Path Integral Molecular Dynamics Research Articles

Ring-Polymer Molecular Dynamics and Kinetics for the H- + C2H2 → H2 + C2H- Reaction Using the Full-Dimensional Potential Energy Surface.

The H- + C2H2 → H2 + C2H- reaction is important in understanding the production mechanisms of anionic molecules in interstellar environments. Herein, the rate coefficients for the H- + C2H2 → H2 + C2H- reaction were calculated using ring-polymer molecular dynamics (RPMD), classical molecular dynamics (MD), and quasi-classical trajectory (QCT) approaches on a newly developed ab initio potential energy surface (PES) in full dimensions. PES was constructed by fitting a large number of ab initio energy points and their gradients using the permutationally invariant polynomial basis set method. There was no barrier in the reaction coordinates, which was a collinear-dominated reaction, and the reaction proceeded exothermically. It is found that the fitted PES provides the appropriate thermal rate coefficients based on all RPMD, classical MD, and QCT simulations at higher temperatures. The evaluation of the rate coefficients at lower temperatures should be conducted carefully because the fitting of the PES associated with the long-range interaction should be further improved. The spatial distribution of the nucleus allows a more effective attraction between the reactants.

First principles molecular dynamics study of proton disorder in [formula omitted] phase of H2 hydrate

The proton-disordered and -ordered crystal structures proposed based on X-ray diffraction experiments for the C1′ phase of H2 hydrate were investigated using first-principles (FP) path-integral ring-polymer molecular dynamics (RPMD) simulations. Our simulated Raman spectra obtained from the FP-RPMD trajectories provide unambiguous evidence for static orientational disorder of H2O molecules forming stacked H-bonded rings. This feature is essential to reproduce the characteristics of the observed Raman spectra. Furthermore, the present study shows that van der Waals interactions need to be treated carefully to achieve satisfactory computational results. The findings of this study can help for better understanding of icy materials.

Accurate path-integral molecular dynamics calculation of aluminum with improved empirical ionic potentials

We show that an accurate description of the interplay between the anharmonic ionic interaction and the zero-point fluctuation of ions in crystalline aluminum (Al) can be achieved using the path-integral molecular dynamics (PIMD) method in conjunction with improved empirical modified embedded-atom method (MEAM) potentials. Our results show that the zero-point fluctuation of ions is noticeable at a temperature between 200 K and 250 K, roughly half of the Al Debye temperature of 428 K, with a selective influence on mechanical properties. The effect provides appreciable corrections to the lattice constant $a$, bulk modulus $B$, and elastic constant ${C}_{11}$ at low temperature, but without much influence on elastic constants ${C}_{12}$ and ${C}_{44}$. With a revised MEAM potential which takes into consideration the influence of zero-point fluctuations, the PIMD method has a much improved accuracy in $a, B$, and the $C$'s up to 700 K, when compared with precision experimental measurements. The largest errors of $a$ and $B$ can even be reduced by about an order in percentage below 300 K.

The hydrogen bond continuum in solid isonicotinic acid

The understanding and correct description of intermolecular hydrogen bonds are crucial in the field of multicomponent pharmaceutical solids, such as salts and cocrystals. Solid isonicotinic acid can serve as a suitable model for the development of methods that can accurately characterize these hydrogen bonds. Experimental solid-state NMR has revealed a remarkable temperature dependence and deuterium-isotope-induced changes of the chemical shifts of the atoms involved in the intermolecular hydrogen bond; these NMR data are related to changes of the average position of the hydrogen atom. These changes of NMR parameters were interpreted using periodic DFT path-integral molecular dynamics (PIMD) simulations. The small size of the unit cell of isonicotinic acid allowed for PIMD simulations with the computationally demanding hybrid DFT functional. Calculations of NMR parameters based on the hybrid-functional PIMD simulations are in excellent agreement with experiment. It is thus demonstrated that an accurate characterization of intermolecular hydrogen bonds can be achieved by a combination of NMR experiments and advanced computations.

