Predictive Capability for Strongly Correlated Systems

Abstract

Diffusion Monte Carlo methods can give highly accurate results for correlated systems, provided that well optimized trial wave functions with accurate nodal surfaces are employed. The Cornell team developed powerful methods for optimizing all the parameters within a multi-determinant Slater-Jastrow form of the wave function. These include the Jastrow parameters within a flexible electron-electron-nucleus form of the Jastrow function, the parameters multiplying the configuration state functions, the orbital parameters and the basis exponents. The method optimizes a linear combination of the energy and the variance of the local energy. The optimal parameters are found iteratively by diagonalizing the Hamiltonian matrix in the space spanned by the wave function and its first-order derivatives, making use of a strong zero-variance principle. It is highly robust, has become the method of choice for correlated wave function optimization and has been adopted by other QMC groups. This optimization method was used on the first-row atoms and homonuclear diatomic molecules, demonstrating that molecular well depths can be obtained with near chemical accuracy quite systematically at the diffusion Monte Carlo level for these systems. In addition the complete ground-state potential energy curve of the C 2 molecule up to the dissociation limit was obtained, and, size consistency and broken spin-symmetry issues in quantum Monte Carlo calculations were studied. The method was used with a eight-electrons-in-eight-orbitals complete active space CAS(8,8) wave function to study the relative energies of the monocyclic and bicyclic forms of m-benzyne. The DMC calculations show that the monocyclic structure is lower in energy than the bicyclic structure by 1.92 kcal/ mole, which is in excellent agreement with the best coupled cluster results (CCSD(T)) and in disagreement with the CCSD results. QMC methods have for the most part been used only for ground states of a given symmetry. We developed a method for calculating low-lying excited states as well and tested it on the ground and lowest three adiabatic excited states of methylene with progressively larger JastrowSlater multideterminant complete active space CAS wave functions. The highest of these states has the same symmetry, 1 A 1 , as the first excited state. The DMC excitation energies obtained using any of the CAS wave functions are in excellent agreement with experiment. In contrast, single-determinant wave functions do not yield accurate DMC energies, indicating that it is important to include in the wave function Slater determinants that describe static strong correlation.