y., et al. (2017). National and subnational all-cause and cause-specific child mortality in China, 1996–2015: A systematic analysis with implications for the Sustainable Development Goals. The Lancet Global Health, 5(2), e186–e197. https://doi.org/10.1016/S2214-109X(16)30334-2
[35] Zhang, J. (2021). Equilibrium sulfur isotope fractionations of several important sulfides. Geochemical Journal, 55(3), 135–147. https://doi.org/10.2343/geochemj.2.0620
[36] Zhang, Y., & Liu, Y. (2018). The theory of equilibrium isotope fractionations for gaseous molecules under super-cold conditions. Geochimica et Cosmochimica Acta, 238, 123–149. https://doi.org/10.1016/j.gca.2018.07.002
[37] Graf, D. L. (1961). Crystallographic tables for the rhombohedral carbonates. American Mineralogist: Journal of Earth and Planetary Materials, 46(11-12), 1283–1316.
[38] Liu, Y., & Tossell, J. A. (2005). Ab initio molecular orbital calculations for boron isotope fractionations on boric acids and borates. Geochimica et Cosmochimica Acta, 69(16), 3995–4006. https://doi.org/10.1016/j.gca.2005.04.008
[39] Cortecci, G. (1974). Oxygen isotopic ratios of sulfate ions-water pairs as a possible geothermometer. Geothermics, 3(2), 60–64. https://doi.org/10.1016/0375-6505(74)90014-9
[40] Lloyd, R. M. (1968). Oxygen isotope behavior in the sulfate-water system. Journal of Geophysical Research, 73(18), 6099–6110. https://doi.org/10.1029/JB073i018p06099
[41] Kusakabe, M., & Robinson, B. W. (1977). Oxygen and sulfur isotope equilibria in the BaSO4-HSO4−-H2O system from 110 to 350°C and applications. Geochimica et Cosmochimica Acta, 41(8), 1033–1040. https://doi.org/10.1016/0016-7037(77)90192-9
[42] Boschetti, T. (2013). Oxygen isotope equilibrium in sulfate–water systems: A revision of geothermometric applications in low-enthalpy systems. Journal of Geochemical Exploration, 124, 92–100. https://doi.org/10.1016/j.gexplo.2012.08.013
[43] Chiba, H., & Sakai, H. (1985). Oxygen isotope exchange rate between dissolved sulfate and water at hydrothermal temperatures. Geochimica et Cosmochimica Acta, 49(4), 993–1000. https://doi.org/10.1016/0016-7037(85)90317-1
[44] Zeebe, R. E. (2010). A new value for the stable oxygen isotope fractionation between dissolved sulfate ion and water. Geochimica et Cosmochimica Acta, 74(3), 818–828. https://doi.org/10.1016/j.gca.2009.10.033
[45] Beck, W. C., Grossman, E. L., & Morse, J. W. (2005). Experimental studies of oxygen isotope fractionation in the carbonic acid system at 15, 25, and 40 °C. Geochimica et Cosmochimica Acta, 69(14), 3493–3503. https://doi.org/10.1016/j.gca.2005.02.003
[46] Pathak, A. K., Mukherjee, T., & Maity, D. K. (2008). Theoretical study on the spectroscopic properties of CO3.−.nH2O clusters: Extrapolation to bulk. ChemPhysChem, 9(15), 2259–2264. https://doi.org/10.1002/cphc.200800350
[47] Chacko, T., & Deines, P. (2008). Theoretical calculation of oxygen isotope fractionation factors in carbonate systems. Geochimica et Cosmochimica Acta, 72(15), 3642–3660. https://doi.org/10.1016/j.gca.2008.06.001
[48] Zolotoyabko, E., Caspi, E. N., Fieramosca, J. S., et al. (2010). Differences between bond lengths in biogenic and geological calcite. Crystal Growth & Design, 10(3), 1207–1214. https://doi.org/10.1021/cg901177h
[49] Althoff, P. L. (1977). Structural refinements of dolomite and a magnesian calcite and implications for dolomite formation in the marine environment. American Mineralogist, 62(7-8), 772–783.
[50] Zheng, Y.-F. (1999). Oxygen isotope fractionation in carbonate and sulfate minerals. Geochemical Journal, 33(2), 109–126. https://doi.org/10.2343/geochemj.33.109
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