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Chapter 12
Introduction to Molecular
Spectroscopy
Molecular Spectra
• Three basic types of optical spectra that we can observe for molecules:
– Electronic or vibronic spectra, which involve transitions between a specific vibrational and rotational level of one electronic state and a vibrational and rotational level of another electronic state;
– Vibrational or vibrational- rotational spectra, which involve transitions from the rotational levels of one vibrational level to the rotational levels of another vibrational level in the same electronic state;
– Rotational spectra, where the transitions are between rotational levels of the same vibrational level of the same electronic state.
• Purely rotational spectra are normally observed in the microwave region of the spectrum,
• vibration-rotation spectra in the infrared region, and electronic spectra in the ultraviolet, visible, and near-IR wavelength regions.
• According to quantum mechanics the wavefunction for a molecule is assumed to be the product of three independent wavefunctions describing the electronic, vibrational, and rotational energy levels.
• The total energy Er of a molecule in a given state is approximately equal to the sum of its electronic energy (Ee), vibrational energy (Ev),and rotational energy (Er or Ej)
Rotational Spectra
• To describe rotational spectra of linear molecules, we use a
dumbbell model system consisting of two mass points m1and
m2 connected by a massless rod of length r.
• Absorption lines are observed in the microwave region of the electromagnetic spectrum.
• Rotational transitions occur only for molecules with a permanent dipole moment (i.e., not homonuclear diatomics).
• For linear molecules, the selection rule is J = 1, where J is the rotational angular momentum quantum number.
• The allowed rotational transitions produce a series of equally spaced lines of wavenumber equal to = 2 (J + 1),
• where is the rotational constant.
• Note that the spacing between energy levels increases with increasing J.
• The degeneracy of rotational energy levels is (2J + 1). • For small J, Ej << kT. Thus at room temperature, the Boltzmann
distribution predicts that typically 30 to 50 rotational levels are appreciably populated
• The relative intensity of the rotational lines depends on the population and degeneracy of each rotational level
BvB
• Application of an electric field splits and shifts the degenerate rotational levels (the Stark effect).
• Hyperfine structure in rotational levels is caused by the nuclear spin interacting with the angular momentum. Here the selection rules must take into account both J and nuclear spin quantum numbers.
• In the gas phase at pressures above 1 torr, collisional broadening determines the line shape and halfwidth of rotational lines.
• The line shape is Lorentzian with typical half-widths of 10-3, 10-4, and 10-5 cm-1 at 0.1, 0.01, and 0.001 atm, respectively.
• For gases at higher pressures, the rotational energies are blurred due to more frequent collisions.
• In condensed phases, rotational structure is not observed.
• In liquids, rotational energies become effectively nonquantized due to molecular collisions more frequent (1012 to 1013 s-1) than the period of rotation (10-10 s).
• In solids rotations are totally restricted. Hence microwave rotational spectroscopy is little used for analytical purposes.
Rotation-Vibrational Transitions
• Molecular vibrations of diatomic molecules are
assumed to behave as a harmonic oscillator model.
• A simple harmonic oscillator is a mechanical system
consisting of a point mass m connected to a
massless spring.
• The mass is under action of a restoring force
proportional to the displacement of the particle from
its equilibrium position and the force constant k of
the spring.
1. Pure Vibrational Transitions
• From the equations, vibrational absorption transitions are observed in the mid or far Ir-region of the spectrum
• The selection rule for transitions between vibrational levels is = 1.
• In addition, a change in dipole moment must occur so that homonuclear diatomic molecules exhibit no vibrational transitions in IR
• Weaker transitions called overtones are sometimes observed. These correspond to = 2 or = 3, and their frequencies are less than two or three times the fundamental frequency ( = 1) because of anharmonicity.
2. Rotation-Vibrational Transitions
• Vibrational spectra of gaseous diatomic molecules observed under high-resolution conditions, showed a large number of closely spaced components, thus it is called band spectra. .
• The structure observed can be explained in terms of excitation of rotational motion during a vibrational transition.
• A vibrational absorption transition from to + 1 gives rise toy three sets of lines called branches,
– The lower-frequency P branch corresponds to transitions with = 1 and J = -1.
– The higher-frequency R branch corresponds to transitions with = 1 and J = + 1
– the Q branch arises from a transition with = 1 and J = 0.
• The Q branch is not observed for diatomics except those with an odd number of electrons (e.g., NO).
• The relative intensities of the components of the R and P bands in absorption spectra are governed by the population and the degeneracies of the various rotational levels in the ground vibrational state.
• Polyatomic molecules give rise to much more complex vibrational motions (e.g., stretching, bending) than diatomics.
• For linear polyatomics with N atoms, there are 3N - 5 normal modes of vibrations,
• while nonlinear polyatomics have 3N - 6 normal modes.
• Often the predicted 3N - 6 (or 3N - 5) bands are not observed in absorption vibrational spectra because some transitions are forbidden or two or more modes may be degenerate and thus have the same vibrational frequency.
• Additional vibrational bands can occur due to overtones.
• Vibrational spectra are often characteristic of various functional groups in a molecule and frequently used for qualitative analysis, As for diatomics, rotational structure is not observed in the condensed phases.
Electronic Absorption Spectra Diatomic Molecules
Molecular orbitals and quantum numbers
• As a first approximation it is assumed that molecular orbitals (MOs) are composed of linear combinations of the atomic orbitals (AOs) of the separate atoms making up the molecule.
