Molecular Geometry and Bonding Theories

1
Molecular Geometry andBonding Theories

• Brown, LeMay Ch 9
• AP Chemistry
• Monta Vista High School

Ch 9 PS 8, 10, 16, 20 (and draw overall dipole
moments), 30, 34, 36, 41, 59, 73 Recommended 9,
11, 13, 19, 25, 31, 40, 55, 60
2
Rationale for VSEPR Theory

• Lewis structure is a flat drawing showing the
  relative placement of atoms, bonds etc. in a
  molecule, but does not tell anything about the
  shape of the molecule.
• VSEPR theory helps construct molecular shape
  (3-D) from the Lewis structures, which are 2-D
  structures.

3
Valence Shell Electron Pair Repulsion Theroy

• The basis principal of VSEPR is that each group
  of valence electrons (electron domains) around a
  central atom tend to be as far as possible from
  each other to minimize repulsions. These electron
  domain repulsions around the central atom
  determine the molecular geometry of a molecule.
• Electron domains areas of valence e- density
  around the central atom
• Includes bonding e- pairs and nonbonding (lone)
  e- pairs
• A single, double, or triple bond counts as one
  domain
• Repulsions between two e domains are lone
  pair-lonepair gtlone pair-bond pairgt bond
  pair-bond pair

4

• Valence-shell electron-pair repulsion theory
• Why is lone pair- lone pair repulsion greater
  than bond pair-bond pair repulsion?
• Good LinksGood Power point on VSEPR, Shapes of
  sp3, sp2, sp Carbon, VSEPR Lecture

Summary of ABE (Tables 9.1 - 9.3) on the next
slide E lone or non-bonding pairs A
central atom B bonded atoms Bond angles
notation used here lt xº means 2-3º less than
predicted ltlt xº means 4-6º less than predicted
5
Tables Link
of e- domains and type of hybrid orbitals e- domain geometry Formula Molecular geometry Predicted bond angle(s) Example(Lewis structure with molecular shape)
2 Two sp hybrid orbitals Linear AB2 Linear 180º BeF2 CO2
A
A
6
3 Three sp2 hybrid orbitals Trigonal planar AB3 Trigonal planar 120º BF3
3 Three sp2 hybrid orbitals Trigonal planar AB3 Trigonal planar Cl-C-Cl ltlt 120º Cl2CO
3 Three sp2 hybrid orbitals Trigonal planar LAB2 Bent lt 120º NO21-
A
A
A
7
Example CH4
H HCH H

• Molecular shape tetrahedral
• Bond angle 109.5º

8
4 Four sp3 hybrid orbitals or Tetrahedral AB4 Tetrahedral 109.5º CH4
4 Four sp3 hybrid orbitals or Tetrahedral LAB3 Trigonal pyramidal lt 109.5º Ex NH3 107º NH3
4 Four sp3 hybrid orbitals or Tetrahedral L2AB2 Bent ltlt109.5º Ex H2O 104.5º H2O
9
PCl5

• Molecular shape trigonal bipyramidal
• Bond angles
• equatorial 120º
• axial 90º

10
5 Five sp3d hybrid orbitals Trigonal bipyramidal AB5 Trigonal bipyramidal Equatorial 120º Axial 90º PCl5
5 Five sp3d hybrid orbitals Trigonal bipyramidal LAB4 Seesaw Equatorial lt 120º Axiallt 90º SF4
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5 Five sp3d hybrid orbitals Trigonal bipyramidal L2AB3 T-shaped Axialltlt 90º ClF3
5 Five sp3d hybrid orbitals Trigonal bipyramidal L3AB2 Linear Axial 180º XeF2
12
6 Six sp3d2 hybrid orbitals or Octahedral AB6 Octahedral 90º SF6
6 Six sp3d2 hybrid orbitals or Octahedral LAB5 Square pyramidal lt 90º BrF5
13
6 Six sp3d2 hybrid orbitals or L2AB4 Square planar 90º XeF4
6 Six sp3d2 hybrid orbitals or L3AB3 T-shaped lt90º KrCl31-
14
Limitations of VSEPR Theory
Even though the VSEPR model is useful in
predicting the shapes of molecules, it does not
differentiate between single, double and triple
bonds and does not account for bond strengths.
15
9.3 Molecular Polarity

• Two factors must be considered in the polarity of
  a molecule
• Are the individual bonds (joining different atoms
  in a molecule) polar? Ex. HCl vs. H2. HCl is
  polar while H2 is not.

