Energy derivatives, electron number ionization potential

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. ... 

The second derivative of the energy with respect to the number of electrons is the hardness r) (the inverse quantity is called the softness), which again may be approximated in term of the ionization potential and electron affinity. 

The typical energy transfer from a plasma electron to an electron sitting in an excited atomic level is about 7),. This means that excited particles with energy about e = 1 — make the major contributions into sum (2-21). Taking into accoimt that I 1/n, the number of states with energy about e = I - Tg and ionization potential about I = has an order of n. Thus, from (2-21) and (2-22), we can derive... 

The experimental spectrum is a plot of intensity (number of ejected electrons) as a function of ionization potential. This gives a representation of the occupied molecular orbitals. The spectrum for H2O, the orbitals of which we have just considered in Section 9.3, is shown in Figure 9.3. The energies of the MOs cannot, of course, be derived purely from symmetry arguments. They are obtained experimentally by photoelectron spectroscopy and they can also be obtained from a quantum mechanical calculation, which, along with the atomic orbital weighting coefficients, allows pictorial representations of the resulting molecular orbitals to be made (Section 3.8.3). 

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