The generalized gradient approximation ͑GGA͒ for the exchange functional in conjunction with accurate expressions for the correlation functional have led to numerous applications in which density-functional theory ͑DFT͒ provides structures, bond energies, and reaction activation energies in excellent agreement with the most accurate ab initio calculations and with the experiment. However, the orbital energies that arise from the Kohn-Sham auxiliary equations of DFT may differ by a factor of 2 from the ionization potentials, indicating that excitation energies and properties involving sums over excited states ͑nonlinear-optical properties, van der Waals attraction͒ may be in serious error. We propose herein a generalization of the GGA in which the changes in the functionals due to virtual changes in the orbitals are allowed to differ from the functional used to map the exact density onto the exact energy. Using the simplest version of this generalized GGA we show that orbital energies are within ϳ5% of the correct values and the long-range behavior has the correct form.

Abstract. One of the most puzzling aspects of fullerenes is how such complicated symmetric molecules are formed from a gas of atomic carbons, namely, the atomistic or chemical mechanisms. Are the atoms added one by one or as molecules (C 2 , C 3 )? Is there a critical nucleus beyond which formation proceeds at gas kinetic rates? What determines the balance between forming buckyballs, buckytubes, graphite and soot? The answer to these questions is extremely important in manipulating the systems to achieve particular products. A difficulty in current experiments is that the products can only be detected on time scales of microseconds long after many of the important formation steps have been completed. Consequently, it is necessary to use simulations, quantum mechanics and molecular dynamics, to determine these initial states. Experiments serve to provide the boundary conditions that severely limit the possibilities. Using quantum mechanical methods (density functional theory (DFT)) we derived a force field (MSXX FF) to describe one-dimensional (rings) and two-dimensional (fullerene) carbon molecules. Combining DFT with the MSXX FF, we calculated the energetics for the ring fusion spiral zipper (RFSZ) mechanism for formation of C 60 fullerenes. Our results shows that the RFSZ mechanism is consistent with the quantum mechanics (with a slight modification for some of the intermediates).

We describe the implementation of a separable pseudopotential into the dual space approach for ab initio density-functional calculations using Gaussian basis functions. We apply this Gaussian dual space method ͑GDS/DFT͒ to the study of II-VI semiconductors ͑IIϭZn, Cd, Hg; VIϭS, Se, Te, Po͒. The results compare well with experimental data and demonstrate the general transferability of the separable pseudopotential. We also introduce a band-consistent tight-binding ͑BC-TB͒ model for calculating the bulk contributions to the valenceband offsets ͑VBO's͒. This BC-TB approach yields good agreement with all-electron ab initio GDS/DFT results. Comparisons between BC-TB results of VBO obtained with and without p-d coupling demonstrate quantitatively the importance of d electrons and cation-d -anion-p coupling in II-VI systems. Agreement between ab initio results and experimental results is excellent.

The use of localized Gaussian basis functions for large scale first principles density functional calculations with periodic boundary conditions ͑PBC͒ in 2 dimensions and 3 dimensions has been made possible by using a dual space approach. This new method is applied to the study of electronic properties of II-VI ͑IIϭZn, Cd, Hg; VIϭS, Se, Te, Po͒ and III-V ͑IIIϭAl, Ga; VϭAs, N͒ semiconductors. Valence band offsets of heterojunctions are calculated including both bulk contributions and interfacial contributions. The results agree very well with available experimental data. The p͑2ϫ1͒ cation terminated surface reconstructions of CdTe and HgTe ͑100͒ are calculated using the local density approximation ͑LDA͒ with two-dimensional PBC and also using the ab initio Hartree-Fock ͑HF͒ method with a finite cluster. The LDA and HF results do not agree very well.

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