Hongxin Huang

A novel method for optimizing quantum Monte Carlo wave functions

We propose an algorithm for optimizing quantum Monte Carlowave functions. An improved steepest‐descent technique is used, with step size automatically adjustable to obtain a procedure that converges superlinearly. We also propose a novel trial function, which has both correct electron–electron cusp conditions and correct electron–nucleus cusp conditions. To test the optimization procedure and the optimized trial function, the ground states for CH4 and H2O molecules were investigated using variational Monte Carlo (VMC) and fixed‐node quantum Monte Carlo (FNQMC) calculations. For CH4 and H2O, the VMC recovered 73.3% and 57.9% of the correlation energy, respectively, and the FNQMC recovered 99.3% and 92.8%, respectively. The optimization procedure is three to five times faster than conventional usual steepest‐descent procedures. The trial functions optimized are more accurate than prior trial functions of similar complexity.

A NOVEL QUANTUM MONTE CARLO STRATEGY : SURPLUS FUNCTION APPROACH

A concept of surplus function for the Schrodinger equation is put forward. A novel quantum Monte Carlo approach, namely, the surplus function method, is suggested with use of a novel trial function of significant physical meaning which is based on the proposed surplus function. The trial function is an iteration type, as given in the text. It is theoretically proved that the energy expectation value obtained from the proposed trial function decreases step by step in iterations. In addition, computation formulas and concrete procedures for energy expectation value are presented. Calculations for H2, LiH, Li2, and H2O molecules indicate that the energy expectation values after only 4–5 iterations achieve over 90% of the correlation energy, indicating that the convergence rates are rapid. The trial function used in the present paper requires no parameter optimization and is of the highest accuracy.

Surplus function variational quantum Monte Carlo approach: Excited state processing

Surplus function variational quantum Monte Carlo approach used for the excited state of electrons has been proposed. If the initial wave functions of both the excited state and ground state belong to the irreducible representation with different symmetries, the surplus function variational quantum Monte Carlo approach of the excited state is identical to that of the ground state, and if they belong to the irreducible representation with an identical symmetry, the surplus function variational quantum Monte Carlo approach of the ground state can also be applied to the excited state only by orthogonal revision for the initial wave function of the excited state. The detailed calculations formulas on the surplus function variational quantum Monte Carlo approach of the excited state have been deduced. A complete set of the surplus function variational quantum Monte Carlo approach for both the ground state and excited state has been established. The energy values of X 3B1, 1 1A1, and 2 1A1 states of CH2 have bee...

Response to “Comment on ‘The surplus function approach’ ” [J. Chem. Phys. 112, 455 (2000)]

The existence of integral (Hi¯) in the surplus function variational quantum Monte Carlo approach is discussed and a method is proposed for avoiding the infinity in the calculation of Hi¯. A rigid model of nucleus was adopted to avoid the infinity appearance of r−i. Discussion of a new solution for Schrodinger’s equation of hydrogen atom, which may make the calculation of the Hi¯ value more accurate is also presented.