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

Liu, Qi; Tossell, J. A.; Liu, Yun

doi:10.1016/j.gca.2010.09.014

Cited by 92 publications

(102 citation statements)

References 84 publications

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“…The simplest and most common approach, usually a) Electronic mail: konstantin.karandashev@epfl.ch b) Electronic mail: jiri.vanicek@epfl.ch referred to as the "harmonic approximation" or "Urey model," assumes (i) separability of rotations and vibrations, (ii) rigid rotor approximation for the rotations, and (iii) harmonic oscillator approximation for the vibrations. 1,2,5 Although there exist various corrections that incorporate the leading effects of rovibrational coupling, nonrigidity of the rotor, or anharmonicity of the vibrations, [6][7][8] this perturbative approach is not always sufficient; indeed, there are examples of systems in which these corrections can even yield worse results than the Urey model. 5 We therefore employ a more rigorous method that avoids these approximations altogether and treats the potential energy surface, rotations, and rovibrational coupling exactly.…”

Section: Introductionmentioning

confidence: 99%

Accelerating equilibrium isotope effect calculations. I. Stochastic thermodynamic integration with respect to mass

Karandashev

Vaníček

2017

The Journal of Chemical Physics

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Noise-assisted energy transfer from the dilation of the set of one-electron reduced density matrices The Journal of Chemical Physics 146, 184101 (2017) Accurate path integral Monte Carlo or molecular dynamics calculations of isotope effects have until recently been expensive because of the necessity to reduce three types of errors present in such calculations: statistical errors due to sampling, path integral discretization errors, and thermodynamic integration errors. While the statistical errors can be reduced with virial estimators and path integral discretization errors with high-order factorization of the Boltzmann operator, here we propose a method for accelerating isotope effect calculations by eliminating the integration error. We show that the integration error can be removed entirely by changing particle masses stochastically during the calculation and by using a piecewise linear umbrella biasing potential. Moreover, we demonstrate numerically that this approach does not increase the statistical error. The resulting acceleration of isotope effect calculations is demonstrated on a model harmonic system and on deuterated species of methane.

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Section: Introductionmentioning

confidence: 99%

Accelerating equilibrium isotope effect calculations. I. Stochastic thermodynamic integration with respect to mass

Karandashev

Vaníček

2017

The Journal of Chemical Physics

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“…Readers are referred to Schauble (2004) and Liu et al (2010) for the details of such calculation. Given the RPFRs of a pair of compounds or minerals in equilibrium, the isotopic fractionation factor a can be derived from the ratio of their RPFRs (or b factors) if there is only one isotope substituted:…”

Section: Introductionmentioning

confidence: 99%

Silicon isotope fractionation during the precipitation of quartz and the adsorption of H4SiO4(aq) on Fe(III)-oxyhydroxide surfaces

Liu

2015

Chin. J. Geochem.

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Equilibrium Si isotope fractionation factors among orthosilicic acid (i.e.,H 4 SiO 4(aq) ), quartz and the adsorption complexes of H 4 SiO 4(aq) on Fe(III)-oxyhydroxide surface were calculated using the full-electron wave-function quantum chemistry methods [i.e., B3LYP/6-311G(2df,p)] with a new cluster-model-based treatment. Solvation effects were carefully included in our calculations via water-droplet method combined with implicit solvent models (e.g., PCM). The results revealed that, if it is under equilibrium conditions, heavy Si isotopes would be significantly enriched in quartz in comparison to H 4 SiO 4(aq) . However, most of the field observations suggested that quartz would have identical or even depleted d 30 Si values compared to that of H 4 SiO 4(aq) . To explain this discrepancy between the equilibrium calculation results and the field observations, the kinetic isotope effect (KIE) associated with the formation of amorphous silica, which usually is the precursor of crystalline quartz, was investigated using quantum chemistry methods. The KIE results showed that amorphous silica would be significantly enriched in light Si isotopes during its formation. Our equilibrium fractionation results, however, matched a special type of quartz (i.e., Herkimer ''diamond'') very well, due to its nearly equilibrated precipitation condition. Opposite to the case of precipitated quartz, a large equilibrium Si isotope fractionation (i.e., -3.0 %) was found between the absorbed bidentate Si surface complexes (i.e., 2 C [ Fe 2 O 2 Si(OH) 2 ) and H 4 SiO 4(aq) . This calculated equilibrium Si isotope fractionation factor largely differed from a previous experimental result (ca. -1.08 %). We found that the formation of transient or temporary surface complexes [e.g., 1 V [ Fe 2 OSi(OH) 3 ] may have accounted for the smaller net fractionation observed. With the equilibrium and kinetic Si isotope fractionation factors provided here, the distributions and changes of Si isotope compositions in the Earth's surface systems can be better understood.

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“…These calculations consider pure harmonic vibrational frequencies and rigid rotator approximations. Such approximations do not apply, however, to the diatomic molecule of hydrogen, especially as anharmonic oscillations are likely to become stronger at high temperatures (Bigeleisen and Mayer, 1947;Bigeleisen, 1955;Wolfsberg, 1969;Wolfsberg et al, 1970;Liu et al, 2010).…”

Section: Introductionmentioning

confidence: 99%

D/H fractionation in the H2–H2O system at supercritical water conditions: Compositional and hydrogen bonding effects

Foustoukos

Mysen

2012

Geochimica et Cosmochimica Acta

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

Cited by 92 publications

References 84 publications

Accelerating equilibrium isotope effect calculations. I. Stochastic thermodynamic integration with respect to mass

Accelerating equilibrium isotope effect calculations. I. Stochastic thermodynamic integration with respect to mass

Silicon isotope fractionation during the precipitation of quartz and the adsorption of H4SiO4(aq) on Fe(III)-oxyhydroxide surfaces

D/H fractionation in the H2–H2O system at supercritical water conditions: Compositional and hydrogen bonding effects

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