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Section 2 (Chapter 3, M&T)

Chemical Bonding

Bonding Models

� We will look at three models of bonding:

� Lewis model

� Valence Bond model

� MO theory

Bonding Models (Lewis)

� Lewis model of bonding is simple: electrons are paired (where possible)

� Radical species have electrons left over after pairing

� In forming Lewis structures, atom symbols are drawn with their valence electrons (dots) and unpaired electrons are paired with those of other atoms to form covalent bonds

� Electrons are added as lone pairs and bonds around atoms to give each atom an octet. In certain cases, some atoms can have more than an octet of electrons, some less.

Bonding Models (Lewis)

� The Lewis model is useful for:

� Showing connectivity between atoms

� Showing lone pairs

� A starting point for valence bond

models and VSEPR theory

Lewis structures are not used to convey anything about the shape of a molecule/ion

Lewis Structures – Multiple Bonds

� In some cases (e.g. CO2, C2H2), multiple bonds

must exist in order to create an octet

� In some cases where multiple bonds exist, there

may be more than one possible structure. For

example, in carbonate ion, CO32-

� Structures which differ only in the placement of

electrons (position of atoms doesn’t change) are

called resonance structures. Resonance structures

increase the stability of an arrangement of atoms

Resonance Structures

� Each resonance structure contributes to the overall

bonding picture in a molecule or ion; none

individually is correct

� Bond lengths in CO32- are all found to be 129 pm.

C-O bond is ~ 143 pm and C=O ~ 116 pm

COO

O

COO

O

COO

O

2-2-2-

*correct Lewis structure also shows lone pairs

2

Formal Charge

• Formal charge is a comparison of the number

of electrons around an atom in a Lewis

structure with what you’d find for an isolated

atom of that element

• Formal charges can be used to assess different

resonance structures (to see which is most

favorable) and to provide a guess at a site’s

electron richness/poorness

Formal Charge = (group # of atom) - (# of electrons around atom in structure)

Formal charges are not actual charges, just a method of book keeping

Formal Charge

• In counting electrons, lone pairs count as two

electrons and bonds as one (only one of the

electrons in each bond is assumed to reside “on”

the atom)

• Consider the NCS- ion; which is most correct?

• Most “correct” structure has:

a. lowest formal charges and

b. most negative formal charge on most

electronegative element

N C S N C S N C S

- --

*again, correct Lewis structures also show lone pairs

Expanded Shells

� Many common organic compounds obey the

octet rule; however, many inorganic ones

incorporating heavier elements* (e.g. 3rd period)

may possess more than eight electrons (an

“expanded octet”)

� Examples include SF6, PCl5, PCl3

P

Cl

Cl

ClCl

ClBr

Cl

Cl

Cl S

F

FF F

F F..

. .

10e- 10e- 12e-

*possibly due to the availability of low lying, empty d-orbitals in these elements

Rem: correct Lewis

structures will also

show non-bonding

electrons

The Lewis structure that seems to agree best with experimental findings

is the one that has expanded octets and lowest formal charges

Less than an octet…� For group II and group III elements such as

Be (in BeF2) and B (in BF3), it is not possible

to obtain an octet without creating

unreasonable formal charges

� For these cases, experimental evidence seems

to indicate several possibilities are important

B

F

FF

••

••

••

••

•••• ••••

••

B

F

FF

-

••••

••••

••

••

+

••

••

••

••••

B

F

FF

••

••

•••• ••

•••• -

+

••

••

VSEPR Theory

� Valence Shell Electron-Pair Repulsion theory is

used to predict the shape of molecules based on

electron-pair repulsions

� Pairs of electrons include bonding pairs and

non-bonding pairs (lone pairs)

� Heirarchy of repulsions

� Lone pair-lone pair

� Lone pair-bonding pair

� Bonding pair-bonding pair

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VSEPR Theory� The repulsions

that exist between electron pairs on the central atom dictates the arrangement of the other atoms

� The number of pairs of electrons around the central atom are sometimes called electron domains/stericnumber

� Each of the following count as one electron domain:� Single bond

� Double bond

� Triple bond

� Lone pair

Effect of Lone Pairs

Increasing the numbers of lone pairs

around the central atom increases the

degree of repulsion experienced by the

bonding pairs

The net effect is a closing of the H-X-H

bond angle

This effect is seen in other geometries also

Notice that while these molecules have differentmolecular geometries, they all have the same

electron domain geometries (tetrahedral)

tetrahedral

MolecularGeometry

trigonalpyramid

bent

A B

bonding pairnon-bondingpair

5-Coordinate (Trigonal bipyramid)

