title: Molecular-orbital-free algorithm for the excited-state force in time-dependent density functional theory.
abstract: Starting from the equation of motion in the density matrix formulation, we reformulate the analytical gradient of the excited-state energy at the time-dependent density functional theory level in the nonorthogonal Gaussian atom-centered orbital (AO) basis. Analogous to the analytical first derivative in molecular-orbital (MO) basis, a Z-vector equation has been derived with respect to the reduced one-electronic density matrix in AO basis, which provides a potential possibility to exploit quantum locality of the density matrix and avoids the matrix transformation between the AO and the MO basis. Numerical tests are finished for the excited-state geometry optimization and adiabatic excitation energy calculation of a series of small molecules. The results demonstrate the computational efficiency and accuracy of the current AO-based energy gradient expression in comparison with the MO-based scheme.
authors.affiliation: Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei 230026, Anhui, PR China.
authors.forename: Jie
authors.initials: J
authors.lastname: Liu
authors.forename: Wan Zhen
authors.initials: WZ
authors.lastname: Liang