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Size-Extensive Wave Functions for Quantum Monte Carlo: A Linear Scaling Generalized Valence Bond Approach.

We propose a new class of multideterminantal Jastrow-Slater wave functions constructed with localized orbitals and designed to describe complex potential energy surfaces of molecular systems for use in quantum Monte Carlo (QMC). Inspired by the generalized valence bond formalism, we elaborate a coupling scheme between electron pairs which progressively includes new classes of excitations in the determinantal component of the wave function. In this scheme, we exploit the local nature of the orbitals to construct wave functions which have increasing complexity but scale linearly. The resulting wave functions are compact, can correlate all valence electrons, and are size extensive. We assess the performance of our wave functions in QMC calculations of the homolytic fragmentation of N-N, N-O, C-O, and C-N bonds, very common in molecules of biological interest. We find excellent agreement with experiments, and, even with the simplest forms of our wave functions, we satisfy chemical accuracy and obtain dissociation energies of equivalent quality to the CCSD(T) results computed with the large cc-pV5Z basis set.