Direct path integral estimators for isotope fractionation ratios

Cheng, Bingqing; Ceriotti, Michele

doi:10.1063/1.4904293

Cited by 35 publications

(41 citation statements)

References 65 publications

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“…31, it would, just as WHAM, require equilibration over the entire λ interval [0, 1] instead of only over each subinterval I j , which would make it less convenient than the simple STI presented. We would also like to mention an alternative approach allowing us to remove the integration error of the isotope effect entirely, which was proposed recently by Cheng and Ceriotti 51 and is a variant of the free energy perturbation method. 20 Cheng and Ceriotti's approach employs the socalled "direct estimators" and is particularly suitable for isotope effects close to unity, which occur frequently, e.g., in the condensed phase, where only a small fraction of molecules is isotopically substituted.…”

Section: Discussionmentioning

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: Discussionmentioning

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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“…Similar expressions can be easily derived in the context of other high-order factorizations such as that introduced by Takahashi and Imada 21 , and it is possible that perturbed path estimators 29 could be derived on top of a full fourth-order path integral Hamiltonian, providing even faster convergence to quantum expectation values. The availability of projected force derivatives also facilitates the implementation of the fourth-order version of estimators for the heat capacity 26 and for isotope fractionation ratios 36 . Finally, further dramatic speed-ups can be obtained whenever one can apply range-separation techniques such as ring-polymer contraction 16 , since we have made sure that our implementation in i-PI 37 is fully compatible with that of conventional real and imaginary-time multiple time stepping 38 .…”

Section: Methodsmentioning

confidence: 99%

High order path integrals made easy

Kapil

Behler

Ceriotti

2016

The Journal of Chemical Physics

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The precise description of quantum nuclear fluctuations in atomistic modelling is possible by employing path integral techniques, which involve a considerable computational overhead due to the need of simulating multiple replicas of the system. Many approaches have been suggested to reduce the required number of replicas. Among these, high-order factorizations of the Boltzmann operator are particularly attractive for high-precision and low-temperature scenarios. Unfortunately, to date several technical challenges have prevented a widespread use of these approaches to study nuclear quantum effects in condensed-phase systems. Here we introduce an inexpensive molecular dynamics scheme that overcomes these limitations, thus making it possible to exploit the improved convergence of high-order path integrals without having to sacrifice the stability, convenience and flexibility of conventional second-order techniques. The capabilities of the method are demonstrated by simulations of liquid water and ice, as described by a neural-network potential fitted to dispersion-corrected hybrid density functional theory calculations.

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“…The models of Webb and Miller (2014) and Cheng and Ceriotti (2014) used path-integral methods, but employed different PESs for integration. Cheng and Ceriotti (2014) used the Adaptive Intermolecular Reactive Empirical Bond Order (AIREBO) force field whereas Webb and Miller (2014) used the Chemistry at Harvard Macromolecular Mechanics (CHARMM) PES. These two models derive dramatically different vibrational frequencies for the fundamental modes of propane.…”

Section: Position-specific Hydrogen Isotope Fractionation At Thermodymentioning

confidence: 99%

Position-specific hydrogen isotope equilibrium in propane

Xie

Ponton

Formolo

et al. 2018

Geochimica et Cosmochimica Acta

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Intramolecular isotope distributions can constrain source attribution, mechanisms of formation and destruction, and temperature-time histories of molecules. In this study, we explore the D/H fractionation between central (-CH 2 -) and terminal (-CH 3 ) positions of propane (C 3 H 8 ) -a percent level component of natural gases. The temperature dependence of position-specific D/H fractionation of propane could potentially work as a geo-thermometer for natural gas systems, and a forensic identifier of specific thermogenic sources of atmospheric or aquatic emissions. Moreover, kinetically controlled departures from temperature dependent equilibrium might constrain mechanisms of thermogenic production, or provide indicators of biological or photochemical destruction. We developed a method to measure position-specific D/H differences of propane with high-resolution gas source mass spectrometry. We performed laboratory exchange experiments to study the exchange rates for both terminal and central positions, and used catalysts to drive the hydrogen isotope distribution of propane to thermodynamic equilibrium. Experimental results demonstrate that D/H exchange between propane and water happens easily in the presence of either Pd catalyst or Ni catalyst. Exchange rates are similar between the two positions catalyzed by Pd. However, the central position exchanges 2.2 times faster than the terminal position in the presence of Ni catalyst. At 200°C in the presence of Pd catalyst, the e-folding time of propane-water exchange is 20 days and of homogeneous exchange (i.e., equilibrium between central and terminal positions) is 28 minutes. An equilibrated (bracketed and time-invariant) intramolecular hydrogen isotope distribution was attained for propane at three temperatures, 30°C, 100°C and 200°C; these data serve as an initial experimental calibration of a new position-specific thermometer with a temperature sensitivity of 0.25‰ per ˚C at 100 ˚C. We use this calibration to test the validity of prior published theoretical predictions. Comparison of data with models suggest the most sophisticated of these discrepant models (Webb and Miller, 2014) is most accurate; this conclusion implies that there is a combined experimental and theoretical foundation for an 'absolute reference frame' for positionspecific H isotope analysis of propane, following principles previously used for clumped isotope analysis of CO 2 , CH 4 and O 2 (Eiler and Schauble, 2004;Yeung et al., 2014;Stolper et al., 2014).

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Direct path integral estimators for isotope fractionation ratios

Cited by 35 publications

References 65 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

High order path integrals made easy

Position-specific hydrogen isotope equilibrium in propane

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