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

Abstract

In this paper, we present a path integral hybrid Monte Carlo ͑PIHMC͒ 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 ͑2004͔͒ 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.

Path integral Monte Carlo study of CO2 solvation in He4 clusters

“…In particular, the rotational degrees of freedom of the dopant molecule have recently been incorporated quantum mechanically into the PIMC framework. 42,43,45,47,48 One of the most intriguing experimental observations on doped 4 He clusters is the size dependence of the effective rotational constant of a linear dopant molecule, which typically has a turnaround near N =5-9. [11][12][13][14]17,19 This turnaround has been interpreted as the onset of microscopic superfluidity, 11 due apparently to the exchange effect in the Bose-Einstein statistics.…”

“…23 To this end, quantum Monte Carlo [24][25][26][27][28][29][30][31][32][33] ͑QMC͒ and path integral Monte Carlo ͑PIMC͒ methods 30,[34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52] have been developed and successfully applied to study doped helium/hydrogen clusters. These theoretical studies provided valuable insights into the structure and dynamics of the quantum solvation environment of the dopant molecule.…”

Quantum rotation of Rb2 (3 Σ u + ) attached to HeN droplets: a path-integral Monte Carlo study

“…In order to fulfill this assumption we have restricted rotation sampling to orientation between contiguous beads to angles confined in the range of 0 to the first nodal point of the orientational propagator (See Fig.1). To clarify the imposed constraint, we can define a potential function u t,t+1 rot using (7): u t,t+1 rot = −β −1 log(ρ t,t+1 ), referred by several authors as an effective [7] or auxiliary [50] potential of quantum rotation. Therefore, the role of the orientational propagator may be viewed as a potential that forces beads t and t+1 to adopt similar orientations (minimum of u t,t+1 function corresponds to θ → 0, Fig.1).…”

“…Motivated by their unique properties as an ideal matrix to perform spectroscopic measurements at low temperature, helium nanodroplets have been the subject of numerous theoretical works in the last decades. In particular path integral Monte Carlo (PIMC) simulations have investigated solvated rotating impurities such as N 2 O [1][2][3][4], HCCH [5], HCCCN [6], OCS [5,7,8] or CO 2 [2,9,10] embedded in He N clusters in order to explore superfluidity effects as a function of the cluster size N at T <1 K. Within the large diversity of possible impurities, alkali dimers have also received a great deal of interest. A wide variety of methods ranging between diffusion Monte Carlo (DMC) [11][12][13][14][15], quantum dynamical calculations [16][17][18][19], variational [13], PIMC treatments [20][21][22] or density functional formalism [23] have been applied to investigate structural and dynamical properties of these He N -X systems.…”

Modelling Water: A Lifetime Enigma

“…This isomorphism provides a way to sample the quantum nuclear configuration through modifications of the classical MD technique. Other quantum simulation methods would include Path Integral Monte Carlo (PIMC), [110,111] Path Integral Hybrid Monte Carlo (PIHMC), [107,112,113] Centroid Molecular Dynamics (CMD) [114][115][116][117][118] and Ring Polymer Molecular Dynamics (RPMD). [119,120] While PIMD simulations have been performed for the HBB2-pol and MB-pol ab initio based models at ambient conditions, [84,85] extreme conditions (low temperatures, critical point) have not been explored to elucidate the anomalous behaviour of water.…”