On nonadiabatic coupling vectors in time-dependent density functional theory

In this note, we show that the development for the calculation of nonadiabatic coupling vectors in the framework of TDDFT introduced by the authors in the series of recent publications [E. Tapavicza , Phys. Rev. Lett.98, 023001 (2007); I. Tavernelli , J. Chem. Phys.130, 124107 (2009)] is rigorous and fully equivalent to the one proposed by Sugino and co-workers [C. P. Hu , J. Chem. Phys.127, 064103 (2007)]. Specific applications of our formulation are also discussed.