Assessing the Accuracy of Tailored Coupled Cluster Methods Corrected by Electronic Wave Functions of Polynomial Cost

Abstract

Tailored coupled cluster theory represents a computationally inexpensive way to describe static and dynamical electron correlation effects. In this work, we scrutinize the performance of various coupled cluster methods tailored by electronic wave functions of polynomial cost. Specifically, we focus on frozen-pair coupled cluster (fpCC) methods, which are tailored by pair-coupled cluster doubles (pCCD), and coupled cluster theory tailored by matrix product state wave functions optimized by the density matrix renormalization group (DMRG) algorithm. As test system, we selected a set of various smalland medium-sized molecules containing diatomics (N 2 , F 2 , C 2 , CN + , CO, BN, BO + , and Cr 2 ) and molecules (ammonia, ethylene, cyclobutadiene, benzene, hydrogen chains, rings, and cuboids) for which the conventional single-reference coupled cluster singles and doubles (CCSD) method is not able to produce accurate results for spectroscopic constants, potential energy surfaces, and barrier heights. Most importantly, DMRG-tailored and pCCD-tailored approaches yield similar errors in spectroscopic constants and potential energy surfaces compared to accurate theoretical and/or experimental reference data. Although fpCC methods provide a reliable description for the dissociation pathway of molecules featuring single and quadruple bonds, they fail in the description of triple or hextuple bond-breaking processes or avoided crossing regions.

Resolving the π-assisted U–N σf-bond formation using quantum information theory

“…A coupled-cluster correction can be applied on top of a pCCD reference function using the tCC formalism, which has been introduced as the frozen-pair coupled-cluster (fpCC) model. 32,36 Most frequently, fpCC is restricted to include at most double excitations (in addition to single excitations), resulting in the fpCCD and fpCCSD flavours with the following ansatz for the latterwhere T̂ 1 and T̂ 2 ′ = T̂ 2 − T̂ pCCD 2 are restricted to contain electron singles and broken-pair double excitations. The fpCC ansatz can also be linearized.…”

“…In general, fpCC and its linearized version fpLCC yield statistically similar relative energies and energy-derived properties for molecules containing main-group elements. 36 Because of its linearized nature, fpLCC may, however, suffer from convergence difficulties and yield potential energy surfaces containing divergencies and poles. 36 Including non-linear terms in the coupled-cluster equations remedies these failures.…”

“…16 Recent numerical studies demonstrate that tailored coupledcluster methods [17][18][19][20] combined with geminal-based approaches [21][22][23][24][25][26][27][28][29][30][31] encapsulate strong and weak electron correlation effects. [32][33][34][35][36] With solely single and double excitations in the tailored coupled cluster (tCCSD) formalism, it is possible to accurately model the electronic structures and bond-breaking processes of diradicals, hydrogen structures, and molecules containing first-row elements. 36 The good performance of geminal-tailored coupled-cluster theory motivates us to target more challenging systems that feature numerous (quasi-) degenerate one-particle states like actinide-containing molecules.…”

“…Recently, coupled-cluster wave functions tailored by active space approaches gained in popularity, including, for instance, the complete active space (CAS) configuration interaction method, 17,20 the CAS self-consistent-field (SCF) approach, 18,38 and the density matrix renormalization group algorithm (DMRG). 36,[39][40][41][42] However, defining active orbital spaces becomes difficult when the number and type of correlated orbitals change along the reaction pathway. [43][44][45][46] Such a situation is encountered in the symmetric dissociation of the U-O bond in the uranyl cation.…”

“…Furthermore, we can improve the accuracy of pCCD a posteriori using density functional approximations, 57,62,63 perturbation theory, [64][65][66] or coupledcluster corrections. 32,34,36 Recent numerical studies 32,34,36,65 suggest that coupled-cluster corrections yield the smallest errors with respect to MRCI, CCSD(T), or CR-CC(2,3) reference data. A coupled-cluster correction can be applied on top of a pCCD reference function using the tCC formalism, which has been introduced as the frozen-pair coupled-cluster (fpCC) model.…”