Dr Lars Goerigk

Melbourne Centre for Theoretical and Computational Chemistry,
School of Chemistry, The University of Melbourne, VIC 3010, Australia

Video Recording

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Abstract

The importance of Density Functional Theory (DFT) to the chemical sciences is well known. However, despite today’s easy access to DFT software packages to everyone, there remains a large communication gap between DFT developers and users that has resulted in various misconceptions and the regular application of outdated procedures. One reason for this is the fact that there is not only one manifestation of DFT, but hundreds of approximations to the true, unknown functional. Naturally, not only users that are new to the field, but also experts can find this ever-growing `zoo’ of DFT approximations confusing.

This presentation provides an overview of the zoo of DFT methods and is suitable to both students that are new to the field and more experienced researchers. Rather than spending too much time on discussing the physical/mathematical foundation of DFT, I will focus on aspects that are relevant to computational applications with guidelines and recommendations as take-home messages that may assist in future research endeavours. After a short overview of the basic idea of DFT and Perdew’s famous Jacob’s Ladder classification of DFT approximations, I will cover how we can identify the best and most robust representatives of the zoo for applications to thermochemistry and kinetics. A special emphasis will be given to the importance of London-dispersion interactions. Towards the end, more specialised aspects will be discussed that may be of interest to more theoretically oriented viewers.

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:

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Presentation 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

31 video lectures on Density Functional Theory.

Benoit Mignolet

Department of Chemistry, UR MOLSYS, University of Liège, Belgium

Video Recording

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Abstract

Upon light absorption, the 5-atom thioformaldehyde S-oxide sulfine (H₂CSO) molecule undergoes a rich and unexpected dynamics resulting in the formation of nine photoproducts(1). In this presentation, we will first shed light on the sulfine photochemistry using state of the art molecular modeling and then investigate its photoexcitation by attosecond and few-femtosecond laser pulses using the XFAIMS mixed-quantum classical method that we recently developed.
We shed light on the sulfine photochemistry by reproducing in silico the dynamics following the photoexcitation of the sulfine to its lowest excited state(2). The nonradiative decay to the ground state as well as the following dynamics occurring on the ground state have been modeled with respectively the ab initio multiple spawning(3) (AIMS) method carried out at the MS-CASPT2 level and the Born-Oppenheimer molecular dynamics carried out at the DFT/PBE0 level. Amongst the nine photoproducts observed experimentally, we retrieve them all but surprisingly most of them (8) are formed on the ground state on a sub-picosecond timescale. Therefore the dynamics occurring on the hot ground state cannot be described by statistical methods such as RRKM because of the highly non-statistical character stemming from the excited-state dynamics. This unexpectedly rich chemistry occurring on the hot ground state challenges our view of typical photochemical or photodecomposition reactions in which it is usually the variety of conical intersections that leads to a variety of photoproducts.
We also investigated the photoexcitation the sulfine by attosecond and few-femtosecond laser pulses. With the recent developments of these short pulses (4), new opportunities for the controlling and probing of the electronic motion in atoms and molecules emerge. Due to the short nature of the laser pulse, the bandwidth can reach several eV and a band of several electronic states can be accessed, which can lead to an ultrafast charge migration. Therefore it becomes paramount to model the interaction with laser pulses. In this goal, we developed the eXternal Field Ab-Initio Multiple Spawning (5) (XFAIMS) method to model both the photoexcitation and nonradiative relaxation in medium-sized molecules. It is based on the well-known AIMS method in which we added the interaction with the electric field and adapted the spawning algorithm to fully model experiments from the photoexcitation of the molecule by the laser pulse to the nonradiative relaxation and/or its dissociation.

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).

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.

Henrique C. S. Junior

Universidade Federal Fluminense (UFF) – Rio de Janeiro, Brazil

Video Recording

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Abstract

Molecular Magnetic Compounds can have several different features, from single molecules with long range couplings to complex polymeric chains with strong interactions. The field of Molecular Magnetism occupy itself in understanding how these systems interact and in chemically modulating magnetic couplings by selecting adequate ligands and paramagnetic centers. The task to devise how the infinity of magnetic systems couple with each other in a crystal structure is possible with a methodological First-priciples Bottom-up (FPBU) approach and the use of Computational Methods like the Density Functional Theory (DFT), allowing for fast and accurate results. In this presentation we show, using examples of weak and strong interactions, how to apply the FPBU approach to choose reasonable magnetic systems as relevant candidates for magnetic coupling studies, functionals and basis sets leading to better results and how to use the broken-symmetry approach to obtain magnetic couplings (J).

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].

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:

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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 .