An improved algorithm of fixed-node quantum Monte Carlo method with self-optimization process

In this paper we propose an improved fixed-node quantum Monte Carlo (FNQMC) algorithm with self-optimization and self-improvement capability. Different from the previous FNQMC method that we put forward [Huang and Liu, J. Mol. Struct. THEOCHEM 636 (2003) 125], the importance function is simultaneously optimized in the diffusion process. An improved steepest descent technique is also used to optimize the importance function, in which the step size can automatically be adjusted. The process is quasi-Newton-like and converges super linearly. In addition, we utilize a novel trial function, which satisfies the correct electron-electron and electron-nucleus cusp conditions. To demonstrate its effectiveness we applied the present approach to calculate the total energy of the 1 1A1 state of CH2, 1Ag state of C8 and the ground-state of H2, LiH, Li2, and H2O molecules, respectively, and significant improvement of the correlation energy percentage recovered for these systems has been observed.