Abstract
In a recent article, we showed that configuration interaction singles (CIS) has a systematic bias against charge-transfer (CT) states: CT vertical excitation energies are consistently too high (by 1-2 eV) as compared with non-CT energies [J. E. Subotnik, J. Chem. Phys. 137, 071104 (2011)]. We now show that this CIS error can be corrected approximately by performing a single Newton-Raphson step to reoptimize orbitals, thus establishing a new set of orbitals which better balances ground and excited state energies. The computational cost of this correction is exactly that of one coupled-perturbed Hartree-Fock calculation, which is effectively the cost of the CIS calculation itself. In other words, for twice the computational cost of a standard CIS calculation, or roughly the same cost as a linear-response time-dependent Hartree-Fock calculation, one can achieve a balanced, size-consistent description of CT versus non-CT energies, ideally with the accuracy of a much more expensive doubles CIS(D) calculation.
Highlights
Configuration interaction singles (CIS) is the simplest and most intuitive approach for constructing excited electronic states
Differentiating with respect to θ pq, we find that ∂ECIS/∂θij (0) = ∂ECIS/∂θab(0) = 0, while
In Ref. 5, we showed that CIS(D) gives a strong correction, lowering the energy of the CT state, and that correction is to a good approximation proportional to the excited state relative dipole moment
Summary
Configuration interaction singles (CIS) is the simplest and most intuitive approach for constructing excited electronic states. Current implementations of TD-DFT fail miserably for CT states because the methods do not recover the correct −1/r asymptotic behavior, which leads to CT excitation energies that are often many eV too low (and getting worse for larger systems).. Current implementations of TD-DFT fail miserably for CT states because the methods do not recover the correct −1/r asymptotic behavior, which leads to CT excitation energies that are often many eV too low (and getting worse for larger systems).7–11 This failure of TD-DFT stems from using approximate exchange-correlation functionals, and Tozer and co-workers have argued that TD-DFT errors can be correlated in general with a measure of charge-transfer (though this is not always true). Here we intend only to improve relative excitation energies between CT and nonCT states, with the aim in mind of using CIS to model electron transfer between excited states in the near future
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