Interpretation of Molecular Spectra

The rotational intensity structure of a vibrational band provides information about the rotational population in the electronically excited state and the vibrational bands originating from an electronically excited state provide information about the corresponding vibrational population. Finally, the sum of the vibrational and rotational populations yields the population in the electronically excited state. 

The rotational temperatures which are obtained from the Q—branch of the v = 0 — v = 0 transition in the hydrogen spectra of Fig. 4.1 are Trot (X) = 6000 K and 4500 K for H2 and D2, respectively. Evaluation of the v = 1 — v = 1 transition yields lower temperatures Trot(X) = 2000 K (H2) and Trot(X) = 1500K (D2) typically decreasing with increasing vibrational quantum number. Detailed experimental investigations of laboratory plasmas have shown that the v = 2 — v = 2 transition should be used preferentially for gas temperature determination. For CH and CD molecules, the dissociative excitation mechanism contributes to the rotational population and therefore, Trot represents the temperature of the excited state only. Calculated spectra of CH and CD bands fit best to the measurements shown in Fig. 4.1 for Trot = 3000 K. 

The radiation of a vibrational band is directly correlated to the vibrational population in the excited state I(v — v ) = n(v ) x Av v . Av v is the transition probability. Thus, several vibrational bands which originate from different vibrational levels yield the corresponding vibrational population. In case of hydrogen or deuterium molecules the population of the first four or five vibrational levels, respectively, is accessible. Higher vibrational levels are disturbed by pre-dissociation processes. For further analysis, it is very convenient to use the relative vibrational population n(v )/n(v = 0). 

In a first step, the vibrational population in the ground state is characterized by a Boltzmann distribution, i.e., n v )/ n v = 0) depends on TVib X). The left column of Fig. 4.3 shows relative vibrational populations in the ground state (X1 ) and in the upper state of the Fulcher transition (d377u) with Tvib(X) as parameter, assigned to the 15 vibrational levels of H2, i.e., v = 0-14. The right column shows the relative vibrational population in the excited state as a function of 7 vib(X) for H2 and D2. Due to the usage of vibrationally resolved excitation rate coefficients a dependence on electron temperature is obtained. Te = 4eV is chosen in Fig. 4.3. 

In the final step, the comparison of measured with calculated vibrational populations yields 7 vib(X). Small corrections are obtained due to the dependence of lifetimes on vibrational quantum number. Details of the method are described in [8]. Due to the strength of the Franck-Condon factors between ground and excited state the sensitivity of the method is limited to relative 

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The projection-operator technique will be employed in several examples presented in the following chapter and Chapter 12. For. the quantitative interpretation of molecular spectra both electronic and vibrational, molecular symmetry plays an all-important role. The correct linear combinations of electronic wavefunctions, as well as vibrational coordinates, are formed with the aid of the projection-operator method. 

The interpretation of molecular spectra in the visible and ultraviolet regions is based on a large number of empirical and semi-empirical rules and has been correlated extensively with many models of bond formation and molecular structure. The complexity of the problem however, is such that despite an impressive body of self-consistency detailed interpretation of most spectra is simply not feasible. 

The interpretation of molecular spectra consists of finding a correlation between observed spectral features and the symmetry of molecular species. 

Interpretation of molecular spectra involves four basic steps. First, major skeletal and functional group components of the molecule are identified, either from assumptions about the compound origin or from features of the spectra. Second, non-localized molecular properties such as the molecular weight, elemental composition, and chromatographic behavior are considered. These global constraints can be used to eliminate unlikely functional groups, deduce the presence of groups and skeletal units which have no distinctive features in the spectra, and detect multiple occurrences of... 

We are developing an expert system to automate the first step of this process, the interpretation of molecular spectra and identification of substructures present in the molecule. The automatic interpretation of spectra would by itself provide a useful tool for an organic chemist who may not be an expert spectroscopist. Also, reported algorithms for the assembly of candidate structures from known substructures, such as the GENOA program. (3-6) rely on the input of accurate and specific substructures in order to function correctly and efficiently. Identification of substructures is thus a logical starting point. 

