Modern Raman Spectroscopy: A Practical Approach

Preface

Since the first edition of our book, there has been a huge expansion in the use of Raman spectroscopy. Advances in optics, electronics and data handling combined with improvements made by manufacturers and spectroscopists have made Raman scattering easier to record and more informative. Small, portable spectrometers are rugged, reliable and are becoming less expensive. Some can work powered by low‐voltage (1.5 V) batteries and give good performance in hostile environments. At the other end of the scale, advanced equipment is simpler, more sensitive, more flexible and more reliable. New methods with improved performance have been developed. As a result, a technique which was once labelled by some as lacking sensitivity can now, in the correct form, probe the electronic structure of a single molecule or be used to help in the diagnosis of cancer. This has attracted many more users into the field with a wide range of backgrounds.

Our aim in writing this book is to provide the understanding necessary to enable new users to apply the technique effectively. In the early chapters we provide basic theory and practical advice to enable the measurement and interpretation of Raman spectra with the minimum barrier to getting started. However, for those with a deeper understanding of the effect, Raman scattering is a very rich technique capable of providing unique information and a unique insight into specific problems. In writing this book some difficult choices have had to be made around the presentation of the theory, particularly with the wide variety of backgrounds we expect readers to possess. We have used as few equations as possible to show how the theory is developed and those are deliberately placed after the chapters on basic understanding. We concentrate on molecular polarizability, the molecular property which controls intensity. The equations are explained, not derived, so that those with little knowledge of mathematics can understand the conclusions reached and those of a more mathematical bent can use the framework for further investigation. This enables selection rules, resonance Raman scattering and some of the language in modern literature to be understood. This is not the traditional approach but, although deriving scattering theory from first principles is good for understanding, it adds little to Raman interpretation. Classical theory which does not use quantum mechanics cannot deliver the information required by most Raman spectroscopists. For these reasons, references to these areas are given but the theory is not explained.

Surface‐enhanced Raman scattering accounts for a significant fraction of the papers on Raman scattering and is employed in quite a few modern developments, so is given a full chapter. We finish with two chapters designed to enable the reader to come up to speed on the way Raman scattering is now applied in some of the main fields and to introduce the new techniques that are providing key insights and greater performance. Some of the new techniques are still expensive and therefore not so widely available but if the improvements continue, as is likely, they will become much more accessible. In any case the reader should be aware of their advantages.

One of the practical difficulties faced is in compliance with the IUPAC convention in the description of spectrum scales. The direction of the wavenumber shift should be consistent but this is not always the case in the literature. Further, Raman scattering is a shift from an exciting frequency and should be labelled Δcm−1 but it is common practice to use cm−1 with the delta implied. As far as possible we have used the format in which the user is most likely to record a spectrum or to see it in the literature. However, where we have used literature examples in this book, it is not possible to change these. We apologize to the purists who would prefer complete compliance with the IUPAC convention, but we have found that this is not practicable.

The authors hope that those who are just developing or reviving an interest in Raman spectroscopy will very quickly gain a practical understanding from the first two chapters. Furthermore, it is hoped that they will be inspired by the elegance and information content of the technique to delve further into the rest of the book, and explore the vast potential of the more sophisticated applications of Raman spectroscopy.

Acknowledgements

We thank professors Duncan Graham and Karen Faulds and members of the Centre for Molecular Nanometrology at Strathclyde University and some members of the older Raman group for supplying diagrams, the proprietors of the Analytical Sciences functions in Blackley, Manchester, UK for their use of facilities and permissions to publish material generated and our respective wives, Frances and Thelma, for putting up with us.

Chapter 1

Introduction, Basic Theory and Principles

1.1 INTRODUCTION

The main spectroscopies employed to detect vibrations in molecules are based on the processes of infrared absorption and Raman scattering. They are widely used to provide information on chemical structures and physical forms, to identify substances from the characteristic spectral patterns (‘fingerprinting’) and to determine quantitatively or semiquantitatively the amount of a substance in a sample. Samples can be examined in a whole range of physical states, for example, as solids, liquids, vapours, hot and cold, in bulk, as microscopic particles or as surface layers. The techniques are very wide ranging and provide solutions to a host of interesting and challenging analytical problems. Raman scattering is less widely used than infrared absorption, largely due to problems with sample degradation and fluorescence. However, recent advances in instrument technology have simplified the equipment and reduced the problems substantially. These advances, together with the ability of Raman spectroscopy to examine aqueous solutions, samples inside glass containers and samples without any preparation, have led to a rapid growth in the application of the technique.

