Showing papers on "Path integral molecular dynamics published in 2019"

Tunneling Splittings in Water Clusters from Path Integral Molecular Dynamics.

Abstract: We present calculations of tunneling splittings in selected small water clusters, based on a recently developed path integral molecular dynamics (PIMD) method. The ground-rotational-state tunneling motions associated with the largest splittings in the water dimer, trimer, and hexamer are considered, and we show that the PIMD predictions are in very good agreement with benchmark quantum and experimental results. As the tunneling spectra are highly sensitive to both the details of the quantum dynamics and the potential energy surface, our calculations are a validation of the MB-Pol surface as well as the accuracy of PIMD. The favorable scaling of PIMD with system size paves the way for calculations of tunneling splittings in large, nonrigid molecular systems with motions that cannot be treated accurately by other methods, such as the semiclassical instanton.

Path integral molecular dynamics for bosons.

Abstract: Trapped bosons exhibit fundamental physical phenomena and are at the core of emerging quantum technologies. We present a method for simulating bosons using path integral molecular dynamics. The main difficulty in performing such simulations is enumerating all ring-polymer configurations, which arise due to permutations of identical particles. We show that the potential and forces at each time step can be evaluated by using a recurrence relation which avoids enumerating all permutations, while providing the correct thermal expectation values. The resulting algorithm scales cubically with system size. The method is tested and applied to bosons in a 2-dimensional (2D) trap and agrees with analytical results and numerical diagonalization of the many-body Hamiltonian. An analysis of the role of exchange effects at different temperatures, through the relative probability of different ring-polymer configurations, is also presented.

On the importance of anharmonicities and nuclear quantum effects in modelling the structural properties and thermal expansion of MOF-5

Abstract: In this article, we investigate the influence of anharmonicities and nuclear quantum effects (NQEs) in modelling the structural properties and thermal expansion of the empty MOF-5 metal-organic framework. To introduce NQEs in classical molecular dynamics simulations, two different methodologies are considered, comparing the approximate, but computationally cheap, method of generalised Langevin equation thermostatting to the more advanced, computationally demanding path integral molecular dynamics technique. For both methodologies, similar results were obtained for all the properties under investigation. The structural properties of MOF-5, probed by means of radial distribution functions (RDFs), show some distinct differences with respect to a classical description. Besides a broadening of the RDF peaks under the influence of quantum fluctuations, a different temperature dependence is also observed due to a dominant zero-point energy (ZPE) contribution. For the thermal expansion of MOF-5, by contrast, NQEs appear to be only of secondary importance with respect to an adequate modelling of the anharmonicities of the potential energy surface (PES), as demonstrated by the use of two differently parametrised force fields. Despite the small effect in the temperature dependence of the volume of MOF-5, NQEs do however significantly affect the absolute volume of MOF-5, in which the ZPE resulting from the intertwining of NQEs and anharmonicities plays a crucial role. A sufficiently accurate description of the PES is therefore prerequisite when modelling NQEs.

Dimension-free path-integral molecular dynamics without preconditioning

Abstract: Convergence with respect to imaginary-time discretization is an essential part of any path-integral-based calculation. However, an unfortunate property of existing non-preconditioned numerical integration schemes for path-integral molecular dynamics (PIMD) - including ring-polymer molecular dynamics (RPMD) and thermostatted RPMD (T-RPMD) - is that for a given MD timestep, the overlap between the exact ring-polymer Boltzmann-Gibbs distribution and that sampled using MD becomes zero in the infinite-bead limit. This has clear implications for hybrid Metropolis Monte-Carlo/MD sampling schemes. We show that these problems can be avoided through the introduction of "dimension-free" numerical integration schemes for which the sampled ring-polymer position distribution has non-zero overlap with the exact distribution in the infinite-bead limit for the case of a harmonic potential. We show that dimension freedom can be achieved via mollification of the forces from the physical potential and with the BCOCB integration scheme. The dimension-free numerical integration schemes yield finite error bounds for a given MD timestep as the number of beads is taken to infinity; these conclusions are proven for harmonic potential and borne out numerically for anharmonic systems, including water. The numerical results for BCOCB are particularly striking, allowing for three-fold increases in the stable timestep for liquid water with respect to the Bussi-Parrinello (OBABO) and Leimkuhler (BAOAB) integrators while introducing negligible errors in the statistical properties and absorption spectrum. Importantly, the dimension-free, non-preconditioned integration schemes introduced here preserve ergodicity and global second-order accuracy, and they remain simple, black-box methods that avoid additional computational costs, tunable parameters, or system-specific implementations.

