Free density

Watson S, Jesson B J, Carter E A and Madden P A 1998 Ab initio pseudopotentials for orbital-free density functional Europhys. Lett. 41 37-42... 

Process details may be summarized powder sizes are fine (usually < 20 Ilm) low (generally < 69 MPa (10,000 psi)) injection pressure low (ca I49°C) mol ding temperature shrinkage (molded part to finished size) typically 20% final part densities are usually 95—98% + of maximum pore-free density and ductility is exceptionally high, elongation values are > 30%. 

Becke, A. D., 1989, Basis-Set-Free Density-Functional Quantum Chemistry , Int. J. Quant. Chem. Symp., 23, 599. 

Glaesemann, K. R., Gordon, M. S., 1998, Investigation of a Grid-Free Density Functional Theory (DFT) Approach , J. Chem. Phys., 108, 9959. 

Pearson, M., E. Smargiassi, and P. A. Madden. Ab initio molecular dynamics with an orbital-free density functional. J. Phys. Cond. Matter 5, 3221. 

Except for the normalization factor this is equal to the spin-averaged n-particle ensemble state. The spin-free density matrices (24), (25), and so on defined previously (in Section II.C) correspond to such an ensemble averaging. 

The easiest and, in many respects, the most satisfactory way is to consider only the totally symmetric tensor components (i.e., the spin-free density matrices) and to define the spin-free cumulants in terms of these [17, 30]. This corresponds to replacing the considered state by an Ms-averaged ensemble. 

The influence of a commensurate lattice potential on a free density wave is considered in section 5. The full finite temperature renormalization group flow equation for this sine-Gordon type model are derived and resulting phase diagram is discussed. Furthermore a qualitative picture of the combined effect of disorder and a commensurate lattice potential at zero temperature is presented in section 6, including the phase diagram. 

With a supermolecule approach, Bock et al. studied the first and second shell of water molecules surrounding various metal ions. They studied M (H20)i8 clusters using parameter-free density-functional calculations and trying to optimize the structures in largely unbiased calculations. Due to the size of the system (55 atoms, or 19 building blocks when assuming that the H2O units stay intact), this is a far from trivial endeavour (see, e.g., ref 2). 

As an example of an older work we mention the study of Jennison et alP who studied some selected geometries of Ru, Pd, and Ag clusters with 55, 135, and 140 atoms with different geometries using parameter-free density-functional calculations. The work, just some 10 years old, appeared at a time... 

Parameter-free density-functional calculations on Ge2o clusters were performed by Li et al." In order to optimize the structures they used a molecular-dynamics approach. They compared the results with those of similar calculations on Si2o clusters and found a remarkable similarity between the two elements. Moreover, many of the structures for Ge20 could be interpreted as being formed by two interacting Ge10 units. 

In two works, Flikkema and Bromley113,114 used a specifically tailored semiempirical potential for describing the interatomic interactions of (Si02)2v clusters. In order to optimize the structure, they used the basin-hopping algorithm. Subsequently, parameter-free density-functional calculations were carried through for the optimized structures. 

In the original approach, E et al 36 combined the string method with a molecular-mechanics method for the calculation of the total energy for a given structure, whereas Kanai et al 31 combined it with the parameter-free density-functional Car-Parrinello method. Below we shall present results from the latter study. 

In studies of wood ehemistry it is important to remove extraetives with a multipurpose solvent sueh as methanol before wood density determination so that the correct extractive-free density data are gathered. Wood density anomalies led to extractive studies on larch species in the 1960s (Uprichard, 1963), with both polyphenols and arabinogalactan making large contributions to the apparent (unextracted) basic wood density. 

The density functional approach naturally offers the possibility of being realized in an algorithm scaling asymptotically like the cube of the number of inequivalent atoms in the system. Most probably, this is the lower limit for the asymptotic scaling law for any delocalized orbital theory. The significantly more favorable multiplier for the cubic component in semiempirical orbital theories translates therefore to not so impressively larger clusters that can be treated as compared to what can be done using a parameter-free density functional method. 

Within density-functional theory, a linear combination of overlapping non-orthogonal orbitals from first principles may be utilized to arrive at at full-potential local orbital (FPLO) method [213], and this k-dependent LCAO approach comes close to full-potential APW-based methods (see Sections 2.15.3 and 2.15.4) in terms of numerical accuracy, although FPLO is much faster simply because of the locality of the basis set. Even faster, due to a strongly simplified potential, is a parameter-free (density-functional) tight-binding method called TB-LMTO-ASA, derived through localization of a delocalized basis set (see Section 2.15.4). 

Zhou, B., Ligneres, V. L., and Carter, E. A. (2005). Improving the orbital-free density functional theory description of covalent materials,/ Chem. Phys. 122(4), 044103. 

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