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Title: Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface

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Journal Article: Publisher's Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 283; Journal Issue: C; Related Information: CHORUS Timestamp: 2016-09-04 18:34:28; Journal ID: ISSN 0021-9991
Country of Publication:
United States

Citation Formats

Geng, Hua Y. Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface. United States: N. p., 2015. Web. doi:10.1016/
Geng, Hua Y. Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface. United States. doi:10.1016/
Geng, Hua Y. 2015. "Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface". United States. doi:10.1016/
title = {Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface},
author = {Geng, Hua Y.},
abstractNote = {},
doi = {10.1016/},
journal = {Journal of Computational Physics},
number = C,
volume = 283,
place = {United States},
year = 2015,
month = 2

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/

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Cited by: 7works
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  • A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model—the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate ismore » about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of r{sub s}=0.912.« less
  • To accurately determine the reaction path and its energetics for enzymatic and solution-phase reactions, we present a sequential sampling and optimization approach that greatly enhances the efficiency of the ab initio quantum mechanics/molecular mechanics minimum free-energy path (QM/MM-MFEP) method. In the QM/MM-MFEP method, the thermodynamics of a complex reaction system is described by the potential of mean force (PMF) surface of the quantum mechanical (QM) subsystem with a small number of degrees of freedom, somewhat like describing a reaction process in the gas phase. The main computational cost of the QM/MM-MFEP method comes from the statistical sampling of conformations ofmore » the molecular mechanical (MM) subsystem required for the calculation of the QM PMF and its gradient. In our new sequential sampling and optimization approach, we aim to reduce the amount of MM sampling while still retaining the accuracy of the results by first carrying out MM phase-space sampling and then optimizing the QM subsystem in the fixed-size ensemble of MM conformations. The resulting QM optimized structures are then used to obtain more accurate sampling of the MM subsystem. This process of sequential MM sampling and QM optimization is iterated until convergence. The use of a fixed-size, finite MM conformational ensemble enables the precise evaluation of the QM potential of mean force and its gradient within the ensemble, thus circumventing the challenges associated with statistical averaging and significantly speeding up the convergence of the optimization process. To further improve the accuracy of the QM/MM-MFEP method, the reaction path potential method developed by Lu and Yang [Z. Lu and W. Yang, J. Chem. Phys. 121, 89 (2004)] is employed to describe the QM/MM electrostatic interactions in an approximate yet accurate way with a computational cost that is comparable to classical MM simulations. The new method was successfully applied to two example reaction processes, the classical S{sub N}2 reaction of Cl{sup -}+CH{sub 3}Cl in solution and the second proton transfer step of the reaction catalyzed by the enzyme 4-oxalocrotonate tautomerase. The activation free energies calculated with this new sequential sampling and optimization approach to the QM/MM-MFEP method agree well with results from other simulation approaches such as the umbrella sampling technique with direct QM/MM dynamics sampling, demonstrating the accuracy of the iterative QM/MM-MFEP method.« less
  • The commensurate Frenkel Kontorova (FK) model is studied using path-integral molecular dynamics (PIMD). We focus on the highly discrete case, in which the embedding potential has a much greater maximum curvature than the harmonic potential connecting two particles in the FK chain. When efficient sampling methods are used, the dynamical interpretation of adiabatic PIMD appears to represent quite accurately the true time correlation functions of this highly correlated many-body system. We have found that the discrete, quantum FK model shows different behavior than its continuum version. The spectral density does not show the characteristic {omega}{sup -2}{theta}({omega}-{omega}{sub c}) cusp of themore » continuum solution in the pinned phase (m>m{sub c}). We also identify a dynamical quantum hysteresis in addition to the regular classical hysteresis when an external force is applied to the FK chain. In the unpinned phase (m{<=}m{sub c}), we find a linear response damping coefficient which is finite and only weakly dependent on temperature T at small values of T.« less
  • The authors present the results of a centrifugal sudden distorted wave (CSDW) quantum scattering study of the reaction Cl + HCl ..-->.. ClH + Cl. The potential energy surface used in this calculation (denoted sf-POLCI) has been chosen to fit a scaled ab initio surface for Cl-H-Cl angles greater than 150/sup 0/ (angles for which the latter surface has been determined), and to fit an extended London-Eyring-Polanyi-Sato (LEPS) surface at smaller angles. This sf-POLCI surface has a noncollinear Cl-H-Cl saddle point with a Cl-H-Cl angle of 161.4/sup 0/. They also compare their CSDW results with those from a LEPS surface,more » which has a collinear geometry saddle point, but is otherwise similar to the sf-POLCI surface. Results presented include partial wave reaction probabilities, integral and differential cross sections, product rotational distributions, and thermal rate coefficients. The sf-POLCI results are generally similar to the LEPS results, although there are a few important differences. In particular, the integral cross sections in the threshold region increase more slowly with energy for the sf-POLCI surface. As a result, the activation energy is smaller for the LEPS surface, even though is has the higher barrier. Both the sf-POLCI and LEPS cross sections exhibit high product rotational excitation, with the sf-POLCI products more excited than the LEPS. Also, the rotational state which contributes most to the thermal rate coefficient is higher for the sf-POLCI surface than for the LEPS. For both surfaces the CSDW rate coefficients agree with experiment within the experimental uncertainties.« less
  • To describe the tunneling dynamics of a stack of two-dimensional fermionic superfluids in an optical potential, we derive an effective action functional from a path integral treatment. This effective action leads in the saddle point approximation to equations of motion for the density and the phase of the superfluid Fermi gas in each layer. In the strong coupling limit (where bosonic molecules are formed) these equations reduce to a discrete nonlinear Schroedinger equation, where the molecular tunneling amplitude is reduced for large binding energies. In the weak coupling (BCS) regime, we study the evolution of the stacked superfluids and derivemore » an approximate analytical expression for the oscillation frequency of the center of mass in an external harmonic potential. In both the weak and intermediate coupling regimes, the detection of the Josephson oscillations described by our path integral formalism constitutes experimental evidence for the fermionic superfluid regime.« less