메뉴 건너뛰기




Volumn 93, Issue 24, 2016, Pages

Boosting the accuracy and speed of quantum Monte Carlo: Size consistency and time step

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84976897930     PISSN: 24699950     EISSN: 24699969     Source Type: Journal    
DOI: 10.1103/PhysRevB.93.241118     Document Type: Article
Times cited : (86)

References (48)
  • 5
    • 64249130695 scopus 로고    scopus 로고
    • Linear-Scaling Methods in Quantum Chemistry, in, edited by K. B. Lipkowitz and T. R. Cundari (John Wiley & Sons, Inc., Hoboken, NJ), pp
    • C. Ochsenfeld, J. Kussmann, and D. S. Lambrecht, Linear-Scaling Methods in Quantum Chemistry, in Reviews in Computational Chemistry, edited by K. B. Lipkowitz and T. R. Cundari (John Wiley & Sons, Inc., Hoboken, NJ, 2007), pp. 1-82.
    • (2007) Reviews in Computational Chemistry , pp. 1-82
    • Ochsenfeld, C.1    Kussmann, J.2    Lambrecht, D.S.3
  • 10
  • 13
    • 68649092014 scopus 로고    scopus 로고
    • J. Harl and G. Kresse, Phys. Rev. Lett. 103, 056401 (2009). PRLTAO 0031-9007 10.1103/PhysRevLett.103.056401
    • (2009) Phys. Rev. Lett. , vol.103 , pp. 056401
    • Harl, J.1    Kresse, G.2
  • 25
  • 29
  • 30
    • 84976879416 scopus 로고    scopus 로고
    • 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
    • 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.
  • 32
    • 84976866837 scopus 로고    scopus 로고
    • 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
    • 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.
  • 38
    • 11244316350 scopus 로고    scopus 로고
    • D. Alfè and M. J. Gillan, Phys. Rev. B 70, 161101 (2004). PRBMDO 1098-0121 10.1103/PhysRevB.70.161101
    • (2004) Phys. Rev. B , vol.70 , pp. 161101
    • Alfè, D.1    Gillan, M.J.2
  • 39
    • 84976866272 scopus 로고    scopus 로고
    • 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
    • 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.
  • 40
    • 84976893773 scopus 로고    scopus 로고
    • 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]
    • 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].
  • 42
    • 84976878762 scopus 로고    scopus 로고
    • 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
    • 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.
  • 43
    • 84976866281 scopus 로고    scopus 로고
    • 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
    • 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.
  • 44
    • 84976889444 scopus 로고    scopus 로고
    • (private communication)
    • J. Hermann (private communication).
    • Hermann, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.