Zero- and High-Pressure Mechanisms in the Complex Forming Reactions of OH with Methanol and Formaldehyde at Low Temperatures

Abstract: A recent Ring Polymer Molecular Dynamics study of the reactions of OH with methanol and formaldehyde, at zero pressure and below 100 K, has shown the formation of long lived complexes, with long lifetimes, longer than 100 ns for the lower temperatures studied, 20-100 K (del Mazo-Sevillano et al., 2019). These long lifetimes support the existence of multi collision events with the He buffer-gas atoms under experimental conditions, as suggested by several transition state theory studies of these reactions. In this work we study these secondary collisions, as a dynamical approach to study pressure effects on these reactions. For this purpose, the potential energy surfaces of He with H2CO, OH, H2O and HCO are calculated at highly accurate ab initio level. The stability of some of the complexes is studied using Path Integral Molecular dynamics techniques, determining that OH-H2CO complexes can be formed up to 100 K or higher temperatures, while the weaker He-H2CO complexes dissociate at approximately 50 K. The predicted IR intensity spectra shows new features which could help the identification of the OH-H2CO complex. Finally, the He-H2CO + OH and OH-H2CO + He collisions are studied using quassi-classical trajectories, finding that the cross section to produce HCO + H2O products increases with decreasing collision energy, and that it is ten times higher in the He-H2CO + OH case.

The UVA response of enolic dibenzoylmethane: beyond the static approach.

Abstract: Enolic dibenzoylmethane is used in cosmetic sunscreens as a UVA filter because it strongly absorbs radiation around 340 nm. Assessing the absorption properties solely on the basis of the vertical excitation spectrum at the minimum of the potential energy surface leads to the conclusion that the nπ* state is not initially photoexcited. Since this molecule exhibits large changes in structure due to nuclear thermal and quantum fluctuations, it is not sufficient to consider one molecular configuration but an ensemble of configurations. In this work, we simulate its UVA response by employing the DFT/MRCI method in conjunction with configurations sampled from density functional theory-based classical and path integral molecular dynamics as well as by computing Franck-Condon factors. Our findings indicate that thermal and nuclear quantum fluctuations symmetrically broaden the excited states' absorption within the semi-classical approximation and thus it is necessary to include vibronic effects in order to correctly reproduce the experimental spectrum. The absorption is largely dominated by the ππ* state but there is a minor contribution from the nπ* state, contrary to the static result. The crossing between these two states occurs during the intramolecular proton transfer. This knowledge is of importance for studying photorelaxation mechanisms of dibenzoylmethane and other β-diketone compounds.

Two-scale coupling for preconditioned Hamiltonian Monte Carlo in infinite dimensions

Abstract: We derive non-asymptotic quantitative bounds for convergence to equilibrium of the exact preconditioned Hamiltonian Monte Carlo algorithm (pHMC) on a Hilbert space. As a consequence, explicit and dimension-free bounds for pHMC applied to high-dimensional distributions arising in transition path sampling and path integral molecular dynamics are given. Global convexity of the underlying potential energies is not required. Our results are based on a two-scale coupling which is contractive in a carefully designed distance.

Using a monomer potential energy surface to perform approximate path integral molecular dynamics simulation of ab initio water at near-zero added cost

Abstract: It is now established that nuclear quantum motion plays an important role in determining water's hydrogen bonding, structure, and dynamics. Such effects are important to include in density functional theory (DFT) based molecular dynamics simulation of water. The standard way of treating nuclear quantum effects, path integral molecular dynamics (PIMD), multiplies the number of energy/force calculations by the number of beads required. In this work we introduce a method whereby PIMD can be incorporated into a DFT simulation with little extra cost and little loss in accuracy. The method is based on the many body expansion of the energy and has the benefit of including a monomer level correction to the DFT energy. Our method calculates intramolecular forces using the highly accurate monomer potential energy surface developed by Partridge–Schwenke, which is cheap to evaluate. Intermolecular forces and energies are calculated with DFT only once per timestep using the centroid positions. We show how our method may be used in conjunction with a multiple time step algorithm for an additional speedup and how it relates to ring polymer contraction and other schemes that have been introduced recently to speed up PIMD simulations. We show that our method, which we call “monomer PIMD”, correctly captures changes in the structure of water found in a full PIMD simulation but at much lower computational cost.

Quantum Stabilization of the Frustrated Hydrogen Bonding Structure in the Hydrogen Fluoride Trimer.

