Convergence of the MBPT Series

  The rapid convergence of the MBPT series mentioned in the last section has been recently challenged by the results from a paper which seem to indicate that some well behaved, convergent systems can become divergent by adding diffuse functions to the basis set.[7] It has yet to be determined whether these effects are real or merely numerical noise.

Nevertheless, there are a few points that are worthy of note--and perhaps of debate.

• Some Pros
  • In almost all cases the MP2 (or MBPT2) energy recovers a large fraction of the correlation energy which represents a significant improvement from an SCF computation (0%).
  • This step is computationally very inexpensive.
• Some Cons
  • If the MBPT energies do not monotonically converge (or diverge), MP3 (4,5,) could be worse than MP2.
  • If the series does not rapidly converge, MBPT methods may be more expensive than other correlated methods.