Introduction to Density Functional Theory

Carsten A. Ullrich, Curators' Distinguished Professor, University of Missouri,Adam Wasserman, Professor of Chemistry, Purdue University

Carsten A. Ullrich received his PhD in 1995 at the University of Würzburg and, after several postdoctoral positions, joined the faculty at the University of Missouri in 2001. He received tenure in 2007 and became a full professor in 2013. In 2023 he was appointed Curator's Distinguished Professor of Physics. His research focuses on the study of the foundations and the development of new methodologies in time-dependent density functional theory (TDDFT) and spin-DFT. He has over 125 publications, including a book on TDDFT, and he is a Fellow of the American Physical Society.


Adam Wasserman is Professor of Chemistry at Purdue University, where he has taught since 2008. His research focuses on understanding why some chemical bonds are weak while others are strong. To do this, he and his research group develop methods based on Density Functional Theory to calculate the electronic properties of molecules directly from those of their constituent atoms. A Purdue University Faculty Scholar, Dr Wasserman holds a courtesy appointment in the Department of Physics and Astronomy, and has been a recipient of numerous awards, including an Alfred P. Sloan research Fellowship and a Camille and Henry Dreyfus Teacher-Scholar award.

1. Introductory remarks2. Review of quantum mechanics3. From densities to Hamiltonians: the main idea of DFT4. Quantum mechanics of N electrons5. More about N-electron wave functions6. What is a functional?7. The variational principle8. The Hohenberg-Kohn theorem9. The Thomas-Fermi model10. Orbitals and Slater determinants11. The Kohn-Sham approach12. A case study: two interacting electrons in 1D13. Defining exchange and correlation14. The homogeneous electron gas15. The local-density approximation16. A brief recap17. Spin in DFT18. Empirical vs. nonempirical approximations19. A taxonomy of functionals20. Orbital functionals and generalized DFT21. Two case studies: H?2 , H222. Chemical Reactivity23. DFT in practice: molecular calculations24. DFT in practice: solid-state calculations25. Time-dependent DFT26. EpilogueAppendix A - The hydrogen atomAppendix B - The Pair Density and the xc holeAppendix C - Adiabatic ConnectionAppendix D - Hellmann-Feynman and Virial TheoremsAppendix E - Exchange energy density of the 1D electron gasAppendix F - The Chemical PotentialAppendix G - Uniform Coordinate ScalingAppendix H - Linear-response TDDFT and excitation energiesAppendix I - Test your knowledgeAppendix J - Answers to selected exercises