Couple cluster methods wave operators

The coupled-cluster method (CCM) is based on the ansatz that an exact many-particle wave function can be written as an exponential cluster operator acting on an independent-particle function,... 

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... 

Paldus, elsewhere in this book, discusses that there is as yet no generally applicable, open-shell, size-extensive, coupled cluster method, and the same holds for open-shell S APT methods. Therefore, for the computation of potentials of open-shell van der Waals molecules one has the choice between CASSCF followed by a Davidson-corrected MRCl calculation of the interaction energy, or the single reference, high spin, method RCCSD(T). When the ground state of the open-shell monomer is indeed a high spin state, then RCCSD(T) is the method of choice. With regard to the latter method we recall that a major difficulty in open-shell systems is the adaptation of the wave function to the total spin operator S for the CCSD method a partial spin adaptation was published by Knowles et al. [219,220] who refer to their method as partially spin restricted . When non-iterative triple corrections [221] are included, the spin restricted CCSD(T) method, RCCSD(T), is obtained. 

This has been the traditional choice in perturbation theory. A more general ansatz is represented by the coupled-cluster method (CCM) of Kiimmel, Coester and co-workers [35]. In the CCM the wave operator is also defined in the Q-space. For a review of the CCM, see e.g. [33] or Lindgren s contribution in these proceedings. 

The CC (Coupled-Cluster) method is an attempt to find such an expansion of the wave function in terms of the Slater determinants, which would preserve size consistency. In this method the wave function for the electronic ground state is obtained as a result of the operation of the wave operator exp(f) on the Hartree-Fock function (this ensures size consistency). The wave operator exp(f) contains the cluster operator T, which is defined as the sum of the operators for the /-tuple excitations, 7) up to a certain maximum I = /max- Each fi operator is the sum of the operators each responsible for a particular l-tuple excitation multiplied by its amplitude t. The aim of the CC method is to find the t values, since they determine the wave function and energy. The method generates non-linear... 

The coupled cluster methods exploit an exponential ansatz for the wave operator. A chosen reference function o). is transformed into the exact wave function IS ), as follows ... 

In order to use wave-function-based methods to converge to the true solution of the Schrodinger equation, it is necessary to simultaneously use a high level of theory and a large basis set. Unfortunately, this approach is only feasible for calculations involving relatively small numbers of atoms because the computational expense associated with these calculations increases rapidly with the level of theory and the number of basis functions. For a basis set with N functions, for example, the computational expense of a conventional HF calculation typically requires N4 operations, while a conventional coupled-cluster calculation requires N7 operations. Advances have been made that improve the scaling of both FIF and post-HF calculations. Even with these improvements, however you can appreciate the problem with... 

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 ... 

R. A. Chiles and C. E. Dykstra,/. Chem. Phys., 74,4544 (1981). An Electron Pair Operator Approach to Coupled-Cluster Wave Functions. Application to He2, Bea, and Mg2 and Comparison with CEPA Methods. 

Chiles RA, Dykstra CE. An electron pair operator approach to coupled cluster wave functions. Applications to He2, Be2 and Mg2 and comparison with CEPA methods. J Chem Phys 1981 74 4544 1556. 

---