Stuart M. Rothstein: Research

QUANTUM MONTE CARLO METHOD

The Schroedinger equation has locally singular potentials which have to be canceled by the kinetic energy (electron-nuclear and electron-electron cusps). Also, by virtue of the repulsion of like charges, each electron influences the locations of all the others (electron correlation). These effects must be reflected in the wave function, and it simply isn't efficient to do this by taking combinations of Slater determinants with a finite set of one-electron basis functions, as in the traditional approaches. Furthermore, the traditional methods make huge computational demands for systems containing a large number of electrons, necessitating approximations or practical limits on the scale of the calculations. 

Facilitated by the speed of modern computers, quantum Monte Carlo methods have been developed to complement the traditional methods. One statistically samples from a pre-specified, explicitly correlated wave function (depends explicitly upon the inter-electronic distances) and thereby treats the various electron correlation effects explicitly. Other features of the exact wave function, such as the electron-electron and electron-nuclear cusps are also treated in a direct manner. 

Our current Monte Carlo research is focused on the accurate estimation of physical properties other than the energy.

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