Low-order Scaling Research Articles

Integral transformation with low-order scaling for large local second-order M�ller-Plesset calculations

An algorithm is presented for the four-index transformation of electron repulsion integrals to a localized molecular orbital (MO) basis. Unlike in most programs, the first two indices are transformed in a single step. This and the localization of the orbitals allows the efficient neglect of small contributions at several points in the algorithm, leading to significant time savings. Thresholds are applied to the following quantities: distant orbital pairs, the virtual space before and after the orthogonalizing projection to the occupied space, and small contributions in the transformation. A series of calculations on medium-sized molecules has been used to determine appropriate thresholds that keep the truncation errors small (below 0.01% of the correlation energy in most cases). Benchmarks for local second-order Møller–Plesset perturbation theory (MP2; i.e., MP2 with a localized MO basis in the occupied subspace) are presented for several large molecules with no symmetry, up to 975 contracted basis functions, and 60 atoms. These are among the largest MP2 calculations performed on a single processor. The computational time (with constant basis set) scales with a somewhat lower than cubic power of the molecular size, and the memory demand is moderate even for large molecules, making calculations that require a supercomputer for the traditional MP2 feasible on workstations. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1241–1254, 1998

The Five-Factor Model for Personality Disorders: Apt or Misguided?

to assess personality pathology, one might expect attenuated correlations but certainly not major shifts in terms of which dimensions relate to which personality disorders. In summary, Widiger has provided an excellent critique of the DSM-III-R system for categorical diagnosis of personality disorders but offers a less than satisfactory resolution to the problems he identifies. Whereas the five-factor model of personality has much to recommend it as a higher order structural model, it may be inadequate for the clinical assessment of personality disorder because the characterizations it provides are too broad and abstract for many clinical purposes-for which lower order scales have the advantage of specificity. Moreover, empirical relations between personality pathology and at least one current measure of the five-factor model were low to moderate and inconsistent with theoretical prediction. In conclusion, although the five-factor model may indeed provide a broad overview of personality that will be useful in developing our understanding of personality disorder, it is premature to foreclose on any one model. It is especially problematic to focus too much attention on the highest level of the trait hierarchy rather than on explorations of the specific dimensions that are particularly relevant and important in the domain of personality pathology.