A new explicitly correlated basis set suitable for nonadiabatic energy calculation on small diatomic molecules is presented. The basis functions consist of correlated Gaussians multiplied by powers of the internuclear distance. N-body formulas for Hamiltonian matrix elements and energy gradient components are derived and presented along with a discussion of the nonadiabatic Hamiltonian and symmetry considerations. A sample calculation is presented for the ground state energy of the benchmark system H-2(+) in which rapid convergence to near exact results was observed.