CHEM 255:

STATES OF MATTER II AND

CHEMICAL KINETICS II:
Electric and magnetic
properties of matter

Dr. Michael Baah Mensah

Department of Chemistry
KNUST, Kumasi
Electrical properties of molecules
• Molecular interactions responsible for the formation of condensed
phases and large molecular assemblies results from the electric
properties of molecules
• The electric properties of molecules are responsible for many of the
properties of bulk matter
• The small imbalances of charge distributions in molecules allow them
to
• interact with one another
• respond to externally applied fields
Electric dipole moments
• An electric dipole consists of two electric charges +Q and –Q with a vector
separation r.

𝝁 = 𝑸𝑹
The magnitude of the electric
dipole moment

Animation showing the electric

field of an electric dipole
• The electric dipole moment is a vector μ that points from the negative
charge to the positive charge and has a magnitude of 𝝁 = 𝑸𝑹
• The charges are of the same magnitude Q but opposite signs
Units of electric dipole moment
• Although the SI unit of dipole moment is coulomb meter (C m), it is
still commonly reported in the non-SI unit debye, D, named after
Peter Debye, a pioneer in the study of dipole moments of molecules.

1𝐷 = 3.33564 × 10−30 𝐶 𝑚

• The magnitude of the dipole moment formed by a pair of charges +e

and –e separated by 100 pm is 1.6 × 10−29 𝐶 𝑚, corresponding to
4.8 D
Polar and nonpolar molecules
• A polar molecule is a molecule with a
permanent electric dipole moment.
• A permanent dipole moment stems
from the partial charges on the atoms in
the molecule that arise from
• differences in electronegativity or,
• variations in electron density through the
molecule
Polar and nonpolar molecules
• Nonpolar molecules acquire an induced dipole moment in an electric
field on account of the distortion the field causes in their electronic
distributions and nuclear positions.
• However, this induced moment is only temporary and disappears as
soon as the perturbing field is removed.
• Polar molecules can also have their existing dipole moments
temporarily modified by an applied field
• All heteronuclear diatomic molecules are polar.
• Examples are HCl and HI with μ values of 1.08 D and 0.42 D
respectively
 Polarity of polyatomic molecules
• Molecular symmetry is of the greatest
importance in deciding whether a
polyatomic molecule is polar or not.
• Indeed, molecular symmetry is more O3 CO2
important than the question of
The angular molecule ozone (O3) is homonuclear. However,
whether or not the atoms in the it is polar because the central O atom is different from the
molecule belong to the same element. outer two (it is bonded to two atoms, which are bonded
only to one). Moreover, the dipole moments associated
• Homonuclear polyatomic molecules with each bond make an angle (116.8 o) to each other and
may be polar if they have low do not cancel. The heteronuclear linear triatomic molecule
symmetry and the atoms are in CO2 is nonpolar because, although there are partial charges
on all three atoms, the dipole moment associated with the
inequivalent positions OC bond points in the opposite direction to the dipole
moment associated with the CO bond, and the two cancel
Polarity of polyatomic molecules
• The dipole moment of a polyatomic molecule can be resolved into
contributions from various groups of atoms in the molecule and their
relative locations
• 1,4-dichlorobenzene is nonpolar by symmetry
on account of the cancellation of two equal but
opposing C–Cl moments (exactly as in carbon
dioxide).
• 1,2-Dichlorobenzene, however, has a dipole
moment which is approximately the resultant of
two chlorobenzene dipole moments arranged
at 60° to each other.
• This technique of ‘vector addition’ can be
applied with fair success to other series of
related molecules.
(a) chlorobenzene, (b) 1,4 dichlorobenzene
(c) 1,2 dichlorobenzene, (d) 1,3 dichlorobenzene
Calculating the polarity of a polyatomic
molecules
• The magnitude of the resultant moment 𝜇𝑟𝑒𝑠 of 𝜇1 and 𝜇2 that make
an angle 𝜃 to each other is approximately
2 2 1ൗ
𝜇𝑟𝑒𝑠 ≈ (𝜇1 + 𝜇2 + 2𝜇1 𝜇2 𝑐𝑜𝑠𝜃) 2
• When the two contributing dipole moments have the same
magnitude (as in the dichlorobenzenes), this equation simplifies to
1Τ 1
• 𝜇𝑟𝑒𝑠 ≈ (2𝜇12 1 + 𝑐𝑜𝑠𝜃 ) 2 = 2𝜇1 𝑐𝑜𝑠 𝜃
2
• Note:
𝟏
𝝁𝒓𝒆𝒔 = 𝟐𝝁𝟏 𝒄𝒐𝒔 𝜽
𝟐
Calculating the polarity of a polyatomic
molecules
• Consider the ortho (1,2-) and meta (1,3-) disubstituted
chlorobenzenes, for which 𝜃ortho = 60° and 𝜃meta = 120°. Calculate
the ratio of the magnitudes of the electric dipole moments

