Abstracts of the CTTC School 2016

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General Introduction

Eduard Matito

Universidad País Vasco

Summary

Carlos Cárdenas

Universidad de Chile

Summary

Andreas Savin

CNRS and Sorbonne Universités, UPMC Univ Paris 06

Density Functional Theory

• Foundations of density functional theory
  • The Hohenberg-Kohn theorem
  • Accurate functionals
  • Response functions
• Methods used in the frame of density theory
  • The Kohn-Sham method
  • Functionals for the kinetic, exchange, correlation energies
  • Scaling
• Tools for constructing approximations, and extending density functional theory
  • Adiabaitc connection
  • Hybrids
• Approximations for density functionals
  • LDA
  • Semi-local approximations
  • Hybrids
    • Combination with Hartree-Fock
    • Combination with multi-reference methods
  • Methods for excited states
• Main limitations of approximations
  • Systematic improvement
  • Treatment of degeneracy and size-consistency
• Methods related to density functional theories
  • Local potentials
  • Random phase approximation
• Judging approximations
  • Concepts from statistics
  • Benchmarks and their limits

José Luis Gazquez

UNAM-Iztapalapa

Summary

Development

Paul Ayers

McMaster Univ.

Summary

Peter Gill

Australian National University

Although density functional theory (DFT) has become extremely popular within the quantum chemistry community, it still suffers from some serious deficiencies and most of these are now well understood. One of the key goals of modern research, therefore, is to develop new methods that preserve the low cost of DFT calculations while offering significantly enhanced accuracy.

Many of the problems of DFT stem from the fact that most functionals are based on the uniform electron gas, a model that consists of an infinite number of electrons in an infinite volume. Unfortunately, this system does not resemble the electron density in most molecules and one route to the improvement of DFT is to replace this foundation with a new one.

Electrons-on-a-sphere is a particularly attractive model because it is defined by a single parameter (the radius R of the sphere) and varying this takes us from a weakly correlated system (small R) dominated by dynamical correlation, to a strongly correlated system (large R) dominated by static correlation.

I will review this model and show how it can be used as the starting point for a new way of understanding and improving DFT.

Miquel Huix-Rotlland

Université Aix-Marseille

Summary

Cyrus Umrigar

Cornell Univ.

Summary

Materials

Perla Balbuena

Texas A&M University

Summary

Varinia Bernales

Minesotta U.

Summary

Juan Peralta

Central Michigan Univ.

Summary

Jorge Seminario

Texas A&M University

Summary

Chemical Bonding

Marco García-Revilla

Univ. Guanajuato, México

Summary The study of the Chemical Bond belongs to the most important issues in Chemistry. The new methodologies in this field enable us to rationalize chemical phenomenon where the traditional models fail. The Interacting Quantum Atoms (IQA)[1,2] and the Electron Distribution Functions EDF[3] belong to such new methodologies. IQA and EDF have been shown to be successful to deal with the study of the Chemical Bond. Two studies are presented in this lecture. 1) Oxygen under extreme pressure conditions, the unexplained physicochemical behavior of O2 under pressure can be finally rationalized by the IQA and EDF methodology.[4] 2) Constructing molecular graphs from IQA bonding descriptors, the exchange-correlation energies can be used to draw molecular graphs with physical insight.[5]

[1] A. Martín Pendás, M. A. Blanco, and E. Francisco. J. Chem. Phys. 2004, 120, 4581; J. Comput. Chem. 2005, 26, 344; J. Chem. Theory Comput. 2005,1,1096; J. Comput. Chem. 2007, 28, 16;. A. Martín Pendás, M. A. Blanco, and E. Francisco. J. Chem. Phys. 2006, 125. 184112 A. Martín Pendás, M. A. Blanco,and E. Francisco. J. Comput. Chem. 2009, 30, 98; D. Tiana et al. J. Chem.Theory Comput. 2010, 6, 1064; D. Tiana et. al. Phys. Chem. Chem. Phys. 2011,13, 5068. [2] A. Martín Pendás, E. Francisco, M. A. Blanco, and Carlo Gatti. Chem. Eur. J. 13, 9362 (2007). [3] E. Francisco, A. Martín Pendás, M. A. Blanco. J. Chem. Phys. 126, 094102 (2007); E. Francisco, M. A. Blanco , A. Martín Pendás. Comp. Phys. Commun. 178, 621 (2008); A. Martín Pendás, E. Francisco, M. A. Blanco, Phys. Chem. Chem. Phys. 9, 1087 (2007). [4] M. A García-Revilla, E.Francisco, A.Martín Pendás, J.M.Recio, M.I.Hernández, J. Campos-Martínez, E. Carmona-Novillo, and R. Hernández-Lamoneda. J. Chem. Theory Comput., 9, 2179 (2013). [5] M. A García-Revilla, E. Francisco, PL. Popelier, and A. Martín Pendás. Chemphyschem, 14,1211 (2013).

Ángel Martín Pendás

Universidad de Oviedo. Spain.

A real space perspective of how energy and electrons distribute in molecules: Interacting quantum atoms and electron distribution functions

The topological approach to chemical bonding in real space, or Quantum Chemical Topology (QCT) has now come of age. Its best known flavor, the Quantum Theory of Atoms in Molecules (QTAIM) [1] has been extremely successful, providing an orbital invariant theory of chemical bonding problems based on an observable, the electron density, amenable to experimental determination. In this course we will consider the basics of QCT as well as two development that expands its scope and predictive power: the Interacting Quantum Atoms (IQA) [2-3] approach, which provides an exact energetic decomposition within the QTAIM valid at general geometries, and the electron distribution functions (EDF) [4].

[1] R. F. W. Bader, Atoms in Molecules , Oxford University Press., Oxford (1990). [2] A. Martín Pendás, M. A. Blanco, and E. Francisco. J. Chem. Phys. 2004, 120, 4581; J. Comput. Chem. 2005, 26, 344; J. Chem. Theory Comput. 2005, 1, 1096; J. Comput. Chem. 2007, 28, 16;. A. Martín Pendás, M. A. Blanco, and E. Francisco. J. Chem. Phys. 2006, 125. 184112 A. Martín Pendás, M. A. Blanco, and E. Francisco. J. Comput. Chem. 2009, 30, 98; D. Tiana et al. J. Chem. Theory Comput. 2010, 6, 1064; D. Tiana et. al. Phys. Chem. Chem. Phys. 2011, 13, 5068. [3] A. Martín Pendás, E. Francisco, M. A. Blanco, and Carlo Gatti. Chem. Eur. J. 13, 9362 (2007). [4] E. Francisco, A. Martín Pendás, M. A. Blanco. J. Chem. Phys. 126, 094102 (2007); E. Francisco, M. A. Blanco , A. Martín Pendás. Comp. Phys. Commun. 178, 621 (2008); A. Martín Pendás, E. Francisco, M. A. Blanco, Phys. Chem. Chem. Phys. 9, 1087 (2007).

Summary

Eloy Ramos-Cordoba

Berkeley Univ.

Summary

Pedro Salvador

Universitat de Girona

Summary