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### Solid State Physics and Quantum Chemistry/Density Functional Theory

### Professor John P. Perdew

Temple group members: Research Assistant Professor Jianwei Sun. Graduate student Bing Xiao.

Our research group develops the fundamentals and approximations of density functional theory for atoms, molecules, and solids. Practical electronic structure calculations in both condensed matter physics and quantum chemistry now usually rely upon this theory, which can predict for example the shape of a molecule or the energy of a bond. The idea is that the complicated many-electron wavefunction can be replaced by something simpler, such as the electron density or a set of occupied orbitals. This replacement is exact in principle, but in practice one must approximate the functional dependence of the exchange-correlation energy upon the density or orbitals. The exchange-correlation energy is "nature's glue" for interatomic binding.

We have developed a "Jacob's Ladder" of approximations, in which higher rungs are more accurate but make use of more complicated ingredients. At least the first three rungs have been constructed non-empirically, using only exact constraints on the exact functional as developed by us and by others. The first rung is the local spin density approximation, which is good enough for many solids but not for molecules. The second rung is the generalized gradient approximation, which achieves a more useful accuracy for chemistry. The third rung is the meta-GGA, which further improves accuracy for both molecules and solids, molecules on surfaces, etc. Higher rungs are also under development.

Our functionals are built into standard software packages, and are widely used not only by theorists but even by experimentalists. Among the problems of current interest are the construction of a better meta-GGA and improved descriptions for strong correlation and for the van der Waals interaction.
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