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This is so WRONG!
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-13.6 eV -18.6 eV -40 eV
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S How is amount of mixing determined: l = - ∫ Y2HY1 dt E2 - E1
energy of perturbation energy separation E2 - E1 How is DE determined: (DE is change in E after mixing) DE = ( ∫ Y2HY1 dt)2 S (energy of perturbation)2 energy separation E2 - E1
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3s Na I Br (-12.5 eV) Cl (-13.7 eV) F (-18.6 eV) F -
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-10.6 eV -15.8 eV -19 eV -32 eV
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s (non-bonding) s (bonding) s (anti- bonding) p (anti- bonding) p (bonding)
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What’s better and worse here?
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Cartesian Coordinates (Angstroms) Atom X Y Z
SPARTAN STUDENT MECHANICS PROGRAM: PC/x Run type: Geometry optimization (Analytical Gradient) (MM/Amide correction used) Model: RHF/PM3 Number of shells: 4 3 S shells 1 P shells Number of basis functions: 6 Number of electrons: 8 Use of molecular symmetry enabled Molecular charge: Spin multiplicity: 1 Point Group = CNV Order = 2 Nsymop = 4 This system has 2 degrees of freedom Initial Hessian option Hessian from MMFF94 calculation used. Max Max Neg. Cycle Energy Grad. Dist Eigen Heat of Formation: kJ/mol Energy Due to Solvation Solvation Energy Semi-Empirical Program CPU Time : Semi-Empirical Program Wall Time: Cartesian Coordinates (Angstroms) Atom X Y Z 1 O O 2 H H 3 H H Point Group = CNV Order = 2 Nsymop = 4
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Closed-Shell Molecular Orbital Coefficients MO # Eigenvalues: (ev): A B A B A1 1 O1 S 2 O1 PX 3 O1 PY 4 O1 PZ 5 H1 S 6 H2 S MO # Eigenvalues: (ev): B1 1 O1 S 2 O1 PX 3 O1 PY 4 O1 PZ 5 H1 S 6 H2 S Atomic Charges: Electrostatic Mulliken Natural 1 O : 2 H : 3 H : Bond Orders Mulliken 1 O H : 2 O H :
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but not equivalent! but not equivalent! anti-bonding non-bonding Two
“lone pairs” but not equivalent! bonding Two “O-H bonds” but not equivalent!
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BH3 Closed-Shell Molecular Orbital Coefficients MO # 1 2 3 4 5
Eigenvalues: (ev): A1' E' E' A2" A1' 1 B1 S 2 B1 PX 3 B1 PY 4 B1 PZ 5 H1 S 6 H2 S 7 H3 S MO # Eigenvalues: (ev): E' E' 1 B1 S 2 B1 PX 3 B1 PY 4 B1 PZ 5 H1 S 6 H2 S 7 H3 S
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Mainly B 2p lcao’s Note p bonds! Mainly B 2s-F 2p lcao’s Mainly F 2s lcao’s
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Benzene
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How does the bonding concepts we’ve seen here relate to what you might have seen before, in Organic?
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Now, can we tackle bigger molecules, like one with six bonds?
z y eg x 3d t2g Now, can we tackle bigger molecules, like one with six bonds? 3p t1u 3s a1g eg t1u a1g . F Oh S valence orbitals (9) F donor (sp) orbitals (6) Instead of; . F 2p Because harder to draw
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. F SF6 . F S valence orbitals (9) F donor (sp) orbitals (6) z y x t1u
a1g z y t1u eg eg x 3d t2g t2g 3p t1u 3s a1g eg eg t1u a1g . F Oh S valence orbitals (9) t1u F donor (sp) orbitals (6) a1g SF6 Instead of; . F 2p Because harder to draw
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. F SF6 Bonding MO’s 8 e- gives 4 bonds! 3d 3p 3s a1g t1u eg eg t2g
Oh t1u Bonding MO’s 8 e- gives 4 bonds! a1g SF6
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SF6 Two views: A) 4 bonds distributed over six S-F pairs
a1g t1u Two views: A) 4 bonds distributed over six S-F pairs B) 4 bonds (covalent ) + 2 “bonds” ionic (S6+-F-) 3p t1u 3s a1g eg eg t1u a1g t1u a1g SF6
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Probably need to use a computer….
