Response to “Comment on ‘Positron and positronium chemistry by quantum Monte Carlo. IV. Can this method accurately compute observables beyond energy?’ ” [J. Chem. Phys. 111, 108 (1999)]

Abstract

We discuss the accuracy and applicability to molecular systems of the model proposed by G. G. Ryzhikh and J. Mitroy [J. Phys. B 31, 5013 (1998), ibid. 32, 2203 (1999)] to compute annihilation rate in positron-containing systems. Moreover, we propose small modifications to this model in order to improve its accuracy for molecular systems.

Annihilation rate in positronic systems by quantum Monte Carlo: e+LiH as test case

“…[9] and Ref. [11]. The G(r −+ , γ) values were extrapolated to γ = 0 by fitting them with the simple function a √ γ + b, the extrapolation law deduced in Ref.…”

“…Although these experiments are relevant both technologically and scientifically [1,2], only few theoretical studies have been devoted to accurately compute annihilation rates for realistic systems like atoms and molecules in order to compare with experimental data or to predict trends [3,4,5,6,7,8,9,10,11]. Moreover, these have been restricted to deal at most with four active electrons, so that only a bunch of systems have been studied so far.…”

“…Although not a solution, a slightly better approach was devised by substituting the simple sphere with a Gaussian function centered at the coalescence point [8,9,11]. The variance of this estimator also goes to infinity upon decreasing of the Gaussian width, but it diverges less faster than the one of the spherical well, therefore allowing a statistically more accurate estimation of δ(r −+ ) = i δ(r i+ ) .…”

“…Even admitting a perfect sampling in the regions where two particles are close to each other, the primitive method of counting the number of times the interparticle distance r is smaller than a given radius r w (i.e. counting the ones that fall into a spherical well of radius r w ) [5] has an associated statistical error that diverges for r w → 0 [11]. This fact means that the estimation of the statistical error of the extrapolated value is based on shaky grounds.…”

“…For these systems beyond the problem of the method used to compute δ , there is another difficulty: as far as we know, nobody has been able to optimize an accurate Ψ T for a positronic system with more than four electrons. More specifically, for large systems explicit correlation between the electrons and the positron has been found difficult to introduce [11]. This means that the "pile up" of the electron density over the positron is not correctly described, therefore giving rise to too small annihilation rates [18].…”