A block variational procedure for the iterative diagonalization of non-Hermitian random-phase approximation matrices

作者：Rocca Dario^*; Bai Zhaojun; Li Ren Cang; Galli Giulia

来源：Journal of Chemical Physics, 2012, 136(3): 034111.

DOI：10.1063/1.3677667

We present a technique for the iterative diagonalization of random-phase approximation (RPA) matrices, which are encountered in the framework of time-dependent density-functional theory (TDDFT) and the Bethe-Salpeter equation. The non-Hermitian character of these matrices does not permit a straightforward application of standard iterative techniques used, i.e., for the diagonalization of ground state Hamiltonians. We first introduce a new block variational principle for RPA matrices. We then develop an algorithm for the simultaneous calculation of multiple eigenvalues and eigen-vectors, with convergence and stability properties similar to techniques used to iteratively diagonalize Hermitian matrices. The algorithm is validated for simple systems (Na-2 and Na-4) and then used to compute multiple low-lying TDDFT excitation energies of the benzene molecule.

• 出版日期2012-1-21