• Each two AOs that combine form two MOs designated bonding and antibonding; the latter are denoted with the superscript *.
Electronic States
• The ordering of the MOs according to energy is often different than shown in the Figure.
• It depends on the atoms involved and the internuclear distance, and usually must be diatomics determined experimentally.
• The ground-state electron configuration of a molecule is determined by successively filling the MOs from lower to higher energy with electrons
• The total number of electrons involved is the sum of the number of electrons from each atom.
• The bonding MOs involve attraction and the overlap of the two AOs
• The antibonding orbitals result in repulsion and a nodal plane corresponding to zero electron density between the atoms.
• A filled bonding MO increases stability of the molecular state,
• whereas a filled antibonding MO contributes instability.
• The bond order is one-half the difference between the number of bonding and antibonding electrons.
• If the bond order is 1/2 or greater (or if the number of bonding electrons is greater than the number of antibonding electrons), the molecular state is stable.
• If the bond order is 0 or less, instability is predicted.
Electronic transitions
• In electronic absorption transitions, electrons are promoted to empty or partially filled MOs.
• The probability and hence intensity of absorption or emission for a specific transition between two electronic states is related to the transition moment,R
• R is a function of: electronic transition moment, electronic spin overlap integral , vibrational overlap integral , rotational overlap integral
Band Intensities. • The breadth and shape of an electronic absorption
band is determined by the vibrational overlap integral.
• The square of the vibrational overlap integral is called the Franck-Condon factor.
• The Franck-Condon principle states that an electronic transition is rapid (10-15 s) with respect to the nuclear motions so that a vibronic transition occurs to a vibrational state of the lower electronic state
• Rotational levels are associated with each vibrational state.
• For a given vibronic transition, the intensities of the possible rotational transitions are determined by the appropriate rotational overlap integral.
• For diatomics the general selection rule AJ = ± 1 applies without the restriction of the permanent dipole moment
• Since many rotational levels are populated, a vibronic band consists of many rotational transitions and P and R branches can be observed.
• The term band is used to describe a specific vibronic transition.
• A band system is an ensemble of bands associated
with the same electronic transition.
• A hot band applies to transitions from an excited
vibrational state in the lower electronic state to a
lower vibrational state in the upper electronic state '
< " and " > 0).
• A series of bands having the same value of ( ' - ")
is called a sequence
• A progression applies to a set of bands with either
the same ' or ".
• Vibronic transitions between two electronic states.
• The intensity of a given vibronic transition depends on the
overlap of the vibrational wavefunctions of the states v" and v'
involved in the
Band Shapes
• The total energy difference (E,) for a transition
between specific vibrational and rotational levels in
the upper and lower electronic states (", J") ( ', J') is given by
• Thus, it is due to the changes in electronic, vibrational,
and rotational energy
• An electronic absorption band or band system consists
of many bands due to the different vibronic transitions
that are probable.
• This vibronic structure is observed for simple molecules
in the gas phase at low temperatures and pressures.
• At higher pressures or temperatures in the gas phase or
in condensed phases, the electronic absorption band is
often a broad envelope of the possible vibronic
transitions as shown in the Figure
(a) potential energy curves involved in the transition;
(b) absorption spectrum of the dilute vapor;
(c) absorption spectrum of the vapor at moderate pressures (rotational
structure smeared out); (
d) absorption spectrum in liquid with weak intermolecular forces
(vibrational structure present, but less pronounced than in vapor
and somewhat shifted in frequency);
(e) absorption spectrum in liquid with strong intermolecular forces
Effect of collisions and intermolecular forces on an idealized absorption band
Vibrational structure
Smeared out
• At room temperature, often only the " = 0 vibrational
state is significantly populated.
• Thus the wavelength of maximum absorption is
determined by the vibronic transition from " = 0 level
to the vibrational level ' in the upper electronic state
yielding the maximum overlap of wavefunctions.
Electronic Absorption Spectra of Polyatomic Molecules
• The description of electronic configurations,
electronic states, and spectra for diatomic molecules
forms a framework to discuss polyatomic molecules.
• Because one atom can be bonded to two or more
atoms in polyatomics, MOs are often formed from
combinations of three or more AOs.
• The familiar concept of hybridization (e.g., sp, sp2,
sp3) is often employed.
• Although not considered in our previous discussion,
it is often necessary even for some diatomics to
consider mixing of AOs before formation of MOs.
Electronic States and Transitions
• For many polyatomic molecules, it is still possible to consider that transitions involve and bonding and antibonding MOs and nonbonding (n) MOs
• typical characteristics and Mulliken's symbolism for these transitions are given in the Table
• N denotes the ground state and V, Q, and R denote excited states.
• N ---> V transitions occur from bonding to antibonding orbitals and are strongly allowed.
• The N --> Q transitions involve promotion of an electron in a nonbonding orbital to an antibonding orbital and are usually weaker than N --> V transitions.
• Of the N --> Q transitions, the n ---> * transitions are generally more intense than n - * transitions.
• Both N - Q and N --> V transitions are called sub-Rydberg transitions.
Electronic Spectra
• Electronic absorption spectra are correlated to the molecular structure of polyatomics in several ways.
• Often, spectral features are correlated to transitions that are localized in a given bond or group in the molecule.
