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 (TDDFT) calculations of charge-transfer excitation energies ωCT are significantly in error when the adiabatic local density approximation (ALDA) is employed for the exchange–correlation kernel fxc. We relate the error to the physical meaning of the orbital energy of the Kohn–Sham lowest unoccupied molecular orbital (LUMO). 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 fxc is required in rigorous TDDFT, and a suitable asymptotically correct form of the kernel fxcasymp is proposed. The importance of the asymptotic correction of fxc is demonstrated with the calculation of ωCT(R) for the prototype diatomic system HeBe at various separations R(He–Be). The TDDFT–ALDA curve ωCT(R) roughly resembles the benchmark ab initio curve ωCTCISD(R) of a configuration interaction calculation with single and double excitations in the region R=1–1.5 Å, where a sizable He–Be interaction exists, but exhibits the wrong behavior ωCT(R)≪ωCTCISD(R) at large R. The TDDFT curve obtained with fxcasymp however approaches ωCTCISD(R) closely in the region R=3–10 Å. Then, the adequate rigorous TDDFT approach should interpolate between the LDA/GGA ALDA xc kernel for excitations in compact systems and fxcasymp for weakly interacting fragments and suitable interpolation expressions are considered.