Practically, modern Raman spectrometers are simple to use. Variable instrument parameters are few, spectral manipulation is minimal and a simple interpretation of the data may be sufficient. This chapter and Chapter 2 aim to set out the basic principles and experimental methods to give the reader a firm understanding of the basic theory and practical considerations so that the technique can be applied at the level often required for current applications. However, with Raman scattering important information is sometimes not used or recognised. Later chapters will develop the minimum theory required to give a more in‐depth understanding of the data obtained and to enable comprehension of some of the many more advanced techniques, which have specific advantages for some applications.

1.2 HISTORY

The phenomenon of inelastic scattering of light was first postulated by A. Smekal in 1923 [1] and first observed experimentally in 1928 by C.V. Raman and K.S. Krishnan [2]. Since then, the phenomenon has been referred to as Raman scattering. In the original experiment, sunlight was focused by a telescope onto a sample, which was either a purified liquid or a dust‐free vapour. A second lens was placed by the sample to collect the scattered radiation. A system of optical filters was used to show the existence of scattered radiation with an altered frequency from the incident light – the basic characteristic of Raman scattering.

1.3 BASIC THEORY

When light interacts with matter, the photons which make up the light may be absorbed or scattered or may not interact with the material and may pass straight through it. If the energy of an incident photon corresponds to the energy gap between the ground state of a molecule and an excited state, the photon may be absorbed and the molecule promoted to the higher energy excited state. It is this change which is measured in absorption spectroscopy by detection of the loss of that energy of radiation. However, it is also possible for the photon to interact with the molecule and scatter from it. In this case there is no need for the photon to have an energy which matches the difference between two energy levels of the molecule. The scattered photons can be observed by collecting them at an angle to the incident light beam. If there is no absorption from any electronic transition, which has a similar energy to that of the incident light, the scattering efficiency increases as the fourth power of the frequency of the incident light.

Scattering is a commonly used technique. For example, it is widely used as a method for measuring particle size and size distribution down to sizes less than 1 μm. One everyday illustration of this is that the sky is blue because the higher energy blue light is scattered from molecules and particles in the atmosphere more efficiently than the lower energy red light. However, for molecular identification, a small component of the scattered light, Raman scattering, is particularly effective.

The word ‘light’ implies electromagnetic radiation within the wavelength range to which the eye is sensitive whereas in spectroscopy, the important point is whether the detector is sensitive to the radiation used and as a consequence much wider ranges of wavelengths can be used. As a result, the process of absorption is used in a wide range of spectroscopic techniques. For example, it is used in acoustic spectroscopy where there is a very small energy difference between the ground and excited states and in X‐ray absorption spectroscopy where there is a very large difference. In between these extremes, many of the common techniques such as NMR, EPR, infrared absorption, electronic absorption and fluorescence emission and vacuum ultraviolet spectroscopy are based on the absorption of radiation. Figure 1.1 indicates the wavelength range of some commonly used types of radiation.

Figure 1.1. The electromagnetic spectrum on the wavelength scale.

Radiation is often characterised by its wavelength (λ). However, in Raman spectroscopy, we are interested in information obtained from the scattered radiation on the vibrational states of the molecule being examined. These are usually more conveniently discussed in terms of energy and consequently it is usual to use frequency (ν) or wavenumber (ϖ) scales, which are linearly related to energy. The relationships between these scales are given in the equations below.

(1.1) equation

(1.2) equation

and

(1.3) equation

It is clear from Eq. (1.1) that the energy is proportional to the reciprocal of wavelength and therefore the highest energy region is shown on the left side in Figure 1.1.

