On the relation between the stabilization energy of a molecular system and the respective charge redistribution

A power series for total energies of molecules is derived using the previously-obtained series for the one-electron density matrix (DM) P [J. Mol. Struct. (Theochem) 343 (1995) 183] and the well-known relation between the energy E and the DM P (E = Trace (PH), where H is the Hamiltonian matrix). Two components are revealed within any correction Elk, of the new series so that one of them describes the kth order energy alteration due to charge redistribution and the another represents the analogous alteration owing to formation of additional bond orders vs. those of the system underlying the zero order Hamiltonian matrix. Molecular-structure-independent but k-dependent relations are established between the above-specified two components for k = 0, 1, 2, 3, 4. These relations allow the total correction E,, to be expressed in terms of charge transfer energy of respective order and thereby yield a general interdependence between the stabilization energy of a molecular system and the relevant charge redistribution for any number of participating orbitals and for any type of change in the structure of the system. Non-trivial consequences of this principal result of the paper also are revealed, in particular an inter-relation between the trans-effect of substituent studied recently [J. Mol. Struct. (Theochem) 532 (2000) 257] and the well-known gauche- and cis-effects describing the most stable conformations of substituted alkanes and alkenes, as well as of related heteroatom-containing compounds. (C) 2002 Elsevier Science B.V. All rights reserved.