Simple and efficient approach to the optimization of correlated wave functions

We present a simple and efficient method to optimize within energy minimization the determinantal component of the many-body wave functions commonly used in quantum Monte Carlo calculations. The approach obtains the optimal wave function as an approximate perturbative solution of an effective Hamiltonian iteratively constructed via Monte Carlo sampling. The effectiveness of the method, as well as its ability to substantially improve the accuracy of quantum Monte Carlo calculations, are demonstrated by optimizing a large number of parameters for the ground state of acetone and the difficult case of the $1{}^{1}B_u$ state of hexatriene.

Figure 1

Convergence of the VMC energy of acetone with the perturbative EFP, the EFP, and the SR method to optimize the 473 orbital parameters. The starting determinantal component is from an unconverged HF calculation. The runs are of $16\times {10}^5$steps. The statistical errors are smaller than the symbol size.