Path Integral Molecular Dynamics Study Research Articles

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

We investigate the effect of nuclear quantum effects (NQEs) of hydrogen atoms on the elasticity of ice VII at high pressure and ambient-temperature conditions using path-integral molecular dynamics (PIMD) calculations. We find that the NQEs of hydrogen contribute to the transition of ice VII from a static disordered structure to a dynamically disordered structure at pressures exceeding 40 GPa. This transition is characterized by a nonlinear increase in the elastic constants. A comparison of molecular dynamics, and PIMD calculations shows that NQEs increase the elastic constants of ice by about 20% at 70 GPa and 300 K. Published by the American Physical Society 2024

Location of the Shared Proton in Proton-Bound Dimer Compound of Hydrogen Sulfate and Formate: Path Integral Molecular Dynamics Study.

The structure of the proton-bound dimer compound of hydrogen sulfate and formate has been studied by considering nuclear quantum effects (NQEs) using the path integral molecular dynamics method. This study unveiled the location of the shared proton and answered the following question: "Is the shared proton localized on either an anion or located around the center of two anions?" We have elucidated that the shared proton is distributed in the region beyond the transition state due to the NQEs, even though the shared proton did not completely overcome the transition state for the proton shuttle.

Nuclear quantum and H/D isotope effects on aromaticity: path integral molecular dynamics study.

Aromaticity is an important concept in organic chemistry, and thus, many theoretical and experimental studies have been conducted so far. However, the majority of theoretical studies have concentrated on the aromaticity of the stationary point structures. Herein, the influence of nuclear quantum fluctuation (nuclear quantum effects: NQEs) and thermal fluctuation on the aromaticity of benzene have been analyzed by path integral molecular dynamics (PIMD) simulation. The PIMD simulations revealed that the NQEs affected not only the C-H bonds but also the C-C bonds. The HOMA and NICS calculations demonstrated that the aromaticity decreased due to the NQEs of carbon atoms, attributed to an increase in the contribution from specific vibrational modes strongly correlated with benzene's aromaticity.

Direct Elucidation of the Vibrationally Averaged Structure of Benzene: A Path Integral Molecular Dynamics Study.

Path integral molecular dynamics (PIMD) simulations for C6H6, C6D6, and C6T6 have been carried out to directly estimate the distribution of projected C-H(D,T) bond lengths onto the principal axis plane. The average values of raw C-H(D,T) bond lengths obtained from PIMD simulations are in the order of ⟨RC-H⟩ > ⟨RC-D⟩ > ⟨RC-T⟩ due to the anharmonicity of the potential energy curve. However, the projected C-H(D,T) bond lengths are almost the same as those reported by Hirano et al. [J. Mol. Struct. 2021, 1243, 130537]. Our PIMD simulations directly and strongly support the explanation by Hirano et al. for the experimental observations that almost the same projected C-H(D) bond lengths are found for C6H6 and C6D6. The PIMD simulations also predicted the same projected bond lengths for C6T6 as those of C6H(D)6. In addition to the previous local mode analysis, the present PIMD simulations predicted, for benzene isotopologues, that the vibrationally averaged structure is planar but non-flat.

Equilibrium and Dynamical Characteristics of Hydrogen Bond Bifurcations in Water-Water and Water-Ammonia Dimers: A Path Integral Molecular Dynamics Study.

We present path integral molecular dynamics results that describe the effects of nuclear quantum fluctuations on equilibrium and dynamical characteristics pertaining to bifurcation pathways in hydrogen bonded dimers combining water and ammonia, at cryogenic temperatures of the order of 20 K. Along these isomerizations, the hydrogen atoms in the molecules acting as hydrogen-bond donors interchange their original dangling/connective characters. Our results reveal that the resulting quantum transition paths comprise three stages: the initial and final ones involve overall rotations during which the two protons retain their classical-like characteristics. Effects from quantum fluctuation are clearly manifested in the changes operated at the intermediate passages over transition states, as the spatial extents of the protons stretch over typical lengths comparable to the distances between connective and dangling basins of attractions. Consequently, the classical over-the-hill path is replaced by a tunneling controlled mechanism which, within the path integral perspective, can be cast in terms of concerted inter-basin migrations of polymer beads from dangling-to-connective and from connective-to-dangling, at practically no energy costs. We also estimated the characteristic timescales describing such interconversions within the approximate ring polymer rate theory. Effects derived from full and partial deuteration are also discussed.

