Abstract:
The self-consistent phonons (SCP) method is a practical approach for computing structural and dynamical properties of a general quantum or classical many-body system while incorporating anharmonic effects. In SCP one finds an effective temperature-dependent harmonic Hamiltonian that provides the “best fit” for the physical Hamiltonian, the “best fit” being defined as the one that optimizes the Helmholtz free energy at a fixed temperature. The numerical bottleneck of the method is the evaluation of Gaussian averages of the potential energy and its derivatives. Several algorithmic ideas/tricks are introduced to reduce the cost of such integration by orders of magnitude, e.g., relative to that of the previous implementation of the SCP approach by Calvo et al. [J. Chem. Phys. 133, 074303 (2010)]. One such algorithmic improvement is the replacement of standard Monte Carlo integration by quasi-Monte Carlo integration utilizing low-discrepancy sequences.
SCP has been used to study the equilibrium properties and the structural transitions in small and large Lennard-Jones clusters. The method was also applied to computations of vibrational spectra of water clusters.


References:
[1] I. Georgescu and V. A. Mandelshtam, Self-Consistent Phonons revisited I. The role of
thermal versus quantum fluctuations on structural transitions in large Lennard-Jones
clusters, J. Chem. Phys. 137, 144106 (2012)
[2] S. E. Brown, I. Georgscu and V. A. Mandelshtam, Self-consistent phonons revisited.
II. A general and efficient method for computing free energies and vibrational spectra
of molecules and clusters J. Chem. Phys. 138, 044317 (2013)
[3] S. E. Brown and V. A. Mandelshtam, Self-consistent phonons: An accurate and practical method to account for anharmonic effects in equilibrium properties of general classical or
quantum many-body systems, Chemical Physics (2016).