Ab Initio Path-integral Molecular Dynamics Research Articles

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.

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.

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.

Competitive nuclear quantum effect and H/D isotope effect on torsional motion of H2O2: An ab initio path integral molecular dynamics study

Ab initio path integral molecular dynamics (PIMD) simulations were performed to understand the nuclear quantum effect and thermal effect on the torsional motion of H2O2 (D2O2). A broad distribution of geometrical parameters (OH and OO bond lengths [ROH and ROO] and HOO bond angle [∠HOO]) was obtained in quantum ab initio PIMD simulations, rather than in classical MD simulations. However, a modest distribution around the trans-configuration TS (∠HOOH = 180°) was found in the quantum ab initio PIMD simulations of H2O2 at low temperatures. Thus, the nuclear quantum effect slightly enhanced the HOOH torsional motion at low temperatures. A series of simulations also revealed that the thermal effect enhanced the HOOH torsional motion. However, it was restrained by the primary nuclear quantum effect on the ROH in quantum simulations at high temperatures. Therefore, an interesting competitive nuclear quantum effect on the torsional motion of H2O2 was observed.

Probing anharmonic phonons by quantum correlators: A path integral approach.

We devise an efficient scheme to determine vibrational properties from Path Integral Molecular Dynamics (PIMD) simulations. The method is based on zero-time Kubo-transformed correlation functions and captures the anharmonicity of the potential due to both temperature and quantum effects. Using analytical derivations and numerical calculations on toy-model potentials, we show that two different estimators built upon PIMD correlation functions fully characterize the phonon spectra and the anharmonicity strength. The first estimator is associated with the force-force quantum correlators and, in the weak anharmonic regime, yields reliable zero-point motion frequencies and thermodynamic properties of the quantum system. The second one is instead connected to displacement-displacement correlators and accurately probes the lowest-energy phonon excitations, regardless of the anharmonicity strength of the system. We also prove that the use of generalized eigenvalue equations, in place of the standard normal mode equations, leads to a significant speed-up in the PIMD phonon calculations, both in terms of faster convergence rate and smaller time step bias. Within this framework, using ab initio PIMD simulations, we compute phonon dispersions of diamond and of the high-pressure I41/amd phase of atomic hydrogen. We find that in the latter case, the anharmonicity is stronger than previously estimated and yields a sizeable red-shift in the vibrational spectrum of atomic hydrogen.

Nuclear quantum effects on autoionization of water isotopologs studied by ab initio path integral molecular dynamics.

In this study, we investigate the nuclear quantum effects (NQEs) on the acidity constant (pKA) of liquid water isotopologs under the ambient condition by path integral molecular dynamics (PIMD) simulations. We compared simulations using a fully explicit solvent model with a classical polarizable force field, density functional tight binding, and ab initio density functional theory, which correspond to empirical, semiempirical, and ab initio PIMD simulations, respectively. The centroid variable with respect to the proton coordination number of a water molecule was restrained to compute the gradient of the free energy, which measures the reversible work of the proton abstraction for the quantum mechanical system. The free energy curve obtained by thermodynamic integration was used to compute the pKA value based on probabilistic determination. This technique not only reproduces the pKA value of liquid D2O experimentally measured (14.86) but also allows for a theoretical prediction of the pKA values of liquid T2O and aqueous HDO and HTO, which are unknown due to their scarcity. It is also shown that the NQEs on the free energy curve can result in a downshift of 4.5 ± 0.9 pKA units in the case of liquid water, which indicates that the NQEs plays an indispensable role in the absolute determination of pKA. The results of this study can help inform further extensions into the calculation of the acidity constants of isotope substituted species with high accuracy.

Mechanism of fast lattice diffusion of hydrogen in palladium: Interplay of quantum fluctuations and lattice strain

Understanding the underlying mechanism of the nanostructure-mediated high diffusivity of H in Pd is of recent scientific interest and also crucial for industrial applications. Here, we present a decisive scenario explaining the emergence of the fast lattice-diffusion mode of interstitial H in face-centered cubic Pd, based on the quantum mechanical natures of both electrons and nuclei under finite strains. Ab initio path-integral molecular dynamics was applied to predict the temperature- and strain-dependent free energy profiles for H migration in Pd over a temperature range of 150--600 K and under hydrostatic tensile strains of 0.0%--2.4%; such strain conditions are likely to occur in real systems, especially around the elastic fields induced by nanostructured defects. The simulated results revealed that, for preferential H location at octahedral sites, as in unstrained Pd, the activation barrier for H migration ($Q$) was drastically increased with decreasing temperature owing to nuclear quantum effects. In contrast, as tetrahedral sites increased in stability with lattice expansion, nuclear quantum effects became less prominent and ceased impeding H migration. This implies that the nature of the diffusion mechanism gradually changes from quantum- to classical-like as the strain is increased. For H atoms in Pd at the hydrostatic strain of $\ensuremath{\sim}2.4%$, we determined that the mechanism promoted fast lattice diffusion ($Q=0.11$ eV) of approximately 20 times the rate of conventional H diffusion ($Q=0.23$ eV) in unstrained Pd at a room temperature of 300 K.

