Chapter 9 Covalent Bonding: Orbitals

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Chapter 9Covalent Bonding Orbitals

• Zumdahl Zumdahl
• M. Todd Tippetts, Ph.D.

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Valence Bond Theory

• Atoms overlap their atomic obitals to form
  covalent bonds
• Bond occurs when two electrons with spins paired
  are shared by two overlapping atomic orbitals
• One electron from each of the two atoms in the
  bond
• Portions of two orbitals overlap to occupy the
  same region of space

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• One pair of electrons can occupy this overlapping
  area
• Electron density is maximizes in overlapped
  region
• H2 bonds form because atomic valence orbitals
  overlap
• Each hydrogen contributed 1s orbital

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Valence Bond Theory

• HF involves overlaps between the s orbital on H
  and the 2p orbital of F

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VB Theory And H2S

• Assume that the unpaired e- in S and H are free
  to form a paired bond
• We may assume that the H-S bond forms between an
  s and a p orbital

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• According to Valence Bond Theory
• Which orbitals overlap in the formation of NH3?
• Ground state of nitrogen
• 2s ?? 2p _? ? _?__

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Difficulties With VB Theory So Far

• Most experimental bond angles do not support
  those predicted by mere atomic orbital overlap
• For example C 1s22s22p2 and H 1s1
• Experimental bond angles in methane are 109.5
  and all are the same
• p orbitals are 90 apart, and not all valence e-
  in C are in the p orbitals
• How can multiple bonds form?

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Hybridization

• The mixing of atomic orbitals to allow formation
  of bonds that have realistic bond angles
• The new shapes that result are called hybrid
  orbitals
• The number of hybrid orbitals required the
  number of bonding domains the number of
  non-bonding domains on the atom

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Hybrid between s and p Orbitals
Two sp Orbitals in Linear Arrangement Formed by
Hybridization of a single s and a single p Orbital
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What Shall We Call These New Orbitals?

• Since we have annexed the spaces previously
  defined by atomic orbitals, we name the hybrid as
  a combination of the orbitals used to form the
  new hybrid
• Name tell what type of atomic orbitals, and how
  many of each
• sp, sp2, sp3 etc.
• One atomic orbital is used for every hybrid
  formed (orbitals are conserved)

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Hybrids From s p Atomic Orbitals explain VSEPR
Geometry
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Hybrids From s p Atomic Orbitals explain VSEPR
Geometry
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Hybrids From s p Atomic Orbitals explain VSEPR
Geometry
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Hybrid Orbitals in BeH2

• Ground state of Be
• 2s?? 2p _ ___ He2s2
• No half filled orbitals available for bonding
• For hybrid sp hybrid orbitals
• sp ? ? 2p ___
• Now bond can form between 1s orbital of hydrogen
  and sp hybrid orbital or berylllium
• sp ?? ?? 2p ___

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Consider the CH4 molecule

• Ground state for carbon
• 2s ? ? 2p ? _ ? ___ He2s2 2p2
• Form sp3 hybrid orbitals
• ? ?_ ? ? .
• Each sp3 hybrid can now overlap with 1s orbital
  of hydrogen
• ?? ??_ ?? ?? .

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Bonding in CH4

• The 4 hybrid orbitals are evenly distributed
  around the C
• The H s-orbitals overlap the sp3 hybrid orbitals
  to form the bonds.

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Bonding in NH3

• The 4 hybrid orbitals are evenly distributed
  around the N
• The H s-orbitals overlap the sp3 hybrid orbitals
  to form three bonds bonds.
• The remaining lone pair occupies the last hybrid
  orbital

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Hybridization for form sp2 orbitals
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Ethene and Double Bonds
Sigma Bonds s Direct overlap of orbitals
between the two nuclei Direct overlap of atomic
orbitals is not affected by rotation around that
bond C--C
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CC double bond consists of one sigma s bond and
one pi p bond
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Orbitals used for bonding in Ethene
Sigma bond sp2 overlaps sp2 Pi bond
unhybridized p orbital overlaps unhybridized p
orbital
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Formation of sp Hybrid Orbitals
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Hybrid Orbitals is CO2 molecule
First bond is sigma bond Second bond is pi bond
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CO2 Molecule
Unhybridized p orbitals are used to form pi bonds
between carbon and oxygen. sp hybrid orbitals of
carbon overlap sp2 hybrid orbitals from oxygen to
form sigma bonds
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• Triple bond in N2 molecule consists of one sigma
  bond and 2 pi bonds
• Sigma bond stems from sp hybrid overlap
• Pi bonds come from unhybridized p orbital overlap

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Expanded Octet Hybridization

• Can be predicted from the geometry as well
• In these situations, d orbitals are be needed to
  provide room for the extra electrons
• One d orbital is added for each pair of electrons
  in excess of the standard octet

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Expanded Octet hybridization

• dsp3 hybridization gives rise to trigonal
  bipyramid geometry of PCl5

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• d2sp3 hybridization gives rise to octahedral
  geometry

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Consider SF6

• Ground state for sulfur
• 3s ? ? 3p ? ? ? ?_ 3d _ _ _ _ _
• Six hybrid orbitals needed
• sp3d2 ? ? ? ? ? ? . 3d
  _ _ _
• Each sp3d2 hybrid can now overlap with 2p orbital
  of fluorine
• ?? ??_ ?? ?? . ?? ??
  

