LCAO models

More elaborated calculations based on theoretical LCAO models have given interesting results within the CNDO/1 and CNDO/2 approximations (251.) Tables 1-32 and 1-33). 

In later chapters we will be concerned with the LCAO model. Suppose we have a set of n atomic orbitals > i(r), X2( )> > d a normalized LCAO orbital... 

Exact solutions to the electronic Schrodinger equation are not possible for many-electron atoms, but atomic HF calculations have been done both numerically and within the LCAO model. In approximate work, and for molecular applications, it is desirable to use basis functions that are simple in form. A polyelectron atom is quite different from a one-electron atom because of the phenomenon of shielding", for a particular electron, the other electrons partially screen the effect of the positively charged nucleus. Both Zener (1930) and Slater (1930) used very simple hydrogen-like orbitals of the form... 

Figure 11.2 Dihydrogen potential energy curve HF-LCAO model...

In Chapter 6, I discussed the open-shell HF-LCAO model. 1 considered the simple case where we had ti doubly occupied orbitals and 2 orbitals all singly occupied by parallel spin electrons. The ground-state wavefunction was a single Slater determinant. I explained that it was possible to derive an expression for the electronic energy... 

In the context of the HF-LCAO model, we seek a solution of the matrix eigenvalue equation... 

The classic case distinguishes between an atomic core, which is essentially unperturbed by bonding, and a valence shell whose content may be accessible to bond formation. Since we suppose this simplifying assumption to be maintained in the MO treatment, an atomic orbital belonging to the valence shell will be termed a valence atomic orbital (VAO). For the construction of MOs, we utilize the following general results of the MO/LCAO model ... 

In conclusion, let us say that even though the method becomes rather complicated here because the factor in polynomial form is replaced by a Fermi function, we consider that the method nevertheless presents a certain interest because at the same time it gives a solid base for comparison between the LCAO model and the metallic model. 

The LCAO Model of tt-MOs of Ethene, Acetylene, and Butadiene Frontier Orbitals... 

The characteristics of most chemical bonds (bond length, bond energy, polarity, and so forth) do not differ significantly from molecule to molecule (see Section 3.7). If the bonding electrons are spread out over the entire molecule, as described by the LCAO model, then why should the properties of a bond be nearly independent of the nature of the rest of the molecule Would some other model be more suitable to describe chemical bonds ... 

As an example of a mature topic, consider Density Functional Theory (DFT). DFT is far from new and can be traced back to the work of John Slater and other solid state physicists in the 1950 s, but it was ignored by chemists despite the famous papers by Hohenberg/ Kohn (1964) and Kohn/ Sham (KS) (1965). The HF-LCAO model dominated molecular structure theory from the 1960 s until the early 1990s and I guess the turning point was the release of the rather primitive KS-LCAO version of GAUSSIAN. DFT never looked back after that point, and it quickly became the standard for molecular structure calculations. So this Volume of the SPR doesn t have a self contained Chapter on DFT because the field is mature. 

Using the same atomic orbital twice in constructing molecular orbitals in the Linear Combination of Atomic Orbitals (LCAO) model. 

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