January 6, 2021
Journal Article

Solving Coupled Cluster Equations by the Newton Krylov Method

Chao Yang
Jiri Brabec
Libor Veis
David Williams-Young
Karol Kowalski


We describe using the Newton Krylov method to solve the coupled cluster equation. The method 4 uses a Krylov iterative method to compute the Newton correction to the approximate coupled 5 cluster amplitude. The multiplication of the Jacobian with a vector, which is required in each 6 step of a Krylov iterative method such as the GMRES method, is carried out through a finite 7 difference approximation, and requires an additional residual evaluation. The overall cost of the 8 method is determined by the sum of the inner Krylov and outer Newton iterations. We discuss 9 the termination criterion used for the inner iteration and show how to apply preconditioners to 10 accelerate convergence. We will also examine the use of regularization technique to improve the 11 stability of convergence and compare the method with the widely used direct inversion of iterative 12 subspace (DIIS) methods through numerical examples.

Revised: January 6, 2021 | Published: December 10, 2020


Yang C., J. Brabec, L. Veis, D.B. Williams-Young, and K. Kowalski. 2020. "Solving Coupled Cluster Equations by the Newton Krylov Method." Frontiers in Chemistry 8. PNNL-SA-155068. doi:10.3389/fchem.2020.590184