Path Integral Molecular Dynamics Research Articles

Two liquid states of distinguishable helium-4: The existence of another non-superfluid frozen by heating.

We show that two liquid states can exist in distinguishable helium-4 (4He) obeying Boltzmann statistics by path integral centroid molecular dynamics (CMD) simulations. This is an indication of quantum liquid polyamorphism induced by the nuclear quantum effect. For 0.08-3.3K and 1-500bar, we extensively conducted the isothermal-isobaric CMD simulations to explore not only possible states and state diagram but also the state characteristics. The distinguishable 4He below 25bar does not freeze down to 0.1K even though it includes no Bosonic exchange effect and, therefore, no Bose condensation. One liquid state, low quantum-dispersion liquid (LQDL), is nearly identical to normal liquid He-I of real 4He. The other is high quantum-dispersion liquid (HQDL) consisting of atoms with longer quantum wavelength. This is another non-superfluid existing below 0.5K or the temperatures of LQDL. The HQDL is also a low-entropy and fragile liquid to exhibit, unlike conventional liquids, rather gas-like relaxation of velocity autocorrelation function, while there the atoms diffuse without noticeable contribution from quantum tunneling. The LQDL-HQDL transition is not a thermodynamic phase transition but a continuous crossover accompanied by the change in the expansion factor of quantum wavelength. Freezing of HQDL into the low quantum-dispersion amorphous solid occurs by heating from 0.2 to 0.3K at 40-50bar, while this P-T condition coincides with the Kim-Chan normal-supersolid phase boundary of real 4He. The obtained state diagram was compared to that of the confined subnano-scale 4He systems, where Bosonic correlation is considerably suppressed.

Collision of rare-gas atoms on helium nanodroplets: Theoretical evidence for an efficient coagulation of heavy rare-gas atoms.

The coagulation of rare-gas atoms (RG = Ne, Ar, Kr, Xe, and Rn) in helium nanodroplets (HNDs) composed of 1000 atoms is investigated by zero-point averaged dynamics where a He-He pseudopotential is used to make the droplet liquid with proper energies. This method reproduces the qualitative abundances of embedded Arn+1 structures obtained by Time-Dependent Density Functional Theory and Ring Polymer Molecular Dynamics for Ar + ArnHe1000 collisions at realistic projectile speeds and impact parameters. More generally, coagulation is found to be much more efficient for heavy rare-gases (Xe and Rn) than for light ones (Ne and Ar), a behavior mainly attributed to a slower energy dissipation of the projectile in the HND. When coagulation does not occur, the projectile maintains a speed of 10-30m s-1 within the HND, but its velocity vector is rarely oriented toward the dopant, and the projectile roams in a limited region of the droplet. The structure of embedded RGn+1 clusters does not systematically match their gas-phase global minimum structure, and more than 30% of RGn-RG unbound structures are due to one He atom located in between the projectile and a dopant atom.

Impact of Nuclear Quantum Effects on the Structural Properties of Protonated Water Clusters.

Nuclear quantum effects (NQEs) play a crucial role in hydrogen-bonded systems due to quantum tunneling and proton fluctuation. Our understanding of how NQEs affect microstructures mainly focuses on bulk phases of liquids and solids but remains deficient for water clusters, including their hydrogen nuclei, hydrogen-bonded configurations, and temperature dependence. Here, we conducted ab initio molecular dynamics (MD) and path integral MD simulations to investigate the influence of NQEs on the structural properties of protonated water clusters H+(H2O)n (n = 3, 6, 9, 12). The results reveal that the NQEs become less evident as the cluster size increases due to the competition between NQEs and electrostatic interactions. Simulations of several H+(H2O)6 isomers at different temperatures indicate that the effect of elevated temperature on proton transfer is related to the initial structure. Interestingly, the process of proton transfer also involves the interconversion between Zundel-type and Eigen-type isomers. These findings significantly deepen our understanding of ion-water and water-water interactions, opening new avenues for the study of hydrated ion clusters and related systems.

Quantum rates in dissipative systems with spatially varying friction.

