Abstracts of the CTTC School 2016

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General Introduction

Eduard Matito

Universidad País Vasco

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

Tomás Rocha

Univ. Autónoma de México

Summary

José L. Gázquez

UAM-Iztapalapa

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

Xin Xu

Fudan Univ., China

Recent advances on the XYG3-type of doubly hybrid density functionals 

Doubly hybrid (DH) functionals present a new class of density functionals, which enfold the non-local orbital-dependent components not only in the exchange part, but also in the correlation part. Different types of DH functionals have been proposed according to different philosophies [1-3], where the XYG3-type of functionals (xDH) [3-11] is unique in its framework that a conventional (general) Kohn-Sham (KS) functional, such as B3LYP [3-6] or PBE0 [7] or PBE [8], is utilized for the self-consistent-field (SCF) calculations to generate orbitals and density, with which a DH functional is used for the final energy evaluations.

This talk focuses on our recent efforts in the development of the xDH functionals. (1) A long-range-corrected XYG3 (i.e., lrc-XYG3) is developed, which includes a range-dependent term from the second order perturbation theory for better description of dispersive interaction [6]. (2) Analytic gradients are developed, where the non-variational contributions from the SCF functional to the final energy functional are solved through a coupled-perturbed KS equation [9]. (3) Fractional charge behaviours of DH functionals are explored [10-12], which lead to good predictions of ionization potentials, electron affinities and fundamental gaps from the perspective of fractional charges. (4) A non-fitted DH functional, namely PBE-ACDH, is constructed based on the adiabatic connection (AC) formalism, coordinate scaling relations, and the second order Görling-Levy perturbation theory [8], where contributions from density scaling and singles are explicitly considered.

Limitations of the present approaches and the direction for future improvements will be discussed.

This research was sponsored by the Ministry of Science and Technology of China (2013CB834606, 2011CB808505), and National Natural Science Foundation of China (21133004, 91427301).

[1] Y. Zhao, B. J. Lynch and D. G. Truhlar, J. Phys. Chem. A 108, 4786 (2004).
[2] S. Grimme, J. Chem. Phys. 124, 034108 (2006).
[3] I. Y. Zhang, X. Xu, and W. A. Goddard III, Proc. Nat. Acad. Sci, USA, 106, 4963 (2009).
[4] I. Y. Zhang, X. Xu, Y. Jung, and W. A. Goddard III, Proc. Nat. Acad. Sci, USA, 108, 19896 (2011).
[5] I. Y. Zhang, X. Xu, Int. Rev. Phys. Chem. 30, 115(2011).
[6] I. Y. Zhang, X. Xu, J. Phys. Chem. Letters, 4, 1669 (2013).
[7] I. Y. Zhang, N. Q. Su, É. A. G. Brémond, C. Adamo, X. Xu, J. Chem. Phys. 136, 174102 (2012). 
[8] N. Q. Su, X. Xu, J. Chem. Phys., 140, 18A512 (2014).
[9] N. Q. Su, I. Y. Zhang, X. Xu, J. Comput. Chem., 34, 1759 (2013).
[10] N. Q. Su, W. T. Yang, P. Mori-Sánchez, X. Xu, J. Phys. Chem. A 118, 9201 (2014).
[11] N. Q. Su, X. Xu, J. Chem. Theory Comput.11:4677 (2015).
[12] N. Q. Su and X. Xu, J. Chem. Theory Comput.(2016) DOI:10.1021/acs.jctc.6b00197.

Materials

Carlos Cárdenas

Universidad de Chile

Summary

Varinia Bernales

Minesotta U.

Summary

Juan Peralta

Central Michigan Univ.

Summary

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

Berkeley Univ.

Summary

Pedro Salvador

Universitat de Girona

Summary