Proton momentum distribution in water: an open path integral molecular dynamics study

We present the aspects of the path integral molecular dynamics (PIMD) method relative to (a) its theoretical fundamental principles, (b) its applicability to model quantum systems and (c) its implementation as a simulation tool. The PIMD method is based on the discretized path integral representation of quantum mechanics. In this representation, a quantum particle is isomorphic to a closed polymer chain. The problem of the indistinguishability of quantum particles is tackled with a non-local exchange potential. When the exact density matrix of the quantum particles is used, the exchange potential is exact. We use a high temperature approximation to the density matrix leading to an approximate form of the exchange potential. This quantum molecular dynamics method allows the simulation of collections of quantum particles at finite temperature. Our algorithm can be made to scale linearly with the number of quantum states on which the density matrix is projected. Therefore, it can be optimized to run efficiently on parallel computers. We apply the PIMD method to the electron plasma in 3-dimension. The kinetic and potential energies are calculated and compared with results for similar systems simulated with a variational Monte Carlo method. Both results show good agreements with each other at all the densities studied. The method is then use to model the thermodynamic behavior of a simple alkali metal. In these simulations, ions and valence electrons are treated as classical and quantum particles, respectively. The simple metal undergoes a phase transformation upon heating. Furthermore, to demonstrate the richness of behaviors that can be studied with the PIMD method, we also report on the metal to insulator transition in a hydrogenoid lattice. Finally, in previous studies of alkali metals, electrons interacted with ions via local pseudo-potentials, an extension of the method to modeling electrons in non-local pseudo-potentials is also presented with applications.

Efficient numerical algorithms are developed for use with two finite temperature semiclassical approximations to quantum dynamics both of which require trajectories generated on potentials of mean force derived from the path integral expression for the density matrix. The numerical algorithms are formed from the combination of a classical adiabatic relation similar to that used in the Car–Parrinello method and an efficient path integral molecular dynamics scheme. Results on model, an anharmonic oscillator and a realistic, fluid para-hydrogen, problem indicate that semiclassical dynamics can be obtained for virtually the same computational cost as structure and thermodynamics.

A variational path integral molecular dynamics study of a solid helium-4

A path integral centroid molecular dynamics method for Bose and Fermi statistics

Theoretical analysis of Muoniated compounds using path integral molecular dynamics method

D. Scharf, J. Jortner and U. Landman, atomic and molecular quantum mechanics by the path integral molecular dynamics method: Chem. Phys. Letters 130 (1986) 504

The mechanism of cluster isomerization induced by electron attachment to Na4Cl4 clusters was explored by the constant temperature quantum path integral molecular dynamics method over the temperature range 50°K–1200°K. The configurational modifications can be related to the role of an excess electron as a pseudonegative ion and to the effect of partial neutralization of the alkali ion(s) by the excess electron which induce isomerization at moderately low temperatures in comparison with the parent neutral Na4Cl4 cluster.KeywordsTemperature DomainExcess ElectronReorganization EnergyElectron AttachmentConfigurational ChangeThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper we explore the mechanisms of cluster isomerization induced by electron attachment to small, neutral Na4Cl4 clusters, with the localization of an excess electron inducing structural configurational changes within the cluster. The constant temperature quantum path integral molecular dynamics method was applied to obtain information of the structure and energetics of the cluster as well as the binding energy and the charge distribution of the excess electron for Na4Cl−4 clusters, over the temperature range of 50–1200 K. The attachment of an excess electron to the ionic cluster induced two types of configurational modifications, which can be traced to the role of the excess electron as a pseudonegative ion and to the partial neutralization of a single cation by the excess electron. Consequently, the induction of isomerization at moderately low temperatures, in conjunction with the appearance of new nuclear configurations of the negative cluster, which have no counterpart in the neutral parent cluster, are exhibited.

The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.

