Path Integral Centroid Molecular Dynamics Research Articles

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

We propose a path integral centroid molecular dynamics (CMD) method extended to Bose and Fermi statistics. An extended method of path integral molecular dynamics (PIMD) for such statistics is also developed as a technique of calculations of static properties. Bose PIMD and CMD simulations have been performed for bulk liquid 4 He and ideal Bose gas, respectively. The remnant of λ transition is observed for bulk liquid 4 He, while the effect of Bose statistics on the centroid dynamics spanning several nanoseconds is observed for ideal Bose gas.

A semiclassical approach to the dynamics of many-body Bose/Fermi systems by the path integral centroid molecular dynamics

We present a formalism of the path integral centroid molecular dynamics (CMD) extended to Bose and Fermi statistics as a semiclassical approach to explore the dynamics of quantum many-body systems. The validity of the method is examined in relation to the time correlation functions. The presently proposed scheme, refined from our previous derivation [Chem. Phys. Lett. 307, 187 (1999)], is aimed at the calculations of not the exact quantum-mechanical dynamics but the semiclassical dynamics under certain approximations. The formalism is based on the projection operator with which the Bose/Fermi system is mapped onto a particular type of pseudo-Boltzmann system. In the pseudo-Boltzmann system the correlation due to the Bose/Fermi statistics is introduced via an extra pseudopotential called the permutation potential and its relevant operator. Using the present semiclassical formalism, the time correlation function of centroid position, which is evaluated from the CMD trajectories in the pseudo-Boltzmann system, is an approximation to the Kubo canonical correlation function of position operator of the exact quantum-statistical system composed of bosons or fermions. There is no such apparent relation between the momentum operator and the corresponding momentum centroid.

Quantum Spin Dynamics by Path Integral Centroid Molecular Dynamics Method

Quantum spin dynamics in mesoscopic magnets has received much attention over the recent years, both experimentally and theoretically. Especially, molecular magnets such as the ferric wheel or Mn12 have emerged as promising candidates for the experimental observation of macroscopic quantum phenomena such as the tunneling of the magnetization. We investigated tunneling rates of model manganese systems by means of the nonlinear σ model. 1) The path integral centroid molecular dynamics (CMD) 2),3) method has been shown to be capable of simulating the real time quantum dynamics of complicated many-body systems, even for reasonably long time, albeit approximately. So far, this method has been applied to calculating dynamical properties in systems consisting of both Fermi and Bose particles. 4) In this study, we demonstrate that the centroid-based path integral method is feasible to investigate real time quantum spin dynamics at low temperature. We introduce a centroid corresponding to a spin variable as an average spin coordinate of a closed isomorphic necklace of each spin space, so-called spin centroid. We calculated magnetization of a system with S = 1.

Quantum Molecular Dynamics Simulations of Low-Temperature High Energy Density Matter: Solid p-H2/Li and p-H2/B

The metastability of atomic impurities, Li and B, trapped in solid parahydrogen is studied by employing path integral molecular dynamics (PIMD) and centroid molecular dynamics (CMD) simulations at 4 K and zero external pressure. Starting from pure solid hydrogen consisting of 1440 particles, doped systems are prepared by substituting impurity atoms for hydrogen molecules at substitutional defect sites. For various concentrations, thermodynamic quantities are then calculated and the stability of the systems is monitored. For the case of lithium, systems containing 2.5 mol % dopants remain metastable with convergent thermodynamic quantities, but systems with 3.3 mol % or more dopants become unstable. For the case of boron, systems containing as high as 15 mol % dopants remain metastable on the time scale of the simulation, while systems with 25 mol % dopants do not. These results provide evidence of the transition from metastability to global instability and a rough estimate of the maximum doping density of...

Path integral centroid molecular dynamics method for Bose and Fermi statistics: formalism and simulation

A method is proposed for path integral centroid molecular dynamics (CMD) extended to Bose/Fermi statistics. It is based on the `pseudo-Boltzmann' canonical partition function of quantum statistical mechanics. An extended technique of path integral molecular dynamics (PIMD) is further presented for the calculation of thermodynamic properties and centroid mean force of Bose/Fermi systems. Bosonic PIMD and CMD simulations have been performed for 4 He and the ideal Bose gas, respectively. The remnant of λ transition is observed for 4 He, while Bose statistics causes a decay of the centroid velocity autocorrelation function of the ideal Bose gas in a nanosecond scale.

