Zumdahl’s Chapter 9

Covalent Bonding Orbitals

Chapter Contents

Hybridization and LE d n sp m Molecular Orbitals Bond Order Bonding in Homonuclear Diatomics Paramagnetism Heteronuclear Bonding LE + MO

Atomic Orbital Hybridization

VSEPR postulates repulsion geometries, but are atomic wavefunctions flexible enough to supply?

A key to wave mechanics is

superposition

, creating new waves from interference of old ones.

Degenerate (same energy) wavefunctions can mix arbitrarily to give new degenerate sets. #  # If energy lowering is possible, even near-degenerate (similar energy) sets of  can mix to new sets.

The Joys of Promotion

Minimization of electron repulsion is the motive for mixing a set of AOs (Atomic Orbitals) that produces new AOs in the VSEPR directions.

In addition, paired electrons in AOs are already satisfied and need no stinking bonds, but if these partners are split up, more bonding is possible, at the bargain expense of promotion to higher energy orbitals.

Extra bond energies pay it back

.

Carbon Wins Big

The electronic configuration of carbon is [He] 2s 2 2p 2 or [He] [  ] [  ] [  ] [ ] As such, only CH 2 or two valence bonds possible for carbon. Not for long.

are Using the energy accessible from bond formation, carbon promotes an

s

e – to a

p

orbital [He] 2s 1 2p 3 or [He] [  ] [  ] [  ] [  ] Making CH 4 and other four valence molecules.

Blending the

l

out of it.

Promotion is necessary but not sufficient; we must still mix s+p x +p y +p z in ways like VSEPR.

The electron density follows the new orbital directions and the nuclei obey the bonding geometry.

We needn’t blend

all

of the available orbitals!

We can mix s  p x and leave p y and p z That would give us linear XAX bonding.

for lone pair.

And that results from constructive interference in  .

Wave Mixture Geometries

2s +

Bonding Direction

2p x =

Node shifted off x=0 plane.

sp Hybridization

Starting with two AOs, mixing must generate no more than nor no fewer than two hybrids.

The s + p x the s – p x combination points up the x-axis while combination points down the x-axis.

Together they give linear XAX molecules (BeF 2 ).

Also, the sp hybrid is elongated in its bonding direction for better penetration and lower energy.

Trigonal Planar Hybridization, sp

2 and mixed with and 2 other combinations gives

sp

2

Hybridization

As with sp, the leftover p orbital(s) are available for electrons as either lone pairs or  bonds.

In contrast, the single bonds created with the hybrids are called  bonds, where  is the Greek

s

and  is the Greek

p

.

All 3 sp 2 together look like: Truly 120 ° apart If your browser supports VRML, try http://www.chm.davidson.edu/vrml/ao/ for details of hybrid orbitals.

sp

3

Tetrahedral Hybridization

The sp 2 are even more penetrating than the sp but less so than sp 3 . The more the p character, the more directional the hybrid. Duhh.

Carbon can hybridize sp 3 , but so can N and O; the difference is in how many hybrids have only one electron. Those bond; the others lone pair.

The four sp 3 together look like: And the angle is now cos –1 (–1/3) = 109.43

°

Hybridization Beyond sp

n The sp 3 hybrid orbitals permit a valence of up to 4 and the expected octet.

Violating the octet demands incorporation of

d

orbitals as in dsp 3 , d 2 sp 3 , etc.

They use d z² and d x²–y²

Trigonal Bipyramidal dsp

3 Mixing d z² with which are axial sp 3 gives and three five orbitals, two of equatorial .

Only one each of the two kinds are shown here, but the other axial is just down the Z while the other two equatorials are around Z at 120° to the one shown.

Octahedral d²sp³

Mixing d

identical

x²–y² with the five dsp³ d²sp³ gives the six orbitals in Cartesian directions.

This picture is merely diagrammatic; it is not an accurate representation of the d²sp³ wave functions. (It is a group of spheres and cones.) Still, if your browser is equipped with VRML, you can play with my first 3d world construction at http://www.utdallas.edu/~parr/chm1315/d2sp3.wrl

How Chemists Use Hybrids

Hybrid orbitals are great shorthand notations for building up a molecule’s geometry center by center … part of every molecular model kit.

The skeletal structure so developed is called the  skeleton because in-line overlap of adjacent bonding hybrids are cylindrically symmetrical about the internuclear axis and thus have

no

(axial) angular momentum (like s for an atom).



and the remainders

The  skeleton sets hybridization for each of the molecule’s central atoms.

Bonded to 3 things? No lone pair? You are sp 2 !

  I not only expect 120° bonds from you but also an unhybridized p orbital  to that plane.

Since the rest of your octet isn’t a lone pair, you must be  bonding to one or more of your partners.