• Groups that are responsible for absorption are called chromophores and are often isolated double bonds.
• The absorption characteristics of common chromophores are listed in Table 12-6.
• The MO approach is still used in some cases but it is usually localized to particular bonds in the molecule.
• For example, for H2C0 the ground-state electron configuration can be written as
• Electrons are associated with AOs of C and O, bonding and antibonding MOs of the CH and CO groups, and nonbonding orbitals of O.
• The three bonds to the carbon atom are formed from sp2 trigonal hybrid orbitals and the bond is formed from the remaining p orbital of C and an O p orbital.
• Only the valence electrons in the CO and nO orbitals are involved in transitions to empty *CO and *CO antibonding orbitals.
Types of Transitions
Three types of transitions
1. , , and n electrons
2. d & f electrons
3. charge transfer electrons
Electronic transition in Formaldehyde
Spectroscopy Nomenclature
* vacuum UV
Effect of Structure on
max Cl < max Br < max I
n * transitions occur at longer wavelengths
is a function of
1. Cross sectional area of absorbing species ( )
2. Transition probability (P)
= 9X1019 P ( = 10-15 cm2 ( = about 105 for the
average organic molecule
Chromophores
• They are groups with one element of
unsaturation (unsaturated linkages or
groups) and cause coloring to the
molecules when they are attached to a
non-absorbing hydrocarbon chain
Effect of Multichromophores on Absorption
• More chromophores in the same molecule cause bathochromic effect
(Red shift: shift to longer wavelength)
and hyperchromic effect (increase in intensity)
• Hypsochromic effect: Blue shift: shift to shorter wavelengths
• Hypochromic effect: decrease in intensity
• In the conjugated chromophores * electrons are delocalized over larger number of atoms causing a decrease in the energy of to * transitionsand an incrase in due to an increase in probability for transition
•Aromatic Hydrocabons
They absorb at three bands: 260, 200
and 180 nm
•Policyclic aromatic (Naphthalene):
exhibit regular shift towards longer
wavelength (Red shift)
•Azo Compounds with the linkage –N=N-
show low intensity bands in the near Uv
and Vis due to n to * transitions
•Azobenzenes absorb at about 445 nm the –
N=N- may be conjugated with the ring
system.
UV absorption spectra of benzene, naphthalene, and anthracene
Auxochromes
• They are groups that do not confer
color but increase the coloring power
of a chromophore.
• They are functional groups that have
non-bonded valence electrons and
show no absorption at > 220 nm; they
absorb in the far UV
• -OH and -NH2 groups cause a red shift
Steric Effect
•Extended conjugation of orbitals requires
coplanarity of the atoms involved in the -
cloud delocalization for maximum resonance
interaction
•Large bulki groups cause a perturbation of
the coplanarity of the system .
•Thus max is usually shifted towards shorter
and also decreases
is a function of
1. Cross sectional area of absorbing species ( )
2. Transition probability (P)
= 9X1019 P ( = 10-15 cm2 ( = about 105 for the
average organic molecule
“Ultraviolet absorption spectra for 1,2,4,5-tetrazine (a.) in
the vapor phase, (b.) in hexane solution, and (c.) in aqueous
solution.”
• The absorption characteristics of a molecule can often be predicted from the chromophores present in a molecule.
• Similarly, the absorption spectrum of an unknown can be used to identify the presence of certain functional groups in a molecule.
• Chromophores separated by a -CH2- behave almost independently.
• If there are two chromophores in a given molecule which absorb at the same wavelength, the total molar absorptivity is approximately the sum of the individual molar absorptivities.
• The absence of absorption bands in the region 200 to 800 nm is a good indication of the absence of chromophores and thus a saturated organic molecule or an inorganic molecule with no double bonds.
• Shifts in the wavelength of absorption of chromophores to longer or shorter wavelengths are denoted bathochromic and hypsochromic shifts, respectively.
• An increase or decrease in molar absorptivity is denoted a hyperchromic or hypochromic effect, respectively.
• Conjugation (i.e., C=C-C=C, C-=C-C=O, Ph-C=C) usually causes a hyperchromic effect and a bathochromic shift.
• Auxophores are groups which do not absorb themselves, but when conjugated to chromophores cause a bathochromic shift and a hyperchromic effect by inductive or resonance effects.
• Examples are -OH, -Br, and -NH2. Usually, they have at least one pair of n electrons which interact to lower the energy of the * orbital associated with the chromophore.
• In solution, solvent-solute interactions often affect the absorption wavelengths of chromophores.
• Peaks from n ---> * transitions often suffer a hypsochromic shift as the polarity of the solvent increases.
• This behavior is attributed to the increased solvation of the nonbonding pair, which lowers the energy of the n orbital.
• In contrast, a bathochromic shift with increased solvent polarity is often observed for ---> * transitions.
• Absorption by inorganic molecules is often due to transitions involving unfilled d and f orbitals on the metals or to charge-transfer transitions.
• In transition metal complexes, the bonding between d orbitals of the metal and orbitals from the ligand breaks the degeneracy of the five d orbitals.
• Thus transitions are between lower-energy filled d orbitals and higher-energy unfilled d orbitals.
• The type of splitting of d orbitals depends on the molecular geometry (e.g., octahedral, tetrahedral)
• The magnitude of the splitting depends on the particular ligand and is quantitatively treated with crystal field theory or ligand field theory.
