Harnessing molecular excited states with Lanczos chains

Abstract

The recursion method of Haydock, Heine and Kelly is a powerful tool for calculatingdiagonal matrix elements of the resolvent of quantum-mechanical Hamiltonian operators byelegantly expressing them in terms of continued fractions. In this paper we extend therecursion method to off-diagonal matrix elements of general (possibly non-Hermitian)operators and apply it to the simulation of molecular optical absorption and photoemissionspectra within time-dependent density-functional and many-body perturbationtheories, respectively. This method is demonstrated with a couple of applicationsto the optical absorption and photoemission spectra of the caffeine molecule.