Interesting notes

While searching for Monte Carlo information on the web, I ran across Jonathon Goodman's Monte-Carlo Course Materials. One interesting part was Alan Sokal's introductory notes near the bottom (see also this CiteSeer link). I liked these notes because they covered a practical method for computing the autocorrelation time.

Optimization

Recently there were two papers in the Journal of Chemical Physics related to QMC optimization. The first, Geometry optimization in quantum Monte Carlo with solution mapping: Application to formaldehyde, is concerned with optimization of nuclear positions using only energy information, and not gradient (force) information, since it is noisier and harder to obtain. They use statistical experiment design techniques to pick coordinates at which to perform the energy computations, and fit that data to a quadratic form. The the geometry was then optimized using that fitted form.

The second paper is concerned with optimizing the one-body part of the wavefunction: Transcorrelated method for electronic systems coupled with variational Monte Carlo calculation. The authors use a transcorrelated Hamiltonian (some of the correlation has been moved into the Hamilitonian), and compute the SCF solution for the one-body orbitals. They use regular VMC to optimize the Jastrow factors. Note that the two calcuations are coupled, and to reach a solution the procedure is to alternately optimize the one-body and Jastrow factors.