I attended a stimulating TYC soirée this week on issues relating to exchange and correlation in Density Functional Theory. Nicola Marzari painted the picture of Narcissus, where the reflection (delocalisation) of an electron arises from the infamous self-interaction error of DFT, or in other words, the absence of electron exchange to exactly cancel the Coulomb interaction of an electron with itself.
The interesting point for me was the distinction between the long and short-range self-interaction error, which manifests in different types of chemical problems, e.g. short-range hybridisation of metal d - anion p orbitals versus long-range charge transfer reactions for mixed oxidation states. Each regime can be corrected differently, depending on the level of approximation: SIC; DFT+U; Hybrid Functionals; Enforced Koopman's Condition, etc. In reality, no correction method solves all issues, but there is now no excuse for blindly applying uncorrected local/semi-local functions to problems that they have been demonstrated to be inappropriate for.
The second talk of the night was from Ali Alavi on Quantum Monte Carlo. I saw the same talk in Shanghai, so on second viewing, it became more digestible. Conceptually, his approach is simple: start with any set of single-particle wavefunctions (e.g. from Hartree-Fock or Density Functional Theory) and sample the multi-determinant space in a stochastic fashion to obtain a good approximation to the many-body wavefunction, at a fraction of the cost of an explicit calculation. The trick is in the algorithm, which Ali appears to have finely crafted over the last few years, combining the best parts of evolution and genocide for his “walkers”. The approach has now been extended to periodic model problems, and has the potential to mature into a new benchmark technique for solid-state calculations.
One difference (of semantics) to note is that while Marzari would argue that the principal error of DFT is in the "exchange" term, by definition in the latter approach the same error falls under electron "correlation" - perhaps, evidence of exchange-correlation duality?