Molecular symmetry selected applications

Stone applied the theory of Longuet-Higgins to deduce the character tables for the multiple internal rotation in neopentane and in octahedral hexa-ammonium metallic complexes [6]. Dalton examined the use of the permutation-inversion groups for determining statistical weights and selection rules for radiative processes in non-rigid systems [7]. Many applications of the Molecular Symmetry Groups have been reviewed later by Bunker [8,9]. 

In this book we shall place only limited emphasis on symmetry, since there is little use of symmetry in the shape characterization of more complicated molecules most of which have only trivial symmetry. The reader may find many excellent texts on molecular. symmetry in the literature (for a selection see references [73-79]). Note, however, that deviations from a given symmetry and various symmetry deficiency measures are important and more generally applicable tools for shape characterization. These latter subjects are discussed in Chapter 8. 

Vibronic-coupling theory has been a well established area of research since many years. The basic elements of the theory are the concept of dia-batic electronic states, the normal-mode description of vibrational motion, and the application of symmetry selection rules to derive appropriate model Hamiltonians. The applications of vibronic-coupling theory cover the full range of molecular spectroscopy, including, in particular, optical absorption and emission and photoelectron spectroscopy. Typical spectroscopic phenomena associated with vibronic interactions are the appearance of nominally forbidden electronic bands, the excitation of nontotally symmetric modes, or unusual and complex vibronic fine structures of electronic spectra. A fairly comprehensive and up-to-date exposition of vibronic-coupling theory is provided by the monograph of Bersuker and Polinger. ... 

In the next chapter, we will present various chemical applications of group theory, including molecular orbital and hybridization theories, spectroscopic selection rules, and molecular vibrations. Before proceeding to these topics, we first need to introduce the character tables of symmetry groups. It should be emphasized that the following treatment is in no way mathematically rigorous. Rather, the presentation is example- and application-oriented. 

In this chapter, we discuss the various applications of group theory to chemical problems. These include the description of structure and bonding based on hybridization and molecular orbital theories, selection rules in infrared and Raman spectroscopy, and symmetry of molecular vibrations. As will be seen, even though most of the arguments used are qualitative in nature, meaningful results and conclusions can be obtained. 

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. 

In addition the reader may find tables with selection rules for the Resonance Raman and Hyper Raman Effect in the book of Weidlein et al. (1982). Special discussions about the basics of the application of group theory to molecular vibrations are given in the books of Herzberg (1945), Michl and Thulstrup (1986), Colthup et al. (1990) and Ferraro and Nakamoto (1994). Herzberg (1945) and Brandmiiller and Moser (1962) describe the calculation of thermodynamical functions (see also textbooks of physical chemistry). For the calculation of the rotational contribution of the partition function a symmetry number has to be taken into account. The following tables give this number in Q-... 

Computer calculations of molecular electronic structure use the orbital approximation in exactly the same way. Approximate MOs are initially generated by starting with trial functions selected by symmetry and chemical intuition. The electronic wave function for the molecule is written in terms of trial functions, and then optimized through self-consistent field (SCF) calculations to produce the best values of the adjustable parameters in the trial functions. With these best values, the trial functions then become the optimized MOs and are ready for use in subsequent applications. Throughout this chapter, we provide glimpses of how the SCF calculations are carried out and how the optimized results are interpreted and applied. 

The quasi-molecular Hamiltonian (4.11) has had an immensely rich past as a model for point impurities in crystals. For reasons of symmetry and also of the wish for simplification only a few modes were normally included in the second sum in (4.11). These modes have been named interaction- , cluster- or configurational- modes. Although as we have remarked, the range of application is very wide we have made a very narrow selection of those instances in which there has been significant experimental information on the character of the interaction mode. 

A related method to interpret the diastereofecial selectivities of the reactions of double bonds has been proposed by Dannenberg and coworkers [8, 13, 14,]. Tins method also relies on the 7t frontier orbitals of non symmetrical molecules, and proposes breaking the symmetry of the n or it orbitals due to polarization induced by the substituents. Application of frontier molecular orbital theory, taking into account only the substrate MOs, gives a qualitative trend of stereoselection in a number of nucleophilic (reductions of carbonyl compounds) and electrophilic reactions. 

Abstract A discussion on conservation of orbital symmetry and its application to select pericyclic reactions is presented. Initially, effort is made to explore the symmetry characteristics of the cr, cr, n and n molecular orbitals (MOs). This is followed by a description of the MOs and their symmetry characteristics for allyl cation, allyl radical, allyl anion, and 1,3-butadiene. This concept is applied to n2 + n2, n4 + it2 (Diels-Alder) and electrocyclic reactions. 

In the following three sections we shall discuss four applications of quantum mechanics to miscellaneous problems, selected from the very large number of applications which have been made. These are the van der Waals attraction between molecules (Sec. 47), the symmetry properties of molecular wave functions (Sec. 48), statistical quantum mechanics, including the theory of the dielectric constant of a diatomic dipole gas (Sec. 49), and the energy of activation of chemical reactions (Sec. 50). With reluctance we omit mention of many other important applications, such as to the theories of the radioactive decomposition of nuclei, the structure of metals, the diffraction of electrons by gas molecules and crystals, electrode reactions in electrolysis, and heterogeneous catalysis. 

Metallo-phthalocyanines [M(Pc)] have attracted attention from view of their practical application to material science, but the vibrational spectra have been much less studied. This is partly due to low solubility in any solvent and difficulty in spectral analysis. The molecular vibrations of M(Pc) with D4h symmetry are factorized into 14 Aig + 13 A2g -I-14 Big -t- 14 B2g -I- 13 Eg -H 6 Ai + 8 A2 + 7 Bi -1- 28 E and their selection rules are the same as those described for M(OEP). 

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