Configuration interaction matrix elements

The energy of this state is denoted by E dct- Based on the singlet GS, CT, MMCT, and DCT states and taking into account the respective configuration interaction matrix elements, the VBCI determinants for the and states are given by... 

The theorem that states that there is no nonvanishing configuration interaction matrix elements between the ground state determinantal wavefunction and those determinants resulting from the excitation of one electron into an empty orbital of the initial SCF calculation. 

The interaction of the various configurations leads to sigma bond formation and this can be pictorialized by reference to the one electron interaction matrix elements responsible for mixing of the various configurations. Typical examples are shown below. 

Paraphrasing the words of Ceulemans the special configurational symmetry of the half-filled shell also affects the interaction matrix elements. In the case of a one-electron Hermitian operator Tim > one has the following [7] ... 

The interaction occurs between half-filled shell states K) and IL) which possess different parities with respect to CL, ttk and ttl, respectively. This implies that necessarily the configurations are different, i.e., I A") lL), and also that the product of parities ttkttl has the value — 1. The hypothesis that Tt% is antisymmetric under time reversal is represented in equation (32) by setting thm = —1. It follows that the interaction matrix element (LlH lK) must vanish if these criteria are met. 

Energies of terms by tensor operators The formulas for evaluating the electrostatic interaction matrix elements within a two electron configuration are given by... 

If the perimeter is uncharged, n = 4N + 2 and the configurations d>j and I>4 belong to the same irreducible representation b = e ,2 — e ,2 of the point group C . They differ in two spin orbitals and therefore interact only through the electron repulsion part iU,j) of the Hamiltonian. Consequently, the one-electron model fails and first-order configuration interaction has to be taken into account. f Q = , f d>4> is the interaction matrix element between configurations ] and d>4, the Cl matrix reads... 

T is the interaction matrix element between the configurations contributing to the ground-state wave-function, and A is the energy difference between the two configurations, as shown in Fig. 6C-a. 

Fig. 4 Structure of the configuration interaction matrix for an SD expansion for the ground state of Be including VV and CV correlation. White regions represent regions where matrix elements...

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