Nuclear quantum effects induce metallization of dense solid molecular hydrogen.

We present an accurate computational study of the electronic structure and lattice dynamics of solid molecular hydrogen at high pressure. The band-gap energies of the C2/c, Pc, and P63/m structures at pressures of 250, 300, and 350 GPa are calculated using the diffusion quantum Monte Carlo (DMC) method. The atomic configurations are obtained from ab initio path-integral molecular dynamics (PIMD) simulations at 300 K and 300 GPa to investigate the impact of zero-point energy and temperature-induced motion of the protons including anharmonic effects. We find that finite temperature and nuclear quantum effects reduce the band-gaps substantially, leading to metallization of the C2/c and Pc phases via band overlap; the effect on the band-gap of the P63/m structure is less pronounced. Our combined DMC-PIMD simulations predict that there are no excitonic or quasiparticle energy gaps for the C2/c and Pc phases at 300 GPa and 300 K. Our results also indicate a strong correlation between the band-gap energy and vibron modes. This strong coupling induces a band-gap reduction of more than 2.46 eV in high-pressure solid molecular hydrogen. Comparing our DMC-PIMD with experimental results available, we conclude that none of the structures proposed is a good candidate for phases III and IV of solid hydrogen. © 2017 Wiley Periodicals, Inc.

Solvent Dependence of Double Proton Transfer in the Formic Acid-Formamidine Complex: Path Integral Molecular Dynamics Investigation.

Solvent dependence of double proton transfer in the formic acid-formamidine (FA-FN) complex at room temperature was investigated by means of ab initio path integral molecular dynamics (AIPIMD) simulation with taking nuclear quantum and thermal effects into account. The conductor-like screening model (COSMO) was applied for solvent effect. In comparison with gas phase, double proton delocalization between two heavy atoms (O and N) in FA-FN were observed with reduced proton transfer barrier height in low dielectric constant medium (<4.8). For dielectric constant medium at 4.8, the chance of finding these two protons are more pronounced due to the solvent effect which completely washes out the proton transfer barrier. In the case of higher dielectric constant medium (>4.8), the ionic species becomes more stable than the neutral ones and the formate anion and formamidium cation are thermodynamically stable. For ab initio molecular dynamics simulation, in low dielectric constant medium (<4.8) a reduction of proton transfer barrier with solvent effect is found to be less pronounced than the AIPIMD due to the absence of nuclear quantum effect. Moreover, the motions of FA-FN complex are significantly different with increasing dielectric constant medium. Such a difference is revealed in detail by the principal component analysis.

Prediction of a Mobile Solid State in Dense Hydrogen under High Pressures.

Solid rigidity and liquid-scale mobility are thought to be incompatible in elemental substances. One cannot have an elemental solid that is long-range positionally ordered wherein the atoms flow like in a liquid simultaneously. The only exception might be the hypothetical supersolid state of 4He. In this work, we demonstrate that such exotic state could exist even in the classical regime. Using ab initio molecular dynamics (AIMD) and ab initio path integral molecular dynamics (AI-PIMD), a novel state of dense hydrogen that simultaneously has both long-range spatial ordering and liquid-scale atomic mobility is discovered at 1 to 1.5 TPa (1 TPa ≈ 10 000 000 atmospheric pressures). The features distinct from a normal solid and liquid are carefully characterized, and the stability and melting behavior are investigated. Extensive AI-PIMD simulations further revealed that this state might be (meta-)stable even at ultralow temperatures, suggesting an emerging candidate for an alternative type of supersolid state in dense metallic hydrogen.

Abinitio Electronic Structure of Liquid Water.

