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Updated: Oct 29, 2025

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Assessment of the performance of DFT functionals in the fulfillment of off-diagonal hypervirial relationships
Francesco F Summa1, Guglielmo Monaco1, Paolo Lazzeretti1
1Dipartimento di Chimica e Biologia "A. Zambelli", Università degli studi di Salerno, via Giovanni Paolo II 132, Fisciano 84084, SA, Italy. fsumma@unisa.it.
Abstract:
Off-diagonal hypervirial relationships, combined with quantum mechanical sum rules of charge-current conservation, offer a way to test electronic excited-state transition energies and moments, which does not need any external reference. A number of fundamental relationships 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 for this purpose, adopting a large basis set to ensure high quality results. A partial agreement with previous benchmarks is observed.
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