**Local field effects**. When an external field encounters the periodic lattice, it induces charge densities that give rise to "local fields" that vary on the atomic scale. These local fields must be included in computing the susceptibilities.- First-order: always reduces; on few to 10% scale.
- Second-order: either sign; typically 10-50%.
- Rotatory power: can change sign and value by factor of 10.

**Importance of accurate band gaps, E_gap**. The susceptibilities scale as 1/E_gap (1st order), 1/E_gap^3 (2nd order) LDA typically underestimates the band gap by 0.5 to 1.0 eV. We use a `scissors operator' to shift conduction bands to match the experimental gap or a gap estimated by many-body theory (see below).**Systematics across related and different materials**. The `scissors operator' works well for small and medium-gap semiconductors. But for wide-gap insulators we find empirically that a smaller or no shift of the conduction bands yields results closer to experiment. This is not understood.

**Momentum space**. Most widely used, suitable for bulk calculations with a few atoms in unit cell and periodic boundary conditions. Applications: superlattices and simple defects.**Real space**. Most suitable for clusters and defects, both simple and extended. There is only one version of this code, due to Godby and recently parallelized.**Localized description**. Designed for very large unit cells and utilizing localized wavefunction of the TB-LMTO type.

An extended defect in Si -- called the (311) defect due to its habit plane -- has been identified as a possible source/sink of Si interstitials believed to dominate boron diffusion. We are engaged in large-scale parallel simulations of extended defects in silicon. Essential to the treating 1000s of atoms is the use of the simpler, tight-binding Hamiltonian. Even so it is necessary to time-evolve a defect for a picosecond at 300-600 K to avoid being trapped in local minima. Then we fully relax the atomic positions by `steepest descent' until the atomic force on each atom is less than 0.1 eV/Angstrom and the effective temperature of the lattice is less than 0.1 K. Initial progress in identifying possible forms of the <311> defect has raised as many new questions as it offered possible answers to the original concerns that provoked the research.

(i)*Partition of the basis*. The partitioning takes advantage
of so-called natural orbits to develop a basis set each of set of which
as an occupancy an order of magnitude smaller than the next.

(ii)*Many-electron state selection*. The one-electron basis
partitioning leads a division of the state space into an external and
internal subspaces. A perturbative calculation of the external
subspace can be combined with an exact treatment of the internal
subspace to yield results comparable to those using the full state
space.

- Minus
- The orthogonal basis functions in each determinant are different so that determinants are not orthogonal. This severely slows down the calculation of matrix elements.
- Plus
- The small number of determinants making up the state allows for a better understanding of the correlations.

More interestingly, almost all the object-oriented software can be adapted to study semiconductor quantum dots in a laser pulse. It turns out that one can readily identify effects demonstrating important correlations in the dots -- that is, easy to measure experimentally. This is such a new area that it is difficult to predict where it is going. But effective probes of correlation in strongly interacting systems are few. This could be an important new probe.

Your comments and suggestions are appreciated.

[OSU Physics] [College of Mathematical and Physical Sciences] [Center for Materials Research] [Ohio State University]

Edited by: wilkins@mps.ohio-state.edu [October 1996]