Long-range multipolar potentials of the 18 spin-orbit states arising from the C($^3$P) + OH(X$^2\Pi$) interaction

31 pages (texte+figures)We present the multipolar potentials at large intermolecular distances for the 18 doubly-degenerate spin-orbit states arising from the interaction between the two open-shell systems, C($^3$P) and OH(X$^2\Pi$). With OH fixed at its ground vibrational state averaged distance $r_0$, the long-range potentials are two-dimensional potential energy surfaces (PESs) that depend on the intermolecular distance $R$ and the angle $\gamma$ between $R$ and $r$. The 18 $\times$ 18 diabatic potential matrix elements are built up from the perturbation theory up to second order and from a two-center expansion of the coulombic interaction potential, resulting in a multipolar expansion of the potential matrix expressed as a series of terms varying in $R^{-n}$. The expressions for the long-range coefficients of the expansion are explicitly given in terms of monomer properties such as permanent multipole moments, static and dynamic polarizabilities. Accurate values for the monomer properties are used to properly determine the long-range interaction coefficients. The diagonalization of the full 18 $\times$ 18 potential matrix generates adiabatic long-range PESs in good agreement with their {\it ab initio} counterparts