Abstract: Adifferential approach for self-optimizing diffusion quantum Monte Carlo calculation was proposed in this paper, which is a new algorithm combining with three techniques such as optimizing, diffusion and correlation sampling. This method can directly be used to calculate the energy differential between two systems in the diffusion process, make the statistical error of calculation reduce to the order of 10^-5hartree, and recover about more than 80% of the correlation energy. We employed this approach to set up a potential energy surface of a molecule, used a "rigid move" model, and utilized Jacobi transformation to make energy calculation for two configurations of a molecule have a good positive correlation. So, an accurate energy differential could be obtained, and the potential energy surface with a good quality can be depicted. In the calculation, a technique called "post-equilibrium remaining sample" was set up firstly, which can save about 50% of computation expense. This novel algorithm can also be applied to studying other related fields such as molecular spectroscopy and the energy variation in chemical reactions.

Key words: Differential approach, Quantum Monte Carlo method, Correlation sampling, Potential energy surface