Repulsive exchange energy

It was mentioned earlier that the dispersion interaction energy (DIS) is the most important attractive term of the correlation energy (CORR) it is usually attributed to the van der Waals interactions, physical meaning of the latter is usually the sum of attraction (DIS) and the repulsive exchange energy (EX). 

It should be noted that several of the proposed functionals violate fundamental restrictions, such as predicting correlation energies for one-electron systems (for example P86 and PW91) or failing to have the exchange energy cancel the Coulomb self-repulsion (Section 3.3, eq. (3.32)). One of the more recent functionals which does not have these problems is due to Becke (B95), which has the form... 

Furthermore, because of the invariance of the exchange energy, exhibited in Eq. (15), maximization of the localization sum of Eq. (28) implies the simultaneous minimization of the interorbital exchange repulsions... 

The exchange contribution in an ab initio perturbation theory is the only repulsive term ) around the energy minimum in most of the stable complexes and consequently we would expect no net repulsion between two closed shell molecules in semiempirical calculations. On the other hand it is known from actual calculations that intermolecular interactions are described more or less correctly by the CNDO/2 procedure. Indeed, strong repulsion is obtained between closed shell molecules. Evidently there must be another approximation which compensates for the neglect of exchange energy. With regard to the simplifications of the CNDO/2 method we find that this is in fact the case. The approximation shown in Eq. (17) is responsible for the repulsive term. 

The operator J corresponds to the classical Coulomb repulsion, while the quantum mechanical exchange operator, K, contains the permutation operator P(12), which has the effect of interchanging the coordinates of electron 1 and 2. This causes the exchange operator to be non-local and difficult to plot, unlike the local, multiplicative Coulomb operator, J. However, the exchange energy is... 

Because electron densities are positive-definite, the contribution of the electron gas to interaction energy takes the same sign as the electron gas functional (see Clugston, 1978). Hence, the kinetic energy term is repulsive (cf eq. 1.148 and 1.154), exchange energy is attractive (cf eq. 1.148 and 1.154), and the correlation term is also attractive (cf eq. 1.149, 1.150, and 1.152). 

Exchange Energy. An attractive (negative) component of the electron-electron interaction energy. Arises due to an overestimation of the repulsive (positive) component or Coulomb energy. 

Which of these represents the ground state Which are excited states Which are impossible states In which configuration would exchange energy be maximized In which configuration would coulombtc repulsion be maximized ... 

---