A new algorithm for the fixed-node quantum Monte Carlo method

A novel algorithm is proposed for the fixed-node quantum Monte Carlo (FNQMC) method. In contrast to previous procedures, its “guiding function ” is not optimized prior to diffusion quantum Monte Carlo (DMC) computation but synchronistically in the diffusion process. The new algorithm can not only save CPU time, but also make both of the optimization and diffusion carried out according to the same sampling fashion, reaching the goal to improve each other. This new optimizing procedure converges super-linearly, and thus can accelerate the particle diffusion. During the diffusion process, the node of the “guiding function” changes incessantly, which is conducible to reducing the “fixed-node error”. The new algorithm has been used to calculate the total energies of states X³B₁ and a¹A₁ of CH₂ as well as Π-X²B₁ and σ^-1a₁ of NH₂. The singlet-triplet energy splitting (ΔE _S-T) in CH₂ and σ-π energy splitting ΔE σ-π in NH₂ obtained with this present method are (45.542 ± 1.840) and ( 141.644 ± 1.589) kJ/mol, respectively. The calculated results show that the novel algorthm is much superior to the conventional fixed-node quantum Monte Carlo in accuracy, statistical error and computational cost.