• Solution
Calculating the polarity of a polyatomic
molecules
• A more reliable approach to the calculation of dipole moments is to take
into account the locations and magnitudes of the partial charges on all the
atoms.
• To calculate the x-component of the dipole moment, for instance, it is
necessary to know the partial charge on each atom and the atom’s x-
coordinate relative to a point in the molecule using
𝝁𝒙 = ෍ 𝑸𝑱 𝒙𝑱
𝑱
• 𝑄𝐽 is the partial charge of atom J, 𝑥𝐽 is the x-coordinate of atom J, and the
sum is over all the atoms in the molecule. Analogous expressions are used
for the y- and z-components.
• The magnitude of μ is related to the three components and is given by
𝟐 𝟐 𝟐 𝟏ൗ𝟐
𝝁 = (𝝁𝒙 + 𝝁𝒚 + 𝝁𝒛 )
Calculating the polarity of a polyatomic
molecules
• Estimate the magnitude and
orientation of the electric
dipole moment of the planar
amide group shown below
Question
• Estimate the magnitude of the electric dipole moment of methanal
(formaldehyde)
Multipoles
• Molecules may have higher multipoles, or arrays of point charges.
• Specifically, an n-pole is an array of point charges with an n-pole moment
but no lower moment.
• A monopole (n = 1) is a point charge, and the monopole moment is what is
normally called the overall charge.
• A dipole (n = 2) is an array of charges that has no monopole moment (no
net charge).
• A quadrupole (n = 3) consists of an array of point charges that has neither
net charge nor dipole moment (e.g. CO2 molecule).
• An octupole (n = 4) consists of an array of point charges that sum to zero
and which has neither a dipole moment nor a quadrupole moment (e.g.
CH4 molecule).
Multipoles

Methane, CH4
Polarizabilities
• The failure of nuclear charges to control the surrounding electrons
totally means that those electrons can respond to external fields.
• Therefore, an applied electric field can distort a molecule as well as
align its permanent electric dipole moment.
• The magnitude of the induced dipole moment, μ*, is proportional to
the electric field strength, E:
𝝁∗ = 𝜶𝑬
• The constant of proportionality α is the polarizability of the
molecule.
• The greater the polarizability, the larger is the induced dipole moment
for a given applied field.
Polarizabilities
• When the applied field is very strong (as in tightly focused laser
beams), the magnitude of the induced dipole moment is not strictly
linear in the strength of the field,
𝟏
𝝁 = 𝜶𝑬 + 𝜷𝑬𝟐 + ⋯
∗
𝟐
• The coefficient β is the (first) hyperpolarizability of the molecule
Units of Polarizability
• Polarizability, α has the units (coulomb metre)2 per joule (C2 m2 J–1).
• However, α is often expressed as a polarizability volume, α′ by using
the relation:
′
𝛼
𝛼 =
4𝜋𝜀𝑜
• where 𝜀𝑜 is the vacuum permittivity
• Because the units of 4π𝜺𝒐 are coulomb-squared per joule per metre
(C2 J–1 m–1), (Note: 1 J = 1 kg m2 s-2), it follows that α′ has the
dimensions of volume.
• Polarizability volumes are similar in magnitude to actual molecular
volumes (of the order of 10−30 m3, 10−3 nm3, 1 Å3).
Polarizability volumes

