2011 Density Functional Theory Workshop, July 23-27
Complete Program (PDF)
Lecture 1: DFT Electronic Structure Calculations by Muffin Tin Orbital Based Basis
(i) Introduction to Basis Sets.
(ii) Muffin-Tin Approximation.
(iii) Envelope Function, Screening and Augmentation: Muffin Tin Orbitals
(iv) Tail Cancellation and KKR.
(v) Linearization: Linear Muffin Tin Orbital (LMTO)
(vi) Improved LMTO -- N-th Order MTO (NMTO) Method
(vii) Applications of NMTO in Deriving Few Band Hamiltonians.
Lecture 2: Correlation Effects in Real Materials
- (i) Introduction: Why Strong Correlations?
- Failure of One-Electron Theories
- Hesitant Electrons: Delocalized Waves or Localized Particles?
- Examples of Strongly Correlated Materials
- Different Energy Scales and MIT in TMO
- Concepts (LDA+U, LDA+DMFT)
- Practical Details
- t-J and Heisenberg
Calculation of electronic structure of Si and CaMnO3 using LMTO method.
Lecture 1: Introduction to Density Functional Theory
A density functional is a formula that expresses the ground-state energy of a many-electron system in terms of its electron density, facilitating the easy computation of both. In Kohn-Sham density functional theory (DFT), most of the energy is expressed exactly in terms of orbitals, leaving the exchange-correlation energy to be expressed exactly or approximately in terms of the density or the orbitals. This lecture will summarize the history of DFT, and explain why it is so widely used in quantum chemistry and condensed matter physics. The theorems and proofs that justify this approach to the ground-state energy and electron spin densities will be reviewed. The exchange-correlation energy will be defined, and the Jacob's ladder of approximations to it will be introduced. Finally, it will be explained why the lower-rung, computationally-efficient semilocal approximations are appropriate for some problems and not for others.
Lecture 2: Advanced Density Functional Theory
The adiabatic connection formula for the exchange-correlation energy as a functional of the density will be introduced, with the related idea of the exchange-correlation hole around an electron. Exact properties of the density functional and hole will be introduced, and used as exact constraints for the nonempirical or minimally empirical construction of density functional approximations. From this discussion, it will be clear why even the simple local density approximation works fairly well, and why higher-rung functionals can work better. The one- and many-electron self-interaction errors, which can be especially problematic for strongly-correlated systems, will be discussed.
Perdew may assign some DFT computations for atoms and small molecules using GAUSSIAN09, to illustrate what the theory and its approximations can or cannot do. He might also assign conceptual or pen-and-paper exercises.
Lecture 1: Plane Waves and Pseudopotentials
(i) Plane Wave Basis
(ii) Problems for Core and Valence Wavefunctions
(iii) The Pseudopotential Approximation
(iv) Generating an Ab initio Pseudopotential
(v) Norm Conservation: Advantages and Disadvantages
(viii) Ultrasoft Pseudopotentials
Lecture 2: Practical Issues in Doing a DFT Calculation (with Plane Waves and Pseudopotentials)
(i) Iterative Solution: The Self-Consistent Loop
(ii) Convergence with Respect to Cut-off
(iii) Brillouin Zone Sampling
(iv) Metals and Smearing
(vi) Output Quantities
- Simple self-consistent-field calculations on silicon
(and, if time permits, aluminum) with the Quantum ESPRESSO code.
Lecture 1: Basic Existence Theorems
Comparisons of the theories of wave functions, density functionals, and density-matrix functionals will be discussed briefly. Then the basic existence theorems will be proven for degenerate and non-degenerate cases, and mathematical aspects of the self-consistent equations will be studied.
Lecture 2: Properties of Exact Functionals
Several fundamental properties of the exact functionals, such as those involving coordinate scaling, will be derived and discussed in terms of their use for obtaining approximations. Properties of the electron density, including its asymptotic decay, will also be discussed.
Discuss solutions to conceptual problems.
Lecture 1: Free energies and mechanisms of chemical reactions in solution and in enzymes with DFT QM/MM method
Multiscale modeling is an effective tool for extending the applicability of DFT to large and complex systems, in particular for processes in condensed environment. The multiscale combined QM/MM methods provide an accurate and efficient energetic description of complex chemical and biological systems, leading to significant advances in the understanding of chemical reactions in solution and in enzymes. Density functional theory based ab initio QM/MM methods capitalize on the accuracy and reliability of the associated quantum mechanical approaches, but at a much higher computational cost compared with semiempirical quantum mechanical approaches. Thus reaction path and activation free energy calculations encounter unique challenges in simulation timescales and phase space sampling. Recent developments of the DFT QM/MM minimum free energy path method overcome these challenges and enable accurate free energy determination for reaction and redox processes in solution and enzymes. Applications to several solution and enzyme reactions and redox processes will be highlighted.
