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The introduction of a small amount of impurities or point defects in a crystalline semiconductor may change the electric properties over several orders of magnitude,(1) and is the basis of electronic devices. The technological importance of such properties has given rise to a lot of theoretical and experimental work devoted to the study of impurity states.

We outline a modern theory of the spontaneous polarization P in pyroelectric and ferroelectric materials. Although P itself isnot an observable, the difference ΔP between two crystal states can indeed be measured and calculated. We define P as the difference between the polar structure and a suitably chosen nonpolar prototype structure. We previously proposed and implemented a supercell scheme in order to evaluate P in pyroelectric BeO; here we adopt an approach recently developed by King-Smith and Vanderbilt, where ΔP is obtained from the computation of Berry's phases, with no use of supercells. We apply this novel approach, which is numerically very convenient, in order to revisit our previous work on BeO. We then perform a first-principles investigation of the spontaneous polarization P of KNbO3 in its tetragonal phase, which is a well studied perovskite ferroelectric. Our calculated P value confirms the most recent experimental data. The polarization is linear in the ferroelectric distortion; the Born effective charges show strong variations from nominal ionic values, and a large inequivalence of the 0 ions. Only the highest nine valence-band states (O 2p) contribute to P, while all the other states behave as rigid core states.

We demonstrate the feasibility of ab initio studies of piezoelectricity within an all-electron scheme. The focus of our analysis is on wurtzite ZnO; for comparison, some results are also presented for the related materials BeO and ZnS. The comparative study is performed in order to understand the microscopic origin of the peculiar behavior of ZnO, whose piezoelectric response is the strongest among the tetrahedrally bonded semiconductors. In all such materials, the piezeoelectric effect results from two different terms of opposite sign: these are usually referred to as the ``clamped-ion'' and the ``internal-strain'' contributions. Cancellation among them is least effective in ZnO, where the dominant effect is due to a rigid-ion-like mechanism. Furthermore, we compute the spontaneous polarization of ZnO and we discuss the puzzling agreement between our calculated value and a very indirect experimental estimate of the same quantity.

The charge "belonging" to a given atom in a condensed system is not a measurable quantity, and can be defined only by means of some arbitrary model and/or theory: the static dipole (or multipole) associated with a given molecule in a molecular solid or liquid is analogously ill-defined. At variance with this, the dynamical (alias infrared, IR) atomic charge is a well defined quantity, much studied in recent years for various materials: it measures the coupling of atomic displacements to macroscopic electric fields, either static or in the IR regime. We present here the generalization of the concept of atomic dynamical charge addressing the dynamical monopole and dipole for a molecule in condensed-either solid or liquid-molecular phase. In the low frequency IR region, dominated by intermolecular modes (translational and librational), such monopole and dipole are responsible for the shape of the spectrum. For an isolated molecule the dynamical monopole and dipole both coincide with the static ones: the changes occurring when embedding a given molecule in a condensed environment carry in compact form outstanding information about the intermolecular interactions. We present first-principle results for the test case of liquid water, where the effects of such interactions are particularly dramatic.

We measure electron localization in different materials by means of a ``localization tensor'', based on Berry phases and related quantities. We analyze its properties, and we actually compute such tensor from first principles for several tetrahedrally coordinated semiconductors. We discuss the trends in our calculated quantity, and we relate our findings to recent work by other authors. We also address the ``hermaphrodite orbitals'', which are localized (Wannier-like) in a given direction, and delocalized (Bloch-like) in the two orthogonal directions: our tensor is related to the optimal localization of these orbitals. We also prove numerically that the decay of the optimally localized hermaphrodite orbitals is exponential., gzipped tar file; 11 pages in two-column format, 7 encapsulated postscript figures

We calculate ab-initio the electronic states and the Born dynamical charge Z* of the alkaline-earth oxides in the local-density approximation. We investigate the trend of increasing Z* values through the series, using band-by-band decompositions and computational experiments performed on fake materials with artificially-modified covalence. The deviations of Z* from the nominal value 2 are due to the increasing interaction between O 2p orbitals and unoccupied cation d states. We also explain the variations, along the series, of the individual contributions to Z* arising from the occupied band manifolds., 12 pages Latex, plus 2 Postscript figures

The authors analyze a recent calculation by themselves. According to a suggestion of Kunz, they include in the Fock matrix terms due to intermolecular self-consistency, thus getting a substantial improvement in calculations. The energy bands of solid methane have been recomputed and the resulting reduction of bandwidth has been discussed.