Targeted Excited State Algorithms

TL;DR

This paper introduces Harmonic Davidson and State-Averaged Harmonic Davidson algorithms within DMRG to improve excited state calculations, demonstrating enhanced accuracy and convergence stability over traditional methods.

Contribution

The paper implements and assesses novel Harmonic Davidson algorithms within DMRG, showing improved accuracy and stability for excited state computations.

Findings

Harmonic Davidson algorithms outperform traditional methods in accuracy.

State-Averaged Harmonic Davidson offers optimal convergence stability.

Algorithms are validated on low-lying excited states of acenes.

Abstract

To overcome the limitations of the traditional state-averaging approaches in excited state calculations, where one solves for and represents all states between the ground state and excited state of interest, we have investigated a number of new excited state algorithms. Building on the work of van der Vorst and Sleijpen (SIAM J. Matrix Anal. Appl., 17, 401 (1996)), we have implemented Harmonic Davidson and State-Averaged Harmonic Davidson algorithms within the context of the Density Matrix Renormalization Group (DMRG). We have assessed their accuracy and stability of convergence in complete active space DMRG calculations on the low-lying excited states in the acenes ranging from naphthalene to pentacene. We find that both algorithms offer increased accuracy over the traditional State-Averaged Davidson approach, and in particular, the State-Averaged Harmonic Davidson algorithm offers an optimal combination of accuracy and stability in convergence.