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12…The Absorption of Light
P. Douglas et al.
The energy match is given by:
E2 À E1 ẳ DE ẳ hm ẳ hc=k
where E1 is the energy of the lower energy state, E2 the energy of the higher
energy state, DE is the difference in energy between the two states, h is Planck’s
constant, c the speed of light, and m and k the frequency and wavelength of the
absorbed light. If this energy-matching criterion is not met, then photons of this
particular energy cannot be absorbed, and the material will transmit, reflect, or
The absorption process involves three waves: the two electronic waves of the
two energy states, plus the EMR wave of the incident light. A detailed understanding of the coupling mechanism between these requires quantum mechanics,
but the essence of the question, in mechanistic terms, is, ‘‘How efficiently can the
incident photon wave perturb the positions and momenta of the electron in the
lower state wave such that it can be pushed into positions and momenta corresponding to the higher energy wave?’’
The mechanism of interaction is via the oscillatory force an electromagnetic
wave exerts on the dipole formed between the nucleus and an electron. For a
‘picture’ of the process it is easiest to consider the case of the hydrogen atom. At
any time there is an instantaneous dipole between the electron and nucleus. The
wavelength of visible light is many times bigger than the atomic diameter, and as
the wave passes, both the electron and nucleus experience essentially the same
magnitude of electromagnetic oscillatory force, but, as they are oppositely
charged, the force acts on the two ends of the dipole, the nucleus and electron, in
opposite directions. This electromagnetic force causes an oscillation in the dipole,
and perturbs the electron wavefunction. If this perturbation is of the right frequency, the electron can be pushed from positions and momenta characteristic of
the lower state to those characteristic of the higher state; the electron wavefunction
is then that corresponding to the higher state rather than the lower state, energy is
absorbed and the transition made. If the perturbation cannot shift the electron from
the lower to the upper orbital, the electron remains in the lower orbital, no energy
is absorbed, although the oscillating electric field caused by the perturbed electron
oscillation can result in a scattered photon of the same frequency as the incident
radiation. (This latter process gives rise to Rayleigh scattering, scattering of light
at the same frequency of incident light, which occurs when any inhomogeneous
material is irradiated.)
In a similar way that the calculation of orbital overlap for the formation of MOs
depends on the integral of two wavefunctions, the transition probability is also
calculated from an integration involving two wavefunctions; this time those corresponding to the lower and upper states. But an additional term, to identify the
effect of the electromagnetic radiation in coupling these two states together is
^, which for a single electron is -er,
required, this is the dipole moment operator, l
where -e is the charge on an electron and r is position relative to the nucleus, i.e.
the vector position along x, y, z axes with the nucleus at zero. The ‘‘allowedness’’
1 Foundations of Photochemistry
of an electric dipole absorption from E1 to E2, is calculated from the transition
dipole moment, M12 (i.e. the electric dipole moment associated with the transition
between the two states):
M12 ẳ W1 l
where W1 and W2 are the wavefunctions for the electronic ground and excited
states, 1 and 2, respectively, and the integral is across all space ($….ds). M12 is a
vector, and the transition probability for absorption is given by the square of the
magnitude of the transition dipole moment, i.e. |M12|2 (the vertical bars indicate it
is the magnitude of the vector, i.e. its length, which is squared, rather than squaring
the vector itself).
If the overall integral is large, then there is a high probability that an incident
photon will be absorbed, the transition takes place, and the molecule is excited into
the higher energy state, 2. If the integral is small, then there is a low probability of
absorption. If the integral is zero, there will be no absorption at all. From equation
(1.23) the two wavefunctions must have some overlap in space, but also the
symmetry of the wavefunctions, when combined with the symmetry properties of
the dipole moment operator, must be such as to give a non-zero resultant integral.
A consideration of those cases, where, for reasons of wavefunction symmetry, the
integral is zero, leads to what are called selection rules.
18.104.22.168 The Parity Selection Rule: Atomic Transitions and Electron
Orbital Angular Momentum
For an atom the dipole moment operator has inversion symmetry across the
nucleus; therefore the absorption integral is zero if both the electron wavefunctions
are of the same parity, but non-zero if they are of different parity. Thus an
s ? s orbital transition is ‘forbidden’, but s ? p orbital transition is ‘allowed’.
