Binding curve of the beryllium dimer using similarity-transformed FCIQMC: Spectroscopic accuracy with triple-zeta basis sets

Abstract

We demonstrate how similarity-transformed full configuration interaction quantum Monte Carlo (FCIQMC) based on the transcorrelated Hamiltonian can be applied to make highly accurate predictions for the binding curve of the beryllium dimer, marking the first case study of a molecular system with this method. In this context, the non-Hermitian transcorrelated Hamiltonian, resulting from a similarity transformation with a Jastrow factor, serves the purpose to effectively address dynamic correlation beyond the used basis set and thus allows for obtaining energies close to the complete basis set limit from FCIQMC already with moderate basis sets and computational effort. Building on results from other explicitly correlated methods, we discuss the role of the Jastrow factor and its functional form, as well as potential sources for size consistency errors, and arrive at Jastrow forms that allow for high accuracy calculations of the vibrational spectrum of the beryllium dimer.

Performance of a one-parameter correlation factor for transcorrelation: the Li-Ne total energies and ionization potentials

“…To obtain the ground state eigenvalue ẼB 0 [u] of a given TC Hamiltonian H[u] B , we use the recently developed similarity transformed full-configuration interaction quantum Monte Carlo (ST-FCIQMC) technique 15,27 which extends the original stochastic projection technique of FCIQMC [28][29][30][31][32][33][34][35] to a non-hermitian and threebody Hamiltonian. The FCIQMC parameters were 10 6 walkers, an initiator threshold of n init = 3 and a semistochastic space of N D = 1000.…”

“…The problems regarding these terms are two-fold: (i) the computation of the intermediate quantities which can be quite demanding and (ii) the computation and storage of all the N 6 integrals. In the context of H[µ] B , point (i) is not really a problem since all intermediate quantities are computed analytically and not numerically in contrast to more complex correlation factors 15,27 pendix of Ref. 26).…”

“…This work has showed the beneficial impact of the e-e-n terms in yielding highly accurate total energies and ionisation potentials using the TC-FCIQMC method with modest basis sets. The TC-FCIQMC method has also been ap-plied to the binding curve of the Be 2 system, yielding spectroscopic accuracy across the entire binding curve using only triple-zeta basis sets, demonstrating how the TC-FCIQMC method can be used in ab initio problems with a delicate balance between static and dynamical correlation 27 . In other work from the Alavi group, the application of the TC-FCIQMC method to the 2D Hubbard model 17 showed how transcorrelation can be beneficial in the treatment of strongly correlated systems, by compressing the right eigenvector of the ground state so that it becomes largely dominated by the Hartree-Fock determinant, in a regime where the ground-state eigenvector of the non-transcorrelated Hubbard Hamiltonian is strongly multi-configurational.…”

Transcorrelated coupled cluster methods

“…This idea goes back to the pioneering work of Boys and Handy and is termed transcorrelation, 58 and it has been recently demonstrated that a combination of the transcorrelation with a stochastic full configuration interaction quantum Monte-Carlo (FCIQMC) [59][60][61] yields very promising results for weakly and strongly correlated systems. [62][63][64][65] Since the Hamiltonian itself is transformed, the transcorrelation approach is not specific for low-order methods and can be used together with any excitation orders. The transcorrelated Hamiltonian has been applied before to linearized coupled cluster with singles and doubles, 66 and for the uniform electron gas for coupled cluster and distinguishable cluster with singles and doubles, 67 however with some approximations to the three-body terms in the transformed Hamiltonian and with a simpler correlation factor.…”

Explicitly correlated electronic structure calculations with transcorrelated matrix product operators

“…102 We note in passing that the same correction was applied in Ref. 103, where the Be 2 PEC was studied with the transcorrelated FCIQMC method. The counterpoise correction was calculated, at each R Be-Be value, from the tcDMRG energy of the Be atom calculated in the presence of a ghost atom carrying the Be cc-pCVDZ basis placed at R Be-Be .…”