Path Integral Molecular Dynamics Techniques Research Articles

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

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 although some orbital evidence was found for a small covalent component of this interaction, the dynamics and electronic structure suggest that electrostatic contributions are the controlling factors for molecular motion in NBNB.

Zero- and high-pressure mechanisms in the complex forming reactions of OH with methanol and formaldehyde at low temperatures.

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.

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

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.

Nuclear quantum effects in molecular dynamics simulations

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 7LiH and 7LiD. 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.

I-PI 2.0: A universal force engine for advanced molecular simulations

Progress in the atomic-scale modeling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by either solving the electronic structure problem explicitly, or by computing accurate approximations of the solution and by the development of techniques that use the Born–Oppenheimer (BO) forces to move the atoms on the BO potential energy surface. As a consequence of these developments it is now possible to identify stable or metastable states, to sample configurations consistent with the appropriate thermodynamic ensemble, and to estimate the kinetics of reactions and phase transitions. All too often, however, progress is slowed down by the bottleneck associated with implementing new optimization algorithms and/or sampling techniques into the many existing electronic-structure and empirical-potential codes. To address this problem, we are thus releasing a new version of the i-PI software. This piece of software is an easily extensible framework for implementing advanced atomistic simulation techniques using interatomic potentials and forces calculated by an external driver code. While the original version of the code (Ceriotti et al., 2014) was developed with a focus on path integral molecular dynamics techniques, this second release of i-PI not only includes several new advanced path integral methods, but also offers other classes of algorithms. In other words, i-PI is moving towards becoming a universal force engine that is both modular and tightly coupled to the driver codes that evaluate the potential energy surface and its derivatives. Program summaryProgram Title: i-PIProgram Files doi:http://dx.doi.org/10.17632/x792grbm9g.1Licensing provisions: GPLv3, MITProgramming language: PythonExternal routines/libraries: NumPyNature of problem: Lowering the implementation barrier to bring state-of-the-art sampling and atomistic modeling techniques to ab initio and empirical potentials programs.Solution method: Advanced sampling methods, including path-integral molecular dynamics techniques, are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic coordinates from the Python interface, and to return the forces and energy that are used to integrate the equations of motion, optimize atomic geometries, etc.Restrictions: This code does not compute interatomic potentials, although the distribution includes sample driver codes that can be used to test different techniques using a few simple model force fields.

Nuclear Quantum Effects in Water at the Triple Point: Using Theory as a Link Between Experiments.

One of the most prominent consequences of the quantum nature of light atomic nuclei is that their kinetic energy does not follow a Maxwell-Boltzmann distribution. Deep inelastic neutron scattering (DINS) experiments can measure this effect. Thus, the nuclear quantum kinetic energy can be probed directly in both ordered and disordered samples. However, the relation between the quantum kinetic energy and the atomic environment is a very indirect one, and cross-validation with theoretical modeling is therefore urgently needed. Here, we use state of the art path integral molecular dynamics techniques to compute the kinetic energy of hydrogen and oxygen nuclei in liquid, solid, and gas-phase water close to the triple point, comparing three different interatomic potentials and validating our results against equilibrium isotope fractionation measurements. We will then show how accurate simulations can draw a link between extremely precise fractionation experiments and DINS, therefore establishing a reliable benchmark for future measurements and providing key insights to increase further the accuracy of interatomic potentials for water.

Quantum localization/delocalization of muonium in the glycine–K+ complex

Previous electronic structure studies have revealed that the glycine–K+ complex has a low-barrier intramolecular proton-transfer pathway between zwitterionic and neutral forms. We have theoretically calculated quantum molecular structures of this complex including the proton-transfer process using a path-integral molecular dynamics technique on an interpolated potential energy surface developed at the B3LYP level of theory. When the transferring proton is substituted by muon, it was found that the muonium atom showed a broad distribution around the proton(muon)-transfer transition state region between the neutral and zwitterionic structures due to extreme nuclear quantum effects of a very light particle although the distribution peak is slightly deviated from the transition state. The present study demonstrates that Mu can be employed to probe transition-state regions of potential energy surfaces of proton-transfer chemical reactions.

