Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 1

Introduction to SpectroscopyProteins are large molecules. Most contain well in excess of 100 amino acids, andtherefore over 1000 non-hydrogen atoms. The large size of proteins means that theirbehavior in solution can be considerably more complex than simpler molecules. Inaddition, it means that a full understanding of most proteins cannot beaccomplished by three-dimensional structure determination; while structure isimportant, the dynamic motions and functional changes are also important inunderstanding the protein.

Electromagnetic radiationMany methods for studying proteins (and molecules in general) involve the use ofelectromagnetic radiation. Electromagnetic radiation can be generated with a widerange of wavelengths. Different wavelengths have differing energies, and interactwith molecules in different ways.

The energy in a mole of 400 nm photons is calculated by:

†

E = hn =hcl

=

6.626x10-34 J •sec( ) 2.9979x108 msec

Ê

Ë Á

ˆ

¯ ˜ 6.022x1023 photons

mol

Ê

Ë Á

ˆ

¯ ˜

400x10-9m

Ê

Ë

Á Á Á Á

ˆ

¯

˜ ˜ ˜ ˜

The table below gives the range of wavelengths and energies of photons in theelectromagnetic spectrum. High-energy photons contain enough energy to breakcovalent bonds, although they only break bonds under certain conditions. Low-energy photons contain too little energy to disrupt covalent interactions, and arelimited to contributing energy to molecules, usually without altering the molecularstructure.

Wavelength Range(meters)

Photon energy(kJ/mol)

Spectroscopicregion

Spectroscopic technique

10–13 109 g-radiation Mössbauer

10–10 106 X-radiation X-ray diffraction and X-rayscattering

10–7 1200 Far ultraviolet Far UV spectroscopy

3 x 10–7 (300 nm) 430 Near ultraviolet UV/Vis spectroscopy

4 x 10–7 to 7 x 10–7 300 to 170 Visible UV/Vis spectroscopy

10–6 to 10–4 120 to 1.2 Infrared IR spectroscopy

0.01 0.01 Microwave Electron paramagnetic resonance

0.1 0.001 Radio Nuclear magnetic resonance

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 2

The interaction of electromagnetic radiation with molecules is complex. Anunderstanding of the process requires an understanding of some of the elements ofquantum mechanics. The discussion below is based on quantum mechanical theory.If you have never had a course in quantum mechanics, you probably will havedifficulty with the theoretical treatments, but will at least be able to see some of thetheory that underlies the experimental techniques.

Review of Quantum Mechanical ConceptsA complex number is a number of the form: a + bi, where i = -1 . The complexconjugate of a complex number is: a – bi. Multiplying a complex number by itsconjugate results in a real number: a

2 + b2 .

Molecular states are described by wavefunctions. Wavefunctions (Y) are complexnumbers that describe the position and spin of all of the particles in the system, aswell as describing the external fields that may perturb the system. Y cannot bemeasured directly. The probability that a system will have a particular propertycan be calculated by multiplying the Y for that property by its complex conjugateY*; the result of this mathematical manipulation is a real number:

P = Y*Y

A system must exist in some state. For convenience, probabilities are frequentlyconsidered to be numbers between zero and one. If the wavefunction is writtenproperly, integration of the probability over all possible states yields an overallprobability of 1. This is called normalization, because it acts as a constraint on thewavefunction.

†

Pdt = Y* YÚÚ dt = Y Y =1

The expression within the angle brackets are the Dirac notation for integration overall states; in Dirac notation, the wavefunction on the left side of the expression isconsidered to be complex.

If a system can hav.e two states (Ya and Yb), the overlap between the states is ameasure of their similarity. If the overlap integral <Ya|Yb> = 1, then the statesare identical. If <Ya|Yb> = 0 then the states do not overlap. It is worth consideringYa and Yb as vectors, with the overlap integral representing the dot product of thevectors. (Dot products are highest for parallel vectors, and are 0 for perpendicularvectors.)

If a system has two states, the overall wavefunction Y will be:

Y = CaYa + CbYb

The coefficients Ca and Cb are related to the probabilities that the system is in thecorresponding state. For essentially all of the systems we will discuss (although notfor all systems), <Ya|Ya> = 1 and <Ya|Yb> = 0. For these systems, the probabilityof state a is:

Pa = Ca*Ca.

