A remark on the disconnected nature of Lagrange equations in the context of a linear-scaling implementation of the coupled-cluster energy gradients

Abstract

It is known that the Λ-tensor (an array of Lagrange multipliers), necessary for evaluating analytic energy gradients in the coupled-cluster theory, is diagrammatically disconnected in general. This means that the number of non-negligible elements in the Λ-tensor grows faster than linearly with the number of calculated particles. At a formal level, when evaluating the gradients of the coupled-cluster energy, this could prevent obtaining a linear scaling of the operational cost with respect to the number of correlated particles. It is shown that in ground/excited-state coupled-cluster calculations, based on localized orbitals, the disconnected part of the Λ-tensor, as well as the disconnected part of the left-hand excited-state eigenvector, can be ignored, thus justifying the use of standard screening techniques employed in linear-scaling schemes.

Keywords:

• coupled cluster
• linear scaling
• analytic gradients
• connectivity
• tensor