Electric and magnetic properties of molecules

A standard question in spectroscopy is does a given molecule have a permanent dipole moment This can usually be decided immediately by inspection, but the formal group-theoretical answer is that a molecule can exhibit a component of permanent dipole for each occurrence of the totally symmetric To in the dipole character T (/u.) = xyz = Ft- Similar reasoning can be extended to other multipole moments, polarisabilities and corresponding magnetic properties. 

Ceulemans and L.G Vanquickenborne, The epikernel principle, Structure and Bonding, 71 (1989) 125-159. 

Each molecular property is defined by an energy derivative taken at the zero-field limit e.g. dipole moment  

Each field index corresponds to a set of cartesian directions, and so each derivative has the symmetry of a power of the set x, y, z, symmetrized and with the trace(s) subtracted. The symmetries spanned by the moments and polarisabilities can therefore be deduced from then-indices as, for the moments 

For each property P, the number of independent components needed to specify the whole property tensor is given by the number of copies of Fq in F(P). This information is available from the GT calculator. Example use the calculator to show that has 1 independent component for a molecule of Id symmetry but no non-vanishing components for a molecule of Oh symmetry. [This illustrates the general rule that electric properties with odd numbers of subscripts vanish identically for any centrosymmetric system]. 

---

Anton, J., Ericke, B. and Engel, E. (2004) Noncollinear and collinear relativistic density-functional program for electric and magnetic properties of molecules. Physical Review A, 69, 012505-1-012505-10. 

D. W. Davies, The Theory of the Electric and Magnetic Properties of Molecules, Wiley, New York, 1967. 

Hinchliffe and Bounds review in detail the calculation of the electric and magnetic properties of molecules. Finally, the use of pseudopotentials in molecular calculations is extending the range of ab initio calculation to molecules containing heavy atoms, and Dixon and Robertson survey this rapidly growing field. 

Ritchie, G.L.D. Field-gradient induced birefringence a direct route to molecular quadrupole moments. In Clary, D.C., Orr, B., (eds) Optical, Electric and Magnetic Properties of Molecules, pg. 67, Elsevier, Amsterdam, The Netherlands (1997)... 

P. Lazzeretti, Electric and magnetic properties of molecules, in S. Wilson (Ed.), Handbook of Molecular Physics and Quantum Chemistry, John Wiley Sons, Chichester, to be... 

Davies DW. 1967. The theory of the electric and magnetic properties of molecules. London John Wiley Sons. 

Lazzeretti P (2003) Electric and magnetic properties of molecules. In Handbook of molecular physics and quantum chemistry, vol 3, Part 1, Chapter 3. Wiley, Chichester, pp 53-145... 

The discussion of electric and magnetic properties of molecules retains its importance, especially with the growth of new and sensitive experimental techniques in spectroscopy and magnetic resonance. Chapter 11, on static properties, is a rewritten and expanded version of the corresponding chapter in the first edition and covers effects due to the presence of small (relativistic) terms in the Hamiltonian and to the application of external fields. Nowadays, however, dynamic effects are also of growing importance, and a new Chapter 12 is devoted to time-dependent perturbations and the general theory of linear response. 

---