Orbital-optimized coupled-cluster model

Chapter 13 discusses coupled-cluster theory. Important concepts such as connected and disconnected clusters, the exponential ansatz, and size-extensivity are discussed the Unked and unlinked equations of coupled-clustCT theory are compared and the optimization of the wave function is described. Brueckner theory and orbital-optimized coupled-cluster theory are also discussed, as are the coupled-cluster variational Lagrangian and the equation-of-motion coupled-cluster model. A large section is devoted to the coupled-cluster singles-and-doubles (CCSD) model, whose working equations are derived in detail. A discussion of a spin-restricted open-shell formalism concludes the chapter. 

In OCC and BCC theories, the wave function has the form of a standard coupled-cluster wave function with vanishing singles amplitudes. However, unlike standard coupled-cluster theory, where the orbitals are determined in a separate optimization of the reference state HF), the OCC and BCC orbitals are determined simultaneously with the optimization of the cluster amplitudes, making them more suitable for the description of correlation, in a manner reminiscent of MCSCF theory. In practice, the differences between the standard coupled-cluster wave functions and the BCC and OCC wave functions are small, except in systems characterized by Hartree-Fock singlet instabilities such as the allyl radical in Section 10.10.6. In such cases, the Harlree—Fock instability makes the standard approach unsuitable - the BCC and OCC models, by contrast, suffer from no such instabilities. 

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