Transcript Molecular Orbitals in Chemical Bonding Chapter 9

Molecular Orbitals in Chemical
Bonding
Chapter 9
Valence Bond Theory
• Explains the structures of covalently bonded
molecules
– ‘how’ bonding occurs
• VSEPR is part of VB theory
• Principles of VB Theory
– Bonds form from overlapping atomic orbitals and electron
pairs are shared between two atoms
• A new set of hybridized orbitals can form
– Lone pairs of electrons are localized on one atom
Molecular Orbital(MO) Theory
• Explains the distributions and energy of electrons in
molecules
• Useful for describing properties of compounds
– Bond energies, electron cloud distribution, and magnetic
properties
• Basic principles of MO Theory
– Atomic orbitals combine to form molecular orbitals
– Molecular orbitals have different energies depending on type
of overlap
• Bonding orbitals (lower energy than corresponding AO)
• Nonbonding orbitals (same energy as corresponding AO)
• Antibonding orbitals (higher energy than corresponding AO)
Formation of Molecular Orbitals
• Recall than an electron in an atomic orbital can be
described as a wave function utilizing the
Schröndinger equation. The ‘waves’ have positive
and negative phases. To form molecular orbitals,
the wave functions of the atomic orbitals combine.
How the phases or signs combine determine the
energy and type of molecular orbital.
• Look at Figure 9-1 to see how the phases combine.
Formation of Molecular Orbitals
• Bonding orbital – the wavefuntions are inphase and overlap constructively (they add).
– Bonding orbitals are lower in energy than AOs
• Antibonding orbital – the wavefunctions are
out-of-phase and overlap destructively (they
subtract)
– Antibonding orbitals are higher in energy than
the AO’s
When two atomic orbitals combine, one bonding
and one antibonding MO is formed.
Overlap of Two 1s Atomic
Orbitals
• Two MO’s are formed when the two 1s
atomic orbitals overlap
– The in-phase combination produces a 1s
molecular bonding orbital.
• Has lower energy than corresponding AO’s
– The out-of-phase contribution produces a  1*s
molecular antibonding orbital
• Has higher energy than corresponding AO’s
Overlap of Two 1s Atomic
Orbitals
2 1s orbitals that are far apart
Constructive interference from the 1s orbitals (1s)
*

Destructive inteference form the 1s orbitals ( 1 s )
*
The  1 s molecular orbital has a nodal plane bisecting the
internuclear axis. A node or nodal plan is a region in which the
probability of finding an electron is zero.
Overlap of 2px Orbitals
• Head-on overalp produces a p (actually  2 p x )
*
*
and a  p (actually  2 p x ). These are also
termed as sigma orbitals since they are
cylindrically symmetric about the internuclear
axis.
• Constructive interference from the 2px orbitals
• Destructive interference for the 2px orbitals
Overlap of 2px Orbitals
Page 356
Overlap of 2py Orbitals
• These atomic orbitals overlap ‘side-on’
forming  molecular orbitals
– The bonding combination is  2 p y
– The antibonding combination is  2* p
y
• Termed as  molecular orbitals because they
have a nodal plane along the internuclear axis
– The antibonding combination also has a nodal
plane bisecting the internuclear axis
Overlap of 2py Orbitals
Constructive interference from the 2py orbitals
Destructive interference from the 2py orbitals
Overlap of 2pz Orbitals
• The 2pz atomic orbitals can overlap in the
same fashion except that the orientation in
space is different
– The 2pz atomic orbitals overlap ‘side-on’ to
produce a bonding and an antibonding  orbital
Together, the 2pz and the 2py atomic orbitals
produce two bonding orbitals and two
antibonding orbitals. MO theory commonly
illustrates these orbitals as the same.
Molecular Orbital Filling-Energy
Diagram
• Order of filling of MO’s obeys same rules
as for atomic orbitals.
