Ring Polymer Molecular Dynamics Simulations Research Articles

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.

Nuclear quantum effects in the acetylene:ammonia plastic co-crystal.

Organic molecular solids can exhibit rich phase diagrams. In addition to structurally unique phases, translational and rotational degrees of freedom can melt at different state points, giving rise to partially disordered solid phases. The structural and dynamic disorder in these materials can have a significant impact on the physical properties of the organic solid, necessitating a thorough understanding of disorder at the atomic scale. When these disordered phases form at low temperatures, especially in crystals with light nuclei, the prediction of material properties can be complicated by the importance of nuclear quantum effects. As an example, we investigate nuclear quantum effects on the structure and dynamics of the orientationally disordered, translationally ordered plastic phase of the acetylene:ammonia (1:1) co-crystal that is expected to exist on the surface of Saturn's moon Titan. Titan's low surface temperature (∼90K) suggests that the quantum mechanical behavior of nuclei may be important in this and other molecular solids in these environments. By using neural network potentials combined with ring polymer molecular dynamics simulations, we show that nuclear quantum effects increase orientational disorder and rotational dynamics within the acetylene:ammonia (1:1) co-crystal by weakening hydrogen bonds. Our results suggest that nuclear quantum effects are important to accurately model molecular solids and their physical properties in low-temperature environments.

Molecular dynamics simulations and machine-learning assisted study of the reaction path bifurcation: Application to the intramolecular Diels–Alder cycloaddition between cyclobutadiene and butadiene

The intramolecular Diels–Alder cycloaddition between cyclobutadiene and butadiene, which involves post-transition-state bifurcation (PTSB), has been investigated using the ring-polymer molecular dynamics (RPMD), classical MD and quasi-classical trajectory (QCT) simulations, and supervised machine-learning (ML) technique. The branching fraction of this reaction strongly depends on the simulation temperature. While QCT, classical MD and RPMD simulations performed at room temperature, starting from the ambimodal transition state (TS), showed the similar dynamics, QCT overestimated the minor branching fraction at low temperature. The supervised machine-learning analysis revealed that the initial coordinates and momenta for low frequency modes at the ambimodal TS contribute to the branching dynamics. The classical MD and RPMD methods follow similar conditions to quantum Boltzmann distributions, whereas the artificially localized phase distribution, considering that the zero-point energy is wedged into the classical particles. As a result, the QCT method can provide inadequate bifurcation dynamics, such as the overestimation of the minor product.

Ring-polymer Molecular Dynamics Simulation for the Adsorption of H2 on Ice Clusters (H2 O)n (n=8, 10, and 12).

In the interstellar medium, the H2 adsorption and desorption on the solid water ice are crucial for chemical and physical processes. We have recently investigated the probabilities of H2 sticking on the (H2 O)8 ice, which has quadrilateral surfaces. We have extended the previous work using classical MD and ring-polymer molecular dynamics (RPMD) simulations to the larger ice clusters, (H2 O)10 and (H2 O)12 , which have pentagonal and hexagonal surfaces, respectively. The H2 sticking probabilities decreased as the temperature increased for both cluster cases, whereas the cluster-size-independent profiles were observed. It is thought that the size independence of the probabilities is qualitatively understood from the similar binding energies for all the three cluster systems. Furthermore, the RPMD sticking probabilities are smaller than the classical ones because of the reduction in the binding energies owing to nuclear quantum effects, such as vibrational quantization.

Competing Nuclear Quantum Effects and Hydrogen-Bond Jumps in Hydrated Kaolinite.

Recent work has shown that the dynamics of hydrogen bonds in pure clays are affected by nuclear quantum fluctuations, with different effects for the hydrogen bonds holding different layers of the clay together and for those within the same layer. At the clay-water interface there is an even wider range of types of hydrogen bond, suggesting that the quantum effects may be yet more varied. We apply classical and thermostated ring polymer molecular dynamics simulations to show that nuclear quantum effects accelerate hydrogen-bond dynamics to varying degrees. By interpreting the results in terms of the extended jump model of hydrogen-bond switching, we can understand the origins of these effects in terms of changes in the quantum kinetic energy of hydrogen atoms during an exchange. We also show that the extended jump mechanism is applicable not only to the hydrogen bonds involving water, but also those internal to the clay.

First-principles surface reaction rates by ring polymer molecular dynamics and neural network potential: role of anharmonicity and lattice motion.

