Interpretation of vibrational spectra

Theoretical interpretation of molecular vibration spectra is not a simple task. It requires knowledge of symmetry and mathematical group theory to assign all the vibration bands in a spectrum precisely. For applications of vibrational spectroscopy to materials characterization, we can still interpret the vibrational spectra with relatively simple methods without extensive theoretical background knowledge. Here, we introduce some simple methods of vibrational spectrum interpretations. 

---

A series of monographs and correlation tables exist for the interpretation of vibrational spectra [52-55]. However, the relationship of frequency characteristics and structural features is rather complicated and the number of known correlations between IR spectra and structures is very large. In many cases, it is almost impossible to analyze a molecular structure without the aid of computational techniques. Existing approaches are mainly based on the interpretation of vibrational spectra by mathematical models, rule sets, and decision trees or fuzzy logic approaches. 

Vibrational spectroscopy has played a very important role in the development of potential functions for molecular mechanics studies of proteins. Force constants which appear in the energy expressions are heavily parameterized from infrared and Raman studies of small model compounds. One approach to the interpretation of vibrational spectra for biopolymers has been a harmonic analysis whereby spectra are fit by geometry and/or force constant changes. There are a number of reasons for developing other approaches. The consistent force field (CFF) type potentials used in computer simulations are meant to model the motions of the atoms over a large ranee of conformations and, implicitly temperatures, without reparameterization. It is also desirable to develop a formalism for interpreting vibrational spectra which takes into account the variation in the conformations of the chromophore and surroundings which occur due to thermal motions. 

For isolated molecules a variety of approaches have proved useful in the interpretation of vibrational spectra. Firstly, a species may approximate to a symmetry higher than its actual. In such cases a correlation with-descent in symmetry from — the higher symmetry usually simplifies the interpretation of its spectra. Secondly, local group vibrations, essentially uncoupled from the vibration of other equivalent or near-equivalent groups, may occur. Thirdly, chemically distinct groups may couple... 

IV. Considerations Relating to the Interpretation of Vibrational Spectra of Adsorbed Species... 

The interpretation of vibrational spectra is dependent on a correct assessment of the symmetry properties of the adsorbed species themselves and of their vibrational modes. Several general accounts have been given of the classification of vibrations of adsorbed species in terms of the symmetry elements associated with a surface complex (89, 90). 

Interpretation of vibrational spectra of C60H2n is difficult because of uncertainty in the isomeric composition of the samples, presence of impurities, and low intensity of many absorption bands. The IR spectra of C60H2, presumably a product of 1,2-addition to the 6-6 bond was reported in (Ballenweg et al. 1993). The IR spectrum of C60H6 considered as a mixture of the C3 and D3 isomers was presented by Bergosh et al. (1997). The IR and Raman spectra of C60H36 and C60Hlg were studied... 

INTERPRETATION OF VIBRATIONAL SPECTRA IN ELECTROCHEMICAL ENVIRONMENTS FROM FIRST-PRINCIPLE CALCULATIONS COMPUTATIONAL STRATEGIES... 

Interpretation of vibrational spectra in electrochemical environments from first-principle calculations computational strategies 211... 

Kubicki, J.D., Interpretation of vibrational spectra using molecular orbital theory calculations, in Molecular Modeling Theory Applications in the Geosciences, Cygan, R.T. and Kubicki, J.D., Eds., Geochemical Society of America, Washington, D.C., 2001, p. 459. 

Qualitative analysis of unknown compounds. Interpretation of vibrational spectra with the help of empirical rules... 

Vibrational spectra of solid carbonyls often differ from those in solution. The latter often exhibit very complicated spectra, since many isomers exist in an equilibrium. Even the interpretation of vibrational spectra of the species Fe3(CO)i2, whose size is small compared to many of the large carbonyl clusters which have been investigated during the past few years, is controversial (Cotton and Hunter, 1974). 

A further problem in the interpretation of vibrational spectra of solid state compounds arises from the different phases of the vibrations in neighboring cells, leading to a wave described by the wave vector k. In the absence of a phase difference, k equals zero. This is the basis for the factor group analysis. If the vibrational motions are oriented parallel to the direction of the wave caused by the phase differences, a longitudinal branch results while transverse branches result from orthogonal vibrational motions. Furthermore, it is necessary to differentiate between optical and acoustic modes. In the optical mode of the NaCl lattice, Na+ and Cl ions have opposite displacements, while the acoustic modes are caused by in-phase motions of Na+ and CF. 