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.

Classical and path-integral molecular-dynamics study on liquid water and ice melting using non-empirical TTM2.1-F model

The TTMF2.1-F model is a non-empirical intermolecular water potential parametrised from ab-initio calculations of the water dimer with a complete basis set limit including dispersion correction from second-order Moller-Plesset perturbation theory. In this work, using two-phase ice-water NVT molecular-dynamics (MD) simulations, we found the ice melting temperature using the TTM2.1-F potential is close to 273 K when the nuclear quantum effects (NQEs) were included using path-integral centroid MD. Detailed analysis of the radial distribution functions, angle distribution functions, and associated joint probability for both liquid water and the two-phase cases showed that the melting-point-temperature drop when using path-integral simulation is due to the weakening of hydrogen bonds vis-à-vis classically-propagated MD.

Quantumness and state boundaries hidden in supercritical helium-4: A path integral centroid molecular dynamics study.

Isothermal-isobaric path integral centroid molecular dynamics simulations were conducted for fluid 4He at more than 600 state points in the proximity of the critical point to reveal the detailed states and relevant quantumness underlying the supercritical state. Through intensive analyses of the thermodynamic, dynamic, and quantum properties, we revealed the hidden state boundaries that separate the liquid-like and gas-like states in the supercritical region of this fluid. The Widom line, defined as the locus of the maxima of isobaric heat capacity C P , is also the quantum boundary at which there are changes in the isobaric temperature-dependence of the quantum wavelength, λ quantum, i.e., maximum amplitude of the Feynman imaginary-time paths (necklaces) of individual atoms. The Frenkel line, the famous dynamic state boundary, was observed to start from nearly the same point, 0.73-0.76 T c, on the P-T plane as observed for classical fluids. Several state boundaries based on the new criteria were found to emanate from the critical point or its vicinity on the P-T plane and are discussed in comparison with these boundaries. The quantumness of this fluid was expressed as (a) non-classical significant depression of C P observed in the liquid-like state; (b) the depression of the slopes dP/dT of the Widom line and the liquid-gas coexistence line near the critical point; and (c) the depression of the heat of pseudo-boiling across the Widom line. This is explained in terms of the decreasing kinetic energy with temperature observed in the liquid-like state below the Widom temperature T Widom, or alternatively in terms of the lattice model heat capacity, including the λ quantum.

A path integral molecular dynamics study on intermolecular hydrogen bond of acetic acid-arsenic acid anion and acetic acid-phosphoric acid anion clusters.

We apply ab initio path integral molecular dynamics simulation employing ωB97XD as the quantum chemical calculation method to acetic acid-arsenic acid anion and acetic acid-phosphoric acid anion clusters to investigate the difference of the hydrogen bond structure and its fluctuation such as proton transfer. We found that the nuclear quantum effect enhanced the fluctuation of the hydrogen bond structure and proton transfer, which shows treatment of the nuclear quantum effect was essential to investigate these systems. The hydrogen bond in acetic acid-arsenic acid anion cluster showed characters related to low-barrier hydrogen bonds, while acetic acid-phosphoric acid anion cluster did not. We found non-negligible distinction between these two systems, which could not be found in conventional calculations. We suggest that the difference in amount of atomic charge of the atoms consisting the hydrogen bond is the origin of the difference between acetic acid-arsenic acid and acetic acid-phosphoric acid anion cluster. © 2018 Wiley Periodicals, Inc.

Converged Colored Noise Path Integral Molecular Dynamics Study of the Zundel Cation Down to Ultralow Temperatures at Coupled Cluster Accuracy.

