Kohn-Sham energy functional

In this paper we will present a way to improve the evaluation of total energies in LMTO calculations. The Kohn Sham energy functional [1] can be written in the form... 

The starting point is the Kohn-Sham energy functional ... 

The orthogonal orbitals, which minimize the Kohn-Sham energy functional are obtained from the following set of one-electron equations21 for / = 1, N ... 

Here the point of view is somewhat different and instead of looking for solving the self-consistency equation (58) itself, we look for minimizing the Kohn-Sham energy functional. With a slight extension with respect to the previous section, (47), we will in fact look for minimizing the total energy ... 

Car and Parrinello in their celebrated 1985 paper [2] proposed an alternative route for molecular simulations of electrons and nuclei altogether, in the framework of density functional theory. Their idea was to reintroduce the expansion coefficients Cj(G) of the Kohn-Sham orbitals in the plane wave basis set, with respect to which the Kohn-Sham energy functional should be minimized, as degrees of freedom of the system. They then proposed an extended Car-Parrinello Lagrangian for the system, which has dependance on the fictitious degrees of freedom Cj(G) and their time derivative Cj (G) ... 

We can also evaluate the lowest typical frequency for the electronic dynamics from the gap Egap, energy difference between the Lowest Unoccupied Molecular Orbital (LUMO) and the Highest Occupied Molecular Orbital (HOMO), of the Kohn-Sham non-interacting electron system, which determines the lowest curvature of the E c) Kohn-Sham energy functional ... 

Note that the extended Kohn-Sham energy functional is dependent on the orbitals and implicitly on through the electron-nucleus attraction terms... 

Only the minimum value of the Kohn-Sham energy fimctional has physical meaning. At the minimum, the Kohn-Sham energy functional is equal to the groimd-state energy of the system of electrons with the ions in positions Ri. 

Are there any remedies in sight within approximate Kohn-Sham density functional theory to get correct energies connected with physically reasonable densities, i. e., without having to use wrong, that is symmetry broken, densities In many cases the answer is indeed yes. But before we consider the answer further, we should point out that the question only needs to be asked in the context of the approximate functionals for degenerate states and related problems outlined above, an exact density functional in principle also exists. The real-life solution is to employ the non-interacting ensemble-Vs representable densities p intro-... 

During the past 10 - 15 years, Kohn-Sham density functional theory has been a major factor in a dramatic expansion of the scope of computational chemistry and its capability for treating systems of practical importance [45-51]. Density functional methodology includes electronic correlation, so that the energies are more accurate than Hartree-Fock however the Kohn-Sham formalism is similar to the latter, as are therefore the demands upon computer resources. It is therefore feasible to treat relatively large systems at a reasonably high (post-Hartree-Fock) level. 

Perdew, J.P. and Norman, M.R. (1982). Electron removal energies in Kohn-Sham density-functional theory, Phys. Rev. B 26, 5445-5450. 

---