Dipole moment functions of carbon dioxide and nitrous oxide

The vibrational wavefunctions obtained from the direct numerical diagonalization of the vibrational Hamiltonian matrix are used to compute the matrix elements of transition dipole moments for carbon dioxide and nitrous oxide. The computed matrix elements are found very close to those obtained previously by the contact transformation method. The least-squares fit of the dipole moment derivatives up to the second order has been attempted. It is shown that the values as well as the signs of the second derivatives can be determined if the mechanical anharmonicity contributes considerably to the corresponding combination and/or difference bands. The bands selected for N₂O include the fundamentals, first overtones, binary combination, and difference bands as well as the bands coupled with the above by Fermi resonances. The converged set of the dipole moment derivatives of N₂O gives the computed matrix elements very close to the observed. This also demonstrates the wider applicability of the direct diagonalization method.