• Generally, transition metal complex absorption transitions are in the visible region of the spectrum.
• An example is the blue Cu(NH3)42+ complex.
• Lanthanide and actinide ions have narrow absorption bands due to transitions to empty f orbitals.
• The spectra are little affected by the solvent or anions present because the f orbitals are well shielded.
• Charge-transfer absorption occurs with many inorganic ions where the components of the complex have donor-acceptor properties.
• These, transitions have very high molar absorptivities in the visible region and occur when an electron in an orbital associated with a donor which has low electron affinity is transferred to an orbital associated with an acceptor of high electron affinity.
• An example is the Fe(III) thiocyanate complex where, in the excited state, Fe(II) and SCN are the predominant species.
• Common anions which undergo chargetransfer transitions are SO4
2-, NO3- , 13
- , CrO42-,and MnO4 .
• For the latter two anions, the absorption transition involves a transfer of an O electron to an empty metal orbital.
• The molar absorptivity or the integrated molar absorptivity over the whole band () can be used to calculate oscillator strengths, transition
• An oscillator strength () value of 1 corresponds to a very strong absorption with a molar absorptivity at the wavelength of maximum absorption (Em) of about 105 L mol-1 cm-'. Typical values off are 10-s to 10-6 for the rare earth ions, 10-4 for aquo complexes of transition metal ions, 0.03 for Mn04 , and nearly unity for organic dyestuffs.
• The particle in a box or free electron model has also been applied to electronic transitions. Consider the electron, which undergoes a transition to be a particle in a box in which the positive charge is symmetrically distributed about the midpoint. It can be shown that
where N is Avogadro's number. This equation indicates that E is
related to the size of the molecule or more correctly to the part
of the molecule over which the electron involved in the
transition resides. This explains the increased molar
absorptivity in conjugated systems. The model also predicts the
bathochromic shift observed with conjugation.
Luminescence Spectra
• So far we dealt with absorption of EMR
• Now we will investigate the ways in which an excited molecule can dissipate its excess energy and return to the ground electronic state.
• The two general modes of deactivation involve non radiative and radiative processes.
• Non-radiative process the excess electonic energy is converted to translational, rotational, or vibrational energy with no emission of radiation.
• In contrast, the radiative dissipation process involves emission of a photon.
• Most analytical luminescence determinations are carried out in solutions or frozen solids, and the following discussion is directed to these applications.
Processes of Deactivation • The energy-level diagram for a hypothetical aromatic molecule
may be shown, in a Jablonski diagram
So
Vibrational relaxation
Internal
conversion
Fluorescence
External conversion
Intersystem crossing
Phosphorescence
• Vibrational relaxation: The energy, b, goes into
thermal or vibrational motion of the solvent
molecules in condensed phases. This
nonradiational process is denoted
– Normally, vibrational relaxation proceeds in a
stepwise fashion (v = 1) in which one vibrational
quantum is lost per collision.
– This typically takes 10-11 to 10-10 s.
– Since a typical vibrational period is 10-13 s, many
vibrations occur before the excess vibrational
energy is lost.
Internal conversion: • The crossover between two states of the same multiplicity is a
nonradiative electron state transition
– This is likely to occur when the potential energy curves for two electronic states cross such that the lower vibrational levels of the higher electronic state are approximately the same energy as higher vibrational levels of the lower electronic singlet state.
– Internal conversion ultimately results in the conversion of excess electronic energy to excess vibrational energy.
– Internal conversion can occur between excited states (e.g., S2to S1 or between the first excited electronic state and the ground electronic state (S1 to So).
– Generally, internal conversion between excited electronic states is rapid (10-12 s).
– Internal conversion from the S1 to the S0 state depends on the molecule but is often less efficient if there is a wide energy separation between S1 and S0, so that there is no overlap of the potential energy wells.
– After internal conversion, the excess vibrational energy is rapidly dissipated through vibrational relaxation to the ground vibrational level of the lower electronic state.
Fluorescence
• Fluorescence is a radiational transition between electronic states of the same multiplicity.
– For most molecules, the electrons are paired in the ground state so that fluorescence involves a singlet-singlet transition.
– Because internal conversion to S1 and vibrational relaxation are more rapid processes than fluorescence, fluorescence usually occurs from the ground vibrational state of S1 to various vibrational levels in So
– For this reason, only one fluorescence band is normally observed even if absorption to different excited singlet states occurs.
– Typically, fluorescence requires 10-10 to 10-6 s to occur.
– Fluorescence usually appears at longer wavelengths than absorption because absorption transitions are to higher excited electronic states or to higher vibrational levels in the S1
– Fluorescence can occur from higher electronic states in rare instances.
– Azulene and its derivatives exhibit S2 --> S0 fluorescence.
External conversion
• External conversion refers to nonradiative processes in which excited states transfer their excess energy to other species, such as solvent or solute molecules.
• One primary mechanism of external conversion is dynamic quenching.
• It involves the nonradiational transfer of energy from excited species to other molecules during collisions.
• Therefore, the rate of dynamic quenching is reduced by cooling the sample.
• Absorption transitions to triplet states are forbidden although weak absorption is possible in some molecules.