We establish a fast and reliable benchmarking protocol for predictions of Muon Spin Resonance observables. To this end, we apply neutron Compton scattering (NCS) to study the nuclear momentum distributions of the proton and deuteron in the condensed phase of the isopropyl and d-isopropyl alcohols. By subtracting the time-of-flight NCS spectra of both compounds we demonstrate that the proton momentum distribution in the OH group of isopropanol and the deuteron momentum distribution in the OD group in d-isopropyl can be studied selectively. The site-selective application of the NCS method enables the calculation of the magnitude of the frequency isotope effect for the proton in OH along the hydrogen bond direction. By comparing the magnitude of the frequency isotope effect with values predicted for simple model potentials we are able to perform the appraisal of the degree of anharmonicity of the OH proton environment. Assuming that the effective potential felt by the OH proton along the hydrogen-bond direction can be satisfactorily described by the Morse potential, we are able to calculate its dissociation constant D and decay constant a. Finally, assuming that the same Morse potential describes the local binding of Muonium in the mioniated isopropyl radical, we are able to predict its width of momentum and position distributions and the kinetic and zero-point energy. Based on these results, we are able to provide a conservative bound for the magnitude of the isotope effect on the muonium hyperfine interaction without resorting to a complicated and computationally expensive methodology based on the application of path integrals.

Coherence in the momentum distribution of protons in dilute acids and bases

We study nucleon momentum distributions of even-even isotopes of Ni, Kr, and Sn in the framework of deformed self-consistent mean-field Skyrme HF+BCS method, as well as of theoretical correlation methods based on light-front dynamics and local density approximation. The isotopic sensitivities of the calculated neutron and proton momentum distributions are investigated together with the effects of pairing and nucleon-nucleon correlations. The role of deformation on the momentum distributions in even-even Kr isotopes is discussed. For comparison, the results for the momentum distribution in nuclear matter are also presented.

In the framework of correlation method so-called coherent density fluctuation model (CDFM) the proton momentum distributions (PMD) of the ground state for some even mass nuclei of fpshell like 70 Zn, 72 Ge and 74 Se nuclei are examined. Proton momentum distributions are expressed in terms of the fluctuation function(|()| 2 ) and determined from theory and experiment. The main characteristic feature of the PMD obtained by CDFM is the existence of high-momentum components, for momenta k 2 fm -1 . For completeness, also elastic electron scattering form factors F(q) are evaluated within the same framework.

Three-body models of $^{6}\mathrm{Li}$ are used to investigate the structure of the $^{6}\mathrm{p}$+(n\ensuremath{\alpha}) vertex amplitude. Within the three-body framework, the formalism of the $^{6}\mathrm{p}$+(n\ensuremath{\alpha}) overlap amplitude is delineated. From this overlap, the formula for the central physical quantity, namely, the $^{6}\mathrm{p}$+(n\ensuremath{\alpha}) joint momentum distribution, is derived. It is shown that the $^{6}\mathrm{p}$+(n\ensuremath{\alpha}) joint momentum distribution satisfies a sum rule consistent with its probability interpretation. The sum rule is used as a check on the numerical calculation of the joint momentum distribution and to isolate terms that contribute insignificantly. By integration of the $^{6}\mathrm{p}$+(n\ensuremath{\alpha}) joint momentum distribution over a given range of the n\ensuremath{\alpha} excitation energy, the momentum distribution of the valence proton in $^{6}\mathrm{Li}$ is obtained. From both the $^{6}\mathrm{p}$+(n\ensuremath{\alpha}) joint momentum distribution and the p-(n\ensuremath{\alpha}) momentum distribution, the dynamical structure of the $^{6}\mathrm{p}$+(n\ensuremath{\alpha}) vertex according to three-body models is uncovered.

Neutron Compton scattering (NCS) experiments were performed on liquid and solid HF, a system where the effective Born-Oppenheimer (BO) potential energy surface is not isotropic. Proton momentum distributions were calculated in the framework of the impulse approximation from measured neutron Compton profiles. A detailed data analysis shows that there are no systematic changes in the width, position of the maximum, or excess kurtosis of proton momentum distributions in both systems with increasing scattering angle. This observation has important implications for further theoretical work on violation of BO approximation in the presence of ultrafast neutron-proton scattering. That is, the picture of proton dynamics in HF emerging from the analysis of NCS data does not seem to support the previously considered model of protons accessing excited electronic states due to ultrafast scattering.