� The trigonal bipyramidal

geometry involves two kinds of

environments (axial and

equatorial)

� Introducing a lone pair into this

geometry creates two possibilities

� Heirarchy of repulsions (angle):

90o>>120o>180o

strongrepulsion

weakrepulsion

ClF3 Geometry

Two lone pairs on a trigonal bipyramidal EDG

6 total 90o

repulsions in each

1x lp-lp3 x lp-bp2 x bp-bp

4 x lp-bp2 x bp-bp

the difference

strongest repulsionleast favorable angle

Effect of Multiple Bonds

� Multiple bonds confine a

greater amount of electron

density between two atoms

than do single bonds. Their

effect on geometries is similar

to lone pairs (though not as

strong)

•Multiple bonds

•Larger groups

Electronegativity and Size Effects

� Observed bond angles in molecules are

influenced by both the size and

electronegativity of atoms

� The influence of size and electronegativity

depends on the position of the atom in the

molecule (central or peripheral)

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Periodic Electronegativity Trends

Electronegativity trend

Increases L ���� R

Decreases top ���� bottom

These electronegativities

are derived from bond-

dissociation enthalpies

(Pauling)

Periodic Electronegativity Trends

� Figure (previous slide) shows Pauling electronegativities, χχχχP, but the trend is the same as for Mulliken (χχχχM) values

� Bond dissociation enthalpy, D:

H2(g) ���� 2H(g) DH2 = 432 kJ.mol-1

Cl2(g) ���� 2Cl(g) DCl2 = 240 kJ.mol-1

½(DH2 + DCl2) = 336 kJ.mol-1

• Pauling electronegativity is related to the difference in the

average of the homonuclear bond dissociation enthalpies and

the value for the heteronuclear (experimental) bond enthalpy

� HCl(g) ���� H(g) + Cl(g) DHCl = 428 kJ.mol-1

Experimental bonddissociation energy

Averaging would describea situation where thebonding electrons are

equally shared

Difference results from unequal sharing of electrons in H-Cl bond

Electronegativity and Size Effects

� Peripheral atoms

� The greater the size of the outer atom, the larger the

bond angle

� The greater the electronegativity of the outer atom, the

smaller the bond angle

� Most times, these effects are cooperative

F is smaller and more electronegative than Cl

Bond angle as a function of outer

atom electronegativity

Effect of size/electronegativity of outer atom

Electronegativity and Size Effects

� Where the electronegativity or size of the

central atom is concerned,

� Bond angle increases as the electronegativity of

the central atom increases

� Decreases as the size of the central atom

increases

FN

FF

FP

FF F

AsF

FF

SbF

F

. . . . . . . .

102.2o 97.8o 96.2o 87.3o

For group 5 elements electronegativity: N > P > As > Sb

Bond angle as a function of center

atom electronegativity

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Polar Molecules

� Bonds between non-identical atoms (heteronuclearbonds) will often involve unequal sharing of electrons

� The situation is one of relative electron deficiency (Q+) at one end and electron excess (Q-) at the other (a dipolar bond) – an electric dipole

� The extent of the polarity of a bond is expressed in units of the dipole moment, m

µµµµ = Q ×××× r

� Where Q is the apparent charge (C) of each atom separated by a distance, r (in m).

� The dipole moment is a measure of the charge separation (bigger the disparity in charge at each end, bigger the dipole moment)

Polar Molecules

� Entire molecules may be polar as a consequence

of their polar bonds

� Molecules with polar bonds may be non-polar as

a consequence of their symmetry

� Sometimes the electronegativity of the atoms

involved makes prediction of the dipole difficult

HN

HH

HO

H FN

FF

. . . ... ..

1.47D 1.85D 0.23D

Valence Bond Theory (A bonding model that

uses combinations of valence atomic orbitals to

explain shapes)

� Consider a H2O molecule. If we try to explain the

bonds of this molecule as overlap of valence atomic

orbitals of H (1s) and O (2s, 2p), we cannot get a

picture that describes a 104.5o H-O-H bond angle

Valence Bond Theory

� One way of describing a bonding picture in

polyatomic molecules is through valence

bond theory (a localized bonding model)

� This model describes the σσσσ-bonding

framework of polyatomic molecules through

overlap of hybrid orbitals

� Orbital hybridization: mixing of atomic

orbitals

Hybrid orbital: orbital that is created by mixing two or more atomic orbitals

Hybrid Orbitals

� Directional hybrid orbitals are obtained by

mixing characters of different atomic orbitals

of similar energies

� Use sp hybrid orbitals to describe bonding in

linear molecules like BeCl2(g)

