Full coupled cluster

Purvis G D III and Bartlett R J 1982 A full coupled-cluster singles and doubles... 

Purvis, G. D. and Bartlett, R. J., A full coupled-clusters single and double model The inclusion of disconnected triples, J. Chem. Phys. 76, 1910-1918 (1982). 

G. D. Purvis and R. J. Bartlett,. Chem. Phys., 76, 1910 (1982). A Full Coupled-Cluster Singles and Doubles Model The Inclusion of Disconnected Triples. 

M. R. Hoffmann and H. F. Schaefer, Adv. Quantum Chem., 18,207 (1986). A Full Coupled-Cluster Singles, Doubles, and Triples Model for the Description of Electron Correlation. 

A Full Coupled-Cluster Singles, Doubles, and Triples Model for the Description of... 

The present work details the derivation of a full coupled-cluster model, including single, double, and triple excitation operators. Second quantization and time-independent diagrams are used to facilitate the derivation the treatment of (diagram) degeneracy and permutational symmetry is adapted from time-dependent methods. Implicit formulas are presented in terms of products of one- and two-electron integrals, over (molecular) spin-orbitals and cluster coefficients. Final formulas are obtained that restrict random access requirements to rank 2 modified integrals and sequential access requirements to the rank 3 cluster coefficients. 

Again the terms to be included were based on a perturbation order argument.6,16 The contribution of connected triples was shown numerically to be not inconsequential in applications of perturbation theory.19,20 More recently, Purvis and Bartlett16 reported the equations and initial implementation of a full coupled-cluster singles and doubles model (CCSD) this theory includes all terms in the first five parentheses, C0-C4, of Eq. (6) except for Ti, r4, and T Ti. The inclusion of disconnected terms is known to enhance the numerical stability of the coupled equations.21,22... 

A formal similarity arises because both the scattering matrix in quantum electrodynamics and the wave operator in a full coupled-cluster method [cf. Equations (1) and (4)] are exponential operators. In Bogo-liubov s axiomatic formulation of the scattering matrix,29... 

Head-Gordon M, Pople JA, Frisch MJ (1988) Chem Phys Lett 153 503-506 Purvis GD, Bartlett RJ, (1982) A full coupled-cluster singles and doubles model the inelusion of disconnected triples. J Chem Phys 76 1910 1918. doi 10.1063/1.443164... 

Without truncation, the FCI and full coupled-cluster functions contain the same number of parameters since there is then one connected cluster amplitude for each determinant. In this special case, the Cl and coupled-cluster models provide linear and nonlinear parametrizations of the same state and there is then no obvious advantage in employing the more complicated exponential parametrization. The advantages of the cluster parametrization become apparent only upon tmncation and are related to the fact that, even at the truncated level, the coupled-cluster state contains contributions from all determinants in the FCI wave function, with weights obtained from the different excitation processes leading to the determinants. 

In a given orbital basis, the full coupled-cluster wave function satisfies the Schrbdinger equation... 

In the CCSD model, for example, the excited projection manifold comprises the fiill set of all singly and doubly excited determinants, giving rise to one equation (13.2.19) for each connected amplitude. For the full coupled-cluster wave function, the number of equations is equal to the number of determinants and the solution of the projected equations recovers the FCI wave function. The nonlinear equations (13.2.19) must be solved iteratively, substituting in eac iteration the coupled-cluster energy as calculated from (13.2.18). 

For the full coupled-cluster wave function, the equivalence of the equations (13.2.16) and (13.2.20) is trivial for truncated cluster expansions, on the other hand, the equivalence of the linked and unlinked forms of the amplitude equations is less obvious and requires special attention. First, the equivalence of the energy expressions (13.2.18) and (13.2.22) is easily established since for any choice of amplitudes... 

Let us consider the simultaneous solution of the Schrodinger and spin equations for high-spin open-shell states. The coupled-cluster wave function may be expressed in terms of a singledeterminant reference function with the excitation operators chosen to yield excitations from this reference state. The full coupled-cluster wave function, being equivalent to the FCI wave function in the same orbital basis, is a simultaneous eigenfunction of the Schrodinger equation and the spin equations ... 

The zero-order wave functions are the Hartree-Fock state and the excited determinants (14.3.3). In coupled-cluster perturbation theory (CCPT), we expand the full coupled-cluster wave function... 

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