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Chapter 5 : Molecular Orbitals N2 NH3 H2O Why do they make chemical bonds ? Chapter 5 : Molecular Orbitals Stabilization Bond energy 1 Types of Chemical Bonds Metallic Bond Ionic Bond Covalent Bond Covalent Bond Localized electron bonding models •Lewis dot structure •VSEPR (Valence shell electron pair repulsion) •Valence bond theory (hybridization) Delocalized electron bonding model •Molecular orbital (MO) theory 2 Molecular Orbital Theory LE is great to predict bondings and structures and geometries of molecules. BUT, there are some short points. •No concept of resonance. •No paramagnetic properties. •No information of bond energy. Fact: O2 is paramagnetic! O O Lewis structure VSEPR Valence bond theory •sp2 hybridized •lone pairs in sp2 hybrid orbitals •bonding pairs in σ and π bonds All show all electrons paired. Molecular Orbital Theory In contrast to LE, molecular orbitals describe how electrons spread over all the atoms in a molecule and bind them together, which can give correct views of • concept of resonance. • paramagnetic properties. • bond energy. Fact: O2 is paramagnetic! O O Lewis structure VSEPR Valence bond theory •sp2 hybridized •lone pairs in sp2 hybrid orbitals •bonding pairs in σ and π bonds All show all electrons paired. 3 How to construct molecular orbitals H2 – 2 protons and 2 electrons Schroedinger Eq => Molecular orbitals But, no way to solve => LCAO (linear combination of atomic orbitals) => Approximate solutions of Schroedinger Eq How to make chemical bonds Overlap of wave functions: – – + – destructive overlap + – φΑ constructive overlap + + Α – Β φ+ φΒ φ+2 Constructive overlap ⇒ enhance e- density between the nuclei ⇒ attract the nuclei ⇒ bonding orbital φΑ Α Β φ− φΒ φ−2 destructive overlap ⇒ node(s) between the nuclei ⇒ repel each other ⇒ antibonding orbital 4 How to make chemical bonds higher energy φΑ Α Β φ+ φΒ φ+2 Constructive overlap ⇒ enhance e- density between the nuclei ⇒ attract the nuclei ⇒ bonding orbital φΑ φ− φΒ Α Β 2 lower energy φ− destructive overlap ⇒ node(s) between the nuclei ⇒ repel each other ⇒ antibonding orbital Molecular orbitals from s orbitals H2 σ*1s antibonding m.o. (higher energy than separate atoms) σ1s bonding m.o. (lower energy than separate atoms) σ (C2 symmetric about the line connecting the nuclei) 5 Molecular orbitals from p orbitals π (C2 antisymmetric about the line connecting the nuclei) Molecular orbitals from p orbitals 6 Molecular orbitals from d orbitals Molecular orbitals from d orbitals 7 3 things to consider to form MOs N atomic orbitals => N molecular orbitals Symmetry match of atomic orbitals Relative energy of atomic orbitals 3 things to consider to form MOs N atomic orbitals => N molecular orbitals Symmetry match of atomic orbitals Relative energy of atomic orbitals 8 3 things to consider to form MOs N atomic orbitals => N molecular orbitals Symmetry match of atomic orbitals Relative energy of atomic orbitals Forming nonbonding orbitals 3 things to consider to form MOs N atomic orbitals => N molecular orbitals Symmetry match of atomic orbitals Relative energy of atomic orbitals dx2-y2 또는 dxy Forming nonbonding orbitals 9 3 things to consider to form MOs N atomic orbitals => N molecular orbitals Symmetry match of atomic orbitals Relative energy of atomic orbitals And remember The more nodes, the higher energy. 