Introduction to Computational Quantum Chemistry Lesson 12: Bond Energy Analysis (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 1 Chemical Bonding Analysis • below are some of the bonding decomposition schemes • EDA-NOCV • NBO • SAPT • IQA(QTAIM based) • NCI • partitioning of classical part and quantum mechanical part of interactions • all include certain degree of arbitrariness • in this session we will be looking into EDA-NOCV and IQA(QTAIM based) (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 2 EDA-NOCV • the energy decomposition analysis (EDA) or extended transition state (ETS) analysis • powerful methods to dissect the interactions that constitute a chemical bond • fragments should be clearly defined F3C—X j NH3 (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 3 EDA-NOCV • the total bonding energy consists of the interaction energy AEint between the fragments and AEstrain AEbond = AEint + AEstrain (1 o the strain or preparation energy involved in deforming the fragments to the geometries in supra molecule (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 4 Interaction Energy {AEint) • the interaction energy AEint is further decomposed: AEint = AVelstat + AEpauli + AEQi + AEdisp (2) • the electrostatic attraction and pauli repulsion (AVeZstat + AEPauu) conveniently summed together into a steric repulsion term • the stabilizing orbital interactions (AEoi) describe the orbital mixing and charge transfer between the fragments when they form the molecule • can be further decomposed into representations of the corresponding point group in the case of symmetric molecules. • the bonding interactions can be partitioned in the context of natural orbitals for chemical valence (NOCV). (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 5 ETS-NOCV NOCV Natural Orbitals for Chemical Valence APCt = v%C%3 where AP = P — P°, matrix of charge and bond order in molecule P, and in promolecule P° M/2 M/2 k=i k=i □ s - = (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis ETS-NOCV • ETS-NOCV representation of the deformation density (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 7 ETS-NOCV, application 9 deformation density, Ap = pmoi - pa- Pb 1 ^)<\(y (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 8 Quantum Theory of Atoms in Molecules (QTAIM) • works with electron density and its derivatives • electron density is a 3-dimensional function in contrast to wavefunction which is 4A/'-dimensional per AT-electrons. • an 'observable property' a IQA in the context of QTAIM • lower dependence of results on basis set • electron derealization Index (Dl) is descriptor of covalency • lean be performed employing overlapping (fuzzy atoms) or non-overlapping (QTAIM) molecular subspaces. • non-overlapping atoms permits defining "chemically meaningful fragments" and studying inter-fragment interactions • satisfy atomic virial theorem. (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 9 IQA-QTAIM : Energy Decomposition Schemes self-interaction energy Eself(n) = T(nA) + ven(nA) + vee{nA) interaction energy energy (6) Eseif(q,a, &b) = Vnn(qa, &b) + VxCee &b) + Vcoulombee (&a, &b) = Vel + VXC (7) (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis IQA-QTAIM : Energy Decomposition Schemes • IQA recovers the binding energy components in terms of physically meaningful terms: EBind — VeL + VxC + Epr • Vel and Vxc represent contribution of all classical and exchange-correlation energy components, respectively. • the promotion energy, EPr, is the sum of all factors that change the energy of an atomic sub-space, including kinetic energy, electron-electron repulsion, and electron-nucleus attraction. • in IQA analysis the kinetic energy has no interatomic component and nuclear-nuclear repulsion clearly has no atomic component. (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 11 ACTIVITY • in order to demonstrate EDA and IQA bond analysis schemes, we will be using at least three systems: 1. H-H 2. H2C=CH2 3. NaF • perform an optimization on Gaussian for this three molecules using: M06-2X with Def2TZVP basis sets • use the geometries for IQA(QTAIM) and EDA(ETS-NOCV) bonding analysis in the manner of this fragments: H-/-H, H2C=/=CH2, and Na/F (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 12 ACTIVITY 1: EDA (ETS-NOCV) • USING ADF • refer to the provided input files and script • there are 3 sets of input files (2 for the separated fragments and 1 for molecule), unless its a bimolecular systems • use M06-2X with tz2p basis sets • don't impose symmetry • complete manual/sample is found in this link: {https://www.scm.com/doc/ADF/Examples/Examples.html} • watch out for the multiplicity of your fragments (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 13 ACTIVITY 1: EDA (ETS-NOCV) • USING ADF, cont. o final results of decomposition can be found in the 3rd (paired) output using keyword: BONDING ENERGY • the results presents Electrostatic Energy, Kinetic Energy, Coulomb (Steric+Orbitlnteraction), Exchange Correlation (XC) • you can also search for NOCV Eigenvalues in the output file • for the visualizations of the channels open the TAPE21 $ adfview TAPE21 • go to Add > Isosurface with phase > open NOCV Def. Dens. for Def. Dens, the direction of electronic polarization is from red to blue region (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 14 ACTIVITY 2: IQA (QTAIM) • using AIMALL o analogous to EDA(ETS-NOCV), there are 3 sets of jobs (2 separated fragments and 1 for molecule), unless it's a bimolecular systems • for the IQA, it consists of Gaussian single point calculation to generate the wavefunction use M06-2X with Def2TZVP basis sets • then AIMALL will use the checkpoint files for IQA analysis • refer to the provided input files and script © watch out for the multiplicity of your fragments the final output will provide .sum and .sumviz files • .sumviz files can be use for the GUI, AimStudio. (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 15 ACTIVITY 2: IQA (QTAIM) • using AIMALL, cont. • the binding energy is not explicitly stated in the output • rather the output only presents "Intraatomic Self Energy Components" and "Diatomic Interaction Energy Components" • these components has corresponding Kinetic (T), Classical (Vcz Exchange Correlation (Vxc) Energy parts • to get the Bonding Energy from the AIMALL output, one must use this scheme: EBe = {Eseif {fragment) - Eseif(free))[A,B] + Eint(A,B) • be sure to subtract only the T, VCi and Vxc parts on the self energy components separately first a then add it with corresponding values on interaction energy (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 16 QUESTIONS TO PONDER * after calculating the energy components of the various systems using the two methods: • how close are the total bonding energy values relative to the experiment? (check online expt. values) © which component of the binding energy they differ?how large are the deviations of the differences • which method distributes the 'classical and quantum' parts more? • which one do you prefer, the method that allows orbital partitioning? or the method that allows atom-atom partitioning? (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 17 END (Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis 18