title: Physical basis for constrained lattice density functional theory.
abstract: To study nucleation phenomena in an open system, a constrained lattice density functional theory (LDFT) method has been developed before to identify the unstable directions of grand potential functional and to stabilize nuclei by imposing a suitable constraint. In this work, we answer several questions about the method on a fundamental level, and give a firmer basis for the constrained LDFT method. First, we demonstrate that the nucleus structure and free energy barrier from a volume constraint method are equivalent to those from a surface constraint method. Then, we show that for the critical nucleus, the constrained LDFT method in fact produces a bias-free solution for both the nucleus structure and nucleation barrier. Finally, we give a physical interpretation of the Lagrange multiplier in the constraint method, which provides the generalized force to stabilize a nucleus in an open system. The Lagrange multiplier is found to consist of two parts: part I of the constraint produces an effective pressure, and part II imposes a constraint to counteract the supersaturation.
authors.affiliation: Division of Molecular and Materials Simulation, State Key Laboratory of Organic-Inorganic Composites, Beijing University of Chemical Technology, Beijing 100029, China.
authors.forename: Yumei
authors.initials: Y
authors.lastname: Men
authors.forename: Xianren
authors.initials: X
authors.lastname: Zhang