Diagrams exclusion-principle-violating

This result evidently arises from a purely algebraic identity, and the fact that some of the diagrams included in the summation may be exclusion-principle violating diagrams (EPVDs), when the same index appears more than once at some given level, is of no consequence. 

There is a price to pay for the separability, or equivalently for the presence of only connected diagrams. Somewhat like in traditional many-body theory, one must be ready to accept so-caUed EPV (exclusion-principle violating) cumulants. Typical EPV cumulants are nonvanishing kk for k> n, while yj = 0 for k > n. 

For the sake of correctness, it is necessary to note that we disregarded such theoretically important concepts as the linked cluster (linked connected graph) theorem and the exclusion principle violating (EPV) diagrams. This is in accordance with our aim to maintain the practical nature of this review. The linked cluster theorem and EPV diagrams are of importance in the fourth and higher orders of the perturbation theory which, in our opinion, shall hardly be accessible to routine calculations in the foreseeable future. For detailed information on the linked cluster theorem and EPV diagrams see Refs.9,33,34,4a ... 

The sum over internal lines is unrestricted so (linked) exclusion principle violating (e-v38 or EPV27) terms are included in the sums. Note that either restricting sums to eliminate both unlinked and linked EPV diagrams or unrestricting summations and doing a simple cancellation of unlinked terms satisfies the Pauli exclusion principle.27... 

Only much later were we able to account for some of these difficulties [109-112] by developing methods that, under certain conditions, account for the T4 clusters. In cases when the projected UHF method provides the exact pair clusters, it can be shown [109] that the T4 contribution cancels the contribution from the non-linear terms representing the important exclusion-principle-violating (EPV) diagrams. Except for a numerical factor associated with the triplet-coupled pp-hh t2-amplitudes, this method—referred to as ACPQ or CCDQ —is identical to the ACCD approach that was developed independently by Dykstra s group [113-116]... 

None of the three arrangements violates the PauU exclusion principle, so we must determine which one will give the greatest stability. The answer is provided by Hand s rule," which states that the most stable arrangement of electrons in subshells is the one with the greatest number of parallel spins. The arrangement shown in (c) satisfies this condition. In both (a) and (b) the two spins cancel each other. Thus the orbital diagram for carbon is... 

Shown below are portions of orbital diagrams representing the ground-state electron configurations of certain elements. Which of them violate the Pauli exclusion principle Which of them violate Hund s rule ... 

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