Intracule Functional Theory

Density functional theory (DFT) has become the most popular by far of the panoply of methods in quantum chemistry and the reason for this is simple. Where other schemes had become bogged down in mindnumbingly expensive and detailed treatments of the electron correlation problem, DFT simply shrugged, pointed at the Hohenberg–Kohn theorem, and asserted that the correlation energy can be written as an integral of a certain function of the one-electron density. The only thing that irritated the wavefunction people more than the cavalier arrogance of that assertion was the astonishing accuracy of the energies that it yields. Well, most of the time. Occasionally, DFT fails miserably and, although the reasons for its lapses are now understood rather well, it remains a major challenge to correct these fundamental deficiencies, while retaining the winsome one-electron foundation upon which DFT rests. Does this mean that, for truly foolproof results, we have no option but to return to the bog of many-body theory? One might think so, at least from a cursory inspection of the current textbooks. But we feel differently, and in this chapter we present an overview of an attractive alternative that lies neither in the one-electron world of DFT, nor in the many-electron world of coupled-cluster theory. Our approach nestles in the two-electron “Fertile Crescent” that bridges these extremes, a largely unexplored land that would undoubtedly have been Goldilocks’ choice. We present results that demonstrate that the new approach — Intracule Functional Theory — is capable of predicting the correlation energies of small molecules with an accuracy that rivals that of much more expensive post-Hartree–Fock schemes. We also show that it easily and naturally models van der Waals dispersion energies. However, we also show that