10 H2 bond order = (no. of e– in bonding m.o.s) - (no. of e– in antibonding m.o.s) 2 σ*1s H2 E 1s 1s σ1s b.o. = 1 (i.e., lower energy than separate atoms) He2 E He2 He2+ σ*1s σ*1s 1s 1s 1s 1s σ1s σ1s b.o. = 0 b.o. = 0.5 11 2nd-row diatomic molecules 2nd-row diatomic molecules No mixing O2, F2, Ne2 Mixing Li2 - N2 Ψ = c1φ(2sa) + c2φ(2sb) + c3φ(2pza) + c4φ(2pzb) 12 2nd-row diatomic molecules No mixing O2, F2, Ne2 Mixing Li2 - N2 Not big Ψ = c1φ(2sa) + c2φ(2sb) + c3φ(2pza) + c4φ(2pzb) 2nd-row diatomic molecules No mixing O2, F2, Ne2 b.o. = 1 Li2 13 2nd-row diatomic molecules No mixing O2, F2, Ne2 b.o. = 0 Be2 b.o. = 0 2nd-row diatomic molecules No mixing O2, F2, Ne2 b.o. = 1 (π) paramagnetic B2 found in gas phase 14 2nd-row diatomic molecules b.o. = 2 (π) No mixing found in gas phase O2, F2, Ne 2 rare C2 C22- is more common C2 d(C-C) 132 pm CaC2 d(C-C) 119.1 pm C2H2 d(C-C) 120.5 pm Bond order ? 2nd-row diatomic molecules b.o. = 3 (2π+σ) No mixing Very high bond energy: 942kJ/mol O2, F2, Ne2 N2 15 Breaking Nitrogen Bonds N N Bond Enthalphy : 946 kJ/mol FACTORY Chemistry: The Study of Change Nitrogen Cycle rearrangement of atoms and molecules 16 2nd-row diatomic molecules O2 b.o. = 2 O Paramagnetic O N2 Other forms of O2n O2+ b.o ? O2- b.o ? O22- b.o ? 2nd-row diatomic molecules F2 b.o. = 1 N2 17 2nd-row diatomic molecules b.o. = 0 Ne2 N2 2nd-row diatomic molecules HOMO (highest occupied molecular orbital) LUMO (lowest unoccupied molecular orbital) Big triumph of MO theory SOMO (singly occupied molecular orbital) Frontier orbitals 18 Bond lengths in 2nd-row diatomic molecules Bond length Covalent radius H-X H-B H-C H-N H-O H-F Length (pm) 120 109 101.2 96 91.8 Any trend found? OK with electronegativity difference Bond lengths in 2nd-row diatomic molecules Bond length Covalent radius H-X H-B H-C H-N H-O H-F Length (pm) 120 109 101.2 96 91.8 Any trend found? 19 Bond lengths in 2nd-row diatomic molecules Bond length Covalent radius H-X H-B H-C H-N H-O H-F Length (pm) 120 109 101.2 96 91.8 Don’t be fooled by the text book. Covalent radii are defined in X-X single bond (Table 2-8). How to measure the energy levels of MOs ? (Photoelectron spectroscopy) hν = UV Æ UPS : outer electrons hν = X-ray Æ XPS : inner electrons photoelectron v IE A + hν Æ A+ + e- Ionization energy = hν - ½ mv2 20 How to measure the energy levels of MOs ? (Photoelectron spectroscopy) N2 Why fine structure? O2 Ionization energy = hν - ½ mv2 Franck-Condon Principle Classically, the Franck–Condon principle is the approximation that an electronic transition is most likely to occur without changes in the positions of the nuclei in the molecular entity and its environment. The resulting state is called a Franck–Condon state, and the transition involved, a vertical transition. Mnucleus >> Melectron e-: faster motion 21 Franck-Condon Principle N2+ N2 Ionization energy = hν - ½ mv2 – Evib+ How to measure the energy levels of MOs ? (Photoelectron spectroscopy) N2 O2 stronger bonding involved less bonding involved 22 Correlation Diagram No mixing O2, F2, Ne2 Mixing Li2 - N2 Not big Correlation Diagram 23 Correlation Diagram non-crossing rule r(X-X)=0 r(X-X)=∞ MOs of Heteronuclear Diatomic Molecules 3 things to consider to form MOs N atomic orbitals => N molecular orbitals Symmetry match of atomic orbitals Relative energy of atomic orbitals |cA| = |cΒ| |cA| = |cΒ| |cA| > |cΒ| |cA| < |cΒ| |cA| >> |cΒ| |cA| << |cΒ| Ψ = cAφA + cΒφB 24 MOs of Heteronuclear Diatomic Molecules Average potential energy of all terms MOs of Heteronuclear Diatomic Molecules 25 MOs of Heteronuclear Diatomic Molecules z C O p orbital w/o considering signs C2v MOs of Heteronuclear Diatomic Molecules C∞v 26 MOs of Heteronuclear Diatomic Molecules M – C≡O M – O≡C ? MOs of Heteronuclear Diatomic Molecules M – C≡O M – O≡C ? 