• Bond polarity is most often represented by an
  arrow that points toward the d- (most EN atom),
  showing the shift in e- density.
• The dipole moment (m) is a vector (i.e., has a
  specific direction) measuring the polarity of a
  bond which contains partial charges (Q) that are
  separated by a distance (r).

d d-
m Q r
16

• 2. If individual bonds are polar, then do
  individual dipole moments cancel out or not. A
  molecule is polar if its centers of () and (-)
  charge do not cancel out- generally happens in a
  distorted molecule (molecules with lone pairs of
  e on the central atom.)
• How to determine if a molecule is polar?
• The sum of the bond dipole moments in a molecule
  determines the overall polarity of the molecule.
• Draw the true molecular geometry (3D geometry).
• Draw each bond dipole as an arrow
• Add the vectors, and draw the overall dipole
  moment. If none, then m 0.
• Generally, a distorted molecule (with lone pairs
  on the central atom) will have a dipole.
  Exception AB2E3 type

17
What is the big deal about polarity?

• The polarity of a molecule will tell you a lot
  about its solubility, boiling point, etc. when
  you compare it to other similar molecules. Water,
  for example, is a very light molecule (lighter
  than oxygen gas or nitrogen gas) and you might
  expect it would be a gas based on its molecular
  weight, however the polarity of water makes the
  molecules "stick together" very well. Hence water
  is present as liquid.
• Polar substances are soluble in water (which is
  polar) and non polar substances are soluble in
  non polar solvents such as benzene and oil.

18

• Ex Draw molecular geometires, bond dipole
  moments, and overall dipole moments. Also, name
  the e- domain geometry and the molecular
  geometry.
• CO2 BF3 H2O
• CCl4 NH3 PH3

19
Rationale For Valence Bond Theory

• VB theory provides a basis for covalent bond
  formation based upon overlapping of atomic
  orbitals to share electrons.
• This theory successfully predicts bond strengths
  based upon orbital overlap (such as H2 bond being
  weaker than N2 bond)- sigma vs. pi bond strength

20
Covalent Bonding and Orbital Overlap Valence
Bond Theory

• The basic principle of VB theory is that a
  covalent bond forms when the orbitals of two
  atoms overlap. Three central themes of VB theory
  derive from this principle
• 1. Opposing spins of e pairs In accordance with
  Paulis exclusion principle, an orbital can have
  max of two e with opposite spins.
• 2. Maximum overlap of bonding orbitals The bond
  strength depends upon the attraction of nuclei
  for the shared e, so the greater the overlap, the
  stronger the bond.
• 3. End to end overlap of the atomic orbitals
  form a sigma bond and allows the free rotation of
  the parts of the molecule. Side-to-side overlap
  forms a pi bond, which restricts rotation. A
  multiple bond consists of one sigma bond and rest
  pi bonds.

