Efficient Solution of the Electronic Eigenvalue Problem Using Wavepacket Propagation

• Published in: Journal of chemical theory and computation Vol. 14; no. 3; pp. 1433 - 1441
• Main Authors: Neville, Simon P, Schuurman, Michael S
• Format: Journal Article
• Language: English
• Published: United States American Chemical Society 13-03-2018
• Subjects: Algorithms; Business travel; Eigenvalues; Iterative methods; Propagation; Relaxation method (mathematics); Subspace methods; Wave propagation
• ISSN: 1549-9618; 1549-9626
• DOI: 10.1021/acs.jctc.7b01258

We report how imaginary time wavepacket propagation may be used to efficiently calculate the lowest-lying eigenstates of the electronic Hamiltonian. This approach, known as the relaxation method in the quantum dynamics community, represents a fundamentally different approach to the solution of the electronic eigenvalue problem in comparison to traditional iterative subspace diagonalization schemes such as the Davidson and Lanczos methods. In order to render the relaxation method computationally competitive with existing iterative subspace methods, an extended short iterative Lanczos wavepacket propagation scheme is proposed and implemented. In the examples presented here, we show that by using an efficient wavepacket propagation algorithm the relaxation method is, at worst, as computationally expensive as the commonly used block Davidson–Liu algorithm, and in certain cases, significantly less so.