Transition Multiplicity
Consider two electrons paired in an orbital, and their possible transitions to an empty orbital.
ground state excited singlet excited triplet
• the ground state has all electrons in the lowest energy orbital • organic compounds almost always have paired spins, thus their ground state is almost always a singlet • singlet-triplet transitions are optically forbidden - light cannot both promote an electron to a new orbital and change its spin • in an organic compound most absorption spectra are due to singlet-singlet electronic transitions
2 1
ii
S s
M S
Intersystem crossing
• Populating the triplet state from the excited singlet
states by a process that is a crossover between
electronic states similar to internal conversion
except that the states have different multiplicities
(usually S1 --> T1).
• After intersystem crossing, a molecule in the T1
state deactivates by vibrational relaxation to the
ground vibrational level of T1.
• Normally, the triplet state deactivates by external
conversion or intersystem crossing to the ground
state (T1- S0)
Phosphorescence
• The triplet state can also deactivate by emission of a photon.
• This radiational deactivation process between electronic states of different multiplicity is called phosphorescence
• Usually, phosphorescence takes 10-4 to 104 s to occur because the process is spin forbidden.
• Thus phosphorescence is usually observed only if external conversion is reduced by cooling or other techniques.
• The wavelengths of phosphorescence for a given molecule are generally longer than those for fluorescence because the energy of T1 is less than S1 , due to the electrons being unpaired and in different molecular orbitals.
prompt fluorescence • Fluorescence caused by direct excitation to the S1
state or internal conversion to the S, state is called more precisely.
Delayed fluorescence
• Fluorescence that has a longer lifetime than prompt fluorescence because S1 is populated by indirect mechanisms.
Photoluminescence
• It is used to describe any emission of photons after photon excitation.
• For molecules, photoluminescence includes prompt; and delayed fluorescence as well as phosphorescence
Dissociation
• If the energy of the excitation photon is greater than the convergence limit of the excited electronic state, a bond is ruptured after absorption. This process is called dissociation.
Predissociation
• If a bond is ruptured after internal conversion the process is called predissociation
• Predissociation or dissociation is more likely in molecules that absorb at wavelengths shorter than 200 nm (200 nm corresponds to 140 kcal mol-1).
• Excited singlet or triplet states can also be depopulated by photochemical reactions.
• This includes reactions of excited states with solvent or solute molecules.
Quantum Efficiencies and Power Yields
• The efficiencies and hence intensities of
fluorescence and phosphorescence depend on
the relative competition between radiative and
non-radiative routes of deactivation.
• Different ways of expressing luminescence
efficiencies are summarized below
Luminescence quantum efficiency or Luminescence quantum yield (L)
• L is the ratio of the luminescence
radiant power to the absorbed radiant
power where the radiant powers are
expressed in photons per second.
• Thus L indicates the fraction of the
absorbed photons which are converted
to luminescence photons (0 L1).
Spectral luminescence quantum efficiency
• Spectral luminescence quantum efficiency (L) is the fraction of the absorbed photons that results in luminescence over a frequency interval to + d , as defined in equation 12-21.
• • This equation also shows that the spectral luminescence
quantum efficiency can be expressed in terms of the luminescence quantum efficiency and the emission band profile (S’)
• In this discussion a prime is used to distinguish an emission frequency or function from excitation quantities.
Luminescence spectral power yield
• Luminescence spectral power yield (YL) is
the ratio of radiant power of luminescence
over frequency interval to + d to A as
shown in equation 12-22.
• If excitation occurs over a small frequency
interval centered at and emission is
observed at ',
Total luminescence power yield
Fluorescence Quantum Efficiency, F
• The fluorescence quantum efficiency is related to the
rate of absorption and the rate of deactivation of the
first excited singlet state.
• The rate of absorption can be expressed as kAnso
and the rate of deactivation is (kF + knr)ns1 where kA, kF, and knr are the firstorder rate constants in s-1 for
absorption, fluorescence, and nonradiative
deactivation, respectively. • By derivation F can be expressed as
If knr >> kF,, Sl is deactivated by nonradiative processes before
the molecule has a chance to fluorescence, F is small and detection of fuorescence is difficult
• The quantum efficiency of a molecule is appreciable only if kF is comparable to or greater than knr since this increases the probability of emission before nonradiative deactivation.
• Typically, kF is 106 to 109 s-1.
• To understand the factors that affect the magnitude of knr, we can break it up into its components:
• The rate of fluorescence photon
emission can be expressed as
• Thus the fluorescence intensity is proportional to the
ground-state population of the fluorophore,
the rate of absorption,
the fluorescence quantum efficiency,
and the volume element of the sample
illuminated.
Phosphorescence Quantum Efficiency, p
• The phosphorescence quantum efficiency depends
on the rate that the triplet state (T1) is populated by
intersystem crossing and the rate of deactivation T1.
p can be expressed as:
• Thus p is the product of two factors, the fraction of
the absorbed photons that produce triplet states
and the fraction of the triplet molecules that
undergo phosphorescence.
• The former factor is often denoted the
quantum efficiency of triplet formation isc
• Phosphorescence is favored for molecules and environmental conditions in which intersystem crossing is favorable (kisc > kF + kec+ kic).
• Thus, if kisc > kF, phosphorescence is favored over fluorescence.
• Even if intersystem crossing is efficient, phosphorescence is not usually observed because nonradiative decay of T1 occurs before phosphorescence occurs (i.e., k’nr > kP).
