Jahn-Teller distortion
/ YAHN-TELL-er /
Some molecules cannot stand to be perfectly symmetric. If a complex would have its electrons sitting in an unevenly filled set of equal-energy orbitals, it can lower its energy by quietly warping its own shape — stretching some bonds and squeezing others — until that awkward degeneracy is broken. This self-distortion is the Jahn-Teller effect, named for the 1937 theorem of Hermann Jahn and Edward Teller that any nonlinear molecule in an orbitally degenerate electronic state will distort to remove the degeneracy.
The textbook case is octahedral copper(II), a d9 ion. In a perfect octahedron its eg pair (dz2 and dx2-y2) holds three electrons, which means one of the two equal-energy eg orbitals is full and the other half-full — an uneven, degenerate arrangement. The molecule escapes this by elongating: it stretches the two ligands along the z axis away from the metal and pulls the four equatorial ligands in. Now dz2 (which points along z) drops in energy and dx2-y2 (which points at the closer equatorial ligands) rises, splitting the eg pair. The three eg electrons can now arrange themselves unambiguously, lowering the total energy. The octahedron has become a tetragonally elongated one with four short bonds and two long ones.
Jahn-Teller distortion is strongest when the degeneracy lives in the eg orbitals, which point straight at ligands — so it is large and obvious for d9 (Cu2+) and high-spin d4 (Cr2+, Mn3+), and much weaker when the degeneracy is only in the t2g set, which points between ligands. It shows up in real structures: copper(II) complexes almost always have two longer axial bonds, and it warps crystal lattices and broadens absorption bands. It is a clean demonstration that a complex's geometry and its electron configuration are locked together.
In [Cu(H2O)6]2+ the six Cu-O bonds are not equal: four equatorial bonds measure about 1.95 angstrom while the two axial bonds stretch to about 2.4 angstrom. Push the elongation all the way to its limit, removing the two axial ligands entirely, and you arrive at a square-planar complex — which is why so many Cu2+ and Ni2+ species end up square planar.
Copper(II)'s tell-tale four-short, two-long bond pattern is Jahn-Teller distortion made visible.
The theorem guarantees that a distortion will happen and lowers the symmetry, but it does NOT predict its direction or size; elongation (two long axial bonds) is far more common than compression, but that is an empirical observation, not something the theorem dictates.