Quantum Monte Carlo calculated potential energy curve for the helium dimer

Diffusion quantum Monte Carlo method on diradicals using single- and multi-determinant-Jastrow trial wavefunctions and different orbitals

In this work, the diffusion quantum Monte Carlo (DMC) method is employed to calculate the energies of singlet and triplet states for a series of organic diradicals and diatomic diradicals with π2 configuration. Single-determinant-Jastrow (SDJ) trial wavefunctions for triplet states, two-determinant-Jastrow (2DJ) trial wavefunctions for the singlet states, and multi-determinant-Jastrow (MDJ) trial wavefunctions are employed in DMC calculations using restricted open-shell B3LYP (ROB3LYP) orbitals, complete-active-space self-consistent field (CASSCF) orbitals, state-average CASSCF orbitals, or frozen-CASSCF orbitals. Our results show that DMC energies using either SDJ/2DJ or MDJ with ROB3LYP orbitals are close to or lower than those with the other orbitals for organic diradicals, while they are not very sensitive to the employed orbitals for diatomic diradicals. Furthermore, using MDJ can reduce DMC energies to some extent for most of the investigated organic diradicals and some diatomic diradicals. The importance of MDJ on DMC energies can be estimated based on the percentage of main determinants in the CASCI wavefunction. On the other hand, singlet–triplet gaps can be calculated reasonably with DMC using MDJ with a mean absolute error of less than 2 kcal/mol with all these orbitals. CASCI wavefunctions using density functional theory orbitals are preferred in constructing MDJ trial wavefunctions in practical DMC calculations since it is easier to obtain such wavefunctions than CASSCF methods.

Singlet-triplet gaps in diradicals obtained with diffusion quantum Monte Carlo using a Slater-Jastrow trial wavefunction with a minimum number of determinants

Diradicals are essential species in a wide range of chemical processes, whereas the computational study of their electronic structure often remains a challenge due to near-degeneracy of the frontier molecular orbitals. The fixed-node diffusion quantum Monte Carlo (FN-DMC) method is employed to calculate adiabatic energy gaps of some typical diradicals with the Slater-Jastrow trial wavefunction. The antisymmetrized part of the trial wavefunction is taken to be a linear combination of a minimum number of determinants using RB3LYP orbitals from the closed-shell singlet state or ROB3LYP orbitals from the triplet state. Our results show that using the two-determinant-Jastrow trial wavefunction is necessary to achieve reliable energy differences between closed-shell singlet states. The energy of the triplet state with MS = 1 is calculated to be lower than that with MS = 0 with FN-DMC even using trial wavefunctions with spin-pure states as their antisymmetrized parts and this difference is reduced with better orbitals. This indicates that the fixed-node error is smaller for the triplet state with MS = 1. Adiabatic energy gaps obtained from the present FN-DMC calculations are in reasonable agreement with available experimental values. Compared with results of the high level EOM-SF-CC method, energy gaps of FN-DMC with RB3LYP orbitals are slightly better than those using ROB3LYP orbitals and results of EOM-SF-CCSD. The present FN-DMC calculations using the simplest ansatz for the trial wavefunction can achieve reasonable results for these diradicals and they can readily be applied to large diradicals.