Linear Scaling Solution of the Time-Dependent Self-Consistent-Field Equations

TL;DR

This paper introduces a linear scaling method for solving the time-dependent self-consistent-field equations using a double quotient formulation, enabling efficient computation of excitonic properties in large molecular systems.

Contribution

It presents a novel variational formulation based on double quotient optimization that achieves linear scaling in solving TD-SCF equations, improving computational efficiency.

Findings

Achieves convergence rates comparable to the Tamm-Dancoff approximation.

Demonstrates linear scaling solution for bulk excitons in complex systems.

Validates the method on polyphenylene vinylene oligomers and carbon nanotube segments.

Abstract

A new approach to solving the Time-Dependent Self-Consistent-Field equations is developed based on the double quotient formulation of Tsiper [J. Phys. B, 34 L401 (2001)]. Dual channel, quasi-independent non-linear optimization of these quotients is found to yield convergence rates approaching those of the best case (single channel) Tamm-Dancoff approximation. This formulation is variational with respect to matrix truncation, admitting linear scaling solution of the matrix-eigenvalue problem, which is demonstrated for bulk excitons in the polyphenylene vinylene oligimer and the (4,3) carbon nanotube segment.