A Universal Power Law Governing the Accuracy of Wave Function-Based Electronic Structure Calculations.

A universal power law governing the accuracy of wave function-based electronic structure calculations is derived from first principles. The resulting expression Δ E ( N , N ) N ≳ 1 9 π 2 g N N , where g is a system-specific factor assuming values between zero and one and ≳ stands for asymptotic inequality at the limit of N → ∞ , allows facile estimation of the error Δ E ( N , N ) in the electronic energy of a singlet state of an N -electron system computed with a basis set of N one-electron functions. Several approaches to the estimation of the factor g , which depends on the on-top two-electron density, are presented.