The Stark effect originates from the interaction between a charge distribution (atom or molecule) and an external electric field. The interaction energy of a continuous charge distribution ρ ρ ( r ) , confined within a finite volume V , with an external electrostatic potential ϕ ϕ ( r ) is V i n t = ∫ ∫ V ρ ρ ( r ) ϕ ϕ ( r ) d 3 r . This expression is valid classically and quantum-mechanically alike. If the potential varies weakly over the charge distribution, the multipole expansion converges fast, so only a few first terms give an accurate approximation. Namely, keeping only the zero- and first-order terms, ϕ ϕ ( r ) ≈ ≈ ϕ ϕ ( 0 ) − − ∑ ∑ i = 1 3 r i F i , where we introduced the electric field F i ≡ ≡ − − ( ∂ ∂ ϕ ϕ ∂ ∂ r i ) | 0 and assumed the origin 0 to be somewhere within V . Therefore, the interaction becomes V i n t ≈ ≈ ϕ ϕ ( 0 ) ∫ ∫ V ρ ρ ( r ) d 3 r − − ∑ ∑ i = 1 3 F i ∫ ∫ V ρ ρ ( r ) r i d 3 r ≡ ≡ q ϕ ϕ ( 0 ) − − ∑ ∑ i = 1 3 μ μ i F i = q ϕ ϕ ( 0 ) − − μ μ ⋅ ⋅ F , where q and μ μ are, respectively, the total charge (zero moment) and the dipole moment of the charge distribution.