Influence of pseudopotentials on excitation energies from selected configuration interaction and diffusion Monte Carlo

Abstract

Due to their diverse nature, the faithful description of excited states within electronic structure theory methods remains one of the grand challenges of modern theoretical chemistry.antum Monte Carlo (QMC) methods have been applied very successfully to ground state properties but still remain generally less e ective than other non-stochastic methods for electronically excited states. Nonetheless, we have recently reported accurate excitation energies for small organic molecules at the xed-node di usion Monte Carlo (FN-DMC) within a Jastrow-free QMC protocol relying on a deterministic and systematic construction of nodal surfaces using the selected con guration interaction (sCI) algorithm known as CIPSI (Con guration Interaction using a Perturbative Selection made Iteratively). Albeit highly accurate, these all-electron calculations are computationally expensive due to the presence of core electrons. One very popular approach to remove these chemically-inert electrons from the QMC simulation is to introduce pseudopotentials (also known as e ective core potentials). Taking the water molecule as an example, we investigate the in uence of Burkatzki-Filippi-Dolg (BFD) pseudopotentials and their associated basis sets on vertical excitation energies obtained with sCI and FN-DMC methods. Although these pseudopotentials are known to be relatively safe for ground state properties, we evidence that special care may be required if one strives for highly accurate vertical transition energies. Indeed, comparing all-electron and valence-only calculations, we show that using pseudopotentials with the associated basis sets can induce di erences of the order of 0.05 eV on the excitation energies. Fortunately, a reasonable estimate of this shi can be estimated at the sCI level.

QUESTDB: A database of highly accurate excitation energies for the electronic structure community

“…Details regarding this specific CIPSI implementation can be found in Refs. 159, 167. A state‐averaged formalism is employed, that is, the ground and excited states are described with the same set of determinants and orbitals, but different CI coefficients.…”

“…A state‐averaged formalism is employed, that is, the ground and excited states are described with the same set of determinants and orbitals, but different CI coefficients. Our usual protocol 15, 93–96, 143, 144, 167 consists of performing a preliminary CIPSI calculation using Hartree–Fock orbitals in order to generate a CIPSI wave function with at least 10 7 determinants. Natural orbitals are then computed based on this wave function, and a new, larger CIPSI calculation is performed with this new set of orbitals.…”

“…Recently, the determinant‐driven CIPSI algorithm has been efficiently implemented 159 in the open‐source programming environment QUANTUM PACKAGE enabling to perform massively parallel computations 127, 138, 145, 159 . CIPSI is also frequently employed to provide accurate trial wave functions for quantum Monte Carlo calculations in molecules 135–137, 139, 140, 143, 144, 165–170 and more recently for periodic solids 171 . We refer the interested reader to Ref.…”

Assessing the Performances of CASPT2 and NEVPT2 for Vertical Excitation Energies

“…54 In this context, some of us, inspired by Thiel's works, have recently proposed a new set of highly-accurate TBEs for VTEs of a large variety of ESs in small-and medium-sized organic molecules and radicals. [123][124][125][126][127][128][129][130] These TBEs were obtained directly from FCI using a selected CI approach, 131,132 CCS-DTQ, [133][134][135][136] and CCSDT, [137][138][139][140][141] for compounds containing 1-to-3, 4, and 5-to-10 non-hydrogen atoms, respectively. Taking advantages of these highly trustworthy values, we were able to resolve some unanswered questions about the relative accuracies of ADC(3), 70 CCSDT-3, 142,143 and CC3.…”

Chemically Accurate Excitation Energies With Small Basis Sets

“…[52][53][54] Both the implementation of the CIPSI algorithm and the computational protocol for excited states is reported in Ref. 55. e total energy of each state is obtained via an e cient extrapolation procedure of the sCI energies designed to reach near-FCI accuracy.…”