H. Hu, Z. Y. Lu, and W. T. Yang, "QM/MM minimum free-energy path: Methodology and application to triosephosphate isomerase," Journal of Chemical Theory and Computation, vol. 3, pp. 390-406, 2007.
H. Hu, Z. Y. Lu, J. M. Parks, S. K. Burger, and W. T. Yang, "Quantum Mechanics/Molecular Mechanics minimum free-energy path for accurate reaction energetics in solution and enzymes: Sequential sampling and optimization on the potential of mean force surface," Journal of Chemical Physics, vol. 128, p. 034105, 2008.
H. Hu and W. T. Yang, "Free energies of chemical reactions in solution and in enzymes with ab initio Quantum Mechanics/Molecular Mechanics methods," Annual Review of Physical Chemistry, vol. 59, pp. 573-601, 2008.
H. Hu, A. Boone, and W. T. Yang, "Mechanism of omp decarboxylation in orotidine 5 '-monophosphate decarboxylase," Journal of the American Chemical Society, vol. 130, pp. 14493-14503, 2008.
X. C. Zeng, H. Hu, X. Q. Hu, A. J. Cohen, and W. T. Yang, "Ab initio quantum mechanical/molecular mechanical simulation of electron transfer process: Fractional electron approach," Journal of Chemical Physics, vol. 128, p. 124510, 2008.
X. C. Zeng, H. Hu, X. Q. Hu, and W. T. Yang, "Calculating solution redox free energies with ab initio Quantum Mechanical/Molecular Mechanical minimum free energy path method," Journal of Chemical Physics, vol. 130, p. 164111, 2009.
Xiangqian Hu, Hao Hu, Jeffrey A. Melvin, Kathleen W. Clancy, Dewey G. McCafferty, and Weitao Yang, "Autocatalytic Intramolecular Isopeptide Bond Formation in Gram-Positive Bacterial Pili: A QM/MM Simulation", J. Am. Chem. Soc., 133, 478-485, 2011.
Lecture 2: Revealing Noncovalent interactions
Molecular or bulk structure does not easily identify the intricate noncovalent interactions that govern many areas of physics, biology and chemistry, including design of new materials and drugs. We develop an approach to detect noncovalent interactions (NCI) in real space, based on the electron density and its derivatives. Our approach reveals the underlying chemistry that compliments the covalent structure. It provides a rich representation of van der Waals interactions, hydrogen bonds, and steric repulsion in small molecules, molecular complexes, and solids. Most importantly, the method, requiring only knowledge of the atomic coordinates, is efficient and applicable to large systems, such as nanostructures, bulk solids, proteins or DNA. Across these applications, a view of nonbonded interactions emerges as continuous surfaces rather than close contacts between atom pairs, offering rich insight into the design of new and improved ligands. We will describe the NCI computational algorithms and their implementation for the analysis and visualization of weak interactions, using both self-consistent fully quantum-mechanical as well as promolecular densities. A wide range of options for tuning the range of interactions to be plotted is also presented. To demonstrate the capabilities of our approach, several examples are given from organic, inorganic, solid state, and macromolecular chemistry, including cases where NCI analysis gives insight into unconventional chemical bonding. The NCI code and its manual are available for download at http://www.chem.duke.edu/~yang/software.htm.
E. R. Johnson, S. Keinan, P. Mori-Sanchez, J. Contreras-Garcia, A. J. Cohen, and W. T. Yang. "Revealing noncovalent interactions." Journal of the American Chemical Society, 132:6498, 2010.
Julia Contreras-Garcia, Erin R. Johnson, Shahar Keinan, Robin Chaudret, Jean-Philip Piquemal, David N. Beratan, and W. T. Yang, "NCIPLOT: A Program for Plotting Noncovalent Interaction Region," J. Chem. Theory Comput. 7: 625, 2011
- Using the Noncovalent Interaction Index (NCI).
Special Videoconference Lecture: The golden age of electronic structure theory
The ever increasing power of computers and algorithms have made it possible to calculate the properties of collections of hundreds of atoms using density functional theory. This capability has already transformed chemistry, and is about to revolutionize materials science. It is a wonderful time to be entering this field and this workshop is a great introduction from the leaders, including several who made this revolution possible.\\ However, we are still far from providing a turn-key tool to solve all problems of materials design, and thus usher in a new age of human control over our environment. While our methods work for many generic cases, failures abound, and we often have no good solution in these cases. Woe betide the naive student who ignores these dangers. My lecture will discuss the past, present, and future of the field.