We investigate whether making the friction spatially dependent on the reaction coordinate introduces quantum effects into the thermal reaction rates for dissipative reactions. Quantum rates are calculated using the numerically exact multi-configuration time-dependent Hartree method, as well as the approximate ring-polymer molecular dynamics (RPMD), ring-polymer instanton methods, and classical molecular dynamics. By conducting simulations across a wide range of temperatures and friction strengths, we can identify the various regimes that govern the reactive dynamics. At high temperatures, in addition to the spatial-diffusion and energy-diffusion regimes predicted by Kramer's rate theory, a (coherent) tunneling-dominated regime is identified at low friction. At low temperatures, incoherent tunneling dominates most of Kramer's curve, except at very low friction, when coherent tunneling becomes dominant. Unlike in classical mechanics, the bath's influence changes the equilibrium time-independent properties of the system, leading to a complex interplay between spatially dependent friction and nuclear quantum effects even at high temperatures. More specifically, a realistic friction profile can lead to an increase (or decrease) of the quantum (classical) rates with friction within the spatial-diffusion regime, showing that classical and quantum rates display qualitatively different behaviors. Except at very low frictions, we find that RPMD captures most of the quantum effects in the thermal reaction rates.

Mean-Field Ring Polymer Rates Using a Population Dividing Surface.

Mean-field ring polymer molecular dynamics offers a computationally efficient method for the simulation of reaction rates in multilevel systems. Previous work has established that, to model a nonadiabatic state-to-state reaction accurately, it is necessary to ensure reactive trajectories form kinked ring polymer configurations at the dividing surface. Building on this idea, we introduce a population difference coordinate and a reactive flux expression modified to only include contributions from kinked configurations. We test the accuracy of the resulting mean-field rate theory on a series of linear vibronic coupling model systems. We demonstrate that this new kMF-RP rate approach is efficient to implement and quantitatively accurate for models over a wide range of driving forces, coupling strengths, and temperatures.

Reactions dynamics for X + H2 insertion reactions (X = C(1D), N(2D), O(1D), S(1D)) with Cayley propagator ring-polymer molecular dynamics.

In this work, rate coefficients of four prototypical insertion reactions, X + H2 → H + XH (X = C(1D), N(2D), O(1D), S(1D)), and associated isotope reactions are calculated based on ring polymer molecular dynamics (RPMD) with Cayley propagator (Cayley-RPMD). The associated kinetic isotope effects are systematically studied too. The Cayley propagator used in this work increases the stability of numerical integration in RPMD calculations and also supports a larger evolution time interval, allowing us to reach both high accuracy and efficiency. So, our results do not only provide chemical kinetic data for the title reactions in an extended temperature range but also consist of experimental results, standard RPMD, and other theoretical methods. The results in this work also reflect that Cayley-RPMD has strong consistency and high reliability in its investigations of chemical dynamics for insertion reactions.

Nuclear quantum effect on the elasticity of ice VII under pressure: A path-integral molecular dynamics study

Nuclear quantum effect on the elasticity of ice VII under pressure: A path-integral molecular dynamics study

Nuclear Quantum Effects Accelerate Charge Separation and Recombination in g-C3N4/TiO2 Heterojunctions.

We combined ring-polymer molecular dynamics (MD) and ab initio MD with nonadiabatic MD to study the effects of nuclear quantum effects (NQEs) on interlayer electron transfer and electron-hole recombination at the g-C3N4/TiO2 interface. Our simulations indicate that NQEs significantly affect electron transfer and electron-hole recombination dynamics, accelerating both processes. NQEs deform the g-C3N4 layer and expedite the movement of carbon and nitrogen atoms, thus, enhancing charge delocalization and interlayer coupling. This improved overlap between electronic state wave functions enhances nonadiabatic couplings, facilitating electron transfer and recombination. In addition to the enhanced nonadiabatic couplings accelerating electron transfer, the presence of NQEs narrows the energy gap and delays decoherence by mitigating overall fluctuations, because of restricted TiO2 movements overwhelming enhanced g-C3N4 fluctuations, thereby making the recombination faster. This work provides valuable insights into NQEs in light-element systems and contributes to guiding the development of highly efficient photocatalysts.

Electronic and Nuclear Quantum Effects on Proton Transfer Reactions of Guanine-Thymine (G-T) Mispairs Using Combined Quantum Mechanical/Molecular Mechanical and Machine Learning Potentials.

