New Theoretical Method for the Accurate Calculation of Expectation Values on Functions of Internuclear Separation in1Sgr;hyphen;State Diatomic Molecules

摘要

A new theoretical method for the calculation of expectation values on1Sgr;hyphen;state diatomic molecular vibrationhyphen;rotation states is developed. Using Dunham's theory of vibrationhyphen;rotation energies, each integral can be expressed as a rapidly converging series of terms, each of which is given to high accuracy as an analytical function of the internuclear potential parameters. Results are presented which allow the rapid calculation of expectation values on any arbitrarily specified algebraic function of intermolecular separation, complete to four orders in the ratio of the rotational to vibrational constant of the molecule. We first apply the method to review and extend the theoretical calculation of rotational energies in H2. In these calculations, agreement with experiment to within the combined limits of accuracy is achieved, the value 60.837 cmminus;1resulting for Dunham's rotational constant,Y01. As a further example, the expectation value on theugr;thinsp;equals;thinsp;0, Jthinsp;equals;thinsp;1state of the inverse third power of the internuclear separation in H2is calculated using theoretical potential constants on the one hand, and potential constants derived from spectroscopic measurements on the other. The greatest accuracy is achieved with the latter, the valuelang;01thinsp;verbar;thinsp;Rminus;3thinsp;verbar;thinsp;01rang;minus;1thinsp;sol;thinsp;3thinsp;equals;thinsp;lpar;0.74695thinsp;plusmn;thinsp;0.00003rpar; Aring;showing good agreement with the experimental value and a value obtained from direct numerical calculation by Wolniewicz.