Linear Scaling Second Order Møller Plesset Perturbation Theory

Abstract

All traditional methods for electron correlation share a steep power law dependence on the molecular size. This high scaling prohibits the use of these methods to large systems in spite of the very impressive advances in computer technology over the past decades. Clearly, this problem cannot be solved with improvements of computers alone, and new methods reducing the power law scaling to one or near one must be developed. In this chapter some linear of low scaling methods for electron correlation will be reviewed. The focus will be on the linear scaling MP2 methods, but other more accurate correlation methods will also be briefly discussed. In addition, the very efficient RI-MP2 will be discussed even though the high power law scaling of conventional MP2 has not been reduced. A discussion of the RI-MP2 method has been included since it is perhaps an order of magnitude more efficient than other efficient MP2 methods. The RI or density fitting approach has now been combined with the local correlation method, and the RI-LMP2 method exhibits linear scaling with the size of the system. Most of the methods discussed herein are based on the local correlation method introduced by Pulay and Saebø in the early eighties and developed further by Schütz, Werner and co-workers. The topic was reviewed in 2002 and this review will focus on the more recent advances in this field. A new linearly scaling LMP2 approach yielding essentially identical results to conventional canonical MP2 will be described, and MP2 calculations with around 5,000 contracted basis functions have been performed without density fitting using this approach.