TY - JOUR

T1 - Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

AU - Lucero, Melissa J.

AU - Niklasson, Anders M.N.

AU - Tretiak, Sergei

AU - Challacombe, Matt

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=49749085203&partnerID=8YFLogxK

U2 - 10.1063/1.2965535

DO - 10.1063/1.2965535

M3 - Article

C2 - 18715058

AN - SCOPUS:49749085203

VL - 129

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 6

M1 - 064114

ER -