Excited States with Selected Configuration Interaction-Quantum Monte Carlo: Chemically Accurate Excitation Energies and Geometries

Abstract

We employ quantum Monte Carlo to obtain chemically accurate vertical and adiabatic excitation energies, and equilibrium excited-state structures for the small, yet challenging, formaldehyde and thioformaldehyde molecules. A key ingredient is a robust protocol to obtain balanced ground- and excited-state Jastrow–Slater wave functions at a given geometry, and to maintain such a balanced description as we relax the structure in the excited state. We use determinantal components generated via a selected configuration interaction scheme which targets the same second-order perturbation energy correction for all states of interest at different geometries, and fully optimize all variational parameters in the resultant Jastrow–Slater wave functions. Importantly, the excitation energies as well as the structural parameters in the ground and excited states are converged with very compact wave functions comprising few thousand determinants in a minimally augmented double-ζ basis set. These results are obtained already at the variational Monte Carlo level, the more accurate diffusion Monte Carlo method yielding only a small improvement in the adiabatic excitation energies. We find that matching Jastrow–Slater wave functions with similar variances can yield excitation energies compatible with our best estimates; however, the variance-matching procedure requires somewhat larger determinantal expansions to achieve the same accuracy, and it is less straightforward to adapt during structural optimization in the excited state.

Quantum Monte Carlo study of ground and first excited state of C, N, O, F, and Ne atoms using Slater‐Jastrow‐Backflow wave function

“…Although among the employed trial wave functions, both of the SOCI‐J and SOCI‐J‐BF wave functions have computed the most accurate energies for the studied systems with similar accuracy. This characteristic feature is not seen in the other wave functions in the present or previous works. Despite very large computational cost, this method could provide efficient trial wave functions for different systems and states.…”

“…The previous studies through using the single‐ and multideterminant trial wave functions show that the QMC methods could provide an accurate description for both the ground and excited state properties . However, these studies have revealed that there is a strong dependence between the accuracy of the obtained energies and the quality of the trial wave function in the ground and excited states.…”

Variational Principles in Quantum Monte Carlo: The Troubled Story of Variance Minimization

“…Using expansions with matched PT2 corrections has recently been shown to lead to accurate QMC excitation energies also for a relatively small number of determinants. 9 (ii) We perform the expansion of the two states simultaneously, using a common set of orbitals [the excited-state CASSCF(6,10) orbitals] and obtain automatically matched PT2 energy corrections during the expansion. 9 For the retinal model where the ground and excited states have the same symmetry, we have only one set of orbitals for the CIPSI expansions.…”

“… 10 − 12 Importantly, recent methodological advancements 13 − 16 have enabled the fast calculation of energy derivatives and the optimization of many thousands of parameters for the internally consistent computation of QMC wave functions and geometries in the ground and excited states. 9 , 17 …”

Molekulare Photochemie: Moderne Entwicklungen in der theoretischen Chemie

“…Es gibt auch noch andere Ansätze,d ie füra ngeregte Zustände eine Annäherung an FCI-Genauigkeit bieten. [69,70] Beispielsweise kçnnen angeregte Zustände mit verschiedenen Va rianten des stochastischen Quanten-Monte-Carlo-Verfahrens (QMC) [71,72] oder dessen Kombinationen mit anderen Te chniken [73,74] berechnet werden. Beispiele fürA nwendungen sind Azobenzol, [75] Festkçrper [76] oder Modelle fürd en Chromophor von Retinal.…”