Orbital interaction kinetic energy density

Time-Dependent Density Functional Theory (TD-DFT) simulations in adiabatic approximation, carried out on a prototype terthiophene oxidized in the inner position (Raganato et al., 2004), indicated that the oxidation of the thiophene ring leads to the formation of new interactions in the LUMO orbital. The kinetic energy of the electrons in this orbital is lowered, while the energy of the electrons in the HOMO orbital is almost unchanged. As a consequence, the electron affinity of the whole molecule is increased. 

Note that, for a non-interacting system of electrons, the kinetic energy is just the sum of the individual electronic kinetic energies. Within an orbital expression for the density, Eq. (8.14) may then be rewritten as... 

The first term in brackets is the usual kinetic energy operator. The noninteracting reference system has the property that its one-determinantal wavefunction of the lowest N orbitals yields the exact density of the interacting system with external potential v(r) as a sum over densities of the occupied orbitals, that is, p(r) = Xl<)>,l2, and the corresponding exact energy E[p(r)]. The Kohn-Sham potential should account for all effects stemming from the electron-nuclear and electron-electron interactions. Not only does the Kohn-Sham potential contain the attractive potential v(r) of the nuclei and the classical Coulomb repulsion VCoul(r) within the electron density p(r), but it also accounts for all exchange and correlation effects, which have so to say been folded into a local potential vxc r) ... 

The first term, the kinetic energy, is difficult to calculate directly from the density, and it is for this reason that the molecular orbitals mentioned above are introduced a very good approximation to the kinetic energy corresponding to the density can be calculated from the orbitals as it would be in HF theory. This approach does not however yield the exact kinetic energy because it assumes that the electrons in each orbital do not interact with electrons in other orbitals. The exact exchange-correlation functional must therefore contain a corrective term to incorporate the effect of electronic interactions on their kinetic energy. In practice, such a term is not explicitly included in common functionals. 

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