Coupled Cluster Method with Single and Double Excitations Tailored by Matrix Product State Wave Functions

Abstract

In the last decade, the quantum chemical version of the density matrix renormalization group (DMRG) method has established itself as the method of choice for calculations of strongly correlated molecular systems. Despite its favourable scaling, it is in practice not suitable for computations of dynamic correlation. We present a novel method for accurate "post-DMRG" treatment of dynamic correlation based on the tailored coupled cluster (CC) theory in which the DMRG method is responsible for the proper description of non-dynamic correlation, whereas dynamic correlation is incorporated through the framework of the CC theory. We illustrate the potential of this method on prominent multireference systems, in particular N2, Cr2 molecules and also oxo-Mn(Salen) for which we have performed the first "post-DMRG" computations in order to shed light on the energy ordering of the lowest spin states.The coupled cluster (CC) approach, introduced to quantum chemistry (QC) by Čížek 1 , is one of the most accurate ab initio methods for the treatment of dynamic electron correlation. The advantages of this scheme include a compact description of the wave function, size-extensivity, invariance to orbital rotations together with a systematic hierarchy of approximations converging towards the full configuration interaction (FCI) limit 2 . Despite the great success of QC and in particular the CC methodology 3 in standard (single-reference) cases, the situation is dramatically different for strongly correlated (multireference) systems 4 , where the usual single-reference approaches become inaccurate or even completely break down. One category of methods designed for the treatment of such systems are multireference coupled cluster (MRCC) approaches, which generalize the CC exponential parameterization of the wave function 5-7 . Out of many formulations of MRCC theories, the class of methods relevant to this work are externally corrected CC, which extract information about the most important higher excitations or active space single and double excitations from an "external" calculation performed by a different method like complete active space self-consistent field (CASSCF) or multireference configuration interaction (MRCI) [8][9][10][11][12][13][14][15][16][17][18][19] . In this letter, we present a further development in this field concerning the tailored CC (TCC) method, where the information for external correction is obtained from a density matrix renormalization group (DMRG) calculation.DMRG is a very powerful approach suitable for treatment of strongly correlated systems originally developed in solid state physics [20][21][22] . The success of DMRG in this field motivated its application to QC problems [23][24][25][26][27][28][29][30][31] where it has proven the potential to outperform traditional QC methods for systems which require very large active spaces, like molecules containing several transition metal atoms 32,33 . Despite the favourable scaling of the DMRG method, it is computationally prohibitive to treat the dynamic cor...

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry

“…A different, computationally feasible approach suitable for strongly-correlated systems uses seniority-zero wavefunctions to describe the static/nondynamic part of the electron correlation en-ergy. [31][32][33][34][35][36][37][38][39][40][41][42][43][44] The missing dynamic electron correlation effects are included a posteriori in these ansätze using, for instance, many-body perturbation theory [45][46][47], coupled-cluster theory [48][49][50][51][52], extended random phase approximation [53], and density functional theory (DFT) corrections [54,55].…”

Quantification of electron correlation effects: Quantum Information Theory vs Method of Increments

“…More elaborate methods to consider both kinds of correlation are available but not considered here. For example, DMRG and coupled cluster are combined in the DMRG‐TCCSD method. Expanding in terms of occupied orbitals does yield good convergence already at the two‐orbital increment level, while the virtual orbital expansion requires three‐orbital increments.…”

“…More elaborate methods to consider both kinds of correlation are available but not considered here. For example, DMRG and coupled cluster are combined in the DMRG-TCCSD [44] method. Expanding in terms of occupied orbitals does yield good convergence already at the two-orbital increment level, while the virtual orbital F I G U R E 3 Polyacetelene: Occupied orbital increments including dynamical correlations based on CCSD/cc-pVTZ calculations F I G U R E 4 One-orbital increments for the Be 6 ring at equilibrium distance (R = 2.2 Å) and dissociation limit (R = 3.5 Å) to the left and right, respectively.…”

Multi-reference Epstein–Nesbet perturbation theory with density matrix renormalization group reference wavefunction

“…[4] However, electron correlation in realistic chemical systems is far more complicated than a restricted active space calculation can handle, and dynamic correlation outside the active space needs to be considered in order to get quantitative results. Over the last few years, a number of methods have been proposed to achieve this goal, including arXiv:1909.11954v1 [cond-mat.str-el] 26 Sep 2019 DMRG-canonical transformation (CT) [22], DMRG-complete active space secondorder perturbation theory (CASPT2) [23,24], DMRG-N -electron valence perturbation theory (NEVPT2) [25,26,27], DMRG-multi-reference configuration interaction (MRCI) [28,29,30], and DMRG-tailored coupled cluster (TCC) [31,32], matrix product state perturbation theory (MPSPT) [33,34]. Because of the too huge number of the reference configurations within a very large active space in DMRG calculation, usually internally contraction (ic) [35,36] or external contraction (ec) [37] approximations and/or a truncation for reference configurations have to be adopted in these post-DMRG dynamic correlation calculations.…”