This is the Laporte selection rule (also known as the parity selection rule), perhaps
the most commonly observed consequence of which is the low intensities of
d–d transitions in transition metal complexes. By itself, the parity selection rule
would suggest that an s ? f transition is allowed. However, consideration of
conservation of angular momentum, restricts changes to those transitions in which
Dl = ± 1. (The possibilities of an increase or decrease in l arise because of the
vector nature of momenta, which can oppose or reinforce one another).
Although the strongest interaction between electromagnetic radiation and
chemical structures is via the dipole interaction, there are weaker multipole and
magnetic interactions which may become important in certain circumstances,
notably when considering f–f transitions in lanthanide (III) ions.
P. Douglas et al.
22.214.171.124 The Spin Selection Rule: Atomic Transitions and Spin–Orbit
The spin-angular momentum of an absorbed photon can be incorporated into an
absorbing atom as electron orbital angular momentum, i.e. a difference of ± 1 in
the l quantum number for atomic transitions. However, there is no electric-dipole
mechanism for the direct conversion of photon spin angular momentum into a
change in electron spin angular momentum. (ESR spectroscopy has its origin in
the interaction of the magnetic, rather than electric, field of the incident radiation).
Thus, the general electron spin selection rule is DS = 0 and absorption takes place
with no change in electron spin angular momentum, so that, notably, transitions
between singlet and triplet states are spin-forbidden.
However, as discussed in Sect. 1.4.3, atoms with high Z, i.e. ‘heavy atoms’, can
have electron spin angular momentum and electron orbital angular momentum
‘coupled’, such that, in optical transitions of heavy atoms, a change in electron
spin angular momentum, an electron ‘spin flip’, can be coupled to a change in
orbital angular momentum while total angular momentum is conserved. Thus,
when all three types of angular momentum involved in absorption: photon, electron spin, and electron orbital angular momentum, can be coupled together,
absorptions for which DS = ± 1 can become allowed. For example, the n = 6
P1 ? 1S0 transition of the Hg atom is very strongly allowed, even though it is a
triplet–singlet transition for which DS = 0.
126.96.36.199 Selection Rules and Light Absorption in Molecules
The probabilities of absorption by structures larger than an atom are determined in
essentially the same way. For diatomic and linear polyatomic molecules the orbital
momentum selection rule becomes DK = 0, ± 1, where K is the symbol for
molecular total orbital angular momentum. For systems with appropriate symmetry, the rules are g $ u, ? $ +, - $ -. For non-linear polyatomic molecules
which have some symmetry, the selection rule for orbital angular momentum can
be given in terms of symmetry properties . For centrosymmetric systems, the
rule g $ u still holds. In addition, the allowed transitions can be related to the
symmetry properties of a particular point group. For example, benzene has D6h
symmetry, and electric dipole transitions are symmetry forbidden from the A1
ground state to B1, B2 or other A1 states (see Fig. 1.15) . However, the
symmetry arguments only hold for completely rigid structures. In practice,
vibrations can act to distort molecular structures sufficiently to allow some
absorption for transitions, which would be ‘forbidden’ if only the symmetry of the
electronic wavefunctions were to be considered. These transitions are usually
much weaker than fully allowed ones. For example, the lowest energy (longest
wavelength) absorption band in benzene corresponds to the symmetry forbidden
A1g ? 1B2u transition (see Fig. 1.15). Although this transition is forbidden for
pure electronic states, the structure of benzene is distorted from that of a pure
1 Foundations of Photochemistry
hexagon because of interaction with the various vibrational modes. This is termed
vibronic coupling (vibrational ? electronic). This reduces the symmetry and the
selection rule is partially relaxed. Nevertheless this band, which is seen around
256 nm, is 30 times weaker than the second band at 203 nm and 200 times weaker
than the third absorption band at 183 nm .
The spin selection rule, DS = 0, also applies to molecules, and transitions
between, for example, molecular singlet and triplet states are spin-forbidden.
However, in the presence of heavy atoms, either in the molecular structure itself,
or in the solvent, the rule may be relaxed enough for singlet to triplet absorptions
to be detected, although usually they are still weak absorption bands.
