Standard CC theory

The determinant 0) plays key role in the CC theory. It is called the reference determinant and in the standard version of the CC theory this is the determinant used to generate all necessary excitations in the wave function. For this reason the standard CC theory is called the single reference theory. Also, in the standard implementation of the theory, the T operator includes only single and double excitations from 0) (the CCSD theory),... 

As the SSMRCC approach is based on the standard CC theory, it assumes the intermediate normalization of the wave function (3.13). Using this condition the equation for the energy can be written as ... 

The present overview is intended to give a brief introduction into CC theory, thereby focusing more on the needs of a computational chemist than on formal aspects. The basic theory of single-reference CC theory is presented together with a discussion of the computationally feasible approaches. Other important topics covered in the following are the treatment of high-spin open-shell systems, the calculation of molecular properties and the description of excited states within standard CC theory. Despite the necessarily brief presentation, emphasis will be laid on adequate discussion of recent developments in order to keep the reader informed about current research. All topics are supplemented by numerical examples which illustrate the performance and accuracy of the CC methods. 

The method of moments of coupled-cluster equations (MMCC) is extended to potential energy surfaces involving multiple bond breaking by developing the quasi-variational (QV) and quadratic (Q) variants of the MMCC theory. The QVMMCC and QMMCC methods are related to the extended CC (ECC) theory, in which products involving cluster operators and their deexcitation counterparts mimic the effects of higher-order clusters. The test calculations for N2 show that the QMMCC and ECC methods can provide spectacular improvements in the description of multiple bond breaking by the standard CC approaches. 

The main reason why existing MR CC methods as well as related MR MBPT cannot be considered as standard or routine methods is the fact that both theories suffer from the Intruder state problem or generally from the convergence problems. As is well known, both MR MBPT/CC theories are built on the concept of the effective Hamiltonian that acts in a relatively small model or reference space and provides us with energies of several states at the same time by diagonalization of the effective Hamiltonian. In order to warrant size-extensivity, both theories employ the complete model space formulations. Although conceptually simpler, the use of the complete model space makes the calculations rather... 

The single-reference coupled cluster (CC) theory [1-5] has become a standard computational tool for studying ground-state molecular properties [6-10]. The basic approximations, such as CCSD (coupled cluster singles and doubles approach) [11-15], and the noniterative CCSD[T] [16,17] and CCSD(T) [18] methods, in which the cleverly designed corrections due to... 

The coupled cluster (CC) method is actually related to both the perturbation (Section 5.4.2) and the Cl approaches (Section 5.4.3). Like perturbation theory, CC theory is connected to the linked cluster theorem (linked diagram theorem) [101], which proves that MP calculations are size-consistent (see below). Like standard Cl it expresses the correlated wavefunction as a sum of the HF ground state determinant and determinants representing the promotion of electrons from this into virtual MOs. As with the Mpller-Plesset equations, the derivation of the CC equations is complicated. The basic idea is to express the correlated wave-function Tasa sum of determinants by allowing a series of operators 7), 73,... to act on the HF wavefunction ... 

It can be easily verified that the stationarity of AfJ(E,T) with respect to E yields Eq. (226). In the exact (full CC) limit, the system of equations defined by Eq. (226) becomes equivalent to standard CC equations for T, Eq. (35), and AE(E,T) becomes identical to AE c [75]. It can be further demonstrated that the stationarity of AE(E, T) with respect to T yields (again, in the full CC limit) the lambda equation of the analytic gradient SRCC theory,... 

The need for the inclusion of higher-order effects increases with the degree of quasidegeneracy of the state considered. For this reason, much effort has been devoted to the formulation of the so-called MR MBPT [28-30]. Here, however, a number of ambiguities arises, which often limits the development of practical algorithms (c/, e.g. attempts to extend the so-called CAS-PT2 method, which is based on the complete active space self-consistent field (CAS SCF) reference, to higher than the second order). In fact, we shall see that the same problem manifests itself, even when extending the standard SR CC theory to the MR case. 

One of us [1] reviewed the situation of electron correlation a quarter of a century ago in a paper with the title electron correlation in the seventies [2]. At that time most quantum chemists did not care about electron correlation, and standard methods for the large scale treatment of electron correlation, like Mpller-Plesset (MP) perturbation theory or coupled-cluster (CC) theory were not yet available. However precursors of these methods such as lEPA (independent electron pair approximation) and CEPA (coupled-electron-pair approximation) had already been developped and were being used, mainly in research groups in Germany [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13]. 

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