2011 Density Functional Theory Workshop, July 2327
Complete Program (PDF) 
Tanusri SahaDasgupta

Lecture 1: DFT Electronic Structure Calculations by Muffin Tin Orbital Based Basis

(i) Introduction to Basis Sets.
(ii) MuffinTin 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  Nth 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 OneElectron 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
 Examples

 tJ and Heisenberg
 SuperExchange
HandsOn Session:

Calculation of electronic structure of Si and CaMnO_{3} using LMTO method.
John Perdew

Lecture 1: Introduction to Density Functional Theory
A density functional is a formula that expresses the groundstate energy of a manyelectron system in terms of
its electron density, facilitating the easy computation of both. In KohnSham density functional theory (DFT),
most of the energy is expressed exactly in terms of orbitals, leaving the exchangecorrelation 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 groundstate energy and electron spin densities will
be reviewed. The exchangecorrelation energy will be defined, and the Jacob's ladder of approximations to it
will be introduced. Finally, it will be explained why the lowerrung, computationallyefficient semilocal
approximations are appropriate for some problems and not for others.
Lecture 2: Advanced Density Functional Theory
The adiabatic connection formula for the exchangecorrelation energy as a functional of the density will
be introduced, with the related idea of the exchangecorrelation 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 higherrung functionals
can work better. The one and manyelectron selfinteraction errors, which can be especially problematic
for stronglycorrelated systems, will be discussed.
HandsOn Session:
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 penandpaper exercises.
Shobhana Narasimhan

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
(vi) Transferability
(vii) Smoothness
(viii) Ultrasoft Pseudopotentials
Lecture 2: Practical Issues in Doing a DFT Calculation (with Plane Waves and Pseudopotentials)

(i) Iterative Solution: The SelfConsistent Loop
(ii) Convergence with Respect to Cutoff
(iii) Brillouin Zone Sampling
(iv) Metals and Smearing
(v) Mixing
(vi) Output Quantities
HandsOn Session:
 Simple selfconsistentfield calculations on silicon
(and, if time permits, aluminum) with the Quantum ESPRESSO code.
Melvyn Levy

Lecture 1: Basic Existence Theorems
Comparisons of the theories of wave functions, density functionals, and densitymatrix
functionals will be discussed briefly. Then the basic existence theorems will be proven for
degenerate and nondegenerate cases, and mathematical aspects of the selfconsistent 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.
HandsOn Session:
Discuss solutions to conceptual problems.
Weitao Yang

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.
References
H. Hu, Z. Y. Lu, and W. T. Yang, "QM/MM minimum freeenergy path: Methodology and application to
triosephosphate isomerase," Journal of Chemical Theory and Computation, vol. 3, pp. 390406, 2007.
H. Hu, Z. Y. Lu, J. M. Parks, S. K. Burger, and W. T. Yang, "Quantum Mechanics/Molecular Mechanics minimum
freeenergy 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. 573601, 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. 1449314503, 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 GramPositive Bacterial Pili:
A QM/MM Simulation", J. Am. Chem. Soc., 133, 478485, 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 selfconsistent fully quantummechanical 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.
References
E. R. Johnson, S. Keinan, P. MoriSanchez, J. ContrerasGarcia, A. J. Cohen, and
W. T. Yang. "Revealing noncovalent interactions." Journal of the American Chemical
Society, 132:6498, 2010.
Julia ContrerasGarcia, Erin R. Johnson, Shahar Keinan, Robin Chaudret, JeanPhilip
Piquemal, David N. Beratan, and W. T. Yang, "NCIPLOT: A Program for Plotting Noncovalent
Interaction Region," J. Chem. Theory Comput. 7: 625, 2011
HandsOn Session:
 Using the Noncovalent Interaction Index (NCI).
Kieron Burke

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 turnkey 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.