Abstracts of the CTTC School 2016

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General Introduction

Eduard Matito

Universidad País Vasco

Chemical Bonding Analysis

In this course we will introduce a few concepts that will be used in the subsequent four Chemical Bonding courses.

• Density and Density Matrices.
• The Atom in a Molecule. Atomic partitions.
  • Three-dimensional partitions
    • The Quantum Theory of Atoms in Molecules (QTAIM) partition.
    • Fuzzy partitions. The Topological Fuzzy Voronoi Cells (TFVC)
  • Hilbert space partitions.
    • Mulliken's partition.
• Population Analysis
• Electron Sharing Indices.

We will follow the next notes [1] and slides [2] (slides will be updated in due time).

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

Tomás Rocha

Universidad Nacional Autónoma de México

• Fock space: creation and annihilation operators.
  • Fundamental anticommutation relationships.
• Representation of operators in second quantization.
• Rank reduction: some useful commutators and anticommutators.
• Singlet tensor operators.
• Use of second quantization in coupled cluster theory
  • Coupled cluster energy.
  • Connected coupled cluster equations.

José L. Gázquez

Universidad Autónoma Metropolitana-Iztapalapa, México

Chemical reactivity in density functional theory

The Taylor series expansion of the energy as a function of the number of electrons and the external potential, around an isolated chemical species, has been the basis of the density functional theory of chemical reactivity. The response functions that appear through this approach describe the inherent or intrinsic chemical reactivity, which may be used to infer the behavior of a molecule when it interacts with different families of reagents. In this presentation we will revise the concepts that arise from the derivatives of the energy with respect to the number of electrons, basically, the chemical potential and the chemical hardness, and the derivatives of the electronic density with respect to the number of electrons, basically, the Fukui function and the dual descriptor. We will also analyze the chemical potential equalization principle, the maximum hardness principle and the hard and soft acids and bases principle, and their importance to describe chemical interactions. Additionally, we will make use of the Hohenberg-Kohn-Mermin formalism in the grand canonical ensemble to derive the temperature dependent expressions. Finally, we will discuss the charge transfer process from the perspective of density functional theory to show the relevance of the concepts of chemical potential and hardness in chemistry.

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-Rotllant

CNRS and Université Aix-Marseille

Time-dependent density functional theory (TDDFT) has become a fundamental tool in quantum chemistry to calculate excited state properties of molecular systems with up to several hundreds of atoms. Despite this success, the approximations performed at the level of the exchange-correlation functional limit its accuracy. Indeed, several important problems have been detected like incorrect description of static correlation, the wrong description of charge-transfer and/or Rydberg states, or the incorrect description of state intersections with the ground state. This course will be divided in two parts: first, I will give a simple introduction to exact TDDFT and the main approximations usually applied to solve TDDFT equations in practice, focusing on the main drawbacks that are frequently encountered in approximate TDDFT. Second, we will do a hands-on tutorial with some practical examples like analysis of excited states and simulation of absorption and emission spectra for some organic molecules.

Cyrus Umrigar

Cornell Univ.

Summary

Materials

Carlos Cárdenas

Universidad de Chile

From molecules to solids

• Free electrons in a box.
• Born–von Karman periodic boundary condition (PBC)
• Free electrons in periodic boundary conditions: a simple model of metals. The concept of density of states will be intruded here.
• Chain Molecule. The reciprocal space will be introduced here.
• The square and cubic lattices
• Brillouin zones
• Energy Bands: insulators, semiconductors and metals.

Varinia Bernales

Minesotta U.

Summary

Juan E. Peralta

Department of Physics and Science of Advanced Materials Program, Central Michigan University, Mount Pleasant, MI 48859, USA.

Magnetic Properties of Transition Metal Complexes from Density Functional Theory

The characterization of the magnetic properties of molecular systems is important to understand and make predictions of the magnetic behavior of materials where magnetism is of molecular origin.[1] In this short course we will first briefly review the physical origin and theory of magnetic properties in molecular systems, and describe current methods to evaluate these properties in complexes containing transition metal atoms using density functional theory (DFT).[1-4] We will emphasize the strengths and deficiencies of DFT for these properties, including those intrinsic of DFT and those of current approximations. Finally, we will analyze real examples using the magnetic anisotropy energy and magnetic exchange couplings in connection to observed magnetic experimental data. [5-7]

[1] O. Kahn, Molecular Magnetism, VCH: New York, NY (1993).

[2] J. Kortus, M. R. Pederson, T. Baruah, N. Bernstein, and C. S. Hellberg, Density functional studies of single molecule magnets, Polyhedron 22, 1871 (2003).

[3] C. van Wüllen, Magnetic anisotropy from density functional calculations. Comparison of different approaches: Mn12O12 acetate as a test case, J. Chem. Phys. 130, 194109 (2009).

[4] J. J. Phillips, and J. E. Peralta, The role of range-separated Hartree-Fock exchange in the calculation of magnetic exchange couplings in transition metal complexes, J. Chem. Phys. 134 034108 (2011).

[5] Jens Kortus, Tunna Baruah, Noam Bernstein, and Mark R. Pederson, Magnetic ordering, electronic structure, and magnetic anisotropy energy in the high-spin Mn10 single molecule magnet, Phys. Rev. B 66 092403 (2002).

[6] J. J. Phillips, J. E. Peralta, and G. Christou, Magnetic couplings in spin frustrated FeIII7 disklike clusters, J. Chem. Theory Comput. 9, 5585 (2013).

[7] R. P. Joshi, J. J. Phillips, and J. E. Peralta, Magnetic exchange couplings in heterodinuclear complexes based on differential local spin rotations, J. Chem. Theory Comput. 12, 1728 (2016).