27 Ionic Compounds LiF View of ionic interaction Li: 1s22s1 Æ Li+: 1s2 F: 1s22s2sp5 Æ F-: 1s22s22p6 Electrostatic interaction View of MO transfer of Li2s e- to F2p orbital which is lowered F2p character Don’t forget that ionic interaction is omnidirectional and more accurate MO description requires bands. Ionic Compounds LiF View of ionic interaction Li: 1s22s1 Æ Li+: 1s2 F: 1s22s2sp5 Æ F-: 1s22s22p6 Is this process really helpful? 28 Ionic Compounds LiF thermodynamically unfavorable!! Ionic Compounds LiF Lattice enthalpy is the deriving force. 29 MOs of Polyatomic Molecules 1. 2. 3. 4. 5. 6. Determine the point group of molecules. (D∞h Æ D2h, C∞v Æ C2v) Assign x, y, z coordinates. Find reducible representations for ns orbitals on the outer atoms. Repeat for np orbitals in the same symmetry. (valence orbitals) Reduce the reducible representations of step 3 to derive group orbitals or symmetry adapted linear combinations (SALCs) Find the atomic orbitals of the central atoms with the same symmetries as those found in step 4. Combine the atomic orbitals of the central atom and the SALCs of the outer atoms with the same symmetry and similar energy to form MOs. MOs of Polyatomic Molecules FHF- D∞h Æ D2h F(2px)+F(2px) 2 -2 0 0 0 0 2 -2 Æ B3u + B2g F(2py)+F(2py) 2 -2 0 0 0 0 -2 2 Æ B2u + B3g F(2pz)+F(2pz) 2 2 0 0 0 0 2 2 Æ Ag + B1u F(2s)+F(2s) 2 2 0 0 0 0 2 2 Æ Ag + B1u 30 MOs of Polyatomic Molecules FHF- Ag can combine to form MOs F---F: SALCs H: 1s orbital MOs of Polyatomic Molecules FHF(-13.6 eV) H 1s (-18.7 eV) (-40.2 eV) H 1s will strongly interact with F2Pzs (Ag). Don't forget if F2s contributes, 3 MOs are formed. 31 MOs of Polyatomic Molecules FHF- antibonding non-bonding * there are slight long-range interactions. bonding MOs of Polyatomic Molecules FHF- MO 3-center 2-electron bond F H F Lewis structure 32 MOs of Polyatomic Molecules CO2 D∞h Æ D2h O(2px)+O(2px) 2 -2 0 0 0 0 2 -2 Æ B3u + B2g O(2py)+O(2py) 2 -2 0 0 0 0 -2 2 Æ B2u + B3g O(2pz)+O(2pz) 2 2 0 0 0 0 2 2 Æ Ag + B1u O(2s)+O(2s) 2 2 0 0 0 0 2 2 Æ Ag + B1u MOs of Polyatomic Molecules CO2 O C O O C O O---O: SALCs combine to form MOs C: valence orbitals 33 MOs of Polyatomic Molecules CO2 Ag stronger interaction MOs of Polyatomic Molecules CO2 O C O O C O O---O: SALCs combine to form MOs C: valence orbitals 34 MOs of Polyatomic Molecules CO2 B1u stronger interaction MOs of Polyatomic Molecules CO2 O C O O C O O---O: SALCs C: valence orbitals 35 MOs of Polyatomic Molecules CO2 B2u MOs of Polyatomic Molecules CO2 O C O O C O O---O: SALCs C: valence orbitals 36 MOs of Polyatomic Molecules CO2 B3u MOs of Polyatomic Molecules forming non bonding orbitals CO2 O C O O C O O---O: SALCs C: valence orbitals 37 MOs of Polyatomic Molecules CO2 O=C=O Lewis structure 2-center 2 electron bond 16 valence e-'s non-bonding π bonding π 3-center 2 electron bond bonding σ non-bonding σ MOs of Polyatomic Molecules H2O C2v H(1s)+H(1s) 2 0 2 0 Æ A1 + B1 Α1 H Β1 H H H Ψa1= (1/√2){φa(H1s)+φb(H1s)} Ψb1= (1/√2){φa(H1s)-φb(H1s)} H------H: SALCs 38 MOs of Polyatomic Molecules H2O C2v 2py B2 Α1 Β1 2pz A1 H 2px B1 2s A1 H H H Ψa1= (1/√2){φa(H1s)+φb(H1s)} Ψb1= (1/√2){φa(H1s)-φb(H1s)} H------H: SALCs O: valence orbitals MOs of Polyatomic Molecules H2O C2v 1b1 