Multiconfiguration VB theory. Orthogonal orbitals

To formulate the algorithm, we first recognize that, whereas a single label K was sufficient to characterize the CFs in (7.2.2) and (7.4.1), a second label will now be required to indicate the orbital configuration. The general CF will be written 

The matrix element (7.5.3) is non-zero only if there are no more than two E-chains, and then reduces to 

The -coefficients have the value unity within a configuration (Ip = kp, all p), while more generally 

The sums in (7.5.6) consequently include only terms that contain 0, 1 or 2 

The relative positions of points i, j in the superposition pattern are indicated in the two central columns and Pii=p,Pj, where the parity factor p, = l is assigned by giving +1 to an arbitrary position in an island, or to an end point in a chain, and then proceeding along the sequence giving 1 to alternate positions. For E-chains, the endpoint chosen is the one where the arrow points into the chain. 

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