Valency interaction formula
The Valency Interaction Formula, or VIF provides a way of interpreting the molecular structural formula based on molecular orbital theory. Valency Points, VP, dots drawn on a page represent valence orbitals. Valency Interactions, VI, that connect the dots show interactions between the orbitals.
Chemical deductions are made from a VIF picture with the application of two pictorial rules. These are linear transformations applied to the quantum operator and preserve invariants crucial to the characterization of the molecules electronic properties, the numbers of bonding, non-bonding, and anti-bonding orbitals and/or the number of doubly, singly, and unoccupied valence orbitals. The two pictorial rules relate all picture with the same electronic properties as characterized by these invariants.
An through presentation of VIF is available through the open access journal symmetry. [1]
Two Pictorial Rules
The Multiplication Rule
The multiplication rule is based on matrix calculations, specifically the row multiplications that are allowed on such matrices. In matrix form, one can multiply an entire row by any non-zero number. Pictorially, this allows for any valency point in the VIF picture to be multiplied by any non-zero value. This allows for diagonalization of the matrix using the addition rule.
The Addition Rule
The addition rule is used in conjunction with the multiplication rule. Pictorally, line segments can be rotated and superimposed on other line segments, canceling the latter while retaining the former. This is used to simplify the picture and ultimately gives an indication of the number of electrons associated with the molecular orbitals (represented by the dots on either side of a given line segment). Mathematically, this results in adding to and canceling rows on a matrix. This matrix is the foundation of the operator that is used on the wave function.