Molecular Geometry and Chemical Bonding

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Molecular Geometry and Chemical Bonding

• Chapter 10

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Introduction

• Each molecule in the nature has a definite shape.
  BF3 and NF3 have the same general formula AX3,
  where A is the central atom to which surrounding
  atoms, X, are bonded.
• BF3 is the planar molecule with a bond angle 1200
  where as NF3 is a nonplanar molecule with a bond
  angle of 960.
• The geometry of BF3 is trigonal planar and that
  of NF3 is trigonal pyramidal. There is no
  relation between the formula of a compound and
  the shape of its molecules.
• How do we explain the geometries of the molecules
  in terms of their electronic structures?

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Topics of Discussion

• The Valence-Shell Electron Repulsion(VSEPR)
  Theory
• Dipole Moment and Molecular Geometry
• Valence Bond Theory
• Description of Multiple Bonding
• Principles of Molecular Orbital Theory
• Electron Configurations of Diatomic Molecules of
  the Second Row Elements
• Molecular Orbitals and Delocalized Bonding

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Molecular Geometry and Directional Bonding

• Molecular geometry of a molecule is the arrange_
  ments of atoms in space.
• Electron-pair geometry is the arrangements of
  electron pairs around the central atom.
• Structural formula(lewis electron-dot) indicates
  which atoms are bonded to each other with bonding
  e-pairs and where the non-bonding e-pairs are
  located in molecule.

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The Valence-Shell Electron Repulsion(VSEPR) Model

• The electrons are in pairs in the valence shell
  of atoms in a molecule. The bonding e-pair forms
  a covalent bond but nonbonding(lone) e-pair
  doesnt.
• VSEPR Model states that valence-shell e-pairs are
  arranged about each atom so that e-pairs stay as
  far away from another as possible, thus
  minimizing e-pair repulsions. The direction in
  space of the bonding pairs gives the geometry of
  the molecule.
• In VSEPR model, each multiple bond is treated as
  though it were a single bonding e-pair(except a
  slight distortion on bond angles)

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Prediction of Geometry by VSEPR

• Steps to be followed to predict the geometry of
  an AXn molecule by VSEPR model. A is the central
  atom (CA) in the molecule.

• Two Electron Pairs
• Write down the Lewis electron dot formula
• Determine the number of e-pairs around the CA
• Arrange the geometry of e-pairs around the CA
• Decide the molecular geometry from direction of
  bonding e-pairs

• Each multiple bond is treated as though it were
  single bonding e-pair(except a slight distortion
  on bond angles)

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Three Electron Pairs

• Write down the Lewis electron dot formula
• Determine the number of e-pairs around the CA
• Arrange the geometry of e-pairs around the CA.
• Decide the molecular geometry from direction of
  bonding e-pairs.

There are four e-pairs in the valence shell of
the carbon atom in formaldehyde, two of these
constitute a double bond between C and O leaves
three e-pairs with trigonal planar arrangement.
However, double bond domain is larger in size
than a single bond. Hence, H-C-H bond decreases
to 1180
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Four Electron Pairs

• 1.Lewis electron dot formula
• 2. Number of e-pairs
• 3. Geometry of e-pairs
• 4. Molecular geometry
• 5. H-A-H Angle

Consider methane, CH4, ammonia, NH3, and water,
H2O. All three have tetrahedral e-pair geometries
but their bond angles differ slightly as shown
above. Due to a lone pair occupies more space
when compared to a bonding pair, the angle of
H-A-H bond decreases as the number of lone pairs
increases.
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Five Electron Pairs
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Six Electron Pairs
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Dipole Moment and Molecular Geometry

• Dipole moment is a quantitative measure of the
  degree of charge separation in a molecule. A bond
  (or a molecule) is said to be polar if its
  centers of positive or negative charge do not
  coincide.
• The dipole moments of substances can be obtained
  by the measurement of the capacitance of the
  charged plates separated by this substances. They
  are usually reported in Debye(D) 1 D equals to
  3.34x10-34 C.m

• The polarity of a bond is denoted by an arrow
  pointing to the negative end of the bond. The
  polarity a molecule is predicted by the sum of
  the bomd dipole vectors.

