A comparison of internal energy calculation methods for diatomic molecules

Abstract

Various methods of calculating the internal energy of diatomic molecules are studied. An accurate and efficient method for computing the eigenvalues of the vibrational Schrodinger equation for an arbitrary potential is developed. The method is based on a finite‐element discretization using the cubic Lobatto element. A combination of spectrum slicing and the Laguerre algorithm is used to solve for the eigenvalues. A simple method to compute the quasibound states is presented. For N2 molecules, all vibrational–rotational states of 11 available electronic potentials are computed and summed to obtain the exact internal energy function with temperature. The total computation required 314 sec of CPU time on NASA’s Cray 2 computer. Various approximate models are discussed and compared with exact calculations. It is shown that the splitting of the macroscopic internal energy into separate electronic, rotational, and vibrational energies is not justified at high temperatures.