Single-reference CC theory

Let us recall that in the single-reference CC theory, the ground-state wave function, ) of an A/-electron system, described by the Hamiltonian H, is given by the following expression ... 

The single-reference CC theory is based on the exponential ansatz for the ground-state wave function,... 

The Cn-kij A) terms are easy to determine. The zero-body term, Cq a)i equals 1 the one-body term, C mA)-> equals Ti the two-body term, C2(mA), equals T2 + if rriA > 2 the three-body term, Cz rnA) equals riT2 + if rriA = 2 and Ts + T1T2 + if rriA > 3, etc. The coefficients, Eq. (27), define the generalized moments of CC equations (for a discussion of the relationship between the method of moments of Krylov [99] and the single-reference CC theory, see Ref. [100]). They are readily available for the basic CC approximations, such as CCSD (the rriA = 2 case). As pointed out in our original work [11,30], the generalized moments represent the most fundamental quantities... 

The above representation of the exact ground-state wave function is reminiscent of the exponential ansatz of the single-reference CC theory, Eq. (3). There is, however, a fundamental difference between Eqs. (124) and (3). The cluster operator T entering Eq. (3) is defined in terms of the excitation operators Eq. (6), where ii,..., in (ai,..., an) are the... 

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. 

We assume that the reader is familiar with basic concepts of CC theory, such as the exponential wave function ansatz defining all single-reference CC methods. However, for the consistency of this presentation, let us recall that the ground-state wave function associated with the CC method A has the form... 

In order to understand what quantities provided by the CC theory may be needed to recover the full Cl ground-state energy from the results of approximate CC calculations, such as CCSD, we should recall that the system of single-reference CC equations, Eq. (5), is formally obtained by inserting the exact CC wave function q/0) = e7 cl) into the electronic Schrodinger equation,... 

As mentioned in the Introduction, the renormalized (R) and completely renormalized (CR) CC approaches, which represent new classes of noniterative single-reference CC methods that are capable of removing the failing of the standard CCSD(T) and similar methods at larger internuclear separations, are based on the formalism of the method of moments of CC equations (MMCC) [11-13, 30-32,36, 75, 76]. Thus, we begin our description of the R-CC and CR-CC methods and their quadratic MMCC (QMMCC) extension for multiple bond breaking with a synopsis of the general MMCC theory. 

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