Mulliken difference potential

Based on Mulliken s [265, 266] prescription for electronegativity, the Mulliken chemical potential can be similarly expressed as a finite-difference approximation of the derivative of the electronic energy with respect to the number of electrons and can be expressed as... 

Energy, geometry, dipole moment, and the electrostatic potential all have a clear relation to experimental values. Calculated atomic charges are a different matter. There are various ways to define atomic charges. HyperChem uses Mulliken atomic charges, which are commonly used in Molecular Orbital theory. These quantities have only an approximate relation to experiment their values are sensitive to the basis set and to the method of calculation. 

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. ... 

In more detail, the interaction energy between donor and acceptor is determined by the ionisation potential of the donor and the electron affinity of the acceptor. The interaction energy increases with lowering of the former and raising of the latter. In the Mulliken picture (Scheme 2) it refers to a raising of the HOMO (highest occupied molecular orbital) and lowering of the LUMO (lowest unoccupied molecular orbital). Alternatively to this picture donor-acceptor formation can be viewed in a Born-Haber cycle, within two different steps (Scheme 3). 

The energy difference AGET° between the vibronically equilibrated reactant and product states can be considered as the difference between the IP of the donor and the EA of the acceptor (in the gas phase) or between the corresponding electrochemical potentials (in solution). For a set of structurally related arene donors in the same solvent, a linear (Mulliken) correlation is usually observed experimentally between the donor strength and the CT energy (due to the relatively small changes in A), i.e. ... 

According to Mulliken charge-transfer theory (7), the separation of AhvCT = 0.61 eV for the two series represents the constant difference in the donor properties (ionization potential) of Co(CO)4- and I- in salt pairs with the same acceptor cation. The latter is a corollary of the Mulliken... 

We define two parameters the absolute electronegativity, which is approximately the same as electronegativity as Mulliken originally defined it for atoms, namely the average of the ionisation potential I and the electron affinity A (Equation 3.1). The other is called the absolute hardness, rj, which is identified with the difference in energy between the ionisation potential I and the electron affinity A (Equation 3.2). 

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