Solving the RPA eigenvalue equation in real-space

Abstract

We present a computational method to solve the RPA eigenvalue equation employing a uniform grid representation in three-dimensional Cartesian coordinates. The conjugate gradient method is used for this purpose as an iterative method for a generalized eigenvalue problem. No construction of unoccupied orbitals is required in the procedure. We expect this method to be useful for systems lacking spatial symmetry to calculate accurate eigen-values and transition matrix elements of a few low-lying excitations. Some applications are presented to demonstrate the feasibility of the method, considering the simplified mean-field model as an example of a nuclear physics system and the electronic excitations in molecules with time-dependent density functional theory as an example of an electronic system.