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

Karandashev, Konstantin; Vaníček, Jiří

doi:10.1063/1.4981260

Cited by 3 publications

(40 citation statements)

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“…(12) in terms of massscaled normal mode coordinates u (see Appendix A of Ref. 16 for details). This leads to a direct estimator ρ (1) (u)/ρ (0) (u), which becomes Eq.…”

Section: Free Energy Perturbation and Direct Estimators For Equilimentioning

confidence: 99%

“…Although several elegant tricks reduce this integration error significantly, 1,2 it can never be removed completely if the integral is evaluated deterministically. This disadvantage of thermodynamic integration led to the introduction of several strategies that avoid the integration error altogether; these can be classified into two main groups: The first group avoids discretizing the mass integral by allowing the mass to take a continuous range of values during the simulation; 15,16 this approach is an example of a more general λ-dynamics method [17][18][19] for calculating free energy differences. Not only do these techniques eliminate the integration error, but they also tend to show faster statistical convergence than does standard thermodynamic integration; 16,20 this property is similar to the improvement achieved by parallel tempering.…”

Section: Introductionmentioning

confidence: 99%

“…This disadvantage of thermodynamic integration led to the introduction of several strategies that avoid the integration error altogether; these can be classified into two main groups: The first group avoids discretizing the mass integral by allowing the mass to take a continuous range of values during the simulation; 15,16 this approach is an example of a more general λ-dynamics method [17][18][19] for calculating free energy differences. Not only do these techniques eliminate the integration error, but they also tend to show faster statistical convergence than does standard thermodynamic integration; 16,20 this property is similar to the improvement achieved by parallel tempering. [21][22][23] The second group is based on the free energy perturbation, 1,15,24,25 which can be derived by rewriting the ratio (2) using the Zwanzig formula; the approach was proposed in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…In Ref. 16, we introduced a method following the first philosophy for eliminating the integration error-in particular, we showed that an effective Monte Carlo procedure for changing the mass reduces the thermodynamic integration error and that a special mass-dependent biasing potential renders the integration error exactly zero. Here, we explore the second strategy, namely the free energy perturbation, or "direct estimator" approach; 3,15 while direct estimators work best for isotope effects close to unity, they can be applied to larger isotope effects as well by rewriting Eq.…”

Section: Introductionmentioning

confidence: 99%

“…Second, since the statistical convergence of thermodynamic integration can be improved by changing the mass stochastically during the simulation, it seems natural to combine this stepwise approach with the procedure for changing mass introduced in Ref. 16; indeed, testing performance of the resulting combined method on large isotope effects was the main goal of this paper. Such a combination with direct estimators is only possible for a mass sampling procedure that allows finite steps with respect to mass, making the Monte Carlo procedure of Ref.…”

Section: Introductionmentioning

confidence: 99%

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Accelerating equilibrium isotope effect calculations. II. Stochastic implementation of direct estimators

Karandashev

Vaníček

2019

The Journal of Chemical Physics

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Path integral calculations of equilibrium isotope effects and isotopic fractionation are expensive due to the presence of path integral discretization errors, statistical errors, and thermodynamic integration errors. Whereas the discretization errors can be reduced by high-order factorization of the path integral and statistical errors by using centroid virial estimators, two recent papers proposed alternative ways to completely remove the thermodynamic integration errors: Cheng and Ceriotti [J. Chem. Phys. 141, 244112 (2015)] employed a variant of free-energy perturbation called "direct estimators", while Karandashev and Vaníček [J. Chem. Phys. 143, 194104 (2017)] combined the thermodynamic integration with a stochastic change of mass and piecewise-linear umbrella biasing potential. Here we combine the former approach with the stochastic change of mass in order to decrease its statistical errors when applied to larger isotope effects, and perform a thorough comparison of different methods by computing isotope effects first on a harmonic model, and then on methane and methanium, where we evaluate all isotope effects of the form CH 4−x D x /CH 4 and CH 5−x D + x /CH + 5 , respectively. We discuss thoroughly the reasons for a surprising behavior of the original method of direct estimators, which performed well for a much larger range of isotope effects than what had been expected previously, as well as some implications of our work for the more general problem of free energy difference calculations.