Elementary gas-surface processes are essential steps in heterogeneous catalysis. A predictive understanding of catalytic mechanisms remains challenging due largely to difficulties in accurately characterizing the kinetics of such steps. Experimentally, thermal rates for elementary surface reactions can now be measured using a novel velocity imaging technique, providing a stringent testing ground for ab initio rate theories. Here, we propose to combine ring polymer molecular dynamics (RPMD) rate theory with state-of-the-art first-principles-determined neural network potential to calculate surface reaction rates. Taking NO desorption from Pd(111) as an example, we show that the harmonic approximation and the neglect of lattice motion in the commonly-used transition state theory overestimates and underestimates the entropy change during the desorption process, respectively, leading to opposite errors in rate coefficient predictions and artificial error cancellations. Including anharmonicity and lattice motion, our results reveal a generally neglected surface entropy change due to significant local structural change during desorption and obtain the right answer for the right reasons. Although quantum effects are found to be less important in this system, the proposed approach establishes a more reliable theoretical benchmark for accurately predicting the kinetics of elementary gas-surface processes.

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.

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.

Nuclear Quantum Effects in H2 Adsorption Dynamics on a Small Water Cluster Studied with Ring-Polymer Molecular Dynamics Simulations

Nuclear Quantum Effects in H₂ Adsorption Dynamics on a Small Water Cluster Studied with Ring-Polymer Molecular Dynamics Simulations

Simulating Raman spectra of hydrogen hydrates using first-principles path-integral ring-polymer molecular dynamics

A variant of first-principles (FP) path-integral ring-polymer molecular dynamics (RPMD) simulations was used to investigate the C0,C1, and C2 H2 hydrates at 280 K aiming at reproducing their experimental Raman spectra. We find that our implementation based on white-noise Langevin thermostat applied to the H2O sub-system only in the formulation of FP-RPMD is able to reproduce with high accuracy the characteristic features of the measured Raman spectra of H2 hydrates in all C0,C1, and C2 phases, demonstrating potential of our computational approach for investigating H-containing materials under pressure.

Comparative studies of IR spectra of deprotonated serine with classical and thermostated ring polymer molecular dynamics simulations.

Here we report the vibrational spectra of deprotonated serine calculated from the classical molecular dynamics (MD) simulations and thermostated ring-polymer molecular dynamics (TRPMD) simulation with third-order density-functional tight-binding. In our earlier study [Inakollu and Yu, “A systematic benchmarking of computational vibrational spectroscopy with DFTB3: Normal mode analysis and fast Fourier transform dipole autocorrelation function,” J. Comput. Chem. 39, 2067 (2018)] of deprotonated serine, we observed a significant difference in the vibrational spectra with the classical MD simulations compared to the infrared multiple photon dissociation spectra. It was postulated that this is due to neglecting the nuclear quantum effects (NQEs). In this work, NQEs are considered in spectral calculation using the TRPMD simulations. With the help of potential of mean force calculations, the conformational space of deprotonated serine is analyzed and used to understand the difference in the spectra of classical MD and TRPMD simulations at 298.15 and 100 K. The high-frequency vibrational bands in the spectra are characterized using Fourier transform localized vibrational mode (FT-νNAC) and interatomic distance histograms. At room temperature, the quantum effects are less significant, and the free energy profiles in the classical MD and the TRPMD simulations are very similar. However, the hydrogen bond between the hydroxyl–carboxyl bond is slightly stronger in TRPMD simulations. At 100 K, the quantum effects are more prominent, especially in the 2600–3600 cm−1, and the free energy profile slightly differs between the classical MD and TRPMD simulations. Using the FT-νNAC and the interatomic distance histograms, the high-frequency vibrational bands are discussed in detail.

Two-dimensional Raman spectroscopy of Lennard-Jones liquids via ring-polymer molecular dynamics.

The simulation of multidimensional vibrational spectroscopy of condensed-phase systems including nuclear quantum effects is challenging since full quantum-mechanical calculations are still intractable for large systems comprising many degrees of freedom. Here, we apply the recently developed double Kubo transform (DKT) methodology in combination with ring-polymer molecular dynamics (RPMD) for evaluating multi-time correlation functions [K. A. Jung et al., J. Chem. Phys. 148, 244105 (2018)], providing a practical method for incorporating nuclear quantum effects in nonlinear spectroscopy of condensed-phase systems. We showcase the DKT approach in the simulation of the fifth-order two-dimensional (2D) Raman spectroscopy of Lennard-Jones liquids as a prototypical example, which involves nontrivial nonlinear spectroscopic observables of systems described by anharmonic potentials. Our results show that the DKT can faithfully reproduce the 2D Raman response of liquid xenon at high temperatures, where the system behaves classically. In contrast, liquid neon at low temperatures exhibits moderate but discernible nuclear quantum effects in the 2D Raman response compared to the responses obtained with classical molecular dynamics approaches. Thus, the DKT formalism in combination with RPMD simulations enables simulations of multidimensional optical spectroscopy of condensed-phase systems that partially account for nuclear quantum effects.

