The Kohn-Sham density functional theory is the most widely used theory for studying electronic properties of molecules and solids. It reduces the need to solve a many-body Schrodinger’s equation to the task of solving a system of single-particle equations coupled through the electron density. These equations can be viewed as a nonlinear eigenvalue problem. Although they contain far fewer degrees of freedom, these equations are more difﬁcult in terms of their mathematical structures. In this talk, I will give an overview on efﬁcient algorithms for solving this type of problems. A key concept that is important for understanding these algorithms is a nonlinear map known as the Kohn-Sham map. The ground state electron density is a ﬁxed point of this map. I will describe properties of this map and its Jacobian. These properties can be used to develop effective strategies for accelerating Broyden’s method for ﬁnding the optimal solution. They can also be used to reduce the computational complexity associated with the evaluation of the Kohn-Sham map, which is the most expensive step in a Broyden iteration.
Computational Research Division, Lawrence Berkeley National Laboratory, Berkeley, CA, US