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