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Examples

• E 10.3 BrF3 has a nonzero dipole moment.Which
  geometry is consistent?
• Trigonal planar
• Trigonal pyramidal
• T-shaped
• E 10.4 Which of the following would be expected
  to have dipole moment of zero on the basis of
  geometry?
• a)SOCl2 b)SiF4 c)OF2
• a) ? ? 0
• b) ? 0
• c) ? ? 0

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Valence Bond Theory

• The VSEPR model is a satisfactory method for
  predicting molecular geometries. But Lewis
  formula does not explain how and why covalent
  bonds are formed. Two theories
• Valence Bond Theory(VB) Individual atoms each
  with its own orbitals and electrons come together
  to form the covalent bonds of molecules. Bond is
  formed when one orbital from each of the atoms
  overlaps and a pair of electrons with opposite
  spins is shared between two atoms. When two
  atomic orbitals from different atom share the
  same space, they overlap.
• Molecular Orbital Theory(MO) Molecules have
  molecular orbitals which are populated by
  electrons

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Overlap of Orbitals-I

• Just two electrons with paired spins can be
  shared between two overlapping atomic orbitals.
  The e-pair becomes concentrated in the region of
  overlap and helps to cement the nuclei together.
• The strength of bonding depends on orbital
  overlap.
• Orbitals bond only in the direction in which
  they point to give maximum overlap.

s orbitals bond in every direction due to their
spherical symmetry. p orbitals bond at 900 angles
to each other due to their orientation in space.
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Overlap of Orbitals-II

• Example Predict the bond angle in H2S in VB.
• 1H 1s1 16S ?Ne? 3s23p4
• Overlap of 1s orbitals of two hydrogen atoms
  with two 3p orbitals of sulfur atom give two
  covalent bonds in H2S with a predicted bond angle
  of 900 (Exp 920).
• Example Predict the bond angle in H2O in VB.
• 1H 1s1 16O ?He? 2s22p4
• predicted bond angle 900 (Exp 1050).
• Example Predict the bond angle in CH4 in VB.
• 1H 1s1 6C ?He? 2s22p2
• Prediction CH2 is a stable compound not CH4.
  No simple atomic orbitals are oriented 109.50 to
  explain the bond angle in CH4.

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Hybrid Orbitals

• When atoms form bonds, their atomic orbitals mix
  to form new orbitals which are called as hybrid
  orbitals.
• The number of hybrid orbitals formed always equal
  to the number of atomic orbitals used.
• sp hybrid orbitals one s and one p atomic
  orbitals (linear)
• sp2 hybrid orbitals one s and two p atomic
  orbitals (trigonal planar)
• sp3 hybrid orbitals one s and three p atomic
  orbitals (tetrahedral)
• sp3d hybrid orbitals one s, three p and one d
  atomic orbitals(trigonal bipyr.)
• sp3d2 hybrid orbitals one s, three p and two d
  atomic orbitals (octahedral)

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Energetics of sp3 Hybridization
sp3
2s
1s
H g.s
C g.s.
C hyb.(CH4)

• Consider the carbon atom in the ground state. An
  e-pair in 2s and an electron in each of two 2p
  atomic orbitals. A set of hybrid orbitals(sp3) is
  constructed from one s orbital and three p
  orbitals of carbon atom. The four sp3 hybrid
  orbitals point in tetrahedral directions. The C-H
  bonds in CH4 are described by the overlap of each
  sp3 hybrid orbital of the carbon atom with 1s
  orbitals of hydrogen atoms.

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Description of Bonding in VB

• Steps to obtain the bonding description in VB
• Write the Lewis electron dot formula of the
  molecule
• Use VSEPR model to obtain the arrangements of
  e-pairs about the central atom.
• Deduce the type of hybrid orbitals
• Assign the electrons of the central atom to the
  hybrid orbitals one at a time, pairing them only
  when necessary
• Form bonds to this central atom by overlaping
  singly occupied orbitals of other atoms with a
  singly occupied hybrid orbitals of the central
  atom.
• E 10.5 Describe the bonding in NH3, according to
  VB

sp3
sp3
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Multiple Bonding-I

• One hybrid orbital is needed for each bond and
  for each lone pair. Two types
• Sigma(?) bond the electron density is
  concentrated between two nuclei of the atoms
  along an imaginary internuclear axis.
• Pi(?) bond the electron density is divided
  between two separate regions that lie on opposite
  sides of internuclear axis.
• In ethylene, C2H4, each sp2 hybrid C orbitals
  overlaps a 1s orbital of a H-atoms or an sp2
  hybrid of another C to form a ? bonds. The ?
  bonds give the molecular framework. The remaining
  2p orbitals form ? bond.

