Linear coupled-cluster approximation

Coupled—Pair Functional (ACPF) and Coupled Electron Pair Approximation (CEPA). The simplest form of CEPA, CEPA-0, is also known as Linear Coupled Cluster Doubles (LCCD). 

Extending the structure of the wave function is not the only way of improving the APSG approximation. In our laboratory [109, 107, 108], we proposed the biorthogonal formulation to take care of intergeminal overlap effects, and derived simple formulae to account for delocalization and dispersion interactions using either perturbation theory or a linearized coupled-cluster-type ansatz with the APSG reference state. 

Approximate Coupled Cluster Methods Combined Reduced Multireference and Almost-Linear Coupled Cluster Methods with Singles and Doubles ... 

Two relevant topics have been ignored completely in this short chapter the treatment of electron correlation with more sophisticated methods than DFT (that remains unsatisfactory from many points of view) and the related subject of excited states. Wave function-based methods for the calculation of electron correlation, like the perturbative Moller-Plesset (MP) expansion or the coupled cluster approximation, have registered an impressive advancement in the molecular context. The computational cost increases with the molecular size (as the fifth power in the most favorable cases), especially for molecules with low symmetry. That increase was the main disadvantage of these electron correlation methods, and it limited their application to tiny molecules. This scaling problem has been improved dramatically by modern reformulation of the theory by localized molecular orbitals, and now a much more favorable scaling is possible with the appropriate approximations. Linear scaling with such low prefactors has been achieved with MP schemes that the... 

MP) perturbation theory, linearized coupled cluster and multiconfigurational self-consistent field (MCSCF) wavefunctions are commonly employed as approximate reference states in polarization propagator approximations and will be discussed in Sections 10.3 and 10.4. 

Sattelmeyer KW, Stanton JF, Olsen J, Gauss J (2001) A comparison of excited state properties for iterative approximate triples linear response coupled cluster method. Chem Phys Lett 347 499-504. 

Every term in the coupled cluster amplitude equations that is nonlinear in T may be factored into linear components. As a result, each step of the iterative solution of the CCSD equations scales at worst as ca. 0(X ) (where X is the number of molecular orbitals). The full CCSDT method in which all Tycon-taining terms are included requires an iterative 0(X ) algorithm, whereas the CCSD(T) method, which is designed to approximate CCSDT, requires a noniterative O(X ) algorithm. The inclusion of all T4 clusters in the CCSDTQ method scales as... 

The ab initio HF calculations reported below have been performed with the GAUSSIAN 76 [26] program package. The atomic basis sets applied are a minimal (STO-3G [26]) one, a split valence (6-31G [26]) one, a split-valence one plus a set of five d-functions on carbon (6-31G [26]), and one with an additional set of p-functions on hydrogen (6-31G [26]). The correlation energy has been computed using Mpller-Plesset many body perturbation theory of second order (MP2) [27], the linear approximation of Coupled Cluster Doubles theory (L-CCD)... 

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