Path Integral Simulations Research Articles

Mechanism of Cations Suppressing Proton Diffusion Kinetics for Electrocatalysis

AbstractProton transfer is crucial for electrocatalysis. Accumulating cations at electrochemical interfaces can alter the proton transfer rate and then tune electrocatalytic performance. However, the mechanism for regulating proton transfer remains ambiguous. Here, we quantify the cation effect on proton diffusion in solution by hydrogen evolution on microelectrodes, revealing the rate can be suppressed by more than 10 times. Different from the prevalent opinions that proton transport is slowed down by modified electric field, we found water structure imposes a more evident effect on kinetics. FTIR test and path integral molecular dynamics simulation indicate that proton prefers to wander within the hydration shell of cations rather than to hop rapidly along water wires. Low connectivity of water networks disrupted by cations corrupts the fast‐moving path in bulk water. This study highlights the promising way for regulating proton kinetics via a modified water structure.

Onset of Rotational Decoupling for a Molecular Ion Solvated in Helium: From Tags to Rings and Shells

Little is known about how rotating molecular ions interact with multiple ^{4}He atoms and how this relates to microscopic superfluidity. Here, we use infrared spectroscopy to investigate ^{4}He_{N}⋯H_{3}O^{+} complexes and find that H_{3}O^{+} undergoes dramatic changes in rotational behavior as ^{4}He atoms are added. We present evidence of clear rotational decoupling of the ion core from the surrounding helium for N>3, with sudden changes in rotational constants at N=6 and 12. In sharp contrast to studies on small neutral molecules microsolvated in helium, accompanying path integral simulations show that an incipient superfluid effect is not needed to account for these findings.

Collective Proton Transfers in Cyclic Water–Ammonia Tetramers: A Path Integral Machine-Learning Study

We present results from machine-learning-based path integral molecular dynamics simulations that describe isomerization paths articulated via collective proton transfers along mixed, cyclic tetramers combining water and ammonia at cryogenic conditions. The net result of such isomerizations is a reverse of the chirality of the global hydrogen-bonding architecture along the different cyclic moieties. In monocomponent tetramers, the classical free energy profiles associated with these isomerizations present the usual symmetric double-well characteristics whereas the reactive paths exhibit full concertedness among the different intermolecular transfer processes. Contrastingly, in mixed water/ammonia tetramers, the incorporation of a second component introduces imbalances in the strengths of the different hydrogen bonds leading to a partial loss of concertedness, most notably at the vicinity of the transition state. As such, the highest and lowest degrees of progression are registered along OH···N and O···HN coordinations, respectively. These characteristics lead to polarized transition state scenarios akin to solvent-separated ion-pair configurations. The explicit incorporation of nuclear quantum effects promotes drastic depletions in the activation free energies and modifications in the overall shape of the profiles which include central plateau-like stages, indicating the prevalence of deep tunneling regimes. On the other hand, the quantum treatment of the nuclei partially restores the degree of concertedness among the evolutions of the individual transfers.

Data-Efficient Machine Learning Potentials from Transfer Learning of Periodic Correlated Electronic Structure Methods: Liquid Water at AFQMC, CCSD, and CCSD(T) Accuracy.

Obtaining the atomistic structure and dynamics of disordered condensed-phase systems from first-principles remains one of the forefront challenges of chemical theory. Here we exploit recent advances in periodic electronic structure and provide a data-efficient approach to obtain machine-learned condensed-phase potential energy surfaces using AFQMC, CCSD, and CCSD(T) from a very small number (≤200) of energies by leveraging a transfer learning scheme starting from lower-tier electronic structure methods. We demonstrate the effectiveness of this approach for liquid water by performing both classical and path integral molecular dynamics simulations on these machine-learned potential energy surfaces. By doing this, we uncover the interplay of dynamical electron correlation and nuclear quantum effects across the entire liquid range of water while providing a general strategy for efficiently utilizing periodic correlated electronic structure methods to explore disordered condensed-phase systems.

