Abstract
Modern Raman spectroscopy covers several noninvasive reflection techniques for identification of molecules and investigation of molecular properties. All are based on the Raman effect, occurring when polarized laser light is inelastically scattered by a molecular sample. Vibrational Raman spectroscopy is the Raman technique most widely used in chemical analysis, and it is relevant for the characterization of molecules in solution, biomolecules, and solids (crystals and powders). In this chapter vibrational Raman spectroscopy is discussed under the headline: “What is vibrational Raman spectroscopy: a vibrational or an electronic spectroscopic technique, or both?” The answer to this question is gained through a discussion of different scattering situations, and it is demonstrated that the Raman technique is more than an alternative technique to infrared and near-infrared absorption spectroscopy. Starting with the Kramers-Heisenberg equation, the answer is obtained through a discussion of: State tensors and Raman tensors, non-resonance and resonance Raman scattering (RRS) excited with a single laser wavelength, and unpolarized and polarization-resolved RRS excited with variable laser wavelengths (RADIS), dispersive Raman vibrations as a tool for noninvasive detection of molecular color changes and that RADIS data are automatically born as three-dimensional multivariate data with high information contents.
Keywords
- Raman
- resonance Raman
- RADIS
- polarization dispersion
- state tensor
- Raman tensor
- noninvasive
1. Introduction
Modern Raman spectroscopy is a class of well-documented, noninvasive, optical reflection techniques with a high spectral resolution applicable for the identification of molecules and investigation of molecular properties. All are based on the Raman effect, discovered by Raman in 1928 [1, 2]. Today more than 25 different Raman spectroscopic techniques are known [3]. The Raman effect occurs when light is inelastically scattered by a molecular sample.
Originally Raman and Krishnan observed the scattering of spectrally filtered sunlight from a liquid and found that the scattered light contained very week components of light, which had slightly different frequencies compared to the frequency of the incoming light. In a description of the scattering process based on quantum mechanics, the appearance of the shifted frequencies in the Raman scattered light is interpreted in the way that the molecules have shifted quantum state during the process. The shifted frequencies appear symmetrically around the frequency of the exciting light, from which one can conclude that the molecule may either be excited or de-excited during the scattering process. The last requires that the molecules have been excited (e.g., thermally) before the scattering event. This is termed anti-Stokes scattering, while the scattering where the molecules are excited during the process is termed Stokes scattering. The molecules may either shift rotational, vibrational, or electronic state during the scattering, depending on the molecule and the specific experimental conditions.
The spectroscopic technique based on Raman scattering, where the molecules shift vibrational state, is termed vibrational Raman spectroscopy. A vibrational Raman spectrum contains the unique and highly resolved vibrational signature of the scattering molecule. Normally only the Stokes part of the entire spectrum is measured, since this is more intense than the anti-Stokes part [3]. Vibrational Raman spectroscopy is the Raman technique most widely used in chemical analysis, and it is relevant for the investigation of molecules in solution, biomolecules, and solids (crystals and powders). Since the Raman technique can be performed as a reflection measurement, which requires no or very little sample preparation, it is well suited for the investigation of molecules in their natural environment such as in the food industry and in medical and environmental applications.
Nowadays vibrational Raman spectra are measured by illuminating the sample with polarized laser light with wave numbers either in the near-infrared (NIR), the visible (VIS), or the ultraviolet (UV) and simultaneously monitoring the reflected light. A vibrational Raman spectrum is then obtained by considering the intensity distribution in the Raman scattered light as a function of the so-called Raman shift
Ever since the discovery of the Raman effect in 1928, the Achilles heel of Raman spectroscopy has been the low Raman cross section where typically
The development of sensitive charge-coupled devices (CCD-detectors) [6, 7]
The development of interference filters, i.e., notch and edge filters
Not before the implementation of these three improvements could Raman spectroscopy really compete with the competing spectroscopic techniques IR, NIR, and UV/VIS.
