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

Abstract

In this article, we investigate the numerical and theoretical aspects of the coupled-cluster method tailored by matrix-product states. We investigate formal properties of the used method, such as energy size consistency 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 what we have defined as a complete active space-external space gap describing the basis splitting between the complete active space and the external part generalizing the concept of a HOMO−LUMO gap. Furthermore, the behavior of the energy error for an optimal basis splitting, i.e., an active space choice minimizing the density matrix renormalization group-tailored coupled-cluster singles doubles error, 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 a complete active space. Moreover, the dependence of the groundstate energy error on the complete active space has been analyzed numerically in order to find an optimal split between the complete active space and external space by minimizing the density matrix renormalization group-tailored coupled-cluster error.

Analysis of the Tailored Coupled-Cluster Method in Quantum Chemistry

“…This caveat will be further discussed in Section 3.3. We also refer to [10] for a case study on the N 2 molecule illustrating the TCC method's sensitivity to the CAS choice.…”

“…Indeed, f (t; t CAS ) = P Vext f CC (t ⊕ t CAS ) with the orthogonal projection P Vext onto V ext , relates the TCC function to the classical CC function in Eq. (10). Note that the CAS-part of the cluster amplitudes is still fixed.…”

“…The DMRG method [45] is a high accuracy tool for statically correlated systems [7], nonetheless, for dynamically correlated problems it requires high computational resources making a wide-ranging application-at this time-intractable. Hence, it is the symbiosis of the DMRG and the CC method that creates a high efficiency scheme suitable for multireference systems [42,43,44,10,2,22]. Granted that the DMRG-TCCSD method is the major motivation for the following analysis, we highlight that the applicability of this article's results exceeds the DMRG-TCCSD method and, more generally, the TNS-TCC method.This paper is organized as follows.…”

Semiclassical Dispersion Corrections Efficiently Improve Multiconfigurational Theory with Short-Range Density-Functional Dynamic Correlation

“…Very recently, a tailored coupled-cluster variant was proposed in combination with DMRG wave functions that reduces the multi-configurational coupled-cluster expressions to their single-configurational counterpart. [45][46][47] The multi-configurational effect is then included by constraining the amplitudes of excitations within the active space to those obtained from the DMRG calculation. Future work on this approach needs to show how universally applicable it actually is for strong multi-configurational cases that require large active spaces and large orbital basis sets.…”

Quantum information-based analysis of electron-deficient bonds

“…These include density matrix renormalization group (DMRG) method 35,36 , which variationally optimizes wave functions in the form of matrix product states (MPS). 37 Other important examples represent characterization of electron correlation into its static (strong) and dynamic contributions 9 , automatic (black-box) selection of the active spaces 1, 6,17,23,24,38 , or the self-adaptive tensor network states with multi-site correlators 25 , all of which harness single-and two-orbital entanglement entropies. Last but not least, correlation measures based on the single-and two-orbital entanglement entropies have also been employed for the purposes of bond analysis 10,20 .…”