Use of Gauss–Hermite quadrature in the treatment of predissociation resonances with the complex-scaling method

An efficient numerical integration procedure based on the Gauss–Hermite quadrature is developed for evaluation of rovibrational Hamiltonian matrix elements in a basis of complex-scaled harmonic oscillator functions. By scaling the basis functions rather than the Hamiltonian itself, it is possible to employ molecular potential energy and coupling data directly in numerical form without first having to fit them to analytical functions. The new method is employed for the treatment of the CO B-D 1Σ+ system by employing model diabatic potentials and coupling elements from the literature. Calculations are carried out in both the original diabatic and the corresponding adiabatic representation of the electronic states. Because of the sharp oscillations in the nonadiabatic coupling functions it is found that the convergence properties in the diabatic basis are somewhat better than in the corresponding adiabatic treatment, but very good agreement is obtained between the two sets of energy and linewidth results for the lowest 11 vibrational states. Comparison is also made with earlier results for the same system obtained by employing the optical potential and close coupling methods, respectively. The second-derivative G12 coupling matrix elements are found to have an important effect on the computations in the adiabatic representation and are essential for obtaining a high level of agreement with the corresponding diabatic results. The present method is well-suited for applications based on ab initio potential energy surfaces and couplings since it requires neither that the pointwise computed data be fitted to polynomials nor that they be subjected to a diabatic transformation.