PART VII: MOLECULAR ABSORPTION SPECTROSCOPY, ULTRAVIOLET AND
VISIBLE (UV/VIS)
(Recommendations 1988)
(Originally prepared by K. Laqua, W.H. Melhuish, and M. Zander)
1. INTRODUCTION
This document, Part VII, is concerned with molecular absorption spectroscopy (UV/VIS).
In the IUPAC Manual of Symbols and Terminology for Physicochemical Quantities and Units,
2nd revision [Pure Appl. Chem., 51, 1-41 (1979)] section 2.8 deals with quantities related to
spectroscopy; see also IUPAC Manual "Quantities, Units and Symbols in Physical Chemistry"
1988 (pub.. for IUPAC by Blackwell Scientific Publications, Oxford 1988) pp. 22-28.
Molecular absorption spectroscopy in the ultraviolet (UV) and visible (VIS) is concerned with the
measured absorption of radiation in its passage through a gas, a liquid or a solid. The wavelength
region generally used is from 190 to about 1000 nm, and the absorbing medium is at room
temperature; however, in some cases measurements at temperatures above (e.g. in enzyme assays)
or below room temperature may be advantageous or necessary. This document is restricted to the
conventional means for measuring UV/VIS spectra, i.e. transmission of radiation as a function of
wavelength.
Not included in this document are terms relating to other methods for obtaining molecular spectra
such as by measuring reflectance or by the variation of radiant power (e.g. fluorescence,
phosphorescence) as a function of the excitation wavelength (excitation spectrum, see Part VI).
Similarly the measurement of the heat generated in the vicinity of absorbing molecules as a result
of the dissipation of excitation energy, which is a measure of the absorbed radiation, (photoacoustic
spectroscopy) is not included.
Although molecular absorption spectra are more meaningfully presented as a function of
wavenumber (cm-1), the more commonly used quantity is wavelength (nm) and this quantity will
accordingly be used for this document. Where wavenumber is used in special cases, this will be
indicated.
Many of the terms relating to instrumental factors in absorption spectroscopy are covered in Parts
I, III and VI.
2. FUNDAMENTALS OF MOLECULAR ABSORPTION SPECTROSCOPY (UV/VIS)
2.1 The UV/VIS absorption spectrum
Molecules which absorb photons of energy corresponding to wavelengths in the range 190 mm to
about 1000 nm exhibit UV /VIS absorption spectra. The quantized internal energy Eint of a
molecule in its electronic ground or excited state can be approximated, with sufficient accuracy
for analytical purposes, by
Eint = Eel + Evib + Erot (VII.1)
where Eel is the electronic, Evib the vibrational and Erot the rotational energy, respectively.
Absorption of a photon results in a change of the electronic energy accompanied by changes in
the vibrational and rotational energies. Each vibronic transition, i.e. a particular electronic plus
vibrational transition, corresponds to an absorption band consisting of rotational lines. In liquids
and solids the rotational lines are broad and overlap so that no rotational structure is
distinguishable.
The UV/VIS absorption spectrum of a molecular species is normally represented as a graph of
some characteristic for the radiation absorbed as a function of wavelength. The graph is
representative for that species, solvent, concentration and temperature. If a linear energy scale for
the abscissa is preferred, then wavenumber,
˜υ is used instead of wavelength, λ.
When the absorption of UV/VIS radiation by a solute is measured in a highly viscous or solid
matrix at low temperature (less than about 100 K) a low temperature UV/VIS absorption spectrum
results.
Highly structured spectra can be obtained when the UV/VIS absorption of a solute in certain
polycrystalline matrices (e.g. n-alkanes, cycloalkanes, inert gases such as rare gases) is measured
at low temperatures. For all spectra the solvent, solvent temperature and solute concentration
should be specified (see Note 1 ).
Direct recordings of these low temperature UV/VIS spectra are very useful for the identification
of compounds; they are less useful in quantitative analysis because of the difficulty in measuring
the true absorbance (see Section 2.2) of the sample, which usually exhibits high radiation
scattering.
2.2 The Beer-Lambert-Bouguer law
The Beer-Lambert-Bouguer law, generally called the Beer-Lambert law, may be written for a
single absorber either gaseous or in solution,
−log10
Φt
Φ0



 = − log10 τi = εcb = A
(VII.2)
where Φt is the monochromatic radiant power transmitted by the absorbing medium, Φ0 is the
monochromatic radiant power incident on the medium, τι is the internal transmittance (= Φt/Φ0),
ε is the molar (decadic) absorption coefficient, c is the amount concentration, b the absorption
path length and A the (decadic) absorbance. These terms and their preferred units have already
been defined in Parts I, III, and VI (Table VI.4).
