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CH2. Molecules and covalent bonding Lewis Structures VSEPR  MO Theory

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Lewis structure H3PO4 • Skeleton is:

• Count total valence electrons:1 P = 53 H = 34 O = 24Total = 32 e- or 16 valence e- pairs.

• 7 e- pairs needed to form skeleton.

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Lewis structure H3PO4 • Add remaining e- pairs:

• Left has a formal charge of +1 on P and -1 on one O, right has 5 e- pairs around P (hypervalence)

• Analysis of phosphoric acid shows purely Td phosphate groups, which requires something beyond either simple Lewis model.

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Resonance in NO3-

experimental data - nitrate is planar with 3 equivalent N-O bonds

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VSEPR model• Count e- pairs about the central atom (draw

Lewis structure if needed). Include non-bonding pairs, but not multiple bonds.

• Geometry maximizes separation:# e pairs geometry example

2 linear HF2-

3 equilateral triangular BF3

4 tetrahedral (Td) CF4

5 trigonal bipyramidal (TBP) PF5

6 octahedral (Oh) SF6

7 pentagonal bipyramidal IF7

8 square antiprismatic TaF83-

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Drawing Oh and Td molecules

It's often useful to draw octahedra and tetrahedra with a cubic framework

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Deviations from ideal geometries:

unshared pairs and multiple bonds require larger bite

ex: CH4, NH3, H2O

<H-C-H = 109.5°,<H-N-H = 107.3,<H-O-H = 104.5

ex: ICl4-

6 e pairs around I, 2 lone pairs and 4 e pair bonds to ClOh coordination, and geometry is square planar (lone pairs are trans, not cis)

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POCl3

based on Td geometry

< ClPCl = 103.3° due to repulsion by multiple bond

note that in :PCl3

the <ClPCl = 100.3, the lone pair is more repulsive towards other ligands than the multiple bond !

Ligands move away from multiple bond

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XeF5+

5 Xe-F bonds and 1 lone pair on Xe geometry based on Oh coordination lone pair repulsion gives

< FeqXeFeq = 87°

< FaxXeFeq = 78°

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Fajan’s rule

bond polarization is towards ligands with higher , decreasing repulsive effect. Lone pairs are the most repulsive.

ex: NH3 vs NF3

< HNH = 107.3°

< FNF = 102.1°

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Inert pair effect• VSEPR geometries require

hybridization (valence bond term) or linear combinations (MO term) of central atom orbitals. For example, Td angles require sp3 hybrid orbitals. More on this in MO theory section.

• Period 5 and 6 p-block central atoms often show little hybridization (ex: they form bond with orbitals oriented at 90° as in purely p orbitals). This can be ascribed to the weaker bonding of larger atoms to ligands.

In Sn Sb Te

Tl Pb Bi

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Inert pair effect - evidence• Bond angles near 90°:

NH3     107.2           H2O     104.5

AsH3     91.8           H2Se      91

SbH3     91.3           H2Te     89.5

• Increased stability of lower oxidation statesex: Si, and Ge are generally 4+, but Sn and Pb are common as 2+ ions (as in stannous fluoride SnF2)ex: In and Tl both form monochlorides, B, Al, Ga form trichlorides.

• Vacant coordination sites where the lone pair resides

ex: PbOPbO unit cell

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Fluxionality

• PF5 if TBP has 2 types of F ligands (equatorial and axial).

• 19F NMR spectra at RT show only a single peak (slightly broadened).

• PF5 is fluxional at RT, i.e. the F ligands exchange rapidly, only a single "average" F ligand is seen by NMR.

• Only occurs if ligand exchange is faster than the analytical method. IR and Raman have shorter interaction times and show 2 types of P-F bonding at RT.

• Even low temp NMR studies cannot resolve two F environments

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Berry pseudo-rotation

Sequences of the MD-Simulation of PF5 at 750K (Daul, C., et al, Non-empirical dynamical DFT calculation of the Berry pseudorotation of PF5, Chem. Phys. Lett. 1996, 262, 74)

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Molecular Orbitals

Use linear combinations of atomic orbitals to derive symmetry-adapted linear combinations (SALCs).  

Use symmetry to determine orbital interactions. Provide a qualitative MO diagram for simple

molecules. Read and analyze an MO diagram by sketching

MO’s / LCAO’s, describing the geometric affect on relative MO energies.

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H2

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Some rules The number of AO’s and MO’s must be equal.

This follows from the mathematics of independent linear combinations.

More on symmetry labels later, but they come from the irreducible representations for the point group. MO’s are symmetric about bond axis, MO’s are not. Subscipt g is gerade (has center of symmetry), u is ungerade. Antibonding orbitals are often given a * superscript.

The bond order = ½ (bonding e- - antibonding e-). The bond energy actually depends on the energies of the filled MO’s relative to filled AO’s.

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O2

• MO theory predicts 2 unpaired e-, this is confirmed by experiment.• Bond order = ½ (8-4) = 2, as in Lewis structure.• MO indicates distribution and relative energies of the MO's, Lewis structure says only bonding or non-bonding.

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I and Ea for atoms and diatomics

species I (kJ/mol) Ea

N 1402

O 1314 142 O2 1165 43 NO 893 F 1681 F2 1515 C 1086 123 C2 300

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Li2 – F2 MO’s

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Some diatomic bond data

bond order r0 in pm D0 in kJ/mol

O2 2 121 494

O2- 1 ½ 126

O22- 1 149

F2 1 142 155 O2

+ 2 ½ 112

NO 2 ½ 115

NO+ 3 106 N2 3 110 942

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Spectroscopic data for MO’s

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HF

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Ketalaar triangle

HF

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Hybridization

• Linear combinations of AO’s from same atom makes hybrid orbitals.

• Hybridization can be included in the MO diagram.

• In MO theory, any proportion of s and p can be mixed (the coefficients of the AO’s are variable). sp and sp3 hybrids are specific examples.

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H3+

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BeH2

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Correlation diagram for MH2

M < HMH

Be 180°

B 131

C 136

N 103

O 105

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Bonding MO’s in H2O

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NH3

Use triangular H3 MO’s from

above as SALC's of the H ligand orbitals. Must relabel to conform with lower symmetry pt group C3v. They

become a1 and e.

Combine with N valence orbitals with same symmetry.

NH3 --calculated MO diagram

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SF6

See textbook Resource Section 5 for SALCs