Chalcogen Bond as a Factor Stabilizing Ligand Conformation in the Binding Pocket of Carbonic Anhydrase IX Receptor Mimic.

It is postulated that the overexpression of Carbonic Anhydrase isozyme IX in some cancers contributes to the acidification of the extracellular matrix. It was proved that this promotes the growth and metastasis of the tumor. These observations have made Carbonic Anhydrase IX an attractive drug target. In the light of the findings and importance of the glycoprotein in the cancer treatment, we have employed quantum-chemical approaches to study non-covalent interactions in the binding pocket. As a ligand, the acetazolamide (AZM) molecule was chosen, being known as a potential inhibitor exhibiting anticancer properties. First-Principles Molecular Dynamics was performed to study the chalcogen and other non-covalent interactions in the AZM ligand and its complexes with amino acids forming the binding site. Based on Density Functional Theory (DFT) and post-Hartree-Fock methods, the metric and electronic structure parameters were described. The Non-Covalent Interaction (NCI) index and Atoms in Molecules (AIM) methods were applied for qualitative/quantitative analyses of the non-covalent interactions. Finally, the AZM-binding pocket interaction energy decomposition was carried out. Chalcogen bonding in the AZM molecule is an important factor stabilizing the preferred conformation. Free energy mapping via metadynamics and Path Integral molecular dynamics confirmed the significance of the chalcogen bond in structuring the conformational flexibility of the systems. The developed models are useful in the design of new inhibitors with desired pharmacological properties.

Full Temperature-Dependent Potential and Anharmonicity in Metallic Hydrogen: Colossal NQE and the Consequences

The temperature-dependent effective potential (TDEP) method for anharmonic phonon dispersion is generalized to the full potential case by combining with path integral formalism. This extension naturally resolves the intrinsic difficulty in the original TDEP at low temperature. The new method is applied to solid metallic hydrogen at high pressure. A colossal nuclear quantum effect (NQE) and subsequent anharmonicity are discovered, which not only leads to unexpectedly large drift of protons, but also slows down the convergence rate substantially when computing the phonon dispersions. By employing direct ab initio path integral molecular dynamics simulations as the benchmark, a possible breakdown of phonon picture in metallic hydrogen due to colossal NQE is indicated, implying novel lattice dynamical phenomena might exist. Inspired by this observation, a general theoretical formalism for quantum lattice dynamics beyond phonon is sketched, with the main features being discussed.

Improved torque estimator for condensed-phase quasicentroid molecular dynamics.

We describe improvements to the quasicentroid molecular dynamics (QCMD) path-integral method, which was developed recently for computing the infrared spectra of condensed-phase systems. The main development is an improved estimator for the intermolecular torque on the quasicentroid. When applied to qTIP4P/F liquid water and ice, the new estimator is found to remove an artificial 25 cm-1 red shift from the libration bands, to increase slightly the intensity of the OH stretch band in the liquid, and to reduce small errors noted previously in the QCMD radial distribution functions. We also modify the mass-scaling used in the adiabatic QCMD algorithm, which allows the molecular dynamics timestep to be quadrupled, thus reducing the expense of a QCMD calculation to twice that of Cartesian centroid molecular dynamics for qTIP4P/F liquid water at 300K, and eight times for ice at 150K.

Importance of Nuclear Quantum Effects on Aqueous Electrolyte Transport under Confinement in Ti3C2 MXenes.

Protons display a high chemical activity and strongly affect the charge storage capability in confined interlayer spaces of two-dimensional (2D) materials. As such, an accurate representation of proton dynamics under confinement is important for understanding and predicting charge storage dynamics in these materials. While often ignored in atomistic-scale simulations, nuclear quantum effects (NQEs), e.g., tunneling, can be significant under confinement even at room temperature. Using the thermostatted ring polymer molecular dynamics implementation of path integral molecular dynamics (PIMD) in conjunction with the ReaxFF force field, density functional tight binding (DFTB), and NequIP neural network potential simulations, we investigate the role of NQEs on proton and water transport in bulk water and aqueous electrolytes under confinement in Ti3C2 MXenes. Although overall NQEs are relatively small, especially in bulk, we find that they can alter both quantitative values and qualitative trends on both proton transport and water self-diffusion under confinement relative to classical MD predictions. Therefore, our results suggest the need for NQEs to be considered to simulate aqueous systems under confinement for both qualitative and quantitative accuracy.