• Nonradiative decay of T1 is due to external conversion and intersystem crossing from T1 to S0
Luminescence Lifetimes
• If the excitation source is turned off instantaneously,
the concentrations of S1 and T1, and hence the
fluorescence and phosphorescence signals, decay.
• Because the excited states are often deactivated by
first-order processes, the decay in either type of
luminescence signal can be described by an
exponential
• where 0L is the luminescence radiant power at the time the
excitation source is shut off and L is the luminescenc lifetime.
• The luminescence lifetime is defined as the time for the luminescence signal to decay to 1/e of its initial value.
• Sometimes the luminescence lifetime is expressed as a
half-life, (L)1/2 , which is the time for decay to one-half of the initial intensity.
• The equations above indicate that nonradiative
decay decreases the steady-state fluorescence and
phosphorescence intensities and lifetimes by the
same factors
• Also from the above equations we can conclude:
Quenching and Excited-State Reactions
• The luminescence signals observed can be reduced by the presence of concomitants through several mechanisms:
• Reabsorption of emitted radiation by other species (or even other analyte molecules) is sometimes called trivial quenching.
• This process is considered as secondary absorption to distinguish it from mechanisms that cause nonradiative deactivation before photon emission
Dynamic Quenching • Quenching normally refers to nonradiative energy
transfer from excited species to other molecules.
• Dynamic quenching or collisional quenching requires contact between the excited lumophore and the quenching species, the quencher (Q).
• The rate of quenching is diffusion controlled and depends on the temperature and viscosity of the solution.
• The quencher concentration must be high enough that the probability of collision between the analyte and quencher is significant during the lifetime of the excited species.
• If external conversion is controlled by collisions with a single quencher, a second-order rate process, the rate constant for external conversion, is given by
where kq is the second-order rate constant in L mol-1 s-1 for quenching and self
quenching is assumed negligible.
The fluorescence quantum efficiency in the absence of
quenching (oF) is given by
where Kq is the Stern-Volmer quenching constant defined as
• Rearrangement of the previous equation:
• The observed fluorescence signal is proportional to the
fluorescence quantum efficienc
• A plot of the reciprocal of the observed fluorescence
signal vs. the quencher concentration should yield a
straight line.
• From the intercept and slope, the Stern-Volmer
constant can be determined.
• Deviations from the ideal behavior are sometimes
observed when the extent of quenching is large
• Note that:
• where F is the fluorescence lifetime in the absence of the quencher
• Similar Stern-Volmer expressions apply to phosphorescence
measurements where P replaces F
• In aqueous solutions at room temperature, the Stern-Volmer constant is approximately 10 L mol-1
• Considering the equation:
• It could be concluded that that dynamic quenching of fluorescence is usually negligible when the quencher concentration is below 1 mM.
• With a lifetime of 1 ms, such as is typical for phosphorescence, Kq can be as high as
107 Lmol-1
• Clearly, phosphorescence is totally quenched by an efficient quencher at 1 mM concentrations.
Effect of dissolved oxygen on quenching
• Dissolved oxygen is a very efficient quencher for
long-lived triplet states, and its equilibrium
concentration is typically about 1 mM in many solvents.
• For this reason it is usually necessary to deoxygenate
solutions or solidify the sample to eliminate diffusion
for successful phosphorescence measurements.
• Oxygen is also a good quencher for some fluorophores,
such as aromatic hydrocarbons, particularly if the
fluorescence lifetime is greater than 10 ns
– Oxygen may induce oxidation of fluorescing species
– Also paramagnetic properties of O2 may promote the
intersystem crossing and conversion of excited
molecules to the triplet state
Static Quenching
•In static quenching the quencher and the
fluorophore in the ground state form a stable complex (i.e., the dark complex).
•Fluorescence is only observed from the unbound
fluorophore.
•The decrease in fluorescence intensity is described
by equation
•Where Kq is the formation constant
(i.e., Kq = [F .Q]/[F][Q] and F is the fluorophore).
•The lifetime is not affected in this case;
measurement of the lifetime provides a means of
distinguishing between dynamic and static
quenching.
Long-Range Quenching
• In long-range quenching or Forster quenching: Energy transfer can occur between molecules without collisions.
• It can be considered to be due to dipole-dipole coupling between a donor (the excited lumophore) and an acceptor (the quencher).
• The rate of energy transfer (kT) to a specific acceptor is given by
• where D is the luminescence lifetime of the donor, R
is the average distance between the donor and
acceptor molecules, and Ro, is the Forster distance.
• Efficient long-range energy transfer is favored in situations where the emission spectrum of the donor and the absorption spectrum of the acceptor overlap and the molar absorptivity of the donor is relatively high in the overlap region.
• The rate of energy transfer increases with acceptor concentration as the average distance between molecules decreases.
• In both dynamic and long-range quenching, the quencher is promoted to an excited state.
• Often, the quencher deactivates by nonradiational processes. However, in some cases, the quencher can luminescence.
• This luminescence is termed sensitized luminescence.
• The overall quantum efficiency of sensitized luminescence can be greater than the luminescence quantum efficiency of the original lumophore if the efficiency of energy transfer is high and the luminescence efficiency of the quencher is higher than that of the species originally excited by photon absorption.
Excited-State Reactions
• Molecules in excited states can react with other molecules to form complexes as follows:
• The excited complex is called an exciplex if Q is different from the analyte molecule and an excimer (an excitedstate dimer( if Q is a ground-state analyte molecule.