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Bonding is XeF4

• Placing lone pairs at axial positions lets them
  be as far as possible from one another
• Square planar geometery

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• Hybrid orbital can also hold nonbonding electrons
• Usually results in polar molecules

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Consider the SF4 molelcule
Lewis Structure

• Four bonding 1 nonbonding pairs around sulfer
• Five hybrid orbitals needed
• sp3d ?? ? ? ? ? . 3d _ _ _
  _
• Four half filled orbitals available to overlap
  with 2p orbital of fluorine
• sp3d ?? ?? ? ? ?? ? ? . 3d _
  _ _ _

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Geometry of SF4

• sp3d requires trigonal bipyramid geometry
• Nonbonding pair goes on equatorial position
• Distorted tetrahedron geometry

F

S
F
F
F
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Bonding Types

• Two types of bonds result from orbital overlap
• sigma s bonds
• from head-on overlap
• lie along the bond axis
• account for the first bond
• Can freely rotate around bond

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Bonding Types

• pi p bonds
• from lateral overlap by adjacent p or d orbitals
• pi bonds are perpendicular to bond axis
• account for the second and third bonds in a
  multiple bond
• Cannot undergo rotation around bond

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Bonding in Ethene C2H4

• Carbon forms sp2 hybrid orbitals, and one
  unhybridized p orbital

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Sigma and Pi Bonding
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H-CC -H

• Each C has a triple bond and a single bond
• Requires 2 hybrid orbitals, sp
• unhybridized p orbitals used to form the pi bond

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Summary of Multiple Bonds

• Molecular skeleton held together by s bonds.
  First bond between two atoms always s.
• Hybrid orbitals are used to form s bonds, and to
  hold nonbonding electrons
• Number of hybrid orbitals needed atoms bonded
  of nonbonding pairs
• p bonds are formed using non-hybridized p or d
  orbitals
• Double bond is one s and one p bond
• Triple bond consists of one s and two p bonds

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Molecular Orbital Theory

• Modification of VB theory that considers that the
  orbitals may exhibit interference.
• Waves may interfere constructively or
  destructively
• Bonding orbitals stabilize, antibonding
  destabilize.

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MO diagram for H2

• Show atomic energy level diagram for each atom
• Show molecular orbitals (bonding and
  antibonding)
• 1 MO for each Atomic orbital.
• Show electron occupancy of the orbitals.

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Filling MO diagrams

•  Electrons fill the lowest-energy orbitals that
  are available.
• No more than two electrons, with spins paired,
  can occupy any orbital.
• Electrons spread out as much as possible, with
  spins unpaired, over orbitals that have the same
  energy.

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H2 vs He2
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Molecular Orbitals Using p Orbitals
Two boron atoms have one set of p orbitals that
can directly overlap to for sigma bond. Two
parallel p orbitals can form pi bonds
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• Two px orbitals overlap for form sigma bonding
  and antibonding molecular orbitals

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• Two p orbitals overlap to form pi bonding and
  anti-bonding orbitals
• Can happen both to py pair and to pz pair,
  resulting in two bonding and two anti-bonding
  orbitals

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Molecular Orbital Diagram for B2
B2 should be a stable molecule
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Diatomic MO diagrams differ by group
Second period used s and p orbitals

• A) I - V B) VI-VIIIA

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Molecular Orbitals Explains Paramagnetic O2

• Paramagnetic weakly attracted to magnetic field
• Usually a result of unpaired electron
• Simple Lewis structure has no unpaired electrons
• However, MO treatment shows two unpaired
  electrons in p orbitals

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Molecular Orbital Diagrams for B2 to F2
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MO Diagram for Group I-V
Draw the MO diagram for N2
p2p
s2p
s2p
2p
2p
p2p
s2s
2s
2s
s2s
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MO Diagram for Group VI-VIII
Draw the MO diagram for O2
s2p
p2p
2p
2p
p2p
s2p
s2s
2s
2s
s2s
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MO also works for heteronuclear diatomics
Draw the MO diagram for NO
2p
2p
2s
2s
oxygen
nitrogen
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MOs and Free Radicals NO.
Free radicals are molecules with an unpaired
electron
s2p
p2p
2p
s2p
2p
p2p
s2s
2s
2s
s2s
oxygen
nitrogen
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Figure 9.44 Resonance Structures for O3 and NO3
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Figure 9.45 (a) benzene molecule (b) two
resonance structures for benzene molecule
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Delocalized Electrons

• Lewis structures use resonance to explain that
  the actual molecule appears to have several
  equivalent bonds, rather than different possible
  structures
• MO theory shows the electrons being delocalized
  in the structure