A challenge particular in in situ resonance Raman investigations of biomolecules is that the excitation of the resonance Raman process is followed by a simultaneous excitation of fluorescence in either the molecule under investigation or in other molecules present in the sample. Since in general the fluorescence cross section is much larger than the Raman cross section, the Raman peaks typically ride on top of the spectrally broad fluorescence background so that it can be time-consuming to determine the true Raman intensity. Sometimes a part of the Raman spectrum may even be hidden behind the fluorescence. However, in most situations the influence from fluorescence may be taken care of by changing the laser wave number to NIR or to UV, by applying a fluorescence quenching technique [8], by applying a pulsed detection technique, or by implementing advanced signal processing including multivariate analysis.
In the present chapter vibrational Raman spectroscopy is discussed under the headline: “What is vibrational Raman spectroscopy: a vibrational or an electronic spectroscopic technique, or both?” Besides giving an answer to this question, the goal of the chapter is twofold: (1) to improve the readers’ understanding of Raman scattering in general and (2) to demonstrate which kind of molecular information one may achieve by choosing different experimental conditions.
Before we begin the discussion, it should be noticed that Raman spectroscopy, like any kind of molecular spectroscopy, can be applied in two different ways: (1) as an analytical technique for the identification and quantification of molecules in a sample and (2) as a technique for studying the physical and chemical properties of molecules. In the first kind of application, the Raman signal is just considered as a source of data, which has to be compared with spectroscopic databases or which has to be combined with the chemometric method being most appropriate for the problem to be solved. For this kind of application, no knowledge of Raman theory and how the theory is applied to molecules is really needed. But it should be noticed that to decide how the chemometrics should be applied together with the Raman data, one must take into account that vibrational Raman spectra are in general characterized by exhibiting high spectral resolution (narrow and well-separated lines) compared to the broader bands typically found in IR and in particular in UV/VIS spectra. For the second kind of applications, a deeper understanding of molecular physics and molecular Raman theory is needed.
2. Some fundamentals of Raman theory
2.1 General theory
A unified treatment of Raman theory can be found in [9, 10] and in [3], where in the last reference a long list of references to the Raman literature is provided. The symmetry aspects, interference phenomena, and polarization properties of resonance Raman scattering have been discussed by Mortensen and Hassing [11] and by Schweitzer-Stenner [12], while the vibronic aspects has been discussed by Siebrand and Zgierski [13].
Raman scattering can be described as a coherent absorption-emission sequence in which a primary photon with wave number
The basic equation for the theoretical description of Raman scattering is the famous Kramers-Heisenberg (KH) dispersion relation. Kramers and Heisenberg derived the equation by the application of the correspondence principle to the classical dispersion relation. The KH equation expresses the transition probability per second for Raman scattering [14]. The original version did not contain the damping of the scattering system, and thus it did not immediately apply to resonance Raman scattering. Later Weisskopf modified the equation by introducing the damping of the atomic and molecular states with the assumption of an exponential decay of the excited states [15]. Within a modern theoretical framework, the KH relation and the expression for the intensity of the Raman scattered light can be derived by using formal scattering theory [16] or time-dependent second-order perturbation theory. In perturbation theory the interaction energy between the molecule and radiation field, normally considered in the electric dipole approximation, is used as the perturbation, when the time-dependent Schrödinger equation for the total system and molecule plus electromagnetic field is solved (e.g., see [17]).
The basic scattering equations are collected in Eq. (1). The transition probability is expressed through the total differential scattering cross section
In the expression for the Raman tensor in Eq. (1),
It follows from Eq. (1) that all the molecular states contribute to the intensity of the specific Raman transition
The state tensor determines the contribution to the scattering from that particular state.
The Raman tensor now becomes
The introduction of the state tensor is more important in RRS, where only relative few states contribute significantly to the Raman intensity than in RS, where all molecular states contribute with the result that the information of their individual contributions is blurred.
