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].

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