21
Sigma and Pi bonds

• Sigma (s) bond
• Covalent bond that results from axial overlap of
  orbitals between atoms in a molecule
• Lie directly on internuclear axis
• Single bonds, could form between s-s orbital or
  s-p orbital or p-p orbital by axial overlapping
• Ex F2
• Pi (p) bond
• Covalent bond that results from side-by-side
  overlap of orbitals between atoms in a molecule.
• Are above below and left right of the
  inter nuclear axis and therefore have less total
  orbital overlap, so they are weaker than s bonds.
  Forms between two p orbitals (py or pz)
• Make up the 2nd and 3rd bonds in double triple
  bonds.
• Ex O2 N2

22
Covalent Bonding and Orbital Overlap

• Valence-bond theory overlap of orbitals between
  atoms results in a shared valence e- pair (i.e.,
  bonding pair)

1. As 2 H atoms approach, the 2 valence e- in the
   1s orbitals begin to overlap, becoming more
   stable.
2. As H-H distance approaches 0.74 Å, energy lowers
   b/c of electrostatic attraction between the
   nuclei the incoming e-.
3. When H-H distance 0.74 Å, energy is at its
   lowest because electrostatic attractions
   repulsions are balanced. (This is the actual H-H
   bond distance.
4. When H-H distance lt 0.74 Å, energy increases b/c
   of electrostatic repulsion between 2 nuclei
   between the 2 e-.

Figure Formation of bond in H2
Energy (kJ/mol) 0    -436
d
a
b
c
0.74 Å H-H distance
23
Limitations of VB Theory

• Valence bond (VB) theory assumes that all bonds
  formed between two atoms are localized bonds and
  are formed by the donation of an electron from
  each atom. This is actually an invalid assumption
  because many atoms bond using delocalized
  electrons.

24
Rationale for Hybrid Orbital TheoryGood youtube
video

• Hybrid orbital theory is seen as an extension of
  VB theory, where atomic orbitals hybridize to
  form new hybrid orbitals. This hybrid orbital
  theory helps explains the bonding in terms of
  quantum mechanical model of atom (s,p,d,f
  orbitals).

25
9.5 Hybrid Orbital TheoryMovie on Hybrid
Orbitals

• Explains the molecular geometries in terms of
  s,p,d,f orbitals.
• VSEPR explains that e domains must be farthest
  from each other around central atom, but fails to
  explain these in terms of orbitals as defined in
  wave mechanical model of atom.
• Hybrid orbital theory of Linus Pauling proposed
  that the valence atomic orbitals in the molecule
  are very different from those in the isolated
  atoms.
• The process of orbital mixing is called
  hybridization, and the new atomic orbitals are
  called hybrid orbitals. Animation on Hybrid
  Orbitals, Hybridization Movie

26
Hybrid Orbital Theory

• Two key points about the number and types of
  hybrid orbitals are that
• 1. The number of hybrid orbitals obtained equals
  the number of atomic orbitals mixed.
• 2. The type of hybrid orbitals obtained varies
  with the types of atomic orbitals mixed.

27
sp hybrid orbitals

• BeF2 (g) observed as a linear molecule with 2
  equal-length Be-F bonds. Valence bond theory
  predicts that each bond is an overlap of one Be
  2s e- and one 2p e- of F. However, Bes 2s e-
  are already paired. So
• To form 2 equal bonds with 2 F atoms
• In Be, one 2s e- is promoted to an empty 2p
  orbital.
• The occupied s and p orbitals are hybridized
  (mixed), producing two equivalent sp
  orbitals.
• As the two sp hybrid orbitals of Be overlap
  with two p orbitals of F, stronger bonds result
  than would be expected from a normal Be s and F p
  overlap. (This makes up for energy needed to
  promote the Be e- originally.)

28
Be (ground state) ? Be (promoted) ? Be (sp hybrid)

• 2p
• 2s

Energy ?

• Orbital shapesOne s one p ? Two sp
  orbitals
• (to bond with 2 Fs)
• A central atom in a Lewis structure with exactly
  2 e- domains has sp hybrid orbitals.

29
sp2 hybrid orbitals

• BF3 (g) observed as trigonal planar molecule
  with 3 equal-length B-F bonds. However, 2
  valence e- in B are paired, and are the s and p
  e- not at the observed 120º angle.

B (ground) ? B (promoted) ? B (sp2 hybrid)
2p 2s

• One s two p ? Three sp2
  orbitals (to bond with 3 Fs)
• A central atom with exactly 3 e- domains has sp2
  hybrid orbitals.

