Simulation of Vibrational Spectrum of Diatomic Molecules Using Morse Potential by Matrix Methods in Gnumeric Workheet

O.S.K.S Sastri, Aditi Sharma, Shikha Awasthi, Anil Kachi and Lalit Kumar

Central University of Himachal Pradesh

The vibrational energy levels of a non-homogeneous diatomic molecule are obtained by solving Time Independent Schrodinger equation (TISE) by choosing Morse potential. Here, we solve this problem using matrix method based numerical technique. The central idea is to embed the Morse potential within an infinite square well potential whose wave functions are chosen as the basis to obtain the H-matrix. The numerical method is implemented in free open source software (FOSS) Gnumeric, a worksheet environment. Relationships, between model parameters of Morse potential and parameter data available from NIST, have been obtained using analytical expressions resulting from solution of TISE using Nikiforov-Uverov (NU) method. Energy eigenvalues of diatomic molecule HCl are obtained to determine its vibrational frequencies to an accuracy ≤ 0.2%. Finally, the fundamental vibrational frequency of various diatomic molecules such as HBr, HI, HF, CO and NO, are determined and have been found to be matching with expected values to an accuracy of ≤ 0.02%.