Ro-vibrational energies of CO molecule via improved generalized Pöschl–Teller potential and Pekeris-type approximation

Abstract

The improved form of the generalized Poschl–Teller potential (GPT) has been introduced to discuss diatomic molecules. Schrodinger equation has been solved for the improved generalized Poschl–Teller (IGPT) potential by applying a new Pekeris-type approximation to the centrifugal term, and then the rotational–vibrational energy eigenvalue equation has been obtained. By using this ro-vibrational energy eigenvalue equation, firstly, we have calculated the vibrational energies of the $$X^{1}\Sigma ^{+}$$ state of CO molecule and compared them with the experimental Rydberg–Klein–Rees (RKR) data and theoretical results obtained by using Morse, improved Tietz and improved Poschl–Teller potentials. It has been showed that the IGPT potential is one of the best potential energy function in fitting experimental RKR data for $$\hbox {CO}(X^{1}\Sigma ^{+})$$ molecule. Secondly, we have obtained the maximum possible ro-vibrational energies of $$\hbox {CO}(X^{1}\Sigma ^{+})$$ molecule by using the IGPT potential. Also, it has been proved that the Pekeris-type approximation should be used for the centrifugal term instead of Greene–Aldrich approximation in order to get most probable (or more accurate) ro-vibrational energies for the carbon monoxide molecule.