One advantage of introducing the state tensor is that it is possible to evaluate the general form of the state tensor in cases, where the symmetry of the molecule is known. First, we notice that when the molecule has no symmetry, the state tensors are determined exclusively by the physical properties of the specific molecule considered, and all state tensor components may a priori be nonvanishing. The same holds for the Raman tensor, since it is a superposition of state tensors scaled with the associated energy factors. However, when the molecule exhibits some symmetry, the state tensors will be determined both by the physics and by the constraints imposed by the symmetry. The consequence of the symmetry is that some tensor components vanish. When the symmetry gets higher, the number of vanishing state tensor components increases. It is also important to notice that the structure of each state tensor contributing to a specific Raman transition can be different and different from the structure of the Raman tensor. This is because the state tensors are determined by the symmetry and the physical properties of the individual states, which contribute to the scattering, while the Raman tenor is a superposition of the state tensors. As we shall see later, this is particularly important in resonance Raman scattering of molecules containing a chromophore with high symmetry such as the molecules containing the heme group.
Traditionally the symmetry of a molecule with well-defined configuration has been described by using point groups and group representation theory, and from the early days of quantum physics, this has been used to derive selection rules, i.e., to give the conditions under which a particular matrix element must vanish. In spectroscopy the symmetry-based selection rules determine when a transition does not appear in the spectrum, i.e., it is a symmetry-forbidden transition.
In cases where the molecular point group has a threefold rotation axis or axes of higher order, one must, however, as demonstrated in [11] and by Mortensen in [19], apply the so-called non-commuting generator (NCG) approach to molecular symmetry in order to be able to evaluate the general form of the state tensors. In [19] the NCG approach is explained in detail, while in [11] it is shown how the method can be applied to calculate the structure of the state tensors both for molecules with integer and half integer spin. Besides all the possible state tensors for molecules with integer spin in the most important point groups have been evaluated and collected as an appendix. The appendix containing the state tensors is also reproduced in [3].
Recently [20] the NCG method has been extended and applied to develop the state and Raman tensors for molecular aggregates. Specifically the tensors for the H-type dimer of two coupled monomers with
2.2 Polarization properties of Raman scattering
The polarization is a unique property of Raman scattering, which distinguishes the Raman technique from the UV/VIS and IR spectroscopy. In general, the polarization of the Raman scattered light is different from the polarization of the incoming laser light. This property is valid for oriented molecules (crystals), but perhaps more surprisingly, it is also valid for randomly oriented molecules like molecules in solutions and in powders. The reason for this is that the Raman process is controlled by a tensor (the Raman tensor) and not by a vector (the electric dipole vector) like in UV/VIS and IR absorption. While a vector only has one quantity, namely, its length, which is not changed (invariant) under rotation of the molecules, a tensor of rank 2 has three combinations of the nine tensor components, which are invariant to rotation. In the Raman case, these are called the rotational invariants of the Raman tensor, and they are denoted as
In polarization-resolved Raman experiments, two spectra are measured from which the parallel
The polarization properties in Raman scattering are expressed through the depolarization ratio (DPR) defined as
The polarization-resolved Raman measurements are illustrated in Figure 1, which shows the 180° scattering geometry (reflection measurement) being the geometry mostly used. The molecule (M) is placed in the center of a space-fixed coordinate system, and the laser light, which is linearly polarized along the
where
2.3 Vibronic expansion of the state and Raman tensors
From the beginning of the history of Raman spectroscopy, it has been an important task to transform the basic and general scattering expressions into a form suitable for the interpretation of experimental Raman data. It follows from Eq. (1) that an important problem is that the calculation of the Raman intensity involves a summation over all molecular states, which are not known. Another problem is that in a molecule, the motions of the electrons and nuclei are not independent, which means that the functions describing the molecular states depend upon coordinates defining the positions of both the electrons and nuclei. It follows that any evaluation of the expression for the Raman intensity requires the introduction of approximations. It seems that there exist two different kinds of approach: the first approach introduces a number of radical approximations in one step, which leads to simple results, but with limited applicability. This approach was first followed by Placzek in 1934 with the development of his polarizability theory, which is valid for non-resonance Raman scattering [9]. The polarizability theory has been reconsidered by Long in 2002 [3] and is also briefly discussed below. The second approach introduces a number of approximations in a stepwise way directed toward Raman scattering in specific molecular systems. This kind of approach became relevant after the invention of the laser and development of commercial lasers, in particular tunable lasers in the 1960s and 1970s by which it became possible to perform resonance Raman experiments where the wave number of the laser was scanned through the visible absorption band of a large molecule. In particular, resonance Raman studies of biological molecules containing a chromophore came into focus [21, 22, 23, 24]. Accordingly, it became necessary to transform the basic equations into a form suitable for the interpretation and extraction of the molecular information obtained under resonance conditions.