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 3

It is often useful to consider portions of a molecule separate from the remainder. Inthese cases, the overall wavefunction can be factored into component wavefunctions.An example is the Born-Oppenheimer approximation, in which nuclei areassumed to be fixed while the electrons can move. For this approximation:

Y = Ye(r,R)FN(R)

where r refers to the electron position, and R refers to the nuclear position. In thisapproximation, the electronic wavefunction Ye is calculated for a fixed nuclearposition, and the nuclear wavefunction FN is calculated for the time-averagedelectronic state.

OperatorsThe wavefunction that describes a system can be studied by using mathematicaloperations on the wavefunction. Although many mathematical operations arepurely mathematical constructs, most operators of interest in quantum mechanicsare related to physically observable properties.

An eigenvalue equation is one in which the product of the specific wavefunction(eigenfunction) and a number (the eigenvalue) equals the effect of the operator onthe wavefunction.

OY = LY

The expectation value for the operator = <Y|O|Y>. Substituting gives <Y|L|Y>.Since <Y|Y> = 1, <Y|L|Y> = L. Therefore, if Y is an eigenfunction, measurementof the effect of an operator will yield an observation of the eigenvalue.1

The Schrödinger equationThe time-dependent Schrödinger equation has the form:

ih dY/dt = H Y

In this equation, h = h/2π, where h is Planck’s constant. H is the Hamiltonianoperator. The Hamiltonian is defined as the operator that has the energy of thesystem as its corresponding eigenvalue.

<Y|H |Y> = E

In general, H = T + V, where T is the kinetic energy operator and V is the potentialenergy operator.

†

1 States that are eigenfunctions of one operator are not necessarily eigenfunctions of other operators.For example, rpY ≠ prY (where r is the position operator, and p is the linear momentum operator).This is the basis of the Heisenberg uncertainty principle; in this case, position and momentumcannot simultaneously be measured accurately.

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 4

In some cases, H is not time-dependent. In these cases, the time-independentSchrödinger equation has the form:

H Y = EY

If H is constant, then E must also be constant. However, Y may still vary.

Combining the two Schrödinger equations yields:

ih dY/dt = EY

Integrating gives:

Y(t) = Y(0)e–itE/h

The probability for the wavefunction is then:

P = Y(t)* Y(t) = (Y(0)e+itE/h)(Y(0)e–itE/h)=|Y(0)|2

Because the exponential parts of the equation have opposite signs be equalmagnitudes, these terms vanish. As a result, the probability is a function only of theinitial condition and therefore is independent of time. Stationary states are statesin which the properties do not change over time.

For stationary states, <Ya|Yb> = 0 if Ea ≠ Eb.

If a system can be in two states, Y = CaYa + CbYb. The probability the system is instate Ya is:

Pa = |<Ya|Y>|2 = |Ca|2

Note that the other state does not appear explicitly in the equation.

For stationary states,

Y = CiYi

iÂ

In other words, the specific two state system discussed here can be generalized to amulti-state system. In most cases, the Ci is very small. If a system in one state isperturbed, only a few Ci will have non-zero values, and probably all of these will besmall except for one. (This is the basis for perturbation theory.)

If a stationary state is perturbed by a potential, the effect will be an alteration ofthe Ci values for some states (possibly by mixing some states). The expectationvalue for the new state will be:

Y V Ya = Ci

i Yi V Ya

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 5

Because stationary states are normally orthogonal, the terms would all be zeroexcept for the identity term. However, the potential operator may make some termsnon-zero; in other words, the potential may induce a transition between onestate and another. The probability of the transition from state a to state i is givenby the expectation value for that transition.

Interactions of electromagnetic radiation and moleculesElectromagnetic radiation consists of a time-varying electric field and a timevarying magnetic field. For most electronic transitions, the effect of the magneticfield can be neglected. For most spectroscopy, the wavelength of the radiation islarge compared with the size of the chromophore, and therefore it is usuallyunnecessary to consider the variation of field strengths across the molecule.

The electric field2 has a maximum amplitude E0; the field experienced by a moleculeis:

E(t) = E0eiwt

The term w is the circular frequency of the light, where:

w = 2pn =

2pcl

Because the electric field is time-dependent, the time-dependent form of theSchrödinger equation must be used. However, the effect of the potential can befactored out, leaving a time-independent Hamiltonian and the potential operator.