Rare tautomeric forms of nucleobases can lead to Watson-Crick-like (WC-like) mispairs in DNA, but the process of proton transfer is fast and difficult to detect experimentally. NMR studies show evidence for the existence of short-time WC-like guanine-thymine (G-T) mispairs; however, the mechanism of proton transfer and the degree to which nuclear quantum effects play a role are unclear. We use a B-DNA helix exhibiting a wGT mispair as a model system to study tautomerization reactions. We perform ab initio (PBE0/6-31G*) quantum mechanical/molecular mechanical (QM/MM) simulations to examine the free energy surface for tautomerization. We demonstrate that while the ab initio QM/MM simulations are accurate, considerable sampling is required to achieve high precision in the free energy barriers. To address this problem, we develop a QM/MM machine learning potential correction (QM/MM-ΔMLP) that is able to improve the computational efficiency, greatly extend the accessible time scales of the simulations, and enable practical application of path integral molecular dynamics to examine nuclear quantum effects. We find that the inclusion of nuclear quantum effects has only a modest effect on the mechanistic pathway but leads to a considerable lowering of the free energy barrier for the GT*⇌G*T equilibrium. Our results enable a rationalization of observed experimental data and the prediction of populations of rare tautomeric forms of nucleobases and rates of their interconversion in B-DNA.

Plugin-based interoperability and ecosystem management for the MolSSI Driver Interface Project.

The MolSSI Driver Interface (MDI) Project is an effort to simplify and standardize the process of enabling tight interoperability between independently developed code bases and is supported by numerous software packages across the domain of chemical physics. It enables a wide variety of use cases, including quantum mechanics/molecular mechanics, advanced sampling, path integral molecular dynamics, machine learning, abinitio molecular dynamics, etc. We describe two major developments within the MDI Project that provide novel solutions to key interoperability challenges. The first of these is the development of the MDI Plugin System, which allows MDI-supporting libraries to be used as highly modular plugins, with MDI enforcing a standardized application programming interface across plugins. Codes can use these plugins without linking against them during their build process, and end-users can select which plugin(s) they wish to use at runtime. The MDI Plugin System features a sophisticated callback system that allows codes to interact with plugins on a highly granular level and represents a significant advancement toward increased modularity among scientific codes. The second major development is MDI Mechanic, an ecosystem management tool that utilizes Docker containerization to simplify the process of developing, validating, maintaining, and deploying MDI-supporting codes. Additionally, MDI Mechanic provides a framework for launching MDI simulations in which each interoperating code is executed within a separate computational environment. This eliminates the need to compile multiple production codes within a single computational environment, reducing opportunities for dependency conflicts and lowering the barrier to entry for users of MDI-enabled codes.

Nuclear quantum effects in phase transition between Ice VII and Ice X.

The theoretical modeling of high-pressure ice remains challenging owing to the complexity in accurately reflecting its properties attributable to nuclear quantum effects. To explore the nuclear quantum effects of the phase transition between Ice VII and Ice X, we introduce an approach based on abinitio path-integral molecular dynamics. The results indicate that quantum effects facilitate the phase transition, with the observed isotope effects consistent with the experimental outcomes. We demonstrate that quantum effects manifest differently across ice phases: In Ice VII, quantum effects reduce the pressure through the centralization of protons. In contrast, in Ice X, quantum effects increase the pressure owing to the increased kinetic energy of zero-point vibration.

Nuclear quantum effects on the vibrational dynamics of the water-air interface.

We have applied path-integral molecular dynamics simulations to investigate the impact of nuclear quantum effects on the vibrational dynamics of water molecules at the water-air interface. The instantaneous fluctuations in the frequencies of the O-H stretch modes are calculated using the wavelet method of time series analysis, while the time scales of vibrational spectral diffusion are determined from frequency-time correlation functions and joint probability distributions. We find that the inclusion of nuclear quantum effects leads not only to a redshift in the vibrational frequency distribution by about 120 cm-1 for both the bulk and interfacial water molecules but also to an acceleration of the vibrational dynamics at the water-air interface by as much as 35%. In addition, a blueshift of about 45 cm-1 is seen in the vibrational frequency distribution of interfacial water molecules compared to that of the bulk. Furthermore, the dynamics of water molecules beyond the topmost molecular layer was found to be rather similar to that of bulk water.

