Recent successes of variational methods in quantum chemistry include (i) a new and simpler proof of Zhislin’s fundamental structure theorem on the spectrum of many-particle Schr”odinger operators,(ii) a generalization of Zhislin’s result to a central approximate method of quantum chemistry (the multiconfiguration self-consistent field method, which may be viewed as a closure assumption on higher oder correlations in terms of lower order correlations), (iii) a rigorous derivation of the celebrated vanderWaals1/r6 law for long range interatomic forces from the many-electron Schr”odinger equation. The last result is joint work with Phil Gardner (Warwick).