Knowledge Bank

The methods previously developed in this group to study vibrational states in polyatomic molecules using Canonical Van Vleck Perturbation Theory (CVPT)$\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ are extended to include rotational interactions and applied to $H2$O$\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ $SO2$ and $H2CO$. For these calculations, we use a Taylor series expansion of the general Hamiltonian derived by $Pickett.2$ In applying CVPT$\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ it is computationally convenient to take advangage of the isomorphism between the SU(2) and SO(3) groups, rewriting the angular momentum operators in terms of harmonic oscillator raising and lowering operators. Calculated energies for $H2O and $SO2 agree well with variationally obtained energies up to $19,000cm-1$ and $11,000cm-1$, respectively. Since we use an analytical expression of the Hamiltonian for these variational calculations, comparision between the variational and perturbative energies provides a check on both the techniques used to obtain the expansions and the convergence of the perturbative results. Further, for $H2$CO, we find that careful description of the internal curvilinear bend coordinates extends the energy regimes over which these calculations are tractable. Proper choice of these coordinates leads to improved convergence in the perturbative energien, sixth order rotation-vibration energies are converged to $8,000cm-1$, and makes high quality variational calculations tractable for vibrational states with energies up to $10,000cm-1$ above the zero point.