Capturing multireference excited states by constrained-density-functional theory

Abstract

The computation of excited electronic states with commonly employed (approximate) methods is challenging, typically yielding states of lower quality than the corresponding ground state for a higher computational cost. In this work, we present a mean field method that extends the previously proposed eXcited Constrained DFT (XCDFT) from single Slater determinants to ensemble 1-RDMs for computing low-lying excited states. The method still retains an associated computational complexity comparable to a semilocal DFT calculation while at the same time is capable of approaching states with multireference character. We benchmark the quality of this method on well-established test sets, finding good descriptions of the electronic structure of multireference states and maintaining an overall accuracy for the predicted excitation energies comparable to semilocal TDDFT.

Method for Calculating Excited Electronic States Using Density Functionals and Direct Orbital Optimization with Real Space Grid or Plane-Wave Basis Set

“…Alternative approaches with wide applicability and similar computational effort can be based on time-independent DFT. These include ensemble DFT, − , excited-state DFT (eDFT) − (also sometimes referred to as Δ self-consistent field, ΔSCF), as well as constrained DFT, − orthogonality constrained, − and constricted DFT approaches. , There are also methodologies where excited-state properties are obtained from ground-state calculations only, as, for example, in electron–hole self-interaction corrected calculations , or the quasi-particle energy DFT (QE-DFT) . In eDFT, excited states are found as stationary states of the energy expressed as a density functional.…”

Comparison of Linear Response Theory, Projected Initial Maximum Overlap Method, and Molecular Dynamics-Based Vibronic Spectra: The Case of Methylene Blue

“…The Δ self-consistent field (ΔSCF) family of methods presents an alternative to LR methods for computing excited states. − , For nonadiabatic dynamics, similar approaches based on constrained DFT have been shown to present a viable path forward for computing excited-state couplings and properties, and locating conical intersections. − A significant challenge of ΔSCF is converging single-determinant representations of excited states using ground-state methods without collapsing to the ground state. In recent years, Gill and co-workers have rejuvenated work in this area using maximum overlap concepts. , Maximum overlap methodologies (MOMs) modify standard ground-state SCF algorithms to maximize the overlap between the occupied molecular orbitals (MOs) of a user-defined SCF target and that computed in the current SCF iteration.…”