Assessment of the Performance of DFT Functionals Using Off-Diagonal Hypervirial Relationships

Off-diagonal hypervirial relationships, combined with quantum mechanical sum rules of charge-current conservation, offer a way for testing electronic excited-state transition energies and moments, which does not need any external reference. A number of fundamental relations were recast into absolute deviations from zero, which have been used to assess the performance of some popular DFT functionals. Extended TD-DFT calculations have been carried out for a pool of molecules chosen to the purpose, adopting a large basis set to ensure high quality results. A general agreement with previous benchmarks is observed.