Coupled Cluster Methods
The Coupled Cluster (CC) Approach
The CI approach for recovering the correlation energy was introduced in detail in Sections 2.2 and 2.3 because of its importance as the matrix mechanics solution of the molecular wave equation and its relation to the MCSCF methods which will consume the next chapter, but it is not the only, or even the best, approach available for determining the correlation energy. As mentioned in Section 2.1, coupled cluster (CC) methods form another popular approach to the problem of constructing correlated wave functions. CC theory has been employed for decades in the physcics commumity, particularly in the area of nuclear physics, but it took a while to find its niche in quantum chemisty due to both its mathematical and theoretical complexity. It was originally introduced into the quantum chemistry community by Cízek and Paldus in the late 1960's.[17,18,19] These early formulations used Feynman-like diagrams and the notation of second quantization to aid in the derivation of programmable CC equations. While both Feynman diagrams and second quantization were familiar to physicists of the period, these two concepts were alien to quantum chemists, and it was not until Hurley[20] presented a derivation of CC theory in terms accessible to chemists that it began to grow in popularity. Despite Huley's derivation, the use of second quantization and diagramatic theory is still beneficial in the efficient derivation of CC equations. The use of these efficient derivation tools is so important to CC theory because, unlike CI theory in which the core problem is the diagonalization of the Hamiltonian matrix with elements given by Slater's rules and in which indvidiual methods only differ in the basis functions used to construct this matrix, standard CC theory requires the iterative solution of algebraic equations which must be rederived with each change in method. Because of the complexity of CC theory, only the basics will be covered in the next few sections, and the reader is referred to an excellent introductory article by Crawford and Shaefer for additional information.[21]