Getting Larger: Probably need to use a computer…. MO # , Energy, eV Mo(CO)6 Molybdenum carbonyl
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MO 24 MO 22 MO 13 MO 1
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MO 50 - LUMO MO 49 - HOMO MO 44 MO 35 MO 39
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LUMO Sometimes MOs are hard to interpret HOMO
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L a.o.’s M a.o.’s ML4 - D4h
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3s Na I Br (-12.5 eV) Cl (-13.7 eV) F (-18.6 eV) F -
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: L ML6 3rd row M, Valence Atomic orbitals 6s-donors s ONLY,
4p t1u 4s a1g eg 3d t2g 3rd row M, Valence Atomic orbitals eg t1u a1g : L Oh 6s-donors s ONLY, Like H or NH3 ML6
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Symmetry Adapted Group Orbitals for 6 s-donors
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: L ML6 3rd row M, Valence Atomic orbitals 6s-donors s ONLY,
t1u a1g eg 4p t1u 4s a1g eg t2g 3d t2g 3rd row M, Valence Atomic orbitals eg t1u a1g : eg L Oh t1u 6s-donors s ONLY, Like H or NH3 a1g ML6
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: L ML6 M-L s anti-bonding MO’s 3rd row M, Valence Atomic orbitals
t1u a1g M-L s anti-bonding MO’s eg 4p t1u 4s a1g eg t2g 3d t2g 3rd row M, Valence Atomic orbitals eg t1u a1g eg : L Oh t1u 6s-donors s ONLY, Like H or NH3 M-L s bonding MO’s a1g ML6
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What is Do? : L ML6 M-L s anti-bonding MO’s 3rd row M, Valence Atomic
t1u a1g M-L s anti-bonding MO’s eg 4p t1u What is Do? 4s a1g eg t2g 3d t2g 3rd row M, Valence Atomic orbitals eg t1u a1g eg : L Oh t1u 6s-donors s ONLY, Like H or NH3 M-L s bonding MO’s a1g ML6
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Symmetry Adapted Group Orbitals for 6 p-donors
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.. L : L M-L s anti-bonding MO’s 12 L p orbitals 3rd row M, Valence
t1u a1g M-L s anti-bonding MO’s 4p t1u eg 4s a1g eg 3d t2g t2g .. 12 L p orbitals t2g t2u L t1g t1u 3rd row M, Valence Atomic orbitals eg t1u a1g eg : L Oh t1u 6s -donors Like Cl- M-L s bonding MO’s a1g
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Effect on Do? : L M-L s anti-bonding MO’s 12 L p orbitals 3rd row M,
t1u a1g M-L s anti-bonding MO’s 4p t1u eg Effect on Do? 4s a1g t2g eg 3d t2g t2g t2u 12 L p orbitals t1g t1u t2g 3rd row M, Valence Atomic orbitals eg t1u a1g eg : L Oh t1u 6s -donors Like Cl- M-L s bonding MO’s a1g
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C O : L ML6 M-L s anti-bonding MO’s 12 L orbitals 12 L p orbitals
t1u a1g M-L s anti-bonding MO’s eg C O 4p t1u t2g 12 L orbitals t2g t2u 4s a1g t1g t1u eg 3d t2g t2g t2g t2u 12 L p orbitals t1g t1u 3rd row M, Valence Atomic orbitals eg t1u a1g eg : L Oh t1u 6s -acceptors Like CO, CN- M-L s bonding MO’s a1g ML6
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Do Do Do Case 1. L is p innocent (sigma donor only) Case 2.
eg eg eg t2g Do t2g Do t2g 12 L orbitals Do eg eg eg t2g t2g t2g t2g 3d t2g 3d 3d t2g 12 L orbitals t2g Case 1. L is p innocent (sigma donor only) Case 2. L is p base (sigma donor and p donor) Case 3. L is p acid (sigma donor and p acceptor)
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Probably need to use a computer….
Getting Larger: Probably need to use a computer…. MO # , Energy, eV Mo(CO)6 Molybdenum carbonyl
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MO 24 MO 22 MO 13 MO 1
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MO 50 - LUMO MO 49 - HOMO MO 44 MO 35 MO 39
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LUMO Sometimes MOs are hard to interpret HOMO
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L a.o.’s M a.o.’s ML4 - D4h
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dx2-y2 dz2 dyz dxz dxy L a.o.’s M a.o.’s ML4 - D4h
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