Spin contamination in quantum Monte Carlo wave functions

Abstract

The wave function usually employed in quantum Monte Carlo (QMC) electronic structure calculations is the product of a Jastrow factor and a sum of products of up-spin and down-spin determinants. Typically, a different Jastrow factor is used for parallel- and antiparallel-spin electrons in order to satisfy the cusp conditions and thereby ensure that the local energy at electron–electron coincidence points is finite. However, when the Jastrow factor is not completely symmetric under interchange of the spatial coordinates of the electrons, the resulting wave function may not be an eigenstate of the spin operator Ŝ2. For the Li and Be atoms, we evaluate the spin contamination in a variety of wave functions with progressively higher body-order correlations in the Jastrow factor. The spin contamination is found to be small for all the wave functions (10−3–10−5), the smaller values being obtained for the more accurate wave functions. On the other hand, if we eliminate the spin contamination by employing a symmetric Jastrow (and sacrificing the parallel-spin cusp condition), the resulting wave functions typically have about 20%–40% larger root mean square fluctuations in the local energy. A wave function which both satisfies the cusp conditions and has definite spin can be constructed, but for systems with many electrons, its computational cost is higher than for the commonly used QMC wave functions.