charges, and , with a displacement vector, , pointing from the negative charge to the positive charge, the electric dipole moment is given by In the presence of an electric field, such as that due to an electromagnetic wave, the two charges will experience a force in opposite directions, leading to a net torque on the dipole. The magnitude of the torque is proportional to both the magnitude of the charges and the separation between them, and varies with the relative angles of the field and the dipole: Similarly, the coupling between an electromagnetic wave and an atomic transition with transition dipole moment depends on the charge distribution within the atom, the strength of the electric field, and the relative polarizations of the field and the transition. In addition, the transition dipole moment depends on the geometries and relative phases of the initial and final states. Origin When an atom or molecule interacts with an electromagnetic wave of frequency , it can undergo a transition from an initial to a final state of energy difference through the coupling of the electromagnetic field to the transition dipole moment. When this transition is from a lower energy state to a higher energy state, this results in the absorption of a photon. A transition from a higher energy state to a lower energy state results in the emission of a photon. If the charge, , is omitted from the electric dipole operator during this calculation, one obtains as used in oscillator strength. Applications The transition dipole moment is useful for determining if transitions are allowed under the electric dipole interaction. For example, the transition from a bonding orbital to an antibonding orbital is allowed because the integral defining the transition dipole moment is nonzero. Such a transition occurs between an even and an odd orbital; the dipole operator, , is an odd function of , hence the integrand is an even function. The integral of an odd function over symmetric limits returns a value of zero, while for an even function this is not necessarily the case. This result is reflected in the parity selection rule for electric dipole transitions. The transition moment integral of an electronic transition within similar atomic orbitals, such as s-s or p-p, is forbidden due to the triple integral returning an ungerade (odd) product. Such transitions only redistribute electrons within the same orbital and will return a zero