30
sp3 hybrid orbitals

• CH4 (g) observed as tetrahedral

C (ground) ? C (promoted) ? C (sp3 hybrid)
2p 2s

• One s three p ? Four sp3 orbitals
  (to bond with 4 Hs)
• A central atom with exactly 4 e- domains has sp3
  hybrid orbitals.

31
sp3d hybrid orbitals (or dsp3)

• PCl5 (g) observed as trigonal bipyramidal forms
  5 bonds of equal energy ( but not equal length
  equatorial are slightly longer)

P (ground) ? P (promoted) ? P (sp3d hybrid)
3d 3p 3s

• One s three p one d ? Five sp3d
  orbitals (to bond with 5 Cls)
• A central atom with exactly 5 e- domains has sp3d
  hybrid orbitals.

32
sp3d2 hybrid orbitals (or d2sp3)

• SF6 (g) observed as octahedral forms 6
  equal-length bonds

• One s three p two d ? Six sp3d2
  orbitals
• A central atom with exactly 6 e- domains has
  sp3d2 hybrids.

33
Non-bonding e- pairs

• Lone pairs occupy hybrid orbitals , too
• Ex H2O (g) observed as bent but e- domain is
  tetrahedral

O (ground) ? O (sp3 hybrid)
2p 2s

• Four sp3 orbitals (2 bonding, 2 non-bonding)

34
9.6 Multiple Bonds

• Draw Lewis structures. For Cs label
  hybridization, molecular geometry, and unique
  bond angles
• C2H6
• C2H4
• C2H2
• C6H6

35
Sigma (s) bonds in C2H4

• Ex ethene C-C s-bonds and C-H s-bonds result
  from axial overlap of H s-orbitals and C
  sp2-orbitals

36
Pi (p) bonds in C2H4
p orbital bonds side-by-side p bond
2p C 2s
sp2 hybrids bond axially s bonds

• Each C has 4 valence e-
• 3 e- for 3 s-bonds
• 1 e- for 1 p-bond, which results from
  side-by-side overlap of one non-hybridized
  p-orbital from each C

37
Sigma (s) bonds in C2H2

• Ex ethyne (a.k.a. acetylene) C-C s-bond and C-H
  s-bonds result from axial overlap of H
  s-orbitals and C sp-orbital

38
Pi (p) bonds in C2H2
p orbital bonds side-by-side p bonds
2p C 2s
sp hybrids bond axially s bonds
p

• Each C has 4 valence e-
• 2 e- for 2 s-bonds
• 2 e- for 2 p-bonds, which result from
  side-by-side overlap of two non-hybridized
  p-orbitals from each carbon

39
Sigma (s) bonds in C6H6

• Ex benzene C-C s-bonds and C-H s-bonds result
  from axial overlap of H s-orbitals and C
  sp2-orbitals
• http//www2.chemistry.msu.edu/faculty/reusch/VirtT
  xtJml/intro3.htmstrc8c

40
Localized v. Delocalized Bonds

• Delocalized bonds are present in compounds
  showing resonance structures, while electrons are
  localized in most other bonds.

41
Localized vs. Delocalized p Bonds
(localized)
(delocalized MINIMUM OF 4 cS)
42
Delocalized p bonds in C6H6

• C-C p-bonds result from overlap of one
  non-hybridized p-orbitals from each C
• Delocalization of e- in p-bonds results in a
  double-donut shaped e- cloud above and below
  the molecular carbon plane.

43
Limitations of Hybrid Orbital Theory
Hybrid orbital theory assumes that all bonds are
formed with localized electrons, which is not
true. MO (Molecular Orbital) theory explains
bonding in terms of delocalized orbitals as well.
44
9.7 Molecular Orbital (MO) theory

• So far we have used valence-bond theory (covalent
  bonds form from overlapping orbitals between
  atoms) with hybrid orbital theory and VSEPR
  theory to connect Lewis structures to observed
  molecular geometries. However, VB theory does not
  explain the magnetic or spectral properties of a
  molecule.
• MO theory is similar to atomic orbital (AO)
  theory (s, p, d, f orbitals) and helps to further
  explain some observed phenomena, like unpredicted
  magnetic properties in molecules like those in
  O2.
• AO are associated with the individual atoms, but
  MO are associated with the whole molecule.

