Kohn–Sham calculations using hybrid exchange-correlation functionals with asymptotically corrected potentials

The theory is presented for asymptotically correcting the potentials of hybrid exchange-correlation functionals, i.e., those that include a fraction of orbital exchange. The Kohn–Sham equations involve a multiplicative potential due to the continuum part of the hybrid functional and a nonmultiplicative term due to the orbital exchange. In asymptotic regions the multiplicative σ-spin potential is corrected to take the form (CX−1)/r+εHOMO,σ+Iσ, where CX is the fraction of orbital exchange; εHOMO,σ is the σ-spin self-consistent highest occupied Kohn–Sham eigenvalue; and Iσ is an approximate ionization energy. For the hydrogen atom, the asymptotic correction leads to a potential that closely resembles the exact potential; the eigenvalue spectrum is intermediate between the Schrödinger and Hartree–Fock eigenvalues, reflecting the presence of orbital exchange. Kohn–Sham orbitals and eigenvalues determined from this procedure have been used to calculate singlet vertical excitation energies for CO, N2, H2CO, C2H4, and C6H6. The correction significantly improves excitation energies to Rydberg states, with mean absolute errors below 0.2 eV. However, despite including orbital exchange, the results do not represent an improvement over the results obtained by asymptotically correcting a recently developed GGA functional. The asymptotic correction is also shown to reduce static isotropic polarizabilities.