Illustration of a TDDFT spatial overlap diagnostic by basis function exponent scaling

The relationship between TDDFT vertical excitation energy accuracy and the degree of occupied-virtual spatial orbital overlap is investigated for the CO molecule, by systematically controlling the overlap through a scaling of the basis function exponents. Increasing the scaling parameter contracts the basis set, increasing the overlap values. The corresponding excitation energies also increase and become more accurate, relative to approximate second-order coupled cluster values determined using the same, scaled basis. For the 36 data points (four excitations, each evaluated using nine exponent scaling parameters) there is a strong correlation between excitation energy accuracy and orbital overlap with a generalised gradient approximation functional. Similar correlation is observed with a hybrid and Coulomb-attenuated functional, but the errors become progressively smaller due to their increased fraction of exact, non-local exchange at long-range. The results are fully consistent with the diagnostic test of J. Chem. Phys. 128 (2008) 044118.