Kohn-Sham approach

Since the Fock operator is a effective one-electron operator, equation (1-29) describes a system of N electrons which do not interact among themselves but experience an effective potential VHF. In other words, the Slater determinant is the exact wave function of N noninteracting particles moving in the field of the effective potential VHF.5 It will not take long before we will meet again the idea of non-interacting systems in the discussion of the Kohn-Sham approach to density functional theory. 

Before we enter a more detailed discussion of various aspects in the Kohn-Sham approach, let us summarize the main features of this procedure ... 

In the preceding paragraph we have given a detailed survey of the Kohn-Sham approach to density functional theory. Now, we need to discuss some of the relevant properties pertaining to this scheme and how we have to interpret the various quantities it produces. We also will mention some areas connected to Kohn-Sham density functional theory which are still problematic. Before we enter this discussion the reader should be reminded to differentiate carefully between results that apply to the hypothetical situation in which the exact functional ExC and the corresponding potential Vxc are known and the real world in which we have to use approximations to these quantities. 

Is the Kohn-Sham Approach a Single Determinant Method ... 

Recall the central ingredient of the Kohn-Sham approach to density functional theory, i. e., the one-electron KS equations,... 

The developments in the implementation of the Kohn-Sham approach, helped also to formulate alternative formalisms aiming at approaching the linear scaling195 218"227. In particular, the divide-and-conquer approach of Yang218 have attracted much attention. 

Lately, the CP-MD approach has been combined with a mixed QM/MM scheme [10-12] which enables the treatment of chemical reactions in biological systems comprising tens of thousands of atoms [11, 26]. Furthermore, CP-MD and mixed QM/MM CP-MD simulations have also been extended to the treatment of excited states within a restricted open-shell Kohn-Sham approach [16, 17, 27] or within a linear response formulation of TDDFT [16, 18], enabling the study of biological photoreceptors [28] and the in situ design of optimal fluorescence probes with tailored optical properties [32]. Among the latest extensions of this method are also the calculation of NMR chemical shifts [14]. 

The calculation of the induced electron density may be done in the context of the Kohn-Sham approach to density functional theory, because the response of a KS system to a change in the one particle effective potential (r) corresponds to that of a system of non-interacting electrons. 

Alternative Formulation of the Kohn-Sham Approach Generalized... 

The second approach to this problem is to derive orbital-based reformulations of existing algorithms based on the spatial representation of the g-density. The resulting formulations are in the spirit of the orbital-resolved Kohn-Sham approach to density functional theory. 

The integrals to be summed are readily calculated. Note that DFT per se does not involve wavefunctions, and the Kohn-Sham approach to DFT uses orbitals only as a kind of subterfuge to calculate the noninteracting-system kinetic energy and the electron density function see below. 

---