188.8.131.52 Selection Rules for Vibrational Transitions, Rotational
Transitions, and Raman Scattering
The vibrational transitions of a molecule can be probed directly using infrared
spectroscopy and are subject to the gross selection rule that for a change in a
vibrational state brought about by the absorption or emission of a photon, there
must be an accompanying change in the dipole moment of the molecule. Homonuclear diatomics are an important group of molecules which do not absorb IR
radiation because of this selection rule.
Pure rotational spectra can be observed in the gas phase; however the selection
rule for rotational transitions requires the molecule to have a permanent electric
dipole. Homonuclear diatomics are, again, an important group of molecules which
do not show microwave absorption because of this selection rule.
Although these selection rules limit IR and microwave absorption, electronic
transitions can be, and usually are, simultaneously accompanied by both vibrational and rotational transitions, and for an electronic transition there is no
restriction on the associated change in vibrational state. Vibrational transitions
accompanying an electronic transition are called vibronic transitions. In high
resolution gas phase work, these, along with their accompanying rotational transitions give rise to what is called an electronic band system. In solution the
vibrational structure is usually not well resolved, but there is often some structure,
a vibrational progression, corresponding to transitions into a number of electronic
levels in the upper electronic state (see Fig. 1.20).
Raman spectroscopy is a complementary technique used to probe vibrational
and rotational modes. It is based on the inelastic scattering of light. Upon irradiation of a sample with a monochromatic light source (typically a laser), some of
the incident photons collide with the molecules and lose energy to vibrational/
rotational modes, and will emerge from the sample with lower energy (Stokes
radiation); other photons may gain energy from vibrationally hot states and will
emerge with a higher energy (anti-Stokes radiation); finally some photons will be
directly scattered without a change in frequency (Rayleigh radiation). The
observed energy ‘losses’ or ‘gains’ provide information about the vibrational and
rotational states of molecules. The gross selection rule for rotational Raman
P. Douglas et al.
Fig. 1.20 UV/Vis absorption spectrum of anthracene in cyclohexane for the S0 ? S1 transition.
The vibrational progression in the absorption spectrum corresponds to transitions to excited-state
vibrations. The hatched area under the peak corresponds to the integrated absorption coefficient
(IAC) as defined in Eq. 1.26
transitions is that the molecule must be anisotropically polarisable, while for
vibrational Raman transitions the polarisability should change as the molecule
184.108.40.206 Absorbance, Transmittance, Molar Absorption (Extinction)
Coefficient, Beer–Lambert Law and Deviations from Beer–
For a parallel monochromatic radiation beam, where the proportion of radiation
absorbed by a substance is independent of the intensity of the incident irradiation,
i.e. the probability of absorption is linearly dependent on incident intensity, which
is the usual case for single photon transitions, each successive layer of thickness
dx absorbs an equal fraction -dI/I of radiant intensity I, and integration across a
finite thickness, x, with an initial irradiation intensity I0 gives:
lnI0 =It ị ẳ bx
where It is the transmitted intensity and b is a constant dependent upon the sample.
This is Lambert’s law. Beer showed that b is proportional to concentration (strictly
limited to low concentrations), and, as is most commonly the case, using log10, this
log10 I0 =It ị ẳ log10 I0 =Io Iabs ịị ẳ ecx
1 Foundations of Photochemistry
Table 1.6 Typical values of molar absorption coefficients (e) for some electronic transitions in
organic molecules and metal complexes
Highly conjugated organic
Small aromatic compounds
Spin-allowed p ? p*
Spin-allowed, symmetry forbidden lowest
energy p ? p*
Spin-allowed n ? p*
Spin- and Laporte-allowed charge transfer
Tetrahedral metal complexes
Spin-allowed, partially Laporte-forbidden
Octahedral and square planar metal Spin-allowed, Laporte-forbidden d ? d
These values increase with systems containing high atomic number atoms due to increased
where Iabs is the absorbed intensity, e is the molar absorption (formerly called
extinction) coefficient, and c is the concentration of absorbing material. If c is
given in mol dm-3, e is the decadic molar absorption coefficient (although usually
the term decadic is omitted); x, the pathlength, is usually give in cm (a 1 cm
pathlength cell being the most commonly used in solution phase experimental
photochemistry; note pathlength is often given the symbol l), so the units of e are
usually mol-1 dm3 cm-1. e is wavelength dependent. log10(I0/It) is called absorbance, or optical density (usually given the symbol A, Abs, or OD), and it varies
linearly with concentration and path length. For a solution made up of a mixture of
absorbers, i, the total absorbance at a given wavelength is the sum of P
the absorbances of the individual components at that wavelength, i.e. Atotal = x eici.
