Virtual Winter School on Computational Chemistry

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DFT

  • Density-Functional Tight-Binding for the Predictive Simulation of Complex Systems

    Speaker: Dr Stephan Irle
    Speaker Link: https://www.ornl.gov/staff-profile/stephan-irle
    Institute: Oak Ridge National Laboratory
    Country: USA

    Dr Stephan Irle

    Computational Chemistry and Nanomaterials Sciences Group, Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6129, U.S.A.

    The density-functional tight-binding (DFTB) method [1] is an approximation to density functional theory (DFT) allowing a speedup of first principles electronic structure calculations by two to three orders of magnitude.  This is achieved by solving the Kohn-Sham equations for valence electrons using a parameterized two-center Hamiltonian in a minimum pseudoatomic orbital basis set.  Since electronic structure is explicitly computed for each atomic configuration, DFTB is capable of simulating chemical processes including the breaking of covalent bonds, changes in aromatic electronic structure, charge transfer, charge polarization, etc. [2].  DFTB methods can therefore be employed in atomistic molecular dynamics (MD) simulations of processes that involve complex chemical processes, electron transfer, and/or mass and ion transport.  Its applicability is limited in part due to the unfavorable cubic scaling of computer time with system size, and in part due to the necessity of parameterization for element pairs.  Linear-scaling algorithms for massively parallel computation [3,4] and semiautomatic parameterization codes [5] have been developed to address these shortcomings.  Recently, systematic bias corrections were proposed based on a D-machine learning approach employing neural network potentials [6].

    In this talk, I will first briefly review the DFTB method and its various “flavors” for including Coulombic interactions, before highlighting challenges associated with the parameterization of the Hamiltonian.  DFTB-based simulations of nanoscale materials self-assembly will illustrate the predictive power of the method to unravel complex chemical processes occurring in nonequilibrium on large length scales [6].

    Recording:

    Video is available only for registered users.

    pdfPresentation slides

    References

    [1] a) Christensen, A. S.; Kubar, T.; Cui, Q.; Elstner, M. Semiempirical Quantum Mechanical Methods for Noncovalent Interactions for Chemical and Biochemical Applications, Chem. Rev. 2016, 116, 5301-5337; b) http://www.dftbplus.org

    [2] Cui, Q.; Elstner, M. Density functional tight binding: values of semi-empirical methods in an ab initio era, Phys. Chem. Chem. Phys.2014, 16,14368-14377.

    [3] Nishizawa, H.; Nishimura, Y.; Kobayashi, M.; Irle, S.; Nakai, H. Three pillars for achieving quantum mechanical molecular dynamics simulations of huge systems: Divide-and-conquer, density-functional tight-binding, and massively parallel computation, J. Comp. Chem. 2016, 37, 1983-1992.

    [4] a) Nishimoto, Y.; Fedorov, D. G.; Irle, S. Density-Functional Tight-Binding Combined with the Fragment Molecular Orbital Method, J. Chem. Theory Comput. 2014, 10, 4801-4812; b) Vuong, V. Q.; Nishimoto, Y.; Fedorov, D. G.; Sumpter, B. G.; Niehaus, T. A.; Irle, S. The Fragment Molecular Orbital Method Based on Long-Range Corrected Density-Functional Tight-Binding, J. Chem. Theory Comput. 2019, 15, 3008-3020. 

    [5] Chou, C.-P.; Nishimura, Y.; Fan, C.-C.; Mazur, G.; Irle, S.; Witek, H. A. Automatized Parameterization of DFTB using Particle Swarm Optimization, J. Chem. Theory Comput. 2016, 12, 53-64.

    [6] Zhu, J.; Vuong, V. Q.; Sumpter, B. G.; Irle, S. Artificial Neural Network Correction for Density-Functional Tight-Binding Molecular Dynamics Simulations, MRS Commun. 2019, 9, 867-873 (2019).

