Multiscale coupling schemes spanning the quantum mechanical, atomistic forcefield, and continuum regimes

Roopam Khare, Steven L. Mielke, George C. Schatz, Ted Belytschko

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


Strategies for coupling quantum mechanical (QM), molecular mechanical (MM), and continuum mechanical (CM) methods are described. For QM/MM coupling, we consider two overlapping domain schemes: the widely-used ONIOM method that involves full overlap, and a new minimal-overlap scheme denoted as the "quantum to molecular mechanical overlapping domain" (QtMMOD) method. In the QtMMOD method, the part of the region that is treated by quantum mechanics does not require MM calculations, which makes the method suitable for systems containing localized regions that cannot be modeled by available empirical potentials. We describe how the QtMMOD method can in turn be coupled to a finite element model by the bridging domain method, another overlapping domain method, yielding a QM/MM/CM model. We also show how the QtMMOD scheme can be used to couple a finite element model directly with a QM model. These coupling methods were used to calculate the fracture properties of graphene sheets containing defects. We obtained good agreement between stress-strain curves and fracture strengths calculated by the three methods and benchmark results of a strictly QM calculation. An extension of an atomistic strain calculation method based on a moving least squares scheme, which is applicable to the treatment of material interfaces, is given.

Original languageEnglish (US)
Pages (from-to)3190-3202
Number of pages13
JournalComputer Methods in Applied Mechanics and Engineering
Issue number41-42
StatePublished - Jul 1 2008

Bibliographical note

Funding Information:
We gratefully acknowledge grant support from the NASA University Research, Engineering, and Technology Institute on Bio Inspired Materials (BIMat) under Award No. NCC-1-02037, from the Army Research Office under Grant No. W911NF-05-1-0049 and from the National Science Foundation.


  • Fracture
  • Graphene sheets
  • Molecular mechanics
  • Multiscale
  • Nanofracture
  • Quantum mechanics


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