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

Molecules in Environments: Toward Systematic Quantum Embedding of Electrons and Drude Oscillators

We develop a quantum embedding method that enables accurate and efficient treatment of interactions between molecules and an environment, while explicitly including many-body correlations. The molecule is composed of classical nuclei and quantum electrons, whereas the environment is modeled via charged quantum harmonic oscillators. We construct a general Hamiltonian and introduce a variational Ansatz for the correlated ground state of the fully interacting molecule-environment system. This wave function is optimized via the variational Monte Carlo method and the ground state energy is subsequently estimated through the diffusion Monte Carlo method. The proposed scheme allows an explicit many-body treatment of electrostatic, polarization, and dispersion interactions between the molecule and the environment. We study solvation energies and excitation energies of benzene derivatives, obtaining excellent agreement with explicit ab initio calculations and experiments.

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.

Diffusion Monte Carlo method on small boron clusters using single- and multi- determinant-Jastrow trial wavefunctions

Multireference character in some small boron clusters could be significant, and a previous all-electron fixed-node diffusion quantum Monte Carlo (FN-DMC) calculation with the single-determinant-Jastrow (SDJ) trial wavefunction shows that the atomization energy (AE) of B₄ ⁺ is overestimated by about 1.4 eV compared with the coupled cluster method with single, doubles, and perturbative triples [CCSD(T)] results. All-electron FN-DMC calculations and those with the pseudopotential (PP) using SDJ and multi-determinant-Jastrow (MDJ) trial wavefunctions with B3LYP orbitals as well as CC calculations at different levels are carried out on B_n ^Q (n = 1-5, Q = -1, 0, 1) clusters. The obtained FN-DMC energies indicate that the node error of the employed SDJ trial wavefunction in all-electron calculations is different from that with the PP for some clusters. The error of AEs and dissociation energies (DEs) from all-electron FN-DMC calculations is larger than that with the PP when the SDJ trial wavefunction is employed, while errors of CC methods do not depend on whether the PP is used. AEs and DEs of the boron clusters are improved significantly when MDJ trial wavefunctions are used in both all-electron calculations and those with the PP, and their error is similar to that of CCSD(T) compared with CCSDT(Q) results. On the other hand, reasonable adiabatic electron detachment energies (ADEs) and ionization potentials (AIPs) are achieved with FN-DMC using SDJ trial wavefunctions and MDJ is less effective on ADEs and AIPs. Furthermore, the relative energy between two structures of B₉ ^- is predicted reliably with FN-DMC using the SDJ trial wavefunction and the effect of MDJ is negligible, while density functional theory results using different exchange-correlation functionals differ significantly.