# Wavefunctions for large electronic systems

## TL;DR

This paper discusses the exponential growth problem of wavefunctions in large electronic systems and proposes a Liouville space approach with cumulants as a potential solution for scalable electronic structure calculations.

## Contribution

It introduces a novel wavefunction framework in Liouville space using cumulants, addressing the exponential wall problem in large systems.

## Key findings

- Cumulants are proposed as a suitable tool for large-scale electronic calculations.
- Wavefunctions in Liouville space can mitigate the exponential growth issue.
- The approach draws analogy from classical gas cluster expansions.

## Abstract

Wavefunctions for large electron numbers suffer from an exponential growth of the Hilbert space which is required for their description. In fact, as pointed out by W. Kohn, for electron numbers $N > N_0$ where $N_0 \approx 10^3$ they become meaningless (exponential wall problem). Nevertheless, despite of the enormous successes of density functional theory, one would also like to develop electronic structure calculations for large systems based on wavefunctions. This is possible if one defines the latter in Liouville space with a cumulant metric rather than in Hilbert space. The cluster expansion of the free energy of a classical monoatomic gas makes it plausible that cumulants are a proper tool for electronic structure calculations.