The energy changes we detect in vibrational spectroscopy are those required to cause nuclear motion but the way in which radiation is employed in infrared and Raman spectroscopies is different. In infrared spectroscopy, infrared energy covering a range of frequencies is directed onto the sample. Absorption occurs where the frequency of the incident radiation matches that of a vibration so that the molecule is promoted to a vibrational excited state. The loss of this frequency of radiation from the beam after it passes through the sample is detected. In contrast, Raman spectroscopy uses a single frequency of radiation to irradiate the sample. It is the radiation scattered from the molecule, one vibrational unit of energy different from the incident beam, which is detected. Thus, unlike infrared adsorption, Raman scattering does not require matching of the incident radiation to the energy difference between the ground and excited states.

In a scattering process, the light interacts with the molecule and distorts (polarizes) the cloud of electrons round the nuclei to form a short‐lived state called a virtual state discussed in Chapter 3. This state is not stable and the photon is quickly reradiated. If only the electron cloud is distorted in the scattering process, when the electron cloud returns to the starting position the photons are scattered with the same frequency as the incident radiation. This scattering process is regarded as elastic scattering and is the dominant process. For molecules, it is called Rayleigh scattering. However, if nuclear motion is induced during the scattering process, energy will be transferred either from the incident photon to the molecule or from the molecule to the scattered photon. In these cases, the process is inelastic and the energy of the scattered photon is different from the incident photon by one vibrational unit. This is Raman scattering. It is inherently a weak process in that only one in every 10⁶–10⁸ photons which scatter is Raman scattered. In itself this does not make the process insensitive since with modern lasers and microscopes very high‐power densities can be delivered to very small samples but it does follow that other possible processes such as sample degradation and fluorescence can occur readily.

Figure 1.2 shows the basic processes which occur for one vibration. At room temperature, most molecules, but not all, are present in the lowest energy vibrational level. The virtual states are not real states of the molecule but are created when the laser interacts with the electrons and causes polarization and the energy of these states is determined by the frequency of the light source used. The Rayleigh process will be the most intense process since most photons scatter this way. Since it does not involve any energy change, the diagram shows the light returning to the same energy state. The Raman scattering process from the ground vibrational state m leads to absorption of energy by the molecule and its promotion to the higher energy excited vibrational state n. This is called Stokes scattering. However, due to thermal energy, some molecules may be present initially in an excited state as represented by n in Figure 1.2. Scattering from these states to the ground state m is called anti‐Stokes scattering and involves transfer of energy from the molecule to the scattered photon. The relative intensities of the two processes depend on the population of the various states of the molecule and also on symmetry selection rules. The populations can be worked out from the Boltzmann equation (see Chapter 3) but at room temperature, the number of molecules expected to be in an excited vibrational state other than really low‐energy states will be small.

Figure 1.2. Diagram of the Rayleigh and Raman scattering processes. The lowest energy vibrational state m is shown at the foot with a state one vibrational unit in energy above it labelled n. Both the excitation energy (upward arrows) and the scattered energy (downward arrows) have much larger energies than the energy of a vibration. Two levels from the next highest electronic state are shown. Clearly with radiation of the frequency used, absorption of the exciting radiation would not occur. Rayleigh scattering also occurs from higher vibrational levels such as n.

Thus, compared to Stokes scattering, anti‐Stokes scattering will be weak and, in general, will become weaker the higher the energy of the vibration, due to the decreasing population of the excited vibrational states. Further, anti‐Stokes scattering will increase relative to Stokes scattering as the temperature rises [3]. Figure 1.3 shows a typical spectrum of Stokes and anti‐Stokes scattering from carbon tetrachloride separated by the intense Rayleigh scattering, which is off scale close to the point where there is no energy shift. Note that no signal is shown in the spectrum in the low‐frequency region because a filter has been added in front of the spectrometer to remove almost all light within about 200 cm−1 of the exciting line. Some breakthrough of the laser light can be seen where there is no energy shift at all.

Figure 1.3. Stokes and anti‐Stokes scattering for cyclohexane. To show the weak anti‐Stokes spectrum, the y‐axis has been extended in the inset.