Self-consistent GW calculations with efficient vertex corrections are employed to determine the electronic structure of liquid water. Nuclear quantum effects are taken into account through abinitio path-integral molecular dynamics simulations. We reveal a sizable band-gap renormalization of up to 0.7eV due to hydrogen-bond quantum fluctuations. Our calculations lead to a band gap of 8.9eV, in accord with the experimental estimate. We further resolve the ambiguities in the band-edge positions of liquid water. The valence-band maximum and the conduction-band minimum are found at -9.4 and -0.5 eV with respect to the vacuum level, respectively.

Quantum ring-polymer contraction method: Including nuclear quantum effects at no additional computational cost in comparison to ab initio molecular dynamics.

We present a simple and accurate computational method which facilitates ab initio path-integral molecular dynamics simulations, where the quantum-mechanical nature of the nuclei is explicitly taken into account, at essentially no additional computational cost in comparison to the corresponding calculation using classical nuclei. The predictive power of the proposed quantum ring-polymer contraction method is demonstrated by computing various static and dynamic properties of liquid water at ambient conditions using density functional theory. This development will enable routine inclusion of nuclear quantum effects in ab initio molecular dynamics simulations of condensed-phase systems.

Simulating Nuclear and Electronic Quantum Effects in Enzymes.

An accurate treatment of the structures and dynamics that lead to enhanced chemical reactivity in enzymes requires explicit treatment of both electronic and nuclear quantum effects. The former can be captured in ab initio molecular dynamics (AIMD) simulations, while the latter can be included by performing ab initio path integral molecular dynamics (AI-PIMD) simulations. Both AIMD and AI-PIMD simulations have traditionally been computationally prohibitive for large enzymatic systems. Recent developments in streaming computer architectures and new algorithms to accelerate path integral simulations now make these simulations practical for biological systems, allowing elucidation of enzymatic reactions in unprecedented detail. In this chapter, we summarize these recent developments and discuss practical considerations for applying AIMD and AI-PIMD simulations to enzymes.

Applications of path-integral molecular dynamics simulations to phase transition problems

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.

Nuclear quantum effects on the high pressure melting of dense lithium.

Using a self-developed combination of the thermodynamic integration and the ab initio path-integral molecular dynamics methods, we quantitatively studied the influence of nuclear quantum effects (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 (Tm) is lowered by only ∼15 K, with values obtained using both classical and quantum nuclei in close proximity to a new experiment. Besides this, a substantial narrowing of the solid/liquid free-energy differences close to Tm was observed, in alignment with a tendency that glassy states might form upon rapid cooling. This tendency was demonstrated by the dynamics of crystallization in the two-phase simulations, which helps to reconcile an important conflict between two recent experiments. This study presents a simple picture for the phase diagram of lithium under pressure. It also indicates that claims on the influence of NQEs on phase diagrams should be carefully made and the method adopted offers a robust solution for such quantitative analyses.

Accelerating ab initio path integral molecular dynamics with multilevel sampling of potential surface

A multilevel approach to sample the potential energy surface in a path integral formalism is proposed. The purpose is to reduce the required number of ab initio evaluations of energy and forces in ab initio path integral molecular dynamics (AI-PIMD) simulation, without compromising the overall accuracy. To validate the method, the internal energy and free energy of an Einstein crystal are calculated and compared with the analytical solutions. As a preliminary application, we assess the performance of the method in a realistic model—the FCC phase of dense atomic hydrogen, in which the calculated result shows that the acceleration rate is about 3 to 4-fold for a two-level implementation, and can be increased up to 10 times if extrapolation is used. With only 16 beads used for the ab initio potential sampling, this method gives a well converged internal energy. The residual error in pressure is just about 3 GPa, whereas it is about 20 GPa for a plain AI-PIMD calculation with the same number of beads. The vibrational free energy of the FCC phase of dense hydrogen at 300 K is also calculated with an AI-PIMD thermodynamic integration method, which gives a result of about 0.51 eV/proton at a density of rs=0.912.

Quantum simulation for muoniated and deuterated methyl radicals in implicit water solvent: combined ab initio path integral molecular dynamics and the polarizable continuum model simulation study

We have combined ab initio path integral molecular dynamics (PIMD) simulation and the polarizable continuum model (PCM) method to efficiently incorporate solvent effects into nuclear quantum fluctuation of molecular systems. Our combined ab initio PIMD–PCM simulation was applied to muoniated and deuterated methyl radical immersed in implicit water solvent to gain information on solvent and isotope effects from one simulation run. We found that solvent effects lead to the bond elongation and a decrease in the magnitude of isotropic hyperfine coupling constants. These are consistent with the trends in conventional static calculations and experiments. In addition, the performance of cavity models (universal force field, united atom specified for Kohn–Sham and these hybrid models) and the conservation of the PIMD–PCM Hamiltonian were accessed. We confirmed that solvent effects on nuclear quantum fluctuation are efficiently computed using our combined simulation of quantum solute in implicit solvent.

