Improved trial wave functions in quantum Monte Carlo: Application to acetylene and its dissociation fragments

Toward Compact Selected Configuration Interaction Wave Functions with Quantum Monte Carlo─A Case Study of C2

The ¹Σ_g⁺ ground state of C₂ is investigated using truncated CIPSI-Jastrow CSF wave functions with Hartree-Fock orbitals within the framework of variational and diffusion quantum Monte Carlo. The truncation is performed based on the absolute value of the CI coefficients, and the Jastrow, molecular orbitals, and CI parameters are either partially or fully reoptimized with respect to the variational energy. Excellent absolute as well as bond dissociation energies are obtained at DMC level with very compact, fully optimized wave functions. By studying the expansions in more detail, we observe a change in the CI picture when reoptimizing the antisymmetric part of the CIPSI-Jastrow wave functions. Furthermore, we demonstrate that a decrease in the VMC energy as well as an improvement of the nodal surface quality can be achieved─with the same expansion size─if the CSFs are selected in the presence of a Jastrow correlation function, laying the foundation for a Jastrow selected CI scheme with quantum Monte Carlo.

Quantum Monte Carlo ground state energies for the atoms Li through Ar

All-electron quantum Monte Carlo energies are reported for the ground state of the atoms Li to Ar. The present work is mainly focused on the atoms Na to Ar as well as in those that have a stronger multiconfiguration nature, i.e., Be, B, and C and Mg, Al, and Si. Explicitly correlated wave functions with a single configuration model function times a Jastrow factor are employed for all of the atoms studied. The accuracy obtained for the atoms Na to Ar is similar to that reached for the atoms Li to Ne. In addition, a restricted multiconfiguration expansion has been employed for the atoms Be, B, and C and Mg, Al, and Si obtaining accurate results. Near degeneracy and the effect of other configurations are systematically analyzed for these systems, at both variational and diffusion Monte Carlo levels.

Inhomogeneous backflow transformations in quantum Monte Carlo calculations

An inhomogeneous backflow transformation for many-particle wave functions is presented and applied to electrons in atoms, molecules, and solids. We report variational and diffusion quantum Monte Carlo (VMC and DMC) energies for various systems and study the computational cost of using backflow wave functions. We find that inhomogeneous backflow transformations can provide a substantial increase in the amount of correlation energy retrieved within VMC and DMC calculations. The backflow transformations significantly improve the wave functions and their nodal surfaces.

One- and two-body densities of carbon isoelectronic series in their low-lying multiplet states from explicitly correlated wave functions

The (3)P ground state and both the (1)D and (1)S excited states arising from the low-lying 1s(2)2s(2)2p(2) configuration of the carbon isoelectronic series are studied starting from explicitly correlated multiconfigurational wave functions. One- and two-body densities in position space have been calculated and different one- and two-body expectation values have been obtained. The effects of electronic correlations have been systematically studied. All the calculations have been done by means of variational Monte Carlo.

An investigation of nodal structures and the construction of trial wave functions

The factors influencing the quality of the nodal surfaces, namely, the atomic basis set, the single-particle orbitals, and the configurations included in the wave-function expansion, are examined for a few atomic and molecular systems. The following empirical rules are found: the atomic basis set must be fairly large, complete active space and natural orbitals are usually better than Hartree-Fock orbitals, multiconfiguration expansions perform better than single-determinant wave functions, but only few configurations are effective and their choice is suggested by symmetry considerations, while too long determinantal expansions spoil the nodal surfaces. These rules allow us to reduce the nodal error and to compute the best fixed node-diffusion Monte Carlo energies for a series of dimers of first-row atoms.

Properties of selected diatomics using variational Monte Carlo methods

Using variational Monte Carlo and highly accurate trial wave functions optimized by Filippi and Umrigar, we calculate a number of molecular properties for the ground state of Li2, Be2, B2, C2, N2, O2, and F2. This is the first time that many of these properties have been computed.