If a transition is forbidden by the spin-selection rule, the molar absorption
coefficient is typically 10-5–10-3 mol-1 dm3 cm-1, irrespective of whether the
transition is Laporte- or vibrationally-allowed. If a transition is spin-allowed but
parity forbidden, e is typically of the order of 100–103 mol-1 dm3 cm-1. If the
transition is both spin- and Laporte-allowed, e is large (103–105 mol-1 dm3 cm-1)
and the absorption is said to be ‘‘fully-allowed’’. Typical values for ‘‘allowed’’ and
‘‘forbidden’’ transitions in some common organic and inorganic complexes are
given in Table 1.6.
Apparent deviations from the Beer–Lambert law arise mainly because of
instrumental factors such as: stray light, sample fluorescence, and use of a wide
radiation bandwidth. Real deviations arise because of high concentrations which
introduce solute–solute interactions and changes in e with solution refractive
index, and concentration dependent chemical equilibria.
P. Douglas et al.
220.127.116.11 The Strength or Probability of Absorption
We saw earlier that the probability of electric dipole absorption is related to the
transition dipole moment. However, there are a variety of terms commonly used to
describe the strength or probability of absorption. The ‘allowedness’ or ‘forbiddenness’ of the transition, and oscillator strength, f, are useful ideas where the
relative, rather than absolute value, of the strength of coupling is required. These
terms are factors used to describe how likely absorption is by reference to the
‘ideal oscillator’ of a free electron where the transition is ‘fully allowed’ and both
the ‘allowedness’ and oscillator strength are unity.
The molar absorption (extinction) coefficient, Einstein coefficient and absorption cross-section are commonly used measures of transition probability. The first
three are used for atomic and molecular species in the gas or solution phase, while
the latter is commonly used in solid-state studies. These are absolute measures of
absorption probability and are ultimately derived from the transition dipole
moment, and are therefore all related. They can be measured experimentally from
the absorption spectrum and can, in some cases, be calculated using molecular
orbital theory programs. (Note that generally MO calculations will give the
oscillator strength for any ‘forbidden’ transition as zero).
The method of calculation of these parameters from the absorption spectrum is
illustrated in Fig. 1.20, where the spectrum is plotted as e vs wavenumber (~m in
units of cm-1), instead of the conventional wavelength units . The integrated
absorption coefficient, (IAC), is the area of the absorption peak, which is given by:
The IAC is proportional to the square of the transition dipole moment, i.e.
|M12|2. The related oscillator strength, f, of the transition is given by:
f ¼ 4:33 Â 10
The maximum value of f for a fully-allowed transition is 1 and it is a unitless
The IAC is also related to the B12 Einstein coefficient for spontaneous
eð~mÞd~m ¼ B12 h~mNA = ln 10
1 Foundations of Photochemistry
where NA is Avogadro’s number, and the term ln10 arises from the use of the
decadic molar absorption coefficient, i.e. one based on log10. Finally, the Einstein
coefficient for spontaneous emission, A21, can be related to B12 by:
B12 ẳ A21 =8phc~m3 ị
and, thus to the IAC by:
8pc~m2 ln 10IACị
18.104.22.168 Types of Transitions
While bearing in mind the limitations of our approximations to the Schrödinger
equation for complex molecules, it is still often found that transitions arise predominantly from the movement of an electron from one molecular or atomic
orbital to another. The nature of the transition is then described by the two orbitals
involved; the most common types of transition are given below.
1. Transitions between orbitals localised on atoms; e.g. d–d transitions of
transition metal salts, f–f transitions of lanthanide ions. Such metal-centred
(MC) transitions are ubiquitous in transition metal and lanthanide complexes.
They are relatively weak because they are symmetry (Laporte) forbidden.
Although they may not be the important transitions for any particular application of transition metal photochemistry, they will almost always be present.
