Local Møller–Plesset Perturbation Theory
The computational cost of most correlated electronic structure methods scales as a high-degree polynomial in the molecular size, typically O(N5)–O(N7), where N is the size of the molecule. This scaling poses a serious challenge to the application of high-level quantum chemical methods to larger molecular systems, and to extend the scope of such methods, it is necessary to employ alternative formulations that reduce the computational complexity. Reduced-scaling approaches that exploit the inherently local nature of dynamic electron correlation have been developed for a number of correlated electronic structure methods, including second-order Møller-Plesset perturbation (MP2) theory. One such method, the local MP2 method LMP2, 1,2
employs an orbital-invariant formulation that makes it possible to express the energy in a basis of noncanonical orbitals. The delocalized nature of the canonical molecular orbitals used in conventional MP2 theory gives rise to the high-order polynomial scaling of the cost, and by permitting the use of localized orbitals, the local MP2 method offers the potential for a significantly reduced computational cost.