Spectra of molecules

Franck-Condon principle According to this principle the time required for an electronic transition in a molecule is very much less than the period of vibration of the constituent nuclei of the molecule. Consequently, it may be assumed that during the electronic transition the nuclei do not change their positions or momenta. This principle is of great importance in discussing the energy changes and spectra of molecules. 

Friedrich B and Herschbach D 1996 Alignment enhanced spectra of molecules in intense non-resonant laser fields Chem. Phys. Lett. 262 41... 

PERMUTATIONAL SYMMETRY AND THE ROLE OF NUCLEAR SPIN IN THE VIBRATIONAL SPECTRA OF MOLECULES IN DOUBLY DEGENERATE ELECTRONIC STATES ... 

Use Coringuration Interaction to predict electronic spectra of molecules. The Con ngiiration Interaction wave function provides a ground state plus soin e excited state energies. You can obtain electron ic absorption frequencies from the differences betw een the energies of the ground state and the excited states. 

For the purposes of studying the rotational spectra of molecules it is essential to classify them according to their principal moments of inertia. 

D. S. McClure, Electronic Spectra of Molecules and Ions in Crystals, Academic Press, Inc., New York, 1959. 

To predict the IR and Raman spectra of molecules (frequencies and intensities). 

Gaussian can compute the vibrational spectra of molecules in their ground and excited states. In addition to predicting the frequencies and intensities of spectral lines, the program can also describe the displacements a system undergoes in its normal modes. Put another way, it can predict the direction and magnitude of the nuclear displacement that occurs when a system absorbs a quantum of energy. 

This Hamiltonian is used in the Schrodinger equation for nuclear motion, describing the vibrational, rotational, and translational states of the nuclei. Solving the nuclear Schrodinger equation (at least approximately) is necessary for predicting the vibrational spectra of molecules. 

Earlier in this review, the relationship between the Raman and infrared spectra of molecules possessing high or low symmetry was considered. It was indicated that for molecules possessing a center of symmetry, no vibration is active in both the Raman and infrared spectra. Several adsorbates in this category and one of intermediate symmetry have been studied by laser Raman spectroscopy (Table IX), and most of these spectra are considered in this section. 

Among the important observations that have been made by studying the Raman spectra of molecules adsorbed on solid surfaces (Table X), the following may be noted. The list is not intended to be exhaustive. 

Inghram and Corner showed that the mass spectra of molecules were much simpler using a field ionization source than with an electron bombardment ion source. Mainly parent ions are formed, unlike under electron impact which gives rise to considerable fragmentation. The simplicity of the mass spectra offers obvious applications in analysis of complex organic mixtures and their use is likely to become widespread... 

The development of molecular orbital theory (MO theory) in the late 1920s overcame these difficulties. It explains why the electron pair is so important for bond formation and predicts that oxygen is paramagnetic. It accommodates electron-deficient compounds such as the boranes just as naturally as it deals with methane and water. Furthermore, molecular orbital theory can be extended to account for the structures and properties of metals and semiconductors. It can also be used to account for the electronic spectra of molecules, which arise when an electron makes a transition from an occupied molecular orbital to a vacant molecular orbital. 

Radii for metal atoms forming only one bond can be found from the interatomic distances obtained from band spectra of molecules such as Ag1, etc. The available data for the silver halides lead to a radius of about 1.12 A for Ag1. The change of radius with change in number of bonds is strikingly shown by silver, with radius 1.53 A for four bonds, 1.36 A for two, and 1.12 A for one. 

FIG. 16. Mass spectra of molecules evolved from ECRRF Nv plasma treatment of an a-C H film, for different treatment conditions. (Reproduced from [70].)... 

Analogous conclusions can of course be extracted from the NMR spectra of molecules of type N bearing an asymmetric carbon atom and two diastereotopie methyl groups on tin (see Table 2) ... 

Lide jr., D. R., and D. E. Mann Microwave spectra of molecules exhibiting internal rotation. III. Trimethylamine. J. Chem. Physics 28, 572 (1958). 

Mass spectra of numerous single compounds are available in reference libraries. However these spectra have not always been obtained in the same conditions as those used in DE or DI EI-MS modes and the spectra of molecules of specific interest in the field of cultural heritage have not been systematically registered. It is thus of importance to achieve mass spectra on a set of standard molecular constituents in order to study their mass spectral fingerprint in detail before investigating the more complex mass spectra of multicomponent materials. 

However, as mentioned above, T c)3) will be orthogonal to all the k states, and T ) is nonzero. This implies that the number of total states of the same eigenvalue E is (k + 1), which contradicts our initial hypothesis. Thus, we conclude that k must be even, and hence proved the generalized Kramers theorem for total angular momentum. The implication is that we can use double groups as a powerful means to study the molecular systems including the rotational spectra of molecules. In analyses of the symmetry of the rotational wave function for molecules, the three-dimensional (3D) rotation group SO(3) will be used. 

The spectra of molecules are much more complicated than those of atoms. Molecular spectroscopy has become much more important now because of the large number of complicated molecules being synthesized. 

Contracted Basis Functions with a Lanczos Eigensolver for Computing Vibrational Spectra of Molecules with Four or More Atoms. 

Quite often, rotational-vibrational spectra of molecules are analyzed by means of empirical formulas. A convenient formula for diatomic molecules is the Dunham expansion (Dunham, 1932 Ogilvie and Tipping, 1983)... 

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