Jorge Seminario

Texas A&M University

Theoretical Chemistry Analyses for the Study and Design of Materials for Rechargeable Batteries

A review of the applications of theoretical chemistry methods for the development of new materials for rechargeable batteries will be shown [1-7]. Including, the concerted use of quantum and classical methods such as DFT on one hand and molecular dynamics on the other to solve key problems such as the solid electrolyte interphase formation and the mechanisms of electrode and electrolyte damage due mostly to electron tunneling from the anode to the electrolyte. The field of electrochemistry presents a challenge to engineers and scientists due to the strict multiscale and multidisciplinary nature of the problems. We will start with a rapid description of the methodology and the programs used, followed by their application to key materials and systems, and ending with some important results and describing possibilities for the future.

[1] L. Benitez, D. Cristancho, J. M. Seminario, J. M. Martinez de la Hoz, and P. B. Balbuena, "Electron transfer through solid-electrolyte-interphase layers formed on Si anodes of Li-ion batteries," Electrochimica Acta, vol. 140, pp. 250-257, 2014.

[2] S. M. Aguilera-Segura and J. M. Seminario, "Ab Initio Analysis of Silicon Nano-Clusters," J. Phys. Chem. C, vol. 118, pp. 1397-1406, 2014.

[3] F. A. Soto, Y. Ma, J. M. Martinez de la Hoz, J. M. Seminario, and P. B. Balbuena, "Formation and Growth Mechanisms of Solid-Electrolyte Interphase Layers in Rechargeable Batteries," Chem. Mat., vol. 27, pp. 7990-8000, 2015.

[4] Y. Ma, J. M. Martinez de la Hoz, I. Angarita, J. M. Berrio-Sanchez, L. Benitez, J. M. Seminario, et al., "Structure and Reactivity of Alucone-Coated Films on Si and LixSiy Surfaces," ACS Appl. Mater. Interfaces., vol. 7, pp. 11948-11955, 2015.

[5] F. A. Soto, J. M. Martinez de la Hoz, J. M. Seminario, and P. B. Balbuena, "Modeling Solid- Electrolyte Interfacial Phenomena in Silicon Anodes," Current Opinion in Chemical Engineering.

[6] G. Ramos-Sanchez, F. A. Soto, J. M. M. d. l. Hoz, Z. Liu, P. P. Mukherjee, F. El-Mellouhi, et al., "Computational Studies of Interfacial Reactions at Anode Materials: Initial Stages of the Solid-Electrolyte-Interphase Layer Formation," Journal of Electrochemical Energy Conversion and Storage.

[7] N. Kumar and J. M. Seminario, "Lithium-Ion Model Behavior in an Ethylene Carbonate Electrolyte Using Molecular Dynamics," J. Phys. Chem. C, In Press.

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

University of California, Berkeley

Quantifying and characterizing the (poly)radical nature of molecules

Diradicals are molecules with two electrons occupying two near degenerate orbitals. Indeed, how close to degeneracy these orbitals are (HOMO-LUMO gap) or more generally the singlet-triplet gap is one of the characteristic features of diradical systems. Diradicals are important in chemistry since they emerge as intermediates of many chemical reactions. Pure, ideal diradicals such as a dissociated H2 singlet can be easily characterized theoretically from different indicators, depending on the nature of the wave function. However, the quantification of the diradical or diradicaloid character of short-lived singlet diradicals is not so trivial because the formally unpaired electrons do interact to some extent. More generally, a polyradical can be considered as a molecule with N electrons occupying N near degenerate orbitals. The design of organic high-spin polyradicals is of major relevance for the development of new organic and organometallic magnetic materials. As opposed to the simplest case of diradicals, the more general case of organic polyradicals adds extra complexity to the puzzle of radical character quantification, as most of the indices and quantities that have been proposed in the literature to detect and quantify the diradical character of molecular systems cannot be trivially generalized beyond diradicals. In this lecture, I will review different methods to characterize unpaired electrons in radical or polyradical systems from ab initio calculations. I will introduce the Local Spin analysis and I will show the ability of this analysis to characterize and quantify the radical nature of molecular systems.

Pedro Salvador

Universitat de Girona

Effective atomic orbitals and its application to Oxidation State analysis

The concept of atom in a molecule has always craved for a proper definition, and we are lacking a single, unambiguous one. Within the LCAO approach, the atom may be identified with the subspace of the basis functions attached to it. Such approach leads to the so-called Hilbert-space analyses. A different strategy is to subdivide the physical (3D) space into atomic regions or domains, which represent (together with the nucleus) the atom. When looking for an atom in a molecule, obviously we are not merely interested in a subdivision of the 3D space into atomic volumes, but rather in assigning different physical quantities to the individual atoms (or their groups).

Probably, the most appropriate entities that serve to characterize the state of the atom within the molecule are the so-called effective atomic orbitals (“effective AOs”). In this approach, one obtains for each atom a set of orthogonal atomic hybrids and their respective occupation numbers, adding up to the net population of the atom, even if no atom-centered basis functions are used at all to expand the molecular orbitals. These atomic hybrids closely mimic the core and valence shells of the atom, as anticipated on the basis of classical notions of electron configuration of the atom/fragment within the molecule.

In this lecture we will review the basic features of the effective AOs, in the framework of fuzzy atoms and disjoints domains such as QTAIM. It is of particular conceptual relevance the fact that in the basis of such orbitals, the Hilbert-space and 3D-space analysis are numerically equivalent. We will end by seeing a direct application of these objects, for the derivation of formal oxidation states from wave function analysis.