Accurately capturing electronic correlation at low-order polynomial cost-scaling for strongly correlated systems is a difficult problem. Although many successful methods in electronic structure theory are exclusively posed in the framework of second-quantization, this representation can be nonetheless limiting when trying to develop flexible and affordable algorithms. We have devised a projection factor that performs particle-number projection in real-space, is easily compatible with existing explicitly-correlating factors and can be evaluated at cubic cost-scaling per particle. This 'Number-counting Jastrow factor' does this by correlating the population of electrons between spatial regions, similar to correlation factors based on Fock-space number operators. These regions are defined through a basis of 'counting functions', which are sigmoidal functions that count electrons in a well-defined region, and can be made to cleanly divide space in a systematic and automatable way.<br/>In randomized hydrogenic systems, these Number-counting Jastrow factors, alongside orbital rotations and existing correlation factors, consistenly recover a fraction of correlation energy comparable with multireference methods like CASPT2, even when applied to a single-determinant reference. In the more complex molecular Calcium Oxide, a more intricate counting function setup can reintroduce the correlation necessary to rectify molecular orbital shapes at stretched geometries, and improve the wavefunction's nodal surface, an important factor for use in the highly-accurate Fixed-Node Diffusion Monte Carlo method.

Partitioning space for electronic correlation: Number-counting Jastrow factors

2019 Fall National Meeting

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