|Spin-Singlet Atoms in Molecules: I. Electrochemical Potential Equalization |
Institute for Advanced Materials and Devices
|Raymond T. Tung, Brooklyn College, CUNY|
11:00 AM, CCR Room 201
Efforts to correlate the properties of a molecule, such as its energy and dipole moment, to identifiable properties of the individual atoms were often hampered by the lack of a satisfactory definition of an atom with a fractional number of electrons. Physically based models of the atom invariably yield a piecewise linear dependence of its energy on the number of electrons, whereas empirical analyses suggest that a quadratic dependence is needed to account for the observed molecular charge distribution. This inconsistency has to do with the fact that an atom in a molecular ground state has essentially equal numbers of spin-up and spin-down electrons. In order to directly account for the charge transfer and the energy of atoms in a molecule, the "basic unit" that represents "the atom" should also have a singlet spin state, and not the doublet state of isolated atoms in reality. To create the singlet condition for an atom, a method inspired by solid state physics is applied to interacting and non-interacting atoms, which allows the energy of an atom with a fractional number of electrons to be calculated within the Hartree-Fock theory. Using this result, the chemical potential of an atom can be written down analytically in terms of a small number of parameters incorporating the effects of nearest neighbors. In essence, the interactions an atom would experience inside a molecule can be folded back into the atom, while it is still in an isolated, or easily distinguishable, state. Significant insight into the charge transfer process between atoms in molecules is gained. Within the general framework of the linear combination of atomic orbital (LCAO) theory, it is explicitly shown that the Hartree-Fock eigenvalue for the molecular orbital is the electrochemical potential. The electrochemical potential in a molecule is exactly equalized in the quantum mechanical sense, although generally not in the classical sense, because of exchange interaction.