Energy representation density-functional theory

In formulating a mathematical representation of molecules, it is necessary to define a reference system that is defined as having zero energy. This zero of energy is different from one approximation to the next. For ah initio or density functional theory (DFT) methods, which model all the electrons in a system, zero energy corresponds to having all nuclei and electrons at an infinite distance from one another. Most semiempirical methods use a valence energy that cor-... 

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-... 

In closing, I want to stress again the essential importance of understanding in a fundamental way the nonlocal structure of exchange-correlation contributions to energy functionals. I believe that a full appreciation of the variety of ways that this nonlocal structure manifests itself, according to the different physical circumstances, will be vital for the construction of improved representations of F[n] as the domain of applications of density functional theory continues to be extended into exciting new areas. 

The orbital representation is not used in most of the recent work on computational methods based on diagonal elements of density matrices. This is partly for historical reasons—most of the work has been done by people trained in density functional theory—and partly this is because most of the available kinetic energy functionals are known only in first-quantized form. For example, the popular generalized Weisacker functional [2, 7-11],... 

The above is the brief introduction to the density-functional theory of solutions. The mathematical development is quite straightforward. The numerical implementation is difficult, however, in the full coordinate representation. As noted in Section 17.3.2, the full coordinate is multidimensional the solute-solvent distribution is a function over high-dimensional configuration space and cannot be implemented in practice. To overcome the problem of dimensionality, it is necessary to introduce a projected coordinate. In Section 17.3.5, we introduce the energy representation and formulate the density-functional theory in the energy representation. 

In the energy representation, the density-functional theory can be formulated by restricting the set of solute-solvent interaction potentials ux( jr,x) to those which are... 

The complexity of the electronic structure problem is in principle dramatically reduced in the framework of Density Functional Theory as the many-body problem amounts to solving a minimization problem of an energy functional EhkVA or solving the much simpler problem of non-interacting electrons. This is ensured by the HK and KS theorems which state the existence of the functionals and Exc[n (assuming u-representability). Unfortunately,... 

---