The broadband transport theory approach to model internal wave induced scattering across deep water acoustic time-fronts.

There are currently no models to fully predict the effects of internal wave induced scattering on acoustic pulses. Existing models, which predict time domain statistics, either use the ray-based path integral method or Monte Carlo type simulations. The path integral method fails to accurately predict all of the effects of scattering. The Monte Carlo methods base the statistics on ensemble averages and are not physics-based models. This paper overcomes these limitations by using the modes of the waveguide in a transport theory application. The transport theory equations have, thus far, been used only to explain diffusion of mode intensities and decorrelation due to internal waves at individual frequencies. This paper extends the current narrowband application predict mode correlations across different frequencies and, from that, the broadband time-front, time wander, travel time bias, and the amount of spread in intensity across time and depth. To validate these predictions, this paper uses separate parabolic equation simulations. The comparisons between the two are good, suggesting a success for the mode-based transport theory approach.

Accurate global machine learning force fields for molecules with hundreds of atoms.

Global machine learning force fields, with the capacity to capture collective interactions in molecular systems, now scale up to a few dozen atoms due to considerable growth of model complexity with system size. For larger molecules, locality assumptions are introduced, with the consequence that nonlocal interactions are not described. Here, we develop an exact iterative approach to train global symmetric gradient domain machine learning (sGDML) force fields (FFs) for several hundred atoms, without resorting to any potentially uncontrolled approximations. All atomic degrees of freedom remain correlated in the global sGDML FF, allowing the accurate description of complex molecules and materials that present phenomena with far-reaching characteristic correlation lengths. We assess the accuracy and efficiency of sGDML on a newly developed MD22 benchmark dataset containing molecules from 42 to 370 atoms. The robustness of our approach is demonstrated in nanosecond path-integral molecular dynamics simulations for supramolecular complexes in the MD22 dataset.

Nuclear quantum and H/D isotope effects on intramolecular hydrogen bond in curcumin.

Curcumin and its derivatives possess intramolecular low-barrier hydrogen bonds for intramolecular proton transfer. The π-delocalization in the OCCCO framework of the hydrogen bond in these compounds is reorganized concomitantly with the proton transfer. To characterize the hydrogen bond and π-delocalization, we performed path integral molecular dynamics simulations, revealing that although the proton migration and reorganization of the π-delocalized structure showed a positive correlation, the correlation was weak.

Origin of Catalysis by Nitroalkane Oxidase.

The rate of proton abstraction of the carbon acid nitroethane by Asp402 is accelerated by a factor of 108 in the enzyme nitroalkane oxidase (NAO) relative to that by the organic base acetate ion in water. The Cα proton of nitroalkanes is known to exhibit an abnormal correlation between its acidity strength and the rate of deprotonation, with an unusually slow rate of deprotonation in water. This work examines the origin of NAO catalysis, revealing that the rate enhancement by the enzyme is due to transition-state stabilization, restoring the normal behavior of the linear free energy relationship of Bronsted acids. Interestingly, NAO employs the ubiquitous cofactor flavin adenosine diphosphate (FAD) to perform the subsequent oxidation. Does the FAD cofactor also affect the catalytic rate of the initial proton transfer process of the overall nitroalkane oxidation? Classical molecular dynamics and path-integral simulations using a reaction-specific combined quantum mechanics/molecular mechanics (QM/MM) approach were carried out to obtain the free energy reaction profiles, or the potentials of mean force, for the enzymatic reaction and for a model reaction in aqueous solution, as well as for the 2'-deoxy-FAD co-factor-modified NAO. Free energy perturbation calculations suggest that transition-state stabilization of the reactive fragment is the primary cause of the catalytic effect. It is found that the FAD cofactor plays a crucial role in increasing the Cα proton acidity, via specific hydrogen bonding and π-stacking interactions, although these factors have a smaller effect on the enhancement of the rate of deprotonation. Model QM calculations of the π-stacking complexes between the FAD isoalloxazine ring and the neutral and anionic nitroethane, respectively, reveal that the anionic π-stacking complex is more stable than the neutral one by 15.7 kcal/mol, and a net π-stacking energy of 17.3 kcal/mol is obtained. Hence, the isoalloxazine ring, in addition to serving as a very potent oxidizing agent via the formation of covalent intermediate structures, is able to exert a considerable amount of catalytic effect through noncovalent π-stacking interactions.