bonding 2b1 antibonding 2py B2 Α1 Β1 2pz A1 H 2px B1 2s A1 O: valence orbitals H H H Ψa1= (1/√2){φa(H1s)+φb(H1s)} Ψb1= (1/√2){φa(H1s)-φb(H1s)} H------H: SALCs 39 MOs of Polyatomic Molecules H2O C2v 2a1 nearly non-bonding 3a1 bonding 4a1 antibonding 2py B2 Α1 Β1 2pz A1 H 2px B1 2s H H H Ψa1= (1/√2){φa(H1s)+φb(H1s)} Ψb1= (1/√2){φa(H1s)-φb(H1s)} A1 H------H: SALCs O: valence orbitals MOs of Polyatomic Molecules H2O C2v O H 2py B2 1b2 non-bonding Α1 Β1 2pz A1 H 2px B1 2s A1 O: valence orbitals H H H Ψa1= (1/√2){φa(H1s)+φb(H1s)} Ψb1= (1/√2){φa(H1s)-φb(H1s)} H------H: SALCs 40 MOs of Polyatomic Molecules H2O C2v MOs of Polyatomic Molecules H2O C2v bonding 41 MOs of Polyatomic Molecules H2O C2v bonding nearly non-bonding (c2<<c1) MOs of Polyatomic Molecules 5.269 eV H2O 4.219 E -12.35 -14.69 -17.51 -37.03 42 MOs of Polyatomic Molecules H2O O Other approach A1 2s 2pz sp sp b1 b2 H----H SALCs A1 B1 b1 O B2 B1 MOs of Polyatomic Molecules H2O 104.5° Why 104.5o in MO theory? 43 MOs of Polyatomic Molecules Walsh Diagram - a diagram showing the variation of orbital energy with molecular geometry a1g σg a1 b1u σu b1 b2 e1u πu a1 b1 b1u σu a1g σg a1 D∞h C2v MOs of Polyatomic Molecules Walsh Diagram - a diagram showing the variation of orbital energy with molecular geometry a1g σg a1 b1u σu b1 b2 e1u πu a1 b1 b1u σu a1g σg a1 D∞h C2v 44 MOs of Polyatomic Molecules Walsh Diagram - a diagram showing the variation of orbital energy with molecular geometry MOs of Polyatomic Molecules Walsh Diagram - a diagram showing the variation of orbital energy with molecular geometry 45 MOs of Polyatomic Molecules NH3 C3v 3H(1s) 3 0 1 Æ A1 + E O 3H SALCs MOs of Polyatomic Molecules NH3 N C3v 3H(1s) 3 0 1 Æ A1 + E 3H SALCs 46 MOs of Polyatomic Molecules C3v NH3 pz character non-bonding 2s MOs of Polyatomic Molecules D3h BF3 F B F F 3F(2s) 3 0 A1' 1 3 0 1 Æ A1' + E' E' 47 MOs of Polyatomic Molecules D3h BF3 F B F F 3F(2px) 3 0 -1 3 0 -1 Æ A2' + E' E' A2' MOs of Polyatomic Molecules D3h BF3 F B F F 3F(2py) 3 0 A1' 1 3 0 1 Æ A1' + E' E' 48 MOs of Polyatomic Molecules D3h BF3 F B F F 3 3F(2pz) 0 -1 -3 0 1 Æ A2'' + E'' E'' A2'' MOs of Polyatomic Molecules D3h BF3 F B F F B 2s A1' 2px 2py E' 2pz A2'' 49 MOs of Polyatomic Molecules BF3 D3h A2'' 2py SALCs 3F(2pxz E'' 2pz A2'' A2' 2px E' 3F(2px) E' 2s A1' A1' 3F(2py) E' B A1' MOs of Polyatomic Molecules BF3 2px SALCs D3h A2'' 2py 3F(2s) E' 3F(2pxz E'' 2pz A2'' A2' E' 3F(2px) E' 2s A1' A1' E' 3F(2py) B A1' E' 3F(2s) 50 MOs of Polyatomic Molecules BF3 D3h Lewis ? VBT? antibonding ? σ and ? π non-bonding almost non-bonding bonding same for SO3, NO3-, CO32- Symmetry Adapted Orbitals (SALCs, Group Orbitals) CO2 FHF- H2O 2px B1 2py B2 2pz A1 2s A1 51 Symmetry Adapted Orbitals (SALCs, Group Orbitals) NH3 Symmetry Adapted Orbitals BF3 D3h A2'' 2py 2px SALCs E'' 3F(2pxz 2pz A2'' A2' E' 3F(2px) E' 2s A1' B A1' A1' E' E' 3F(2py) 3F(2s) 52 Symmetry Adapted Orbitals Symmetry Adapted Orbitals 53 Symmetry Adapted Orbitals Molecular Shapes in MO Semiempirical or Estimated shape Æ Determination of overall energy and molecular orbitals Æ Different shape Æ Determination of overall energy and molecular orbitals Æ Different shape Æ ..... Æ until minimum energy is found calculated minimum energy ≥ true energy 54 Hybrides Which atomic orbitals form hybrides? 4 1 0 0 2 Æ A1+ T2 s px, py, pz sp3 why not d ? 55 Which atomic orbitals form hybrides? F B F F 3 0 1 3 0 1 Æ A1' + E' s px, py sp2 pz is left over. Expanded Shells and MO from MO 56