Imaginary-time open-chain path-integral approach for two-state time correlation functions and applications in charge transfer.

Quantum time correlation functions (TCFs) involving two states are important for describing nonadiabatic dynamical processes such as charge transfer (CT). Based on a previous single-state method, we propose an imaginary-time open-chain path-integral (OCPI) approach for evaluating the two-state symmetrized TCFs. Expressing the forward and backward propagation on different electronic potential energy surfaces as a complex-time path integral, we then transform the path variables to average and difference variables such that the integration over the difference variables up to the second order can be performed analytically. The resulting expression for the symmetrized TCF is equivalent to sampling the open-chain configurations in an effective potential that corresponds to the average surface. Using importance sampling over the extended OCPI space via open path-integral molecular dynamics, we tested the resulting path-integral approximation by calculating the Fermi's golden rule CT rate constant within a widely used spin-boson model. Comparing with the real-time linearized semiclassical method and analytical result, we show that the imaginary-time OCPI provides an accurate two-state symmetrized TCF and rate constant in the typical turnover region. It is shown that the first bead of the open chain corresponds to physical zero-time and that the endpoint bead corresponds to final time t; oscillations of the end-to-end distance perfectly match the nuclear mode frequency. The two-state OCPI scheme is seen to capture the tested model's electronic quantum coherence and nuclear quantum effects accurately.

Centroid Molecular Dynamics Can Be Greatly Accelerated through Neural Network Learned Centroid Forces Derived from Path Integral Molecular Dynamics.

For nearly the past 30 years, centroid molecular dynamics (CMD) has proven to be a viable classical-like phase space formulation for the calculation of quantum dynamical properties. However, calculation of the centroid effective force remains a significant computational cost and limits the ability of CMD to be an efficient approach to study condensed phase quantum dynamics. In this paper, we introduce a neural network-based methodology for first learning the centroid effective force from path integral molecular dynamics data, which is subsequently used as an effective force field to evolve the centroids directly with the CMD algorithm. This method, called machine-learned centroid molecular dynamics (ML-CMD), is faster and far less costly than both standard "on the fly" CMD and ring polymer molecular dynamics (RPMD). The training aspect of ML-CMD is also straightforwardly implemented utilizing the DeepMD software kit. ML-CMD is then applied to two model systems to illustrate the approach: liquid para-hydrogen and water. The results show comparable accuracy to both CMD and RPMD in the estimation of quantum dynamical properties, including the self-diffusion constant and velocity time correlation function, but with significantly reduced overall computational cost.

Path integral Brownian chain molecular dynamics: A simple approximation of quantum vibrational dynamics.

An approximate approach to quantum vibrational dynamics, "Brownian chain molecular dynamics (BCMD)," is proposed to alleviate the chain resonance and curvature problems in the imaginary time-based path integral (PI) simulation. Here the non-centroid velocity is randomized at each step when solving the equation of motion of path integral molecular dynamics. This leads to a combination of the Newton equation and the overdamped Langevin equation for the centroid and non-centroid variables, respectively. BCMD shares the basic properties of other PI approaches such as centroid and ring polymer molecular dynamics: It gives the correct Kubo-transformed correlation function at short times, conserves the time symmetry, has the correct high-temperature/classical limits, gives exactly the position and velocity autocorrelations of harmonic oscillator systems, and does not have the zero-point leakage problem. Numerical tests were done on simple molecular models and liquid water. On-the-fly ab initio BCMD simulations were performed for the protonated water cluster, , and its isotopologue, .

