Nature of the fine structure of rotational levels of the ground X$^{2}\Sigma^{+}$-state of the radical CN

Based on non-empirical high-level quantum-chemical calculations of off-diagonal matrix elements of spin–orbital and electron-rotational coupling between the ground X$^{2}\Sigma^{+}$- and excited (1–4)$^{2}\Pi$-states, it has been established that the observed regular effect of $\gamma$-doubling of the rotational levels of the X$^{2}\Sigma^{+}$ state is mainly determined by intra-molecular interactions with distant states (2–4)$^{2}\Pi$. Within the nonadiabatic model of the effective radial Hamiltonian of the isolated electronic state, it was possible to construct the analytical potential of the X$^{2}\Sigma^{+}$ state and the corresponding function $\gamma(R)$, which reproduce the frequencies of rotational and vibrational–rotational transitions (for the lowest vibrational levels $\nu\le$ 3) of the CN molecule at the experimental (spectroscopic) level of accuracy.