Localized orbital approach

What has been said applies to approximate as well as to ab-initio molecular orbital wavefunctions,i.e. those obtained by solving the self-consistent-field equations exactly. Hence, the localized orbital approach also offers an attractive tool for bridging the gap between rigorous quantitative calculations and qualitative chemical intuition. The experience gained so far has shown that interpretations suggested by the localized orbital picture correspond closely to intuitive chemical thinking. 

The reader will recall that in Chapter 2 we gave examples of H2 calculations in which the orbitals were restricted to one or the other of the atomic centers and in Chapter 3 the examples used orbitals that range over more than one nuclear center. The genealogies of these two general sorts of wave functions can be traced back to the original Heitler-London approach and the Coulson-Fisher[15] approach, respectively. For the purposes of discussion in this chapter we will say the former approach uses local orbitals and the latter, nonlocal orbitals. One of the principal differences between these approaches revolves around the occurrence of the so-called ionic structures in the local orbital approach. We will describe the two methods in some detail and then return to the question of ionic stmctures in Chapter 8. 

The purpose of this article is to describe our limited contribution to the study of the chemical problems mentioned in this introduction. We shall successively envisage the electronic structure, the thermodynamical properties, and the reactivity of chemical species. Most of our theoretical results have been obtained at the SCF level using the localized orbital approach. 

The performance of both the link-atom and local-orbital approaches has been examined by extensive test calculations. The conclusion is that reasonably good accuracy can be achieved by both approaches if they are used with special care. 

Cohen and coworkers 113] used the pseudopotential localized-orbital approach and found that this allotropic carbon structure is a low-compressibility metal because of the nearly perfect lattice match with the diamond (100) surface, they preposed that it may be possible to grow this structure epitaxially on the diamond OOO) surface. 

There are several approximate methods often useful in understanding the trends in the quadrupole parameters in a related series of molecules containing the same quadrupolar nucleus. One. due to Townes and Dailey, is essentially a localized orbital approach, in which attention is focused on changes in the orbital populations of the atom containing the quadrupolar nucleus, and polarization of the core electrons (the so-called Sternheimer polarization factor) is assumed to vary negligibly from one molecule to another. In the case for example,... 

The starting point in this type of work has generally been a relationship originally derived by Townes and Dailey [175] using a localized orbital approach to describe the covalent bond involving the quadrupolar nucleus. This relationship may be written... 

The localized orbital approach is probably not the best choice today however, since LCAO-MO treatments at different levels of sophistication... 

Recently, Vidossich and Lledds [11] proposed the analysis of the chemical bonding by the use of the localized orbitals approach. The outcome of this approach provides the centroid of the charge and the area covered by each orbital. The molecular structure together with the orbital centroids will... 

As seen above, CeSb is a more difficult system. To probe further the limitation previously described and to explore the effect of using a local-orbital approach. 

Two apparent drawbacks of the localized-orbital approach exist. First, the convergence of the total energy stalls at a value above the exact numerical solution depending on the size of the cutoff radius for the orbitals. This makes sense because physical information is lost in the truncation. Second, the convergence rate appears to slow somewhat with increasing system size. The observed convergence rates are still good, and competitive with other numerical methods, but this slowdown does not fit with standard MG orthodoxy—the... 

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