A path integral centroid molecular dynamics study of nonsuperfluid liquid helium-4

Path integral centroid molecular dynamics (CMD) calculation for normal liquid 4He has been performed. Dynamical behavior of the liquid at 4 K, which can not be reproduced by classical approximation, was well described by the CMD formalism. The calculated self-diffusion coefficient was found to be 5.06±0.04×10−5 cm2/s, which is in the same order of magnitude as that of ordinary liquids. Relaxation function of density fluctuation has also been calculated within the CMD approximation. Detailed comparison between the static susceptibility function χ̂(k) and the static structure factor of the centroid density Ŝ(c)(k) has been made. These correspond to the initial value of the exact and the centroid relaxation functions, respectively. For small k (⩽1.0 Å−1), χ̂(k) is well approximated by Ŝ(c)(k). For larger k, both the correlation functions have identical peak position. However, the intensity of Ŝ(c)(k) is systematically larger than that of χ̂(k). The calculated dynamic structure factor has been compared with the spectrum obtained from neutron scattering experiment. The agreement is satisfactory for 0.2<k<2.2 Å−1. The calculated peak frequency as a function of k, i.e., the dispersion relation, has a minimum around 1.9 Å−1, where the static correlation function shows maximum intensity. This behavior has also been experimentally observed for the dispersion relation for superfluid 4He. The peak continuously loses collective character and shows single-particle behavior with increasing k around the minimum. This behavior gives rise to the minimum in the dispersion relation for normal liquid 4He. The spectrum becomes narrow as the peak approaches the minimum, showing that the single-particle contribution becomes dominant in the dynamic structure factor. This narrowing is widely found among classical liquid; but is not observed in the spectrum of the superfluid 4He, indicating that the excitation around the minimum for the superfluid may have a different molecular origin than that for normal liquid 4He.

Path integral centroid molecular dynamics study of the dynamic structure factors of liquid para-hydrogen

The dynamic structure factors S(k,ω) of liquid p–H2 in the range of 0.29≤k≤5.9 Å−1 have been calculated by means of a path integral centroid molecular dynamics simulation at 14.7 K and zero-pressure. The quantization of the nuclei has caused a red-shift of the spectrum of the phonon density of states owing to quantum dispersion. As in classical liquids, the calculated spectra of S(k,ω) clearly indicate the existence of the longitudinal acoustic-like mode and the de Gennes slowdown of structural relaxation at k=2.0 Å−1. The sound velocity and the self-diffusion coefficient of p–H2 agree well with the experimental values.

A quantum model for water: Equilibrium and dynamical properties

Path integral molecular dynamics and centroid molecular dynamics have been applied to study and modify an empirical flexible model for water, the simple point charge/flexible (SPC/F) model. The quantum structural, thermodynamic and dynamical properties have been calculated and compared to their classical counterparts, as well as to experiment. The path integral molecular dynamics simulations demonstrate that the quantum liquid is less structured and exhibits less hydrogen bonding than its classical analog. Quantization also leads to a lower dielectric constant, relative to the corresponding classical value. Centroid molecular dynamics has been used to calculate single molecule time correlation functions, the Debye dielectric relaxation correlation function, and the power spectrum for the quantum model. These time correlation functions decay more rapidly than the classical ones, indicating that nuclear rotational tunneling occurs in the liquid. The power spectrum of the quantized liquid also exhibits red shifted bend and stretch frequencies relative to the classical model. A modification of the parametrization of the harmonic intramolecular potential for the simple point charge/flexible (SPC/F) model is suggested and tested in order to improve the dielectric properties as well as the values of the vibrational frequencies. The quantum simulation of the modified water model, called SPC/F2, gives better agreement with the experimental IR spectrum of water and the measured value of the dielectric constant. However, the self-diffusion constant for the modified SPC/F model is still somewhat too large relative to experiment. In addition, the NMR rotational time constant is too small compared to experiment. While these discrepancies leave room for future modifications (e.g., including electronic polarizability), the model represents the first parametrization of an empirical flexible water potential explicitly developed for quantum path integral simulations.