• Often the complexes are charge-transfer in nature.
• These excited complexes can dissipate their excess energy by
– releasing heat to the solvent,
– by dissociating into solvated ions,
– or by emission of a photon.
• Luminescence from singlet or triplet excimers is generally shifted red with respect to the luminescence of the original excited state.
• Excimer formation is likely only at relatively high analyte concentrations (i.e., greater than 1 mM).
Band shapes • A fluorescence emission band is broad because many vibronic
transitions are possible from the ground vibrational level of S1 (' = 0) to many vibrational levels in S0,
• The absorption and fluorescence
emission spectra are represented
by the solid and dashed lines,
respectively.
• The fluorescence transitions occur
generally at longer wavelengths
because the energy differences are
less.
• In solution the vibronic detail is
often not present and only a broad
band is observed.
Relationship between absorption and fluorescence
• As for absorption, the breadth of the emission band is determined by the range of vibrational levels (") over which the vibrational overlap integral is significant.
• Often, the fluorescence spectrum is a mirror image of the absorption spectrum, as also shown in the Figure
• This occurs if the vibrational levels in S0 and S1 are similar.
• There are many exceptions to the mirror image rule such as when the molecular geometry of So and S, are different or if the fluorescence is from an excimer.
• Also, more than one fluorescence band is observed in molecules such as biphenyl, where fluorescence originates from different parts of the molecule.
• Usually, one phosphorescence band is observed and the breadth is determined by the range of probable transitions from the ground vibrational level of T, to different vibrational levels in S,
• The mirror image rule does not apply because of the very different nature of singlet and triplet states.
Structural Effects
• The luminescence efficiency of a molecule depends on its structure and on the environment in which the luminescence is measured.
• Although it is difficult to predict if a molecule exhibits luminescence, some general rules can be stated.
• In organic molecules, the transitions between S0 and S1 can involve -* transitions or n- * transitions
• Similarly, the triplet state (T1) can be -* or n- * excited state.
• The most efficient fluorescence usually involves -* transitions because the transition probability is high (i.e., large , kA, and kF and small F).
• Fox n, * states, the fluorescence transition probability is lower because of the low degree of overlap between n and * orbitals.
• This makes fluorescence less favorable.
• However, the rate of intersystem crossing is usually enhanced because the energy difference between the singlet and triplet is smaller and the degree of spin-orbit coupling is greater.
• This can result in high phosphorescence yields.
• The rate of intersystem crossing is generally 1000 times faster between states of different electronic origin (S1(n, * ) T1( , *) or .S1( , *) T1(n, *)
• Phosphorescence from an n, * triplet tends to be short lived and more efficient than transitions from a , * triplet.
General observations
1. Luminescence is generally not observed from saturated hydrocarbons as there are no or n electrons
– Weak fluorescence is sometimes observed in the vacuum UV due to -* transitions.)
2. Luminescence is rarely observed from nonaromatic hydrocarbons that have some double bonds ( electrons)
– Weak fluorescence in the UV is observed for some aliphatic carbonyl compounds involving n-* transitions.
– Some highly conjugated, but nonaromatic hydrocarbons (e.g., (3-carotene and vitamin A) do exhibit substantial fluorescence due to - * transitions.
– Diacetyl exhibits significant phosphorescence even at room temperature.
3. Many aromatic hydrocarbons are intensely
fluorescent because they possess a low-lying
-* singlet state.
– The energy required for excitation is often
low enough to prevent bond disruption.
– Phosphorescence is less likely without atoms
providing n electrons or substitutent groups
that promote intersystem crossing.
4.Phosphorescence is often favorable in aromatic molecules containing carbonyl groups (e.g., benzophenones) or heteroatoms such as nitrogen (e.g., pyrimidine, pyrazine). These groups r~troduce nonbonding electrons and the pos~lbility-of n-7r* transitions. The resulting increased rate of intersystem crossing generally reduces fluorescence intensities. Strong fluorescence is observed for some heterocyclic molecules (tryptophan and others that include the indole ring moiety in which nitrogen is not part of the aromatic ring system) because the 7r,,a* state is lower in energy than the n,7r* state.
5. Substituents attached to aromatic rings can dramatically influence quantum efficiencies and emission wavelengths as summarized in Table 12-8. The groups often influence the nature of the lowest-lying excited state (n,7r* or ~r,~r*). In general, all groups except those having little effect on (~F, cause a red (bathochromic) shift of the fluorescence emission. The table shows that electron-donating groups (ortho-para directing groups) such as -OH in general increase (~F relative to the parent compound. By contrast, electron-withdrawing groups (metadirecting groups) such as -N02 decrease (~F. by introducing a low-lying n,Tr* state.
6.The effect of halide substituents is specifically known as the internal heavy atom effect. Heavy atoms perturb the electron spins and enhance state mixing. This increases the rates of Sl -Tt intersystem crossing, Tl -j So phosphorescence, and Tt --> So intersystem crossing. Because the third effect is often minor, the net effect is a decrease in (~F, an increase in (~P, and a decrease in TP. This dramatic effect is illustrated in Table 12-9, where the ratio ~P/~F varies from 0.60 to > 1000 as the halide changes from fluoride to iodide.
