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Quasi-continuum Density Functional Theory is the first full quantum mechanics simulation of a system
at the micron scale and a ground-breaking progress in computational mechanics of materials. This method
was first developed by Q. Peng and his collaborators (PRB 78,054118,2008). QDFT is a multiscale approach that is based
entirely on density functional theory and allows quantum simulations at the micron scale and beyond. This
method combines the coarse graining idea of the adaptive finite element method and the coupling strategy of
the quantum mechanics/molecular mechanics (QM/MM) method, and represents a major advance in the
quantum simulation of materials properties. It should be stated at the outset that QDFT is not a brute-force
electronic structure method, but rather a multiscale approach that can treat large systems - effectively up to
billions of electrons. Therefore, some of the electronic degrees of freedom are reduced to continuum degrees
of freedom in QDFT. On the other hand, although QDFT utilizes the idea of QM/MM coupling, it does not
involve any classical/empirical potentials (or force fields) in the formulation - the energy calculation of
QDFT is entirely based on DFT. This is an important feature and advantage of QDFT, which qualifies it as a
bona fide quantum simulation method. The method was verified by a multitude of tests, including nano-
indentation of an Al thin film.
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