Fock space orbitals/sector

Equations for the Fock space coupled cluster method, including all single, double, and triple excitations (FSCCSDT) for ionization potentials [(0,1) sector], are presented in both operator and spin orbital form. Two approximations to the full FSCCSDT equations are described, one being the simplest perturbative inclusion of triple excitation effects, FSCCSD+T(3), and a second that indirectly incorporates certain higher-order effects, FSCCSD+T (3). 

In the Fock space coupled cluster method, the Hartree-Fock solution for an iV-electron state, 0), is used as the vacuum. The Fock space is divided into sectors, (m,n), according to how many electrons are added to and removed from 0). Thus, the vacuum is in the (0,0) sector, single ionizations are in the (0,1) sector, one-electron attached states are in (1,0), and (1,1) are single excitations relative to 0). The orbitals are also divided into active, which can change occupation, and inactive, for which the occupation is fixed. All possible occupations of the active orbitals in all possible sectors constitute the multireference space for the system. 

It may be shown that for the (0,1) sector of Fock-space, the values of the roots obtained by diagonalizing Hn s are independent of the active space used for the calculation. In other words, if two orbitals, a and b are taken as active, the resulting ionization potentials would be identical to those obtained from separate calculations with either a or 6 alone active. This is a very useful result because it means that we do not have to worry about choosing the right active space for a given calculation in order to get good results. However the proof of this invariance rests on the FSCC amplitudes and /7jv,eff satisfying the Fock-space Bloch equation 13. The approximate FSCCSDT methods described above do not satisfy Eq. 13, so the invariance is lost. 

Excitation energies of atomic barium and radium were calculated in 1996 using the Fock-space coupled cluster method [57]. The model space in the 2-electron sector included all states with two electrons in the 5d, 6s and 6p orbitals, except the 6p states inclusion of the latter led to intruder states and divergence, so that incomplete model spaces had to be employed. In the intermediate Hamiltonian approach all these states (including 6p ) were in Pm, Pi was defined by adding states with occupied 7s-10s, 7p-10p, 6d-... 

The structure of the model space P in the Fock-space method and of Pm and P in the intermediate Hamiltonian approach is shown in Table 2.4. All determinants constructed from the orbitals listed in the table constitute the relevant space. is a subspace of P in the IH-FSCC approach. Convergence difficulties of the FSCC formalism in sector (2) made it necessary to use an incomplete model space [62,63], moving certain determinants from P to Q. The IH calculations employ much larger P spaces, which are always complete (i.e., include all combinations of relevant orbitals). Orbital selection was determined primarily on the basis of orbital energies. 

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