45
AO MO in H2
Atomic orbitals
Anti-bonding orbital
s1s
Molecular orbitals
E
1s 1s
Bonding orbital
s1s

• Combination of two 1s AO from each H forms two MO
  in H2 molecule.
• Bonding MO form between nuclei and are stable
• Antibonding MO marked with form behind
  nuclei and are less stable.

46
Types of MO

• Sigma (s) MO form from combinations of
• Two 1s or 2s orbitals from different atoms
  written as s1s or s2s.
• Two 2pz orbitals from different atoms (axial
  overlap) written as s2pz.(Some sources say 2 px
  orbitals?)
• Pi (p) MO form from combinations of
• Two 2px or 2py orbitals from different atoms
  written as p2px or s2py.
• Do not appear until B2 molecule

47
MO s from Atomic p-Orbital Combinations

• P orbitals can interact with each other forming
  either sigma molecular orbitals, s2p , in a
  end-to-end overlap or pi molecular obrbitals,
  p2p, in a side-to-side overlap.
• The order of energy for MO s derived from 2p
  orbitals is s2p lt p2p lt p2plt s2p
• There are three perpendicular p orbitals, so two
  sigma p orbitals (one bonding and one
  antibonding) and four pi p orbitals (two bonding
  and two antibonding) are formed.
• This energy order gives the expected MO diagram
  for most of the p-block elements for homonuclear
  diatomic molecules.

48
MO s for B, C and N

• The energy order of p orbitals results from the
  assumption that since s and p orbitals have
  differences in energy, they do not interact with
  each other. (or mix)
• However, when 2p atomic orbitals are half filled,
  such as in B, C and N, the repulsions between e
  are little and the energy of these p orbitals is
  not much different than the s atomic orbital,
  which leads to s and p orbital mixing. This
  mixing lowers the energy of the 2s bonding and
  antibonding orbitals and increases the energy of
  sigma 2p (bonding and antibonding) orbitals.The
  pi 2p orbitals are not affected. This mixing
  gives a different energy order
• s2s lt s2slt p2plts2p lt p2plt s2p

49
MO diagrams for lt O2

• Resulting MO for diatomic molecules with lt 16 e-
  (B2, C2, N2, etc.)

• Bond order
• ½ ( bonding e- - antibonding e-)
• B.O. (N2) ½ (10 4) 6 / 2 3 (triple bond)
• N2 has no unpaired electrons which makes it
  diamagnetic.

N atom
N atom
50
MO diagrams for O2

• Resulting MO for diatomic molecules with 16 e-
  (like O2, F2, Ne2, etc.)

• Bond order
• ½ ( bonding e- - antibonding e-)
• B.O. (O2) ½ (10 6) 2 (double bond)
• O2 has unpaired electrons which makes it
  paramagnetic.

O atom
O atom
51
Liquid N2 and liquid O2

• From U. Illinois
• http//www.chem.uiuc.edu/clcwebsite/liquido2.html

N2
O2
52
Magnetism

• In an element or compound
• Diamagnetism all e- paired no magnetic
  properties
• Paramagnetism at least 1 unpaired e-
• Drawn into exterior magnetic field since spins
  of atoms become aligned unlikely to retain
  alignment when field is removed
• Ex N O
• Sc Mn
• O2
• Ferromagnetism occurs primarily in Fe, Co, Ni
• Drawn into exterior magnetic field since spins of
  atoms become aligned very likely to retain
  alignment when field is removed (i.e., a
  permanent magnet)
• Nd2Fe14B is very ferromagnetic