Renormalization of excitonic properties by polar phonons.

We employ quasiparticle path integral molecular dynamics to study how the excitonic properties of model semiconductors are altered by electron-phonon coupling. We describe ways within a path integral representation of the system to evaluate the renormalized mass, binding energy, and radiative recombination rate of excitons in the presence of a fluctuating lattice. To illustrate this approach, we consider Fröhlich-type electron-phonon interactions and employ an imaginary time influence functional to incorporate phonon-induced effects nonperturbatively. The effective mass and binding energies are compared with perturbative and variational approaches, which provide qualitatively consistent trends. We evaluate electron-hole recombination rates as mediated through both trap-assisted and bimolecular processes, developing a consistent statistical mechanical approach valid in the reaction limited regime. These calculations demonstrate how phonons screen electron-hole interactions, generically reducing exciton binding energies and increasing their radiative lifetimes.

2D spectroscopies from condensed phase dynamics: Accessing third-order response properties from equilibrium multi-time correlation functions

The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two-dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopic techniques provide access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established, it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, centroid molecular dynamics, and Ring Polymer Molecular Dynamics (RPMD), naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.

On the thermodynamic properties of fictitious identical particles and the application to fermion signproblem.

By generalizing the recently developed path integral molecular dynamics for identical bosons and fermions, we consider the finite-temperature thermodynamic properties of fictitious identical particles with a real parameter ξ interpolating continuously between bosons (ξ = 1) and fermions (ξ = -1). Through general analysis and numerical experiments, we find that the average energy may have good analytical properties as a function of this real parameter ξ, which provides the chance to calculate the thermodynamical properties of identical fermions by extrapolation with a simple polynomial function after accurately calculating the thermodynamic properties of the fictitious particles for ξ ≥ 0. Using several examples, it is shown that our method can efficiently give accurate energy values for finite-temperature fermionic systems. Our work provides a chance to circumvent the fermion signproblem for some quantum systems.

Quantum effects in two-dimensional silicon carbide

Two-dimensional (2D) silicon carbide is an emergent direct band-gap semiconductor, recently synthesized, with potential applications in electronic devices and optoelectronics. Here, we study nuclear quantum effects in this 2D material by means of path-integral molecular dynamics (PIMD) simulations in the temperature range from 25 to 1500 K. Interatomic interactions are modeled by a tight-binding Hamiltonian fitted to density-functional calculations. Quantum atomic delocalization combined with anharmonicity of the vibrational modes cause changes in structural and thermal properties of 2D SiC, which we quantify by comparison of PIMD results with those derived from classical molecular dynamics simulations, as well as with those given by a quantum harmonic approximation. Nuclear quantum effects are found to be appreciable in structural properties such as the layer area and interatomic distances. Moreover, we consider a real area for the SiC sheet, which takes into account bending and rippling at finite temperatures. Differences between this area and the in-plane area are discussed in the context of quantum atomic dynamics. The bending constant (κ=1.0eV) and the 2D modulus of hydrostatic compression (Bxy = 5.5 eV/Å 2) are clearly lower than the corresponding values for graphene. This study paves the way for a deeper understanding of the elastic and mechanical properties of 2D SiC.

Coarse-Graining of Imaginary Time Feynman Path Integrals: Inclusion of Intramolecular Interactions and Bottom-up Force-Matching.

Feynman's imaginary time path integral formalism of quantum statistical mechanics and the corresponding quantum-classical isomorphism provide a tangible way of incorporating nuclear quantum effect (NQE) in the simulation of condensed matter systems using well-developed classical simulation techniques. Our previous work has presented the many-body coarse-graining of path integral (CG-PI) theory that builds an isomorphism between the quantum partition function of N distinguishable particles and the classical partition function of 2N pseudoparticles. In this present work, we develop a generalized version of the many-body CG-PI theory that incorporates many-body interactions in the force field. Based on the new derivation, we provide a numerical CG-PI (n-CG-PI) modeling strategy parametrized from the underlying path integral molecular dynamics (PIMD) trajectories using force matching and Boltzmann inversion. The n-CG-PI models for two liquid systems are shown to capture well both the intramolecular and intermolecular structural correlations of the reference PIMD simulations. The generalized derivation of the many-body CG-PI theory and the n-CG-PI model presented in this work extend the scope of the CG-PI formalism by generalizing the previously limited theory to incorporate force fields of realistic molecular systems.

