Single reference unrestricted coupled cluster theory

1 Single reference unrestricted Coupled Cluster Theory 

The many-electron wave function for the groundstate g is parametrized via an exponential excitation operator 

To write these equations in a compact form permutation operators 

Jayatilaka and Lee [42]. The purpose of the intermediate quantities is not only to make the equations more compact but also serves to make the number of operations necessary in the algorithm as small as possible by ordering the different contraction steps in an optimal way. 

By correct ordering of the integrals and amplitudes (as matrix or vector in the pair indices) this step can be achieved by two calls to the BLAS [46] routines XCOPY and XAXPY (with X = S, D, C, Z, depending on machine precision and the appropriate algebra). By changing the order of the integrals the same technique can be used for the addition to the second term in the A-intermediate, Eq. (93)  

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If we except the Density Functional Theory and Coupled Clusters treatments (see, for example, reference [1] and references therein), the Configuration Interaction (Cl) and the Many-Body-Perturbation-Theory (MBPT) [2] approaches are the most widely-used methods to deal with the correlation problem in computational chemistry. The MBPT approach based on an HF-SCF (Hartree-Fock Self-Consistent Field) single reference taking RHF (Restricted Hartree-Fock) [3] or UHF (Unrestricted Hartree-Fock ) orbitals [4-6] has been particularly developed, at various order of perturbation n, leading to the widespread MPw or UMPw treatments when a Moller-Plesset (MP) partition of the electronic Hamiltonian is considered [7]. The implementation of such methods in various codes and the large distribution of some of them as black boxes make the MPn theories a common way for the non-specialist to tentatively include, with more or less relevancy, correlation effects in the calculations. 

The use of coupled-cluster (CC) wave functions within EOM theory for excitation energies, IPs and EAs has been developed [34,35] upon slightly different lines than outlined in Section 17.2. The CC wave function ansatz for Q,N) is written as usual in terms of an exponential operator acting on a single-determinant (e.g. unrestricted HF) reference function lO >... 

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