Chapter 3. Simple Bonding Theory
▪ The elementary description of molecules and their chemical bonding using simpler methods
provides approximate picture of the shape and polarities of molecules
▪ Overview of Lewis dot str., valence-shell electron-pair repulsion (VSEPR) & related topics
▪ The description of bonding should be consistent w/ experimental results.
▪ bond lengths, bond angles, bond strengths are experimentally determined by diffraction (X-ray
diffraction, electron diffraction, neutron diffraction) or spectroscopic (microwave, IR)
▪ This chapter provides a starting point for the molecular orbital description.
▪ This chapter describes some useful qualitative approaches on describing the bonding.
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3.1 Lewis Electron-Dot Diagram
▪ Lewis electron-dot diagram: oversimplified, but a good starting point for the bonding
▪ bond: when two or more atoms share one or more pairs of e▪ nonbonding pair of e- (= lone pair): no bond to atoms, but contribute to shape & reactivity of
molecule
▪ 8 ve- concept: s2p6 configuration for a stable arrangement
exception) H atom (2 ve-)
▪ octet rule: 8e- surround the central atom
EX) H2O:
O: 8 e- requirement
H: 2 e- requirement
▪ double bond: 4e▪ triple bond: 6eInorganic Chemistry
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3.1.1 Resonance
▪ There is more than one possible way in which the ve- can be placed in a Lewis str.
▪ Several choices exist of which atoms are connected by multiple bonds.
▪ ex) CO2-3: 3 possible double bond positions of C-O
→ experimentally all C-O bonds are identical (d(C-O) = 129 pm)
→ single bond C-O: 143 pm, double bond C-O: 116 pm
▪ CO2-3, NO-3, SO3: isoelectronic → the same Lewis str.
▪ several resonance strs. → lowered overall electric E → more stable
a particle in a box: the larger the box, the lower the E
the larger space an e- occupy, the lower the e- E levels
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3.1.2 Expanded Shell
▪ If impossible to keep the octet rule, increase the # of e- around the central atom → more
than the octet rule
(10 e- around Cl)
(12 e- around S)
expanded shell, expanded e- count: increase # ehypervalent: central atoms w/ e- counts greater than the atom’s usual requirement
Ex) IF7 (14 e-) → [TaF8]3- (16 e-) → [XeF8]2- (18 e-) → rarely more than 18 e-
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3.1.3 Formal Charge
▪ electric charge of each atom in a molecule → help assess resonance str. & molecule topology
Help to understand bonding when there are several possibilities
But, only a tool for assessing Lewis strs., not a measure of any actual charge on the atoms
Formal Charge =
(# of ve- in a free
atom of the element)
-
(# of unshared
e-
on the atom)
-
(# of bonds
to the atom)
lone pair
bonding pair
(counting as two e-) (counting as one e-)
▪ charge on molecule or ion = sum of formal charges
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3.1.3 Formal Charge
▪ conditions for assigning formal charge on strs.
1) minimizing formal charges
2) placing negative formal charges on more electronegative elements
3) smaller separation of charges
Example) (1) SCN- (thiocynate ion)
- only one negative
charge
- on the most electronegative element
- only one negative
charge
- two electronegativities
- large charge separation
- on the less electronegative element
A: most important
B: next important
C: minor contribution
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3.1.3 Formal Charge
▪ negative charge on N in SCN▪ bond length → double bond length
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3.1.3 Formal Charge
Example) (2) OCN- (cyanate ion): larger electronegativity on O atom
- B is more important than in thiocyanate.
- protonation: 97 % HNCO + 3 % HOCN
- Bond length of HNCO → double bond
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3.1.3 Formal Charge
Example) (3) CNO- (fulminate ion):
- larger formal charges than those of OCN- due to the electronegativity C < N < O,, none of these are satisfactory str.
