A general tensorial expansion for the interaction potential between two atoms in arbitrary angular momentum states is derived and the relations between the expansion coefficients and the Born-Oppenheimer potentials of the diatomic molecule are obtained. It is demonstrated that a complete expansion of the interaction potential must employ tensors that are invariant under the inversion of the coordinate system, and the expansion in terms of conventional spherical harmonics is not adequate for the case of two atoms in states with nonzero electronic orbital angular momenta. The concept of the interaction anisotropy between two open-shell atoms is introduced. The correctness of the formalism is demonstrated by the example of two atoms in P states.