Theoretical analysis of Muoniated compounds using path integral molecular dynamics method

We present the aspects of the path integral molecular dynamics (PIMD) method relative to (a) its theoretical fundamental principles, (b) its applicability to model quantum systems and (c) its implementation as a simulation tool. The PIMD method is based on the discretized path integral representation of quantum mechanics. In this representation, a quantum particle is isomorphic to a closed polymer chain. The problem of the indistinguishability of quantum particles is tackled with a non-local exchange potential. When the exact density matrix of the quantum particles is used, the exchange potential is exact. We use a high temperature approximation to the density matrix leading to an approximate form of the exchange potential. This quantum molecular dynamics method allows the simulation of collections of quantum particles at finite temperature. Our algorithm can be made to scale linearly with the number of quantum states on which the density matrix is projected. Therefore, it can be optimized to run efficiently on parallel computers. We apply the PIMD method to the electron plasma in 3-dimension. The kinetic and potential energies are calculated and compared with results for similar systems simulated with a variational Monte Carlo method. Both results show good agreements with each other at all the densities studied. The method is then use to model the thermodynamic behavior of a simple alkali metal. In these simulations, ions and valence electrons are treated as classical and quantum particles, respectively. The simple metal undergoes a phase transformation upon heating. Furthermore, to demonstrate the richness of behaviors that can be studied with the PIMD method, we also report on the metal to insulator transition in a hydrogenoid lattice. Finally, in previous studies of alkali metals, electrons interacted with ions via local pseudo-potentials, an extension of the method to modeling electrons in non-local pseudo-potentials is also presented with applications.

A path integral centroid molecular dynamics method for Bose and Fermi statistics

A variational path integral molecular dynamics study of a solid helium-4

Tunneling splittings observed in molecular rovibrational spectra are significant evidence for tunneling motion of hydrogen nuclei in water clusters. Accurate calculations of the splitting sizes from first principles require a combination of high-quality inter-atomic interactions and rigorous methods to treat the nuclei with quantum mechanics. Many theoretical efforts have been made in recent decades. This Perspective focuses on two path-integral based tunneling splitting methods whose computational cost scales well with the system size, namely, the ring-polymer instanton method and the path-integral molecular dynamics (PIMD) method. From a simple derivation, we show that the former is a semiclassical approximation to the latter, despite that the two methods are derived very differently. Currently, the PIMD method is considered to be an ideal route to rigorously compute the ground-state tunneling splitting, while the instanton method sacrifices some accuracy for a significantly smaller computational cost. An application scenario of such a quantitatively rigorous calculation is to test and calibrate the potential energy surfaces of molecular systems by spectroscopic accuracy. Recent progress in water clusters is reviewed, and the current challenges are discussed.

Efficient numerical algorithms are developed for use with two finite temperature semiclassical approximations to quantum dynamics both of which require trajectories generated on potentials of mean force derived from the path integral expression for the density matrix. The numerical algorithms are formed from the combination of a classical adiabatic relation similar to that used in the Car–Parrinello method and an efficient path integral molecular dynamics scheme. Results on model, an anharmonic oscillator and a realistic, fluid para-hydrogen, problem indicate that semiclassical dynamics can be obtained for virtually the same computational cost as structure and thermodynamics.

Recent neutron Compton scattering experiments have detected the proton momentum distribution in water. The theoretical calculation of this property can be carried out via "open" path integral expressions. In this work, present an extension of the staging path integral molecular dynamics method, which is then employed to calculate the proton momentum distributions of water in the solid, liquid, and supercritical phases. We utilize a flexible, single point charge empirical force field to model the system's interactions. The calculated momentum distributions depict both agreement and discrepancies with experiment. The differences may be explained by the deviation of the force field from the true interactions. These distributions provide an abundance of information about the environment and interactions surrounding the proton.

D. Scharf, J. Jortner and U. Landman, atomic and molecular quantum mechanics by the path integral molecular dynamics method: Chem. Phys. Letters 130 (1986) 504

The mechanism of cluster isomerization induced by electron attachment to Na4Cl4 clusters was explored by the constant temperature quantum path integral molecular dynamics method over the temperature range 50°K–1200°K. The configurational modifications can be related to the role of an excess electron as a pseudonegative ion and to the effect of partial neutralization of the alkali ion(s) by the excess electron which induce isomerization at moderately low temperatures in comparison with the parent neutral Na4Cl4 cluster.KeywordsTemperature DomainExcess ElectronReorganization EnergyElectron AttachmentConfigurational ChangeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper we explore the mechanisms of cluster isomerization induced by electron attachment to small, neutral Na4Cl4 clusters, with the localization of an excess electron inducing structural configurational changes within the cluster. The constant temperature quantum path integral molecular dynamics method was applied to obtain information of the structure and energetics of the cluster as well as the binding energy and the charge distribution of the excess electron for Na4Cl−4 clusters, over the temperature range of 50–1200 K. The attachment of an excess electron to the ionic cluster induced two types of configurational modifications, which can be traced to the role of the excess electron as a pseudonegative ion and to the partial neutralization of a single cation by the excess electron. Consequently, the induction of isomerization at moderately low temperatures, in conjunction with the appearance of new nuclear configurations of the negative cluster, which have no counterpart in the neutral parent cluster, are exhibited.