Almost all theoretical treatments of optical spectroscopic processes in molecules, including UV/VIS and Raman spectroscopy, are formulated within the adiabatic formalism. This formalism is based upon the assumption that in a molecule the motions of the light electrons are only weakly correlated to the motions of the heavy nuclei, so that it is possible to approximately separate these motions, when the Schrödinger equation for the molecule is solved. In this chapter we focus on vibrational Raman spectroscopy of larger molecules, i.e., either crystals or solutions and powders. In these molecules, the rotational spectra are not resolved, which means that it is not necessary to consider the rotational motion explicitly. In the adiabatic Born-Oppenheimer (ABO) approximation (e.g., see [17]), each molecular eigenstate is therefore, as a first step, approximated by a product of an electronic state and a vibrational state, where the ladder is normally considered within the harmonic approximation. Within the ABO approximation, the states in the state and Raman tensors are replaced by the product states:
Since the ABO approximation only allows a partial separation of the electronic and nuclear motions, the functions describing the electronic states will depend on both the electronic coordinates and on the nuclear coordinates, while the vibrational functions only depend on the nuclear coordinates. However, the vibrational motion depends indirectly on the electronic state, since the electronic eigenvalue is a function of the nuclear coordinates and is found to play the role of the potential energy function for the vibrational motion.
The vibronic version of the state tensor in Eq. (2) may now be written as
where
In general, the functions describing the excited electronic states in larger molecules are not known. In fact, one important task in optical spectroscopy is to provide knowledge of these functions. Since also their dependence on the nuclear coordinates is not known, the formal integrations over the nuclear coordinates in the state tensor given in Eq. (6) are performed by introducing an appropriate Taylor expansion in the nuclear coordinates. The expansion of the state tensors may be performed in two different ways: (1) the electronic functions are expanded using perturbation theory and then the integration over the nuclear coordinates are performed (e.g., see [27]), and (2) the electronic transition moments
where all vibrational states are functions of the set of normal coordinate
The vibronic models developed for RRS, which are found in the Raman literature, differ essentially from each other in two ways: (1) whether expansion scheme 1 or 2 has been applied and (2) the degree of approximation that has been introduced.
3. What is vibrational Raman spectroscopy: a vibrational or an electronic spectroscopic technique or both?
3.1 Non-resonance Raman spectroscopy
In most molecules, the energy differences between the electronic ground state and the excited electronic states are much larger that the mutual energy difference between the excited electronic states. Typically, there will therefore exist a relatively large spectral region between the energy of the final state in the Raman process and the energy of the first electronically excited state, where the wave number of the laser
where
To obtain Eq. (9) “the closure rule,” i.e.,
where
3.2 Vibrational resonance Raman spectroscopy
In resonance Raman scattering, the wave number of the laser is chosen within the UV or visible absorption band of the molecule. Since the assumption
Vibrational resonance Raman spectroscopy (VRRS)
Raman dispersion spectroscopy (RADIS) (see Section 3.3.)
