# Spectroscopy

Analysis of white light by dispersing it with a prism is an example of spectroscopy.

Spectroscopy is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, by a prism. Later the concept was expanded greatly to comprise any interaction with radiative energy as a function of its wavelength or frequency.

## Absorption spectroscopy

Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs energy, i.e., photons, from the radiating field. The intensity of the absorption varies as a function of frequency, and this variation is the absorption spectrum.

Absorption spectroscopy is employed as a tool to determine the presence of a particular substance in a sample and, in many cases, to quantify the amount of the substance present. Infrared and ultraviolet-visible spectroscopy are particularly common in analytical applications. Absorption spectroscopy is also employed in studies of molecular and atomic physics, astronomical spectroscopy and remote sensing.

There are a wide range of experimental approaches to measuring absorption spectra. The most common arrangement is to direct a generated beam of radiation at a sample and detect the intensity of the radiation that passes through it. The transmitted energy can be used to calculate the absorption. The source, sample arrangement and detection technique vary significantly depending on the frequency range and the purpose of the experiment.

An overview of electromagnetic radiation absorption.

Absorption lines are typically classified by the nature of the quantum mechanical change induced in the molecule or atom. Rotational lines, for instance, occur when the rotational state of a molecule is changed. Rotational lines are typically found in the microwave spectral region. Vibrational lines correspond to changes in the vibrational state of the molecule and are typically found in the infrared region. Electronic lines correspond to a change in the electronic state of an atom or molecule and are typically found in the visible and ultraviolet region. X-ray absorptions are associated with the excitation of inner shell electrons in atoms. These changes can also be combined (e.g. rotation-vibration transitions), leading to new absorption lines at the combined energy of the two changes.

The energy associated with the quantum mechanical change primarily determines the frequency of the absorption line but the frequency can be shifted by several types of interactions. Electric and magnetic fields can cause a shift. Interactions with neighboring molecules can cause shifts. For instance, absorption lines of the gas phase molecule can shift significantly when that molecule is in a liquid or solid phase and interacting more strongly with neighboring molecules.

### Beer–Lambert law

The Beer–Lambert law relates the attenuation of light to the properties of the material through which the light is traveling.

As light passes through a sample, its intensity decreases. This decrease is proportional to the concentration c of the substance, the intensity I and a constant termed ε':

${\displaystyle {\frac {\mathit {dI}}{\mathit {dx}}}=-\mathrm {\epsilon } {\text{'}}\cdot c\cdot I}$

this equals

${\displaystyle {\frac {\mathit {dI}}{I}}=-\mathrm {\epsilon } {\text{'}}c{\mathit {dx}}}$

and can be integrated

${\displaystyle {\underset {{I}_{0}}{\overset {I}{\int }}}{\frac {1}{I}}{\mathit {dI}}={\underset {{x}_{0}}{\overset {x}{\int }}}-\mathrm {\epsilon } {\text{'}}c{\mathit {dx}}}$
${\displaystyle \ln \left({\frac {I}{{I}_{0}}}\right)=-\mathrm {\epsilon } {\text{'}}c\left(x-{x}_{0}\right)}$

The path length x-x0 is commonly referred to as d. The equation can be transformed into an exponential function which describes the decrease of the intensity as light passes through a sample:

${\displaystyle I={I}_{0}{e}^{-\mathrm {\epsilon } {\text{'}}cd}}$

Exchanging the natural for the decadic logarithm in the previous equation results in the common form of the Beer-Lambert law

${\displaystyle E={\mathit {\lg }}\left({\frac {{I}_{0}}{I}}\right)=\mathrm {\epsilon } \cdot c\cdot d}$

where ε is the molar attenuation coefficient. This coefficient is a measurement of how strongly a chemical species absorbs light at a given wavelength. The SI units for ε are m2/mol, but in practice, they are usually taken as M−1 cm−1 or L mol−1 cm−1. In older literature, cm2 mol−1 is sometimes used with corresponding values 1000 times larger.

In biochemistry, the extinction coefficient of a protein at 280 nm depends almost exclusively on the number of aromatic residues, particularly tryptophan, and can be predicted from the sequence of amino acids. If the extinction coefficient is known, it can be used to determine the concentration of a protein in solution. When there is more than one absorbing species in a solution, the overall absorbance is the sum of the absorbances for each individual species.

Absorption maximum / nm ε / M-1 cm-1
Peptide bond 190 7000
215 100
Tryptophan 280 5600
Tyrosine 275 1500
Phenylalanine 250 220
Disulfide 250 300

### Measurement setup

A spectrophotometer.

The instrument used in ultraviolet-visible spectroscopy is called a UV/Vis spectrophotometer. The basic parts of a spectrophotometer are a light source, a holder for the sample, a diffraction grating in a monochromator or a prism to separate the different wavelengths of light, and a detector. The radiation source is often a deuterium arc lamp, which is continuous over the ultraviolet region (190-400 nm), a Xenon arc lamp, or more recently, light emitting diodes (LED) for the visible wavelengths. The detector is typically a photomultiplier tube, a photodiode, a photodiode array or a charge-coupled device (CCD). Single photodiode detectors and photomultiplier tubes are used with scanning monochromators, which filter the light so that only light of a single wavelength reaches the detector at one time. The scanning monochromator moves the diffraction grating to "step-through" each wavelength so that its intensity may be measured as a function of wavelength. Fixed monochromators are used with CCDs and photodiode arrays. As both of these devices consist of many detectors grouped into one or two dimensional arrays, they are able to collect light of different wavelengths on different pixels or groups of pixels simultaneously.