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.

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, .

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.

Neural network interaction potentials for para-hydrogen with flexible molecules.

The study of molecular impurities in para-hydrogen (pH2) clusters is key to push forward our understanding of intra- and intermolecular interactions, including their impact on the superfluid response of this bosonic quantum solvent. This includes tagging with only one or very few pH2, the microsolvation regime for intermediate particle numbers, and matrix isolation with many solvent molecules. However, the fundamental coupling between the bosonic pH2 environment and the (ro-)vibrational motion of molecular impurities remains poorly understood. Quantum simulations can, in principle, provide the necessary atomistic insight, but they require very accurate descriptions of the involved interactions. Here, we present a data-driven approach for the generation of impurity⋯pH2 interaction potentials based on machine learning techniques, which retain the full flexibility of the dopant species. We employ the well-established adiabatic hindered rotor (AHR) averaging technique to include the impact of the nuclear spin statistics on the symmetry-allowed rotational quantum numbers of pH2. Embedding this averaging procedure within the high-dimensional neural network potential (NNP) framework enables the generation of highly accurate AHR-averaged NNPs at coupled cluster accuracy, namely, explicitly correlated coupled cluster single, double, and scaled perturbative triples, CCSD(T*)-F12a/aVTZcp, in an automated manner. We apply this methodology to the water and protonated water molecules as representative cases for quasi-rigid and highly flexible molecules, respectively, and obtain AHR-averaged NNPs that reliably describe the corresponding H2O⋯pH2 and H3O+⋯pH2 interactions. Using path integral simulations, we show for the hydronium cation, H3O+, that umbrella-like tunneling inversion has a strong impact on the first and second pH2 microsolvation shells. The automated and data-driven nature of our protocol opens the door to the study of bosonic pH2 quantum solvation for a wide range of embedded impurities.

Artificial neural network-based path integral simulations of hydrogen isotope diffusion in palladium

The contribution of nuclear quantum effects (NQEs) to the kinetics and dynamics of interstitial H isotopes in face-centered cubic Pd was intensively investigated using several path-integral techniques, along with a newly developed machine-learning interatomic potential based on artificial neural networks for Pd–H alloys. The diffusion coefficients (D) of protium, deuterium, and tritium in Pd were predicted over a wide temperature range (50–1500 K) based on quantum transition-state theory (QTST) combined with path-integral molecular-dynamics simulations. The importance of NQEs even at high temperatures was illustrated in terms of the characteristic temperature dependence of the activation free energies for H-isotope migration in Pd. This illuminates the overall picture of anomalous D crossovers among the three H isotopes in Pd. In addition, the D of protium in Pd was directly computed using two approximate quantum-dynamics methods based on Feynman’s path-integral theory, i.e. centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD), in the temperature range 370–1500 K. The D values obtained from the CMD and RPMD simulations were very similar and agreed better with the reported experimental values than the QTST results in this temperature range. Our machine learning-based path-integral calculations elucidate the underlying quantum nature of the ‘reversed S’-type nonlinear behavior of D for the three H isotopes in Pd on the Arrhenius plots.

B800-to-B850 relaxation of excitation energy in bacterial light harvesting: All-state, all-mode path integral simulations.

