Approximate solutions for diatomic molecules under combined potentials in a global monopole and Aharonov–Bohm flux field

Bound state energy eigensolutions of nine different diatomic molecules, specifically, ${\text{H}}_2$, TiH, ${\text{N}}_2$, CO, NO, ScH, CrH, HCl and LiH, placed in a point-like global monopole, have been calculated by solving the time-independent Schrödinger equation (SE). The molecules are confined by the Aharonov–Bohm (AB) flux field and the interaction potential among the charged particles is governed by the combined screened modified Kratzer potential (SMKP) plus Hulthén potential model. Three other special cases of the interaction potential have also been discussed here. Asymptotic iteration method has been used for the mathematical calculations. It is difficult to solve the SE exactly for any non-zero values of the azimuthal quantum number $l$ due to the presence of the centrifugal barrier term. The well-known Pekeris approximation technique for the terms $\frac{1}{r^2}$ and $\frac{1}{r}$ has taken into consideration for the purpose of performing numerical computations connected to an arbitrary $l$ state. The outcomes of this study are in reasonable agreement with the results of previous research on SMKP, Kratzer-Fues potential, and modified Kratzer potential in the Minkowski space. It is observed that the energy spectra of the diatomic molecules suffer considerable change due to the effects of the background AB-flux field and topological defect parameter.