2019
DOI: 10.1016/j.cma.2019.04.020
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Adaptive QM/MM coupling for crystalline defects

Abstract: QM (quantum mechenics) and MM (molecular mechenics) coupling methods are widely used in simulations of crystalline defects. In this paper, we construct a residual based a posteriori error indicator for QM/MM coupling approximations. We prove the reliability of the error indicator (upper bound of the true approximation error) and develop some sampling techniques for its efficient calculation. Based on the error indicator and Dörfler marking strategy, we design an adaptive QM/MM algorithm for crystalline defects… Show more

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Cited by 22 publications
(27 citation statements)
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“…The rigorous statement of this result is given in Theorem 4.4. An analogous result has recently been proven for a tight binding model in [14]. This result not only gives a strong justification for the construction of classical shortranged interatomic potentials in metals, but in fact it allows us to treat the TFW mechanical response as if it emanated from such a classical potential.…”
Section: Introductionsupporting
confidence: 68%
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“…The rigorous statement of this result is given in Theorem 4.4. An analogous result has recently been proven for a tight binding model in [14]. This result not only gives a strong justification for the construction of classical shortranged interatomic potentials in metals, but in fact it allows us to treat the TFW mechanical response as if it emanated from such a classical potential.…”
Section: Introductionsupporting
confidence: 68%
“…Our main technical result to achieve this is the following pointwise stability estimate for the TFW equations, which establishes the locality of the electron response to changes in the nuclear configuration. Compared with [14] it is noteworthy that our result takes Coulomb interaction fully into account. Rigorous statements, under different conditions, are given in Theorems 3.4 and 3.5.…”
Section: Introductionmentioning
confidence: 95%
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“…Here D I,J is the force constant matrix corresponding to the periodic lattice structure, defined as the second derivative of the energy. In the context of QM/MM coupling, such approximation has also been used in [8]. The force constant matrix D I,J can be computed by means of a finite difference approach (also called the "frozen phonon approach"), or by density functional perturbation theory [3] in electron structure software packages.…”
Section: Geometric Relaxation By Atomistic Green's Functionmentioning
confidence: 99%