The Path-Integral Monte Carlo Method for Rotational Degrees of Freedom
Very recent progress in the path-integral simulation of quantum mechanical rotational degrees of freedom (RDOF) is reviewed. Unlike translational degrees of freedom, where the free particle kernel can be obtained by a Gaussian integral, the kernel for RDOF is not analytically accessible. However, it can be obtained numerically to high precision on a fine grid so that all systematic errors can be kept controllably small. The formulae to generate the kernel for RDOF are given explicitly for one, two, and three-dimensional rotation. In particular, we discuss the consequences of confining the rotational state of a rigid body to one representation for the sign problem and the correlation time. A linear rotor in a Devonshire potential and solid methane are considered as examples.
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