state properties of high-Tc superconducting oxides (e.g., structural parameters, phonon spectra, Fermi surfaces); prediction of new phases of materials under high pressures (e.g., superconductivity in the simple hexagonal phase of Si); prediction of a superhard material (C3N4); determination of the structure and properties of surfaces, interfaces, and clusters; and calculation of the structure and properties of the fullerenes and fullerides.

The Car-Parrinello-type ab initio molecular dynamics approach and the less accurate but less time-consuming tight-binding molecular dynamic schemes have made possible the quantum mechanical calculation of the dynamics and thermodynamical properties of systems in the solid, liquid, and gaseous states. The first-principles quasi-particle approach based on the GW approximation (which evaluates the electron self-energy to the first order in the electron Green's function G and screened Coulomb interaction W) has been used to calculate electron excitation energies in solids that, in turn, are used for the quantitative interpretation of spectroscopic measurements. The excitation spectra of crystals, surfaces, and materials as complex as the C60 fullerites have been computed. Quantum Monte Carlo methods have yielded cohesive properties of unprecedented accuracy for covalent crystals and have provided the means to study highly correlated electron systems, such as two-dimensional electrons at semiconductor heterojunctions in a strong magnetic field.

Very accurate determination of the properties of specific materials by itself is not sufficient, however, for the general goal of materials by design. A critical issue is how one can intelligently sample the vast phase space of taking different elements in various proportions over the periodic table to make a material of specific desired properties. Even with computers that are several orders of magnitude more powerful than existing machines, it would not be possible to sample the phase space adequately. Together with accurate methods, there must be guiding principles (e.g., those based on structure-property relationships) in the theoretical search for new materials. The discovery of general principles regarding materials behavior is thus as important in the theoretical design of materials as are accurate computational methods.

Another important related issue is the process of starting from conception to the final synthesis of a useful new material. Because of the large phase space discussed above, it is unlikely that a material of optimal desired properties will be obtained on the first try. Many iterations involving theoretical prediction, experimental synthesis, and characterization are needed. A major challenge then is to find ways to accelerate convergence in this iterative process.

A case in point is the recent provocative and potentially useful prediction of a new material, carbon nitride, which rivals or exceeds the hardness of diamond. In 1989, based on an empirical idea and through first-principles total energy calculations, a new compound, C3N4, was predicted to be stable and to have bulk modulus comparable to that of diamond. Its structural and electronic properties were predicted by using LDA. Subsequent to the theoretical work, several groups proceeded to synthesize and characterize this possible material in the laboratory. In 1992 independent experimental evidence was obtained from three groups lending support for the theoretical prediction. This case provides a concrete example of how ideas, computations, and experimental characterization may work together in the design of materials of intrinsic scientific interest and potential utility.

Future Theoretical Developments and Computing Forecast

In the past several years much effort has been devoted to developing algorithms to extend the applicability of the above new methods to ever larger systems. The LDA Car-Parrinello-type calculations have been successfully implemented on scalable parallel machines. Recent calculations of semiconductor systems using this method have reached the size of



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