No abstract

For two model systems, a dimer of N,N‘-dimethyl thiacarbocyanine and a dimer of C.I. Pigment Yellow 12, we compare results of several approaches to calculation of the exciton interaction energy. The sum over Coulombic interactions between atomic transition charges is compared to the point-dipole and extended-dipole approximations and to the direct evaluation of the Coulomb interaction integral over transition charge densities, for a range of dimer configurations. Calculations are carried out at semiempirical, ab initio Hartree−Fock, and ab initio configuration interaction−singles levels. Finally, we discuss the relation of these interaction energies to those calculated using a supermolecular approach. We conclude that for the materials studied, semiempirical methods are adequate to describe the excitonic shift.

Nuclear cusp conditions are obtained for the full electron-electron interaction energy density as well as for the exchange and correlation energy densities of density-functional theory. Their form is the same as the form of the well known Kato cusp condition for the electron-number density. All these cusp conditions are valid for both the ground and excited states of a molecule or solid.

In earlier work, expressions have been constructed for the single-particle kinetic-energy functional T s ͓͔ for independent fermions subject to harmonic confinement in low dimensions, with the particle density. Here, the differential equation for is first obtained in d dimensions for an arbitrary number of closed shells. Then, by using the known Euler-Lagrange equation, the functional derivative ␦T s /␦(r) is constructed. T s ͓͔ itself is proved to take the form of a linear combination of three pieces: ͑i͒ a von Weizsäcker inhomogeneity kinetic energy, but with the original coefficient reduced by a dimensionality factor 1/d, ͑ii͒ a Thomas-Fermi kinetic energy, and ͑iii͒ a truly nonlocal contribution that, however, is shown to involve only the density itself and its first derivative. Thus, for this model, which is currently highly relevant to the interpretation of experiments on the evaporative cooling of dilute, and hence almost noninteracting, fermions, a complete density-functional theory now exists.