• There is a correlation between the polarizability volumes and

the electronic structure of atoms and molecules.
Question
• The polarizability volume of H2O is 1.48 × 10−30 m3. Calculate the
induced dipole moment μ* if the molecule is induced by an applied
electric field of strength 1.0 × 105 V m−1 (1 V = 1 J C-1, 𝜀𝑜 = 8.854 ×
10−12 J−1 C2 m−1)

𝝁∗ = 4𝜋𝜀𝑜 𝜶′ 𝑬
Correlation of polarizability volumes
• Polarizability volumes correlate with the HOMO–LUMO separations
in atoms and molecules.
• The electron distribution can be distorted readily if the LUMO lies
close to the HOMO in energy, so the polarizability is then large.
• If the LUMO lies high above the HOMO, an applied field cannot
perturb the electron distribution significantly, and the polarizability is
low.
• Molecules with small HOMO–LUMO gaps are typically large, and
have numerous electrons, and hence has larger polarizability
Anisotropy of polarizability
• For most molecules, the polarizability is ‘anisotropic’, which means
that its value depends on the orientation of the molecule relative to
the applied field.
• For example, the polarizability volume of benzene when the field is
applied perpendicular to the ring is 0.0067 nm3 and it is 0.0123 nm3
when the field is applied in the plane of the ring.
• The anisotropy of the polarizability determines whether a molecule is
rotationally Raman active
Electromagnetic Spectrum
Polarization
• The polarization, P, of a bulk sample is the electric dipole moment
density, which is the mean electric dipole moment of the molecules,
𝝁 , multiplied by the number density, ℵ = 𝑁/𝑉

𝑃= 𝜇ℵ

• A dielectric is a polarizable, non-conducting medium

• The study of dielectric properties concerns the storage and
dissipation of electric and magnetic energy in materials
The frequency dependence of the polarization
• The polarization of a fluid dielectric is zero in the absence of an
applied field because the molecules adopt ceaselessly changing
random orientations due to thermal motion, so 𝝁 = 0.
• In the presence of a weak electric field, the energy depends on the
orientation of the dipole with respect to the field, with lower energy
orientations being more populated; as a result, the ⟨𝝁⟩ is no longer
zero.
• The average molecular dipole moment (in a weak electric field) is
𝝁𝟐 𝑬
𝝁𝒛 =
𝟑𝒌𝑻
Where E is the electric field
The frequency dependence of the polarization
• As the electric field strength is increased to very high values, the
orientations of molecular dipole moments fluctuate less about the field
direction and the mean dipole moment approaches its maximum value of
𝝁𝒛 = 𝝁
• When the applied field changes direction slowly, the orientation of the
permanent dipole moment has time to change—the whole molecule
rotates into a new orientation—and follows the field.
• However, when the electric field changes direction rapidly, a molecule
cannot change orientation fast enough to follow and the permanent
dipole moment then makes no contribution to the polarization of the
sample.
• The orientation polarization, the polarization arising from the permanent dipole
moments, is lost at such high frequencies.
The frequency dependence of the polarization
• Because a molecule takes about 1 ps to turn through about 1 radian
(57.3o) in a fluid, the loss of the contribution of orientation
polarization to the total polarization occurs when measurements are
made at frequencies greater than about 1011 Hz (in the microwave
region).
• The next contribution to the polarization to be lost as the frequency
increases is the distortion polarization, the polarization that arises
from the distortion of the positions of the nuclei by the applied field.
• The molecule is bent and stretched by the applied field, and the
molecular dipole moment changes accordingly.
The frequency dependence of the polarization
• The time taken for a molecule to bend is approximately the inverse of
the molecular vibrational frequency, so the distortion polarization
disappears when the frequency of the radiation is increased through
the infrared.
• Polarization disappears in stages: each successive stage occurs as the
frequency of oscillation of the electric field rises above the frequency
of a particular mode of vibration.
The frequency dependence of the polarization
• At even higher frequencies, in the visible region, only the electrons
are mobile enough to respond to the rapidly changing direction of the
applied field.
• The polarization that remains is now due entirely to the distortion of
the electron distribution, and the surviving contribution to the
molecular polarizability is called electronic polarizability.
• Thus, there is a successive decrease in polarizability as the
frequency is increased, which applies to each type of
excitation.
Molar polarization
• When two charges Q1 and Q2 are separated by a distance r in a
medium, the Coulomb potential energy of their interaction is
𝑸𝟏 𝑸𝟐
𝑽=
𝟒𝝅𝜺𝒓
• where ε is the permittivity of the medium, which is reported by
introducing the relative permittivity
𝜺 = 𝜺𝒓 𝜺𝒐
• The relative permittivity of a substance is large if its molecules are
polar or highly polarizable.
Molar polarization
• The quantitative relation between the relative permittivity and the
electric properties of the molecules is obtained by considering the
polarization of a medium, and is expressed by the Debye equation
𝜺𝒓 − 𝟏 𝝆𝑷𝒎
=
𝜺𝒓 + 𝟐 𝑴
• where ρ is the mass density of the sample, M is the molar mass of the
molecules, and Pm is the molar polarization, which is defined as:
𝑵𝑨 𝝁𝟐
𝑷𝒎 = 𝜶+
𝟑𝜺𝒐 𝟑𝒌𝑻
• where α is the polarizability. The term μ2/3kT stems from the thermal
averaging of the electric dipole moment in the presence of the
applied field
Molar polarization
• The corresponding expression without the contribution from the
permanent dipole moment is called the Clausius–Mossotti equation:

𝜺𝒓 − 𝟏 𝝆𝑵𝑨 𝜶
=
𝜺𝒓 + 𝟐 𝟑𝑴𝜺𝒐
• The Clausius–Mossotti equation is used when there is no contribution
from permanent electric dipole moments to the polarization, either
because the molecules are nonpolar or because the frequency of the
applied field is so high that the molecules cannot orientate quickly
enough to follow the change in direction of the field.
Relationship between refractive index and
relative permittivity
• The refractive index, nr, of the medium is the ratio of the speed of light in a
vacuum, c, to its speed c′ in the medium: nr = c/c′
• According to Maxwell’s theory of electromagnetic radiation, the refractive
index at a specified (visible or ultraviolet) wavelength is related to the
relative permittivity at that frequency by

𝟏ൗ Relation between refractive

𝒏𝒓 = 𝜺𝒓 𝟐 index and relative permittivity

• A beam of light changes direction (‘bends’) when it passes from a region of

one refractive index to a region with a different refractive index.
Relationship between refractive index and
relative permittivity
• Therefore, the molar polarization, Pm, and the molecular
polarizability, α, can be measured at frequencies typical of visible
light (about 1015–1016 Hz) by measuring the refractive index of the
sample and using the Clausius–Mossotti equation.
Determining dipole moment and polarizability
of a molecule
Question
• The relative permittivity of camphor was measured at a series of
temperatures with the results given below. Determine the dipole
moment and the polarizability volume of the molecule. (M = 152.23 g
mol−1 for camphor)

camphor
Steps

• Calculate (εr − 1)/(εr + 2) at

each temperature, and then
multiply by M/ρ to form Pm

𝜺𝒓 − 𝟏 𝝆𝑷𝒎
=
𝜺𝒓 + 𝟐 𝑴

• Plot Pm against 1/T

𝑵𝑨 𝝁𝟐
𝑷𝒎 = 𝜶+
𝟑𝜺𝒐 𝟑𝒌𝑻
Figure 14A.4:The plot of Pm/(cm3 mol−1) against (103 K)/T
The intercept on the vertical axis lies at
Pm/(cm3 mol−1) = 83.5
The slope is 10.55 cm3 mol−1 K

Because the Debye equation describes

molecules that are free to rotate, the data
show that camphor, which does not melt until
175 °C, is rotating even in the solid. It is an
approximately spherical molecule