Transition state symmetry number

Quack M 1985 On the densities and numbers of rovibronic states of a given symmetry species rigid and nonrigid molecules, transition states and scattering channels J. Chem. Phys. 82 3277-83... 

These selection rules are affected by molecular vibrations, since vibrations distort the symmetry of a molecule in both electronic states. Therefore, an otherwise forbidden transition may be (weakly) allowed. An example is found in the lowest singlet-singlet absorption in benzene at 260 nm. Finally, the Franck-Condon principle restricts the nature of allowed transitions. A large number of calculated Franck-Condon factors are now available for diatomic molecules. 

The vibrational sum rule (Equation 4.99) applies to transition states even when one of the frequencies is imaginary (and if is negative for that frequency). In that case one finds for ki /k2, with omission of the symmetry number factor, the analogue of Equation 4.105 for the exchange equilibrium constant... 

Transition states for a number of simple reactions can be located simply by geometry optimization subject to an overall symmetry constraint. 

As with the summaries of the other sections, we mention a number of calculation parameters or variables that have been demonstrated to be of critical importance for accurate prediction of aspects of the interactions. Symmetry constraints on the clusters have been shown to introduce arti-factual behavior. Corrections to account for the correlation of electrons have become essential in a calculation, and they must be incorporated self-consistently rather than as postoptimization corrections. Basis sets need to have the flexibility afforded by double- or triple-zeta functionality and polarization functions to reproduce known parameters most accurately. The choice of the model cluster and its size affect the acid strength, and the cluster must be large enough not to spatially constrain reactants or transition states. The choice of cluster is invariably governed by the available resources, but a small cluster can still perform well. Indeed, some of the... 

Biradicals are frequently postulated to arise as intermediates in a number of chemical reactions and unimolecular isomerizations. Sometimes there are reasonable alternative concerted mechanisms in which the intermediate (or transition-state complex) is not a biradical. Such a case of much interest37,61 involves the reactions of singlet [5] and triplet [7] methylenes with olefins. We note that the permutational symmetry does not determine whether or not a reaction is concerted rather it is determined by the shapes of the intermolecular potential surfaces.78 The lowest 1Ai methylene is expected to react by a concerted mechanism, since it correlates with the ground state of the product cyclopropane higher excited singlets need not react via a concerted mechanism. 

All systems studied in this way until now have a spherical distribution of the non-bonding electrons, so no account need be taken of the symmetry relationships between the ground state and the possible transition states. Consequently, the size of the reaction centre, the coordination number and the effective size and packability of the ligands determine whether the mode of activation is associative or dissociative. There is, as yet, no suitable evidence to decide whether the nucleophilicity of the entering group plays a significant part in deciding the mode of activation. 

An important question is whether the JT vibronic coupling (JT, RT, and PJT) mechanism of SB is unique, or it is applicable to a limited number of special cases and hence there may be other mechanisms of SB that are in principle different from the JT one. The answer is that the JT mechanism of spontaneous distortions of high-symmetry configurations (chemically stable systems and transition states of chemical reactions) that leads to SB is unique, and there is no other in principle different mechanism that produces such distortions [1,2,5,11], It was also shown that in ensembles of systems (e.g. local centers in crystals), just the interaction between them (e.g. mutual polarization) cannot produce SB without local (JT) distortions of each system [12]. The JT effects provide thus the necessary and sufficient condition of SB in the systems under consideration. 

A parameterization method of the Hamiltonian for two electronic states which couple via nuclear distortions (vibronic coupling), based on density functional theory (DFT) and Slaters transition state method, is presented and applied to the pseudo-Jahn-Teller coupling problem in molecules with an s2-lone pair. The diagonal and off-diagonal energies of the 2X2 Hamiltonian matrix have been calculated as a function of the symmetry breaking angular distortion modes and r (Td)] of molecules with the coordination number CN = 3... 

In connection with transition-state theory, one will also occasionally meet the concept of a statistical factor [13]. This factor is defined as the number of different activated complexes that can be formed if all identical atoms in the reactants are labeled. The statistical factor is used instead of the symmetry numbers that are associated with each rotational partition function (see Appendix A.l) and, properly applied, the... 

Several factors affect intensities of crystal field spectra. In addition to enhancement by increased temperature and pressure discussed in chapter 9 ( 9.4), intensities of absorption bands depend on first, the spin-state or number of unpaired electrons possessed by a transition metal ion second, whether or not the cation is located at the centre of symmetry of a coordination site and third, interactions with next-nearest-neighbour cations. 

There have been a large number of measurements of angular distributions in desorption which show sharply peaked distributions and these have recently been reviewed by Kislyuk [44]. In some cases the products of reaction on fcc(l 1 0) surfaces are found to be peaked at an angle to the surface normal along the [001] azimuth (Fig. 9) notably for N2 produced by NO [77, 78] or N20 [79] decomposition, C02 formed by CO oxidation [80, 81] and CO formed by C + O recombination [82]. Sharply peaked distributions indicate a repulsive energy release which lies at an angle to the surface normal [83]. This occurs either because reaction takes place on (111) facets on the reconstructed (1x2) missing row surface (e.g., CO formation on Pt(l 1 0)-(l x 2) surface [82]) or, as in the case of N20 decomposition, because the symmetry of the transition state creates a repulsion which is directed away from the surface normal [84, 85]. 

Chemical mechanisms for l60 enrichment It was discovered in the lab, in molecular clouds and in the Earth s atmosphere that purely chemical processes exist that can enrich only l60, leaving the ratio 170/l80 unchanged. This is observed in the formation of ozone. Itis understood by quantum mechanical symmetries, in which the ozone l60-l60-l60 is more symmetrical than either 170-l60-l60 or l80-l60-l60 and therefore has different numbers of quantum transition states. 

Symmetry factors, o, do not appear in eqn. (28) because the numbers of equivalent pathways have been allowed for in the definition of the kinetic isotope effect. F0(d is the critical energy of the decomposition involving the lighter isotope and F0(II) that of the decomposition involving the heavier isotope. The density of states, N(E), of the reactant ion is, of course, common to both decompositions and does not affect the intramolecular kinetic isotope effect. The intramolecular kinetic isotope effect is, therefore, dependent only upon transition state properties. 

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