These are the transitions that give many transition metal salts their characteristic colour and are found in some gemstones and minerals. For example, the
red colour in ruby is due to the d–d transitions in chromium (III) present at
certain sites in an aluminium oxide (corundum) crystal.
2. Transitions between atomic orbitals in mixed oxidation state transition
metal complexes. These transitions can be relatively strong and are known as
metal to metal charge transfer (MMCT) transitions. Two common examples
are those involving the Fe2+/Fe3+ centres in the pigment prussian blue and the
Fe2+/Ti4+ ions in sapphire.
3. Transitions between ligand and metal orbitals in transition metal complexes. These are called metal to ligand, and ligand to metal charge transfer
(MLCT and LMCT) transitions, respectively. These can be fully-allowed
transitions and are usually the source of colour in intensely coloured transition
metal complexes, e.g. the LMCT transitions in chromate, CrO42-, and permanganate, MnO-,
4 ions, and the intense absorptions in ferroin (tris(phenanthroline) iron(II)) and tris(2,20 -bipyridyl)ruthenium(II) (see Chap. 4).
4. Transitions between molecular orbitals in organic compounds: e.g. polyaromatics, organic dyes, biological colorants such as chlorophylls and carotenes
(see Chap. 4). The lowest energy transitions are those between the HOMO and
P. Douglas et al.
Fig. 1.21 Structures of some organic molecules that show charge transfer: a naphthazarin;
b quinhydrone (a complex between quinone and 1,4-dihydroxybenzene); c TMPD (electron
donor) and d TCNE (electron acceptor)
LUMO. The two most important types of transitions in organic molecules are
n ? p* and p ? p* transitions; r ? p* and r ? r* transitions; are usually
of such high energy that they occur in the vacuum UV region. Most molecules
are not of particularly high symmetry and for these, p ? p* transitions are
generally highly allowed and have high molar absorption coefficients. For those
molecules which do have high symmetry, some p ? p* transitions may be
symmetry forbidden and show significantly reduced molar absorption coefficients (e.g. some transitions of pyrene). Pure n ? p* transitions are symmetry
forbidden when the n orbital has r symmetry, such as carbonyls; but vibrations
are effective in reducing the degree of forbiddenness; and a phenomenon known
as intensity borrowing, by which the intensity of a forbidden transition lying
close to an allowed transition can be increased, allows many n ? p* transitions
to have significant molar absorption coefficients. (The need to introduce the
concept of ‘intensity borrowing’ is an example of the failure of the simple MO
approach to match the solutions of the Schrödinger equation for complex
systems.) For many organic molecules containing heteroatoms, such as O and
N, n ? p* and p ? p* transitions are energetically close and in some cases
the relative positions of the absorptions can be reversed in solvents of differing
polarity. In certain cases, transitions can take place between electron rich and
electron poor regions in complex organic molecules. These charge transfer
transitions usually have very high molar absorption coefficients and are
responsible for many of the intense colours found in typical organic dyes (see
Chap. 4), such as naphthazarin (Fig. 1.21a).
5. Transitions between the valence and conduction bands in semiconductors.
These are the origin of colour in semiconductor pigments and quantum dots. In
addition to colour from bandgap transitions, introduction of dopants or impurities
into semiconductors leads to localised energy levels on the dopant or impurity
atoms/molecules (so-called colour centres) and transitions between these levels
and those of the semiconductor conduction and valence bands become possible;
the colour in blue and yellow diamonds arises from these types of transitions.
6. Transitions between electronic energy levels in imperfect crystals. The
colours of some minerals and semi-precious gems, notably: Cairngorms or
smoky quartz where colour comes from defects in the quartz lattice caused by
1 Foundations of Photochemistry
radiation from nearby radioactive minerals, and blue topaz where similar
defects are introduced into otherwise colourless stones deliberately in the
7. Transitions of the hydrated electron. One of the effects of radiation on
aqueous systems is the ejection of electrons, which are then hydrated by surrounding water molecules. The blue colour of the hydrated electron arises
because of transitions between the electronic energy levels of the electron held
in the potential well created by these water molecules. Similar intense colours
due to solvated electrons are seen upon dissolving sodium or other alkali metals
in liquid ammonia or aliphatic amines.
