Use of the bond-projected superposition principle in determining the conditional probabilities of orbital events in molecular fragments

The problem of defining and determining the multi-conditional probabilities of many-orbital events in the chemical bond system of a molecule is addressed anew within theoretical framework of the one-determinantal orbital representation of molecular electronic structure. Its solution is vital for determining the information-theoretic indices of bond couplings between molecular fragments or the reactant/product subsystems in chemical reactions. The superposition principle of quantum mechanics, appropriately projected into the occupied subspace of molecular orbitals, is used to condition the atomic orbitals or general basis functions of the self-consistent-field calculations. The conditional probabilities between the subspaces of basis functions (atomic orbitals) are derived from an appropriate generalization of the bond-projected superposition principle. They are then used to define the triply-conditional probabilities, relating one conditional event to another. The resulting expression is shown to satisfy the relevant non-negativity and symmetry requirements. It is applied to probe the pi-bond coupling in butadiene and benzene.