Usually, Raman scattering is recorded only on the low‐energy side to give Stokes scattering but on occasion anti‐Stokes scattering is preferred. For example, where there is fluorescence interference this will occur at a lower energy than the excitation frequency and consequently anti‐Stokes scattering can be used to avoid interference. The difference in intensities of the bands in Stokes and anti‐Stokes scattering for any one vibration can also be used to measure the temperature.

Figure 1.2 illustrates one key difference between infrared absorption and Raman scattering. As described above, infrared absorption would involve direct excitation of the molecule from state m to state n by a photon of exactly the energy difference between them. In contrast, Raman scattering uses much higher energy radiation and measures the difference in energy between n and m by subtracting the scattered photon energy from that of the incident beam (the two vertical arrows in each case).

The cyclohexane spectrum in Figure 1.3 shows that there is more than one vibration which gives effective Raman scattering (i.e. is Raman active) and the nature of these vibrations will be discussed in the next section. However, there is a basic selection rule which is required to understand this pattern. Intense Raman scattering occurs from vibrations which cause a change in the polarizability of the electron cloud round the molecule. Usually symmetric vibrations cause the largest changes. This contrasts with infrared absorption where the most intense absorption is caused by a change in dipole and hence asymmetric vibrations which cause this are the most intense. As will be seen later not all vibrations of a molecule need, or in some cases can, be both infrared and Raman active and the two techniques usually give quite different intensity patterns. As a result, the two are often complementary and, used together, give a better view of the vibrational structure of a molecule.

One specific class of molecule provides an additional selection rule. In a centrosymmetric molecule, no band can be active in both Raman scattering and infrared absorption. This is sometimes called the mutual exclusion rule. In a centrosymmetric molecule, reflection of any point through the centre will reach an identical point on the other side (planar C2H4 is centrosymmetric, tetrahedral CH4 is not). This distinction is useful particularly for small molecules where a comparison of the spectra obtained from infrared absorption and Raman scattering can be used, for example, to differentiate cis and trans forms of a molecule.

Figure 1.4 shows a comparison of the infrared and Raman spectra for benzoic acid. The x axis is given in wavenumbers for which the unit is cm−1. Wavenumbers are not recommended SI units but the practice of spectroscopy is universally carried out using these and this is unlikely to change. For infrared absorption each peak represents an energy of radiation absorbed by the molecule. The y‐axis gives the amount of the light absorbed and is usually shown with the maximum absorbance as the lowest point on the trace. As is often the case, Raman scattering is presented in Figure 1.4 only as the Stokes spectrum and along the x‐axis each vibration is presented as the shift in energy from the energy of the laser beam. In this way the difference in energy between the ground and excited vibrational states for each vibration (n and m in Figure 1.2) is shown in the spectrum.

Figure 1.4. Infrared and Raman spectra of benzoic acid. The top trace is infrared absorption given in % transmission (%T) so that the lower the transmission value the greater the absorption. The lower trace is Raman scattering and the higher the peak the greater the scattering.

Strictly speaking, since Raman scattering is expressed as a shift in energy from that of the exciting radiation, it should be referred to as Δcm−1 but it is often expressed simply as cm−1. This practice is followed in this book for simplicity. The information of interest, to most users, is in the 3600–400 cm−1 (2.8–12 μm) range commonly used in infrared spectroscopy since this includes most modes, which are characteristic of a molecule. In some applications, much larger or smaller energy changes are studied and modern Raman equipment can cope with much wider ranges. One specific advantage of Raman scattering is that shifts down to about 100–200 cm−1 can easily be recorded and, with the correct equipment, much smaller shifts can be measured so that features such as lattice vibrations can be studied.

The intensities of the bands in the Raman spectrum are dependent on the nature of the vibration being discussed and on instrumentation and sampling factors. Modern instruments should be calibrated to remove the instrument factors but this is not always the case and these factors are dealt with in the next chapter. Sampling can have a large effect on the absolute intensities, band widths observed and band positions. Again these will be dealt with later. This chapter will set out a step‐by‐step approach to interpreting the Raman scattering from the set of vibrations present in a molecule without reference to instrumental or sampling factors.

