Vibrational Spectroscopic

Vibrational spectroscopic studies of heterogeneously catalyzed reactions refer to experiments with low area metals in ultra high vacuum (UHV) as well as experiments with high area, supported metal oxides over wide ranges of pressure, temperature and composition [1]. There is clearly a need for this experimental diversity. UHV studies lead to a better understanding of the fundamental structure and chemistry of the surface-adsorbate system. Supported metals and metal oxides are utilized in a variety of reactions. Their study leads to a better understanding of the chemistry, kinetics and mechanisms in the reaction. Unfortunately, the most widely used technique for determining adsorbate molecular structure in UHV,... 

The molecular point groups of (CF3)2S02, ( 03)2802 and (CBr3)2S02 can be either C2V or C2 according to electron diffraction and vibrational spectroscopic data. The molecular model and projection formula for ( 13)2802 are shown in Figure 11. The molecular geometry of the bromine derivative has not been determined but its vibrational... 

Principles and Characteristics Vibrational spectroscopic techniques such as IR and Raman are exquisitely sensitive to molecular structure. These techniques yield incisive results in studies of pure compounds or for rather simple mixtures but are less powerful in the analysis of complex systems. The IR spectrum of a material can be different depending on the state of the molecule (i.e. solid, liquid or gas). In relation to polymer/additive analysis it is convenient to separate discussions on the utility of FUR for indirect analysis of extracts from direct in situ analysis. 

The revalues are distances between atoms separated by a chain of three (four) or more bonds (Section 2.1.5.). Mainly because of the introduction of the nonbonded interactions, Eq. (8) and (9) no longer represent simple harmonic force fields. We therefore denote the constants of these expressions as potential constants and not as force constants. In principle, all the constants of the force fields (2), (3), (4), (8), and (9) are different, as indicated by different indices (V FFF , U f/BFF , v = vibrational (understood in the sense of standard vibrational-spectroscopic computational techniques)). In what follows we shall be primarily concerned with force fields of the type of Eq. (8) which we therefore formulate with the simplest symbols. 

The influence of bilinear cross terms of this type in force field caculations has been studied systematically only once so far (79). They are standard for vibrational-spectroscopic force field expressions (20), and accordingly vibrational frequencies depend considerably more sensitively on cross terms than e.g. conformational parameters. An example for the significant influence of cross terms also with respect to the latter is described in Section 6.1.3. 

We have seen that for our calculations essentially two types of force fields have to be considered VFF- and UBFF-expressions. The main difference with repect to spectroscopic force fields consists in the superposition of nonbonded interactions. The force fields used so far for our purposes are almost exclusively simple valence force fields without cross terms, and a veriety of UB-force fields. Only recently could experiences be gathered with a valence force field that includes a number of important cross terms (79). Vibrational spectroscopic force fields of both types have been derived and tested with an overwhelming amount of experimental data. The comprehensive investigations of alkanes by Schachtschneider and Snyder (26) may be mentioned out of numerous examples. The insights gained from this voluminous spectroscopic work are important also when searching for suitable potentials for our force-field calculations. 

A force field is considered transferable from an arbitrary molecule A to another molecule B if the agreement of properties calculated fori (geometrical, vibrational, thermochemical, and other properties) with the respective experimental values is as good as for A. In our calculations we are dealing with force fields which describe entire families of molecules. Within these families, properties of only a fraction of their members are known experimentally while it is our aim to predict the others computationally. It is therefore clear that the problem of transferability is of decisive importance for force field calculations of unknown systems or those with unknown properties or. Traditional vibrational spectroscopic force fields in most cases reproduce well the frequencies of a single molecule or a family of closely related molecules however, they are not transferable to molecules of different strain. Subsequently we comment on this point in somewhat more detail. 

In the course of conventional vibrational spectroscopic calculations in internal coordinates the following eigenvalue-problem has to be solved for the molecule under consideration (FG-method terminology of Wilson, Decius, and Cross (5)) ... 

