Transcorrelated self‐consistent calculation for electronic systems with variational Monte Carlo method

Abstract

AbstractWe propose a new approach to calculate the electronic states for strongly correlated systems. Our calculation is based on the transcorrelated method, in which the eigen value problem of the original Hamiltonian is transformed to that of an effective Hamiltonian. The effective Hamiltonian, the so‐called “transcorrelated Hamiltonian” is obtained through a similarity transformation of the original Hamiltonian with aid to a Jastrow factor that represents the correlation effects. A single Slater determinant is assumed as a trial function and both the Slater determinant and the two‐body Jastrow factor are optimized self‐consistently by minimizing the variance of the transcorrelated Hamiltonian. The so‐called “variational Monte Carlo” (VMC) method is adopted to overcome the time‐consuming calculation of the variance. We found that this method gives remarkably good results for heliumlike two‐electron systems (H−, He, Li+, Be2+), and we reproduced about 90% of their respective correlation energies, despite using the simplest Jastrow factor. We also display results for three‐ and four‐electron systems (Li, Be). © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003