The atomic orbitals (AO) contributed by bonded atoms of molecular systems emit or receive the “signals” of electronic allocations to these basis functions, thus acting as the signal source (input) or receiver (output), respectively, in the associated communication network. Each orbital simultaneously participates in both the through-space and through-bridge probability propagations: the former involve direct communications between two AO while the latter are realized indirectly via orbital intermediates. This work examines the interference effects of the amplitudes of molecular probability scatterings, and introduces the operator representation of AO communications. The eigenvalue problem of the associated Hermitian operator combining the forward and reverse information propagations defines the stationary modes (“standing” waves) of the molecular propagation of electronic conditional probabilities. The combined effect of interference between the multiple (direct and indirect) information scatterings, which establishes the stationary distribution of electronic probabilities, is probed. The wave-superposition principle for the conditional-probability amplitudes of the generalized through-bridge information propagation is linked to the idempotency relations of the system density matrix. It explicitly demonstrates that the resultant effect of the probability propagations involving bridges containing all basis functions, at arbitrary bridge orders indeed generates the (stationary) molecular distribution of conditional probabilities.
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