Asymptotic correction of the exchange–correlation kernel of time-dependent density functional theory for long-range charge-transfer excitations

Abstract

Time-dependent density functional theory ͑TDDFT͒ calculations of charge-transfer excitation energies CT are significantly in error when the adiabatic local density approximation ͑ALDA͒ is employed for the exchange-correlation kernel f xc . We relate the error to the physical meaning of the orbital energy of the Kohn-Sham lowest unoccupied molecular orbital ͑LUMO͒. The LUMO orbital energy in Kohn-Sham DFT-in contrast to the Hartree-Fock model-approximates an excited electron, which is correct for excitations in compact molecules. In CT transitions the energy of the LUMO of the acceptor molecule should instead describe an added electron, i.e., approximate the electron affinity. To obtain a contribution that compensates for the difference, a specific divergence of f xc is required in rigorous TDDFT, and a suitable asymptotically correct form of the kernel f xc asymp is proposed. The importance of the asymptotic correction of f xc is demonstrated with the calculation of CT (R) for the prototype diatomic system HeBe at various separations R(He-Be). The TDDFT-ALDA curve CT (R) roughly resembles the benchmark ab initio curve CT CISD (R) of a configuration interaction calculation with single and double excitations in the region Rϭ1 -1.5 Å, where a sizable He-Be interaction exists, but exhibits the wrong behavior CT (R) Ӷ CT CISD (R) at large R. The TDDFT curve obtained with f xc asymp however approaches CT CISD (R) closely in the region Rϭ3 -10 Å. Then, the adequate rigorous TDDFT approach should interpolate between the LDA/GGA ALDA xc kernel for excitations in compact systems and f xc asymp for weakly interacting fragments and suitable interpolation expressions are considered.

Time-dependent density functional theory: Past, present, and future

“…Thus, in the density-density response, the oscillator strength for these transitions is exponentially small. Recently [82], it has been shown how to build an empirical approximation to an adiabatic f XC that can capture these effects, but it is one that grows exponentially with |r − r ′ |. Thus this is a sin of locality, in which local approximations to f XC miss a qualitative feature.…”

Long-range excitations in time-dependent density functional theory

“…There is no exponential growth of the kernel matrix element with separation, that one would expect from an adiabatic single pole analysis of longrange CT with localized (atomic)orbitals [28]; there the kernel would need to grow as e R in order to get a non-vanishing xc affinity. However, as shown here, for a long-range molecule consisting of openshell fragments, this does not occur with the correct delocalized molecular orbitals, provided our nonadiabatic approximation is used, as the CT state is "carried along" with the local excitation, through KS excitation out of the bonding orbital.…”

“…The latter is equal to minus the ionization energy of the donor, I D , while the former is the KS electron affinity [32,33,35,36], A A,S = A A − A A,XC , not the true electron affinity of the acceptor, A A . The resulting frequency, ω = I D − A A,S , is a severe underestimate to the true CT energy: aside from the usual local/semi-local approximations underestimating the ionization energy, it lacks the xc contribution to the electron affinity, as well as the −1/R tail [25,26,27,28]. The exact CT energy is I D − A A − 1/R in the large-R limit.…”

“…Closely linked are the difficulties in obtaining long-range chargetransfer (CT) excitations. The latter are notoriously underestimated in ATDDFT [21,22,24,25,26,27,28,29,30,31], yet are vital in biological and chemical systems large enough that density functional methods are the only feasible approach.…”

A DFT/TD‐DFT study for the ground and excited states of peramine and some pyrrolopyrazinone compounds

“…[36] In some cases [37,38,39,40,41] , there are some limitations of TD-DFT which overestimate the electronic transitions up to 1 eV. [42,43] In Table 7 and in Figs 6 and 7 (lowest panels) excitation energies (∆E in eV) of singlet-singlet transitions and oscillator strengths f of the excited states of peramine (1) and chloro derivative (3) for bent and flat conformations are presented. Theoretically calculated data for peramine were compared with experimental electronic spectra (Fig.…”