Localized electron shortcomings

For many decades the LDA has been applied in, e.g., calculations of band structures and total energies in solid-state physics. The LDA provides surprisingly good results for metalhc sohds with delocalized electrons, i.e. those that most closely resemble the uniform electron gas (jellium). At the same time, there are well-known disadvantages of LDA for solids. LDA revealed systematic shortcomings in the description of systems with localized electrons and as a result the underestimation of... 

We see that the shortcomings of the quasi-chemical theory for dilute solutions also lead to the idea that the interaction between two atoms in solution may be very different from the interaction between the same atoms in the pure state. This is a point of view that can be reached from a consideration of the screening11 by localized or by conduction-band electrons that must occur about... 

In this section we will attempt to make these simple models even more useful by addressing a particular shortcoming of the LE model—its assumption that electrons are localized (restricted to the space between a given pair of atoms). This problem is most apparent for molecules where several valid Lewis structures can be drawn. Recall that none of the resonance structures taken alone adequately describes the electronic structure of the molecule. The concept of resonance was invented to solve this problem. However, even with... 

Density Functional theory [4] (DFT) has been widely recognized as a powerful alternative computational method to traditional ab initio schemes, particularly in studies of transition metal complexes where large size of basis set and an explicit treatment of electron correlation are required. The local spin density approximation [5] (LDA) is the most frequently applied approach within the families of approximate DFT schemes. It has been used extensively in studies on solids and molecules. Most properties obtained by the LDA scheme are in better agreement with experiments [4a] than data estimated by ab initio calculations at the Hartree-Fock level. However, bond energies are usually overestimated by LDA. Thus, gradient or nonlocal corrections [6] have been introduced to rectify the shortcomings in the LDA. The non-... 

This theory, however, treats electrons as localized, does not account for unpaired electrons, and does not give information on bond energies. The molecular orbital theory attempts to solve these shortcomings by considering nuclei arranged as in a molecule and determining the resulting molecular orbitals when electrons are fed in one by one. 

A shortcoming of both NRA and SIMS is that the spatial resolution is not high in all three directions. While depth resolutions on the order of a few hundred nanometers or less are routine, the profiles are measured over surface areas of a few hundred square micrometers or even millimeters. Thus, the concentration profile can be an average from various localized reaction or fast diffusion (e.g. pipe diffusion). The consequences of dual-diffusion mechanisms on the geometry of isotopic profiles is discussed in more detail below. There is no available method to by pass these problems for isotopic diffusion, although for elemental diffusion, alytical Transmission Electron Microscopy (ATEM) offers an alternative (Meissner et al. 1997). 

Of the three approximations outlined, the one-electron approximation, i.e., the local density approximation, is the weakest. This approximation fails to replicate features such as image charges at a surface. Also, it fails to describe excited states properly, but this is not a concern for structural energies. Despite such shortcomings, the local density remains one of the most successful approaches to calculating many-body energies in solids. 

In this chapter, we reviewed different quantum chemical approaches to determine local quantities from (multireference) wave functions in order to provide a qualitative interpretation of the chemical bond in open-shell molecules. Chemical bonding in open-shell systems can be described by covalent interactions and electron-spin coupling schemes. For different definitions of the (effective) bond order as well as various decomposition schemes of the total molecular spin expectation value into local contributions, advantages and shortcomings have been pointed out. For open-sheU systems, the spin density distribution is an essential ingredient in the... 

There is one overarching shortcoming of the standard model, which is slightly more philosophical. It treats the f-electrons as localized and the sd-electrons as itinerant, that is, it treats electrons within the same material on a completely different basis. This is aesthetically unsatisfactory and furthermore makes it impossible to define a reference energy. In principle, one has to know, a priori, which electrons to treat as band electrons and which to treat as core electrons. It would be infinitely better if the theory itself contained the possibility of both localized and itinerant behaviour and it chose for itself how to describe the electrons. 

The present authors have used the dielectric screening method for all their ab-initio computations of the macroscopic dielectric constant and phonon frequencies of Si and Ge. For the calculation of the electron energies and wave functions needed in the expression of the electron density response matrix they apply the local density approximation in the Hamiltonian. The advantage and shortcomings of this approximation are treated at length in the papers by J.T. Devreese, R. Martin, K. Kune, S. Louie, A. Baldereschi and R. Resta in these proceedings. 

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