The Morse function and other functions somewhat similar to it have been found to be useful in the interpretation of molecular spectra and the discussion of molecular structure. Some examples are mentioned in Chapter 3. 

In 1955, I attended the first of the Summer Schools in Theoretical Chemistry, organised by Charles Coulson, then Rouse-Ball Professor of Mathematical Physics at Oxford, to introduce young chemists to the Molecular Orbital (MO) Theory, to which he made outstanding contributions. The MO theory gave me a wider perspective for the interpretation of molecular spectra and the study of molecular structures and reaction mechanisms. 

The following first section of this appendix describes quantities that are measured when registering spectra obtained using various experimental set-ups and their relations with molecular quantities. These relations form the basis of the interpretations of molecular spectra. The second section describes some general properties of a distribution that are used in various chapters of this book when this distribution is the band of a spectram. The third section deals with such concepts as normal modes in the harmonic approximation, while the fourth section deals with force constants, reduced masses, etc., and offers comparisons of these various quantities. The last section provides a more specific calculation of the first and second moment of a band such as which corresponds to a normal mode characterized by a strong anharmonic coupling with a much slower mode. 

For more sophisticated purposes (e g. interpretation of molecular spectra) some refinements need to made to this simple picture. In particular, the possibility of overlap between a 2s orbital on one atom and the 2po on the other can change the order of MO energies. This does not alter the electron configurations of any species shown in Table 1. but is important for some molecules such as C2... 

The energy of the molecule does not depend on M (unless there is a magnetic field present), so that this rule is not ordinarily of importance in the interpretation of molecular spectra. 

CASSAM software consists of various programs for the comparison or interpretation of molecular spectra. A brief description of some of these programs and examples of results are given in the following sections. 

The fundamental principles upon which the calculation of selection rules are based have been given in Secs. 3-4, 3-5, and 3-6. In this chapter these principles will be applied to the problem of determining the vibrational selection rules for symmetrical molecules. It will be found that certain transitions are forbidden merely because of the symmetry properties of the molecule. Other transitions are found not to be forbidden by symmetry considerations such transitions may nevertheless be missed experimentally because of low intensity due to other causes. On the other hand, transitions forbidden by symmetry sometimes seem to appear in the spectra of liquids, presumably due to the distortion of the symmetry by the neighboring molecules. However, in spite of the fact that so-called forbidden transitions may occur weakly in liquids and so-called allowed transitions are quite frequently not observed, the selection rules given by symmetry considerations are of very great importance as a guide in the interpretation of molecular spectra. 

German chemist Eriedrich Hund and American chemist Robert S. Mulliken propose the Hund-Mulliken interpretation of molecular spectra, which gives a description of the molecular orbital theory of bonding. 

The present data collection is intended to serve as an aid in the interpretation of molecular spectra for the elucidation and confirmation of the structure of organic compounds. It consists of reference data, spectra, and empirical correlations from and nuclear magnetic resonance (NMR), infrared (IR), mass, and ultraviolet-visible (UV/vis) spectroscopy. It is to be viewed as a supplement to textbooks and specific reference works dealing with these spectroscopic techniques. The use of this book to interpret spectra only requires the knowledge of basic principles of the techniques, but its content is structured in a way that it will serve as a reference book also to specialists. 

Quantisation, or the existence of discrete energy levels, is not confined to the energies associated with the motion of electrons. Once we move to molecules, it is necessary additionally to consider the energy levels that are associated with other motions in particular, with the overall rotation of the molecule and with the molecular vibrations in which the nuclei move their positions relative to one another. The interpretation of molecular spectra is facilitated by the fact that the gaps between energy levels associated with different kinds of motion are quite different, with the result that the spectra associated with them occur at different wavelengths or frequencies in the electromagnetic spectrum. 

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