Quantum-Mechanical Definition of Atoms and Chemical Bonds in Molecules

Abstract

Abstract : The apparent impossibility of making meaningful assignments of indistinguishable electrons to particular atomic nuclei in a chemical aggregate has seemingly precluded quantum-mechanical definition of fragment atomic Hamiltonian operators in a molecule. Structural symmetry, conformations, and isomers, as well as the electronic energies of constituent atoms and of their interactions in a molecule, are accordingly perceived as open problems in molecular quantum theory. Here we address assignments of electrons to atoms in molecules and provide corresponding definitions of atomic energies and of the chemical bonds between atoms from the perspective of representation theory. Molecular basis functions in the form of orthonormal (Eisenschitz-London) outer-products of atomic eigenstates allow assignments of electrons to particular atomic nuclei, and provide support for totally antisymmetric solutions of the Schrodinger equation. Self-adjoint atomic and atomic-interaction operators within a molecule defined in this context are shown to have Hermitian matrix representatives and physically significant expectation values in molecular eigenstates. Adiabatic (Born-Oppenheimer) molecular energies emerge naturally from this representation in the form of sums of the energies of individual atomic constituents and of their interaction energies in the absence of any additional auxiliary conditions. A nuanced description of chemical bonding is provided thereby which includes the interplay between atomic promotion and bonding energies, insightful com- mon representations of hybridization and atomic charge apportionment, measurable atomic entanglements, and other attributes revealed by calculations illustrating the formalism.