Degenerate orbits

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... 

Jahn-TeHer effect The Jahn-Teller theorem states that, when any degenerate electronic slate contains a number of electrons such that the degenerate orbitals are not completely filled, the geometry of the species will change so as to produce non-degenerate orbitals. Particularly applied to transition metal compounds where the state is Cu(II)... 

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. 

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. 

Cs subgroup which was used above in the allyl ease) has no degenerate representations. Moleeules with higher symmetry sueh as NH3, CH4, and benzene have energetieally degenerate orbitals beeause their moleeular point groups have degenerate representations. 

Point groups in whieh degenerate orbital symmetries appear ean be treated in like fashion but require more analysis beeause a symmetry operation R aeting on a degenerate... 

For the ease given above, one finds n(ai) =1, n(a2) = 1, and n(e) =1 so within the eonfiguration e there is one Ai wavefunetion, one A2 wavefunetion and a pair of E wavefunetions (where the symmetry labels now refer to the symmetries of the determinental wavefunetions). This analysis tells one how many different wavefunetions of various spatial symmetries are eontained in a eonfiguration in whieh degenerate orbitals are fraetionally oeeupied. Considerations of spin symmetry and the eonstruetion of proper determinental wavefunetions, as developed earlier in this Seetion, still need to be applied to eaeh spatial symmetry ease. 

Table 7.5 lists the states arising from a few electron configurations in diatomic molecules in which there are two electrons in the same degenerate orbital. 

The 21 23 excitation has an equally large coefficient these are the other halves of the two pairs of doubly degenerate orbitals. 

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. 

Degenerate orbitals (Section 15.2) Two or more orbitals that have the same energy level. 

Degenerate orbitals, 522 Degree of unsaturation. 174 calculation of, 174-176 Dehydration, 214... 

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. 

At the start, the relative energies of the four orbitals are represented in Fig. 33. The correct procedure requires that we first interact the degenerate orbitals nj and n2, and then mix the resulting combinations with orcc and significantly different energies. This is true even though the overlap between n and n2 is extremely small, because n, and n2 are symmetry-equivalent orbitals. The... 

It should be noted, on the other hand, that a symmetry reduction is predicted even in molecules II, VIII and XIII whose peripheral skeletons correspond to 4n-l-2 cyclic polyenes. The transannular bonds in these molecules are different in nature from those mentioned above. For example, the introduction of the transannular bonds between atoms 2 and 8 and between 3 and 7 of cyclododecapentaene to form bowtiene (II) (Fig. 3) brings about the splitting of the top filled degenerate orbitals of the unperturbed system into two levels, one with its energy raised and... 

Azulene (XI) possesses a transannular bond which has the same effect as those of bowtiene (Fig. 3). The splittings of the top filled and bottom empty degenerate orbitals of cyclododecapentaene in this case are half the corresponding splitting in the case of bowtiene, and are not large enough to produce an effective vibronic interaction between the ground and lowest excited states of the resultant azulene molecule. 

The Jahn-Teller effect is always to be expected when degenerate orbitals are unevenly occupied with electrons. In fact, it is observed for the following electronic configurations ... 

For the triply degenerate orbitals t2g and flM only one of each is plotted for each of them, two further, equal orbitals exist which are oriented along the other two octahedron axes. Right energy sequence of the seven occupied bonding orbitals... 

Orbitals of equal energy are said to degenerate orbitals. 

---