Orbital-free DFT

Almost all DFT-based computations use the Kohn-Sham method. This approach, however, arguably violates the spirit of DFT. The simplicity and computational efficiency of DFT are compromised because, instead of needing to determine only one three-dimensional function (the electron density), in KS-DFT one must determine N three-dimensional functions (the Kohn-Sham spin orbitals). The conceptual beauty of DFT is compromised because, unlike the electron density, which is physically observable with a simple interpretation, the Kohn-Sham orbitals are neither physically observable nor directly interpreted. For these reasons, there is still interest in 

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The so-called orbital-free DFT teclmique, which aims to directly calculate the electron density for which the... 

One current limitation of orbital-free DFT is that since only the total density is calculated, there is no way to identify contributions from electronic states of a certain angular momentum character /. This identification is exploited in non-local pseudopotentials so that electrons of different / character see different potentials, considerably improving the quality of these pseudopotentials. The orbital-free metliods thus are limited to local pseudopotentials, connecting the quality of their results to the quality of tlie available local potentials. Good local pseudopotentials are available for the alkali metals, the alkaline earth metals and aluminium [100. 101] and methods exist for obtaining them for other atoms (see section VI.2 of [97]). 

Cortona embedded a DFT calculation in an orbital-free DFT background for ionic crystals [183], which necessitates evaluation of kinetic energy density fiinctionals (KEDFs). Wesolowski and Warshel [184] had similar ideas to Cortona, except they used a frozen density background to examine a solute in solution and examined the effect of varying the KEDF. Stefanovich and Truong also implemented Cortona s method with a frozen density background and applied it to, for example, water adsorption on NaCl(OOl) [185]. 

Computational solid-state physics and chemistry are vibrant areas of research. The all-electron methods for high-accuracy electronic stnicture calculations mentioned in section B3.2.3.2 are in active development, and with PAW, an efficient new all-electron method has recently been introduced. Ever more powerfiil computers enable more detailed predictions on systems of increasing size. At the same time, new, more complex materials require methods that are able to describe their large unit cells and diverse atomic make-up. Here, the new orbital-free DFT method may lead the way. More powerful teclmiques are also necessary for the accurate treatment of surfaces and their interaction with atoms and, possibly complex, molecules. Combined with recent progress in embedding theory, these developments make possible increasingly sophisticated predictions of the quantum structural properties of solids and solid surfaces. 

What is needed for a correct computation of momentum-space properties from DPT is an accurate functional for approximating the exact first-order reduced density matrix r f f ), or failing that, good functionals for each of the p-space properties of interest. Of course, a sufficiently good functional for (p ) would obviate the necessity of using Kohn-Sham orbitals and enable the formulation of an orbital-free DFT. Unfortunately, a kinetic energy functional sufficiently accurate for chemical purposes remains an elusive goal [118,119]. 

Extensions of the QC Method Because of its versatility, the QC method has been widely applied and, naturally, extended as well. While its original formulation was for zero-temperature static problems only, several groups have modified it to allow for finite-temperature investigations of equilibrium properties as well. A detailed discussion of some of these methodologies is presented in the discussion of finite-temperature methods below. Also, Dupoy et al. have extended it to include a finite-temperature alternative to molecular dynamics (see below). Lastly, the quasi-continuum method has also been coupled to a DFT description of the system in the OFDFT-QC (orbital-free DFT-QC) methodology discussed below. 

The foundation for the use of DFT methods in computational chemistry is the introduction of orbitals, as suggested by Kohn and Sham (KS). The main flaw in orbital-free models is the poor representation of the kinetic energy, and the idea in the KS formalism is to split the kinetic energy functional into two parts, one which can be calculated exactly, and a small correction term. The price to be paid is that orbitals are re-introduced, thereby increasing the complexity from 3 to 3N variables, and that electron correlation re-emerges as a separate term. The KS model is closely related to the HF method, sharing identical formulas for the kinetic, electron-nuclear and Coulomb electron-electron energies. 

Since orbitals are model dependent, different models will have different orbitals. The basic distinction between DFT fi -orbitals and LFT fi -orbitals arises from their respective treatments of interelectron repulsions. In LFT, d-d repulsion is treated within a spherical approximation. For d and d configurations, there is a single free-ion term and hence no need to consider d-d interelectron repulsion at all. In contrast, the Kohn-Sham orbitals in DFT are computed relative to the total molecular potential. For a tetragonal d copper(II) complex, dx -y is singly occupied while the remaining -functions are doubly occupied. Hence, to a first approximation, the hole in the equatorial plane results in less d-d repulsion in the plane than perpendicular to the plane with the result that the in-plane dxy orbital falls relative to the out-of-plane dxzjdyz pair. 

SPIN-DENSITIES IN CHARGE-TRANSFER COMPLEXES DERIVED FROM DFT CALCULATIONS USING AN ORBITAL-FREE EMBEDDING SCHEME FOR INTERACTING... 

Spin-Densities in Charge-lVansfer Complexes Derived from DFT Calculations Using An Orbital-Free Embedding... 

Continuum Orbital-Free Density-Functional Theory A Route to Multi-Million Atom Non-Periodic DFT Calculation. 

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