• Including
– Aufbau principle
– Hund’s Rule
Recall that bonding orbitals have lower energies
than the corresponding atomic orbitals and
antibonding orbitals have higher energies than
corresponding atomic orbitals
Molecular Orbital Filling-Energy
Diagram for Homonuclear Molecules
Page 357
Using Energy Diagrams in MO
Theory
• Draw (or select) the appropriate molecular orbital
energy level diagram
• Determine the total number of electrons in the
molecule.
– In MO theory, this includes all the electrons
• Add these electrons to the energy level diagram,
putting each electron into the lowest energy level
available
– Only two electron can be in a given orbital
– Electrons must occupy all the orbitals of the same
energy singly before pairing
Bond Order and Bond Stability
# of bonding electrons # of antibondin g electrons
bond order 
2
Usually, the bond order corresponds to the number of bonds
described by the VB theory
A bond order equal to zero indicates that there are the same number
of electron in bonding and antibonding orbitals
The greater the bond order, the more stable the molecule or ion.
Also, the greater the bond order, the shorter the bond length and the
greater the bond energy. Bond energy is the amount of energy
necessary to break a mole of bonds.
Homonuclear Diatomic
Molecules
• Draw the energy level diagrams and write the MO
electron configurations
– H2
– He2
– B2
– N2
– O2 and O2Notice the differences in the energy diagrams (it switches)
Homonuclear Diatomics
• Look at Table 9-1
• Trends in bond order versus bond length and bond
energy
• A few diatomics have unpaired electrons in the
MO’s. These diatomics would be classified as
being paramagnetic. Diamagnetic species have no
unpaired electrons.
What molecules (or ions) form the previous slide are
paramagetic?
Heavier Homonuclear Diatomic
Molecules
• Many heavy atoms such as S2 are instable
due to inability to form strong  bonds
– Bond length is too great for effective ‘side-on’
overlap of p orbitals.
• N2 is much more stable than P2
• The effectiveness of the ‘side-on’ overlap decreases
much quicker than the ‘head-on’ overlap
Heteronuclear Diatomic Molecules
• Molecular orbital diagrams for heteronuclear
molecules have skewed energies for the
combining atomic orbitals to take into account
the differing electronegativities.
• The more electronegative elements are
lower in energy than those of the less
electronegative element.
Heteronuclear Diatomic Molecules
• Let’s examine the energy level diagram for
NO (in your books on page 363)
• The closer the energy of a MO is to the one
of the AO from which it is formed, the more
of the character of that atomic orbital it
shows
– Illustrate with NO
Energy Level Diagram for NO
Heteronuclear Diatomic Molecules
• The energy differences between bonding
orbitals depend on the electronegativity
differences between the two atoms
– The larger the difference the more polar the
bond that is formed (ionic character increases)
– The difference reflects the amount of overlap
between the bonding orbitals. If the difference
is too great the orbitals cannot overlap
effectively and nonbonding orbitals will be
formed.
Formation of MO’s in HF
• The bond in HF involves the 1s electron of
H and the 2p orbital of F
– A bonding and antibonding MO are produced
• sp and  sp* MO’s
– The remaining 2p orbitals on F have no overlap
with H orbitals. They are termed as
‘nonbonding’ orbitals. These orbitals retain the
characteristics of the F 2p atomic orbitals.
Lack of overlap to produce nonbonding orbitals is
much more pronounced for side-on bonding
The Energy Level Diagram for HF
Delocalization and Shapes of MO’s
• Molecular orbital theory describes shapes in
terms of delocalization of electrons.
– All the contributing AO’s will be combined
• Let’s look at the structure of benzene
– VB theory indicates sp2 hybridization
– There are sigma bonds from each C atom to the two
adjacent C atoms and to one H atom. There is one
unhybridized 2pz orbital on each C atom remaining
Benzene
Resonance structures with VB theory. MO theory, however,
indicates that the electrons are delocalized. Experiemental data
shows that all the C-C bond are equal.
Benzene
Overlap according to VB theory. This theory does not describe the
molecule accurately.
Benzene
Structure according to MO theory. The electrons are
delocalized over the 6 C-C bonds. The electrons contribute to
bonding throughout the molecule as a whole.
Molecular Orbital Diagram for H2O
Molecular Orbital Diagram for Cr(Cl)63+