The analytical potential energy function (APEF) of SiH⁺(X¹Σ⁺) is fitted by Aguado-Paniagua function with 112 ab initio energy points, which are calculated by Molpro 2012 Package with the multi-reference configuration interaction including the Davidson correction method using AVX Z and AVX dZ (X = Q, 5, 6) basis sets. Moreover, the calculated ab initio energy points are subsequently extrapolated to complete basis set (CBS) limit to avoid the basis set superposition error. All the fitting parameters of APEFs for AV6Z, CBS(Q, 5), AV6dZ, CBS(Qd, 5d), SA-AV6dZ and SOC-AV6dZ methods are gathered. The potential energy curves (PEC) and the corresponding ab initio points are also shown. As can be seen, the PECs show excellent agreement with the ab initio points and a smooth behavior both in short range and long range, which ensures the high quality of fitting process for the current APEFs.

Based on these APEFs of different basis sets and methods including AVQZ, AV5Z, AV6Z, CBS(Q, 5), AVQdZ, AV5dZ, AV6dZ and CBS(Qd, 5d), the spectral constants D_e, R_e, ω_e, B_e, α_e and ω_eχ_e are obtained. In addition, the effects of spin-orbit coupling interaction (SOC) on the system are also investigated. By comparing the spectral constants of SA-AV6dZ with the ones of SOC-AV6dZ, it is found that the effect of SOC on SiH⁺(X¹Σ⁺) is small and can be ignored. We also compare the spectral constants in this work with the experimental values and other theoretical results. The results of this work accord well with the corresponding experimental and other theoretical results. It is worth noting that the deviation of dissociation energy between the theoretical calculations and experimental values is relatively large. Based on this conclusion, we suggest that the spectral constants including the dissociation energy for SiH⁺(X¹Σ⁺) should be remeasured.

Based on the APEF of SOC-AV6dZ which should be more accurate than others in theory, the top 23 vibrational states (j = 0) of SiH⁺(X¹Σ⁺) are calculated first by solving the radial Schrödinger equation. All the vibrational energy levels, classical turning points, rotation constants and six centrifugal distortion constants are also provided. The results of this work can provide significant references for the experimental and other theoretical work.