Density functional computation of large systems: Approximations of kinetic energy

Density Functional Theory (DFT) has developed in the last decade into a major tool for ab initio electronic structure computations for systems which are too large for other methods. The current status of DFT is reviewed in chapter 1. But when applied to even larger systems with the number of atoms exceeding 100, the required computation scales as the third power of the number of atoms. As a result, it is still impractical to compute large systems.; In the current DFT, all energies are expressed in terms of the total density, except kinetic energy which is computed by the N single electron wave functions in the Kohn-Sham scheme. So to speed up the computation, one needs to have a simpler approximation of the kinetic energy.; The third power scale is due to the orthonormal requirement of the N single electron wave functions of the Kohn-Sham scheme. The only way to lower that scale is to reduce the number of wave functions used in the computation. The first method we developed in chapter 2 is to use a fixed number of reduced wave functions independent of the size of the system. To get the correct kinetic energy we applied some additional orthonormal constraints on the wave functions. The computation required is linear in the size of the system.; The simplest method is to express the kinetic energy by the density function itself. This is called the kinetic energy density functional. The current status of such functional is reviewed in chapter 3. The biggest problem is that there is no quantum oscillation in the densities computed by the current functionals. We believe that by adding a integral term in the kinetic energy functional, the required quantum oscillations can be achieved. Such new kinetic energy functional is introduced and applied to real systems in chapter 4. A method of modifying {dollar}ksb{lcub}f{rcub}{dollar} in the kernel of the integral depending on the local density is discussed in chapter 5, and the resulting formula is applied to isolated atoms. Finally, the second order formula in this approach is discussed and applied to the sample systems in chapter 6.; Although, our final formula is still one step away from chemical accuracy, we believe some small modifications might make it work. At least, it opens a vast ground for future studies, as discussed in chapter 7.