Anharmonic Force Constants of Polyatomic Molecules. Test of the Procedure for Deducing a Force Field from the Vibration-Rotation Spectrum

The vibrational Hamiltonian of linear HCN, DCN, and TCN is solved by the finite-difference boundary value method and the eigenenergies and expectation values of the reciprocal of the moment of inertia are calculated for the seven lowest energy states. These values provide information equivalent to an observed vibration-rotation spectrum for each isotopic molecule but for a known potential energy surface. The “inversion” procedure by which a general quartic force field is obtained from experimental data is applied to this set of data. The anharmonic force constants thus obtained have errors in the cubic force constants less than 10% of the largest cubic force constant and errors in the quartic force constants less than 13% of the largest quartic force constant.