On the room-temperature phase diagram of high pressure hydrogen: an ab initio molecular dynamics perspective and a diffusion Monte Carlo study.

The finite-temperature phase diagram of hydrogen in the region of phase IV and its neighborhood was studied using the ab initio molecular dynamics (MD) and the ab initio path-integral molecular dynamics (PIMD). The electronic structures were analyzed using the density-functional theory (DFT), the random-phase approximation, and the diffusion Monte Carlo (DMC) methods. Taking the state-of-the-art DMC results as benchmark, comparisons of the energy differences between structures generated from the MD and PIMD simulations, with molecular and dissociated hydrogens, respectively, in the weak molecular layers of phase IV, indicate that standard functionals in DFT tend to underestimate the dissociation barrier of the weak molecular layers in this mixed phase. Because of this underestimation, inclusion of the quantum nuclear effects (QNEs) in PIMD using electronic structures generated with these functionals leads to artificially dissociated hydrogen layers in phase IV and an error compensation between the neglect of QNEs and the deficiencies of these functionals in standard ab initio MD simulations exists. This analysis partly rationalizes why earlier ab initio MD simulations complement so well the experimental observations. The temperature and pressure dependencies for the stability of phase IV were also studied in the end and compared with earlier results.

Nuclear quantum dynamics in dense hydrogen.

Nuclear dynamics in dense hydrogen, which is determined by the key physics of large-angle scattering or many-body collisions between particles, is crucial for the dynamics of planet's evolution and hydrodynamical processes in inertial confinement confusion. Here, using improved ab initio path-integral molecular dynamics simulations, we investigated the nuclear quantum dynamics regarding transport behaviors of dense hydrogen up to the temperatures of 1 eV. With the inclusion of nuclear quantum effects (NQEs), the ionic diffusions are largely higher than the classical treatment by the magnitude from 20% to 146% as the temperature is decreased from 1 eV to 0.3 eV at 10 g/cm3, meanwhile, electrical and thermal conductivities are significantly lowered. In particular, the ionic diffusion is found much larger than that without NQEs even when both the ionic distributions are the same at 1 eV. The significant quantum delocalization of ions introduces remarkably different scattering cross section between protons compared with classical particle treatments, which explains the large difference of transport properties induced by NQEs. The Stokes-Einstein relation, Wiedemann-Franz law, and isotope effects are re-examined, showing different behaviors in nuclear quantum dynamics.

Ab Initio Path Integral Molecular Dynamics Study of the Nuclear Quantum Effect on Out-of-Plane Ring Deformation of Hydrogen Maleate Anion.

Ab initio path integral molecular dynamics (PIMD) simulation was performed to understand the nuclear quantum effect on the out-of-plane ring deformation of hydrogen maleate anion and investigate the existence of a stable structure with ring deformation, which was suggested in experimental observation (Fillaux et al., Chem. Phys. 1999, 120, 387-403). The isotope effect and the temperature effect are studied as well. We first investigated the nuclear quantum effect on the proton transfer. In static calculation and classical ab initio molecular dynamics simulations, the proton in the hydrogen bond is localized to either oxygen atom. On the other hand, the proton is located at the center of two oxygen atoms in quantum ab initio PIMD simulations. The nuclear quantum effect washes out the barrier of proton transfer. We next examined the nuclear quantum effect on the motion of hydrogen maleate anion. Principal component analysis revealed that the out-of-plane ring bending modes have dominant contribution to the entire molecular motion. In quantum ab initio PIMD simulations, structures with ring deformation were the global minimum for the deuterated isotope at 300 K. We analyzed the out-of-plane ring bending mode further and found that there are three minima along a ring distortion mode. We successfully found a stable structure with ring deformation of hydrogen maleate for the first time, to our knowledge, using theoretical calculation. The structures with ring deformation found in quantum simulation of the deuterated isotope allowed the proton transfer to occur more frequently than the planar structure. Static ab initio electronic structure calculation found that the structures with ring deformation have very small proton transfer barrier compared to the planar structure. We suggest that the "proton transfer driven" mechanism is the origin of stabilization for the structure with out-of-plane ring deformation.