Zumdahl

1
Zumdahls Chapter 9

• Covalent Bonding
• Orbitals

2
Chapter Contents

• Hybridization and LE
• dnspm
• Molecular Orbitals
• Bond Order

• Bonding in Homonuclear Diatomics
• Paramagnetism
• Heteronuclear Bonding
• LE MO

3
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.

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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.

5
Carbon Wins Big

• The electronic configuration of carbon is
• He 2s2 2p2 or He ?? ? ?
• As such, only CH2 or two valence bonds are
  possible for carbon. Not for long.
• Using the energy accessible from bond formation,
  carbon promotes an s e to a p orbital
• He 2s1 2p3 or He ? ? ? ?
• Making CH4 and other four valence molecules.

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Blending the l out of it.

• Promotion is necessary but not sufficient we
  must still mix spxpypz in ways like VSEPR.
• The electron density follows the new orbital
  directions and the nuclei obey the bonding
  geometry.
• We neednt blend all of the available orbitals!
• We can mix s?px and leave py and pz for lone
  pair.
• That would give us linear XAX bonding.
• And that results from constructive interference
  in ?.

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Wave Mixture Geometries
2s
2px
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sp Hybridization

• Starting with two AOs, mixing must generate no
  more than nor no fewer than two hybrids.
• The s px combination points up the x-axis while
  the s px combination points down the x-axis.
• Together they give linear XAX molecules (BeF2).
• Also, the sp hybrid is elongated in its bonding
  direction for better penetration and lower energy.

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Trigonal Planar Hybridization, sp2
and
mixed with
and 2 other combinations
gives
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sp2 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 sp2 together look like

If your browser supports VRML, try
http//www.chm.davidson.edu/vrml/ao/ for details
of hybrid orbitals.
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sp3 Tetrahedral Hybridization

• The sp2 are even more penetrating than the sp but
  less so than sp3. The more the p character, the
  more directional the hybrid. Duhh.
• Carbon can hybridize sp3, 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 sp3 together look like

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Hybridization Beyond spn

• The sp3 hybrid orbitals permit a valence of up to
  4 and the expected octet.
• Violating the octet demands incorporation of d
  orbitals as in dsp3, d2sp3, etc.
• They use dz²

• and dx²y²

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Trigonal Bipyramidal dsp3

• Mixing dz² with sp3 gives five orbitals, two of
  which are axial and three 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.
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Octahedral d²sp³

• Mixing dx²y² with the five dsp³ gives the six
  identical d²sp³ 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

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How Chemists Use Hybrids

• Hybrid orbitals are great shorthand notations for
  building up a molecules 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).

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? and the remainders

• The ? skeleton sets hybridization for each of the
  molecules central atoms.
• Bonded to 3 things? No lone pair? You are sp2!
• I not only expect 120 bonds from you but also an
  unhybridized p orbital ? to that plane.
• Since the rest of your octet isnt a lone pair,
  you must be ? bonding to one or more of your
  partners.
• Bonded to 3 with a lone pair? Youre sp3!
• I expect 109.43 bond angles or there abouts.

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? 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, theyre vulnerable to chemical attack
  ? bonds are reactive while ? are relatively
  inert.
• Unsaturated fats have ?s to permit metabolic
  degrade.

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Vitamin B12
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Vitamin B12 withits multiple bonds
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Molecular Orbital (MO) Theory

• Electrons dont ignore all other nuclei beyond
  the adjacent bonding pair. Theyre really
  global.
• Instead of building molecules atom by atom, well
  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?

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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, H2s MOs are LC of 1sA and 1sB where A and
  B are the labels for the two hydrogen atoms.
• 1s? ? 1sA 1sB while 1s? ? 1sA 1sB (2 in 2
  out)

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1s? H2
A
B
Fortunately, this MO holds both electrons.
See http//www.chm.davidson.edu/vrml/mo/h2/h2.html
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1s? H2 MO
A
B
Any electron in this antibonding MO reduces BO by
½.
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Bond Order (BO) in MO

• MOs 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 MOs, but they do not influence
  BO.
• BO ½ (? electrons MO ? electrons MO )
• First surprising consequence H2 has BO ½
• A stable one-electron bond is possible.
• Correlates with Diss. E. and negatively with Bond
  R.

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Using p AOs

• If internuclear axis is Z, then 2pZA 2pZB binds
  and is called 2pz?. The combo antibinds.
• More interesting are PX and PY which combine off
  the internuclear axis as ? MOs.
• 2pX? ? 2pXA 2pXB for example.
• Note that some combinations are meaningless
  because they do not overlap in bonding regions
  e.g., 2pXA 2pYB produces no MO.

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Degenerate MOs

• The energies of 2pX? and 2pY? are identical.
• Hunds Rule applies to MOs just as it did AOs.
• 1s?2 1s?2 2s?2 2s?2 2pZ?2 2pX?1 (C2)
• is followed by
• 1s?2 1s?2 2s?2 2s?2 2pZ?2 2pX?1 2pY?1 (C2)
• Implying not only CC but also ? ? or a
  paramagnetic C2 diatom.

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Decline of Bond Order

• The pinnacle of A2 (2nd row generic diatom) comes
  at N2 with electronic configuration
• Be2 2pZ?2 2pX?2 2pY?2 and bond order 3, N?N.
• Weve run out of bonding MOs of the 2 shell.
• Starting with O2, antibonding highest occupied
  MOs (HOMO) diminish BO.
• Be2 2pZ?2 2pX?2 2pY?2 2pX?1 2pY?1
• Only bond order 2 but paramagnetic.

See http//www.chem.technion.ac.il/ElBookOrb/molec
ule.htm
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Formic Acid, HCO2H

• Lewis Structure would have resonance in the
  conjugate base with the C-O bonds at 1.5 order.
• MO generates this naturally by mixing 2pX from
  both oxygens and the carbon to create

An example of the delocalized nature of ?
bonding.
? bonding is better described as local.
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Benzene, a textbook delocalization
Their mixing generates these double bonds.

• After hybridizing sp2 for the ? skeleton,
• Yes, you can build MOs from hybridized AOs.
• The 6 leftover pX orbitals mix to give global
  MOs ? the plane of the nuclei.
• Before mixing they are

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C6H6 ? Bonding

• After mixing, six new MOs arise, 3 bonding and 3
  antibonding.
• Best case at top, and worst case at bottom.
• The 6 electrons from each carbons p pair up in
  the 3 bonding ?s.

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Knowing Where the Electrons are is

• POWER

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