Ionization energies average local

Politzer and coworkers170 have recently presented a linear relationship (r = 0.99) between the measured aqueous pK values171 of a series of azines and azoles (9 pKa units) and the magnitude of the lowest value (/s,min>eV) of the average local ionization energy, 7(r), on the molecular surface 7(r) is defined within the framework of SCF-MO theory as... 

We introduced such a quantity, the average local ionization energy 7(r) °, in equation 6 ... 

The quantity Is in in equation 13 is site-specific it is the lowest value of the average local ionization energy J(r) computed on the molecular surface. The quantity J(r) is defined by equation 1779 where p,(r) is the electronic density of zth molecular orbital at the point r, is its orbital energy and p(r) is the total electronic density function. We interpret 7(r) as the energy required on the average to remove an electron from a point r in the space of an atom or molecule. In particular, we have found that the positions where /(r) has its lowest values on the molecular surface, the IS min, are indicative of the sites that are most susceptible to charge transfer with electrophiles74,79. 

The computed properties that will be discussed in this chapter are the electrostatic potential Vs(r) and the average local ionization energy Is(r). We will begin by reviewing some background for each. 

Some time ago, we introduced the concept of an average local ionization energy I(r), by which we mean the average energy required to remove an electron at the point r in the space of a system.51 Note that we are focusing here upon a point in... 

In Eq. (6), p (r) is the electronic density function of the ith occupied orbital of the system, having energy . The Hartree-Fock formalism plus Koopmans theorem52 provide support for the common interpretation of the lej as the electrons ionization energies hence our introduction of I(r) as the average local ionization energy. When computed on the surface of the system, as we normally do, it is denoted by s(r). 

Curvature also affects the computed average local ionization energy Is(r).28,29,32 On the lateral outer surfaces of carbon tubes, for example, there are minima ls min above the carbons, primarily in the 13-14 ev range, which is considerably less than the 14.8-14.9ev found for graphene.74 This difference can be attributed to the same factors that cause the outer surface Vs(r) to be more negative, since this leads to the electrons being less tightly held, more easily removed. 

Sjoberg P, Murray JS, Brinck T, Politzer P (1990) Average local ionization energies on the molecular surfaces of aromatic systems as guides to chemical reactivity. Can. J. Chem. 68 1440-1443... 

Politzer P, Abu-Awwad F, Murray JS (1998) Comparison of density functional and Hartree-Fock average local ionization energies on molecular surfaces. Int. J. Quantum Chem. 69 607-613... 

Politzer P, Murray JS, Concha MC (2002) The complementary roles of molecular surface electrostatic potentials and average local ionization energies with respect to electrophilic processes. Int. J. Quantum Chem. 88 19—27... 

Politzer P, Murray JS, Grice ME, Brinck T, Ranganathan S (1991) Radial behavior of the average local ionization energies of atoms. J. Chem. Phys. 95 6699-6704... 

Politzer P, Grice ME, Murray JS (2005) Electronegativity and average local ionization energy. Coll. Czech. Chem. Comm. 70 550-558... 

Murray JS, Seminario JM, Politzer P, Sjoberg P (1990) Average local ionization energies computed on the surfaces of some strained molecules. Int. J. Quantum Chem., Quantum Chem. Symp. 24 645-653... 

Politzer P, Murray JS (2006) The average local ionization energy Concepts and applications, In Toro-Labbe A (ed) Theoretical Approaches to Chemical Reactivity. Elsevier, Amsterdam, (In press)... 

Another descriptor used in this MEP approach is the average local ionization energy, 7(r), defined at some point, r, as the following sum, Eq. [38]. 

The average local ionization energy was introduced [Sjdberg et al, 1990] to estimate the average energy required to remove an electron located at the point r from the molecule and is defined as ... 

Sjoberg, R, Murray, J.S. and Brinck, T. (1990). Average Local Ionization Energies on the Molecular Surfaces of Aromatic Systems as Guides to Chemical Reactivity. Can.J.Chem., 68, 1440-1443. 

The average local ionization energy concepts and applications... 

This study verified that the average local ionization energy is relatively constant within an atomic shell, that this can be used to distinguish the shell and that 7(r) as defined by (4) is capable of revealing these features. This is relevant to the application of 7(r) to be discussed in the next section. 

In analysing, interpreting and predicting the reactive behaviour of molecules, we have made extensive use of two local properties the average local ionization energy 7(r), defined by (4), and the electrostatic potential V(r) that is produced by the nuclei and electrons,... 

The average local ionization energy 7(r) has many interesting and significant aspects and applications. It is related to local temperature and atomic shell structure, it is linked to electronegativity and shows promise as a measure of local polarizability. It permits the characterization of bonds and radical sites, and - in conjunction with volume -the prediction of molecular and group polarizabilities. Finally, it is an effective guide to reactivity towards electrophiles, especially when complemented by the electrostatic potential. All of these areas continue to be studied. 

Is min is the lowest value of the —> average local ionization energy found on the molecular surface this refiects the tendency for charge transfer and polarization at any particular molecular site [Haeberlein and Brinck, 1997]. 

Murray JS, Politzer P. Average local ionization energies significance and applications. In Parkanyi C, ed. Theoretical Organic Chemistry. Amsterdam Elsevier, 1998 189-202. 

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