Density Functional Extension to Excited-State Mean-Field Theory

Abstract

We investigate an extension of excited-state mean-field theory in which the energy expression is augmented with density functional components in an effort to include the effects of weak electron correlations. The approach remains variational and entirely time independent, allowing it to avoid some of the difficulties associated with linear response and the adiabatic approximation. In particular, all of the electrons’ orbitals are relaxed state specifically, and there is no reliance on Kohn–Sham orbital energy differences, both of which are important features in the context of charge transfer. Preliminary testing shows clear advantages for single-component charge transfer states, but the method, at least in its current form, is less reliable for states in which multiple particle–hole transitions contribute significantly.

Variational coupled cluster for ground and excited states

“…Recently, there has been a renewed interest in singlereference methods for excited states in the context of Hartree-Fock, density-functional, and coupled-cluster theories. [102][103][104][105][106][107][108][109][110][111][112][113][114][115][116][117][118][119][120][121]125,142,168 This has been made possible thanks to the development of new algorithms specifically designed to target higher-energy solutions of these non-linear equations. These so-called non-standard solutions provide genuine alternatives to the usual linear response and equation-of-motion formalisms (which are naturally biased towards the reference ground state) for the determination of accurate excited-state energies in molecular systems.…”

“…101,102 Lee et al refers to this type of methods as ∆CC 102 by analogy with the ∆SCF methods where one basically follows the same procedure but at the self-consistent field (SCF) level. Indeed, the use of Hartree-Fock (HF) or Kohn-Sham higher-energy solutions corresponding to excited states is becoming more and more popular and new algorithms designed to target such solutions, like the maximum overlap method (MOM) [103][104][105][106] or more involved variants, [107][108][109][110][111][112][113][114][115][116][117][118][119][120][121] are being actively developed. Besides providing a qualitatively good description of excited states, 121 these solutions can also be very helpful for ∆CC methods, as we shall illustrate below (see also Ref.…”

Variational calculations of excited states via direct optimization of the orbitals in DFT

“…Furthermore, unless long-range corrected functionals are used, TDDFT shows systematic errors for excitations that involve displacement of electrons between orbitals of different spatial extent (such as excitations to Rydberg states) 6,10,11 or large spatial separation (such as charge-transfer states) [12][13][14] . There, orbital relaxation effects are important but are missing in practical implementations of TDDFT [15][16][17] . Alternatively, excited states can be obtained as optimized single Slater determinants corresponding to higher-energy stationary points of the energy surface that represents the variation of the energy of the system as a function of the electronic degrees of freedom.…”

“…However, excitation energies can still be affected by systematic errors. This is because, due to the typically more diffuse character of the excited-state orbitals, many excited states, especially those with Rydberg, charge-transfer and double excitation character, are more affected by the self-interaction error than ground states when using common semi-local KS functionals 15,45 . The self-interaction correction (SIC) 46 applied to KS functionals can alleviate some of these problems by correcting the long-range form of the effective potential 45,47 .…”

Supporting Notebook for "Energy Landscape of State-Specific Electronic Structure Theory"

“…17,21 In principle, statespecific approaches can approximate both single and double excitations, 1,22,23 although the open-shell character of single excitations requires a multi-configurational approach. 4,[24][25][26][27] Underpinning excited state-specific methods is the fundamental idea that ground-state wave functions can also be used to describe an electronic excited state. This philosophy relies on the existence of additional higher-energy mathematical solutions, which have been found in Hartree-Fock (HF), 22, density functional theory (DFT), [49][50][51][52] multiconfigurational self-consistent field (MC-SCF), [53][54][55][56][57][58][59][60][61] and coupled a) Electronic mail: hugh.burton@chem.ox.ac.uk cluster (CC) theory.…”