Effective electron displacements: A tool for time-dependent density functional theory computational spectroscopy

We extend our previous definition of the metric Delta r for electronic excitations in the framework of the time-dependent density functional theory [C. A. Guido, P. Cortona, B. Mennucci, and C. Adamo, J. Chem. Theory Comput. 9, 3118 (2013)], by including a measure of the difference of electronic position variances in passing from occupied to virtual orbitals. This new definition, called Gamma, permits applications in those situations where the Delta r-index is not helpful: transitions in centrosymmetric systems and Rydberg excitations. The Gamma-metric is then extended by using the Natural Transition Orbitals, thus providing an intuitive picture of how locally the electron density changes during the electronic transitions. Furthermore, the Gamma values give insight about the functional performances in reproducing different type of transitions, and allow one to define a "confidence radius" for GGA and hybrid functionals. (C) 2014 AIP Publishing LLC.