Twofold degenerate

The zeroth-order energy level is twofold degenerate. The corresponding vibronic basis functions are ur K+2 0 0 —) = 11) and luj- A"—2 0 0 +) = 2). The first-order energy correction is... 

In other cases, the zeroth-order vibronic levels are generally more than twofold degenerate and the perturbative handling is much more complicated. An exception is the case 07= , U( =li K = 0 with the twofold degenerate zeroth-order level. The basis functions are 1 1 1 1 —) = 1) and 1 —1 1 —l- -)s 2). The zeroth-order energy is... 

The zeroth-order energy level is >j K 100 ) = 14) twofold degenerate—... 

In contrast with 1, for which only four threefold degenerate modes are active, 30 and 33 exhibit 86 and 45 IR active modes, respectively, 58 and 31 of which are twofold degenerate. The lower symmetry of 30 and 33 as compared to 1 also results in a higher number of nonequivalent carbon atoms producing more expected signals... 

Boron trifluoride has two nondegenerate and two twofold degenerate fundamental vibrational frequencies, (a) From Fig. 6.11, how many fundamental bands should appear in the IR spectrum of BF3 (b)... 

The twofold degenerate rearrangement of 51 may involve unpopulated puckered 1,2,4-trimethylcyclobutyl cation 52 as an intermediate. In the threefold degenerate rearrangement of 53, isomeric 54 may be involved as an NMR unpopulated intermediate80. 

The twofold degenerate equilibrium in the case of the l-(2-methylcyclopropyl)ethyl cation 55 is also fast compared to that of the 1-methyl analogue. The static cation could not be frozen even at low temperatures. At-108 °C, the average cationic peaks at<5l3C 167.4... 

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