INDEX coupled-cluster approaches

The preceding step to both MP2 and coupled-cluster calculations is to solve the Hartree-Fock equations. The standard approach is, of course, to solve the equations in a basis set expansion (Roothaan-Hall method), using atom-centered basis functions. This set of basis functions is used to expand the molecular orbitals and we will call it orbital basis set (OBS). It spans the computational (finite) orbital space. Occupied spin orbitals will be denoted (pi and virtual (unoccupied) spin orbitals pa- In order to address the terms that miss in a finite OBS expansion, the set of virtual spin orbitals in a formally complete space is introduced, pa- If we exclude from this space all those orbitals which can be represented by the OBS, we obtain the complementary space, with orbitals denoted cp i. The subdivision of the orbital space and the index conventions are summarized in the left part of Fig. 2. 

Here, Xni l) denotes the harmonic oscillator wave-functions, (pa(r) and (pb(r) correspond to the states of electrons localized on a and b ions, the index v numbers the hybrid cluster states in the molecular field. It should be noted that, within the scope of the adopted approach, the quantum properties of the vibronic states in a self-consistent field are taken into account. Therefore, it is reasonable to call the proposed approximation quasidynamical. The vibronic states obtained within the scope of the quasidynamical approach are hybrid, i.e. retaining the quantum properties of both electronic and vibrational states. In the case of strong vibronic coupling, i.e. in the case of adiabatic potentials possessing deep minima both the... 

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