Of degenerate

Hund s rules Rules which describe the electronic configuration of degenerate orbitals in the ground state. The electronic configuration will have the maximum number of unpaired... 

The co-ordination number in ionic compounds is determined by the radius ratio - a measure of the necessity to minimize cationic contacts. More subtle effects are the Jahn-Teller effect (distortions due to incomplete occupancy of degenerate orbitals) and metal-metal bonding. 

Variational RRKM theory is particularly important for imimolecular dissociation reactions, in which vibrational modes of the reactant molecule become translations and rotations in the products [22]. For CH —> CHg+H dissociation there are tlnee vibrational modes of this type, i.e. the C—H stretch which is the reaction coordinate and the two degenerate H—CH bends, which first transfomi from high-frequency to low-frequency vibrations and then hindered rotors as the H—C bond ruptures. These latter two degrees of freedom are called transitional modes [24,25]. C2Hg 2CH3 dissociation has five transitional modes, i.e. two pairs of degenerate CH rocking/rotational motions and the CH torsion. 

Baer M, Yahalom A and Engelman R 1998 Time-dependent and time-independent approaches to study effects of degenerate electronic states J. Chem. Phys. 109 6550... 

The Role of Degenerate States in Chemistry Advances in Chemical Physics, Volume 124. Edited by Michael Baer and Gert Due Billing. Series Editors T, Prigogine and Stuart A, Rice,... 

This analysis is heuristic in the sense that the Hilbert spaces in question are in general of large, if not infinite, dimension while we have focused on spaces of dimension four or two. A form of degenerate perturbation theory [3] can be used to demonstrate that the preceding analysis is essentially correct and, to provide the means for locating and characterizing conical intersections. 

Figure 1- Representatiori of degenerate states from nonrelativistic components, (a) Degenerate zeroth-order states at (b) Spin-orbit interaction splits 11 state, (c) With full spin-orbit...

INTRODUCTION TO THE ROLE OF DEGENERATE STATES IN CHEMISTRY Kill... 

Be careful when you use the Orbital Criterion for symmetrical system s. To get correct resnlis, you in u st include all or none of any set of degenerate orbitals in the Cl, n ot jn si some of them. Carrying out an RIIF calculation first and studying the Orbitals dialog box will help you to spot degenerate orbitals and avoid this pitfall. 

For the hermitian matrix in review exereise 3b show that the pair of degenerate eigenvalues ean be made to have orthonormal eigenfunetions. 

In the absence of an electric or magnetic field all the functions with f 0 are (2f + l)-fold degenerate, which means that there are (2f + 1) functions, each having one of the (2f + 1) possible values of m, with the same energy. It is a property of degenerate functions that linear combinations of them are also solutions of the Schrddinger equation. For example, just as IJ2p,i solutions, so are... 

Consider now the rr-system in benzene. The MO approach will generate linear combinations of the atomic p-orbitals, producing six rr-orbitals delocalized over the whole molecule with four different orbital energies (two sets of degenerate orbitals). Figure 7.3. The stability of benzene can be attributed to the large gap between the HOMO and LUMO orbitals. 

Apart from the IH and 2H tautomers 2a and 2b, isomeric forms in which the migrating proton takes up its position on one of the carbon atoms in the ring are formally possible. For the case of unsubstituted pyrazole 2, R = r2 = r3 = tjjg tautomeric equilibrium should be represented by the scheme involving 4H 2e and a pair of degenerate 5H species 2c and 2d (Scheme 2). 

The choice of degenerate orbitals is not unique it is also possible to construct Walsh orbitals for cyclohutane. These are precisely the 3E and 4EU pairs of 111.82. 

Lynden-Bell R. M. The effect of molecular reorientation on the line-shapes of degenerate vibrations in infra-red and Raman spectra of liquids, Mol. Phys. 31, 1653-62 (1976). 

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