In VRRS the vibrational Raman spectrum is measured in the same way as in RS, i.e., the spectral distribution in the Raman scattered light is measured as a function of the Raman shift
Larger molecules, typically biomolecules, are often colored because they contain a chromophore with high symmetry. Important examples are the metal-porphyrins, where the ring structure has the ideal symmetry of
The resonance enhancement and the interference between the resonating state tensors are very sensitive to the magnitude of the damping constants
3.3 Raman dispersion spectroscopy (RADIS)
In RADIS the resonance Raman signal is monitored as a function of the excitation wave number. In practice a series of resonance Raman spectra are measured using either a number of discrete laser wave numbers or a tunable laser. RS, VRRS, and RADIS are illustrated in Figure 2. The figure illustrates, for a thought molecule, the changes in a series of Raman spectra obtained with increasing wave number toward resonance with an electronic state. The electronic resonance is illustrated by the UV/VIS absorption spectrum. One excitation spectrum, normally called an excitation profile (dotted curve), is obtained by plotting the intensity of a specific Raman band in the Raman spectrum versus the excitation wave number. It follows from the figure that there will be one excitation profile for each Raman band. It should be stressed that a complete RADIS experiment requires that two spectra are measured at each excitation wave number, namely, the parallel and perpendicular polarized spectra. From the polarized resolved spectra, the excitation profile can be calculated as the sum of these, but more importantly the DPR as a function of the excitation wave number can be determined. The DPR versus excitation wave number is called the polarization dispersion curve.
In a typical UV/VIS absorption experiment performed on a solution, one measures the absorbance
where
It follows that while VRRS is mainly a vibrational spectroscopic technique, RADIS has more in common with electronic spectroscopy. It follows that each Raman-active vibration just plays the role of a “sensor” used to monitor the vibrational fine structure in the UV/VIS absorption spectrum.
Since the late 1980s, a very large amount of systematic resonance Raman studies on different metal complexes [28, 29] and different metal-porphyrins [12] including heme-proteins have been performed with the goal of determining their structure, their bio-functionality, and the conditions for aggregation. In these studies both the VRRS and RADIS including both excitation profiles and polarization dispersion have been applied. Recently polarization-resolved VRRS has been combined with dynamic light scattering to study among other things the aggregation of
4. Examples
As has been shown, vibrational RS is exclusively a vibrational spectroscopic technique like IR and NIR. However, vibrational Raman spectroscopy performed under resonance conditions may be considered as either a vibrational spectroscopic technique or as an electronic spectroscopic technique, which of the two depends on the way the experiments are performed. Three examples are briefly discussed below. For more applications, the interested reader should consult the comprehensive Raman literature [31, 32, 33, 34, 35, 36].
4.1 Example 1: perturbation of molecular symmetry
As demonstrated in [11], the non-commuting generator approach to molecular symmetry may be applied to calculate the structure of the state tensors. Figure 3 shows an example for two vibrations in point group
For the asymmetric
It follows that through the application of RADIS, it is possible to study small changes of the molecular configuration in excited electronic states and estimate the various molecular parameters influenced by these changes. As shown in numerous RRS papers on biomolecules, these structural changes, which are typically induced by minor changes in the environment of the molecule, can be studied in vivo, which is of course a major advantage [31, 32, 33, 34, 35, 36].
4.2 Example 2: noninvasive color detection using polarization dispersion
The color of a molecular species is associated with the properties of the electronic excited states of the molecule, and in large biomolecules, it is due the presence of a chromophore being typically a metal complex. The red color of the heme-proteins, which is due to the presence of the Fe-porphyrin complex, is a well-known example. A change in color may be due to a change of the molecular configuration (distortion, aggregation) or be a result of a chemical reaction. By monitoring the color change before and after a chemical reaction, the substance concentration in solutions can be determined from the absorbance measured by a UV/VIS spectrophotometer or in the case of a solid by applying the spectrophotometer with an integrating sphere. In the literature several color detection methods have been developed for the detection of various substances. A book on color detection is in the process of publication by IntechOpen and will be published later in 2019.
