Natural Coulomb energy

For the NPA-based atomic charges (Section 3.2) at the chosen geometry, Equation (6.11) expresses the Natural Coulombic Energy (NCE) Vnce(Ra> Rbv ) as a qualitative measure of overall atom-atom electrostatics. 

He did not think of it then, and when he did, he showed that apparently the formation of a metal-carbon bond was unlikely on thermochemical grounds [68] in other words, he was taken in by his own propaganda but in a Note added in Proof in that same work he indicated that electrochemical factors (solvation and Coulombic energies) could make this initiation exo-energetic. However, at that time, 1960-1970, such a suggestion would have been no more plausible than when it was made by others. It was only the painstaking and detailed exploration of the nature of the solutions of A1X3 in alkyl halides [104, 112] that provided the basis of fact which was required to make the theory plausible. 

Two properties render electrolyte theories difficult, namely the long-range nature of the Coulomb interactions and the high figures of the Coulomb energy at small ion separations. 

In density functional theory it is natural to define the (direct) Coulomb energy by the first term on the right of (25). The exact exchange-correlation energy functional ic[p( )] cancels the spurious self-Coulomb repulsions as well as taking care of the effects of true exchange and of correlation. The approximate functional used in the LSD method does not do so exactly. As a result, in an LSD treatment of a one-electron system, the Coulomb energy is not exactly... 

One qualitative defect in LDA for example is the imperfect cancellation of the Coulomb self-interaction in the mean field Coulomb energy (Hartree energy Eh - see eq. 2.2.) and the corresponding potential Vh (eq. 2.5.), due to the approximate nature of Ex[c)- There are hints that this defect might have a significant influence on reaction barriers [29] - see also chapter 3.3. The self-interaction may be corrected in DFT by a self-interaction correction (SIC) [29, 30, 31]. However, these corrections are rather cumbersome and therefore they have been applied up to now only very rarely. 

The HF equations F ( )i = 8i (jii comprise a set of integro-differential equations their differential nature arises from the kinetic energy operator in h, and the coulomb and exchange operators provide their integral nature. The solutions of these equations must be... 

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