1. Physical Chemistry Chapter V Polyatomic Molecular Structure 2019/4/10
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2. §5-1. Saturated Polyatomic Molecules
§ Delocalized Molecular Orbital
Molecular Orbital Theory
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3. Chemistry Department of Fudan University
B-O approximate
single electronic approximate
LCAO-MO
Secular equation
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Taking CH4 as an example H
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5. Chemistry Department of Fudan University
Taking the four H 1s orbitals as bases Td E
8C3
3C2
6S4
6σd 4 1 2
Reduce to the irreducible components
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orthonormal
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four symmetry matched molecular orbitals are:
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9. §5-1-2. Localized Molecular Orbital
Valence Bond Theory 1 2 3 x z y
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C: sp3 hybridization
Hybrid Orbitals
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four molecular orbitals are:
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§ Connection & Conversion
1. VB theory is an approximate method, whereas MO theory is quite accurate
Localized orbital  No constant Energy
Delocalized orbital  Energy Eigenvalue
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13. VB MO 2. Conversion between the two kinds of orbitals 2019/4/10
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14. Localized Molecular Orbital Delocalized Molecular Orbital
Bond length, Binding energy, Charge density, etc.
Delocalized Molecular Orbital
Spectrum
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§5-2.Conjugate Molecules
The particular characters of the conjugate molecules:
The length of the bond is between the double bond and the single bond;
Reactivity
The stability to the heat
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§5-2-1.Hückel Molecular Orbital Theory (HMO)
The main idea of HMO
1.Take σ-πorbitals Apart
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2.To the π orbitals, HMO assumes:
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18. §5-2-2.Illustrative Examples of HMO
Straight chain alkene---butadiene
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Delocalization Energy
The four πelectrons fill two lowest orbitals, the total energy of the  system is:
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For isolated double bond system, the total energy of the four π electrons will be:
The energy difference is called delocalization energy (DE)
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§ Graphic Theory
1. Conjugate straight chain alkene
Number of C atom: n
n order secular determinant:
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The general solution of in
(m=1, 2, ……, n)
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2. Conjugate Carbocyclic Alkene
The general solution of in
(m=1, 2, ……, n)
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30. §5-2-4. Conjugate Inorganic Molecule
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CO2 molecule
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For CO2:
Therefore:
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§ The Form of Conjugate  Bonding
1. Conjugate atoms must be in the same plane and they both have a p obital perpendicular to the plane. 2.
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Normal m=n
Electron sufficient m>n
Electron defficient m<n
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Exercise
Work out the energy levels and molecular orbitals of propene radical using HMO method. Show the electronic configurations, bondings and delocalization energies of the propene radical, cation and anion.
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§5-3. Electron-deficient Molecules
Structure of B2H6
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38. 1. Open three-center bonding Chemistry Department of Fudan University
3c-2e bonding in B2H6
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40. 2. Closed three-center bonding
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42. Structure and 3c-2e bonding in Al2(CH3)6
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43. Chemistry Department of Fudan University
§5-4. Coordination Compounds
A coordination compound is composed of
An electron donor (ligand or Lewis base), an individual atom or molecule which possesses non-bonding lone-pair electrons;
An electron acceptor (metal atom, cation or Lewis acid) which possesses a low-lying empty orbital.
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44. Chemistry Department of Fudan University
Donor Atom
Ligand
Central Atom
[Ag(NH3)2]+
Coordination Number
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§ Crystal Field Theory(CFT)
A complex is regarded as consisting of a central metal cation surrounded by ionic or dipolar ligands which are electrostatically attracted by the cation.
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1. The splitting of the d orbitals
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Octahedral Field
Taking 5 d orbitals of metal as bases E
8C3
6C2
6C4
3C2 i
6S4
8S6
3 σh
6σd 5 -1 1 2 3
The d orbitals split into two sets
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Characteristic Symmetry Element
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sphere d
Free atom
Octahedral
Splitting energy:
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Tetrahedral Field E
8C3
3C2
6S4
6σd 5 -1 1 2 3 Td E T2
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52. Characteristic Symmetry Chemistry Department of Fudan University1 2 3 x z 4
Characteristic Symmetry
Element y
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Square Planar Field
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58. 2. Spectrochemical Series
I- < Br- < Cl- < SCN- < NO3- < F- < OH-
< H2O < NCS- < gly < Py < NH3 < en <
NO2- < PPH3 < CN- < CO
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3. Crystal field stabilization energy
The crystal field stabilization energy is defined as the energy by which a complex is stabilized due to the splitting of the d-orbitals. It is determined by Pairing Energy(P) and Splitting Energy( )
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Weak field complexes:
  P (high spin)
Strong field complexes:
  P (low spin)
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Electron Arrangement d1 d2 d3 d8 d9
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62. high spin for d4-d7 octahedral complex
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63. Low spin for d4-d7 octahedral complex
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4. Jahn-Teller Effect
Any non-linear ion or molecule which is in an orbitally degenerate term will distort to relieve this degeneracy.
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For octahedral coordination
High Spin
Low Spin
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66. 5. The Applications of CFT Chemistry Department of Fudan University
￭The model can be used to understand, interpret and predict the magnetic behavior, colors and some structures of coordination complexes.
￭ But does not explain the bonding in coordination complexes.
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The most serious defect of the CFT model is that it does not recognize the existence of overlap, and hence the existence of specific bonding interactions, between the ligands and the metal orbitals.
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68. §5-4-2. Molecule Orbital Theory (MOT)
LCAO-MO
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1. Metal-ligand  interactions
Orbital of Central Metal Atom
dxy, dyz, dxz
T2g
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Taking 6 -type orbitals of the ligands as bases:
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Ligand Orbitals
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73. The metal-ligand  bonding in an octahedral complex
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2. Metal-ligand  interactions
Taking 12 -type orbitals of the ligands as bases:
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Ligand Orbitals
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78. Chemistry Department of Fudan University
Case a
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Case b
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§ - bonding complexes
1. Carbonyl Complex
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2. Unsaturated Hydrocarbon Complex
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Exercises
Use the molecular orbital theory to explain the spectrochemical series (Taking the Cl-, NH3 and CO for example).
Work out which coordination compounds listed below show Jahn-Teller distortion:
[Co(NH3)6]3+, (2) [MnCl6]4-;
(3) TiCl4, (4) Fe(CO)4 (tetrahedral)
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83. §5-5-1. Ab initio methods §5-5-2. Density functional theory
§5-5. Quantum Chemical Computational Methods and Molecular Property Calculations
§ Ab initio methods
§ Density functional theory
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§ Molecular property calculations
1. Ionization energy and total energy
Koopmans rule:
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85. 2. Bond energy and dissociation energy
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86. 3. Geometry and dipole moment Chemistry Department of Fudan University
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87. 4. Charge density, bond order and free valence
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Example:cyclopropene
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(2)Bond order
Example:cyclopropene
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Note
(A)
(B)Conjugate molecule (CH2)3C can show the biggest bonding capacity of C atom,that is
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(3)Free Valence
Example:C atom
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