unstable ion
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3.1.4 Multiple Bonds in Be and B Compounds
▪ BeF2, BeCl2, BF3 → usually no multiple bonds for F & Cl
→ multiple bonds for Be & B to satisfy the octet rule
(1) minimizing the formal charge: not satisfy the octet rule
(2) follow the octet rule: unusual formal charges
(3) actual strs.: Be w/ coordination # 4 for solid, 3 for vapor
Fig.3.7
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3.1.4 Multiple Bonds in Be and B Compounds
▪ BF3: bond length → shorter than a single-bond
1) possible partial double-bond character
2) strong polarity of B-halogen & ligand close-packing (LCP) may explain
the length w/o using multiple bonding
→ combine w/ other molecules contributing a lone pair of e- (Lewis base)
tetrahedral str. w/ 4-bonds
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3.2 Valence Shell Electron-Pair Repulsion Theory (VSEPR)
▪ provide a method for predicting the shape of molecules based on the electron-pair electrostatic
repulsion
can predict approximate shape comparable to those from experiments
▪ e-s & pairs repel each other due to their negative charges
∴ geometries → ve- pairs position themselves as far as possible
to minimize the e- - e- repulsion
▪ AXmEn: A – central atom
X – surrounding atom
E – lone pair e-
▪ steric number: # of positions occupied by atoms & lone-pairs around a central atom
SN = m + n
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3.2 Valence Shell Electron-Pair Repulsion Theory (VSEPR)
▪ CO2 - SN = 2 (two bond positions)
- linear str. due to the repulsion b/w e- in the double bonds
▪ SO3 - SN = 3 (three bonding positions)
- partial double-bond character
- O position: the corners of an equilateral triangle
(to minimize e- - e- repulsion)
- angle of O-S-O: 120º
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3.2 Valence Shell Electron-Pair Repulsion Theory (VSEPR)
Fig. 3.8 VSEPR Predictions (for molecules w/ the steric # from 2 to 8)
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3.2 Valence Shell Electron-Pair Repulsion Theory (VSEPR)
▪ SN = 2, 3, 4, 6 → completely regular w/ same bond angles & distances
▪ SN = 5, 7 → no uniform angles or distances (∵ no polyhedra w/ these # vertices)
→ SN = 5: trigonal bipyramidal
triangular plane
+
two positions (above & below the center of the plane)
→ SN = 7: pentagonal bipyramidal
pentagonal plane
+
two positions (above & below the center of the plane)
▪ SN = 8: square antiprism → a cube that has had the top frame twisted by 45º
Fig.3.9
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3.2.1 Lone-Pair Repulsion
▪ lone pairs, single bonds, double bonds, triple bonds → can be treated similarly when predict
molecular shape
▪ consider the difference b/w lone pair & bonding pair → better prediction of shape
ex) ∠H-O-H (H2O) < ∠H-N-H (NH3) < ∠H-C-H (CH4)
▪ steric number = 4: CH4, NH3, H2O (Fig. 3.10)
1) CH4: 4 identical bonds
: 4 pairs of e- → as far from each other as possible
tetrahedral, angle of H-C-H = 109.5º
Fig.3.10
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3.2 Valence Shell Electron-Pair Repulsion Theory (VSEPR)
2) NH3: 4 pairs = 3 bonding pairs + 1 lone pair on N
(trigonal pyramid)
tetragonal shape
: lone pair – no confinement to a small region of shape
tend to spread out
occupy more space around N atom than the bonding pair
angle of H-N-H = 106.6º (3º smaller than CH4)
Fig.3.10
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3.2 Valence Shell Electron-Pair Repulsion Theory (VSEPR)
3) H2O: 2 lone pairs + 2 bonding pairs
tetrahedral shape (atom = V shape)
: lone pair – lone pair repulsion → not measurable
: lone pair – bonding pair repulsion > bonding pair-bonding pair
angle of H-O-H = 104.5º (2.1 º smaller than NH3)
Fig.3.10
∴ lone pairs → attracted to one nucleus → spread out & occupy more space
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3.2.1 Lone-Pair Repulsion
▪ steric number = 5 : trigonal bipyramid
: two possible lone pair locations → axial & equatorial
1) single lone pair : SF4 → occupy an equatorial position (Fig. 3.11)
most space
minimizes the interaction b/w the lone pairs & bonding pairs
→ if occupy the axial position
3 X 90º interactions w/ bonding pairs
* in an equatorial → two such interactions
→ actual str.: distorted by lone pair
Fig.3.11
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3.2.1 Lone-Pair Repulsion
2) two lone pairs: ClF3 → 3 possible strs. (Fig. 3.12)
→ importance (1) lone pair - lone pair interactions
(2) lone pair - bonding pair interactions
→ interactions at < 90º are more important
Fig.3.12
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3.2.1 Lone-Pair Repulsion
▪ Fig.3.13 Structure Containing Lone Pairs
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3.2.1 Lone-Pair Repulsion
▪ steric number = 6
- octahedral shape → all six positions are equivalent
1) if a single lone pair → more compress on the other side
(IF5, Fig. 3.13)
2) if two lone pairs → minimize lp-lp by putting them in trans positions
(XeF4, Fig. 3.13)
Fig.3.13
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3.2.1 Lone-Pair Repulsion
▪ steric number = 7: pentagonal bipyramidal (Fig.3.8, IF7, [TeF7]2-)
1) if a single lone pair → distortion (XeF6)
2) if two lone pairs → axial (trans) position to minimize repulsion
XeF5-, IF2-5
Fig.3.8
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3.2.1 Lone-Pair Repulsion
▪ Examples
1) SbF-4 - one lone pair (SN = 5)
- similar to SF4
- lone pair → equatorial position
causing distortion
2) SF-5 - one lone pair (SN = 6)
- based on an octahedron w/ distortion as in IF5
3) SeF+3 - one lone pair (SN = 4)
- reduce ∠F-Se-F = 94º
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3.2.2 Multiple Bond
▪ bond angles of double & triple bonds > single bond
greater repulsive effect due to the π e▪ Fig.3.15: multiple bonds → occupy the same position as lone pairs
e.g.) SN = 5, SOF4, ClO2F3, XeO3F2 → double bonds are all equatorial
(SF4, BrF3, XeF2 w/ lone pairs)
Fig.3.15
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3.2.2 Multiple Bond
▪ multiple bonds: occupy more space → distortions on the rest of molecule
▪ both lone pair & multiple bonds: competition for space
Fig.3.16
▪ Example: 1) HCP: H-C P, linear
2) IOF-4: lone pair > double bond → ∠O-I-F = 89º
3) SeOCl2: both lone pair & double bond exist
repulsion of lp > double bond
∠Cl-Se-Cl = 97º, ∠Cl-Se-O = 106º
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