We report fully quantum mechanical simulations of excitation energy transfer within the peripheral light harvesting complex (LH2) of Rhodopseudomonas molischianum at room temperature. The exciton-vibration Hamiltonian comprises the 16 singly excited bacteriochlorophyll states of the B850 (inner) ring and the 8 states of the B800 (outer) ring with all available electronic couplings. The electronic states of each chromophore couple to 50 intramolecular vibrational modes with spectroscopically determined Huang-Rhys factors and to a weakly dissipative bath that models the biomolecular environment. Simulations of the excitation energy transfer following photoexcitation of various electronic eigenstates are performed using the numerically exact small matrix decomposition of the quasiadiabatic propagator path integral. We find that the energy relaxation process in the 24-state system is highly nontrivial. When the photoexcited state comprises primarily B800 pigments, a rapid intra-band redistribution of the energy sharply transitions to a significantly slower relaxation component that transfers 90% of the excitation energy to the B850 ring. The mixed character B850* state lacks the slow component and equilibrates very rapidly, providing an alternative energy transfer channel. This (and also another partially mixed) state has an anomalously large equilibrium population, suggesting a shift to lower energy by virtue of exciton-vibration coupling. The spread of the vibrationally dressed states is smaller than that of the eigenstates of the bare electronic Hamiltonian. The total population of the B800 band is found to decay exponentially with a 1/e time of 0.5ps, which is in good agreement with experimental results.

Quantum and temperature effects on the crystal structure of superhydride LaH10 : A path integral molecular dynamics study

By classical and path-integral molecular dynamics simulations, we study the pressure-temperature ($P$-$T$) phase diagram of LaH$_{10}$ to clarify the impact of temperature and atomic zero-point motions. We calculate the XRD pattern and analyze the space group of the crystal structures. For 125 GPa $\leq P\leq$ 150 GPa and $T=300$ K, we show that a highly symmetric $Fm\bar{3}m$ structure, for which superconductivity is particularly favored, is stabilized only by the temperature effect. On the other hand, for $T=200$ K, the interplay between the temperature and quantum effects is crucial to realize the $Fm\bar{3}m$ structure. For $P=$100 GPa and $T=$300 K, we find that the system is close to the critical point of the structural phase transition between the $Fm\bar{3}m$ structure and those with lower symmetries.

Learning the Quantum Centroid Force Correction in Molecular Systems: A Localized Approach.

Molecular mechanics (MM) is a powerful tool to study the properties of molecular systems in the fields of biology and materials science. With the development of ab initio force field and the application of ab initio potential energy surface, the nuclear quantum effect (NQE) is becoming increasingly important for the robustness of the simulation. However, the state-of-the-art path-integral molecular dynamics simulation, which incorporates NQE in MM, is still too expensive to conduct for most biological and material systems. In this work, we analyze the locality of NQE, using both analytical and numerical approaches, and conclude that NQE is an extremely localized phenomenon in nonreactive molecular systems. Therefore, we can use localized machine learning (ML) models to predict quantum force corrections both accurately and efficiently. Using liquid water as example, we show that the ML facilitated centroid MD can reproduce the NQEs in both the thermodynamical and the dynamical properties, with a minimal increase in computational time compared to classical molecular dynamics. This simple approach thus largely decreases the computational cost of quantum simulations, making it really accessible to the studies of large-scale molecular systems.

Evidence of a liquid\u2013liquid phase transition in H_2O and D_2O from path-integral molecular dynamics simulations

