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8 Electric and Magnetic Phenomena
(a) Permanent dipole moments are associated with asymmetric distributions of
separated charges {δq i } located at corresponding positions {r i } that give rise
to a permanent electric dipole moment, μ d , defined via
μ d =
i
δq i r i .
(8.1.1a)
Ionically-bonded molecules typically possess large permanent electric dipole
moments while covalently-bonded molecules typically possess much smaller or,
should they have highly symmetric charge distributions, no permanent electric
dipole moments. Common examples of covalently-bonded molecules that do
possess permanent electric dipole moments range from small nonlinear polyatomic molecules like water and acetonitrile (CH 3 CN), which have relatively
large permanent dipole moments, to heteronuclear diatomic molecules like the
hydrogen halides, which have fairly small permanent electric dipole moments.
(b) An electric dipole moment that is proportional to the field strength, E, of an
applied electric field can be induced in any atom or molecule. This induced
electric dipole moment is given by
μ i = α · E,
(8.1.1b)
in which α, a second rank tensor known as the polarizability tensor, is a basic
property of an electron distribution that is a measure of the ease with which
charge separations can be induced by an electric field. Additional information
on the microscopic quantum mechanical origins of the polarizability tensor can
be found, for example, in Chapter 5 of [1]. Even though many atoms and ions
(which often have spherical symmetry) and molecules having a high level of
symmetry (corresponding to symmetry point groups T d , O h , and I h ) do not
possess permanent electric dipole moments, it is possible to create induced
electric dipole moments by subjecting these species to an applied constant
electric field. For very strong applied electric fields, such as those generated
by intense laser radiation, additional (nonlinear) contributions may also need
to be taken into account. As electric field manipulations play important roles
in many modern devices involving nanomaterials, it is important to outline the
role that statistical mechanics/thermodynamics plays in electric-field-dependent
phenomena.
Electrons in atoms tend to execute orbital motion about positively-charged nuclei
and, in so doing, generate orbital angular momenta l ¯
h, with magnitude
√
l(l + 1) ¯
h,
l = 0, 1, 2, · · · . In addition, individual electrons also possess an intrinsic angular
momentum s ¯
h, of magnitude
√
3
2 ¯
h, referred to as electron spin angular momentum.
The resultant total electronic angular momentum, ¯
hJ, for an individual multielectron atom or molecule is given by a vector sum of all individual electronic
angular momenta. An atom (or molecule) that possesses a net total electronic
angular momentum ¯
hJ has an electronic magnetic dipole moment, μ
(m)
d , given by
8 Electric and Magnetic Phenomena
(a) Permanent dipole moments are associated with asymmetric distributions of
separated charges {δq i } located at corresponding positions {r i } that give rise
to a permanent electric dipole moment, μ d , defined via
μ d =
i
δq i r i .
(8.1.1a)
Ionically-bonded molecules typically possess large permanent electric dipole
moments while covalently-bonded molecules typically possess much smaller or,
should they have highly symmetric charge distributions, no permanent electric
dipole moments. Common examples of covalently-bonded molecules that do
possess permanent electric dipole moments range from small nonlinear polyatomic molecules like water and acetonitrile (CH 3 CN), which have relatively
large permanent dipole moments, to heteronuclear diatomic molecules like the
hydrogen halides, which have fairly small permanent electric dipole moments.
(b) An electric dipole moment that is proportional to the field strength, E, of an
applied electric field can be induced in any atom or molecule. This induced
electric dipole moment is given by
μ i = α · E,
(8.1.1b)
in which α, a second rank tensor known as the polarizability tensor, is a basic
property of an electron distribution that is a measure of the ease with which
charge separations can be induced by an electric field. Additional information
on the microscopic quantum mechanical origins of the polarizability tensor can
be found, for example, in Chapter 5 of [1]. Even though many atoms and ions
(which often have spherical symmetry) and molecules having a high level of
symmetry (corresponding to symmetry point groups T d , O h , and I h ) do not
possess permanent electric dipole moments, it is possible to create induced
electric dipole moments by subjecting these species to an applied constant
electric field. For very strong applied electric fields, such as those generated
by intense laser radiation, additional (nonlinear) contributions may also need
to be taken into account. As electric field manipulations play important roles
in many modern devices involving nanomaterials, it is important to outline the
role that statistical mechanics/thermodynamics plays in electric-field-dependent
phenomena.
Electrons in atoms tend to execute orbital motion about positively-charged nuclei
and, in so doing, generate orbital angular momenta l ¯
h, with magnitude
√
l(l + 1) ¯
h,
l = 0, 1, 2, · · · . In addition, individual electrons also possess an intrinsic angular
momentum s ¯
h, of magnitude
√
3
2 ¯
h, referred to as electron spin angular momentum.
The resultant total electronic angular momentum, ¯
hJ, for an individual multielectron atom or molecule is given by a vector sum of all individual electronic
angular momenta. An atom (or molecule) that possesses a net total electronic
angular momentum ¯
hJ has an electronic magnetic dipole moment, μ
(m)
d , given by