Theory density

March, N. H. (1992) Electron Density Theory of Atoms and Molecules, Academic Press, London. 

But alas most of what has been described so far concerning density theory applies in theory rather than in practice. The fact that the Thomas-Fermi method is capable of yielding a universal solution for all atoms in the periodic table is a potentially attractive feature but is generally not realized in practice. The attempts to implement the ideas originally due to Thomas and Fermi have not quite materialized. This has meant a return to the need to solve a number of equations separately for each individual atom as one does in the Hartree-Fock method and other ab initio methods using atomic orbitals. 

Number of bilayers Reacted H2S (theory) Reacted H2S (exptl.) Fatty acid density (theory) Fatty acid density (exptl.) Residual film (theory) Residual film (exptl.)... 

Becke, A. D. A new mixing of Hartree-Fock and local density theories. J. Chem. Phys. 98, 1372. 

G. D. Mahan and K. R. Subbaswamy. Local Density Theory of Polarisability. London Plenum, 1990. 

March NH (1992) Electron density theory of atoms and molecules. Academic Press, New York. 

The importance of N-representability for pair-density functional theory was not fully appreciated probably because most research on pair-density theories has been performed by people from the density functional theory community, and there is no W-representability problem in conventional density functional theory. Perhaps this also explains why most work on the pair density has been performed in the first-quantized spatial representation (p2(xi,X2) = r2(xi,X2 xi,X2)) instead of the second-quantized orbital representation... 

Arsenious oxide is not appreciably volatile at ordinary temperatures,2 but vapour is emitted at 100° C.3 Vapour density determinations 4 indicate that at lower temperatures the molecules are mainly As4Oe but, as the temperature rises, dissociation occurs, which is appreciable at 850° C. and practically complete at 1800° C., simple As203 molecules being formed. The following values for the vapour density (Theory As406 = 13-76) were obtained by Biltz 5... 

G.D. Mahan, K.R. Subbhaaswamy, Local Density Theory of Polarizability, Plenum Press, New York, 1990. 

REF80] G. Reffo, "Phenomenological Approach to Nuclear Level Densities," Theory and Applications of Moment Methods in Many-Fermion Systems (Plenum Press, New York, 1980). 

The formalism of nonlocal functional density theory provides an attractive way to describe the physical adsorption process at the fluid - solid interface.65 In particular, the ability to model adsorption in a pore of slit - like or cylindrical geometry has led to useful methods for extracting pore size distribution information from experimental adsorption isotherms. At the moment the model has only been tested for microporous carbons and slit - shaped materials.66,67 It is expected that the model will soon be implemented for silica surfaces. 

It must be emphasized that such phenomena are to be expected for a statistical system only in the regime of low level densities. Theories like RRKM and phase space theory (PST) (Pechukas and Light 1965) are applicable when such quantum fluctuations are absent for example, due to a large density of states and/or averaging over experimental parameter such as parent rotational levels in the case of incomplete expansion-cooling and/or the laser linewidth in ultrafast experiments. However, in the present case, it is unlikely that such phenomena can be invoked to explain why different rates are obtained when using ultrafast pump-probe methods that differ only in experimental detail. 

R.G. Pair and W. Yang, Density Functioned Theory of Atoms and Molecules (Oxford University Press, Oxford, 1989) R.M. Dreizler and E.K.U. Gross, Density Functioned Theory (Springer-Verlag, Berlin, 1990) N.H. March, Electron Density Theory of Atoms and Molecules (Academic, London, 1992). 

Mahan GD, Subbaswamy KR (1990) Local density theory of polarizability. Plenum, New York p 109ff... 

The principle underlying the whole of the density theory of atoms and molecules has essentially been exposed by the argument leading to equation (24). We shall see below, however, that there is a need to refine the elementary approximation (18) for the kinetic energy density, in order to transcend TF statistical theory. Nevertheless, even without refinement, certain useful relations follow from this simplest form of density theory and we will discuss these now for positive atomic ions. 

Thus,/0(A7Z) in equation (42) can be calculated from the known solutions of equation (10), the form of f0(N/Z), taken from the work of March and White,7 being plotted in Figure 2. Since the density description focuses so directly on E(Z, N), as in equation (42), it is natural that we should bring the result (42) of this simplest (TF) density theory into contact with the 1/Z expansion of E(Z, N) for atomic ions. That these two treatments are very intimately related... 

Figure 9 Variation of orbital energies in HAH molecule on going from 90° bent molecule to linear molecule. The classification of states, built from s and p atomic orbitals, is discussed in the main text. The steep rise in the curve joining ai and favours the bent molecular form for H2O, whereas with four valence electrons, as in BeH2 or HgH2, the linear configuration is favoured. This argument is based on an intimate relation, which Walsh assumed, between the sum of orbital energies and total energy. Density theory in its simplest form supplies such a relation, namely equation (84). The figure is a schematic version of that of Walsh,46 who noted that the line 180° must be either a maximum or a minimum...

Should it prove possible, in the future, to solve the Euler equation (146) to full chemical accuracy, the values of p for isolated atoms, and the single value of p for the molecule built up from these atoms, will be of great interest. It is clear from the way that p was introduced in the density theory [see especially equation (23)] that one could contemplate estimating it in an atomic ion from... 

Rather than go into detail of approximate numerical calculations of the chemical potential from various approximate forms of the density theory, for instance the Hartree-Fock-Slater equation (51), we shall focus some attention on models that have been built as a result of this recognition of the very intimate relation between the chemical potential and electronegativity. 

---