In this section a reflection technique with high spectral resolution is discussed. The technique is suitable for the detection of minor color differences between similar molecules, i.e., molecules where a number of identical vibrations can be identified in the vibrational signature of the molecules. The method has been applied in combination with polarized resolved fluorescence to study the stability of the Ruthenium-based dye N719 [37] and to study in vitro the stability of N719 and the adsorption and desorption processes of this complex to the
Recently the method has also been proposed as a possible noninvasive screening technique for revealing a content of carbon monoxide in fresh tuna fish or meat. Preliminary experimental results were presented at the Raman conference ICORS 2016 in Brazil [39] and are discussed in the following.
The method is based on the presence of dispersive Raman modes combined with a small spectral difference between the visible absorption spectra of similar molecules. The idea is as follows: the resonance condition for a specific molecule in RRS depends, as we have seen above, on the difference in the wave number between the electronic absorption and the excitation laser. Due to the tensor property of resonance Raman scattering, the value of the DPR depends on this difference (polarization dispersion). Thus, a small spectral shift in the absorption will essentially be equivalent to a displacement of the polarization dispersion curve relative to the excitation wave number of the laser, as illustrated in Figure 5. The change of the DPR value at a specific wave number depends on the shape of the dispersion curve, which depends on the nature of the vibration and the Raman tensor. When the molecule has low or no symmetry, most Raman-active vibrations will be dispersive. Although the ideal symmetry of a chromophore is often high, which limits the number of dispersive modes, the real symmetry is frequently lowered due to perturbations of the chromophore, which opens up for dispersion. The heme group with the ideal symmetry
In the
First, it is noticed that the DPR values of five out the six modes indicate that they are dispersive, since all the DPR values are changed due to the exposure to
4.3 Example 3: unpolarized RADIS as a source of three-way multivariate data
In the last decade, chemometrics has become essential in the analysis of small differences of the chemical composition of samples in medical and environmental applications as well as in the food industry. Typically the chemical data are generated by different kinds of molecular spectroscopy: UV/VIS, fluorescence, NIR, IR, Raman, and others. A large number of mathematical methods have been developed and are in most cases part of the software package delivered with the spectrometer. The data from spectroscopy are in most cases two-way data set. Using vibrational Raman spectroscopy as an example, the elements
In [41] a new application of RADIS has been proposed, where the coherent absorption-emission property of Raman scattering is utilized. When we compare the construction of three-way data by combining UV/VIS and fluorescence data with the RADIS in Figure 2, we see that the unpolarized RADIS data must automatically be born as three-way data and more importantly the spectral resolution is very high. Consequently, only few data points along the Raman shift axis
5. Conclusions
What is vibrational Raman spectroscopy: a vibrational or an electronic spectroscopic technique or both? Although the Raman signal reflects the vibrational motions of the molecule in the electronic ground state, our discussion shows that the answer to the question is that the Raman technique can be applied both as a vibrational and as an electronic spectroscopic technique depending on the experimental conditions chosen.
