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

Kai Guther,Hongjun Luo,Ali Alavi,Aron J Cohen

doi:10.1063/5.0055575

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.

Highlights

Correlated electronic structure problems belong to the most challenging problems in quantum chemistry, due to the exponential scaling of the Hilbert space with system size
We show that this method, combined with Jastrow factors obtained from variational Monte Carlo (VMC), yields high-accuracy binding curves from standalone calculations in relatively small basis sets
We evaluate the ground state potential energy curve of the beryllium dimer using the ST-full configuration interaction quantum Monte Carlo (FCIQMC) method to calculate the ground state energies at different geometries

Summary

Introduction

Correlated electronic structure problems belong to the most challenging problems in quantum chemistry, due to the exponential scaling of the Hilbert space with system size. While the common approach among wavefunction based methods—to represent the wavefunction within a discrete basis—is often a necessary step in applying a method, it introduces a systematic basis set error, which only slowly converges with increasing basis set size.. Explicitly correlated methods have been developed to address these issues and approach the wavefunction or energetics of the complete basis set limit. Prominent representatives of these are the R12 and F12 methods, which use an a posteriori correction of the wavefunction or the geminal basis sets.. The transcorrelated method has been investigated by Ten-no using Slater-type geminals in a linearized coupled cluster theory, as a precursor to F12 methods, and Tsuneyuki as a very promising application of a wavefunction technique to solid-state systems

Methods

Results

Conclusion