Local ionization

In the spirit of Koopmans theorem, the local ionization potential, IPi, at a point in space near a molecule is defined [46] as in Eq. (54), where HOMO is the highest occupied MO, p( is the electron density due to MO i at the point being considered, and ej is the eigenvalue of MO i. 

This quantity is found to be related to the local polarization energy and is complementary to the MEP at the same point in space, making it a potentially very useful descriptor. Reported studies on local ionization potentials have been based on HF ab-initio calculations. However, they could equally well use semi-empirical methods, especially because these are parameterized to give accurate Koopmans theorem ionization potentials. 

Fig. 1. Evolution of 3He/H in the solar neighborhood, computed without extra-mixing (upper curve) and with extra-mixing in 90% or 100% of stars M < 2.5 M (lower curves). The two arrows indicate the present epoch (assuming a Galactic age of 13.7 Gyr) and the time of formation of the solar system 4.55 Gyr ago. Symbols and errorbars show the 3He/H value measured in meteorites (empty squares) Jupiter s atmosphere (errorbar) the local ionized ISM (filled triangle) the local neutral ISM (filled circle) the sample of simple Hll regions (empty circles). Data points have been slightly displaced for clarity. The He isotopic ratios has been converted into abundances relative to hydrogen assuming a universal ratio He/H= 0.1. See text for references.

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. ... 

Wavelet descriptors that describe the same basic value as DGNH6. Wavelet descriptors that describe the same basic value as DGNH6. Wavelet descriptors that describe the same basic value as DGNH6. Descriptor that conveys information about the local ionization potential of the molecule. 

Descriptor that conveys information about the local ionization potential of the molecule. 

This chapter introduces a number of useful graphical models, including molecular orbitals, electron densities, spin densities, electrostatic potentials and local ionization potentials, and relates these models both to molecular size and shape and molecular charge distributions. The chapter also introduces and illustrates property maps which simultaneously depict molecular size and shape in addition to a molecular property. Properties include the electrostatic potential, the value of the LUMO, the local ionization potential and the spin density. 

Among the quantities which have proven of value as graphical models are the molecular orbitals, the electron density, the spin density (for radicals and other molecules with unpaired electrons), the electrostatic potential and the local ionization potential. These may all be expressed as three-dimensional functions of the coordinates. One way to display them on a two-dimensional video screen (or on a printed page) is to define a surface of constant value, a so-called isovalue surface or, more simply, isosurface. ... 

This chapter introduces and illustrates isosurface displays of molecular orbitals, electron and spin densities, electrostatic potentials and local ionization potentials, as well as maps of the lowest-unoccupied molecular orbital, the electrostatic and local ionization potentials and the spin density (on top of electron density surfaces). Applications of these models to the description of molecular properties and chemical reactivity and selectivity are provided in Chapter 19 of this guide. 

Another quantity of some utility is the so-called local ionization potential, I(r). This is defined as the sum over orbital electron densities, pi(r) times absolute orbital energies, e i, and divided by the total electron density, p(r). 

The local ionization potential is intended to reflect the relative ease of electron removal ( ionization ) at any location around a molecule. For example, a surface of low local ionization potential for sulfur tetrafluoride demarks the areas which are most easily ionized. 

A more important application of the local ionization potential is as an alternative to the electrostatic potential as a graphical indicator of electrophilic reactivity. This is in terms of a property map rather than as an isosurface. Further discussion is provided later in this chapter. 

The local ionization potential does not fall to zero with increasing distance from the molecule. 

Mapping the local ionization potential onto a size surface reveals those regions from which electrons are most easily ionized. 

Such a representation is referred to as a local ionization potential map. Local ionization potential maps provide an alternative to electrostatic potential maps for revealing sites which may be particularly susceptible to electrophilic attack. For example, local ionization potential maps show both the positional selectivity in electrophilic aromatic substitution (NH2 directs ortho para, and NO2 directs meta), and the fact that TC-donor groups (NH2) activate benzene while electron-withdrawing groups (NO2) deactivate benzene. 

The author wishes to thank Dr. Denton Hoyer at Pfizer for pointing ont the ntility of local ionization potential maps for this purpose. 

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