8. Charge transfer transitions between molecules in association. Here, the
transition occurs between the molecules themselves, with an electron transferred from one molecule to the other. The various colours observed with
molecular iodine (I2) with aromatic molecules are due to charge-transfer .
Intermolecular charge transfer is also responsible for the yellow colour in
quinhydrone, a complex formed between quinone and 1,4-dihydroxybenzene
(Fig. 1.21b). Naphthazarin can be considered as an intramolecular equivalent of
quinhydrone. Organic charge transfer complexes having strong absorption
bands can also be readily formed between aromatic molecules and strong
electron donors, such as N,N,N’,N’-tetramethyl-p-phenylenediamine (TMPD or
Wurster’s blue), Fig. 1.21c or acceptors, such as tetracyanoethylene ((TCNE),
1.12.2 Absorption Spectra
22.214.171.124 Absorption Spectra in the Gas Phase
Atoms lack vibrational and rotational energy levels. Low pressure atomic gases
show absorption lines which are extremely narrow, limited in width by Doppler
broadening due to the range of molecular velocities in a thermally equilibrated gas.
(The Doppler effect is a change in absorption/emission frequency due to relative
motion of the absorber/emitter and the source/detector. The reader will almost
certainly have experienced the effect while standing at a railway station as a nonstopping train passes sounding its horn. The sound of the horn shifts from a high
frequency to low frequency tone as it first approaches and then leaves the station).
At high pressures and temperatures interatomic interactions, i.e. collisions, and the
perturbing effects of neighbouring molecules, also cause lines to broaden.
For molecular species, gas-phase absorption spectra show a series of electronic
transitions upon which vibrational and rotational structure are superimposed. For
simple molecules in the gas phase this structure is simple enough for individual
electronic-vibrational–rotational transitions to be seen, particularly at low temperatures where only the very lowest vibrational and rotational energy states are
P. Douglas et al.
populated in the ground state. However, for molecules of any complexity there are
many vibrational levels, and since rotational energy spacings decrease with
molecular mass  rotational levels are much closer together, so that even in the
gas phase, where molecules are isolated from one another, the absorption spectrum
can become so complex that it resembles more a series of overlapping bands than
groups of discrete lines.
126.96.36.199 Absorption Spectra in Solution
Absorption bands in solution are less structured and broader than those in the gas
phase. In solution, molecular rotation is hindered through collision with solvent
molecules such that rotational quantisation is lost and solvent–solute interactions
broaden vibrational bands further. The magnitude of the latter effect depends on
the strength of the solute–solvent interaction and it is therefore most pronounced in
polar solvents, so that spectra in a non-polar solvent such as hexane will generally
show more distinct vibrational structure than those recorded in a more polar solvent such as acetone or an alcohol. While molecular absorption bands in solution
may be very broad, there is almost always some electronic/vibrational structure
and usually a number of electronic absorption bands can be identified.
188.8.131.52 Absorption Spectra in Solution: Effect of Aggregation
Consider the relatively simple case of two aromatic molecules. If they are close
enough, they may interact, or couple, leading to splitting of the excited-state into
two levels . The effect of this coupling depends upon the way the transition
dipole moments of the two molecules are arranged. If they are parallel, the transition to the upper excited state becomes more probable, and this leads to a blue or
hypsochromic shift in the absorption spectrum. If, in contrast, the transition dipoles
are in a head-to-tail arrangement, the transition to the lower excited state becomes
more probable, and there is a red or bathochromic shift in the absorption spectrum.
(There are corresponding shifts in the fluorescence spectra and changes in the
emission quantum yield.) A third possibility is that the transition dipoles are
arranged in an oblique fashion. In this case the absorption band is split into two.
These cases are shown in Fig. 1.22. Similar behaviour exists with larger aggregates. For historical reasons, if the shift is to longer wavelengths, these are termed
J-aggregates. (After the scientist Edwin Jelley, who observed the effect with
photographic dyes . It was also reported independently by G. Scheibe .) Jaggregates frequently have very sharp absorption bands and show considerable
potential in various functional dye systems . The aggregates where there is a
shift to shorter wavelengths are termed H-aggregates (after the hypsochromic or
blue shift in the spectrum).