Two linear combinations

of valence atomic orbitals

sp Hybrid Orbital Scheme

� In this scheme, there are two different combinations

of the 2s orbital and the 2px orbital of Be, yielding

two different sp hybrid orbitals

� First combination adds the 2px orbital to the 2s

orbital. The overlap region where the phases (signs)

are similar is reinforced, producing a bigger function

here. Where the signs are opposite, the lobe becomes

smaller (cancellation)

)(2

122_ xpshybridsp ϕϕϕ +=

A coefficient which describes the contribution of each orbital to the hybrid

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sp Hybrid Orbital Scheme

� The second combination involves the “subtraction” of

the 2px orbital from the 2s orbital – this implies

overlap of the 2px-orbital drawn pointing in the

opposite direction

� This hybrid is degenerate (same energy) with the one

discussed on the previous slide

)(2

122_ xpshybridsp ϕϕϕ −=

Orbital Energy Diagram

Atomic orbitals Hybrid orbitals

Singly occupied hybrid orbitals can overlap

with other singly occupied hybrid orbitals

sp2 Hybridization

� For trigonal planar molecular geometries,

there must be a hybrid orbital picture that

describes three equivalent orbitals available

for overlap with the orbitals (atomic or hybrid)

of other atoms

� sp2 hybrids involves mixing of an s and two p

orbitals. There are three combinations

considered

sp2 Hybridization

yx

yx

x

ppshybridsp

ppshybridsp

pshybridsp

222_

222_

22_

2

1

6

1

3

1

2

1

6

1

3

1

3

2

3

1

2

2

2

ϕϕϕϕ

ϕϕϕϕ

ϕϕϕ

−−=

+−=

+=

Coefficients which describe the

contribution of each atomic orbital

to the hybrid orbital The combination of “n” atomic

orbitals will yield “n” hybrid orbitals

Bonding in BH3

� Each bond is described by the overlap of a

H 1s orbital with a sp2 hybrid orbital of B

� The bonds in this picture are 2c, 2e- bonds

sp3 Hybridization

� For tetrahedral molecules, we need a scheme

that involves four equivalent hybrid orbitals

(s, px, py, pz)

( )

( )

( )

( )zyx

zyx

zyx

zyx

pppshybridsp

pppshybridsp

pppshybridsp

pppshybridsp

2222_

2222_

2222_

2222_

2

1

2

1

2

1

2

1

3

3

3

3

ϕϕϕϕϕ

ϕϕϕϕϕ

ϕϕϕϕϕ

ϕϕϕϕϕ

+−−=

−+−=

−−+=

+++=

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NH3 Hybrid Orbital Picture

NHH

H

..

N

H

H

H

N-atom uses sp3-hybrid orbitals

H-atoms use 1s-atomic orbitals

Use sp3-hybrid orbitals to describe atoms having four electron domains

Other Hybridization Schemes

� Other orbital hybridization schemes

should involve different combinations

of atomic obitals

� Examples:

� sp3d: trigonal bipyramidal

� sp3d2: square-base pyramid

� sp3d2 : octahedral

5-coordinate

6-coordinate

Molecules having multiple bonds

� Ethene, C2H4; ask the questions

� What is the central atom?

� What is the geometry (electron domain) around

the central atom?

� What orbital hybridization scheme will enable

this geometry?

� Are there orbitals left over? Which? How are

they involved?

C C

H

HH

H

Unhybridized pz orbitals are

available for ππππ-bond formation

overlap yields π-bond

A Quick Discussion of Bond Symmetry

� Sigma bonding symmetry implies that the orbital

overlap picture which described the bond is

symmetric with respect to a 180o rotation about

the internuclear axis

Symmetric ���� no sign change

Sign change for 180o rotation: ππππ-bond

Hydrogen Cyanide, HCN

� Same questions:

� What is the central atom?

� What is the geometry (electron domain)

around the central atom?

� What orbital hybridization scheme will

enable this geometry?

� Are there orbitals left over? Which?

How do they become involved?

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Hs-Csp overlap

Csp-Nsp overlap

2 unhybridized p-orbitalsper atom, available for

formation of 2 π-bonds

What is the other sp-orbital on nitrogen for?

Boron Trifluoride, BF3

� Central atom

� e- domain geometry

� Orbital hybridization scheme (do for F also)

� Unperturbed orbitals – what do they do?

•BF3 is trigonal planar

•Requires sp2 hybrid orbitals for boron

•Fluorine could have sp3 or sp2

•Empty pz-orbital on boron can accept

lone pair from an adjacent F-atom to

form a ππππ-bond