An improvement to the grid-based algorithm of Henkelman et al. for the calculation of Bader volumes is suggested, which more accurately calculates atomic properties as predicted by the theory of Atoms in Molecules. The CPU time required by the improved algorithm to perform the Bader analysis scales linearly with the number of interatomic surfaces in the system. The new algorithm corrects systematic deviations from the true Bader surface, calculated by the original method and also does not require explicit representation of the interatomic surfaces, resulting in a more robust method of partitioning charge density among atoms in the system. Applications of the method to some small systems are given and it is further demonstrated how the method can be used to define an energy per atom in ab initio calculations.

Quantum Monte Carlo ͑QMC͒ calculations are only possible in finite systems and so solids and liquids must be modeled using small simulation cells subject to periodic boundary conditions. The resulting finite-size errors are often corrected using data from local-density functional or Hartree-Fock calculations, but systematic errors remain after these corrections have been applied. The results of our jellium QMC calculations for simulation cells containing more than 600 electrons confirm that the residual errors are significant and decay very slowly as the system size increases. We show that they are sensitive to the form of the model Coulomb interaction used in the simulation cell Hamiltonian and that the usual choice, exemplified by the Ewald summation technique, is not the best. The finite-size errors can be greatly reduced and the speed of the calculations increased by a factor of 20 if a better choice is made. Finite-size effects plague most methods used for extended Coulomb systems and many of the ideas in this paper are quite general: they may be applied to any type of quantum or classical Monte Carlo simulation, to other many-body approaches such as the GW method, and to Hartree-Fock and density-functional calculations.

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A variational and diffusion quantum Monte Carlo study of germanium in the diamond structure is reported, in which local pseudopotentials are used to represent the ion cores. We calculate the energy of the free atom and the energy of the solid as a function of volume. The calculations for the solid are performed using a supercell method. We analyze the translational symmetry of the supercell Hamiltonian and show that the eigenstates can be labeled by two wave vectors, k, and k".The wavevector k, arises from the invariance of the Hamiltonian under the translation of any oneelectron coordinate by a supercell translation vector, while the wave vector k", which is the crystal momentum of the wave function, arises from the invariance under the simultaneous translation of all electron coordinates by a translation vector of the crystal lattice. Our solid calculations are performed using wave functions with nonzero supercell wave vectors k"which gives better convergence with the size of supercell than previous zero-wave-vector calculations. The relationship of this method to the special k-points techniques commonly used in band-structure calculations is discussed.

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