M. Diem, Introduction to Modem Vibrational Spectroscopy , John Wiley Sons, New York, 1993. This easy to read book features detailed discussion of the theoretical and experimental aspects of IR and Raman spectroscopy and provides many examples for the interpretation of vibrational spectra. 

Luinge, H.J. Automated interpretation of vibrational spectra. Vibr. Spectrosc. 1990, 1, 3-18. 

A major goal of fundamental research aiming to rationalize the interplay of structure, dynamics, and chemical reactivity, is to determine multidimensional potentials for nuclei in various environments. On the one hand, potential surfaces can be calculated with quantum chemistry methods at various levels of approximation. On the other hand, from the experimentalist viewpoint, vibrational spectroscopy techniques can probe dynamics of atoms, molecules and ions, in various states of the matter. However, there are fundamental and technical limitations to the determination of potential hypersurfaces from vibrational spectra of complex systems, and the confrontation of experiments with theory is far from being free of ambiguities. Consequently, the interpretation of vibrational spectra remains largely based on experiments. Recent progress in neutron scattering techniques have revealed new dynamics, specially for... 

The definition of a theory as a set of hypotheses that has passed a test of experimental verification is uncontroversial. However, the equation of theories and models proposed by Zumdahl and Petrucci and Harwood is less straightforward, I think. It surely is true that all but the most grandiose of scientists would admit that their theories were approximations to reality, and so, to the extent that a model requires a specified list of approximations, all theories are models. However, not all models are theories. If I make the approximation of treating molecules as perfect spheres or springs as massless, I am creating a model that will make subsequent calculation easier or comprehension of the results easier, but I presumably do not believe these approximations to be true in my theory of what is occurring in reality. Chemists will talk of the harmonic-oscillator model as a mathematically convenient approximation for the interpretation of vibrational spectra, but I do not think many people would consider this to be a theory of vibrational spectroscopy. 

Many expert systems contain a knowledge base in the form of a decision tree that is constructed from a series of decision nodes connected by branches. For instance, in expert systems developed for the interpretation of vibrational spectra, decision trees are typically used in a sequential manner. Similar to the interpretation of a spectrum... 

The problem of the interpretation of vibrational spectra is to calculate all possible combinations of substructures that may be present in a molecule consistent with the characteristic frequencies of a given infrared spectrum. Elyashberg and his team showed with an example that the infrared spectrum-structure correlation, as simply expressed by the characteristic frequency approach, does not allow one to establish the structure unambiguously due to a lack of information in characteristic frequencies [32]. They pointed out that the use of ANNs appears to be particularly promising. 

As an approach to using 2D-IR for the examination of the structures and dynamics of individual residues of extended structures, it is natural to turn to isotopic substitution. The use of isotopic replacements has been essential in the interpretation of vibrational spectra and their relationship to structure. Iso-topomers have frequencies, force fields, and anharmonicities that are different from one another. Of particular interest in applications of 2D-1R is the use of isotopes to shift frequencies into regions where their couplings can be measured, free from interference by other modes of the system. For the amide-I mode, which is mainly a C=0 stretching coordinate, the shifts by and... 

Normal coordinate analysis has been used for many years in the interpretation of vibrational spectra for small molecules.88 It provided the motivation for the application of the harmonic approximation to proteins and their constituent elements (e.g., an a-helix).35 133-136 In this alternative to conventional dynamical methods, it is assumed that the displacement of an atom from its equilibrium position is small and that the potential energy (as obtained from Eq. 6) in the vicinity of the equilibrium position can be approximated as a sum of terms that are quadratic in the atomic displacements i.e., making use of Cartesian coordinates, which are simplest to employ for large molecules, we have... 

Until the last few years, most force-fields described in the literature were developed exclusively for the interpretation of vibrational spectra. Such force-fields are usually of limited use in the present context, because typically they neglect many or all of the van der Waals interactions, and were not parameterized with structure and energy (apart from the spacing of the vibrational levels) in mind. Recently Lifson (Lifson and Warshcl, 1968 Warshel and Lifson, 1970) and Boyd (Boyd, 1968 Shieh et al., 1969 Boyd etal., 1971 Chang et al., 1970) have each developed force-fields aimed at fitting simultaneously to vibrational spectra, structure, and energy... 

---