For a long time, performing converged path integral simulations at ultralow but finite temperatures of a few Kelvin has been a nearly impossible task. However, recent developments in advanced colored noise thermostatting schemes for path integral simulations, namely, the Path Integral Generalized Langevin Equation Thermostat (PIGLET) and the Path Integral Quantum Thermal Bath (PIQTB), have been able to greatly reduce the computational cost of these simulations, thus making the ultralow temperature regime accessible in practice. In this work, we investigate the influence of these two thermostatting schemes on the description of hydrogen-bonded systems at temperatures down to a few Kelvin as encountered, for example, in helium nanodroplet isolation or tagging photodissociation spectroscopy experiments. For this purpose, we analyze the prototypical hydrogen bond in the Zundel cation (H5O2+) as a function of both oxygen-oxygen distance and temperature in order to elucidate how the anisotropic quantum delocalization and, thus, the shape of the shared proton adapts depending on the donor-acceptor distance. The underlying electronic structure of the Zundel cation is described in terms of Behler's Neural Network Potentials of essentially converged Coupled Cluster accuracy, CCSD(T*)-F12a/AVTZ. In addition, the performances of the PIQTB and PIGLET methods for energetic, structural, and quantum delocalization properties are assessed and directly compared. Overall, our results emphasize the validity and practical usefulness of these two modern thermostatting approaches for path integral simulations of hydrogen-bonded systems even at ultralow temperatures.

A path integral molecular dynamics study of the hyperfine coupling constants of the muoniated and hydrogenated acetone radicals

The on-the-fly ab initio density functional path integral molecular dynamics (PIMD) simulations, which can account for both the nuclear quantum effect and thermal effect, were carried out to evaluate the structures and “reduced” isotropic hyperfine coupling constants (HFCCs) for muoniated and hydrogenated acetone radicals (2-muoxy-2-propyl and 2-hydoxy-2-propyl) in vacuo. The reduced HFCC value from a simple geometry optimization calculation without both the nuclear quantum effect and thermal effect is −8.18 MHz, and that by standard ab initio molecular dynamics simulation with only the thermal effect and without the nuclear quantum effect is 0.33 MHz at 300 K, where these two methods cannot distinguish the difference between muoniated and hydrogenated acetone radicals. In contrast, the reduced HFCC value of the muoniated acetone radical by our PIMD simulation is 32.1 MHz, which is about 8 times larger than that for the hydrogenated radical of 3.97 MHz with the same level of calculation. We have found that the HFCC values are highly correlated with the local molecular structures; especially, the Mu—O bond length in the muoniated acetone radical is elongated due to the large nuclear quantum effect of the muon, which makes the expectation value of the HFCC larger. Although our PIMD result calculated in vacuo is about 4 times larger than the measured experimental value in aqueous solvent, the ratio of these HFCC values between muoniated and hydrogenated acetone radicals in vacuo is in reasonable agreement with the ratio of the experimental values in aqueous solvent (8.56 MHz and 0.9 MHz); the explicit presence of solvent molecules has a major effect on decreasing the reduced muon HFCC of in vacuo calculations for the quantitative reproduction.

Can low-barrier hydrogen bond exist in systems with second row elements? An ab initio path integral molecular dynamics study for deprotonated hydrogen sulfide dimer

Nuclear quantum effect and thermal effect on deprotonated hydrogen sulfide dimer anion $${\text{H}}_{3} {\text{S}}_{2}^{-}$$ , composed of a second row element, are widely explored by ab initio on-the-fly path integral molecular dynamics simulation. At low temperature, the hydrogen-bonded proton tends to be diffusively located at the central position between two sulfur atoms, which is the typical characteristic feature of so-called low-barrier hydrogen bond (LBHB). This is the first case of the LBHB systems composed of the second row elements, although the hydrogen-bonded distance in $${\text{H}}_{3} {\text{S}}_{2}^{-}$$ (over 3.4 A) is much longer than the previously reported LBHB composed of first row elements (<2.5 A). At high temperature, the distance between two sulfur atoms is longer than that at low temperature, and the hydrogen-bonded proton localizes to each sulfur atom. Similar tendency is obtained in the deuterated $${\text{D}}_{3} {\text{S}}_{2}^{-}$$ species at all temperature. Analyzing the relationship between the position of the hydrogen-bonded proton and the quantum fluctuation effect of the proton, we elucidate that the LBHB is induced by the quantum tunneling at low temperature, while such trend becomes weak and the character of LBHB vanishes at room temperature for $${\text{H}}_{3} {\text{S}}_{2}^{-}$$ .

