Multiscale quantum/atomistic coupling using constrained density functional theory

Multiscale coupling of a quantum mechanical (QM) domain to a coarser-scale material description in a larger surrounding domain should yield forces and energies in the QM domain that are the same as would be achieved in a QM simulation of the entire system. Here, such a coupling is achieved by using constrained density functional theory (DFT) in which the quantum mechanical interaction between the domains is captured via a constraint potential arising from an imposed constraint on the charge density in a boundary region between the two domains. The implementation of the method, including the construction of the constraint charge density and the calculation of the constraint potential, is presented. The method is applied to problems in three different metals (Al, Fe, and Pd) and is validated against periodic DFT calculations. The method reproduces the QM charge density and magnetic moments of bulk materials, produces a reasonable edge dislocation core structure for Fe, and also gives accurate vacancy formation energy for Al and chemisorption energy on a flat Pd surface. Finally, the method is used to study the chemisorption energy of CO on a stepped Pd surface. In general, the method can mitigate fictitious interactions between surface steps and other extended defects, and accommodate long-range deformation fields, and thus improves upon periodic DFT calculations.