Ionization potential, definition

In this equation, the electronegativity of an atom is related to its ionization potential, 1, and its electron affinity, E. Mulhken already pointed out that in this definition the ionization potential, and the electron affinity, E, of valence states have to be used. This idea was further elaborated by Hinze et al. [30, 31], who introduced the concept of orbital electronegativity. 

Besides the already mentioned Fukui function, there are a couple of other commonly used concepts which can be connected with Density Functional Theory (Chapter 6). The electronic chemical potential p is given as the first derivative of the energy with respect to the number of electrons, which in a finite difference version is given as half the sum of the ionization potential and the electron affinity. Except for a difference in sign, this is exactly the Mulliken definition of electronegativity. ... 

Figure 7.13. The definitions of ionization potential, Ie, work function, , Fermi level, EF, conduction level, Ec, valence level Ev, and x-potential Xe without (a) and with (b) band bending at the semiconductor-vacuum interface.

For a given molecule and a given intemuclear separation a would have a definite value, such as to make the energy level for P+ lie as low as possible. If a happens to be nearly 1 for the equilibrium state of the molecule, it would be convenient to say that the bond is an electron-pair bond if a is nearly zero, it could be called an ionic bond. This definition is somewhat unsatisfactory in that it does not depend on easily observable quantities. For example, a compound which is ionic by the above definition might dissociate adiabatically into neutral atoms, the value of a changing from nearly zero to unity as the nuclei separate, and it would do this in case the electron affinity of X were less than the ionization potential of M. HF is an example of such a compound. There is evidence, given bdow, that the normal molecule approximates an ionic compound yet it would dissociate adiabatically into neutral F and H.13... 

Franck and Hertz (1913) first demonstrated that an electron has to acquire a minimum energy before it can ionize. Thus, they provided an operational definition of the ionization potential and showed that it is an atomic or molecular property quite free from experimental artifacts. However, this kind of experiment does not tell anything about the nature of the positive ion for this, one needs a mass spectrometric analysis. Although Thompson had demonstrated the existence of H+, H2+, and H3+ in hydrogen discharge, it seems that Dempster (1916) was the first to make a systematic study of the positive ions. 

The ionization potential and electron affinity of the molecule are I and A, respectively. By constmction, these definitions involve three Hamiltonians (IV-1, N, N+ 1). However, one may define Fukui functions without invoking any actual derivative relative to the number of electrons by using the derivative of the chemical potential relative to the potential [8]... 

Here Zg is the number of tt electrons provided by atom is essentially an ionization potential for an electron extracted from in the presence of the part of the framework associated with atom r alone (a somewhat hypothetical quantity), is a framework resonance integral, and is the coulomb interaction between electrons in orbitals < >, and <(>,. The essential parameters, in the semi-empirical form of the theory, are cug, and and from their definition these quantities are expected to be characteristic of atom r or bond r—s, not of the particular molecule in which they occur (for a discussion see McWeeny, 1964). In the SCF calculation, solution of (95) leads to MO s from which charges and bond orders are calculated using (97) these are used in setting up a revised Hamiltonian according to (98) and (99) and this is put back into (95) which is solved again to get new MO s, the process being continued until self-consistency is achieved. It is now clear that prediction of the variation of the self-consistent E with respect to the parameters is a matter of considerable difficulty. 

This is true for our procedure for calculating partial atomic charges in a-bonded molecules (16). The method starts from Mulliken s definition of electronegativity, x> derived from atomic ionization potentials, IP, and electronegativities, EA (Equation 3)(17). 

A familiar way of handling this question is offered by the notion of electronic shells. By definition, an electronic shell collects all the electrons with the same principal quantum number. The K shell, for example, consists of U electrons, the L shell collects the 2s and 2p electrons, and so on. The valence shell thus consists of the last occupied electronic shell, while the core consists of all the inner shells. This segregation into electronic shells is justified by the well-known order of the successive ionization potentials of the atoms. 

In the next section we shall recall the definitions of the chemical concepts relevant to this paper in the framework of DFT. In Section 3 we briefly review Strutinsky s averaging procedure and its formulation in the extended Kohn-Sham (EKS) scheme. The following section is devoted to the presentation and discussion of our results for the residual, shell-structure part of the ionization potential, electron affinity, electronegativity, and chemical hardness for the series of atoms from B to Ca. The last section will present some conclusions. 

In the gaseous phase, an electron ejected from a molecule becomes free, and so for each filled electron level we have only one ionization potential. However, in the condensed phase an ejected electron can be in three different states free, quasi-free, and solvated. So the definition of the ionization potential becomes ambiguous. 

There seems to be a linear relationship between the mean value of L and the first ionization potential (IP) of MMe4 when M is Si, Ge, Sn and probably Pb as well. As the IP of PbMe4 is regarded as uncertain31b and only one data set for lead derivatives was available, making the L value for lead uncertain, no definite conclusion regarding the fit of lead compounds in this relationship can be reached. The only L value available for carbon at this time is reliable but does not fit the L-IP relationship. 

Vinylamine (11) has a vertical ionization potential IPV = 199.5 kcal mol-1 15 which, together with its PA ( = 219.1 kcal mol - J), results in 105 kcal mol -1, i.e. a very different value from the 120.9 kcal mol-1 for ethylamine (IPV = 217.4 kcal mol-1, PA = 217.0 kcal mol-1). Therefore, vinylamine is definitely not a nitrogen base. This is consistent with both theoretical data and the analysis of intrinsic effects, as shown below. 

The property describing the binding force of an electron to a nucleus is the ionization potential, IP, which is the energy required to remove an electron from an atom or molecule in the gas phase. The electron affinity, EA, is the energy released when an electron combines with an atom or molecule. On the basis of these definitions, electron transfer is feasible when the electron affinity exceeds the ionization potential ... 

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