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Minimising biases in full configuration interaction quantum Monte
19.A. Sokal, Functional Integration, NATO ASI Series (Springer, US, 1997), Vol. 361, p. 131.
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27. Hartree–Fock energy: −1.117 505 884 3Eh.
28. Hartree–Fock energy: −0.933 898 055 2Eh.
30. Hartree–Fock energy: −128.488 775 551 6Eh.
31. FCIQMC projects out the ground state using , whereas is used in DMC. This means weighting with Eq. (12) is an approximation. The error introduced is second order in δτ (this can be shown using a Taylor expansion). The reweighting requires the projected energy and population at every individual time step.
35. We assume that the independent psip probabilities are less than or equal to one for simplicity; the generalisation is straightforward.
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We show that Full Configuration Interaction
Carlo (FCIQMC) is a Markov chain in its present form. We construct the
matrix of FCIQMC for a two determinant
hence compute the stationary distribution. These solutions are used to quantify the
dependence of the population dynamics on the parameters defining the Markov chain. Despite the
simplicity of a system with only two determinants, it still reveals a population control
bias inherent to the FCIQMC algorithm. We investigate the effect of simulation
parameters on the population control bias for the neon atom and suggest simulation
setups to, in general, minimise the bias. We show a reweight ing scheme to remove the
bias caused by population control commonly used in diffusion Monte Carlo [Umrigar
et al., J. Chem. Phys. 99, 2865 (1993)] is effective
and recommend its use as a post processing step.
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