Stuart M. Rothstein: Research

QUANTUM MONTE CARLO DETERMINATION OF PROPERTIES OTHER THAN THE ENERGY

Traditionally there is a strong interest in energy-related physical properties, such as the force constant and other spectroscopic constants. For example, we showed how to estimated these using quantum Monte Carlo methods for a transition metal containing molecule: CuH [Ref. 49] . 

It is a challenge to estimate physical properties other than the energy, because the electron distribution obtained in quantum Monte Carlo is not sufficiently accurate for these properties. In principle, the exact electron distribution is required, the square of the exact wavefunction. 

Although we do not have an analytic form for the exact wavefunction, we know how to sample it by Monte Carlo methods [Ref 43,45]. Recently we developed a quantum Monte Carlo algorithm, practical for properties represented by non-differential operators, where indeed we can sample from the "exact" electron distribution [Ref. 53].

Our goal now is to derive within the framework of quantum Monte Carlo a systemized methodology to estimate the non-trivial electrical properties of atoms and molecules, such as high order polarizabilities and hyperpolarizabilities. We are building on previous work in our laboratory {Ref. 44], promising higher accuracy for these properties. [Ref 45, 53]. Polarizabilities are potentially fundamental in determining the molecular geometry of products of chemical reactions.

Thanks to the speed of high performance computers at the University of Alberta made available through MACI, we have been able develop methodologies to estimate polarizabilities to fourth order in the external field perturbation. Details appropriate for spherically symmetric systems, such as atoms, will be published [Ref. 60].

Referenced citations appear in link to Rothstein's full set of publications.

Return to Rothstein's Home Page