The three adiabatic potential surfaces of the Br(P-2)-HCN complex that correlate to the P-2 ground state of the Br atom were calculated ab initio. With the aid of a geometry-dependent diabatic mixing angle, also calculated ab initio, these adiabatic potential surfaces were transformed into a set of four diabatic potential surfaces required to define the full 3 x 3 matrix of diabatic potentials. Each of these diabatic potential surfaces was expanded in terms of the appropriate spherical harmonics in the atom-linear molecule Jacobi angle theta. The dependence of the expansion coefficients on the distance R between Br and the HCN center of mass and on the CH bond length was fit to an analytic form. For HCN in its equilibrium geometry, the global minimum with D-e = 800.4 cm(-1) and R-e = 6.908a(0) corresponds to a linear Br-NCH geometry, with an electronic ground state of Sigma symmetry. A local minimum with D-e = 415.1 cm(-1), R-e = 8.730a(0), and a twofold degenerate Pi ground state is found for the linear Br-HCN geometry. The binding energy, D-e, depends strongly on the CH bond length for the Br-HCN complex and much less strongly for the Br-NCH complex, with a longer CH bond giving stronger binding for both complexes. Spin-orbit coupling was included and diabatic states were constructed that correlate to the ground P-2(3/2) and excited P-2(1/2) spin-orbit states of the Br atom. For the ground spin-orbit state with electronic angular momentum j = ((3)/(2)) the minimum in the potential for projection quantum number omega = +/-((3)/(2)) coincides with the local minimum for linear Br-HCN of the spin-free case. The minimum in the potential for projection quantum number omega = +/-((1)/(2)) occurs for linear Br-NCH but is considerably less deep than the global minimum of the spin-free case. According to the lowest spin-orbit coupling included adiabatic potential the two linear isomers, Br-NCH and Br-HCN, are about equally stable. In the subsequent paper, we use these potentials in calculations of the rovibronic states of the Br-HCN complex.