Internal transmittance τι, i.e. transmittance of the medium itself disregarding boundary effects, has
to be distinguished from the total transmittance τ. The difference, which is mainly due to
reflection losses associated with cell windows, can be compensated by using matched cells ( see
Section 3.2.1).
Absorptance (or absorption factor) α is defined by α = 1 - τ where reflection is assumed to be
negligible.
The Beer-Lambert law holds only if the absorbing species behave independently of each other,
and if the absorption occurs in a uniform medium. Further, the incident radiation must be parallel,
monochromatic (see Note 2) and there should be no measurable saturation effect due to depletion
of the ground state molecules. Causes for deviations from the Beer-Lambert law are listed in
Section 7.
3. INSTRUMENTAL FACTORS
1 Terms such as Shpol'skii or quasi-linear spectra should not be used.
2 In practice parallel, monochromatic radiation is not always used. Convergence or divergence of the light beam as
found in practice, will cause only minor deviations from the Beer-Lambert law. Section 6.3 discusses errors due to
non-monochromatic radiation.
An instrument for measuring molecular absorption spectra ( UV/VIS) usually consists of a
radiation source, an optical system including a spectral apparatus, a sample compartment, a
radiation detector and a system for data acquisition and data processing. Means for amplitude
modulation and/or wavelength modulation may also be part of the instrument.
The classification of instruments according to single beam or double beam operation, recording,
non-recording etc. is covered in Part IX, which also contains definitions and nomenclature on
optical systems relevant to molecular absorption spectroscopy. Radiation detectors and
modulators are treated in Parts VI and XI. Part V (radiation sources) does not deal with sources
used in molecular spectroscopy. These will be covered in this section.
3.1 Radiation sources (see Note 3)
Pertinent factors relating to the properties of continuum radiation sources are
the spectral distribution defined as the variation of the spectral radiance Lλ, with
wavelength,
the maximum spectral radiance, Lλ(max) within the usable wavelength range,
the wavelength at this maximum, λmax,
the usable wavelength range, defined by the lower limit λl and the upper limit λu, at which
the spectral radiance is a specified fraction of Lλ(max).
Continuum sources are normally used for molecular absorption measurements, whereas spectralline
sources (see Part V) are employed for wavelength calibration of a spectrometer. Examples of
continuum sources commonly used are
tungsten-halogen lamps, which have a radiance temperature (see Part V) T of ~ 3000 K
and therefore have maximum spectral radiance at a wavelength of about 1.2 µm; they are
widely used in the visible and near ultraviolet spectral region (above 330 nm),
deuterium lamps (gas-discharge lamps) which emit strongly in the UV region below 330
nm; the continuous spectrum has deuterium atomic emission lines superimposed on it,
xenon arc lamps which give a continuum from below 190 nm to above 1000 nm.
Examples of spectral-line sources are
low-pressure mercury-discharge lamps, which are sometimes used for measuring
absorbances at fixed wavelengths. Such lamps are also useful for wavelength calibration,
Tunable lasers with and without frequency doubling and/or Raman shifting are high
intensity sources with narrow spectral bandwidths. Their use may enable the spectral
apparatus to be omitted. They may be either continuous (cw) or pulsed in nature.
3.2 Sample compartment
3.2.1 Liquid samples
Liquid samples are usually contained in sample cells which are placed in sample cell holders. Cell
holders may be heated or cooled in order to control the temperature of the liquid in the sample
cell.
The important characteristics of sample cells are,
cell shape (e.g. rectangular, cylindrical),
3 Radiative properties of sources should not be described by photometric units (e.g. candela m ) (see Part I).
absorption path length, b, defined as the length of the radiation path through the absorbing
medium; it is equal to the cell path length, l, in the case of single-pass cells at normal
incidence of radiation,
volume and cross section,
window material (window thickness and degree of deviation from parallelism of the
windows are also important).
A pair of cells with closely similar optical properties are called matched cells. One cell is the
sample cell while the other, the reference (or blank) cell contains the solvent or a reference
solution (see Section 4.4). In double beam spectrometers, radiation is passed either
simultaneously or alternately through the cells. In single beam instruments the cells are moved
sequentially into the radiation beam.
