Dependence of Excited State Potential Energy Surfaces on the Spatial Overlap of the Kohn−Sham Orbitals and the Amount of Nonlocal Hartree−Fock Exchange in Time-Dependent Density Functional Theory

Abstract

Time-dependent density functional theory (TDDFT) with standard GGA or hybrid exchange-correlation functionals is not capable of describing the potential energy surface of the S1 state of Pigment Yellow 101 correctly; an additional local minimum is observed at a twisted geometry with substantial charge transfer (CT) character. To investigate the influence of nonlocal exact orbital (Hartree-Fock) exchange on the shape of the potential energy surface of the S1 state in detail, it has been computed along the twisting coordinate employing the standard BP86, B3LYP, and BHLYP xc-functionals as well as the long-range separated (LRS) exchange-correlation (xc)-functionals LC-BOP, ωB97X, ωPBE, and CAM-B3LYP and compared to RI-CC2 benchmark results. Additionally, a recently suggested Λ-parameter has been employed that measures the amount of CT in an excited state by calculating the spatial overlap of the occupied and virtual molecular orbitals involved in the transition. Here, the error in the calculated S1 potential energy curves at BP86, B3LYP, and BHLYP can be clearly related to the Λ-parameter, i.e., to the extent of charge transfer. Additionally, it is demonstrated that the CT problem is largely alleviated when the BHLYP xc-functional is employed, although it still exhibits a weak tendency to underestimate the energy of CT states. The situation improves drastically when LRS-functionals are employed within TDDFT excited state calculations. All tested LRS-functionals give qualitatively the correct potential energy curves of the energetically lowest excited states of P. Y. 101 along the twisting coordinate. While LC-BOP and ωB97X overcorrect the CT problem and now tend to give too large excitation energies compared to other non-CT states, ωPBE and CAM-B3LYP are in excellent agreement with the RI-CC2 results, with respect to both the correct shape of the potential energy curve as well as the absolute values of the calculated excitation energies.

Benchmarking the performance of time-dependent density functional methods

“…Several studies have demonstrated errors in calculated excitation energies for small lambda values and large long-range character. 50,[53][54][55][56][57] …”

“…Several benchmark studies [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50] have explored the performance of using ground-state density functionals within the adiabatic approximation for the calculation of vertically excited states using TDDFT. The scope of the previous benchmark studies has been primarily limited to singlet valence excited states [36][37][38][39] with very few benchmarks considering triplet valence [40][41][42] or singlet and triplet Rydberg excited states.…”

Assessment of low-scaling approximations to the equation of motion coupled-cluster singles and doubles equations

“…LR-TDDFT, for example, often underestimates excitation energies of charge-transfer states, 2 fails to describe excitations containing multi-electron character, and generally fails to describe the effects of dispersion. Attempts have been made to correct these features of LR-TDDFT, [4][5][6] often with some success, but it is clear that a reliable black-box method for calculating excitation energies must look beyond the HF/DFT regime.…”

Calculating singlet excited states: Comparison with fast time-resolved infrared spectroscopy of coumarins

“…[24][25][26] However, in some cases these functionals show larger errors than conventional functionals, 27 especially for calculating accurate vibrational frequencies, 28 and there is evidence to suggest that TDDFT predicts the potential energy surface less accurately compared to ground state DFT methods. 29,30 An alternative approach to such problems is to apply ground state methods directly to study excited states. While this is straightforward for the lowest energy state of a given multiplicity, for example the lowest triplet excited state (T 1 ) of a molecule with a singlet ground state, in order to compute other excited states such as the S 1 state, some modifications to the methodology are required to prevent variational collapse to the electronic ground state during the self-consistent field (SCF) process.…”