Symmetry-adapted perturbation theory convergence

Table 1-3. Summary of the symmetry forcing operators, convergence properties, and asymptotic correctness of various symmetry-adapted perturbation theories...

Korona T, Moszynski R, Jeziorski B (1997) Convergence of symmetry adapted perturbation theory for the interaction between helium atoms and between a hydrogen molecule and a helium atom. Adv Quantum Chem 28 171-188... 

Patkowski K, Korona T, Jeziorski B (2001) Convergence behavior of the symmetry-adapted perturbation theory for states submerged in Pauli forbidden continuum. J Chem Phys 115 1137-1152... 

Since the symmetry-adapted perturbation theory provides the basis for the understanding of weak intermolecular interactions, it is useful to discuss the convergence properties of the sapt expansion. High-order calculations performed for model one-electron (Hj) (30), two-electron (H2) (14, 15), and four-electron (He and He-Hz) (31) systems show that the sapt series converges rapidly. In fact, already the second-order calculation reproduces the exact variational interaction energies with errors smaller than 4%. Several recent applications strongly indicate that this optimistic result holds for larger systems as well. 

Convergence of Symmetry-Adapted Perturbation Theory for the Interaction between Helium Atoms and between a Hydrogen Molecule and a Helium Atom... 

SAPT The review articles by Jeziorski, Szalewicz, and others (Jeziorski and Szalewicz 1998, 2002 Jeziorski et al. 1994 Szalewicz 2002 Szalewicz et al. 2005) are probably the most comprehensive articles on symmetry-adapted perturbation theory. See also the discussion of these theories in Stone (1996). For a detailed examination of symmetry-forcing techniques and the convergence of intermolecular perturbation theories see Szalewicz et al. (2005). SAPT(DFT) The theory of the SAPT(DFT) method is described in Misquitta et al. (2005b) and DF-SAPT(DFT) in Podeszwa et al. (2006b). The DF-DFT-SAPT method is described in Hesselmann et al. (2005). 

It is worth noting that the convergence pattern of the polarization series for He2 is very similar to that found for Hj (9) and H2 (18). Thus, at the distances of the van der Waals minimum the Rayleigh-Schrodinger perturbation theory provides only a part of the interaction energy (15), and in practical applications symmetry-adapted perturbation formalisms must be used. 

---