State‐specific multireference coupled‐cluster theory

Köhn, Andreas; Hanauer, Matthias; Mück, Leonie Anna; Jagau, Thomas-C.; Gauß, Jürgen

doi:10.1002/wcms.1120

Cited by 128 publications

(108 citation statements)

References 152 publications

(241 reference statements)

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“…[21][22][23] Analogues of these methods for multireference problems, such as multireference perturbation theory, [24][25][26][27][28][29] multireference configuration interaction, [30][31][32][33] and multireference coupled cluster and canonical transformation [34][35][36][37][38][39][40][41][42][43][44] theories have also been formulated. However, all of these multireference formulations are algebraically more opaque and computationally much more expensive than their singlereference counterparts.…”

Section: Introductionmentioning

confidence: 99%

A transformed framework for dynamic correlation in multireference problems

Sokolov

Chan

2015

The Journal of Chemical Physics

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We describe how multireference dynamic correlation theories can be naturally obtained as singlereference correlation theories in a canonically transformed frame. Such canonically transformed correlation theories are very simple and involve identical expressions to their single-reference counterparts. The corresponding excitations involve quasiparticles rather than the bare particles of the system. High-order density matrices (or their approximations) and the numerical metric instabilities common to multireference correlation theories do not appear. As an example, we formulate the Bogoliubov canonically transformed version of second-order Møller-Plesset perturbation theory and demonstrate its performance in H 2 , H 2 O, N 2 , and BeH 2 bond dissociation. C 2015 AIP Publishing LLC. [http://dx

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Section: Introductionmentioning

confidence: 99%

A transformed framework for dynamic correlation in multireference problems

Sokolov

Chan

2015

The Journal of Chemical Physics

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“…In such cases, higher excitation amplitudes can no longer be approximated by clusters of lower excitation amplitudes. In this respect, many authors have attempted to generalize CC to the multi‐reference (MR) regime …”

Section: Introductionmentioning

confidence: 99%

“…In this respect, many authors have attempted to generalize CC to the multi-reference (MR) regime. [1,2] A different means of treating static correlation has recently emerged in the framework of symmetry-breaking and restoration. At the mean-field level, spin-projected unrestricted HF (SUHF) provides a valuable multi-configuration wave function because of the many-body structure of a spin-projection operator, [3,4] as is clear from the operator proposed by Löwdin in his pioneering work, [5]…”

Section: Introductionmentioning

confidence: 99%

Extending spin‐symmetry projected coupled‐cluster to large model spaces using an iterative null‐space projection technique

Tsuchimochi

Ten‐no

2018

J Comput Chem

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Recently, we introduced an orbital‐invariant approximate coupled‐cluster (CC) method in the spin‐projection manifold. The multi‐determinantal property of spin‐projection means that the parametrization in the spin‐extended CC (ECC) ansatz is nonorthogonal and overcomplete. Therefore, the linear dependencies must be removed by an orthogonalization procedure to obtain meaningful solutions. Multi‐reference methods often achieve this by diagonalizing a metric of the equation system, but this is not feasible with ECC because of the enormous size of the metric, a consequence of the incomplete active space of the spin‐projected Hartree–Fock reference. As a result, the applicability of ECC has been limited to small benchmark systems, for which the ansatz was shown to be superior to the configuration interaction and linearized approximations. In this article, we provide a solution to this problem that completely avoids the metric diagonalization by iteratively projecting out its null‐space from the working equations. As the additional computational cost required for this iterative projection is only marginal, it greatly expands the application range of ECC. We demonstrate the potential of approximate ECC by studying the complete basis set limit of F2 and transition metal complexes such as NiO, Mn2, and [Cu2O2]2+, which have all been hindered by the prohibitively large metric size. We also identify the potential inadequacy of the molecular orbitals given by spin‐projected Hartree–Fock in some cases, and propose possible solutions. © 2018 Wiley Periodicals, Inc.

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“…We instead quote here pertinent references for comprehensive reviews on the recent developments of the various MRCCs. 4,[88][89][90][91][92] We choose UGA-SSMRPT2 as a prototype for a size-extensive non-invariant MRPT theory, because in our opinion it is structurally the simplest perturbation theory which is rigorously sizeextensive and is also spin-free. Since it is non-invariant with respect to transformation among active orbitals, localized active orbitals have to be used to study size-consistency numerically.…”

Section: Introductionmentioning

confidence: 99%

Aspects of Size-Consistency of Orbitally Noninvariant Size-Extensive Multireference Perturbation Theories: A Case Study Using UGA-SSMRPT2 as a Prototype

Sen

Mukherjee

2015

J. Chem. Theory Comput.

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Profiling a potential energy surface (PES), all the way to dissociate a molecular state into particular fragments and to display real or avoided crossings, requires a multireference description and the maintenance of size-consistency. The many body methods, which suit this purpose, should thus be size-extensive. Size-extensive theories, which are invariant with respect to transformation among active orbitals are, in principle, size-consistent. Relatively cheaper size-extensive theories, which do not possess this invariance, can still be size-consistent if the active orbitals are localized on the asymptotic fragments. Such methods, if perturbative in nature, require the use of an unperturbed Hamiltonian, which has orbital invariance with respect to the transformation within active, core, and virtual orbitals. The principal focus of this paper is to numerically realize size-consistency with localized active orbitals using our recently developed orbitally noninvariant Unitary Group Adapted State Specific Multireference second order Perturbation Theory (UGA-SSMRPT2) as a prototype method. Our findings expose certain generic potential pitfalls of size-extensive but orbitally noninvariant MRPT theories, which are mostly related to the inability of reaching proper localized active orbitals in the fragments due to the artifacts of the orbital generation procedure. Despite the invariance of the zeroth order CAS function, lack of invariance of the MRPT itself then leads to size-inconsistency. In particular, reaching symmetry broken fragment active orbitals is an issue of concern where suitable state-averaging might ameliorate the problem, but then one has to abandon full orbital optimization. Additionally, there can be situations where the orbitals of the fragment reached as an asymptote of the supermolecule are not the same as those obtained from the optimization of the fragments individually and will require additional transformation. Moreover, for a certain PES, one may either abandon the use of optimized orbitals for that state to preserve proper symmetry and degeneracy in the fragment orbitals or be satisfied with the use of optimized orbitals, which generate broken symmetric orbitals in the fragmentation limit. All these pathologies are illustrated using the PES of various electronic states of multiply bonded systems like N2, C2H2, HCN, C2, and O2. Subject to such proviso, the UGA-SSMRPT2 turns out to be an excellent theory for studying the PES leading to fragmentation of strongly correlated systems satisfying the requirements of size-consistency with localized active orbitals. An unexpected spin-off of our studies is the realization that the size-inextensive MRMP2, which bears a close structural similarity with our theory, might under certain situations display size-consistency. We analyze this feature concretely in our paper. Our studies may serve as a benchmark for monitoring numerically the size-consistency of any state specific multireference theory which is size-extensive but not invariant with respect to trans...

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State‐specific multireference coupled‐cluster theory

Cited by 128 publications

References 152 publications

A transformed framework for dynamic correlation in multireference problems

A transformed framework for dynamic correlation in multireference problems

Extending spin‐symmetry projected coupled‐cluster to large model spaces using an iterative null‐space projection technique

Aspects of Size-Consistency of Orbitally Noninvariant Size-Extensive Multireference Perturbation Theories: A Case Study Using UGA-SSMRPT2 as a Prototype

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