3.2.2 Gaseous samples.
Gases and vapours are measured in gas cells similar to those used for liquids. Generally the cell
pathlength is much greater. Gases at any pressure are contained in closed cells for measurement.
3.2.3 Solid samples.
Solid samples are held in solid-sample holders. When solid samples are measured, difficulties
may be experienced e.g. in matching the sample and reference pathlengths.
3.2.4 Special cells.
Low temperature cells are required for certain applications. These may include cooled cells,
thermally insulated cells, and cold-finger cells.
A stopped-flow cell comprises a small-volume absorption cell connected to a rapid mixing
chamber.
A multiple-pass cell is constructed in such a way that mirrors either form part of the cell or are
mounted in the sample cell holder. It permits multiple passage of radiation to increase the
absorption pathlength.
A continuous-flow cell allow the liquids (or gaseous) sample to pass through the cell continuously
while absorption measurements are made.
A variable pathlength cell is a cell whose pathlength can be varied either continuously or in steps
by means of spacers.
3.3 Data acquisition and data processing
The equipment used for data acquisition and data processing can be classified according to the
form of the information required. In the simplest case the output may present the transmittance or
absorptance in an analog or digital form. Further processing of the output signal enables various
functions of the original signal to be obtained. These include
• absorbance
• log absorbance
• averaged spectra (with enhanced signal-to-noise ratio)
• derivative spectra (see Section 4.6)
• with additional processing, background correction (see Section 4.3)
For the fast acquisition of data, a polychromator (see Part III) fitted with a detector that enables
spatial resolution, e.g. a vidicon tube or silicon photodiode array, (see Part XI) together with a
multichannel analyser may be used. The whole detection system is called an optical multichannel
analyser.
4. MEASURING TECHNIQUES
The sample type and the information required determine which of the various techniques
available will be used when conducting a molecular absorption analysis. The following are some
of the more important methods.
4.1 Qualitative analysis
The identification of an analyte may be achieved by comparing the absorption spectrum of the
unknown substance with graphs or tables of the spectra of known substances. In some cases two
or more analytes may be recognized.
4.2 Quantitative analysis
A known analyte can be determined by measuring the absorbance at one or more wavelengths
and using the Beer-Lambert law and the molar absorption coefficient to calculate its amount
concentration. If the concentration is expressed in other units (e.g. g/L) the corresponding specific
(decadic) absorption coefficient has to be used. Concentrations can also be determined from an
analytical function or analytical calibration curve where the latter is obtained by plotting the
measured absorbance of different reference solutions (or gases or solids) against their known
concentrations. A graph of absorbance against concentration is a straight line passing through the
origin if the Beer-Lambert law applies (see Section 7 for causes of deviations).
Multicomponent analysis of a mixture consisting of n absorbing analytes is possible provided the
Beer-Lambert law holds, by measuring the absorbance at k suitable wavelengths with k > n. For
each wavelength λ a (a = 1,2 ... k-l, k) the total absorbance is given by
A λa( )= b εi λa( )ci
i=1
n
∑
(VII.3)
where εi(λ a) is the molar (decadic) absorption coefficient of analyte i at the wavelength λ and ci
its molar concentration. The ratio A(λ a)/b is called linear (decadic) absorption coefficient. This
quantity is also called linear absorbance.
The concentrations of the n analytes may then be calculated from the k simultaneous equations.
4.3 Spectral background correction
The spectral background absorbance of a sample arising, for example, from the presence of an
impurity with a weak, broad absorption band, can be subtracted from the analyte absorbance by
graphical or algebraic methods when the spectral background absorbance is known. In practice,
however, this applies only when the spectral background absorbance varies in a simple way (e.g.
as a linear or quadratic function of wavelength; for other methods see Sections 4.5 and 4.6).
4.4 Difference absorption spectroscopy
A highly concentrated analyte in the analytical sample can be determined with better precision by
replacing the blank (reference) cell by one containing a solution of the analyte or other absorber
of known concentration (difference absorption spectroscopy). Difference spectra can also be
obtained by computer or other subtraction methods.
4.5 Double-wavelength spectroscopy
The effect of spectral background due to impurities, solvent or radiation scattering may be
reduced if the difference in the absorbances of a sample measured at two selected wavelengths is
obtained. This is often achieved by repetitively switching from one wavelength to the other.
Double-wavelength spectroscopy does this automatically by allowing two beams of radiation of
different wavelength to pass through the cell. One beam is fixed at a longer wavelength and the
other measures absorbance while being scanned over a limited wavelength range at shorter
wavelengths.