Accurate Quantum Dynamics Calculations for the Cl + CH4/CHD3/CD4 Reaction Rates.

Full-dimensional quantum dynamics simulations of the reaction of Cl with methane and its isotopomers are reported. Thermal rate constants are computed for the Cl + CH4 → HCl + CH3, Cl + CHD3 → HCl + CD3, and Cl + CD4 → DCl + CD3 reactions. Temperatures between 200 and 500 K are considered. In this temperature range, excellent agreement with the experiment is obtained. A detailed analysis of the kinetic isotope effect reveals the crucial importance of the CH3/CD3 umbrella motion. Comparison with approximate ring-polymer molecular dynamics simulations shows significant differences depending on the isotope studied.

Finite-Temperature Correlation Functions Obtained from Combined Real- and Imaginary-Time Propagation of Variational Thawed Gaussian Wavepackets.

We apply the so-called variational Gaussian wavepacket approximation (VGA) for conducting both real- and imaginary-time dynamics to calculate thermal correlation functions. By considering strongly anharmonic systems, such as a quartic potential and a double-well potential at high and low temperatures, it is shown that this method is partially able to account for tunneling. This is contrary to other popular many-body methods, such as ring polymer molecular dynamics and the classical Wigner method, which fail in this respect. It is a historical peculiarity that no one has considered the VGA method for representing both the Boltzmann operator and the real-time propagation. This method should be well suited for molecular systems containing many atoms.

Neutron scattering and neural-network quantum molecular dynamics investigation of the vibrations of ammonia along the solid-to-liquid transition

Vibrational spectroscopy allows us to understand complex physical and chemical interactions of molecular crystals and liquids such as ammonia, which has recently emerged as a strong hydrogen fuel candidate to support a sustainable society. We report inelastic neutron scattering measurement of vibrational properties of ammonia along the solid-to-liquid phase transition with high enough resolution for direct comparisons to ab-initio simulations. Theoretical analysis reveals the essential role of nuclear quantum effects (NQEs) for correctly describing the intermolecular spectrum as well as high energy intramolecular N-H stretching modes. This is achieved by training neural network models using ab-initio path-integral molecular dynamics (PIMD) simulations, thereby encompassing large spatiotemporal trajectories required to resolve low energy dynamics while retaining NQEs. Our results not only establish the role of NQEs in ammonia but also provide general computational frameworks to study complex molecular systems with NQEs.

Water at negative pressure: nuclear quantum effects

Various condensed phases of water, spanning from the liquid state to multiple ice phases, have been systematically investigated under extreme conditions of pressure and temperature to delineate their stability boundaries. This study focuses on probing the mechanical stability of liquid water through path-integral molecular dynamics simulations, employing the q-TIP4P/F potential to model interatomic interactions in flexible water molecules. Temperature and pressure conditions ranging from 250 to 375 K and − 0.3 to 1 GPa, respectively, are considered. This comprehensive approach enables a thorough exploration of nuclear quantum effects on various physical properties of water through direct comparisons with classical molecular dynamics results employing the same potential model. Key properties such as molar volume, intramolecular bond length, H–O–H angle, internal and kinetic energy are analysed, with a specific focus on the effect of tensile stress. Particular attention is devoted to the liquid-gas spinodal pressure, representing the limit of mechanical stability for the liquid phase, at several temperatures. The quantum simulations reveal a spinodal pressure for water of − 286 and − 236 MPa at temperatures of 250 and 300 K, respectively. At these temperatures, the discernible shifts induced by nuclear quantum motion are quantified at 15 and 10 MPa, respectively. These findings contribute valuable insights into the interplay of quantum effects on the stability of liquid water under diverse thermodynamic conditions.

