Using quadrature and an iterative eigensolver to compute fine-structure ro-vibrational levels of Van der Waals complexes: NH(${}^3{\Sigma }^{-}$)-He, O${}_2$(${}^3{\Sigma }_g^{-}$)-Ar and O${}_2$(${}^3{\Sigma }_g^{-}$)-He

Abstract

We introduce a new method for computing spectra of molecules for which a spin-spin term in the Hamiltonian has an important effect. In previous calculations, matrix elements of the spin-spin term and of the potential were obtained by expanding the potential and using analytic equations in terms of $3-j$ symbols. Instead, we use quadrature. Quadrature is simple and makes it possible to do calculations with a general potential and without using the Wigner-Eckart theorem. In previous calculations, the Hamiltonian matrix was built and diagonalized. Instead, we use an iterative eigensolver. It makes it easy to work with a large basis. The ideas are tested by computing energy levels of NH(${}^3{\Sigma }^{-}$)-He, O${}_2$(${}^3{\Sigma }_g^{-}$)-Ar and O${}_2$(${}^3{\Sigma }_g^{-}$)-He.