Local ionization energy

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 ... 

In equation 6, pi r) is the electronic density of orbital i, having energy e . The formalism of Hartree-Fock theory (within the framework of which eqnation 6 was proposed) and Koopmans theorem provide support for interpreting 7(r) as the local ionization energy, which focuses upon the point in space rather than an orbital. 

Just as it is useful to have a local ionization energy, so would it be desirable, in the context of reactive behavior, to have a local polarizability, a(r). Reflecting the discussion earlier in this section, we have suggested that 7s(r) be viewed as an inverse measure of as(r) we focus upon the surface local ionization energy and surface local polarizability because the outermost electrons are expected to make the greatest contributions to a. The volume dependence that is so important on a macroscopic scale should not be a factor on the local level, which considers only infinitesimal volume elements dr. We have presented evidence in support of the concept expressed by equation 14 ... 

The same geometries were also used to compute electrostatic potentials and local ionization energies, at the HF/6-31G level. Hartree-Fock F(r) and 7(r) are known to be quite satisfactory ... 

The dominant feature of the local ionization energy on the surface of 6 is the low 7s(r) of the nitrogen lone pair. Figure 2(a). The oxygen lone pairs, so much in evidence in terms of Vs(r), do not stand out at all now. Figure 2(b). 

Computational levels bond lengths and bond angles, B3LYP/6-31G electrostatic potentials and local ionization energies, HF/6-31GV/B3LYP/6-31G . 

Some idea of the relative polarizabilities of various portions of the molecules in Table 8 can be obtained by looking at the group values in Table 7. However, a more detailed picture is provided by the variation of the local ionization energy 7s(r) over the molecular surface, if it is accepted that this is an inverse measure of local polarizability (equation 14). 

We have approached these multi-faceted systems by looking in particular at two local molecular properties the electrostatic potential, P(r) and Vs(r). and the local ionization energy, /s(r). In terms of these, we have addressed hydrogen bonding, lone pair-lone pair repulsion, conformer and isomer stability, acidity/basicity and local polarizability. We have sought to show how theoretical and computational analyses can complement experimental studies in characterizing and predicting molecular behavior. ... 

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. 

As was mentioned earlier, our open tubes have hydrogens at the ends, simply as a means of avoiding unfulfilled valencies. How are the surface electrostatic potentials and local ionization energies affected by replacing one or more of these hydrogens by functional groups, e.g. OH, NH2, N02, etc. ... 

Politzer P, Murray JS, Lane P, Concha MC (2005) Computed electrostatic potentials and local ionization energies on model nanotube surfaces. In Balandin AA, Wang WL (eds) Handbook of Semiconductor Nanostructures and Devices, American Scientific Publishers, Los Angeles (in press)... 

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... 

Murray JS, Peralta-Inga Z, Politzer P, Ekanayake K, LeBreton P (2001) Computational characterization of nucleotide bases Molecular surfaceelectrostatic potentials and local ionization energies, and local polarization energies, Int. J. Quantum Chem. 83 245-254... 

Brinck T, Murray JS, Politzer P (1993) Molecular surface electrostatic potentials and local ionization energies of groups V-VII hydrides and their anions. Relationships for aqueous and gas phase acidities. Int. J. Quantum Chem. 48 73-88... 

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]. 

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