MO-LCAO approach

The Jahn-Teller principle finds applications both in the framework of crystal field theory and in the evaluation of energy levels through the LCAO-MO approach. In both cases, practical apphcations are restricted to 3d transition elements. 

Actually it is a defect of the simple Huckel LCAO MO approach that spin correlation is not included and is responsible for poor success of these approximate wave functions in calculating nuclear spin-spin interactions and also spin density distributions in nonalternate and odd alternate paramagnetic molecules. 

This brief discussion cannot do justice to the MO approach to stereochemistry, but it does illustrate the reduced importance of electron-electron repulsions (usually omitted in simple approximations) and the increased importance of overlap in this approach. Although the VSEPR approach and the LCAO-MO approach to stereochemistry appear on the surface to be very different, all valid theories of bonding, when carried sufficiently far, are in agreement that the most stable molecule will have the best compromise of (I) maximizing electron-nucleus attractions and (2) minimizing electron-electron repulsions. 

In the often used linear combination of atomic orbitals-molecular orbital (LCAO-MO) approach, the molecular orbitals are built from atomic orbitals according to ... 

Suppose that we are interested in minimizing the energy function of a molecule, which we are describing by a close-shell one-determinant function, in the usual LCAO-MO approach, with respect to the linear coefficients and the atomic orbital exponents. The energy function is simply... 

A. M. Karo, /. Chem. Phys., 30, 1241 (1959). Configuration Interaction in the Lithium Hydride Molecule. 11. A SCF-LCAO-MO Approach. 

Hiickel theory was the first LCAO-MO approach to calculating the electronic structure of molecules. Hiickel theroy considers only the p-orbitals perpendicular to a planar jt-system, does not include electron-electron repulsion and assumes that all bonding overlaps are equal and all nonbonding zero. 

Another example is provided by the H2 molecule at long intemuclear distances. In the simplest LCAO MO approach, two electrons are described by the bonding orbital (Xa Xb orbitals centered on the H nuclei, a and b, respectively both obtained by using the symmetry requirement) ... 

The phosphane molecule is the subject of numerous quantum-chemical calculations. The methods applied range from simple LCAO MO approaches to high-quality calculations, such as Hartree-Fock (SCF MO), configuration interaction (Cl), perturbation theory (MP, MBPT), and, more recently, density function procedures. 

In MO theory, the network of chemical bonds is determined by the occupied MO in the system ground state. For reasons of simplicity, assume the closed-shell (cs) configuration of N = 2n electrons in the standard spin-restricted HF (RHF) description, which involves the n lowest (doubly occupied, orthonormal) MO. In the familiar LCAO MO approach, they are expanded as linear combinations (LC) of the (Lbwdin) orthogonalized AO x = iXoXi - -XJ = iXi) contributed by the system constituent atoms (x x)= 8, si, = ( 2,... ) = J = xC, where the rectangular matrix C = = (x ) groups the relevant expansion coefficients of MO (i.e., LC... 

Field (1982) has combined the well-known molecular-orbital pictures of s and p orbitals with the ligand-field theoretical treatment of the d and f orbitals. This approach has provided very simple and yet promising interpretation for lanthanide oxides. Lanthanide oxides such as CeO, PrO, etc. are highly ionic. The conventional MO theory for the AB diatomic molecule by itself ignores the A B or A B ionic character of such compounds. Although indirectly from MO theory, this can be rationalized as well but the amount of effort is usually more significant using the LCAO-MO approach. 

Some alternative approaches have been taken to study the positron annihilation characteristics without explicit band-structure calculations. As far as YBa2Cu307 is concerned, the LCAO-MO approach developed by Chiba (1976) for oxides has been applied by Chiba (1992), Turchi et al. (1988, 1990) and Saul and Weissmann (1990). Although the Fermi surface is not a concept in the LCAO-MO description, this method is quite appropriate for the direct physical insights it provides for the analysis of the anisotropies A(r,d) of the 2D-ACAR distribution, eq. (15). 

The principal computational approaches to molecular electronic structme that developed from about 1950 onwards had molecular orbitals (MOs) as their basis. Since the molecular orbitals were expressed in terms of linear combinations of atomic orbitals (LCAOs), the orbital remained a feature of the quantum mechanical account of molecular structure. Initially at least it was not possible to realise fully the LCAO MO approach because, except in diatomic systems, the integrals over the orbitals, which were exponential in their radial parts (Slater orbitals) proved too difficult to evaluate quickly enough to make non-empirical calculation feasible. But even given these limitations, it was already clear that the role of the bond in the emerging discipline of computational quantum chemistry was going to be problematic... 

The above arguments are substantiated by a detailed LCAO MO analysis on dipole moment contributions to infiared intensities carried out by Orville-Thomas and co-workers [41-44,48]. In the framework of the LCAO MO approach a Cartesian... 

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