The operator relevant to light interactions is the electric dipole operator m.

m = ei ri

iÂ

where ei is each charge, and r i is the position operator. (The Franck-Condonprinciple state that light interacts with molecules on such short time scales that thenuclear motions can be ignored; this is a modified restatement of the Born-Oppenheimer approximation. Thus, only the electrons must be considered.)

The effect of the light electric field is a distortion of the state a wavefunction into astate close to state b. Classically, mind = a•E, where a is the polarizability of themolecule, and mind is the induced dipole moment. For the interaction of light with amolecule, the integral <Yb|m|Ya> is the dipole induced by light.

Extinction coefficientThe rate of absorption of light by a system is:

2 Most textbooks use a capital “E” for both energy and electric field. To attempt to minimizeconfusion, I will use E to refer to energy, and E to indicate electric field.

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 6

dPb

dt= BabI(n)

where Bab is the transition rate per unit energy density of the radiation and I(n) isthe energy density at the frequency n. The energy density of light is I(n) = |E0|2/4π;it is a function of the number of photons present at that frequency, because eachphoton contributes to the electric field strength. The transition rate Bab (theEinstein coefficient for stimulated absorption) is:

Bab =

23

p

h2 Yb m Ya2

(The derivation of the expression for Bab is complicated and I will not attempt toreproduce it here.)

The rate at which energy is removed from the light is dependent on the probabilityof absorption transitions, the rate of emission transitions of the same frequency, onthe energy per transition (hn = Eb – Ea), and on Na and Nb, which are the number ofmolecules per cm3 in states a and b.3

–dI(n)dt

= hn NaBab – NbBba( )I (n)

The absorption of light through a slice dl of the sample at concentration C (where dlis so thin that the light intensity does not change as it passes through the slice) isgiven by:

–dII

= Ce¢ dl

Integrating from I0 to I and 0 to l:

†

-dIII 0

I

Ú = Ce¢dl0

l

Ú gives:

†

lnI0

I

Ê

Ë Á Á

ˆ

¯ ˜ ˜ = Ce¢l

Converting to base 10 gives:

†

logI0

I

Ê

Ë Á Á

ˆ

¯ ˜ ˜ = Cel

where e is the molar extinction coefficient, and l is the pathlength in centimeters.Abbreviating the log term as the absorbance, A, gives: A = Cel, which is the usualform of the Beer-Lambert law.

3 In most systems, Na >> Nb, and, for simple systems Bab = Bba. If, however, Nb > Na, the changein light intensity will be positive. In other words, the light intensity exiting the system will begreater than the light intensity entering it. This observation is the basis of lasers.

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 7

Assuming that the molecules in solution do not interact, the extinction coefficient eis a constant for a given molecule in solution at a given wavelength. (If themolecules interact with one another in a way that changes the energy levels of thetransition, the extinction coefficient will change in a concentration-dependentmanner.)

Absorption and energy statesElectromagnetic radiation only interacts with molecules at specific energies. Inorder for the electric field to induce a dipole, the energy difference between the twostates must be equal to the energy contained in the photon, and the orientation ofthe electric field vector must match the orientation of the molecule. (Themathematical derivation of this is very complex; instead, we will consider theinteraction with light using a more qualitative approach.)

The state of a molecule can be described by an energy diagram such as the oneshown below. The energy diagram shows two electronic states, with each electronicstate comprised of a variety of vibrational and rotational states. The difference inenergy between one rotational state and the next is ~4 kJ/mol, which is in the rangeof thermal energy of the molecule, allowing molecules to adopt more than onerotational mode. However, the vibration energy levels are about 40 kJ/mol apart,and electronic states are 150 to 450 kJ/mol apart (depending on the molecule).Because these energies are well above the thermal energy range, in the absence ofan external energy input only the lowest vibrational level of the lowest energyelectronic level will be populated.

Each of the energy states the molecule can adopt is described by a wavefunction.The lowest energy state, the ground state, is Y0. Other states within the groundelectronic state are Y0,y,r, where the v and r subscripts refer to the specificvibrational and rotational states.

