Molecular dipole

Being a charge distribution consisting of electrons and nuclei, a molecule may possess a permanent electric dipole, called a molecular dipole.

The fact whether or not a molecule has a non-zero permanent dipole depends on the symmetry of the molecule and the symmetry species of the molecular state under consideration. Usually one considers molecules in their ground (lowest energy) state and this state is almost always totally symmetric, i.e., invariant under all symmetry operations. For a molecule that is in a totally symmetric state, it can be shown that  the  components of the molecular dipole (a vector) that are totally symmetric (invariant under all symmetry operations) are the only ones that are  non-vanishing. If a dipole component changes under the action of one or more symmetry operations, it is zero.

This rule can be proved formally, but also understood intuitively. By definition a symmetry operation changes a molecule to a conformation that is indistinguishable from the original conformation. If a dipole component would change under a symmetry operation, it would give a handle for distinguishing the old from the new conformation, so that the two conformations would be distinguishable. This is a contradiction and, hence, either a dipole component is zero or it is invariant (does not change).

More technically: the symmetry operations of a rigid molecule&mdash;the nuclei are clamped in space, but the electrons "move" in the quantum mechanical sense of the word&mdash;form a group, the point group of the molecule. This point group has irreducible representations among which the totally symmetric one, commonly denoted by A1. Most molecular ground states transform as A1 (the symmetry species of the ground state is A1). Only the components of the dipole that also transform according to A1 are non-vanishing. This is true not only for A1 states of the molecule, but for any non-degenerate state (which is a state that transforms according to a one-dimensional irreducible representation of the point group).

An electric dipole moment has the dimension charge times length. The SI unit of dipole is therefore coulomb times meter. However, this unit is very large and hardly used in chemistry and molecular physics. The Gaussian unit of debye (D) is still widely applied. It is 10&minus;10 esu times ångstrom. An ångstrom = 10&minus;8 cm = 10&minus;10 m. An esu (electrostatic unit of charge, now called statcoulomb) is  C/(10&sdot;c) &asymp; 3.335&thinsp;640&thinsp;95&sdot;10&minus;10 C  (where C is coulomb and c is speed of light.) Hence

1\; \mathrm{D} = 10^{-10}\; \frac{10^{-10}}{10 c}\; \mathrm{C\,m}  \approx 3.335\,640\,95\cdot 10^{-30}\;\; \mathrm{C\,m} $$