    [7] Irle, S; Page, A. J.; Saha, B.; Wang, Y.; Chandrakumar, K. R. S.; Nishimoto, Y.; Qian, H.-J.; Morokuma, K. Atomistic mechanism of carbon nanostructure self-assembly as predicted by nonequilibrium QM/MD simulations, in: J. Leszczynski, M. K. Shukla, Eds. “Practical Aspects of Computational Chemistry II: An Overview of the Last Two Decades and Current Trends”, Springer-European Academy of Sciences, Chapter 5, pp. 105-172 (April 2, 2012).  ISBN 978-94-007-0922-5. DOI: 10.1007/978-94-007-0923-2_5 Preprint: https://www.dropbox.com/s/n2o3sjnb0t1z6mr/5_Online%20PDF.pdf?dl=0

  • DFT-theory (Pedagogical lectures)

    Lecture date: 2017-06-11
    URL: https://www.cecam.org/workshop-9-1326.html
    Lecturer: CECAM

    31 video lectures on Density Functional Theory.

  • Integrating Electronic and Nuclear Quantum Effects via the Nuclear-Electronic Orbital Method

    Speaker: Professor Sharon Hammes-Schiffer
    Speaker Link: https://www.hammes-schiffer-group.org/
    Institute: Yale University
    Country: USA

    Professor Sharon Hammes-Schiffer

    Yale University

    Nuclear quantum effects such as zero point energy, nuclear delocalization, and tunneling play an important role in a wide range of chemical processes. The nuclear-electronic orbital (NEO) approach treats specified nuclei, typically protons, quantum mechanically on the same level as the electrons with multicomponent density functional theory (DFT) or wave function methods. Electron-proton correlation functionals have been developed to address the significant challenge within NEO-DFT of producing accurate proton densities and energies. Moreover, time-dependent DFT and related methods within the NEO framework have been developed for the calculation of electronic, proton vibrational, and electron-proton vibronic excitations. An effective strategy for calculating the vibrational frequencies of the entire molecule within the NEO framework has also been devised and has been shown to incorporate the most significant anharmonic effects. Furthermore, multicomponent wave function methods based on coupled cluster, configuration interaction, and orbital-optimized perturbation theory approaches, as well as multicomponent equation-of-motion coupled cluster methods for computing excited electronic and proton vibrational states, have been developed within the NEO framework. Multistate DFT methods within the NEO framework enable the calculation of tunneling splittings and vibronic couplings relevant to proton transfer and proton-coupled electron transfer reactions. Recently, real-time NEO methods have been developed and used to study nonequilibrium dynamical processes such as photoinduced proton transfer. These combined NEO methods enable the inclusion of nuclear quantum effects and non-Born-Oppenheimer effects in calculations of proton affinities, optimized geometries, vibrational frequencies, isotope effects, minimum energy paths, excitation energies, tunneling splittings, vibronic couplings, and nonequilibrium dynamics for a wide range of chemical applications.

    Recording:

    References

    1. S. P. Webb, T. Iordanov, and S. Hammes-Schiffer, Multiconfigurational nuclear-electronic orbital approach: Incorporation of nuclear quantum effects in electronic structure calculations, J. Chem. Phys. 117, 4106-4118 (2002).
    2. F. Pavošević, T. Culpitt, and S. Hammes-Schiffer, Multicomponent quantum chemistry: Integrating electronic and nuclear quantum effects via the nuclear-electronic orbital method, Chem. Rev. 120, 4222-4253 (2020).
    3. L. Zhao, Z. Tao, F. Pavošević, A. Wildman, S. Hammes-Schiffer, and X. Li, Real-time time-dependent nuclear-electronic orbital approach: Dynamics beyond the Born-Oppenheimer approximation, J. Phys. Chem. Lett. 11, 4052-4058 (2020).
  • Kieron Burke - DFT introduction

    Lecture date: 2017-05-14
    URL: http://dft.uci.edu/learnDFT.php
    Lecturer: Kieron Burke

    Density Functional Theory (DFT) is the choice method of calculating quantum chemistry today. Here, we've assembled many review articles from our group as well as the ABC of DFT.