Schematic of a double-beam UV/Vis spectrophotometer.

There are two major classes of devices: single beam and double beam. A double beam spectrophotometer compares the light intensity between two light paths, one path containing a reference sample and the other the test sample. A single-beam spectrophotometer measures the relative light intensity of the beam before and after a test sample is inserted.

A disposable, plastic cuvette.

Samples for UV/Vis spectrophotometry are most often liquids, although the absorbance of gases and even of solids can also be measured. Samples are typically placed in a transparent cell, known as a cuvette. Cuvettes are typically rectangular in shape, commonly with an internal width of 1 cm. (This width becomes the path length d in the Beer-Lambert law.) The type of sample container used must allow radiation to pass over the spectral region of interest. The most widely applicable cuvettes are made of high quality fused silica or quartz glass because these are transparent throughout the UV, visible and near infrared regions. Glass and plastic cuvettes are also common, although glass and most plastics absorb in the UV, which limits their usefulness to visible wavelengths.

The following tools can be used to calculate the molar attenuation coefficient of a protein:

## Circular dichroism

Circular dichroism in nature: The rose chafer's external surface reflects almost only left circularly polarized light.

Circular dichroism (CD) is dichroism involving circularly polarized light, i.e., the differential absorption of left- and right-handed light. Left-hand circular (LHC) and right-hand circular (RHC) polarized light represent two possible spin angular momentum states for a photon. This phenomenon is exhibited in the absorption bands of optically active chiral molecules. CD spectroscopy has a wide range of applications. Most notably, UV CD is used to investigate the secondary structure of proteins.

CD is closely related to the optical rotatory dispersion (ORD) technique, and is generally considered to be more advanced. CD is measured in or near the absorption bands of the molecule of interest, while ORD can be measured far from these bands. CD's advantage is apparent in the data analysis. Structural elements are more clearly distinguished since their recorded bands do not overlap extensively at particular wavelengths as they do in ORD. In principle these two spectral measurements can be interconverted through an integral transform, if all the absorptions are included in the measurements.

### Physical principles

Electromagnetic radiation consists of an electric (E) and magnetic (B) field that oscillate perpendicular to one another and to the propagating direction, a transverse wave. While linearly polarized light occurs when the electric field vector oscillates only in one plane, circularly polarized light occurs when the direction of the electric field vector rotates about its propagation direction while the vector retains constant magnitude. At a single point in space, the circularly polarized-vector will trace out a circle over one period of the wave frequency, hence the name. The two diagrams below show the electric vectors of linearly and circularly polarized light, at one moment of time, for a range of positions; the plot of the circularly polarized electric vector forms a helix along the direction of propagation (k). For left circularly polarized light (LCP) with propagation towards the observer, the electric vector rotates counterclockwise. For right circularly polarized light (RCP), the electric vector rotates clockwise.

When circularly polarized light passes through an absorbing optically active medium, the speeds between right and left polarizations differ as well as their wavelengthand the extent to which they are absorbed (εL≠εR). Circular dichroism is the difference Δε ≡ εL- εR.

Effect of a circular dichroism on a left- or right-handed circularly polarized wave.

Simply put, since circularly polarized light itself is "chiral", it interacts differently with chiral molecules. That is, the two types of circularly polarized light are absorbed to different extents. In a CD experiment, equal amounts of left and right circularly polarized light of a selected wavelength are alternately radiated into a (chiral) sample. One of the two polarizations is absorbed more than the other one, and this wavelength-dependent difference of absorption is measured, yielding the CD spectrum of the sample. Due to the interaction with the molecule, the electric field vector of the light traces out an elliptical path after passing through the sample.

Elliptical polarized light (violet) is composed of unequal contributions of right (blue) and left (red) circular polarized light.

It is important that the chirality of the molecule can be conformational rather than structural. That is, for instance, a protein molecule with a helical secondary structure can have a CD that changes with changes in the conformation.

By definition,

${\displaystyle \mathrm {\Delta } A={A}_{L}-{A}_{R}}$

where ΔA is the difference between absorbance of left circularly polarized (LCP) and right circularly polarized (RCP) light (this is what is usually measured). ΔA is a function of wavelength, so for a measurement to be meaningful the wavelength at which it was performed must be known.

The molar circular dichroism is defined as

${\displaystyle \mathrm {\Delta } \mathrm {\epsilon } ={\mathrm {\epsilon } }_{L}-{\mathrm {\epsilon } }_{R}}$

where εL and εR are the molar extinction coefficients for LCP and RCP light.

