Knowledge Bank

A computer program has been written to evaluate the second-order perturbation sums which occur in the calculation of quadrupole hyperfine splittings in pure rotational spectra. The program is suitable for molecules of arbitrary asymmetry containing a single nucleus of spin greater than 1/2 Application has been made to the microwave spectra of 2-bromopropane and ethyl bromide. In 2-bromopropane deviations of frequency separations of hyperfine components from first-order predictions were of the order of several tenths of a megacycle---not large enough to allow determination of the off-diagonal quadrupole coupling constant, but large enough to affect the determination of rotational constants. The inclusion of second-order terms reduced the mean deviation between fifty-eight calculated and observed frequency differences averaging 9.30 Mc/sec from 0.254 to 0.059 Mc/sec. Furthermore the mean difference between calculated and observed hypothetical unsplit frequencies for seven transitions was reduced from 0.16 to 0.06 Mc/sec, and the derived values of the rotational constants were significantly altered. The computer program was also used to perform complete second-order quadrupole calculations for an analysis of the microwave frequencies reported for ten isotopic species by Flanagan and $Pierce.1$ Only slightly different values were obtained for the off-diagonal quadruple coupling constants determined by Flanagan and Pierce by means of a partial second-order analysis. How-ever, it was found that the discrepancies previously $noted1$ in the hyperfine splittings in $CH3CD279$Br and $CH3CD281$Br were the result of a third-order perturbation effect.