Numerical and Theoretical Aspects of the DMRG-TCC Method Exemplified by the Nitrogen Dimer

TL;DR

This paper explores the numerical and theoretical properties of the DMRG-TCC method, focusing on energy accuracy, basis splitting, and active space selection, supported by numerical experiments on the nitrogen dimer.

Contribution

It provides a detailed mathematical and numerical analysis of the DMRG-TCC method, including energy size extensivity, basis splitting effects, and active space dependence.

Findings

Energy error depends on basis splitting

Robustness of the method with respect to bond dimensions

Active space choice significantly influences accuracy

Abstract

In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate chemical properties of the used method, such as energy size extensivity and the equivalence of linked and unlinked formulation. The existing mathematical analysis is here elaborated in a quantum chemical framework. In particular, we highlight the use of a so-called CAS-ext gap describing the basis splitting between the complete active space and the external part. Moreover, the behavior of the energy error as a function of the optimal basis splitting is discussed. We show numerical investigations on the robustness with respect to the bond dimensions of the single orbital entropy and the mutual information, which are quantities that are used to choose the complete active space. Furthermore, we extend the mathematical analysis with a numerical study on the complete active space dependence of the error.