4.6 Derivative spectroscopy
The first (second, ...) derivative absorption spectrum of a molecule is defined as first (second, ...)
derivative, dA( ˜υ )/d ˜υ , (d2A( ˜υ )/d ˜υ 2, ...) of the absorbance A as a function of wavenumber ˜υ .
Wavelengths may be used in place of wavenumbers but the shape of the derivative spectra will be
slightly different. When derivative spectra are obtained at low temperature, they are called first
(second, ....) derivative low temperature absorption spectra, (specifying the solvent, temperature
and solute concentration).
Derivative spectra are usually obtained by digital differentiation or by wavelength modulation of
the radiation entering the sample cell. The wavelength modulation interval has to be much less
than the bandwidth of any absorption band in the spectrum. The derivative spectrum in terms of
wavenumber can be calculated from the spectrum in terms of wavelength by
dA ˜υ( ) d ˜υ = −λ
2
( )dA λ( ) dλ
(VII.4)
d2
A ˜υ( ) d ˜υ
2
= λ
4
( )d2
A λ( ) dλ2
+ 2λ3
dA λ( ) dλ
(VII.5)
The use of derivative spectroscopy decreases the signal-to-noise-ratio. However, it can improve
the detection of a sharp band in a broad background, or a narrow shoulder on a broad main band.
Also gradual changes in spectral background or source flux will be less pronounced in derivative
spectroscopy.
The first and second derivatives of the Beer-Lambert law are (assuming dΦ0/d ˜υ ≡ 0),
dΦt d˜υ
Φt
= −2.303cb
dε
d ˜υ (VII.6)
d2Φt d˜υ2
Φt
= 2.303cb
dε
d˜υ




2
− 2.303cb
d2ε
d ˜υ2
(VII.7)
Second derivative spectra are predominantly used in quantitative analysis.
The possible methods for the quantitative evaluation of derivative spectra are illustrated in Fig. 1
and are called tangent (Fig. la), peak-peak (Fig. lb) and peak-zero (Fig. lc) methods.
4.7 Absorbance matching
Absorbance matching is a procedure where the concentration of a known analyte may be
determined by diluting the sample with solvent until the absorbance matches the absorbance of a
known concentration of the analyte in the reference cell. This method is particularly useful if the
Beer-Lambert law does not hold.
5. FACTORS INFLUENCING PRECISION OF ABSORBANCE MEASUREMENTS
5.1 Random fluctuations
Random errors limit the precision of analysis (see Part II). When measuring very large or very
small absorbances, uncertainties due to random fluctuations become particularly large. To obtain
better precision in the absorption measurement it is necessary to adjust the sample concentration
or cell pathlength to bring the absorbance into the range 0.1 to 1.0. The theoretical minimum error
occurs at a best precision absorbance of about 0.43 for a spectrometer with a detector which is
thermal noise limited, e.g. phototube or photodiode; and of about 0.86 for a spectrometer with a
detector which is shot noise limited, e.g. photomultiplier.
5.2 Temperature effects
Temperature variations will to a greater or lesser extent affect all instrument functions. The
absorbance of the sample, as well as the sample factors considered in section 6.7, may also
depend on temperature. All of these effects give rise to temperature errors.
5.3 Inhomogeneous samples
Errors due to inhomogeneous distribution of absorbing species in the analytical sample are called
inhomogeneity errors. They may be observed by probing the sample volume with an incident
beam of radiation of reduced cross-section.
6. FACTORS INFLUENCING ACCURACY OF ABSORBANCE MEASUREMENTS
Accuracy, discussed in this section, refers to systematic errors which introduce bias in the
measurement. Additional measurements must be made before errors such as those specified below
can be detected and corrected.
6.1 Spectrometric factors
Any deviation from linearity of the response of the detector to the measured radiant power may
cause a non-linearity error.
If insufficient time is allowed for the reading to settle or if an absorption peak is scanned too
rapidly a settling error results.
If the two beams in a double-beam spectrometer are not fully equivalent in transmitted power nor
are corrected to be so, a base-line error occurs, e.g. due to unmatched cells.
6.2 Wavelength accuracy
If there is a difference between the (mean) wavelength of the radiation entering the sample cell
and the indicated wavelength on the spectrometer scale, an error in absorbance may occur. This
error is called a wavelength error.
6.3 Spectral bandwidth
To measure the true shape, particularly the true maximum of an absorption band, the spectral
bandwidth ∆λ of the instrument (see Part I) must be much less than the width of the absorption
band. A spectral bandwidth error results from using too large a bandwidth relative to the
absorption band being measured.
