Numerical simulation of ro-vibrational spectra for diatomic molecules using the Numerov matrix method

Abstract

In this paper, the Numerov matrix method is implemented in a pedagogic manner for simulation of a CO molecule. First, the Numerov algorithm is implemented in the spreadsheet environment ‘Gnumeric’ to obtain coarse vibrational, rotational and ro-vibrational spectrum. Then, the code is written in Scilab so that simulation can be performed for smaller step-sizes so as to achieve greater accuracy for frequencies in ro-vibrational fine-structure spectrum. The simulated vibrational frequencies have been obtained to an accuracy of 0.01% with respect to the experimental ones. The values of rotational constant (B e ) and anharmonicity constant ( ω ¯ e x e ) have been obtained to accuracies of 0.6 and 1.22% respectively. This procedure can be easily integrated as a simulation activity for determination of ro-vibrational spectra of various heterogenous diatomic molecules at undergraduate level.