Size Consistency Error in the Antisymmetric Geminal Power Wave Function can be Completely Removed

The accurate but expensive product of geminals ansatz may be approximated by a geminal power, but this approach sacrifices size consistency. Here, we show both analytically and numerically that a size consistent form very similar to the product of geminals can be recovered using a network of location-specific Jastrow factors. Upon variational energy minimization, the network creates particle number projections that remove the charge fluctuations responsible for size inconsistency. This polynomial cost approach captures strong many-electron correlations, giving a maximum error of just $1.8\mathrm{kcal}/\mathrm{mol}$ during the double-bond dissociation of ${\mathrm{H}}_2\mathrm{O}$ in an STO-3G atomic orbital basis.

Figure 1

A cartoon schematic of our JAGP ansatz, in which the geminal power is constructed from nonorthogonal local geminals (ovals) describing bonds between neighboring atoms (circles). Particle number projectors (rectangles) built from Jastrow factors constrain electron counts on atoms and groups of atoms to remove the “ionic” AGP terms responsible for size consistency errors.

Figure 2

The average number of unphysical charge transfers per molecule in a system of $n$ well-separated ${\mathrm{H}}_2$ molecules. The wave function is a PP-parameterized AGP with various partial number projections. The dotted line is a fit showing the asymptotic $1/n$ decay for $\alpha =0.1$.

Figure 3

Energy errors per molecule for $n$ well-separated ${\mathrm{H}}_2$ molecules. For AGP, both the PP and optimized versions of the wave function are shown.

Figure 4

Energy errors relative to FCI for the symmetric dissociation of minimal basis ${\mathrm{H}}_2\mathrm{O}$ with bond angle 109.57°. JAGP’s statistical uncertainties are smaller than the symbols.