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We note that other QMC approaches, such as the variational Monte Carlo (VMC) or the lattice regularized diffusion Monte Carlo (LRDMC) [11] methods, do not suffer from these problems. This has been shown in Ref. [12], where the effect of the cutoff in the local energy on the size-consistency issue was carefully considered also for LRDMC. In this paper, however, we are concerned with the much more widely used DMC
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We note that other QMC approaches, such as the variational Monte Carlo (VMC) or the lattice regularized diffusion Monte Carlo (LRDMC) [11] methods, do not suffer from these problems. This has been shown in Ref. [12], where the effect of the cutoff in the local energy on the size-consistency issue was carefully considered also for LRDMC. In this paper, however, we are concerned with the much more widely used DMC.
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See Supplemental Material at for a short review of the DMC method, followed by a description of the DMC algorithm, the problem of the divergences in proximity of the nodal surface, the instabilities in DMC simulations and the size-consistency issue met when DMC is stabilized by slightly modifying the algorithm. The last three sections provide further details on the three examples shown in the paper, including the atomic coordinates. Finally we report results on the relative computational cost of the old and new methods
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See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.93.241118 for a short review of the DMC method, followed by a description of the DMC algorithm, the problem of the divergences in proximity of the nodal surface, the instabilities in DMC simulations and the size-consistency issue met when DMC is stabilized by slightly modifying the algorithm. The last three sections provide further details on the three examples shown in the paper, including the atomic coordinates. Finally we report results on the relative computational cost of the old and new methods.
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Note that this is not the water-methane dimer equilibrium configuration, but just a configuration in which the C-O distance is near the equilibrium value. The coordinates of the atoms in this configuration are reported in the SI
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Note that this is not the water-methane dimer equilibrium configuration, but just a configuration in which the C-O distance is near the equilibrium value. The coordinates of the atoms in this configuration are reported in the SI.
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For example, in the case of a cluster formed by a large number of molecules the construction of the system with all molecules far enough away from each other could be difficult, or even impossible, and alternative correction schemes would be required [21]
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For example, in the case of a cluster formed by a large number of molecules the construction of the system with all molecules far enough away from each other could be difficult, or even impossible, and alternative correction schemes would be required [21].
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84976878762
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Note that, given (Equation presented) the distribution of the branching factor (Equation presented) of some system (Equation presented), the distribution (Equation presented) of a system containing (Equation presented) noninteracting copies of (Equation presented) does not have, in general, the same form. This is because the central limit theorem implies that (Equation presented) becomes Gaussian for large enough (Equation presented), but in general (Equation presented) is not Gaussian. Thus the distribution cannot be modified in a way that is exactly size consistent and our proposed method is therefore only approximate
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Note that, given (Equation presented) the distribution of the branching factor (Equation presented) of some system (Equation presented), the distribution (Equation presented) of a system containing (Equation presented) noninteracting copies of (Equation presented) does not have, in general, the same form. This is because the central limit theorem implies that (Equation presented) becomes Gaussian for large enough (Equation presented), but in general (Equation presented) is not Gaussian. Thus the distribution cannot be modified in a way that is exactly size consistent and our proposed method is therefore only approximate.
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The standard deviation (Equation presented) of the DMC distributions will, in general, be different from the (Equation presented) of the VMC distributions, but the same arguments would apply
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The standard deviation (Equation presented) of the DMC distributions will, in general, be different from the (Equation presented) of the VMC distributions, but the same arguments would apply.
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