Hydrogen phase-IV characterization by full account of quantum anharmonicity

We devise a framework to compute accurate phonons in molecular crystals even in case of strong quantum anharmonicity. Our approach is based on the calculation of the static limit of the phononic Matsubara Green's function from path integral molecular dynamics simulations. Our method enjoys a remarkably low variance, which allows one to compute accurate phonon frequencies after a few picoseconds of nuclear dynamics, and it is further stabilized by the use of appropriate constrained displacement operators. We applied it to solid hydrogen at high pressure. For phase III, our predicted infrared (IR) and Raman active vibrons agree very well with experiments. We then characterize the crystalline symmetry of phase IV by direct comparison with vibrational data and we determine the character of its Raman and IR vibron peaks.

New Stable and Fast Ring-Polymer Molecular Dynamics for Calculating Bimolecular Rate Coefficients with an Example of OH + CH4

The accurate and efficient calculation of the rate coefficients of chemical reactions is a key issue in the research of chemical dynamics. In this work, by applying the dimension-free ultrastable Cayley propagator, the thermal rate coefficients of a prototypic high dimensional chemical reaction OH + CH4 → H2O + CH3 in the temperature range of 200 to 1500 K are investigated with ring polymer molecular dynamics (RPMD) on a highly accurate full-dimensional potential energy surface. Kinetic isotope effects (KIEs) for three isotopologues of the title reaction are also studied. The results demonstrate excellent agreement with experimental data, even in the deep tunneling region. Especially, the Cayley propagator shows a high calculation efficiency with little loss of accuracy. The present results confirmed the applicability of the RPMD method, particularly the speed-up using a Cayley propagator, in theoretical calculations of bimolecular reaction rates.

ℏ2 expansion of the transmission probability through a barrier.

Ninety years ago, Wigner derived the leading order expansion term in ℏ2 for the tunneling rate through a symmetric barrier. His derivation included two contributions: one came from the parabolic barrier, but a second term involved the fourth-order derivative of the potential at the barrier top. He left us with a challenge, which is answered in this paper, to derive the same but for an asymmetric barrier. A crucial element of the derivation is obtaining the ℏ2 expansion term for the projection operator, which appears in the flux-side expression for the rate. It is also reassuring that an analytical calculation of semiclassical transition state theory (TST) reproduces the anharmonic corrections to the leading order of ℏ2. The efficacy of the resulting expression is demonstrated for an Eckart barrier, leading to the conclusion that especially when considering heavy atom tunneling, one should use the expansion derived in this paper, rather than the parabolic barrier approximation. The rate expression derived here reveals how the classical TST limit is approached as a function of ℏ and, thus, provides critical insights to understand the validity of popular approximate theories, such as the classical Wigner, centroid molecular dynamics, and ring polymer molecular dynamics methods.

Stability and distortion of fcc LaH10 with path-integral molecular dynamics

The synthesis of the high temperature superconductor LaH$_{10}$ requires pressures in excess of 100 GPa, wherein it adopts a face-centered cubic structure. Upon decompression, this structure undergoes a distortion which still supports superconductivity, but with a much lower critical temperature. Previous calculations have shown that quantum and anharmonic effects are necessary to stabilize the cubic structure, but have not resolved the low pressure distortion. Using large scale path-integral molecular dynamics enabled by a machine learned potential, we show that a rhombohedral distortion appears at sufficiently low pressures, even with quantum and anharmonic effects. We also highlight the importance of quantum zero point motion in stabilizing the cubic structure.