1 Introduction

The basis of computational quantum mechanics is the equation posed by Erwin Schr dinger in 1925 that bears his name. Solving this equation for multielectron systems remains as the central problem of computational quantum mechanics. The difficulty is that because of the interactions, the wave function of each electron in a molecule is affected by, and coupled to, the wave functions of all other electrons, requiring a computationally intense self-consistent iterative calculation. As computational equipment and methods have improved, quantum chemical calculations have become more accurate, and the molecules to which they have been applied more complex, now even including proteins and other biomolecules.

However, ab initio quantum mechanical calculations increase dramatically in scale with N, the number of basis functions ( e.g., Gaussian functions) used to represent the wave functions of all electrons in a system (a molecule or a collection of molecules). ^[1] Hartree-Fock methods (which do not adequately account for the correlation between electrons) scale between N ² and N ³, and it is higher for levels of theory that introduce increasing extents of correlation: Moller-Plesset (MP) second-order perturbation theory scales as N ³ to N ⁴, more accurate coupled cluster ( i.e., CCSD(T)) methods scale as N ⁵ to N ⁶, and full configuration interaction (Full CI) methods, which should be almost exact, scale as N ⁷ to N ⁸. Because of this high-order scaling (referred to as the...