The interaction of a molecule with electromagnetic radiation in the ultraviolet orvisible energy range induces a transition from one electronic state to another. Theprobability of any transition can be calculated using the overlap integral for the two

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 8

states. For an electronic transition, the overlap integral is <Y1,y,r|m|Y0>. Theoverlap integral can only be significantly different from zero as a result of the moperator; this will only occur if the energy of the photon is equal to the energydifference between the states Y0 and Y1,y,r, and even then only with a probabilityless than one if the electric field vector can induce a dipole in the molecule as it isoriented when the photon approaches (in other words, as indicated earlier, not allphotons of the appropriate energy will induce transitions in all molecules).

In principle, the absorption spectrum of a molecule, theabsorbance intensity as a function of the frequency (ormore commonly, wavelength) of light should be a series ofsharp bands, with each band corresponding to thetransition from one energy level to another. The height ofeach absorbance band is related to the probability of thattransition.

For many molecules, the effects of solvent environment,Doppler effects, and other influences tend to result in arelatively broad and featureless absorbance band thatextends over ~50 nm. The overall absorbance bandcorresponds to a single electronic transition, which isbroadened by the vibration and rotational transitions.

It is possible to see the absorbance fine structure for somemolecules. This tends to be especially apparent in the gasphase, although for some molecules different vibrationalbands are distinct enough to show spectral structure insolution.

Spectral analysisAn absorbance band represents a single electronic transition. (This assumes thatthe band is well enough separated from other electronic transitions; some moleculeshave more than one transition, and therefore may exhibit merged absorbancebands.) Analysis of the properties of the band allows assessment of some molecularproperties.

In a 1 cm3 volume containing a 1 molar solution, the rate of energy uptake is:

–dI(n)dt

=hnN0Bab

1000 mlL

I(n)

Light travels at c, and therefore, the intensity change in distance dl is:

dI (n) =

1c

dI(n)dt

dl =hnN0Bab

1000cI (n)dl

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 9

Because molecules do not absorb single wavelengths, the above equation cannot besolved using the Beer-Lambert law. Instead, it is necessary to calculate theintensity change over a range of wavelengths. Since intensity is a linear function offrequency, in most cases the integration is performed using frequencies rather thanwavelength:

†

Bab =1000cN0h

e¢

nÚ dn

The parameter of interest is the dipole strength = D = |<Yb|m|Ya>|2 = |m|2

Since, as was noted before, Bab =

23

p

h2 Yb m Ya

2=

23

p

h2 D , it is possible to combine

the equations to obtain an expression for D:

D =

†

1000cN0h23

p

h2

ln(10)e

nÚ dn

where the “ln(10)” allows the conversion of e´ to e. Evaluating the fundamentalconstants using cgs units results in:

†

9.18x10-39 e

nÚ dn = 9.18x10-3 e

nÚ dn(debye)2

where a debye = 10-18 electrostaticunits•cm = 3.336x10-30 C•m. Thedipole length is |m|= D

An alternative method forperforming the calculation uses theassumption of a gaussianabsorbance band. Because agaussian curve has a symmetricalshape, measurement of appropriateparameters in the curve avoid thenecessity of converting to frequencyor of integrating. In the graph atright, e0 is the maximal extinctioncoefficient, and e is the base fornatural log (2.71828182846…)

D = 9.180x10–3 e 0e– ((l -l 0 ) / D )2

l0

•

Ú dl (debye)2 = 1.63x10–2 e 0D

l 0

È

Î Í ˘

˚ ˙ (debye)2

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 10

The oscillator strength of a transition, fab, is a unitless number between 0 and 1.When fab = 0, transitions do not occur. When fab = 1, transition always occurs whenl = l0.

f ab = 7.5x10–2 e0D

l02

Ê

Ë Á Á

ˆ

¯ ˜ ˜

Electronic transitions in moleculesAs an example of how light affects an actual molecule, we willconsider the peptide backbone. The peptide backbone contains sbonds, p bonds, and non-bonding electrons. For a given peptidebond, a total of six electrons are distributed among the threehighest energy molecular and atomic orbitals. In addition, we needto consider the lowest energy unoccupied molecule orbital.

The strongly bonding p+ orbital has the lowest energy. The porbital is a more weakly bonding orbital; the non-bonding n orbitalcontains the lone pair of electrons associated with the carbonyl oxygen. The highestenergy orbital of interest is the anti-bonding p* orbital.

