a) Γ K M (b) FIG. 1. (Color online) (a) Honeycomb lattice with the different spin exchange interactions considered in this paper; (b) corresponding Brillouin zone with relevant k points. 2 2.5 Velocity [arb. units] J 3 =0 J 3 =0.3

We present a detailed study of the electronic properties of CdSe nanocrystals in the absence and presence of a dielectric medium. The electronic structure of the nanocrystal is modeled within the framework of the empirical pseudopotential method. We use a real-space grid representation of the wave function, and obtain the eigenvalues and eigenstates of the one-electron Hamiltonian using a slightly modified version of the filter-diagonalization method. The band gap, density of states, charge density, multipole moments, and electronic polarizabilities are studied in detail for an isolated nanocrystal. We discuss the implications of the results for the long range electrostatic and dispersion interactions between two CdSe nanocrystals. To study the effects of the surroundings we develop a self-consistent reaction field method consistent with the empirical pseudopotential method. We use the eigenstates of the isolated nanocrystal and iterate the self-consistent equations until converged results are obtained. The results show that the electronic properties of polar CdSe nanocrystals are quite sensitive to the environment.

We calculate the near-edge x-ray-absorption fine structure of H(2)O in the gas, hexagonal ice, and liquid phases using heuristic density-functional based methods. We present a detailed comparison of our results with experiment. The differences between the ice and water spectra can be rationalized in terms of the breaking of hydrogen bonds around the absorbing molecule. In particular the increase in the pre-edge absorption feature from ice to water is shown to be due to the breaking of a donor hydrogen bond. We also find that in water approximately 19% of hydrogen bonds are broken.

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We propose a sampling scheme to reduce the CPU time for Monte Carlo simulations of atomic systems. Our method is based on the separation of the potential energy into parts that are expected to vary at different rates as a function of coordinates. We perform n moves that are accepted or rejected according to the rapidly varying part of the potential, and the resulting configuration is accepted or rejected according to the slowly varying part. We test our method on a Lennard-Jones system. We show that use of our method leads to significant savings in CPU time. We also show that for moderate system sizes the scaling of CPU time with system size can be improved ͑for nϭ40 the scaling is predominantly linear up to 1000 particles͒.