2008/05/21 by Melissa J. Lucero, Anders M. N. Niklasson, Sergei Tretiak +1
Physics and Astronomy · #Advanced Chemical Physics Studies #Algorithm #Computer science #Excited state #Perturbation (astronomy) #Perturbation theory (quantum mechanics) #Physics #Quantum mechanics #Quantum optics and atomic interactions #Spectroscopy and Quantum Chemical Studies #Statistical physics #cond-mat.mtrl-sci
paper · pdf · doi:10.1063/1.2965535
published as J. Chem. Phys. 129, 064114 (2008) · 9 pages, 7 figures
arxiv created 2008/05/21 · openalex publication_date 2008/08/14 · arxiv updated 2011/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A nonlinear conjugate gradient optimization scheme is used to obtain excitation energies within the random phase approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size N is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular-orbital-free algorithm is found to be robust and computationally efficient, providing a first step toward large-scale, reduced complexity calculations of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent density functional theory.