New developments to the quantum Monte Carlo approach are presented that
improve the scaling of the time required to calculate the total energy of
a configuration of electronic coordinates from N^3 to nearly linear[1].
The first factor of N is achieved by applying a unitary transform to the
set of single particle orbitals used to construct the Slater determinant,
creating a set of maximally localized Wannier orbitals. These localized
functions are then truncated beyond a given cutoff radius to introduce
sparsity into the Slater determinant. The second factor of N is achieved
by evaluating the maximally localized Wannier orbitals on a cubic spline
grid, which removes the size dependence of the basis set (e.g. plane
waves, Gaussians) typically used to expand the orbitals. Application of
this method to the calculation of the binding energy of the carbon
fullerenes, C60 C120 and C180 will be discussed .
An extension of this approach to deal with excited states of systems will
also be presented in the context of the calculation of the excitonic gap
of a variety of systems. We demonstrate this powerful application by
calculating the excitonic gap of silicon nanoclusters with diameters
ranging from 0 to 1.5 nm, containing 5 to 163 atoms. Brief comparisons
with alternative methods for calculating the excitonic gap of these
systems will also be presented.
This work was performed under the auspices of the U.S. Dept. of Energy at
the University of California/LLNL under contract no. W-7405-Eng-48.
[1] A.J. Williamson, R.Q. Hood and J.C. Grossman, Phys. Rev. Lett. 87
246406 (2001)
Copyright. All Rights Reserved.