Nuclear quantum effect for hydrogen adsorption on Pt(111)

Nuclear quantum effect and many-body interaction importantly interplay in the hydrogen on the Pt(111) system under the high coverage conditions of electrochemical interest, as revealed by our ab initio path integral and ring polymer molecular dynamics simulations done at room temperature. At the full monolayer coverage, hydrogen atoms are close-packed either at the atop sites or the fcc sites owing to their strong repulsion and the nearly degenerate nature of the adsorption sites. While at the 2/3 monolayer, they are delocalized over the fcc and hcp sites via the bridge sites because of the hopping. The quantum many-body effect is thus crucially important in determining the coverage dependence and provides a clue for reconciling the long-standing controversy on this system.

Density dependence of the dynamical processes governing the velocity autocorrelation function of a quantum fluid.

We present an exponential mode analysis of the dynamical processes determining the time behavior of the Kubo velocity autocorrelation function (KVAF) of fluid para-H_{2}, as obtained by ring polymer molecular dynamics simulations at various fluid densities. The mechanisms contributing to the decay of the KVAF are thoroughly characterized at a slightly supercritical temperature, in a density interval ranging from the critical point to the fluid-solid transition. We show that the quantum nature of the system does not influence the specific phenomena and decay channels through which a loss in velocity correlation takes place, since these are the same as found in classical fluids. Similarly, a dynamical crossover is observed with increasing density, signaling the onset of a transverse-like dynamics like in classical systems. We also investigate the effect of density on the processes contributing to the most relevant property of a quantum fluid, namely, the large values of the total and zero-point kinetic energy arising through the Heisenberg uncertainty principle.

Dynamical Origin of the Total and Zero-Point Kinetic Energy in a Quantum Fluid.

By applying an exponential mode analysis to ring polymer molecular dynamics simulations of dense fluid parahydrogen, we find that the dynamical processes establishing the time behavior of the Kubo velocity autocorrelation function display the same nature as those already observed in high-density classical fluids. This result permits us to demonstrate that the exponential mode decomposition is a unique tool to identify which dynamical processes lead to one of the most notable properties of quantum fluids: the large value of the mean kinetic energy per particle and the importance of the zero-temperature quantum effects in determining it.

Ionization dynamics of Ne-doped helium clusters at low temperature: Ring-polymer molecular dynamics simulations including electronically nonadiabatic transitions

Ionization dynamics of NeHen (n ≤ 100) clusters has been studied by path-integral molecular dynamics (PIMD) and ring-polymer molecular dynamics (RPMD) simulations that can effectively describe nuclear quantum effects. The pairwise-additive interatomic potential model was used for the neutral NeHen clusters while the diatomics-in-molecule (DIM) model including spin-orbit coupling in Ne+(2P) was employed to describe the electronic structures of the cationic NeHen+ clusters. We found that the calculated ionization spectra of NeHen were very similar to those of Hen except for Ne ionization transitions. This indicates that helium density distributions are similar for both the Ne-doped and undoped clusters. The RPMD simulations have been performed to understand the initial charge migration dynamics and its associated nuclear dynamics through the instantaneous ionization of NeHe100. We found that, when the Ne atom is preferentially ionized, the He atoms in the first solvation shell are readily attracted by Ne+ to form a snowball structure.

Characterization of a trans–trans Carbonic Acid–Fluoride Complex by Infrared Action Spectroscopy in Helium Nanodroplets

The high Lewis basicity and small ionic radius of fluoride promote the formation of strong ionic hydrogen bonds in the complexation of fluoride with protic molecules. Herein, we report that carbonic acid, a thermodynamically disfavored species that is challenging to investigate experimentally, forms a complex with fluoride in the gas phase. Intriguingly, this complex is highly stable and is observed in abundance upon nanoelectrospray ionization of an aqueous sodium fluoride solution in the presence of gas-phase carbon dioxide. We characterize the structure and properties of the carbonic acid–fluoride complex, F–(H2CO3), and its deuterated isotopologue, F–(D2CO3), by helium nanodroplet infrared action spectroscopy in the photon energy range of 390–2800 cm–1. The complex adopts a C2v symmetry structure with the carbonic acid in a planar trans–trans conformation and both OH groups forming ionic hydrogen bonds with the fluoride. Substantial vibrational anharmonic effects are observed in the infrared spectra, most notably a strong blue shift of the symmetric hydrogen stretching fundamental relative to predictions from the harmonic approximation or vibrational second-order perturbation theory. Ab initio thermostated ring-polymer molecular dynamics simulations indicate that this blue shift originates from strong coupling between the hydrogen stretching and bending vibrations, resulting in an effective weakening of the OH···F– ionic hydrogen bonds.

