Unconventional Aspects of Coupled-Cluster Theory

Kutzelnigg, Werner

doi:10.1007/978-90-481-2885-3_12

Cited by 18 publications

(15 citation statements)

References 111 publications

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“…This may be done since expanding (118), the term proportional to the highest power of ε i is w∈W P A w and must therefore vanish. Rather than Γ P it is convenient to use the…”

Section: B Sklyanin Summentioning

confidence: 99%

“…APSG has long been known to describe bond-breaking processes correctly. 40,41,[118][119][120][121][122][123][124][125][126][127][128][129] Variational APSG is equivalent to the Piris natural orbital functional PNOF5, 130,131 meaning that the APSG 2-RDM is expressible directly in terms of its 1-RDM elements. Recently, the PNOF7 functional [132][133][134][135][136][137] has shown convincing numerical results.…”

Section: Apsg: Sparsitymentioning

confidence: 99%

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Density Matrices of Seniority-Zero Geminal Wavefunctions

Moisset,

Fecteau,

Johnson

2022

Preprint

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Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analogue of Wick's theorem for fermions or bosons. This expression is in general intractable, but it is shown how it becomes feasible in three distinct ways for Richardson-Gaudin (RG) states, the antisymmetrized geminal power, and the antisymmetrized product of strongly-orthogonal geminals. Dissociation curves for hydrogen chains are computed with off-shell RG states and the antisymmetrized product of interacting geminals.Both are near exact suggesting that the incorrect results observed with ground state RG states are fixable using a different RG state.

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“…This may be done since expanding (118), the term proportional to the highest power of ε i is w∈W P A w and must therefore vanish. Rather than Γ P it is convenient to use the…”

Section: B Sklyanin Summentioning

confidence: 99%

Section: Apsg: Sparsitymentioning

confidence: 99%

Density Matrices of Seniority-Zero Geminal Wavefunctions

Moisset,

Fecteau,

Johnson

2022

Preprint

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“…The most general formulation of an n electron wave function Ψ, compatible with the separability theorem 1,8,9 is the exponential ansatz where W ) e S is the wave operator, Φ is a separable normalized reference function, e.g., a Slater determinant or an MC-SCF function, {Ξ µ } is a basis of particle-number conserving Fock space operators, e.g., of the type (1), and s µ is an expansion coefficients. The energy expectation value is then a i a ; a ij ab ; a ijk abc ; etc.…”

Section: General Formulationmentioning

confidence: 99%

An Alternative Hierarchy of Electron Correlation beyond the Electron Pair Approximation^†

Kutzelnigg¹

2010

J. Phys. Chem. A

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Starting from the Nakatsuji theorem, a hierarchy of approximations is considered that begins with traditional coupled cluster theory with singles and doubles (CCSD) and proceeds via the ansatz of semigeneralized singles and doubles (CCSGSD), with operators of the types a(ab)(ic) and a(ka)(ij) included, to the generalized singles and doubles (CCGSD) ansatz with the full basis {a(pq)(rs); a(p)(q)}, and if necessary, beyond. The simplest realization of CCSGSD is the constrained coupled cluster ansatz with singles, doubles, and triples (CCCSDT). It is related to traditional coupled cluster with singles, doubles, and triples (CCSDT), but it requires (for sufficiently large n) a smaller number of parameters of O(nm3) vs O(n3m3) in CCSDT, n being the number of electrons and m the size of the basis. A linear system of equations for the CCCD[T] approximation is derived and strategies toward its solution are discussed.

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“…We are not aware of any proposed cumulant parameterization for DCT that maintains this property, only an ambiguous remark. 34 Instead, Kutzelnigg and others 14 parameterized the DCT cumulant by unitary coupled cluster [35][36][37][38][39][40][41][42][43][44] amplitudes, for historical reasons 45 . The resulting orbital-optimized, unitary ansatz 14 is called OUDCT.…”

Section: Introductionmentioning

confidence: 99%

Cumulants as the Variables of Density Cumulant Theory: A Path to Hermitian Triples

Misiewicz,

Turney,

Schaefer

2021

Preprint

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We study the combination of orbital-optimized density cumulant theory and a new parameterization of the reduced density matrices in which the variables are the particlehole cumulant elements. We call this combination OλDCT. We find that this new ansatz solves problems identified in the previous unitary coupled cluster ansatz for density cumulant theory: the theory is now free of near-zero denominators between occupied and virtual blocks, can correctly describe the dissociation of H 2 , and is rigorously size-extensive. In addition, the new ansatz has fewer terms than the previous unitary ansatz, and the optimal orbitals delivered by the exact theory are the natural orbitals. Numerical studies on systems amenable to full configuration interaction show that the amplitudes from the previous ODC-12 method approximate the exact amplitudes predicted by this ansatz. Studies on equilibrium properties of diatomic molecules show that even with the new ansatz, it is necessary to include triples to improve the accuracy of the method compared to orbital optimized linearized coupled cluster doubles. With a simple iterative triples correction, OλDCT outperforms other orbital-optimized methods truncated at comparable levels in the amplitudes, as well as CCSD(T). By adding four more terms to the cumulant parameterization, OλDCT outperforms CCSDT while having the same O(V 5 O 3 ) scaling.

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Unconventional Aspects of Coupled-Cluster Theory

Cited by 18 publications

References 111 publications

Density Matrices of Seniority-Zero Geminal Wavefunctions

Density Matrices of Seniority-Zero Geminal Wavefunctions

An Alternative Hierarchy of Electron Correlation beyond the Electron Pair Approximation^†

Cumulants as the Variables of Density Cumulant Theory: A Path to Hermitian Triples

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Unconventional Aspects of Coupled-Cluster Theory

Cited by 18 publications

References 111 publications

Density Matrices of Seniority-Zero Geminal Wavefunctions

Density Matrices of Seniority-Zero Geminal Wavefunctions

An Alternative Hierarchy of Electron Correlation beyond the Electron Pair Approximation†

Cumulants as the Variables of Density Cumulant Theory: A Path to Hermitian Triples

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Product

Resources

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An Alternative Hierarchy of Electron Correlation beyond the Electron Pair Approximation^†