Fifth Order Energy Components

2 Fifth order energy components. - The general fifth order term for the correlation energy expansion of the closed-shell system described in zero order by a single determinant is 

The numerator is a product of five matrix elements. Specifically, it takes the form 

The fifth order Hugenholtz diagrams were listed by Lyons, Moncrieff and Wilson.194 These authors generated the (symmetric) connectivity matrices for undirected Hugenholtz diagrams. Putting 

The element I / defines the number of undirected line segments between vertex 

The undirected Paldus-Wong diagrams provide the most compact representation of the fifth-order correlation energy terms. The connectivity matrices for the undirected Paldus-Wong diagrams are  

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Higher order energy components. - The higher order terms can be analyzed in much the same way as the fifth order terms. The levels of excitation which occur in fifth order may be represented schematically as follows ... 

S4 model, the Eglp energy component, Eq. (120), vanishes, since = 0. Thus, the entire fifth-order effect due to T4 can be estimated in this case by the contribution, Eq. (83), which, as mentioned earlier, appears in... 

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