I-PI: A Python interface for ab initio path integral molecular dynamics simulations

Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water. Program summaryProgram title: i-PICatalogue identifier: AERN_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AERN_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 138626No. of bytes in distributed program, including test data, etc.: 3128618Distribution format: tar.gzProgramming language: Python.Computer: Multiple architectures.Operating system: Linux, Mac OSX, Windows.RAM: Less than 256 MbClassification: 7.7.External routines: NumPyNature of problem:Bringing the latest developments in the modelling of nuclear quantum effects with path integral molecular dynamics to ab initio electronic structure programs with minimal implementational effort.Solution method:State-of-the-art path integral molecular dynamics techniques are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic coordinates from the Python interface, and to return the forces and energy that are used to integrate the equations of motion.Restrictions:This code only deals with distinguishable particles. It does not include fermonic or bosonic exchanges between equivalent nuclei, which can become important at very low temperatures.Running time:Depends dramatically on the nature of the simulation being performed. A few minutes for short tests with empirical force fields, up to several weeks for production calculations with ab initio forces. The examples provided with the code run in less than an hour.

The vibrational proton potential in bulk liquid water and ice

We present an empirical flexible and polarizable water model which gives an improved description of the position, momentum, and dynamical (spectroscopic) distributions of H nuclei in water. We use path integral molecular dynamics techniques in order to obtain momentum and position distributions and an approximate solution to the Schrodinger equation to obtain the infrared (IR) spectrum. We show that when the calculated distributions are compared to experiment the existing empirical models tend to overestimate the stiffness of the H nuclei involved in H bonds. Also, these models vastly underestimate the enormous increase in the integrated IR intensity observed in the bulk over the gas-phase value. We demonstrate that the over-rigidity of the OH stretch and the underestimation of intensity are connected to the failure of existing models to reproduce the correct monomer polarizability surface. A new model, TTM4-F, is parametrized against electronic structure results in order to better reproduce the polarizability surface. It is found that TTM4-F gives a superior description of the observed spectroscopy, showing both the correct redshift and a much improved intensity. TTM4-F also has a somewhat improved dielectric constant and OH distribution function. It also gives an improved match to the experimental momentum distribution, although some discrepancies remain.

Simulations of one- and two-electron systems by Bead-Fourier path integral molecular dynamics

The Bead-Fourier path integral molecular dynamics technique introduced earlier [S. D. Ivanov, A. P. Lyubartsev, and A. Laaksonen, Phys. Rev. E 67 066710 (2003)] is applied for simulation of electrons in the simplest molecules: molecular hydrogen, helium atom, and their ions. Special attention is paid to the correct description of electrons in the core region of a nucleus. In an attempt to smooth the Coulomb potential at small distances, a recipe is suggested. The simulation results are in excellent agreement with the analytical solution for the "harmonic helium atom", as well as with the vibrational potential of the H(2) molecule and He ionization energies. It is demonstrated, that the Bead-Fourier path integral molecular dynamics technique is able to provide the accuracy required for the description of electron structure and chemical bonds in cases when electron exchange effects need not be taken into account.

Path integral hybrid Monte Carlo algorithm for correlated Bose fluids.

Path integral hybrid Monte Carlo (PIHMC) algorithm for strongly correlated Bose fluids has been developed. This is an extended version of our previous method [S. Miura and S. Okazaki, Chem. Phys. Lett. 308, 115 (1999)] applied to a model system consisting of noninteracting bosons. Our PIHMC method for the correlated Bose fluids is constituted of two trial moves to sample path-variables describing system coordinates along imaginary time and a permutation of particle labels giving a boundary condition with respect to imaginary time. The path-variables for a given permutation are generated by a hybrid Monte Carlo method based on path integral molecular dynamics techniques. Equations of motion for the path-variables are formulated on the basis of a collective coordinate representation of the path, staging variables, to enhance the sampling efficiency. The permutation sampling to satisfy Bose-Einstein statistics is performed using the multilevel Metropolis method developed by Ceperley and Pollock [Phys. Rev. Lett. 56, 351 (1986)]. Our PIHMC method has successfully been applied to liquid helium-4 at a state point where the system is in a superfluid phase. Parameters determining the sampling efficiency are optimized in such a way that correlation among successive PIHMC steps is minimized.

Ab initio molecular orbital calculation considering the quantum mechanical effect of nuclei by path integral molecular dynamics

We present an accurate calculational scheme for many-body systems composed of electrons and nuclei, by path integral molecular dynamics technique combined with the ab initio molecular orbital theory. Based upon the scheme, the simulation of a water molecule at room temperature is demonstrated, applying all-electron calculation at the Hartree–Fock level of theory.

Ab initio path-integral molecular dynamics

A path-integral molecular dynamics technique for strongly interacting atoms using ab initio potentials derived from density functional theory is implemented. This allows the efficient inclusion of nuclear quantum dispersion in ab initio simulations at finite temperatures. We present an application to the quantum cluster H 5 + .

