Quantum-mechanical definition of atoms and their interactions in molecules

Assignments of indistinguishable electrons to particular atomic nuclei in a molecule are generally regarded as meaningless, as are associated definitions of fragment atomic and atomic-interaction operators. As a consequence, a generally agreed upon quantum-mechanical definition of a ``chemical bond'' between atoms in a molecule is largely absent. In the present report, a computationally-viable quantum-mechanical definition of chemical bonding between atoms in a molecule is presented based on the Born-Oppenheimer approximation, the Couloumb Hamiltonian operator, and the conditional context afforded by representation theory. An orthonormal (Eisenschitz-London) outer product of atomic spectral eigenstates is employed to provide meaningful assignments of electrons to particular atomic nuclei in a molecule, as well as support of corresponding well-defined self-adjoint atomic and atomic-interaction fragment operators. Total molecular energies obtained in this representation are partitioned into a sum of atomic terms which describe distributions of atomic energy promotions for the individual atoms and a pairwise-atomic sum of distributions among universal interaction energies which describe chemical bonds among the constituent atoms. Illustrative clarifying applications are reported.