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.

The impact of quantum nuclear effects on hydrogen (H-) bond strength has been inferred in earlier work from bond lengths obtained from path integral molecular dynamics (PIMD) simulations. To obtain a direct quantitative assessment of such effects, we use constrained-centroid PIMD simulations to calculate the free energy changes upon breaking the H-bonds in dimers of HF and water. Comparing ab initio simulations performed using PIMD and classical nucleus molecular dynamics (MD), we find smaller dissociation free energies with the PIMD method. Specifically, at 50 K, the H-bond in (HF)(2) is about 30% weaker when quantum nuclear effects are included, while that in (H(2)O)(2) is about 15% weaker. In a complementary set of simulations, we compare unconstrained PIMD and classical nucleus MD simulations to assess the influence of quantum nuclei on the structures of these systems. We find increased heavy atom distances, indicating weakening of the H-bond consistent with that observed by direct calculation of the free energies of dissociation.

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.

In order to predict the properties of materials from first principles simulations, both the electronic structures and the movement of nuclei should be accurately described. Till now, the electronic structure calculation methods have been relatively well developed, like the density-functional theory, the quantum chemical methods, and the diffusion quantum monte carlo method, etc. By using them, we can get the electronic structures of materials with different levels of accuracy. But the movements of nuclei are still often treated at a clasical level. More and more experimental and theoretical works have found that, the nuclear quantum effects (NQEs) are playing an important role in some phase transition porcesses. Melting line of hydrogen at high pressures were reported through coexistance simulations based on ab initio PIMD methods. We determined the melting temperature as a function of pressure and finded an atomic solid phase from 500 to 800 GPa, which melts at less than 200 K. Beyond this and up to 1200 GPa, a metallic atomic liquid is stable at temperatures as low as 50 K. The quantum motion of the protons is the key to the low melting temperature reported, as simulations with classical nuclei lead to considerably higher melting temperatures of about 300 K across the entire pressure range considered. Then, a combination of state-of-the-art theoretical methods were used to obtain an atomic level picture of classical and quantum ordering of protons in cold high-pressure solid hydrogen. Besides, Using a self-developed combination of the thermodynamic integration and the ab initio PIMD methods, we quantitatively studied the influence of NQEs on the melting of dense lithium at 45 GPa. We find that although the NQEs significantly change the free-energies of the competing solid and liquid phases, the melting temperature is lowered by only about 15 K, with values obtained using both classical and quantum nuclei in close proximity to a new experiment. So, by combining the path-integral molecular dynamics (PIMD) method with techniques like coexistance simulation and free-energy calculation method, the NQEs in many phase transition processes can be well understood.

Path integrals offer a robust approach for simulating open quantum dynamics with advancements transcending initial system size limitations. However, accurately modeling systems governed by mechanisms that do not conserve the number of quantum particles, such as lossy cavity modes, remains a challenge. We present a method to incorporate such empirical source and drain mechanisms within a path integral framework using quantum master equations. This technique facilitates rigorous inclusion of bath degrees of freedom while accommodating empirical time scales via Lindbladian dynamics. Computational costs are primarily driven by the path integral method with minimal overhead from Lindbladian terms. We use it to study exciton transport in a four-site Fenna-Matthews-Olson model, examining the potential loss of the exciton to the reaction center. This path integral Lindblad method promises an enhanced ability to simulate dynamics and will be fundamental to simulation of spectra in diverse quantum processes in open systems.

Solid hydrogen, a simple system consisting only of protons and electrons, exhibits a variety of structural phase transitions at high pressures. Experimental studies based on static compression up to about 230 GPa revealed three relevant phases of solid molecular hydrogen: phase I (high-temperature, low-pressure phase), phase II (low-temperature phase) and phase III (high-pressure phase). Spectroscopic data suggest that symmetry breaking, possibly related to orientational ordering, accompanies the transition into phases II and III. The boundaries dividing the three phases exhibit a strong isotope effect, indicating that the quantum-mechanical properties of hydrogen nuclei are important. Here we report the quantum distributions of protons in the three phases of solid hydrogen, obtained by a first-principles path-integral molecular dynamics method. We show that quantum fluctuations of protons effectively hinder molecular rotation--that is, a quantum localization occurs. The obtained crystal structures have entirely different symmetries from those predicted by the conventional simulations which treat protons classically.