Quantum simulations of conformation reorganization in the electron transfer reactions of tuna cytochrome c

Quantum simulation schemes based on the Feynman path integral molecular dynamics technique have been used to calculate the effective activation energy associated with nuclear reorganization in the self-exchange reaction of tuna cytochrome c. In addition, a quench technique is used to exhibit the instantons or most probable tunneling paths involved in the reorganization motion. At room temperature, the activation energy is calculated to be 8.8 kJ/mol, close to the estimate by Warshel et al., from purely classical considerations. The quantum contribution is small, 2.6 kJ/mol at room temperature. At lower temperature, the quantum tunneling becomes more significant and the free energy associated with the quantum correction factor begins to dominate, 4.2 kJ/mol at 150 K. The transient tunneling paths can deviate significantly from the transition direction, contrary to the picture one would expect for a purely harmonic system. Corrections to short time dynamics are discussed and shown to be small for tuna cytochrome c at room temperature, using an approximation based on the dispersed polaron method. In addition, the problem of conformational substates and their effect on the tunneling calculation is noted.

The effect of particulate SiC on fatigue crack growth in a cast-extruded aluminium alloy composite: Davidson, D.L. Metall. Trans. A Jan. 1991 22A (1), 97–112

Recent developments in path integral methodology have significantly reduced the computational expense of including quantum mechanical effects in the nuclear motion in ab initio molecular dynamics simulations. However, the implementation of these developments requires a considerable programming effort, which has hindered their adoption. Here we describe i-PI, an interface written in Python that has been designed to minimise the effort required to bring state-of-the-art path integral techniques to an electronic structure program. While it is best suited to first principles calculations and path integral molecular dynamics, i-PI can also be used to perform classical molecular dynamics simulations, and can just as easily be interfaced with an empirical forcefield code. To give just one example of the many potential applications of the interface, we use it in conjunction with the CP2K electronic structure package to showcase the importance of nuclear quantum effects in high-pressure water.Program title: i-PICatalogue identifier: AERN_v1_0Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AERN_v1_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 3No. of lines in distributed program, including test data, etc.: 138626No. of bytes in distributed program, including test data, etc.: 3128618Distribution format: tar.gzProgramming language: Python.Computer: Multiple architectures.Operating system: Linux, Mac OSX, Windows.RAM: Less than 256 MbClassification: 7.7.External routines: NumPyNature of problem:Bringing the latest developments in the modelling of nuclear quantum effects with path integral molecular dynamics to ab initio electronic structure programs with minimal implementational effort.Solution method:State-of-the-art path integral molecular dynamics techniques are implemented in a Python interface. Any electronic structure code can be patched to receive the atomic coordinates from the Python interface, and to return the forces and energy that are used to integrate the equations of motion.Restrictions:This code only deals with distinguishable particles. It does not include fermonic or bosonic exchanges between equivalent nuclei, which can become important at very low temperatures.Running time:Depends dramatically on the nature of the simulation being performed. A few minutes for short tests with empirical force fields, up to several weeks for production calculations with ab initio forces. The examples provided with the code run in less than an hour.

Quantum simulation of nuclear rearrangement in electron transfer reactions

A quantum simulation scheme based on the path integral molecular dynamics technique has been used to calculate the effective activation energies associated with nuclear rearrangement in the electron transfer reactions Co(NH(3))(6) (2+) + Co(NH(3))(6) (3+) --> Co(NH(3))(6) (3+) + Co(NH(3))(6) (2+) and Ru(NH(3))(6) (2+) + Ru(NH(3))(6) (3+) --> Ru(NH(3))(6) (3+) + Ru(NH(3))(6) (2+). Even with a simple Hamiltonian and short time dynamic simulations, the results are in satisfactory agreement with other theoretical calculations. This simulation approach can be used in chemical and biological systems where the reactions are largely controlled by nuclear rearrangements, such as those of electron transfer reactions in some electron carrier proteins.

ChemInform Abstract: Electron Excitation Dynamics, Localization, and Solvation in Small Clusters.

The energetics and dynamics of electronically excited rare-gas clusters and modes of electron attachment and solvation in alkali halide clusters and in water clusters are investigated by classical and quantum path-integral molecular dynamics techniques. The authors demonstrate the versatility and degree of spatial and temporal detail afforded by computer simulations and the new avenues which such studies open for studies of physical and chemical phenomena, not accessible by other modes of investigation.

Electron excitation dynamics, localization and solvation in small clusters

The energetics and dynamics of electronically excited rare-gas clusters and modes of electron attachment and solvation in alkali halide clusters and in water clusters are investigated by classical and quantum path-integral molecular dynamics techniques. The authors demonstrate the versatility and degree of spatial and temporal detail afforded by computer simulations and the new avenues which such studies open for studies of physical and chemical phenomena, not accessible by other modes of investigation.