10. Fluorescence from metals usually occurs only in organometallic complexes, particularly rigid metal chelates. Often, the ligand is nonflurescent. The complex exhibits fluorescence if the lowest-lying singlet state of the ligand is changed from an n,7r* to a Tr,7r* state. Sometimes fluorescence involves chargetransfer transitions with metal d electrons and ligand orbitals. In some rare earths, luminescence is due to f-f transitions of metal electrons.
Environmental Effects
• Environmental factors such a temperature,
solvent, pH, and the presence of other
species can have a profound affect on the
luminescence characteristics of a given
molecule. These factors can affect the rate
constants of luminescence and
nonradiational deactivation or the nature of
the lowest-lying excited state.
• Temperature. In general, increasing the temperature decreases luminescence efficiencies because the rate of dynamic quenching is increased. The effect is much more dramatic for_pliosphorescence measurements. Delayed fluorescence (E-type) intensities can actually increase at higher temperatures because the rate of thermally assisted Tl --> S1 intersystem crossing is enhanced.
• Solvent. The viscosity, polarity, and
hydrogenbonding characteristics of the solvent
can significantly affect luminescence
characteristics. In some cases, luminescence
efficiencies increase with solvent viscosity due to
the reduced rate of bimolecular collisions and
the rate of dynamic quenching.The solvent
polarity and hydrogen-bonding characteristics
are critical because they affect the nature of the
excited state.
There is often a rapid (10-'t to
10-12 s) reorientation of
solvent molecules around the
excited species that occurs
before photon emission. Thus
the energies of the excited
state during emission and the
ground state immediately
following emission can be
different than they were at the
time of absorption. For Tr-ir*
transitions, the excited state is
often more polar and basic
than the ground state.
Increasing the solvent polarity
or protic nature decreases the
7.There is often an increase in (~F, a
decrease in (~P, and a bathochromic shift
in the emission bands as the size of the
ring system and the extent of conjugation
increases (see Table 12-10). For a given
number of aromatic rings, the linear ring
molecules usually fluoresce at longer
wavelengths than the corresponding
nonlinear molecules.
8.Luminescence is favored in molecules with rigid planar structures. These characteristics increase the interaction and conjugation of the 7r-electron system with a resultant decrease in the interaction with the solvent, internal conversion from St ---> So, and external conversion. For example, fluorescein is very fluorescent, while phenolphthalein is nonfluorescent. The only difference is the oxygen bridge, which forces planarity. When aryl groups are separated by an- alkene group, the more planar trans isomer is usually more fluorescent than the nonplanar cis isomer, The nonplgnarity forced by steric hinderance is also manifested by the lower fluorescence quantum efficiency of hexamethylbenzene relative to less substituted benzenes.
9.For molecules consisting of two or more
aromatic ring systems separated by alkyl
groups, the fluorescence characteristics
are sometimes those of the independent
aromatic groups. However, in some cases,
emission from one ring system results
from excitation and energy transfer from
another ring system in the molecule.
There is often a rapid (10-'t to 10-12 s) reorientation of
solvent molecules around the excited species that
occurs before photon emission. Thus the energies of the
excited state during emission and the ground state
immediately following emission can be different than
they were at the time of absorption. For Tr-ir* transitions,
the excited state is often more polar and basic than the
ground state. Increasing the solvent polarity or protic
nature decreases the energy of the excited state more so
than that of the ground state, with a resultant red shift in
the wavelengths of luminescence. By contrast, the
excited state is less polar than the ground state for rc-Tr*
transitions and a blue shift occurs with increasing solvipt
polarity or hydrogen-bond-forming capability.
• In polar or protic solvents, the lowest-lying singlet state can switch from being n,,a* to a,Tr* if these states are relatively close in energy. This explains why some heterocyclic or carbonyl-containing compounds fluoresce weakly or not at all in nonpolar, aprotic solvents, but appreciably in polar, protic solvents. The overall luminescence quantum efficiency is often less in hydrogen-bonding solvents, due to an increased rate of Sl --> S, internal conversion.
pH Effects
• The pH of solutions in protic solvents can be
critical for aromatic molecules with acidic or
basic functional groups (e.g., phenols, amines).
In some cases, only the protonated or
unprotonated form of the acid or base may be
fluorescent. For example, many phenols are
fluorescent only in the nonionized form. The
fluorescence of amine containing compounds
can decrease in acidic solution as -NH3 forms
and withdraws electrons from the ring system.
• The pKQ of the excited state can be a factor of 4 to 9 lower than that of the ground state. For example, the pKQ of the ground state of 2-naphthol is 9.5, whil the pKu of the excited state is 3.1. Different fluorescence excitation and emission spectra are observed for 2-naphthol and the 2-naphtholate anion. Fluorescence from the unprotonated form is observed at pHs much less than 9.5 because after excitation of 2-naphthol, rapid deprotonization to the anion form occurs before emission.
External Heavy Atom Effect
• We have already observed how other solutes can affect luminescence efficiencies through different quenching mechanisms. Solvents or solutes containing heavy atoms such as haloalkanes (e.g., propyl bromide), alkali halide salts (e-g., NaBr), or some heavy metal ion salts (e.g., T1N03) can increase the rate of intersystem crossing and phosphorescence yields. For these cases, the effect is termed the external heavy atom effect. This effect is to be distinguished from the internal heavy atom effect, which involves heavy atoms in the molecule of interest.
