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Molecular Structure
Bonding mechanisms:
Atoms interact primarily via electrostatic forces.
Electrons in different atoms repel each other but are attracted to the
protons in the nucleus.
At long range, the force is primarily attractive.
At very short range, the force is primarily repulsive.
The net potential energy is due to a combination of attractive and
repulsive potentials:
U = !A
rn+B
rm
Molecular Structure
Bonding mechanisms:
Ionic bonds:
In an ionic bond electrons are transferred from 1 atom to the other.
Example: Sodium Chloride : NaCl
Electronic structure of sodium: 1s22s22p63s1
Energy input required to ionize sodium (remove 3s electron): 5.1eV
Electronic structure of chlorine: 1s22s22p5.
Adding an electron completes the 2p shell and lowers the energy
Energy released by adding an electron (electron affinity) = 3.7eV
Net energy of the system: 5.1eV-3.7eV = 1.4eV
Molecular StructureBonding mechanisms:
Ionic bonds:
Example: Sodium Chloride : NaCl
At large separations the total energy is 5.1eV-3.7eV = 1.4eV
At smaller separations, the energy decreases due to electrostatic
attraction.
At the equilibrium separation energy is minimized: -4.2eV.
This is the dissociation energy: energy required to break the ionic bond
At very small separations, repulsive forces dominate and energy
increases
Molecular StructureBonding mechanisms:
Covalent bonds:
In a covalent bond, electrons are shared between atoms
Example: Hydrogen molecule: H2.
Each hydrogen atom shares its electron with the other atom.
The shared electrons are most likely to be found between the nuclei.
The probability distribution is concentrated here.
The spins of the the two electrons are oppositely aligned to satisfy the
exclusion principle.
CH4 molecule:
Molecular StructureBonding mechanisms:
van der Waal’s bonds:
Very weak electrostatic bonds called van der Waals bonds can occur
between molecules or neutral atoms with a dipole moment.
Neutral molecules or atoms in which the charge distribution is not
uniform (polarized) have a permanent dipole moment.
These molecules or atoms can interact with other molecules or atoms
with a dipole moment.
Hydrogen bonds: Bond created between molecules by a hydrogen atom.
Example: Water (ice)
HF2 molecule:
Molecular StructureMolecular energies:
Molecular rotation: Consider a diatomic molecule
The speeds of the rotating atoms are v1 and v2 with
Erot
=1
2m1v1
2+1
2m2v2
2=1
2m1r1
2+ m
2r2
2( )! 2
Total angular momentum:
L = m1v1r1+ m
2v2r2
= m1r1
2+ m
2r2
2( )!
Total kinetic energy:
Erot
=1
2
L2
m1r1
2+ m
2r2
2( )
v1=!r
1v2=!r
2
Molecular StructureMolecular energies: Molecular rotation
Icm
= m1r1
2+ m
2r2
2= µR
0
2
Erot
=1
2
L2
m1r1
2+ m
2r2
2( )
Erot
=L2
2Icm
L is quantized,
L2= l(l +1)!, l = 0,1,2...
Rotational energy is quantized,
Erot
=!2
2Icm
l(l +1), l = 0,1,2...
Molecular StructureMolecular energies: Molecular vibration
U =1
2k(!x)
2
p1= ! p
2
In the centre of mass frame,
Bonds in diatomic molecules act like springs.
If the bond is stretch or compressed the atoms vibrate:
Total kinetic energy,
KE =p1
2
2m1
+p2
2
2m2
=1
2
1
m1
+1
m2
!"#
$%&p1
2=1
2
m1+ m
2
m1m2
!"#
$%&p1
2=p1
2
2µ
Molecular StructureMolecular energies: Molecular vibration
U =1
2k(!x)
2
Bonds in diatomic molecules act like springs.
If the bond is stretch or compressed the atoms vibrate:
Total energy,
KE =p1
2
2µ
Evib = KE +U =p1
2
2µ+1
2k(!x)
2
This describes the familiar harmonic oscillator with quantized energies,
Evib
= ! +1
2
"#$
%&'!( , ! = 0,1,2... ! =
k
µOscillation frequency:
Molecular StructureMolecular energies: Molecular vibration
The ground vibrational energy of a hydrogen (H2) molecule is 0.273eV.
What is the spring constant ?
Evib
= ! +1
2
"#$
%&'!( , ! = 0,1,2...
For !=0,
Evib
=1
2!! =
1
2!
k
µ= 0.273eV
! =k
µ
k =4(0.273eV )
2µ
!2
=4(0.273eV )
2
!2
mH
2
2mH
!"#
$%&= 576N / m
Molecular Spectra
Total energy:
A molecule can simultaneously rotate and vibrate.
These can be treated as independent motions, so the total energy is a
sum of the two energies:
E!l =h2
2ICM
l(l +1) + ! +1
2
"#$
%&'!( , l = 0,1,2.....,! = 0,1,2....
Separation of rotational energies are
much smaller than the separation of
vibrational energies.
For each vibrational level l there is a
whole set of closely spaced rotational
levels
Molecular SpectraTotal energy:
E!l =h2
2ICM
l(l +1) + ! +1
2
"#$
%&'!( , l = 0,1,2.....,! = 0,1,2....
!E = Ef " Ei = hf
All rules have to be satisfied simultaneously. Hence we cannot get a
pure rotational or pure vibrational transitions since !l or !! cannot be
0. In general we get a mixed rotational-vibrational spectrum.
!" = " f #" i = 1!l = l f " li = 1
HCl spectrum
Molecular SpectraTotal energy:
E!l =h2
2ICM
l(l +1) + ! +1
2
"#$
%&'!( , l = 0,1,2.....,! = 0,1,2....
!E = Ef " Ei = hf
Absorption spectra: If a molecule is excited so
that !! = 1, then there is a sequence of transitions
for which !l =1 and another sequence with
!l=-1:
!" = " f #" i = 1!l = l f " li = 1
!E = !" +!2
ICM
(l +1)
!E = !" #!2
ICM
l
l is the quantum number of the initial state. This
explains the two lobes seen in molecular spectra
Molecular Spectra
The l=5 to l=6 rotational absorption line of a diatomic molecule occurs
at a wavelength of "1 whereas the l=1 to l=0 rotational absorption line
of a diatomic molecule occurs at a wavelength of "2. What is the
moment of inertia of the molecule ?
!l =+1:
!E = !" +!2
ICM
(l +1)
!E = !" #!2
ICM
l!l=-1:
For l=5:
hc
!1
= !" +6!
2
ICM
For l=1:
hc
!2
= !" #!2
ICM
hc
!1
"hc
!2
= !# +6!
2
ICM
" !# +!2
ICM
=7!
2
ICM
ICM
=7!
2
hc
!1
"hc
!2
=7!
2#c!1!2
!2" !
1
$
%&'
()
Molecular SpectraTotal energy:
E!l =h2
2ICM
l(l +1) + ! +1
2
"#$
%&'!( , l = 0,1,2.....,! = 0,1,2....
Global warming:
In CO2 (carbon dioxide) molecules, absorption lines lie in the infrared
rather than visible part of the spectrum.
Hence incoming visible light from the Sun is not absorbed.
However, infrared radiation (heat) emitted by the earth is absorbed by
the CO2 molecules.
Thus CO2 molecules act like a one-way valve to trap heat and help to
raise the temperature of the surface.
This greenhouse effect is one of the factors leading to global warming.