Understanding X-ray absorption in liquid water using triple excitations in multilevel coupled cluster theory

X-ray absorption (XA) spectroscopy is an essential experimental tool to investigate the local structure of liquid water. Interpretation of the experiment poses a significant challenge and requires a quantitative theoretical description. High-quality theoretical XA spectra require reliable molecular dynamics simulations and accurate electronic structure calculations. Here, we present the first successful application of coupled cluster theory to model the XA spectrum of liquid water. We overcome the computational limitations on system size by employing a multilevel coupled cluster framework for large molecular systems. Excellent agreement with the experimental spectrum is achieved by including triple excitations in the wave function and using molecular structures from state-of-the-art path-integral molecular dynamics. We demonstrate that an accurate description of the electronic structure within the first solvation shell is sufficient to successfully model the XA spectrum of liquid water within the multilevel framework. Furthermore, we present a rigorous charge transfer analysis of the XA spectrum, which is reliable due to the accuracy and robustness of the electronic structure methodology. This analysis aligns with previous studies regarding the character of the prominent features of the XA spectrum of liquid water.

Operator Formulation of Feynman Path Centroid Dynamics for Rotations.

An operator formulation of centroid molecular dynamics (CMD) for rotational degrees of freedom is presented. The quasi-density operator concept was introduced by Jang and Voth [J. Chem. Phys 111, 2357 (1999)] and is used to obtain a phase-space mapping without the need for discretized path integrals. The approach allows the calculation of approximate Kubo-transformed time correlation functions. The particle on a ring is chosen as an illustrative example. Numerical results demonstrate that the proposed approach leads to accurate results when compared with exact diagonalization calculations for linear operators. At very low temperatures, it is found that rotational CMD yields results that are in exact agreement with the quantum dynamics of a spin-1 system.

Multiple-time scale integration method based on an interpolated potential energy surface for abinitio path integral molecular dynamics.

A new multiple-time scale integration method is presented that propagates abinitio path integral molecular dynamics (PIMD). This method uses a large time step to generate an approximate geometrical configuration whose energy and gradient are evaluated at the level of an abinitio method, and then, a more precise integration scheme, e.g., the Bulirsch-Stoer method or velocity Verlet integration with a smaller time step, is used to integrate from the previous step using the computationally efficient interpolated potential energy surface constructed from two consecutive points. This method makes the integration of PIMD more efficient and accurate compared with the velocity Verlet integration. A Nosé-Hoover chain thermostat combined with this new multiple-time scale method has good energy conservation even with a large time step, which is usually challenging in velocity Verlet integration for PIMD due to the very small chain mass when a large number of beads are used. The new method is used to calculate infrared spectra and free energy profiles to demonstrate its accuracy and capabilities.

Microscopic self-dynamics in liquid Ne-D_{2} mixtures: Quantum features and itinerant oscillators reexamined.

In this paper, we report the results of a centroid molecular dynamics (CMD) study of the canonical velocity autocorrelation functions (VACFs) in liquid Ne-D_{2} mixtures at a temperature of T=30K and in the full D_{2}-concentration range (0%≤x_{D_{2}}≤100%). This binary system was selected because of its moderate, although sizable, quantum effects which, as far as its equilibrium properties are concerned, are fully described by the path integral Monte Carlo (PIMC) simulations that have been also implemented. A comprehensive test of the VACF spectral moments carried out using three physical quantities (namely, mean kinetic energy, Einstein frequency, and mean-squared force) obtained from PIMC was performed revealing the potentialities, as well as the limitations, of the CMD approach to the single-particle dynamics in these low-T liquid mixtures. Additional physical information was extracted from the canonical VACFs by fitting their spectra via two distinct methods: the Levesque-Verlet model (LV, very flexible but highly heuristic) and the itinerant oscillator model (IO, based on the physical ground of a single particle rattling inside a short-lived diffusing pseudocage). Both provided good fits of the CMD outputs, with LV being always more adequate than IO in the case of the Ne VACFs, while, as for the D_{2} VACFs, the LV superiority is evident only at high x_{D_{2}} values. However, a peculiar and systematic effect was found after analyzing the IO-fitted parameters: the estimated pseudocage masses turned out to be at least one order of magnitude lower than the corresponding values inferred from the PIMC simulations. This outcome concerns both the Ne and the D_{2} rattling molecule and, as we also discovered, had already been observed (but promptly forgotten) in purely classical simulations of liquid Ar. The possible physical origins of this finding have been finally discussed in some detail, also in connection with the result of the more recent exponential expansion theory (EET), which manages to shed more light on the concept of single particles rattling inside short-lived pseudocages, ultimately demonstrating its untenability.