Quantum-thermodynamic definition of electronegativity.

(1) Introduction.-Rigorous definitions of electronegativity of atoms, neutral or ionized, and of atomic orbitals are given. The definitions are consistent with the rules of the statistics of ensembles and the quantum-mechanical picture of atomic structure. The definitions have been extended to atoms in a molecule and to atoms in a solid. The extensions, however, will be presented in future communications. The concept of electronegativity, "the power of an atom in a molecule to attract electrons to itself,"' has been found to be a useful tool for the correlation of a vast field of chemical knowledge and experience.2 But in spite of the great amount of literature on the subject, no rigorous definition of electronegativity has been suggested. The lack of definition has resulted in some confusion with respect to both the physical concept represented by electronegativity and the units of electronegativity.'-8 In the present communication, a free atom or a free ion is regarded as a thermodynamic system, and the electronegativity of such a system is identified with the negative of its electrochemical potential. The electrochemical potential of a component in a phase may be evaluated by means of the theory of statistical ensembles. This theory, whether related to classical or quantum mechanics, applies to thermodynamic systems of any size.9 Consequently, it is possible to find ensemble (thermodynamic) properties, such as the electrochemical potential, even of an atom representative of an ensemble of one-atom members. If the center of mass of each atom is fixed in space, both the one-atom members and the one-atom thermodynamic system representative of the ensemble may be regarded as open systems having one independent component, namely, electrons. Even when all the mechanical properties of an atom, such as the energy eigenvalues and the number of electrons, assume only discrete values, the thermodynamic properties of the one-atom system representative of the ensemble, such as the energy E and the number of electrons n, assume continuous values. Each of these properties may be expressed as a continuous function of two independent thermodynamic variables. The electrochemical potential M is defined as the partial derivative of E with respect to n at constant entropy. This derivative must be evaluated for the ensemble passing through equilibrium states because otherwise it is indeterminate. This fact in turn implies that in any calculation of ju, two independent thermodynamic variables, say, n and temperature T, must be considered even if the interest is in results at 00K. For example, if ,u is computed as the derivative mentioned above, in order to vary n at constant entropy while the ensemble