Density functionals universal

R. G. Parr and W. Yang, Density Functional Theory of Atoms and Molecules, Oxford University Press, Oxford, U.K., 1989. 

As readers of this volume are also aware, the best of both approaches have been blended together with the result that many computations are now performed by a careful mixture of wavefunction and density approaches within the same computations (Hehre et al., 1986). But the unfortunate fact is that, as yet, there is really no such thing as a pure density functional method for performing calculations. The philosophical appeal of a universal solution for all the atoms in the periodic table based on observable electron density, rather than fictional orbitals, has not yet borne fruit.21,22... 

The existence of the first HK theorem is quite surprising since electron-electron repulsion is a two-electron phenomenon and the electron density depends only on one set of electronic coordinates. Unfortunately, the universal functional is unknown and a plethora of different forms have been suggested that have been inspired by model systems such as the uniform or weakly inhomogeneous electron gas, the helium atom, or simply in an ad hoc way. A recent review describes the major classes of presently used density functionals [10]. 

This, at first glance innocuous-looking functional FHK[p] is the holy grail of density functional theory. If it were known exactly we would have solved the Schrodinger equation, not approximately, but exactly. And, since it is a universal functional completely independent of the system at hand, it applies equally well to the hydrogen atom as to gigantic molecules such as, say, DNA FHK[p] contains the functional for the kinetic energy T[p] and that for the electron-electron interaction, Eee[p], The explicit form of both these functionals lies unfortunately completely in the dark. However, from the latter we can extract at least the classical Coulomb part J[p], since that is already well known (recall Section 2.3),... 

The importance of chemical-reaction kinetics and the interaction of the latter with transport phenomena is the central theme of the contribution of Fox from Iowa State University. The chapter combines the clarity of a tutorial with the presentation of very recent results. Starting from simple chemistry and singlephase flow the reader is lead towards complex chemistry and two-phase flow. The issue of SGS modeling discussed already in Chapter 2 is now discussed with respect to the concentration fields. A detailed presentation of the joint Probability Density Function (PDF) method is given. The latter allows to account for the interaction between chemistry and physics. Results on impinging jet reactors are shown. When dealing with particulate systems a particle size distribution (PSD) and corresponding population balance equations are intro-... 

See for example, Jones, R., and Gunnarsson, O. Rev. Mod. Phys. 61, 689 (1990) Parr, R.G., and Yang, W. (1990), Density Functional Theory of Atoms and Molecules, Oxford University Press, New York Kryachko, E.S., and Ludena, E.V. Energy Density Functional Theory of Many Electron Systems Kluwer Academic Publishers, 1990 Callaway, J., and March, N.H. Solid State Phys. 38, 135 (1984). 

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