The Raman signal provides a highly resolved vibrational signature of the molecule. However, the signature depends on whether the molecular system (molecule or ion) is excited in non-resonance or in resonance with an electronic transition. In non-resonance it follows from Eqs. (9) to (10) that the Raman signal depends on the molecular polarizability tensor evaluated in the electronic ground state and not on the molecular dipole moment as in IR and NIR. In principle all fundamental vibrations in the molecule, where
In resonance, where the laser wave number is chosen within an electronic absorption band of the molecule, Eq. (3) shows that the state tensors being closest to resonance with the laser will contribute most to the Raman tensor and to the Raman signal (resonance enhancement). Thus, the vibrations appearing in the resonance Raman spectra are mainly those associated with the electronic absorption. As discussed in Sections 3.2 and 3.3 and illustrated in Figure 2, resonance Raman scattering may form the basis of two different kinds of resonance Raman techniques termed VRRS and RADIS. In VRRS the focus is on the vibrational Raman spectra, just like in RS, but now obtained under resonance conditions, while in RADIS the focus is on the excitation profiles and the polarization dispersion curves. In RADIS the total Raman signal and the polarization-resolved Raman signals (giving the DPR defined in Eq. (5)) for a specific Raman-active vibration are monitored as a function of the excitation wave number. The vibronic expansion of the state tensor given in Eq. (7) shows that the Raman signal in resonance is determined by the electronic transition moment of the resonating state and its derivatives and by the relations between the vibrational sub-states associated with the electronic ground state (i.e.,
Since the VRRS technique can be applied also as time-resolved spectroscopy, it is an attractive tool for the investigation of both the structure and dynamics of biomolecules. The main advantage of VRRS is the ability to investigate different parts of a large protein molecule by tuning the excitation wave number into the absorption band of the chromophore of interest. In a recent paper [42], the application of VRRS in the study of the structure and dynamics of various proteins is discussed. [42] gives an excellent review of this field covering both visible and UV resonance Raman as well as cw and time-resolved versions of VRRS.
The polarization properties of the resonance Raman signal are more important in resonance than in non-resonance. For example, as discussed in [43], the uniqueness of the polarization-resolved VRRS spectra combined with standard PCA chemometrics enables one to discriminate between closely related biomolecules with almost identical unpolarized VRRS spectra. The key point is that structural molecular change manifests itself through a change of the polarization of the Raman signal (DPR). The DPR defined in Eqs. (4) and (5) is an absolute quantity, which in combination with standard PCA renders the multivariate analysis insensitive to sample and experimental variations.
The discussion in Section 3.3 and the examples presented in Section 4 demonstrate that RADIS is closer to UV/visible absorption spectroscopy than it is to vibrational spectroscopy. Besides the spectral resolution is much higher enabling the vibrational fine structure of the absorption spectra to be resolved. In resonance, the interference between the state tensors, which is the origin of the sensitivity of the Raman signal with respect to changes of the molecular parameters, is restricted to those with energy denominators closest to the laser wave number. It was also demonstrated that the polarization properties of the Raman signal, expressed through the DPR, play a more important role than in non-resonance. As said already, the DPR is defined as the ratio between two Raman signals with different polarization. The interference, which can be both constructive and destructive, will in general be different in the two Raman signals depending on the wave number of the laser and the structure of the state tensors, which again is determined by the molecular symmetry and physical properties of the molecule. Section 4.1 and Figure 3 illustrate a simple example, where the molecular configuration in an electronically excited state is distorted, which, as seen, creates a significant polarization dispersion. To fully exploit the sensitivity of the DPR to changes in the molecular parameters, one must determine the polarization dispersion, i.e., one must monitor two resonance Raman spectra (the parallel and perpendicular polarized) at each laser wave number available. Traditionally the Raman spectra with different polarizations are measured in sequence. However, with CCD technology it is possible to measure the two Raman signals simultaneously, which will improve the accuracy of the DPR considerably. This requires a modification of the entrance and collection optics of a standard Raman spectrometer, so that the upper and lower halves of the CCD monitor the parallel and perpendicular polarized Raman signals, respectively [44, 45].
The examples discussed in Section 4.2 show that it is possible to detect a small change in color of a molecular sample by determining the change of the DPR of a dispersive Raman mode, applying only a single excitation wave number in the absorption spectrum. To be detected the color change must be due to a modification of the chromophore, so that the same Raman modes are present before and after the color change. Also in these examples, the resonance Raman technique performs as a kind of electronic technique.
Finally, it is shown in Section 4.3 that due to the coherent nature of the Raman process it generates automatically the so-called three-way multivariate data. This property is applied to solve chemical classification problems by using only a few (2–3) excitation wave numbers in un-polarized RADIS in combination with a three-way multivariate model. As shown, only very few samples (<10) are needed, instead of the very large (500–600) number of samples required, when the visible absorption and fluorescence spectra are combined to produce the three-way data.
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