1.4 MOLECULAR VIBRATIONS

If there is no change in electronic energy, for example, by absorption of a photon and the promotion of an electron to an excited electronic state, the energy of a molecule can be divided into a number of different parts or ‘degrees of freedom’. Three of these degrees of freedom are taken up to describe the translation of the molecule in space and three to describe rotational movement except for linear molecules where only two types of rotations are possible. The rest are vibrational degrees of freedom or in other words the total number of vibrations which could appear in a spectrum. Thus, if N is the number of atoms in a molecule, the number of vibrational degrees of freedom and therefore the number of vibrations possible is 3N − 6 for all molecules except linear ones where it is 3N − 5. For a diatomic molecule, this means there will be only one vibration. In a molecule such as oxygen, this is a simple stretch of the O─O bond. This will change the polarisability of the molecule but not the dipole moment since there is no dipole in the molecule and the vibration is symmetric about the centre. Thus, the selection rules already discussed would predict, and it is true, that oxygen gas will give a band in the Raman spectrum and no bands in the infrared spectrum. However, in a molecule such as nitric oxide, NO, there will be only one band but, since there is both a dipole change and a polarizability change, it will appear in both the infrared and Raman spectrum.

A triatomic molecule will have three modes of vibration. They are a symmetrical stretch, a bending or deformation mode and an anti‐symmetrical (often referred to as asymmetrical stretch, as shown). Figure 1.5 shows these for water (H2O) and carbon dioxide (CO2).

Figure 1.5. Spring and ball models for three modes of vibration for H2O and CO2.

These diagrams use ‘spring and ball’ models. The spring represents the bond or bonds between the atoms. The stronger the bond the higher the frequency. The balls represent the atoms and the heavier they are the lower the frequency. The expression which relates the mass of the atoms and the bond strength to the vibrational frequency is Hooke’s law, which is dealt with in Chapter 3, but for the present, it is clear that strong bonds and light atoms will give higher frequencies of vibration and heavy atoms and weak bonds will give lower ones.

This simple approach of estimating the likely frequencies of a vibration based on the atoms and the nature of the bonds is widely used to interpret vibrational spectra and is backed up by an extensive literature which has enabled the frequency range in which common vibrations are likely to appear has been defined. However, the intensities of the bands are also important. The molecule actually exists as a three‐dimensional structure with a pattern of varying electron density covering the whole molecule. A simple depiction of this for the carbon dioxide and water molecules is shown in Figure 1.6. When the molecule is vibrating, the electron cloud will alter as the positive nuclei change position and depending on the nature of the change this can cause a change of dipole moment or polarization.

Figure 1.6. Electron cloud model of water and carbon dioxide.

In these triatomic molecules, the symmetrical stretch causes large polarization changes and hence strong Raman scattering with weak or no dipole change and hence weak or no IR absorption. The deformation mode causes a dipole change but little polarisation change and hence strong IR absorption and weak or nonexistent Raman scattering. However, it should be noted that from the 3N − 5 rule there should be four vibrations. There are two bending modes, only one of which has been illustrated. Figure 1.7 illustrates the vibrations possible for carbon disulphide along with the corresponding IR absorption and Raman scattering spectra.

Figure 1.7. Dipole and polarisation changes in carbon disulphide, with resultant infrared and Raman spectra.

Source: Reprinted from Fadini, A. and Schnepel, F.‐M. (1989). Vibrational Spectroscopy: Methods and Applications. Chichester: Ellis Horwood Ltd [4].

Although this type of analysis is suitable for small molecules, it is more difficult to apply in a more complex molecule. Figure 1.8 shows one vibration from a dye in which a large number of atoms are involved. This is obtained from a theoretical calculation using density functional theory (DFT), which is discussed briefly later. It probably gives a depiction of the vibration, which is close to the truth. However, even if it were possible to calculate the spectrum of every molecule quickly in the laboratory, which at present it is not, this type of diagram is only of limited utility to the spectroscopist. A comparison between molecules of similar type is difficult unless a full calculation is available for all of them and each subtle change in the nuclear displacements is drawn out or accurately described for each