In a similar way the potential constant method as described here allows the simultaneous vibrational analysis of systems which differ in other strain factors. Furthermore, conformations and enthalpies (and other properties see Section 6.5. for examples) may be calculated with the same force field. For instance, vibrational, conformational, and energetic properties of cyclopentane, cyclohexane and cyclodecane can be analysed simultaneously with a single common force field, despite the fact that these cycloalkanes involve different distributions of angle and torsional strain, and of nonbonded interactions 8, 17). This is not possible by means of conventional vibrational spectroscopic calculations. 

Most of the force fields described in the literature and of interest for us involve potential constants derived more or less by trial-and-error techniques. Starting values for the constants were taken from various sources vibrational spectra, structural data of strain-free compounds (for reference parameters), microwave spectra (32) (rotational barriers), thermodynamic measurements (rotational barriers (33), nonbonded interactions (1)). As a consequence of the incomplete adjustment of force field parameters by trial-and-error methods, a multitude of force fields has emerged whose virtues and shortcomings are difficult to assess, and which depend on the demands of the various authors. In view of this, we shall not discuss numerical values of potential constants derived by trial-and-error methods but rather describe in some detail a least-squares procedure for the systematic optimisation of potential constants which has been developed by Lifson and Warshel some time ago (7 7). Other authors (34, 35) have used least-squares techniques for the optimisation of the parameters of nonbonded interactions from crystal data. Overend and Scherer had previously applied procedures of this kind for determining optimal force constants from vibrational spectroscopic data (36). 

Bartell and coworkers investigated the structures of a series of noncyclic alkanes by means of gas electron diffraction (14, 44, 45) and invoked for the interpretation of their results a simple force field which contained to a high extent vibrational spectroscopic constants of Snyder and Schachtschneider. This force field reproduces bond lengths and bond angles of acyclic hydrocarbons well, energies of isomerisation satisfactorily. As an example, Fig. 8 shows geometry parameters of tri-t-butylmethane as observed by electron diffraction and calculated with this force field (14). 

The simple cycloalkanes (CH2)n with n = 5 to 12 are the compounds most frequently studied by force field calculations (8, 9, 11, 12,17, 21). This preference results from their simple structure, from the abundant available experimental material (structural (46), thermo-chemical (47) and vibrational spectroscopic (27, 48, 49) data), and from the fact that, apart from bond length deformations, all other strain factors (angle deformations, unfavourable torsion angles, strongly repulsive nonbonded interactions) are important for the calculation of their properties. The cycloalkanes are thus good candidates for testing force fields. For a more detailed discussion we choose cyclodecane, a so-called medium-ring compound. 

Bowmaker, G. A. Kennedy, B. J. Reid, J. C. Crystal structures of AuCN and AgCN and vibrational spectroscopic studies of AuCN, AgCN, and CuCN. Inorg. Chem. 1998, 37, 3968-3974. 

Recent advances in instrumentation range from novel (laser) sources and highly compact spectrometers over waveguide technology to sensitive detectors and detector arrays. This, in combination with the progress in electronics, computer technology and chemometrics, makes it possible to realise compact, robust vibrational spectroscopic sensor devices that are capable of reliable real-world operation. A point that also has to be taken into account, at least when aiming at commercialisation, is the price. Vibrational spectroscopic systems are usually more expensive than most other transducers. Hence, it depends very much on the application whether it makes sense to implement IR or Raman sensors or if less powerful but cheaper alternatives could be used. 

As this chapter aims at explaining the basics, operational principles, advantages and pitfalls of vibrational spectroscopic sensors, some topics have been simplified or omitted altogether, especially when involving abstract theoretical or complex mathematical models. The same applies to methods having no direct impact on sensor applications. For a deeper introduction into theory, instrumentation and related experimental methods, comprehensive surveys can be found in any good textbook on vibrational spectroscopy or instrumental analytical chemistry1"4. 

The theory behind molecular vibrations is a science of its own, involving highly complex mathematical models and abstract theories and literally fills books. In practice, almost none of that is needed for building or using vibration spectroscopic sensors. The simple, classical mechanical analogue of mass points connected by springs is more than adequate. 

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