Aspects of size extensivity in unitary group adapted multi-reference coupled cluster theories: the role of cumulant decomposition of spin-free reduced density matrices

Maitra, Rahul; Sinha, Debalina; Sen, Sangita; Mukherjee, Debashis

doi:10.1007/s00214-014-1522-5

Cited by 10 publications

(11 citation statements)

References 79 publications

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“…The connectivity of the g μ amplitudes is sufficient to ensure the size‐extensivity of the UGA‐SSMRPT2 theory unlike the UGA‐SSMRCC where the occurrence of density matrices in the projection equations, which are the working equations, necessitates the use of rather involved arguments to analytically prove size‐extensivity although this has been demonstrated . The connectivity of the g μ is well established and follows closely the proof presented for other state‐specific theories developed in our group …”

Section: Theorysupporting

confidence: 64%

“…Also,

{\overset{H}{true}}_{μ ν} = 〈 ϕ_{μ} | {\overset{true︹}{H e^{T_{ν}}}} | ϕ_{ν} 〉 = 〈 ϕ_{μ} | W_{μ ν} | ϕ_{ν} 〉

. For a detailed discussion on the various theoretical and computational issues of the UGA‐MRCC theories, we refer to our recent exhaustive papers …”

Section: Theorymentioning

confidence: 99%

“…One immediate advantage of this approach is the ease with which we can discern manifest size extensivity of the working equations. In a projection equation as is done in the UGA‐SSMRCC, either reduced density matrices (RDMs) or the corresponding cumulants of various ranks appear which makes the proof of size‐extensivity much more involved . The overall structure of the amplitude equations suggests in a natural manner the most appropriate choice of the multipartitioned unperturbed Hamiltonian.…”

Section: Summarizing Remarksmentioning

confidence: 99%

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Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications

Sen

Samanta

et al. 2015

J Comput Chem

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We present here a comprehensive account of the formulation and pilot applications of the second-order perturbative analogue of the recently proposed unitary group adapted state-specific multireference coupled cluster theory (UGA-SSMRCC), which we call as the UGA-SSMRPT2. We also discuss the essential similarities and differences between the UGA-SSMRPT2 and the allied SA-SSMRPT2. Our theory, like its parent UGA-SSMRCC formalism, is size-extensive. However, because of the noninvariance of the theory with respect to the transformation among the active orbitals, it requires the use of localized orbitals to ensure size-consistency. We have demonstrated the performance of the formalism with a set of pilot applications, exploring (a) the accuracy of the potential energy surface (PES) of a set of small prototypical difficult molecules in their various low-lying states, using natural, pseudocanonical and localized orbitals and compared the respective nonparallelity errors (NPE) and the mean average deviations (MAD) vis-a-vis the full CI results with the same basis; (b) the efficacy of localized active orbitals to ensure and demonstrate manifest size-consistency with respect to fragmentation. We found that natural orbitals lead to the best overall PES, as evidenced by the NPE and MAD values. The MRMP2 results for individual states and of the MCQDPT2 for multiple states displaying avoided curve crossings are uniformly poorer as compared with the UGA-SSMRPT2 results. The striking aspect of the size-consistency check is the complete insensitivity of the sum of fragment energies with given fragment spin-multiplicities, which are obtained as the asymptotic limit of super-molecules with different coupled spins.

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Section: Theorysupporting

confidence: 64%

“…Also,

{\overset{H}{true}}_{μ ν} = 〈 ϕ_{μ} | {\overset{true︹}{H e^{T_{ν}}}} | ϕ_{ν} 〉 = 〈 ϕ_{μ} | W_{μ ν} | ϕ_{ν} 〉

. For a detailed discussion on the various theoretical and computational issues of the UGA‐MRCC theories, we refer to our recent exhaustive papers …”

Section: Theorymentioning

confidence: 99%

Section: Summarizing Remarksmentioning

confidence: 99%

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Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications

Sen

Samanta

et al. 2015

J Comput Chem

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“…The latter approach involves the use of reduced density matrices (RDMs) in the working equations making them more complicated and the proof of the connectivity of the t-amplitudes and the consequent size-extensivity of the theory more difficult. However this has been achieved by Maitra et al 97 The former approach,…”

Section: Uga-ssmrpt2mentioning

confidence: 94%

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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“…Extensivity is always an issue to consider, especially for a CC theory. While the expressions reported above appear connected at first glance, spin cumulants represent a non trivial problem [44,45] and for this reason the analysis is put off to further study.…”

Section: Resultsmentioning

confidence: 99%

Ring coupled-cluster doubles correction to geminal wavefunctions

Szabados

Margócsy

2017

Molecular Physics

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A ring approximation in coupled cluster (CC) theory is worked out at the multi reference (MR) level. The underlying CC framework is based on generalized normal ordering and applies the corresponding generalized Wick-theorem. Contractions among cluster operators is avoided by adopting a normal ordered exponential Ansatz.The MR ring CC doubles (MR rCCD) theory is found to represent a companion to the previously introduced extended random phase approximation (ERPA). Equations for wavefunction parameters are derived in parallel and compared. Condition for the ground state consistent with ERPA is obtained. This paves the way towards comparison with the ERPA based correction to the Antisymmetrized Product of Strongly Orthogonal Geminal (APSG) reference, ERPA-APSG.

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Aspects of size extensivity in unitary group adapted multi-reference coupled cluster theories: the role of cumulant decomposition of spin-free reduced density matrices

Cited by 10 publications

References 79 publications

Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications

Unitary group adapted state specific multireference perturbation theory: Formulation and pilot applications

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

Ring coupled-cluster doubles correction to geminal wavefunctions

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