Car-Parrinello and path integral molecular dynamics study of the intramolecular hydrogen bonds in the crystals of benzoylacetone and dideuterobenzoylacetone.

The dynamics of the intramolecular short hydrogen bond in the molecular crystal of benzoylacetone and its deuterated analogue are investigated using ab initio molecular dynamics simulations. A study on intramolecular hydrogen bonding in 1-phenyl-1,3-butadione (I) and 1-deuteroxy-2-deutero-1-phenylbut-1-en-3-one (II) crystals has been carried out at 160 K and 300 K on the CPMD method level and at 300 K on the PIMD method level. The analysis of the two-dimensional free-energy landscape of reaction coordinate δ-parameter and ROO distances shows that the hydrogen (deuter) between the two oxygen atoms adopts a slightly asymmetrical position in the single potential well. When the nuclear quantum effects are taken into account, very large delocalization of the bridging proton is observed. These studies indicate that hydrogen bonds in the crystal of benzoylacetone have characteristic properties for the type of bonding model resonance-assisted hydrogen bonds (RAHB) without existing the equilibrium of the two tautomers. The infrared spectrum has been calculated, and a comparative vibrational analysis has been performed. The CPMD vibrational results appear to qualitatively agree with the experimental ones.

Variational path integral molecular dynamics study of a water molecule

In the present study, a variational path integral molecular dynamics method developed by the author [Chem. Phys. Lett. 482, 165 (2009)] is applied to a water molecule on the adiabatic potential energy surface. The method numerically generates an exact wavefunction using a trial wavefunction of the target system. It has been shown that even if a poor trial wavefunction is employed, the exact quantum distribution is numerically extracted, demonstrating the robustness of the variational path integral method.

Low-temperature anharmonicity of barium titanate: A path-integral molecular-dynamics study

We investigate the influence of quantum effects on the dielectric and piezoelectric properties of barium titanate in its (low-temperature) rhombohedral phase, and show the strongly anharmonic character of this system even at low temperature. For this purpose, we perform path-integral molecular-dynamics simulations under fixed pressure and fixed temperature, using an efficient Langevin thermostat-barostat, and an effective hamiltonian derived from first-principles calculations. The quantum fluctuations are shown to significantly enhance the static dielectric susceptibility (~ by a factor 2) and the piezoelectric constants, reflecting the strong anharmonicity of this ferroelectric system even at very low temperature. The slow temperature-evolution of the dielectric properties observed below ~ 100 K is attributed (i) to zero-point energy contributions and (ii) to harmonic behavior if quantum effects are turned off.

Nuclear quantum effects on protonated lysine with an asymmetric low barrier hydrogen bond: an ab initio path integral molecular dynamics study

The nuclear quantum effect on the short and asymmetric hydrogen bond of protonated lysine (LysH+) at room temperature is explored by ab initio path integral molecular dynamics (PIMD) simulation. From static electronic structure calculations, the barrier height of proton transfer in LysH+ is 1.1 kcal mol−1, which is much lower than that of typical hydrogen bonds. The hydrogen-bonded proton is delocalized in between two nitrogen atoms in the PIMD simulation including both thermal and nuclear quantum effects, while the proton is localized on a nitrogen atom in a conventional ab initio molecular dynamics simulation including thermal effects alone. We found that the proton transfer barrier found in the static calculation and conventional ab initio simulation is completely washed out in the PIMD simulation. Meanwhile, the proton distribution at the Nζ atom was larger than that at the N atom, as found in the static calculation and conventional ab initio molecular dynamics simulation. We clarified that an asymmetric low barrier hydrogen bond exists in LysH+ at room temperature from our PIMD simulation.

Spherical momentum distribution of the protons in hexagonal ice from modeling of inelastic neutron scattering data

The spherical momentum distribution of the protons in ice is extracted from a high resolution deep inelastic neutron scattering experiment. Following a recent path integral Car-Parrinello molecular dynamics study, data were successfully interpreted in terms of an anisotropic Gaussian model, with a statistical accuracy comparable to that of the model independent scheme used previously, but providing more detailed information on the three dimensional potential energy surface experienced by the proton. A recently proposed theoretical concept is also employed to directly calculate the mean force from the experimental neutron Compton profile, and to evaluate the accuracy required to unambiguously resolve and extract the effective proton potential from the experimental data.

