On the divergent behavior of Møller–Plesset perturbation theory for the molecular electric dipole moment

We have recently shown [J. Chem. Phys. 110, 7127 (1999)] that the Moller–Plesset perturbation theory series diverges for the equilibrium dipole and quadrupole moments of HF when the basis set contains diffuse functions. Here, we show that the divergence, as for the energy, is caused by highly excited diffuse back-door intruder states. The HF study is extended to include a stretched geometry, where divergence is also observed in a basis set that does not contain diffuse functions. For BH and CH2, a very slow monotonic convergence is observed. The different convergent/divergent behaviors are qualitatively reproduced by a simple two-state model. The slow convergence or divergence is more pronounced for the dipole moment than for the energy. These observations seriously question the use of higher-order Moller–Plesset perturbation theory for calculations of simple electric properties.