Elucidating the Nuclear Quantum Dynamics of Intramolecular Double Hydrogen Transfer in Porphycene.

We address the double hydrogen transfer (DHT) dynamics of the porphycene molecule, a complex paradigmatic system in which the making and breaking of H-bonds in a highly anharmonic potential energy surface require a quantum mechanical treatment not only of the electrons but also of the nuclei. We combine density functional theory calculations, employing hybrid functionals and van der Waals corrections, with recently proposed and optimized path-integral ring-polymer methods for the approximation of quantum vibrational spectra and reaction rates. Our full-dimensional ring-polymer instanton simulations show that below 100 K the concerted DHT tunneling pathway dominates but between 100 and 300 K there is a competition between concerted and stepwise pathways when nuclear quantum effects are included. We obtain ground-state reaction rates of 2.19 × 1011 s–1 at 150 K and 0.63 × 1011 s–1 at 100 K, in good agreement with experiment. We also reproduce the puzzling N–H stretching band of porphycene with very good accuracy from thermostated ring-polymer molecular dynamics simulations. The position and line shape of this peak, centered at around 2600 cm–1 and spanning 750 cm–1, stem from a combination of very strong H-bonds, the coupling to low-frequency modes, and the access to cis-like isomeric conformations, which cannot be appropriately captured with classical-nuclei dynamics. These results verify the appropriateness of our general theoretical approach and provide a framework for a deeper physical understanding of hydrogen transfer dynamics in complex systems.

Nuclear Quantum Effects in Sodium Hydroxide Solutions from Neural Network Molecular Dynamics Simulations.

Nuclear quantum effects (NQEs) cause the nuclei of light elements like hydrogen to delocalize, affecting numerous properties of water and aqueous solutions, such as hydrogen-bonding and proton transfer barriers. Here, we address the prototypical case of aqueous NaOH solutions by investigating the effects of quantum nuclear fluctuations on radial distribution functions, hydrogen-bonding geometries, power spectra, proton transfer barriers, proton transfer rates, water self-exchange rates around the Na+ cations, and diffusion coefficients, for the full room-temperature solubility range. These properties were calculated from classical and ring-polymer molecular dynamics simulations employing a reactive high-dimensional neural network potential based on dispersion-corrected density functional theory reference calculations. We find that NQEs have a very small impact on the solvation structure around Na+, slightly strengthen the water-water and water-hydroxide hydrogen bonds, and lower the peak positions in the power spectra for the HOH bending and OH stretching modes by about 50 and 100 cm-1, respectively. Moreover, NQEs significantly lower the proton transfer barriers, thus increasing the proton transfer rates, resulting in an increase of the diffusion coefficient in particular of OH-, as well as a decrease of the mean residence time of molecules in the first hydration shell around Na+ at high NaOH concentrations.

Nuclear quantum effects in the direct ionization process of pure helium clusters: path-integral and ring-polymer molecular dynamics simulations on the diatomics-in-molecule potential energy surfaces.

The direct photoionization of pure helium clusters, Hen (n = 100, 200 and 300), and its subsequent short-time process have been studied by path integral molecular dynamics (PIMD) and ring-polymer molecular dynamics (RPMD) simulations that can effectively describe the nuclear quantum effects in large systems. The modified diatomics-in-molecule (DIM) model [Calvo et al., J. Chem. Phys., 2011, 135, 124308] has been used to describe the electronic structures of Hen+ clusters. The PIMD simulations were able to reproduce the experimental ionization spectra having a broad and asymmetric nature, which can be ascribed to the inhomogeneity of the energy levels of He atoms in the inner and outer regions of the cluster. From the RPMD simulations, it is found that the ionized helium cluster in the higher excited state is followed by fast electronic state relaxation via nonadiabatic charge transfer including a small contribution of nuclear motions, and subsequently by slow relaxation of the cluster structure.