Bonded to 3 with a lone pair? You’re sp 3 !

 I expect 109.43° bond angles or there abouts.



bonds? Piece of cake.

Unhybridized p orbitals on adjacent bonding centers can overlap (inefficiently) sideways.

Density not cylindrically symmetric (like  ) but does allow for buildup between nuclei (off line-of-centers).

 bonds weaker than  but add 1 to the bond order.

Off axis, they’re vulnerable to chemical attack;  bonds are reactive while  are relatively inert.

 “Unsaturated” fats have  ’s to permit metabolic degrade.

Vitamin B12

sp C  N ligand sp 2 C=O d 2 sp 3 Co sp 3 sp 3 SO 4

Vitamin B12 with its multiple bonds

Molecular Orbital (MO) Theory

Electrons don’t ignore all other nuclei beyond the adjacent bonding pair. They’re really global.

Instead of building molecules atom by atom, we’ll pour electrons onto a nuclear skeleton.

Hess assures us that when all the electrons are finally present, the (binding) energies will be the same either way.

So how do electrons respond differently this way?

Add electrons to proton framework

They see a wavefunction that spans molecule!

First approximation model to that is LCAO , Linear Combination of Atomic Orbitals.

Study the diatomics for simplicity. The advantages to MO will become apparent even there.

Thus, H 2 ’s MOs are LC of 1s A and 1s B where A and B are the labels for the two hydrogen atoms.

1s

 

1s A + 1s B

while 1s 

*



1s A – 1s B

(2 in; 2 out)

1s



H

2

A B

MO also builds density between bonded nuclei.

Fortunately, this MO holds both electrons.

See http://www.chm.davidson.edu/vrml/mo/h2/h2.html

Electron density vacates region between nuclei!

A B

1s



* H

2

MO

Any electron in this antibonding MO reduces BO by ½.

Bond Order (BO) in MO

MO’s come in constructive (e.g., 1s  ) and destructive (e.g., 1s  *) combinations as regards the internuclear region.

Since they must mimic lone pairs as well, there are nonbonding MO’s, but they do not influence BO.

BO = ½ (  electrons MO –  electrons MO* First surprising consequence: H 2 + ) has BO = ½ A stable one-electron bond is possible.

Correlates with Diss. E. and negatively with Bond R.

Using p AO’s

If internuclear axis is Z , then 2p ZA – 2p ZB binds and is called 2p z  . The “+” combo anti*binds.

More interesting are P X and P Y which combine off the internuclear axis as  MO’s.

2p X  *  2p XA – 2p XB for example.

Note that some combinations are e.g., 2p

X

A + 2p

Y

B meaningless because they do not overlap in bonding regions: produces no MO.

Degenerate MO’s

The energies of 2p X  and 2p Y  are identical.

Hund’s Rule applies to MO’s just as it did AO’s.

1s  2 1s  * 2 2s  2 2s  * 2 2p Z  2 2p X  1 (C 2 + ) is followed by 1s  2 1s  * 2 2s  2 2s  * 2 2p Z  2 2p X  1 Implying not only C = C but also   paramagnetic C 2 diatom.

2p Y or a  1 (C 2 )

Decline of Bond Order

The pinnacle of A 2 comes at N 2 (2 nd row generic diatom) with electronic configuration: [Be 2 ] 2p Z  2 2p X  2 2p Y  2 and bond order 3, N  N.

We’ve run out of bonding MO’s of the 2 shell.

Starting with O 2 , antibonding MO’s (HOMO) diminish BO.

highest occupied [Be 2 ] 2p Z  2 2p X  2 2p Y  2 2p X  * 1 2p Y  * 1 Only bond order 2 but paramagnetic.

See http://www.chem.technion.ac.il/ElBookOrb/molecule.htm

Formic Acid, HCO

2

H

Lewis Structure would have resonance in the conjugate base with the C-O bonds at 1.5 order.

MO generates this naturally by mixing 2p X both oxygens and the carbon to create: from An example of the

delocalized

of  nature bonding.

 bonding is better described as local.

Their mixing generates these double bonds.

Benzene, a textbook delocalization

After hybridizing sp 2 the  skeleton,  for Yes, you can build MO’s from hybridized AO’s.

The 6 leftover p X orbitals mix to give global MO’s  the plane of the nuclei.

Before mixing they are:

Evidence of delocalized electrons comes from benzene’s magnetic “ring current.”

C

6

H

6 

Bonding

After mixing, six new MO’s arise, 3 bonding and 3 antibonding.

Best case at top, and worst case at bottom.

The 6 electrons from each carbon’s p pair up in the 3 bonding  ’s.

Knowing Where the Electrons are is

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