Knowledge Bank

The line strengths, rotational transition frequencies, and measured Stark effect spectra are usually used to determine the molecular dipole moments, so that the accuracy of the line strengths is very important. The line strengths are generally calculated by the linear interpolation within $\Delta \kappa =0.10$ of the tabulated magnitudes, the values calculated by this procedure are only precise up to three decimals. Strictly speaking, these magnitudes are not adequately accurate for deciding the dipole moments. Therefore it is worthwhile and necessary to realize the differences between the actual line strengths and those computed by the linear interpolation within $\Delta \kappa$ less than 0.10. The evaluations of the precision of the linearly interpolated line strengths for several different increments have been made for some molecules. The comparisons of $211\to 220$ for water were listed in Table 1. From calculations, it is evident that the linearly interpolated values are significiantly accurate only when the increments Of $\Delta \kappa$ are less than 0.05. The line strengths as a function of J have been shown graphically, but it is not of use for the real computations, because they don’t give any specific asymmetry parameter $\kappa$ and transition states. The polynomial interpolation may be used, but it is tedious for hand, calculation and only good for slow changes of line strengths as a function of $\kappa$. In order to provide the theoretical data which can be used to calculate the line Strengths much more accurately by linear interpolation, the strengths calculated by a smaller step are needed badly. The formulas explicitly expressed in terms of 3j symbols were used for the calculations in this work. [FIGURE]