Abstract: We performed ab initio path integral molecular dynamics (PIMD) and molecular dynamics (MD) simulations to discuss the thermal and nuclear quantum effects on the stabilities of hydrogen bonding netw...

A path integral molecular dynamics study on intermolecular hydrogen bond of acetic acid-arsenic acid anion and acetic acid-phosphoric acid anion clusters.

Abstract: We apply ab initio path integral molecular dynamics simulation employing ωB97XD as the quantum chemical calculation method to acetic acid-arsenic acid anion and acetic acid-phosphoric acid anion clusters to investigate the difference of the hydrogen bond structure and its fluctuation such as proton transfer. We found that the nuclear quantum effect enhanced the fluctuation of the hydrogen bond structure and proton transfer, which shows treatment of the nuclear quantum effect was essential to investigate these systems. The hydrogen bond in acetic acid-arsenic acid anion cluster showed characters related to low-barrier hydrogen bonds, while acetic acid-phosphoric acid anion cluster did not. We found non-negligible distinction between these two systems, which could not be found in conventional calculations. We suggest that the difference in amount of atomic charge of the atoms consisting the hydrogen bond is the origin of the difference between acetic acid-arsenic acid and acetic acid-phosphoric acid anion cluster. © 2018 Wiley Periodicals, Inc.

Nuclear quantum effects in molecular dynamics simulations

Abstract: To take into account nuclear quantum effects on the dynamics of atoms, the path integral molecular dynamics (PIMD) method used since 1980s is based on the formalism developed by R. P. Feynman. However, the huge computation time required for the PIMD reduces its range of applicability. Another drawback is the requirement of additional techniques to access time correlation functions (ring polymer MD or centroid MD). We developed an alternative technique based on a quantum thermal bath (QTB) which reduces the computation time by a factor of ~20. The QTB approach consists in a classical Langevin dynamics in which the white noise random force is replaced by a Gaussian random force having the power spectral density given by the quantum fluctuation-dissipation theorem. The method has yielded satisfactory results for weakly anharmonic systems: the quantum harmonic oscillator, the heat capacity of a MgO crystal, and isotope effects in 7 LiH and 7 LiD. Unfortunately, the QTB is subject to the problem of zero-point energy leakage (ZPEL) in highly anharmonic systems, which is inherent in the use of classical mechanics. Indeed, a part of the energy of the high-frequency modes is transferred to the low-frequency modes leading to a wrong energy distribution. We have shown that in order to reduce or even eliminate ZPEL, it is sufficient to increase the value of the frictional coefficient. Another way to solve the ZPEL problem is to combine the QTB and PIMD techniques. It requires the modification of the power spectral density of the random force within the QTB. This combination can also be seen as a way to speed up the PIMD.

Classical and path-integral molecular-dynamics study on liquid water and ice melting using non-empirical TTM2.1-F model

Abstract: The TTMF2.1-F model is a non-empirical intermolecular water potential parametrised from ab-initio calculations of the water dimer with a complete basis set limit including dispersion correction fro...

Nuclear Motion in the Intramolecular Dihydrogen-Bound Regime of an Aminoborane Complex.

Abstract: The 1,3-diaza-2,4-diborobutane (NBNB) molecule serves as the smallest model complex of an intramolecular “dihydrogen bond,” which involves a nominally hydrogen-bonding interaction between amine and borane hydrogen atoms. In the present study, the role of this dihydrogen bond in influencing the inherent molecular dynamics of NBNB is investigated computationally with ab initio molecular dynamics and path integral molecular dynamics techniques, as well as vibrational spectra analysis and static quantum chemistry computations. These simulations indicate that the dihydrogen-bonding interaction impacts both the high- and low-frequency motions of the molecule, with the dominant motions involving low-frequency backbone isomerization and terminal amine rotation. Geometric isotope effects were found to be modest. The analysis also addresses the paradoxical fostering of amine rotation via a relatively strong dihydrogen bond interaction. Electrostatic and geometric factors most directly explain this effect, and altho...

Quantum Momentum Distribution and Quantum Entanglement in the Deep Tunneling Regime

Abstract: In this paper, we consider the momentum operator of a quantum particle directed along the displacement of two of its neighbors. A modified open-path path integral molecular dynamics is presented to sample the distribution of this directional momentum distribution, where we derive and use a new estimator for this distribution. Variationally enhanced sampling is used to obtain this distribution for an example molecule, Malonaldehyde, in the very low temperature regime where deep tunneling happens. We find no secondary feature in the directional momentum distribution, and that its absence is due to quantum entanglement through a further study of the reduced density matrix.