The ground electronic state of CS: the potential curve and associated Born-Oppenheimer rovibrational spectrum

Abstract: Basics of the Born-Oppenheimer (B-O) approximation are reviewed. Assuming the domain of applicability of B-O approximation is limited to 4 significant digits (s.d.) in energy spectrum, where mass, relativistic and QED corrections do NOT contribute, it is shown that for carbon monosulfide ${\rm C}\,{\rm S}$ the potential curve $V(R)$ for the electronic ground state $X^1\Sigma^+$ can be constructed analytically in the form of two-point Pade approximant $\frac{1}{R}\ P(5,10)(R)$ in the whole range of internuclear distances $R \in [0,\infty)$. Pade approximant is fixed by taking into account the turning points with 4 s.d. accuracy, found by Coxon and Hajigeorgiou (2023), and asymptotics at small and large internuclear distances, By solving two-body radial nuclear Schr\"odinger equation with the potential $V(R)$ (with standard centrifugal potential included) in the Lagrange Mesh method, the whole B-O rovibrational spectrum for ${}^{12} {\rm C}\,{}^{32} {\rm S}$ diatomic molecule (taken as a particular example) is found: the $\sim 14562$ rovibrational energy states with angular momentum $L_{max}=289$ and vibrational quantum number $\nu_{max} \sim 82$ with accuracy $\sim 10^{-4}$ hartree in energy. It is shown that the experimentally observed transition energies are reproduced within 3-5 s.d. Critical analysis of existing theoretical (phenomenological) results on the rovibrational spectrum is carried out and its comparison with present ones is made.