Each orbital can contain two electrons of opposite spin. Distributing thesix electrons to the lowest energy states results in the diagram at right.As mentioned above, the p* orbital is unoccupied; each of the otherorbitals contains two electrons.

If a photon contains an energy equal to the difference in energy ∆Ebetween one occupied orbital and the first unoccupied orbital, atransition may occur. For this system, two transitions are possible atreasonable energies: n‡p* and p‡p*.

The absorbance spectrum shown at right reflects the results of exposing the peptidebond to light. The energy difference between the p and p* orbitals is greater thanthat between the n and p* orbitals, and therefore requires shorter wavelengthphotons. However, the overlap between the p and p* wavefunctions is much greaterthan that for the n and p* orbitals. The transition probability fnp* is very small(about 10-2 to 10-3, compared to ~0.25 for fpp*). The limited overlap between the nand p* wavefunctions make the transition “forbidden” (in the diagram, then‡p*peak is exaggerated to make it visible). In quantum mechanics, forbiddenprocesses are possible, although the probability is low.

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 11

Performing spectroscopic measurementsA single beam spectrophotometer is comprised of a light source, a monochromator, asample holder, and a detector. An ideal instrument has a light source that emitswith equal intensity at all wavelengths, a monochromator that is equally efficient insplitting light into narrow groups of wavelength for all wavelengths, and a detectorthat is sensitive and responds equally to all wavelengths.

Light sourcesBecause no single light source with the appropriate characteristics exists, mostspectrophotometers use two lamps, with one for the ultraviolet spectrum and onefor the visible region. The visible lamp is usually a tungsten lamp, while theultraviolet lamp is a deuterium lamp. An alternative, relatively rarely used inspectrophotometers, although commonly used in other types of spectroscopicinstruments, is a xenon arc lamp. In a xenon arc, the flow of electrons through anelectrode gap in a pressurized xenon chamber ionizes the xenon atoms; the bindingof electrons to the ionized xenon results in fairly consistent light emission over alarge range of wavelengths. However, the light intensity from a xenon arc dropsrapidly below 280 nm.

MonochromatorsAlthough prisms can be used as monochromators, most instruments use diffractiongratings. Light shining on the closely spaced grooves of a diffraction grating at anangle is separated into different wavelengths in a consistent manner, assuming thatthe grooves are consistently produced.

DetectorsThe most commonly used detector is a photomultiplier tube (PMT). An incomingphoton hits a thin metal film inside a vacuum tube. The metal film is maintained ata large negative potential, and emits electrons. These collide with a series ofdynodes maintained at progressively lower potentials; each dynode emits severalelectrons in response to each incoming electron, resulting in a large amplification ofthe signal. Because the initial photon is required to initiate the process, most PMTshave very little dark current (“dark current” is signal without light). Properfunctioning of a PMT requires a constant voltage across the PMT; maintaining aconstant voltage in the face of a high signal requires a well-designed instrument.

PMTs are wavelength dependent, with the degree of dependence being related tothe metal used in the thin film; most PMTs exhibit the greatest sensitivity at ~400nm.

An alternative type of detector uses photodiodes. Photodiodes are inexpensive butnot very sensitive. Their low cost has allowed arrays of photodiodes to be set up toallow simultaneous detection of many wavelengths. In this type of

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 12

spectrophotometer, the monochromator is located after the sample, so that it splitsthe multiwavelength light leaving the sample.

A charge coupled device (CCD) is a sensitive array detector. CCDs store chargesreleased in response to photon impacts. Because the stored charges are stable forprolonged periods, a CCD can collect data for considerable time prior to readout ofthe signal. They are therefore potentially extremely sensitive. They will probablydisplace PMTs from some uses as their price decreases. CCDs are used in digitalcameras and other consumer products and are rapidly becoming less expensive as aresult of both economies of scale and the development of improved productiontechniques.

CuvettesMost samples studied using spectrophotometry are liquid. The sample musttherefore be placed in a transparent container to allow measurement. Thesecontainers are called cuvettes.

