Excitation energies expressed as orbital energies of Kohn–Sham density functional theory with long‐range corrected functionals

Abstract

A new simple and conceptual theoretical scheme is proposed for estimating oneelectron excitation energies using Kohn-Sham (KS) solutions. One-electron transitions that are dominated by the promotion from one initially occupied orbital to one unoccupied orbital of a molecular system can be expressed in a two-step process, ionization, and electron attachment. KS with long-range corrected (LC) functionals satisfies Janak's theorem and LC total energy varies almost linearly as a function of its fractional occupation number between the integer electron points. Thus, LC reproduces ionization energies (IPs) and electron affinities (EAs) with high accuracy and one-electron excitation energies are expressed as the difference between the occupied orbital energy of a neutral molecule and the corresponding unoccupied orbital energy of its cation. Two such expressions can be used, with one employing the orbital energies for the neutral and cationic systems, while the other utilizes orbital energies of just the cation. Because the EA of a molecule is the IP of its anion, if we utilize this identity, the two expressions coincide and give the same excitation energies. Reasonable results are obtained for valence and core excitations using only orbital energies.

Assessment of long‐range corrected density functional theory on the absorption and vibrationally resolved fluorescence spectrum of carbon nanobelts

“…The optimized μ parameters of LC‐BLYP with 6‐31G(d,p), 6‐311G(d,p), 6–31+G(d,p), and 6–311+G(d,p) in 12‐CNB were 0.20, 0.19, 0.18, and 0.18, respectively, which shows that the μ parameter decreases when basis set becomes larger, and those of LC‐BLYP with 6–311+G(d,p) in 16‐CNB and 24‐CNB were 0.18 and 0.19, respectively (Figure 2). The optimized μ parameter is reported to, generally, decrease as the size of system becomes larger 51–53 , but contrary to all expectations it is observed that optimized μ values in CNB system are increased depending on the system size. Moreover, all the optimized μ parameters obtained in the gas‐phase were applied to PCM calculations with dichloromethane as the same value.…”

XABOOM: An X-Ray Absorption Benchmark of Organic Molecules Based on Carbon, Nitrogen, and Oxygen 1s → π ∗ Transitions

“…183,184 This approach was developed as approximate KS-DFT eigenvalues do not directly correspond to ionization energies or electron affinities and the dependence of the total energy with respect to occupation is not piecewise linear. 183,185 LDA and GGA exchangecorrelation functionals generate a convex deviation from piecewise linearity, in contrast to the Hartree-Fock method which generates a concave deviation. 185 Thus, if the right amount of exact exchange is mixed with GGA exchange, piecewise linearity can be restored.…”

“…183,185 LDA and GGA exchangecorrelation functionals generate a convex deviation from piecewise linearity, in contrast to the Hartree-Fock method which generates a concave deviation. 185 Thus, if the right amount of exact exchange is mixed with GGA exchange, piecewise linearity can be restored. For such a corrected functional, it has been shown that the excitation energies are more correctly modelled using a full core-hole (or cation) model, 185 and decreasing occupations of core levels with increasing amounts of exact exchange are required to balance the description of core-hole relaxation.…”

“…185 Thus, if the right amount of exact exchange is mixed with GGA exchange, piecewise linearity can be restored. For such a corrected functional, it has been shown that the excitation energies are more correctly modelled using a full core-hole (or cation) model, 185 and decreasing occupations of core levels with increasing amounts of exact exchange are required to balance the description of core-hole relaxation. The problem is that the amount of exact exchange which restores piecewise linearity is expected to be system-(and even orbital-) dependent, 186 so the balance between core-hole model and amount of exact exchange would also show this dependence.…”

Density Functional Prediction of Quasiparticle, Excitation, and Resonance Energies of Molecules With a Global Scaling Correction Approach

“…Such a method is referred to as the QE-DFT (QP energies from DFT), which has been employed to describe excited-state potential energy surfaces and conical intersections . Following the idea of QE-DFT, molecular excitation energies have also been expressed by KS/GKS orbital energies obtained with long-range corrected functionals (Hirao et al, 2020). Details about QE-DFT are to be presented in section 2.1.…”