6.4 Stray radiation
A spectrometer set to pass radiation of a particular wavelength band always has a small amount of
stray radiation of other wavelengths. Since the sample may absorb more (or less) of this stray
radiation than of the radiation at the selected wavelength an error can occur. This error is called
stray radiation error.
6.5 Polarization (for definitions see Part IX)
The radiation leaving the monochromator will rarely be completely unpolarized. Polarization
errors may arise from the fact that the absorbance of a sample (especially a solid) could depend
on the polarization of the incident radiation and from the polarization dependent response of the
photodetector.
6.6 Optical beam effects
For wavelength-scanning spectrometers, an error may be introduced if the image position on the
photodetector changes. Reflection of the incident radiation, e.g. between the cell walls, is another
source of error and results in a measured absorbance slightly higher than the true absorbance.
These errors are collectively termed optical-beam errors.
6.7 Scattering
The presence of particulate matter, emulsions, micelles, etc. may cause radiation scattering. This
will result in further attenuation of the transmitted beam and the measured absorbance will be too
high. This error is called the scattering error.
6.8 Fluorescence effects
Some samples are excited to fluoresce by the incident radiation beam. Added to the transmitted
radiation beam, the fluorescence results in an erroneous reading, called the fluorescence error. It
is particularly noticeable if the photodetector is situated close to the sample.
6.9 Cell factors
An error in the measured absorbance of a sample can occur if the incident beam does not fall
perpendicularly to the windows of the cell, or if the cell windows are contaminated or have some
other imperfection. These factors result in cell errors.
6.10 Sample stability
The absorbance of some samples may change with time, e.g. as a result of photochemical
reaction, formation of aggregates or adsorption on the cell wall. Errors due to these changes are
called sample errors ( see Section 7).
Table X.1 Factors other than instrumental that influence absorption spectra
Factor Cause Information Process*
(1) concentration self-association association
equilibrium
constant
nA↔An (n ³ 2)
(2) pH acid/base (protolytic)
equilibrium
protonation
equilibrium
constant
A+H30+ ↔ AH+
+H20
(3) time thermal chemical
reaction
(including
solvolysis)
rates of reaction A -> B
(4) (radiant) power photochemical
reaction
rates of reaction
A
h ˜ν
 → B
photochromism equilibrium
constant and
reaction rates
A
h ˜ν
← → B
(5) presence of
component B
complex
formation
equilibrium
constant
A + B ↔ AB
(6) temperature thermochromism equilibrium
constant
A ↔ B
(7) solvent solute-solvent
interactions
transition type
* A and B are reacting species
7. FACTORS OTHER THAN INSTRUMENTAL THAT INFLUENCE ABSORPTION
SPECTRA
The main factors that may affect the absorption spectrum and often result in deviations from the
Beer-Lambert law are listed in Table X.1. These alterations in the spectrum may appear either as a
wavelength shift with little change in band shape, or as major alterations in band shape and
position. Often more than one of the factors listed below are relevant as causes for changes in
absorption spectra.
8. TERMS, SYMBOLS AND UNITS USED IN MOLECULAR ABSORPTION
SPECTROSCOPY
Term Symbol Practical Unit Notes
radiant energy Q J see Parts I and II
radiant power Φ = dQ/dt W see Part I
radiant intensity I W sr-1 see Parts I and II
spectral radiance Lλ(Bλ) W m-1 sr-1 nm-1
radiant power incident on absorbing
medium
Φ0 W
radiant power transmitted by
absorbing medium
Φt W
radiant power reflected by sample Φr W
radiant power absorbed by medium Φa W
transmittance or transmission factor τ 1 = Φt/Φ0
reflectance or reflection factor ρ 1 = Φr/Φ0
absorptance or absorption factor α 1 = 1-τ
internal transmittance τi 1
internal absorptance αi 1
(decadic) internal absorbance A 1 = -log10 τi
linear (decadic) absorption coefficient a, K cm-1 = A/b
molar (decadic) absorption coefficient ε L mol-1 cm-1 = A/(c b)
specific (decadic) absorption
coefficient
d L g-1 cm-1
molar concentration of absorber c mol L-1
wavelength λ nm
wavenumber ˜ν cm-1 = 1/λ
spectral bandwidth of spectrometer ∆λ nm see Part I
wavelength modulation interval ∆λmod nm wavenumber may also
be used
absorption pathlength b cm
cell pathlength l cm