Scaling behavior of dynamic correlation effects

Abstract

We present an analytical estimate of the intrinsic errors of second-order perturbation theory in the complete basis set limit in the framework a scaling theory, which employs the maximal “sharpness” of the orbitals in a given basis set, quantified by the average momentum, as its fundamental variable. We find that the intrinsic errors of second-order perturbation theory fall with the third inverse power of the maximal momentum representable in the basis set, while the basis set truncation errors fall with the second inverse power of the momentum. These analytical arguments are verified in a numerical investigation employing distributed basis sets of up to 600 orbitals for the helium atom, water, and ethene. Extending our analysis to generic multireference perturbation theory (MRPT) we find that the leading contribution for the relaxation of the orthogonal complement of the zero-order wave function in the primary space scales with the same power as the leading overall perturbative correction, which yields an analytical argument for the perturbation inclusion of such feedback effects in the formulation of efficient versions of MRPT. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 147–157, 1998