We perform path-integral molecular dynamics (PIMD), ring-polymer MD (RPMD), and classical MD simulations of H_2O and D_2O using the q-TIP4P/F water model over a wide range of temperatures and pressures. The density rho (T), isothermal compressibility kappa _T(T), and self-diffusion coefficients D(T) of H_2O and D_2O are in excellent agreement with available experimental data; the isobaric heat capacity C_P(T) obtained from PIMD and MD simulations agree qualitatively well with the experiments. Some of these thermodynamic properties exhibit anomalous maxima upon isobaric cooling, consistent with recent experiments and with the possibility that H_2O and D_2O exhibit a liquid-liquid critical point (LLCP) at low temperatures and positive pressures. The data from PIMD/MD for H_2O and D_2O can be fitted remarkably well using the Two-State-Equation-of-State (TSEOS). Using the TSEOS, we estimate that the LLCP for q-TIP4P/F H_2O, from PIMD simulations, is located at P_c = 167 pm 9 MPa, T_c = 159 pm 6 K, and rho _c = 1.02 pm 0.01 g/cm^3. Isotope substitution effects are important; the LLCP location in q-TIP4P/F D_2O is estimated to be P_c = 176 pm 4 MPa, T_c = 177 pm 2 K, and rho _c = 1.13 pm 0.01 g/cm^3. Interestingly, for the water model studied, differences in the LLCP location from PIMD and MD simulations suggest that nuclear quantum effects (i.e., atoms delocalization) play an important role in the thermodynamics of water around the LLCP (from the MD simulations of q-TIP4P/F water, P_c = 203 pm 4 MPa, T_c = 175 pm 2 K, and rho _c = 1.03 pm 0.01 g/cm^3). Overall, our results strongly support the LLPT scenario to explain water anomalous behavior, independently of the fundamental differences between classical MD and PIMD techniques. The reported values of T_c for D_2O and, particularly, H_2O suggest that improved water models are needed for the study of supercooled water.

Path integral molecular dynamics simulations for Green's function in a system of identical bosons.

Path integral molecular dynamics (PIMD) has been successfully applied to perform simulations of large bosonic systems in a recent study [Hirshberg et al., Proc. Natl. Acad. Sci. U. S. A. 116, 21445 (2019)]. In this work, we extend PIMD techniques to study Green's function for bosonic systems. We demonstrate that the development of the original PIMD method enables us to calculate Green's function and extract momentum distribution from our simulations. We also apply our method to systems of identical interacting bosons to study Berezinskii-Kosterlitz-Thouless transition around its critical temperature.

Static and Dynamic Correlations in Water: Comparison of Classical Ab Initio Molecular Dynamics at Elevated Temperature with Path Integral Simulations at Ambient Temperature.

It is a common practice in ab initio molecular dynamics (AIMD) simulations of water to use an elevated temperature to overcome the overstructuring and slow diffusion predicted by most current density functional theory (DFT) models. The simulation results obtained in this distinct thermodynamic state are then compared with experimental data at ambient temperature based on the rationale that a higher temperature effectively recovers nuclear quantum effects (NQEs) that are missing in the classical AIMD simulations. In this work, we systematically examine the foundation of this assumption for several DFT models as well as for the many-body MB-pol model. We find for the cases studied that a higher temperature does not correctly mimic NQEs at room temperature, which is especially manifest in significantly different three-molecule correlations as well as hydrogen bond dynamics. In many of these cases, the effects of NQEs are the opposite of the effects of carrying out the simulations at an elevated temperature.

Nonlocal Screening Dictates the Radiative Lifetimes of Excitations in Lead Halide Perovskites.

We use path integral molecular dynamics simulations and theory to elucidate the interactions between charge carriers, as mediated by a lead halide perovskite lattice. We find that the charge-lattice coupling of MAPbI3 results in a repulsive interaction between electrons and holes at intermediate distances. The effective interaction is understood using a Gaussian field theory, whereby the underlying soft, polar lattice contributes a nonlocal screening between quasiparticles. Path integral calculations of this nonlocal screening model are used to rationalize the small exciton binding energy and low radiative recombination rate observed experimentally and are compared to traditional Wannier-Mott and Fröhlich models, which fail to do so. These results clarify the origin of the high power conversion efficiencies in lead halide perovskites. Emergent repulsive electron-hole interactions provide a design principle for optimizing soft, polar semiconductors.