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Coupled cluster (CC) is a numerical technique used for describing many-body systems. Its most common use is as one of several post-Hartree–Fock ab initio quantum chemistry methods in the field of computational chemistry. It essentially takes the basic Hartree–Fock molecular orbital method and constructs multi-electron wavefunctions using the exponential cluster operator to account for electron correlation. Some of the most accurate calculations for small to medium-sized molecules use this method. The method was initially developed by Fritz Coester and Hermann Kümmel in the 1950s for studying nuclear physics phenomena, but became more frequently used when in 1966 Jiři Čížek (and later together with Josef Paldus) reformulated the method for electron correlation in atoms and molecules. It is now one of the most prevalent methods in quantum chemistry that includes electronic correlation. CC theory is simply the perturbative variant of the Many Electron Theory (MET) of Oktay Sinanoğlu, which is the exact (and variational) solution of the many electron problem, so it was also called "Coupled Pair MET (CPMET)". J. Čížek used the correlation function of MET and used Goldstone type perturbation theory to get the energy expression while original MET was completely variational. Čížek first developed the Linear-CPMET and then generalized it to full CPMET in the same paper in 1966. He then also performed an application of it on benzene molecule with O. Sinanoğlu in the same year. Because MET is somewhat difficult to perform computationally, CC is simpler and thus, in today's computational chemistry, CC is the best variant of MET and gives highly accurate results in comparison to experiments.〔 and references therein〕 == Wavefunction ansatz == Coupled-cluster theory provides the exact solution to the time-independent Schrödinger equation : where is the Hamiltonian of the system, the exact wavefunction, and ''E'' the exact energy of the ground state. Coupled-cluster theory can also be used to obtain solutions for excited states using, for example, linear-response, equation-of-motion, state-universal multi-reference coupled cluster, or valence-universal multi-reference coupled cluster approaches. The wavefunction of the coupled-cluster theory is written as an exponential ansatz: :, where , the reference wave function, which is typically a Slater determinant constructed from Hartree–Fock molecular orbitals, though other wave functions such as Configuration interaction, Multi-configurational self-consistent field, or Brueckner orbitals can also be used. is the cluster operator which, when acting on , produces a linear combination of excited determinants from the reference wave function (see section below for greater detail). The choice of the exponential ansatz is opportune because (unlike other ansatzes, for example, configuration interaction) it guarantees the size extensivity of the solution. Size consistency in CC theory, also unlike other theories, does not depend on the size consistency of the reference wave function. This is easily seen, for example, in the single bond breaking of F when using a restricted Hartree-Fock (RHF) reference, which is not size consistent, at the CCSDT level of theory which provides an almost exact, full CI-quality, potential energy surface and does not dissociate the molecule into F and F ions, like the RHF wave function, but rather into two neutral F atoms. If one were to use, for example, the CCSD, CCSD(), or CCSD(T) levels of theory, they would not provide reasonable results for the bond breaking of F, with the latter two approaches providing unphysical potential energy surfaces, though this is for reasons other than just size consistency. A criticism of the method is that the conventional implementation employing the similarity-transformed Hamiltonian (see below) is not variational, though there are bi-variational and quasi-variational approaches that have been developed since the first implementations of the theory. While the above ansatz for the wave function itself has no natural truncation, however, for other properties, such as energy, there is a natural truncation when examining expectation values, which has its basis in the linked- and connected-cluster theorems, and thus does not suffer from issues such as lack of size extensivity, like the variational configuration interaction approach. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「coupled cluster」の詳細全文を読む スポンサード リンク
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