  The dipole-dipole interaction influences nanoscopic matter by fixing the
patterns of permanent, displacive, and induced dipole moments, subject to
constraints of molecular size and other short range interactions. Prediction of
these arrangements is a challenging problem. The eigenvector of maximum
eigenvalue of the dipole-dipole interaction matrix can provide insights and
sometimes a complete solution. As an example, the octahedral tilt instabilities
of perovskite-type crystals is shown to optimize dipolar interactions.
Therefore this instability can be designated as antiferroelectric, because
dipole-dipole interactions are a dominant driving force.
