# 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

## TL;DR

This paper presents a new computational approach combining quadrature and iterative eigensolvers to efficiently calculate fine-structure rovibrational spectra of Van der Waals complexes, accommodating general potentials and large basis sets.

## Contribution

The paper introduces a novel method that replaces traditional matrix element calculations with quadrature and employs iterative eigensolvers for improved efficiency in spectral computations.

## Key findings

- Successfully computed energy levels of NH(3Σ−)-He, O2(3Σ−g)-Ar, and O2(3Σ−g)-He.
- Method handles general potentials without Wigner-Eckart theorem.
- Enables calculations with larger basis sets.

## 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.