Fock space single-reference

J. F. Stanton, R. J. Bartlett, and C. M. L. Rittby,/. Chem. Phys., 97,5560 (1992). Fock Space Multireference Coupled-Cluster Theory for General Single Determinant Reference Functions. 

This application of FSCC methods is a recent development, but along with its IP-EOM-CC twin, there are few such applications in the literature (8, 33), and they frequendy deal with symmetry-breaking problems. Comparisons are possible with single reference calculations, though as we shall see, the comparison of high-level SRCC calculations with Fock-space results does not always lead to an unambiguous determination of which approach is more reliable. Nevertheless, FSCC is very well suited to such applications and will undoubtedly... 

Because of its size-extensivity and faster convergence with respect to excitation level Coupled cluster theory has replaced Cl theory as the dominant approach in ab initio correlation calculations. Like MBPT the theory is still mainly applied in cases where the exact wave function is dominated by a single determinant, but multireference methods have been formulated and begin to enter mainstream quantum chemistry. Generalization of the algorithms to the relativistic no-pair level can again be achieved via the spinorbital formulation of the methods. I will first discuss the single reference method and then consider the Fock space method [40] that uses multi-reference wavefiinctions for ionized or excited states. 

Studies of rare earth or transition metal complexes often necessitate use of multireference wave functions. Among the Coupled Cluster type methods one can distinguish two main lines of approach to incorporate multireference character in the reference wave function. In the Hilbert space method one computes a single wave function for a particular state, while in the Fock space method one tries to obtain a manifold of states simultaneously. Since the latter method [40] has recently been implemented and applied in conjunction with the relativistic Hamiltonian [48-50] we will focus on this approach. 

Note that the terms G and J are proportional to the single-particle density Pij — (V l W) of secondary reference state extended states A,B). The choice of this reference wavefunction is arbitrary for the algebraic properties of the extended wave-function and, in particular, for the derivation of the Dyson equation. Here it obviously introduces differences and the freedom of choice can be used to change the static self energy. The only condition that tp) has to comply with in order to have the full formalism at hand, is to be cm eigenfunction of the Fock-space Hamiltonian H (c. f. Sec. IIC). The two obvious choices for y )... 

We consider for simplicity the single-reference case and start with theFock-space relation (34) and the corresponding Fock-space Bloch equation... 

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