Molecular calculations of excitation energies and (hyper)polarizabilities with a statistical average of orbital model exchange-correlation potentials

An approximate Kohn–Sham exchange-correlation potential νxcSAOP is developed with the method of statistical averaging of (model) orbital potentials (SAOP) and is applied to the calculation of excitation energies as well as of static and frequency-dependent multipole polarizabilities and hyperpolarizabilities within time-dependent density functional theory (TDDFT). νxcSAOP provides high quality results for all calculated response properties and a substantial improvement upon the local density approximation (LDA) and the van Leeuwen–Baerends (LB) potentials for the prototype molecules CO, N2, CH2O, and C2H4. For the first three molecules and the lower excitations of the C2H4 the average error of the vertical excitation energies calculated with νxcSAOP approaches the benchmark accuracy of 0.1 eV for the electronic spectra.