Monte Carlo integration method

Miller, T. F., Ill Clary, D. C., Torsional path integral Monte Carlo method for calculating the absolute quantum free energy of large molecules, J. Chem. Phys. 2003,119, 68-76... 

IV. Fourier Path Integral Monte Carlo Methods... 

IV. FOURIER PATH INTEGRAL MONTE CARLO METHODS... 

By increasing pressure and/or decreasing temperature, ionic quantum effects can become relevant. Those effects are important for hydrogen at high pressure [7, 48]. Static properties of quantum systems at finite temperature can be obtained with the Path Integral Monte Carlo method (PIMC) [19]. We need to consider the ionic thermal density matrix rather than the classical Boltzmann distribution ... 

D. M. Ceperley (1996) Path integral Monte Carlo methods for fermions. In Monte Carlo and Molecular Dynamics of Condensed Matter Systems, ed. by K. Binder and G. Ciccotti, Editrice Compositori, Bologna, Italy... 

Garza et al. [52] studied the problem by using the Khon-Sham equations, where their results are also close to the most accurate figures published hitherto. March and Tosi [53] used the path-integral Monte Carlo Method. 

The quantum mechanical generalization of the anisotropic-planar-rotor Hamiltonian (2.5) is devised and investigated by quasiharmonic, quasiclas-sical, and path-integral Monte Carlo methods in Refs. 213 and 218. Here, thermal fluctuations compete with quantum fluctuations which adds a qualitatively new dimension to the scarce one-dimensional phase diagram of the classical anisotropic-planar-rotor model (2.5). The phase behavior of this model is much richer, and the phenomenon of reentrant orientational quantum melting is observed in a certain regime of the phase diagram. 

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