Structure of Molecular Spectra

It may be observed here that inferences may be drawn from the rotation fine structure of molecular spectra, using equation (13), regarding the presence and proportions of isotopes, a circumstance that led to the discovery of the isotopes of nitrogen and oxygen. ... 

Rotational fine structure of molecular spectra (infra-red and Raman spectrum)... 

The spectrum of Figure lb is a fingerprint of the presence of a CO molecule, since it is different in detail from that of any other molecule. UPS can therefore be used to identify molecules, either in the gas phase or present at surfaces, provided a data bank of molecular spectra is available, and provided that the spectral features are sufficiently well resolved to distinguish between molecules. By now the gas phase spectra of most molecules have been recorded and can be found in the literature. Since one is using a pattern of peaks spread over only a few eV for identification purposes, mixtures of molecules present will produce overlapping patterns. How well mixtures can be analyzed depends, obviously, on how well overlapping peaks can be resolved. For molecules with well-resolved fine structure (vibrational) in the spectra (see Figure lb), this can be done much more successfiilly than for the broad. 

Applications of neural networks are becoming more diverse in chemistry [31-40]. Some typical applications include predicting chemical reactivity, acid strength in oxides, protein structure determination, quantitative structure property relationship (QSPR), fluid property relationships, classification of molecular spectra, group contribution, spectroscopy analysis, etc. The results reported in these areas are very encouraging and are demonstrative of the wide spectrum of applications and interest in this area. 

To identify a colorant, its excitation and emission spectra must be measured. This can be done under standard conditions if the colorant has been extracted from a foodstuff. Usually the spectral patterns taken from real conditions will not deviate too much from standard conditions. One must be aware that the main spectral patterns are determined by the chromophore of the colorant and that further molecular identification needs to recognize special fine structures of the spectra or employ additional analytical tools. 

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. 

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. 

Studies of molecular spectra (UV, IR and NMR) are potentially useful in providing information about aromaticity. Further information may be obtained from magnetic susceptibilities and dipole moment measurements. The UV spectra of pyran-2-one and some of its analogues have been reported (71PMH(3)67), and are consistent with the enol lactone structure (17). 

Herzberg G., Molecular Spectra and Molecular Structure, 2nd Ed., Van Nostrand-Reinhold, Princeton, New Jersey, 1950 Pearse, R. W. B., and Gaydon, A. G., The Identification of Molecular Spectra. Chapman Hall, London, 1960. 

K. P. Huber and G. Herzberg, Molecular Structure and Molecular Spectra IV. Constants of... 

Rigid Molecule Group theory will be given in the main part of this paper. For example, synunetry adapted potential energy function for internal molecular large amplitude motions will be deduced. Symmetry eigenvectors which factorize the Hamiltonian matrix in boxes will be derived. In the last section, applications to problems of physical interest will be forwarded. For example, conformational dependencies of molecular parameters as a function of temperature will be determined. Selection rules, as wdl as, torsional far infrared spectrum band structure calculations will be predicted. Finally, the torsional band structures of electronic spectra of flexible molecules will be presented. 

For radicals with magnetic nuclei, the hyperfine structure of ESR spectra is produced by the interaction of the electron magnetic moment with the nuclear spin of those nuclei covered by the molecular orbital of the unpaired electron. This interaction splits further the two spin levels in a magnetic field. The hyperfine coupling is often given by the Hamiltonian HgN ... 

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. 

Much more attention has been given to the computation of molecular spectra (for ensembles of molecules) for this the actual structure of molecules is not really necessary. The difference between the spectroscopy of molecular ensembles and that of single molecules has been discussed in ref. 11. Here, only a simple example will be cited to illustrate that molecular structure constants (such as bond lengths or bond angles) are... 

G. Herzberg, Electronic Spectra and Electronic Structure of Polyatomic Molecules, volume m of Molecular Spectra and Molecular Structure, D. Van Nostrand, Princeton, New Jersey, 1966. 

Let us consider the last point. The reader is already familiar with two important implications of the timescale separation between electronic and nuclear motions in molecular systems One is the Bom-Oppenheimer principle which provides the foundation for the concept of potential energy surfaces for the nuclear motion. The other is the prominent role played by the Franck-Condon principle and Franck-Condon factors (overlap of nuclear wavefunctions) in the vibrational structure of molecular electronic spectra. Indeed this principle, stating that electronic transitions occur at fixed nuclear positions, is a direct consequence of the observation that electronic motion takes place on a timescale short relative to that of the nuclei. 

The FD spectra of these compounds are relatively complex. Although it is possible to attribute to the high-mass peaks at m/z 857 and 880 the respective structures of molecular ions (M", m/z 857) and adduct ions ([M -l- Na] , m/z 880), it is difficult to determine the origin of peaks corresponding to lower masses m/z 554, 617 and 731. Collisional-induced metastable decomposition spectra (B/E/CAD) enable two of them to be attributed (Fig. 106). 

Laboratory of Molecular Spectra and Structure, Physics Department, University of Chicago. Professor Mulliken would not necessarily have considered himself a computational chemist, a term that did not come into vogue until about 1980, Nevertheless, his research helped lay the conceptual foundation from which computational chemistry evolved in part. 

When great accuracy is desired, and in certain cases when only ordinary accuracy is required, it is necessary to consider the coupling between electronic and nuclear motions, and especially between the electronic angular momentum (either spin or orbital) and the rotation of the molecule. We shall not discuss these questions,1 but shall treat only the simplest problems in the complex field of molecular structure and molecular spectra in the following sections. Some further discussion is also given in Chapter XII and in Section 48 of Chapter XIV. 

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