^{1,a)}

### Abstract

In this paper, we present a path integral hybrid Monte Carlo (PIHMC) method for rotating molecules in quantum fluids. This is an extension of our PIHMC for correlated Bose fluids [S. Miura and J. Tanaka, J. Chem. Phys.120, 2160 (2004)] to handle the molecular rotation quantum mechanically. A novel technique referred to be an effective potential of quantum rotation is introduced to incorporate the rotational degree of freedom in the path integral molecular dynamics or hybrid Monte Carlo algorithm. For a permutation move to satisfy Bose statistics, we devise a multilevel Metropolis method combined with a configurational-bias technique for efficiently sampling the permutation and the associated atomic coordinates. Then, we have applied the PIHMC to a helium-4 cluster doped with a carbonyl sulfide molecule. The effects of the quantum rotation on the solvation structure and energetics were examined. Translational and rotational fluctuations of the dopant in the superfluid cluster were also analyzed.

The author thanks Research Center for Computational Science, National Institutes of Natural Sciences for the use of supercomputers. This work was supported by the Next Generation Super Computing Project, Nanoscience Program, MEXT, Japan.

I. INTRODUCTION

II. METHODOLOGY

A. The partition function

B. Path-variable sampling

C. Permutation sampling

III. COMPUTATIONAL DETAILS

IV. RESULTS

V. DISCUSSION

A. Molecular dynamics and hybrid Monte Carlo methods for rigid bodies

B. Multilevel Metropolis method with a configurational-bias technique

### Key Topics

- Monte Carlo methods
- 22.0
- Superfluids
- 22.0
- Doping
- 21.0
- Molecular fluctuations
- 20.0
- Helium-4
- 16.0

## Figures

Averaged total energy for the He–OCS dimer at calculated by the primitive and Takahashi-Imada (T-I) approximations as a function of . The OCS molecule is fixed at the origin. Open triangles are for the primitive approximation and open circles for the T-I approximation. The numerically exact result for the system is indicated by dashed line, which was reported in Ref. 55. Energies are in units of kelvin. The error bar is expressed at 95% confidence level, and is smaller than the size of the corresponding data symbol when it is not shown.

Averaged total energy for the He–OCS dimer at calculated by the primitive and Takahashi-Imada (T-I) approximations as a function of . The OCS molecule is fixed at the origin. Open triangles are for the primitive approximation and open circles for the T-I approximation. The numerically exact result for the system is indicated by dashed line, which was reported in Ref. 55. Energies are in units of kelvin. The error bar is expressed at 95% confidence level, and is smaller than the size of the corresponding data symbol when it is not shown.

The total helium density distribution around the OCS molecule in the cluster [top: for the quantum OCS case; bottom: for the fixed OCS case]. is the molecular axis and the radial distance from the axis. The OCS center of mass is located at the origin and the molecule is oriented as O–C–S from to . All distances are in units of angstrom.

The total helium density distribution around the OCS molecule in the cluster [top: for the quantum OCS case; bottom: for the fixed OCS case]. is the molecular axis and the radial distance from the axis. The OCS center of mass is located at the origin and the molecule is oriented as O–C–S from to . All distances are in units of angstrom.

(Color online) The radial density profiles of the helium atoms measured from the OCS center of mass are shown for the quantum OCS (upper panel) and the fixed OCS (lower panel). Total density profile (black solid line), (red solid line), for (black dashed lines), and (blue solid line) are presented. All distances are in units of angstrom.

(Color online) The radial density profiles of the helium atoms measured from the OCS center of mass are shown for the quantum OCS (upper panel) and the fixed OCS (lower panel). Total density profile (black solid line), (red solid line), for (black dashed lines), and (blue solid line) are presented. All distances are in units of angstrom.

(Color online) The mean square correlation function of the OCS center of mass in the imaginary time, for the Bose cluster (blue solid line), and the Boltzmann cluster (red solid line). The function for the free OCS molecule (black solid line) is also presented. The error bar of is expressed at 95% confidence level.

(Color online) The mean square correlation function of the OCS center of mass in the imaginary time, for the Bose cluster (blue solid line), and the Boltzmann cluster (red solid line). The function for the free OCS molecule (black solid line) is also presented. The error bar of is expressed at 95% confidence level.

(Color online) The orientational correlation function of the OCS molecule for the Bose cluster (blue solid line) and the Boltzmann cluster (red solid line) as a function of the imaginary time . The size of the cluster is 64 for both cases. The free-rotor correlation function with a gas-phase experimental (black solid line) and that with a estimated by the value of the Bose cluster (blue dashed line) are also shown. The error bar about is expressed at 95% confidence level.

(Color online) The orientational correlation function of the OCS molecule for the Bose cluster (blue solid line) and the Boltzmann cluster (red solid line) as a function of the imaginary time . The size of the cluster is 64 for both cases. The free-rotor correlation function with a gas-phase experimental (black solid line) and that with a estimated by the value of the Bose cluster (blue dashed line) are also shown. The error bar about is expressed at 95% confidence level.

## Tables

Averaged total energy for the fully quantized He–OCS dimer at calculated by the primitive and Takahashi-Imada (T-I) approximations with . The exact result was reported in Ref. 55 by the basis set calculations. Energies are in units of kelvin. Statistical error in the last digit at 95% confidence level is indicated in parentheses.

Averaged total energy for the fully quantized He–OCS dimer at calculated by the primitive and Takahashi-Imada (T-I) approximations with . The exact result was reported in Ref. 55 by the basis set calculations. Energies are in units of kelvin. Statistical error in the last digit at 95% confidence level is indicated in parentheses.

The translational kinetic energy , the rotaional kinetic energy , the He–OCS, and He–He interaction energies ( and ), and the total energy for the cluster obeying the Bose-Einstein statistics. The translational kinetic energy of the OCS molecule is also shown. The energies are presented for the quantum and fixed OCS cases and are in units of kelvin. Statistical error in the last digit at 95% confidence level is indicated in parentheses.

The translational kinetic energy , the rotaional kinetic energy , the He–OCS, and He–He interaction energies ( and ), and the total energy for the cluster obeying the Bose-Einstein statistics. The translational kinetic energy of the OCS molecule is also shown. The energies are presented for the quantum and fixed OCS cases and are in units of kelvin. Statistical error in the last digit at 95% confidence level is indicated in parentheses.

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