Information Channels in Orbital Resolution

The system electron density p(r) and hence the one-electron probability distribution p(r) = p(r)/N, that is, the density per electron or the shape factor of p, are determined by the first-order density matrix y in the AO representation, also called the charge and bond order (CBO) matrix, 

The CBO matrix reflects the promoted, valence state of AO in the molecule, with the diagonal elements measuring the effective electron occupations of the basis functions, yiii = Ni = Npi. The AO-probability vector in this state, p = pi = Ni/N], groups the probabilities of the basis functions being occupied in the molecule. 

The information system in the (condensed) orbital resolution involves the AO events / in its input a = xi] and output b = / . It represents the effective promotion of these basis functions in the molecule via the probability/information scattering described by the conditional probabilities of AO outputs given AO inputs, with the input (row) and output (column) indices, respectively. In the one-electron approach [46-48], these AO-communication connections P(XjlXi) = P(j i) result from the appropriately generalized superposition principle of quantum mechanics [51], 

In the open-shell (os) case [48] one partitions the CBO matrix into contributions originating from the closed-shell (doubly occupied) MO pcs and the open-shell (singly occupied) MO p° , p = ( cs, os)  

Roman F. Nalewajski, Dariusz Szczepanik, and Janusz Mrozek 

---

R.F. Nalewajski, Entropic bond indices from molecular information channels in orbital resolution Excited configurations, Mol. Phys. 104 (2006) 3339. 

---