Abstract:
Our objective is to develop a diffusion Monte Carlo (DMC) algorithm to estimate
the exact expectation values, ($o|^|^o), of multiplicative operators, such as polarizabilities
and high-order hyperpolarizabilities, for isolated atoms and molecules.
The existing forward-walking pure diffusion Monte Carlo (FW-PDMC) algorithm
which attempts this has a serious bias. On the other hand, the DMC
algorithm with minimal stochastic reconfiguration provides unbiased estimates of
the energies, but the expectation values ($o|^|^) are contaminated by ^, an user
specified, approximate wave function, when A does not commute with the Hamiltonian.
We modified the latter algorithm to obtain the exact expectation values
for these operators, while at the same time eliminating the bias.
To compare the efficiency of FW-PDMC and the modified DMC algorithms
we calculated simple properties of the H atom, such as various functions of coordinates
and polarizabilities. Using three non-exact wave functions, one of moderate
quality and the others very crude, in each case the results are within statistical
error of the exact values.
