Introduction to Computational Quantum Chemistry
Lesson 12: Bond Energy Analysis
(Prepared by Radek Marek Research Group) Lesson 12 - Bond Energy Analysis
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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END
(Prepared by Radek Marek Research Group)	
Lesson 12 - Bond Energy Analysis	18