molecule, then the incoming light may be absorbed by the molecule. This
outcome, in turn, promotes the molecule to an excited energy state and
decreases the intensity of the light at that frequency according to the
probability of photons of light interacting with the molecule or material.
This entire process is called absorption, and the absorption of different
frequencies of electromagnetic radiation corresponds to different types of
energy transitions in a molecule. For example, absorption of light in the
ultraviolet and visible region of the electromagnetic spectrum typically
causes transitions between electronic energy states of a molecule. Alternatively, absorbed infrared radiation causes a transition between vibrational states of the molecule. It is important to emphasize that the
incoming radiation is only absorbed by the molecule if the frequency of
the radiation matches the exact energy difference between allowed energy
states of the molecule. Otherwise, the radiation is only transmitted
through the substance. Additionally, the transition must conserve spin
and angular momentum and must involve a shift in the charge distribution in the molecule or nanosystem. The shift in electron density can be
characterized by the overlap of two orbitals,
r overlap = f ground f excited
(6.3)
where f ground represents the orbital from which an electron is being
excited (e.g., the HOMO) and f excited represents the orbital to which that
electron is being excited (e.g., the LUMO). For most transitions to have a
significant probability of occurring, the shift in electron density must form
a nonzero dipole, known as the transition dipole, which can be written in
one dimension as
μ ge = −e
ð
f ground x
ð Þxf excited x
ð Þdx
(6.4)
where e is the elementary unit of charge.
If the transition dipole moment is zero, the transition is not allowed and
has a zero or weak intensity. Note that while the transition dipole moment
represents an induced polarization in the molecule as it interacts with the
electric field of the light and absorbs a photon, it does not imply that
either the ground or excited state must have a permanent dipole moment.
Figure 6.3 shows the HOMO, LUMO, transition density, and transition
dipole for butadiene. Note that while the charge distribution of both the
ground and excited state are symmetric (no dipole moment), the transition density is not, and thus this transition would be allowed.
SPECTROSCOPIC METHODS 185
outcome, in turn, promotes the molecule to an excited energy state and
decreases the intensity of the light at that frequency according to the
probability of photons of light interacting with the molecule or material.
This entire process is called absorption, and the absorption of different
frequencies of electromagnetic radiation corresponds to different types of
energy transitions in a molecule. For example, absorption of light in the
ultraviolet and visible region of the electromagnetic spectrum typically
causes transitions between electronic energy states of a molecule. Alternatively, absorbed infrared radiation causes a transition between vibrational states of the molecule. It is important to emphasize that the
incoming radiation is only absorbed by the molecule if the frequency of
the radiation matches the exact energy difference between allowed energy
states of the molecule. Otherwise, the radiation is only transmitted
through the substance. Additionally, the transition must conserve spin
and angular momentum and must involve a shift in the charge distribution in the molecule or nanosystem. The shift in electron density can be
characterized by the overlap of two orbitals,
r overlap = f ground f excited
(6.3)
where f ground represents the orbital from which an electron is being
excited (e.g., the HOMO) and f excited represents the orbital to which that
electron is being excited (e.g., the LUMO). For most transitions to have a
significant probability of occurring, the shift in electron density must form
a nonzero dipole, known as the transition dipole, which can be written in
one dimension as
μ ge = −e
ð
f ground x
ð Þxf excited x
ð Þdx
(6.4)
where e is the elementary unit of charge.
If the transition dipole moment is zero, the transition is not allowed and
has a zero or weak intensity. Note that while the transition dipole moment
represents an induced polarization in the molecule as it interacts with the
electric field of the light and absorbs a photon, it does not imply that
either the ground or excited state must have a permanent dipole moment.
Figure 6.3 shows the HOMO, LUMO, transition density, and transition
dipole for butadiene. Note that while the charge distribution of both the
ground and excited state are symmetric (no dipole moment), the transition density is not, and thus this transition would be allowed.
SPECTROSCOPIC METHODS 185