Analysis of the Tailored Coupled-Cluster Method in Quantum Chemistry

Abstract

In quantum chemistry, one of the most important challenges is the static correlation problem when solving the electronic Schrödinger equation for molecules in the Born-Oppenheimer approximation. In this article, we analyze the tailored coupled-cluster method (TCC), one particular and promising method for treating molecular electronic-structure problems with static correlation. The TCC method combines the single-reference coupled-cluster (CC) approach with an approximate reference calculation in a subspace [complete active space (CAS)] of the considered Hilbert space that covers the static correlation. A one-particle spectral gap assumption is introduced, separating the CAS from the remaining Hilbert space. This replaces the nonexisting or nearly nonexisting gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital usually encountered in standard single-reference quantum chemistry. The analysis covers, in particular, CC methods tailored by tensor-network states (TNS-TCC methods). The problem is formulated in a nonlinear functional analysis framework, and, under certain conditions such as the aforementioned gap, local uniqueness and existence are proved using Zarantonello's lemma. From the Aubin-Nitscheduality method, a quadratic error bound valid for TNS-TCC methods is derived, e.g., for lineartensor-network TCC schemes using the density matrix renormalization group method.Even if most molecules are single-reference systems in their equilibrium configuration, multireference character arises even in the simplest of chemical reactions, e.g., dissociation of N 2 . Yet, the static correlation problem is a long-lasting challenge in quantum chemistry. Many different MRCC approaches have been formulated to deal with the problem of static correlation. However, aside from formal difficulties and implementational complications, none of these methods have become a widely applicable tool. A review of different MRCC approaches is beyond the scope of this article, and we refer to Lyakh et al.[26] for a detailed description of the different benefits and disadvantages.We are here concerned with an MRCC method that is based on the single-reference methodology (also called an externally corrected ansatz): The tailored CC (TCC) method extends a precomputed solution for a chosen subsystem of the full system by including further electron correlations via CC theory. We refer to the subsystem as the complete active space (CAS) and to the remaining system as the external space. Given the single-reference CC method's major drawback, this subsystem needs to contain the static correlations. Consequently, the TCC method can be seen as a special type of an embedding method. Mathematically this corresponds to a division of excitation operators in two disjoint sub-algebras [19]. Nevertheless, in comparison with other "genuine" MRCC schemes, the TCC method suffers from the drawback that it is based on a single-reference theory and therewith introduces a certain bias towards a particular reference determinant....

Guaranteed convergence for a class of coupled-cluster methods based on Arponen's extended theory

“…Thus, a modified analysis of the ECC method that includes multireference assumptions, such as the steerable CAS-ext gap of Ref. [34], could potentially lead to a deeper understanding of how CC methods generally behave in the presence of static correlation.…”

“…Monotonicity is an important notion in connection with the local analysis of the CC method and its variations [23][24][25][26][27]34]. The use of monotonicity in the analysis of the standard CC method was introduced by Schneider and Rohwedder [25,27].…”

The Role of Relativistic Many-Body Theory in Electron Electric Dipole Moment Searches Using Cold Molecules

“…Relativistic coupled cluster theory is well suited for the calculations associated with eEDM searches mentioned above. It would be necessary to develop different variants of the theory for this purpose: normal CC method, the analytical derivative approach, ECCM [77,81], and tensor network tailored CC theory for open-shell molecules [82].…”

A state-specific multireference coupled-cluster method based on the bivariational principle

“…For an analysis of standard CC without the BIVP, see the works of Rohwedder and Schneider. 30,31 A key analysis tool for studying CC theory 3,[29][30][31][32][33] was that of local strong monotonicity 4 of the flipped gradient F :Ṽ ⊕ V →Ṽ ⊕ V given by…”