Abstract
A Monte Carlo path integral method to study the coupling between the rotation and bending degrees of freedom for water is developed. It is demonstrated that soft internal degrees of freedom that are not stretching in nature can be mapped with stereographic projection coordinates. For water, the bending coordinate is orthogonal to the stereographic projection coordinates used to map its orientation. Methods are developed to compute the classical and quantum Jacobian terms so that the proper infinitely stiff spring constant limit is recovered in the classical limit, and so that the nonconstant nature of the Riemann Cartan curvature scalar is properly accounted in the quantum simulations. The theory is used to investigate the effects of the geometric coupling between the bending and the rotating degrees of freedom for the water monomer in an external field in the 250 to 500 K range. We detect no evidence of geometric coupling between the bending degree of freedom and the orientations.
Highlights
Despite a number of recent advances, the majority of path integral simulations have focused on atomic systems with strict adherence to Cartesian coordinates
In a recent article we have demonstrated that MCPI simulations of rigid molecular condensed matter, when all intramolecular DF are constrained, yield massive efficiency gains.[24]
The work reported in this article contains the first fundamental steps necessary to develop efficient algorithms for walks and estimators of important thermodynamic properties obtained from MCPI simulations of a cluster of molecules in which some selected internal DF are constrained by infinite spring constant, while other, softer, internal modes are included in the configuration space
Summary
The path integral[1] approach to statistical mechanics has become a tool of choice for the investigation of quantum effects in clusters and other types of condensed matter at finite temperatures.[2–23] Despite a number of recent advances, the majority of path integral simulations have focused on atomic systems with strict adherence to Cartesian coordinates. This limitation is technical in nature, as the simple remapping of a Euclidean space by curvilinear coordinates greatly complicates both the formal and the numerical aspect of Monte Carlo path integralMCPImethods. This pattern is observed with both linear as well as cubically convergent solutions
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