  • The physical meaning of orbitals and orbital energies in DFT and TDDFT

    Evert Jan Baerends

    Theoretical Chemistry,Vrije Universiteit, Amsterdam, The Netherlands


    Video Recording

    Abstract

    We will first review many wrong statements in the literature on the nature and the (lack of) physical meaning of Kohn-Sham orbitals.
    Next the nature of the occupied KS orbitals, and their advantages over Hartree-Fock orbitals are highlighted.
    Then we address orbital energies. Exact KS orbitals have many virtues:

    1. the orbital energies of the occupied orbitals are close to ionization potentials (an order of magnitude better agreement than the Koopmans’ type agreement in Hartee-Fock) [1];
    2. virtual orbital energies are realistic: occupied-unoccupied orbital energy differencies are very close to excitation energies. There is no “gap problem” in DFT! [2,3]
    3. the KS virtual orbitals are typically bound states and have good (valence type) shapes (not unphysically diffuse like the Hartree-Fock virtuals); excitations can be described in most cases as simple single orbital-to-orbital transitions [2,3].

    Unfortunately, orbital energies in the common LDA and GGA calculations are very wrong: they are typically 5 eV (more than 100 kcal/mol) higher than the exact Kohn-Sham orbital energies, an error that would be completely unacceptable in total energies. We will first analyze where this error comes from - it is not due to wrong asymptotic behavior of LDA/GGA potentials, or to a “self-interaction error” but it is caused by erroneous density dependence of the standard Exc[ρ] functionals, hence a wrong derivative (= potential). We will demonstrate that approximate potentials can be formulated that have similar good properties for ionization and excitation energies as the exact KS potential [4].

  • Understanding intermolecular interactions and chemical bonding via energy decomposition analysis

    Speaker: Professor Martin Head-Gordon
    Speaker Link: https://mhggroupberkeley.com/
    Institute: UC Berkley
    Country: USA

    Professor Martin Head-Gordon

    University of California, Berkeley

    Energy decomposition analysis (EDA) aims to quantitatively bridge the gap between quantum chemistry calculations and chemical intuition by providing values for the chemical drivers of intermolecular interactions, such as permanent electro- statics, Pauli repulsion, dispersion, and charge transfer. The goal is similar for chemical bonding, where one must also carefully account for bond formation via spin-coupling. These energetic contributions are identified by performing DFT calculations with constraints that disable components of the interaction. The second generation version of the absolutely localized molecular orbital EDA (ALMO- EDA-II) will be described. The effect of different physical contributions on changes in observables such as structure, vibrational frequencies etc, upon complex formation is achieved via the adiabatic EDA. A variety of chemical examples will be presented to illustrate the usefulness of this approach, including bonding and frequency shifts of CO, N2, and BF bound to a [Ru(II)(NH3)5]2+ moiety, and the nature of the strongly bound complexes between pyridine and the benzene and naphthalene radical cations. The origin of the chemical bond will also be discussed, as will a few of the other controversies concerning the character of chemical interactions.

    Recording:

    Video is available only for registered users.

  • Understanding time-dependent density-functional theory (TD-DFT)

    Mark E. Casida

    Professeur, chimie théorique, Laboratoire de Chimie Inorganique REdox (CIRE),
    Département de Chimie Moléculare (DCM, UMR CNRS/UGA 5250), Institut de Chimie Moléculaire  de Grenoble(ICMG, FR-2607),
    Université Grenoble Alpes, 301 rue de la Chimie, CS 40700, 38058 Grenoble
    Cedex 9, FRANCE.


    Video Recording

    Abstract

    Ordinary density-functional theory (DFT) is restricted to calculating the static electronic energy and density of the electronic ground state. Time-dependent (TD) DFT is a parallel formalism which
    allows us to extend the power of DFT to treat time-dependent perturbations. Time-dependent response theory then allows us to calculate absorption spectra from TD-DFT and hence to treat excited states. This formalism is explained at the level of a Masters student, first by setting the stage with a reminder of simple wave function theory for excited states as well as some more advanced ab initio quantum chemistry ideas, and then by focusing on TD-DFT. Some illustrative examples are also presented 1,2 . We also direct the interested reader to highly-cited review articles, including our own 3,4 .