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“…(12) in terms of massscaled normal mode coordinates u (see Appendix A of Ref. 16 for details). This leads to a direct estimator ρ (1) (u)/ρ (0) (u), which becomes Eq.…”

Section: Free Energy Perturbation and Direct Estimators For Equilimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Accelerating equilibrium isotope effect calculations. II. Stochastic implementation of direct estimators

Karandashev

Vaníček

2019

The Journal of Chemical Physics

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Nuclear quantum effects enter the mainstream

2018

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Over the past decades, atomistic simulations of chemical, biological and materials systems have become increasingly precise and predictive thanks to the development of accurate and efficient techniques that describe the quantum mechanical behavior of electrons. However, the overwhelming majority of such simulations still assume that the nuclei behave as classical particles. While historically this approximation could sometimes be justified due to complexity and computational overhead, the lack of nuclear quantum effects has become one of the biggest sources of error when systems containing light atoms are treated using current state-of-the-art descriptions of chemical interactions. Over the past decade, this realization has spurred a series of methodological advances that have led to dramatic reductions in the cost of including these important physical effects in the structure and dynamics of chemical systems. Here we show how these developments are now allowing nuclear quantum effects to become a mainstream feature of molecular simulations. These advances have led to new insights into chemical processes in the condensed phase and open the door to many exciting future opportunities.The Born Oppenheimer approximation to separate the electronic and nuclear wavefunctions underpins the concept of potential energy surfaces and forms the bedrock of any modern chemistry course. Much less attention, however, is generally given to the routinely assumed additional approximation employed in atomistic simulations that the nuclear motion and sampling on the resulting electronic energy surface can be treated classically. Within the classical nuclei approximation, one loses the ability to describe nuclear zero-point energy, quantization of energy levels, and tunneling, as well as exchange and coherence effects. However, even at room temperature the zero-point energy of a typical chemical bond of frequency ω (∼ ω/2) exceeds the thermal energy scale of that coordinate at temperature T (∼k B T ) by an order of magnitude. These effects can thus make large changes to the structure and dynamics in processes ranging from proton delocalization and tunneling in enzymes [1][2][3][4] to changes in the stability of crystal polymorphs [5] to the the phase diagram of high pressure melts [6]. A revealing consequence of neglecting nuclear quantum effects (NQEs) is that equilibrium isotope effects would be predicted to be zero, despite forming the basis of vital analysis methods in fields ranging from the atmospheric sciences to biochemistry and materials science.In addition to the importance of calculating and understanding these properties, modelling the quantum nature of the nuclei has become increasingly important due to the greater availability of accurate and affordable methods to describe the electronic potential energy surface on which the nuclei evolve. The accuracy of these surfaces is constantly improving, and the most recent generation of state-of-the art potential energy surfaces are now usually generated either by on-the-fly evalu...

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Semiclassical analysis of the quantum instanton approximation

Vaillant

Thapa

Vaníček

et al. 2019

The Journal of Chemical Physics

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We explore the relation between the quantum and semiclassical instanton approximations for the reaction rate constant. From the quantum instanton expression, we analyze the contributions to the rate constant in terms of minimum-action paths and find that two such paths dominate the expression. For symmetric barriers, these two paths join together to describe the semiclassical instanton periodic orbit. However, for asymmetric barriers, one of the two paths takes an unphysically low energy and dominates the expression, leading to orderof-magnitude errors in the rate predictions. Nevertheless, semiclassical instanton theory remains accurate. We conclude that semiclassical instanton theory can only be obtained directly from the semiclassical limit of the quantum instanton for symmetric systems. We suggest a modification of the quantum instanton approach which avoids sampling the spurious path and thus has a stronger connection to semiclassical instanton theory, giving numerically accurate predictions even for very asymmetric systems in the low temperature limit.

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

Cited by 3 publications

References 63 publications

Accelerating equilibrium isotope effect calculations. II. Stochastic implementation of direct estimators

Accelerating equilibrium isotope effect calculations. II. Stochastic implementation of direct estimators

Nuclear quantum effects enter the mainstream

Semiclassical analysis of the quantum instanton approximation

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