Density matrix structure for saturated molecules

Conclusion

The existence of a common Hamiltonian matrix structure for saturated systems results in common structural properties of the density matrices for the whole class of molecules, such as the zero occupation of AO in the first approximation, the density matrix perturbations due to a heteroatom, etc. This fact can be taken as a quantum-mechanical foundation for viewing saturated molecules as a separate class of compounds. The endowment of this system with the transferability of electronic structure properties, relative to atoms and bonds, to high accuracy, within the framework of the effective Hamiltonian method follows from an analysis of the general expressions for the density matrix elements. The transferability of the saturated system Hamiltonian matrix elements requisite for this is supported by a comparison among the self-consistent Fock matrix elements of various hydrocarbons in a localized orbital basis [9]. Independently of the detailed structure of the actual molecules, the influence of a heteroatom on the electron density distribution in saturated systems dies off quickly with distance from the heteroatom. From an analysis of expressions for the nondiagonal elements of the density matrix corresponding to nonneighboring AO we establish a connection between the degree of electron localization in saturated systems and the size or certain Hamiltonian matrix elements.

There is a consequent analogy between saturated and alternatively conjugated hydrocarbons, which, starting from the common structure of the Hamiltonians, also leads to common properties of the density matrices [14]. However, the study of the influence of heteroatoms on the density matrices in these systems by means of perturbation theory is complicated by the dependence of the matrix N(4) on the molecular structure, which makes it necessary to introduce highly simplified approaches for the solution of Eq. (2) [8]. Therefore, for alternating hydrocarbons we have succeeded in establishing only the sign of the orbital — orbital polarizability (alternating polarity theorem [14]), while, as for saturated systems, the equality N=1 permits an analytic expression for the polarizability.