  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.
