Breaking the curse of dimension for the electronic Schrödinger equation with functional analysis.

Graphical abstract Highlights • If the wavefunction is sufficiently differentiable, it can be approximated with polynomial cost in the high-accuracy limit. • A strategy for picking configurations is proposed and used to define a selected configuration interaction method called GKCI. • Griebel-Knapek configuration interaction (GKCI) is appropriate for wavefunctions with dominating mixed smoothness. • Errors due to truncating the Slater determinant expansion and the one-electron basis set should be balanced. • GKCI gives promising results when tested for small systems. Abstract Most approaches for solving the electronic Schrödinger equation do not fully exploit the functional-analytic simplicity of the electronic wavefunction. Because of this, the cost of these methods explodes exponentially with increasing electron number, an effect that is often called the curse of dimension. Recent work in mathematics and computer science shows how, by exploiting the smoothness of molecular wavefunctions, one can design methods that achieve the same accuracy as full configuration interaction, but with polynomial cost. The mathematical background of this approach is presented, along with a detailed prescription for identifying the relevant Slater determinants and a demonstration of the method's effectiveness for atomic systems. In the basis-set limit, this truncated configuration interaction method is size-consistent. [ABSTRACT FROM AUTHOR]