Path integral methods for rotating molecules in superfluids

Abstract

We present a path integral Monte Carlo (PIMC) methodology for quantum simulation of molecular rotations in superfluid environments such as helium and para-hydrogen that combines the sampling of rotational degrees of freedom for a molecular impurity with multilevel Metropolis sampling of Bose permutation exchanges for the solvating species. We show how the present methodology can be applied to the evaluation of imaginary time rotational correlation functions of the molecular impurity, from which the effective rotational constants can be extracted. The combined rotation/permutation sampling approach allows for the first time explicit assessment of the effect of Bose permutations on molecular rotation dynamics, and the converse, i.e., the effect of molecular rotations on permutation exchanges and local superfluidity. We present detailed studies showing that the effect of Bose permutations in the solvating environment is more significant for the dynamics of heavy than light molecules in helium, and that Bose permutation exchanges are slightly enhanced locally by molecular rotation. Finally, the examples studied here reveal a size dependence of rotational excitations for molecules possessing a strongly anisotropic interaction with helium in 4HeN clusters between N approximately 20 and N approximately 10(3).

Rotational fluctuation of molecules in quantum clusters. II. Molecular rotation and superfluidity in OCS-doped helium-4 clusters

“…For N ജ 20, the C͑␤ /2͒ has a plateau in the size dependence, which shows clear contrast with the Boltzmann clusters where C͑␤ /2͒ still increases over N = 20. Recently, Zillich et al 19 have performed path integral Monte Carlo calculations for OCS͑ 4 He͒ N clusters for N = 8, 12, and 64. Although size dependence on C͑␤ /2͒ by their calculations shows similar trend with our calculations for the selected cluster sizes, the rotational fluctuation of the OCS molecule for N = 64 by their calculation is much larger than that by our calculation.…”

“…3,4,[11][12][13][14][15][16][17][18][19][20] Among them, a carbonyl sulfide ͑OCS͒ molecule is one of the most widely studied dopants in the helium nanodroplets. Recently, Tang et al 7 have determined the vibrational and rotational spectra of the OCS͑He͒ N clusters in a small-to-medium size regime, N =2-8.…”

“…20 Then, the PIHMC was applied to a OCS-doped helium-4 cluster OCS͑ 4 He͒ 64 to demonstrate the impact of the Bose statistics on the rotational correlation in the solvated molecule. Independently, Zillich et al 19 have developed a PIMC method to treat rotating molecules in superfluids and applied the method to the OCS-doped helium clusters. In this paper, the size dependence on the rotational fluctuation of the OCS molecule is systematically studied by the PIHMC method and connected with the superfluidity of the doped clusters in the small-to-large size regime ͑N =2-64͒.…”

Rotational fluctuation of molecules in quantum clusters. I. Path integral hybrid Monte Carlo algorithm

“…[20][21][22][23][24] For finite temperature calculations corresponding to the experimental condition, we developed a path integral hybrid Monte Carlo ͑PIHMC͒ method to handle the molecular rotation quantum mechanically, and reported preliminary results on the OCS molecule in a helium-4 cluster. 25 Independently, Zillich et al 26 and Blinov and Roy 27 extended the PIMC technique to rotating molecules in superfluids. In this paper, we present the full account on our PI-HMC method for rotors in superfluids.…”

A stereographic projection path integral study of the coupling between the orientation and the bending degrees of freedom of water

“…[30][31][32][33][34][35][36][37][38] There remain several numerical difficulties for the development and implementation of MCPI methods in curved spaces such as the imposition of spacial periodic boundary conditions on the time evolution propagator and the presence of multiply connected spaces. These difficulties have forced investigators to use relatively expensive alternatives to random walks like the vector-space MCPI method [31][32][33][34][35][36] or the use of fixed axes approximations. 30 It is difficult to define the path integral measure when using open sets and periodic boundaries and special methods have to be developed to evaluate the path integral even in the most trivial cases.…”