The method of combination differences uses differences of wavenumbers in the P- and R- branches to obtain data that depend only on rotational constants in the vibrational ground or excited state. For the excited state
This function can be fitted, using the method of least-squares to data for carbon monoxide, from Harris and Bertolucci. The data calculated with the formula
in which centrifugal distortion is ignored, are shown in the columns labelled with (1). This formula implies that the data should lie on a straight line with slope 2B′′ and intercept zero. At first sight the data appear to conform to this model, with a root mean square residual of 0.21 cm. However, when centrifugal distortion is included, using the formula
the least-squares fit is improved markedly, with ms residual decreasing to 0.000086 cm. The calculated data are shown in the columns labelled with (2).