Although ΔA is usually measured, for historical reasons most measurements are reported in degrees of ellipticity. Molar ellipticity is circular dichroism corrected for concentration. Molar circular dichroism and molar ellipticity, [θ], are readily interconverted by the equation:

${\displaystyle \mathrm {\theta } =3298.2\mathrm {\Delta } \mathrm {\epsilon } }$

In many practical applications of circular dichroism (CD), the measured CD is not simply an intrinsic property of the molecule, but rather depends on the molecular conformation. In such a case the CD may also be a function of temperature, concentration, and the chemical environment, including solvents. In this case the reported CD value must also specify these other relevant factors in order to be meaningful.

### Application to biological molecules

The far-UV (ultraviolet) CD spectrum of proteins can reveal important characteristics of their secondary structure. CD spectra can be readily used to estimate the fraction of a molecule that is in the alpha-helix conformation, the beta-sheet conformation, the beta-turn conformation, or some other (e.g. random coil) conformation. These fractional assignments place important constraints on the possible secondary conformations that the protein can be in. CD cannot, in general, say where the alpha helices that are detected are located within the molecule or even completely predict how many there are. Despite this, CD is a valuable tool, especially for showing changes in conformation. It can, for instance, be used to study how the secondary structure of a molecule changes as a function of temperature or of the concentration of denaturing agents, e.g. Guanidinium chloride or urea. In this way it can reveal important thermodynamic information about the molecule (such as the enthalpy and Gibbs free energy of denaturation) that cannot otherwise be easily obtained. Anyone attempting to study a protein will find CD a valuable tool for verifying that the protein is in its native conformation before undertaking extensive and/or expensive experiments with it. Also, there are a number of other uses for CD spectroscopy in protein chemistry not related to alpha-helix fraction estimation.

The near-UV CD spectrum (>250 nm) of proteins provides information on the tertiary structure. The signals obtained in the 250–300 nm region are due to the absorption, dipole orientation and the nature of the surrounding environment of the phenylalanine, tyrosine, cysteine (or S-S disulfide bridges) and tryptophan amino acids. Unlike in far-UV CD, the near-UV CD spectrum cannot be assigned to any particular 3D structure. Rather, near-UV CD spectra provide structural information on the nature of the prosthetic groups in proteins, e.g., the heme groups in hemoglobin and cytochrome c.

Visible CD spectroscopy is a very powerful technique to study metal–protein interactions and can resolve individual d–d electronic transitions as separate bands. CD spectra in the visible light region are only produced when a metal ion is in a chiral environment, thus, free metal ions in solution are not detected. This has the advantage of only observing the protein-bound metal, so pH dependence and stoichiometries are readily obtained.

CD gives less specific structural information than X-ray crystallography and protein NMR spectroscopy, for example, which both give atomic resolution data. However, CD spectroscopy is a quick method that does not require large amounts of proteins or extensive data processing. Thus, CD can be used to survey a large number of solvent conditions, varying temperature, pH, salinity, and the presence of various cofactors.

Upper panel: Circular dichroism spectrometry in the ultraviolet wavelength region (UV-CD) of MBP-cytochrome b6 fusion protein in different detergent solutions. It shows that the protein in DM, as well as in Triton X-100 solution, recovered its structure. However the spectra obtained from SDS solution shows decreased ellipticity in the range between 200–210 nm, which indicates incomplete secondary structure recovery. Lower panel: The content of secondary structures predicted from the CD spectra using the CDSSTR algorithm. The protein in SDS solution shows increased content of unordered structures and decreased helices content.

### Experimental limitations

CD spectroscopy is usually used to study proteins in solution, and thus it complements methods that study the solid state. This is also a limitation, in that many proteins are embedded in membranes in their native state, and solutions containing membrane structures are often strongly scattering.

Measurement of CD is complicated by the fact that typical aqueous buffer systems often absorb in the range where structural features exhibit differential absorption of circularly polarized light. Phosphate, sulfate, carbonate, and acetate buffers are generally incompatible with CD unless made extremely dilute, e.g. in the 10–50 mM range. The Tris buffer system should be completely avoided when performing far-UV CD. Borate and Onium compounds are often used to establish the appropriate pH range for CD experiments. Some experimenters have substituted fluoride for chloride ion because fluoride absorbs less in the far UV, and some have worked in pure water. Another, almost universal, technique is to minimize solvent absorption by using shorter path length cells when working in the far UV, 0.1 mm path lengths are not uncommon in this work.

In addition to measuring in aqueous systems, CD, particularly far-UV CD, can be measured in organic solvents e.g. ethanol, methanol or trifluoroethanol (TFE). The latter has the advantage to induce structure formation of proteins, inducing beta-sheets in some and alpha helices in others, which they would not show under normal aqueous conditions. Most common organic solvents such as acetonitrile, THF, chloroform, dichloromethane are however, incompatible with far-UV CD.

It may be of interest to note that the protein CD spectra used in secondary structure estimation are related to the π to π* orbital absorptions of the amide bonds linking the amino acids. These absorption bands lie partly in the so-called vacuum ultraviolet (wavelengths less than about 200 nm). The wavelength region of interest is actually inaccessible in air because of the strong absorption of light by oxygen at these wavelengths. In practice these spectra are measured not in vacuum but in an oxygen-free instrument (filled with pure nitrogen gas).