There are geometric, or cis-trans isomers of
1,2-dichloroethene because the formation of a ?
bond locks all the atoms into a flat, rigid
molecule.
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Multiple Bonding-II

• In acetylene, H-C?C-H, each C atom is bonded to
  two other atoms with sp hybrid orbitals with
  linear arrangement. Remaining two 2p orbitals
  form two ? bonds. Geometry is linear.

• E 10.7 Describe the bonding on the C atom in CO2
  using VB.
• The remaining two 2p orbitals of C atom form
  ? bonds with 2p atomic orbital on each O atom.
  One of sp2 hybrid orbitals on oxygen atom forms a
  sigma bond with C and remaining two are occupied
  by the lone pairs on each O atom.

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Molecular Orbital Theory

• VB predicts any molecule with even number of
  valence electrons should be diamagnetic. For
  example O2
• But O2 is a paramagnetic substance.
• Molecular Orbital(MO) Theory Molecules have
  molecular orbitals which may spread over several
  atoms or entire molecule and electrons are
  distributed in them.
• Each MO has a definite energy
• For the grond state, electrons are put into
  orbitals of lowest energy, consistent with Pauli
  Principle (each MO can take maximum of two
  electrons with opposite spins) and Hunds Rule
  (MOs with equal energies is filled with
  electrons to give minimum number of e-pairs)

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Molecular Orbitals-I

• Bonding (?) orbitals are MOs their electron
  densities are concentrated between two
  nuclei.(constructive interference of ?s)
• Antibonding (?) orbitals are MOs their
  electron densities are concentrated in regions
  other than between two nuclei.(destructive
  interference of ?s)

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Molecular Orbitals-II

• The strength of interaction between two atomic
  orbitals to form MO is determined
• The energy difference between the interacting
  atomic orbitals
• The magnitude of their overlap
• For the interaction to be strong, the energies of
  the two orbitals must be approximately equal and
  the overlap must be large.
• 1s1s??1s?1s, 1s2s? No, 2s2s ??2s?2s,
  
• 2s2p ? No, 2p2p ??2p?2p ?2p ?2p
  ?2p ?2p

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Electron Configuration of Diatomic Molecules

• 2s and 2p atomic orbitals interact with each
  other to change the energy ordering of MOs
• For B2,C2 and N2 smaller energy difference causes
  larger 2s2p interaction and puches the energy of
  ?2p above that of ?2p.
• For O2,F2 and Ne2 2s2p interaction is small, the
  energy ordering of MOs is as predicted before.

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Order, Length and Energy of a Bond

• Bond order (nb-na)/2 nb is the number of
  electrons in the bonding orbitals, na is the
  number of electrons in the antibonding orbitals.

Bond length decreases as the bond order
increases. Bond energy increases as the bond
order increases. Molecules with BO 0 are
unstable. He2, Ne2. Molecules with unpaired
electrons in their electronic configuration is
paramagnetic.
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Delocalized Bonding

• In VB, two or more resonance formulas are
  required to explain bonding.
• In MO, the bonding is described in terms of a
  single electron configuration. One sp2 hybrid
  orbital on side Os and two for the center O form
  two ? bonds between atoms. The remaining sp2 are
  filled by five lone e-pairs. Three 2p orbitals
  overlap sideways to produce three ? bonds of
  bonding,antibonding and nonbonding. The
  delocalized e-pair is in bonding, lone pair is in
  nonbonding MO. Benzene can also be explain by sp2
  hybrids.

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Arrangement of Electron Pairs
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Molecular Geometries-I
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Molecular Geometries-II
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Molecular Geometries-III