Cuvettes are generally made from transparent plastic, glass, or quartz. Differentcuvettes have different optical properties. Plastic cuvettes are increasingly popularbecause their low price makes them disposable. However, plastic cuvettes tend tohave considerable absorbance in the ultraviolet. Performing measurements in thefar ultraviolet (below ~250 nm) requires relatively expensive (and relatively fragile)quartz cuvettes. The graph below shows absorbance spectra for cuvettes of differentcomposition, where each cuvette only contained water. It is apparent that theplastic cuvettes become opaque in the ultraviolet, and that only the quartz cuvetteis useful below about 260 nm.

In addition to interference by the cuvette, buffer components may absorb. Disulfidebonds absorb at ~250 – 270 nm, which means that oxidized b-mercaptoethanol ordithiothreitol will interfere with some measurements of proteins. In addition, manybuffer components absorb light below 210 nm. Oxygen absorbance increases rapidlybelow 200 nm, and nitrogen absorbance is significant below 190 nm. Experimentsrequiring measurements below 200 nm are generally performed in an instrument

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 13

purged with nitrogen; measurements below 185 nm generally require instrumentscontaining a vacuum chamber.

Types of absorbance spectroscopic experiments:Absorbance spectroscopy is frequently used to measure concentration. According tothe Beer-Lambert law measurements of absorbance for molecules of known e allowcalculation of concentration. Alternatively, if the concentration of the absorbingspecies is known, the e can be determined.

Absorbance is used to determine properties of the chromophore, such as the dipolestrength. For proteins, because the chromophores are generally well characterized,absorbance spectroscopy is frequently used as a method for probing theenvironment around the chromophore. As an example, the absorbance spectra ofboth tryptophan and tyrosine change as a result of transfer from an organic to anaqueous environment.

This change is more apparent when difference spectra are measured.

Difference spectra are much more readily measured using dual beam instruments.

Protein spectroscopyThe peptide bond has a p ‡ p* transition with a maximum at 190 nm. It also has aforbidden n ‡ p* transition at 210-220 nm. Secondary structure can result incoupling of the dipoles, and somewhat altered spectra. However, many side-chainsalso absorb in this region, which makes interpretation difficult.

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 14

For proteins without prosthetic groups, the only absorbance beyond ~250 nm is dueto aromatic amino acids (and –S-S-, but these are fairly rare and have e of only~300).

Tyrosine undergoes a large red-shift when deprotonated; because the pKa oftyrosine is ~10.5 deprotonation is rare in native proteins. However, for proteins inhigh pH media, observation of spectral changes can yield information regarding thedegree of tyrosine side-chain solvent exposure.

The extinction coefficient of tryptophan and tyrosine are fairly insensitive toenvironment. The ∆e is usually ~100 for tyrosine and ~200 for tryptophan. Thismeans that the extinction coefficient for a protein can be calculated based on theamino acid content:

For proteins:

†

e280 =# Trp•5615+# Tyr •1380

Difference spectra can be used to assess binding of small molecules to the protein, orto assess the environment near aromatic residues.

Copyright © 1999 – 2003 by Mark Brandt, Ph.D. 15

Some prosthetic groups have characteristic differencespectra. An example is the carbon monoxide differencespectrum for cytochrome P450 enzymes. The spectral shift(shown at right) is the source of the name for the enzyme:the difference spectrum (protein with carbon monoxideminus protein without carbon monoxide) has a large positivepeak at 450 nm, although the absorbance peak is ~408 nm.

Spectroscopic probes can be attached to proteins. As anexample, 5, 5´-dithio-bis-(2-nitrobenzoic acid) (DTNB)changes its absorbance spectrum dramatically upon forminga disulfide bond to another molecule. It therefore can beused to measure the number of free cysteine sulfhydrylgroups in a protein.

S SNO2

NO2

OOH O

OH

5, 5´-dithio-bis -(2-nitrobenzoic acid) (DTNB)

Many compounds exhibit spectral changes. If a single chromophore within thecompound is changing its spectrum, the spectra will exhibit an isosbestic point,an unchanging point where the different spectra meet.

PhotochemistryThe excited state of many molecules has altered reactivity. An intense light sourcemay result in large numbers of molecules in excited states. If these moleculesdecompose or react with other molecules in solution, the absorbance spectrum willeventually change. This phenomenon is especially noticeable for very intense lightsources such as xenon arcs.