Car-Parrinello and path integral molecular dynamics study of the hydrogen bond in the acetic acid dimer in the gas phase

In the paper are described studies of the double proton transfer (DPT) processes in the cyclic dimer of acetic acid in the gas phase using Car-Parrinello (CPMD) and path integral molecular dynamics (PIMD). Structures, energies and proton trajectories have been determined. The results show the double proton transfer in 450 K. In the classical dynamics (CPMD) a clear process mechanism can be identified, where asynchronized DPT arises due to coupling between the O-H stretching oscillator and several low energy intermolecular vibrational modes. The DPT mechanism is also asynchronic when quantum tunneling has been allowed in the simulation. It has been found that the calculated values of barrier height for the proton transfer depends very strongly on the used approaches. Barrier received from the free-energy profile at the CPMD level is around 4.5 kcal mol(-1) whereas at the PIMD level is reduced to 1 kcal mol(-1). The nature of bonding in acetic acid dimer and rearrangement of electron density due to the proton movement has been also studied by the topological analysis of Electron Localization Function and Electron Localizability Indicator function.

Path Integral Molecular Dynamics Study of Small H2 Clusters in the Large Cage of Structure II Clathrate Hydrate: Temperature Dependence of Quantum Spatial Distributions

We report a path integral molecular dynamics (PIMD) study of the temperature dependence of the spatial distribution of two and four H2 molecules inside the large cage of the structure II clathrate hydrate. The PIMD calculations were performed at five temperatures ranging from 25 to 200 K. Their results were combined with those from an earlier diffusion Monte Carlo (DMC) study of this system at T = 0 K [Sebastianelli, F.; Xu, M.; Bačić, Z. J. Chem. Phys. 2008, 129, 244706]. The spatial distribution of the confined H2 molecules at each of the temperatures considered was characterized with the help of several one-dimensional (1D) and three-dimensional (3D) distribution functions of suitably chosen intermolecular coordinates, generated by the PIMD and DMC calculations. The 1D distribution that proved to be the most strongly temperature dependent, and also the most revealing about the structural properties of the system as a function of temperature, involves the H2−cage center−H2 angle. In the case of four caged H2 molecules, this angular distribution provides clear evidence that between 50 and ∼100 K the system undergoes a qualitative change. At 50 K and below, the system is fully localized in the global minimum of the intermolecular potential, corresponding to a tetrahedral configuration of H2 molecules with a unique orientation relative to the cage frame. At temperatures of 75−100 K and higher, nearly degenerate local minima ∼200 cm−1 above the global minimum become accessible and are increasingly sampled by the system. The 3D spatial distributions also show this growing delocalization above 75−100 K. Our findings are in accord with the localization−delocalization transition observed experimentally to occur at 50 K for four D2 molecules in the large cage [Lokshin, K. A.; Zhao, Y.; He, D.; Mao, W. L.; Mao, H. K.; Hemley, R. J.; Lobanov, M. V.; Greenblatt, M. Phys. Rev. Lett. 2004, 93, 125503].

Car–Parrinello and path integral molecular dynamics study of the hydrogen bonds in 2-acetyl-1,8-dihydroxy-3,6-dimethylnaphthalene

Theoretical studies of the structure and proton motion in the intramolecular O–H…O hydrogen bonds in 2-acetyl-1,8-dihydroxy-3,6-dimethylnapthlane were carried out at the DFT and molecular dynamics levels. Geometry optimization at the PBE1PBE/6-311++G(2d,2p) level demonstrate the existence of two tautomers on the potential energy surface. Dynamics of proton motion in intramolecular hydrogen bonds was investigated in vacuo at 100 K using Car–Parrinello and path integral molecular dynamics. For the strong intramolecular hydrogen bond very large delocalization of bridging proton is noted, especially in the path integral simulation where quantum effects are taken into account. No tautomerism was found for this intramolecular hydrogen bond.