Molecular Orbitals for Larger Molecules

The lattice enthalpy for crystal formation is large enough to overcome all the endothermic processes (and the negative entropy change) and to make formation of LiF from the elements a very favorable reaction. 

MOLECULAR molecular orbitals for molecules consisting of three or more atoms, but more complex ORBITALS FOR cases benefit from the use of formal methods of group theory. The process uses the LARGER MOLECULES following steps  

Determine the point group of the molecule. If it is a linear molecule, substituting a simpler point group that retains the symmetry of the orbitals (ignoring the signs) makes the process easier. Substitute Dih for Doo/, C21, for This substitution retains the symmetry of the orbitals without the infinite-fold rotation axis. 

Assign X, y, and z coordinates to the atoms, chosen for convenience. Experience is the best guide here. The general rule in all the examples in this book is that the highest order rotation axis of the molecule is chosen as the z axis of the central atom. In nonlinear molecules, the y axes of the outer atoms are chosen to point toward the central atom. 

Find the characters of the representation for the combination of the 2s orbitals on the outer atoms and then repeat the process, finding the representations for each of the other sets of orbitals (pj, Py, and p ). Later, these will be combined with 

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Molecular Orbitals for Larger Molecules 159 Atomic orbitals used Hybrid orbitals... 

The same principles that we used to build up molecular orbitals for diatomic molecules can be applied to larger and, indeed, very large molecules. We shall consider a few examples and then some general points that apply to calculations on any molecule. For our first example, we pick up on the molecules that we only partially dealt with using hybrid orbitals. 

The valence bond model of covalent bonding is easy to visualize and leads to a satisfactory description for most molecules. It does, however, have some problems. Perhaps the most serious flaw in the valence bond model is that it sometimes leads to an incorrect electronic description. For this reason, another bonding description called molecular orbital (MO) theory is often used. The molecular orbital model is more complex than the valence bond model, particularly for larger molecules, but sometimes gives a more satisfactory accounting of chemical and physical properties. 

For larger molecules it is assumed that a molecular wave function, , is an anti-symmetric product of atomic wave functions, made up by linear combination of single-electron functions, called orbitals. The Hamiltonian operator, H which depends on the known molecular geometry, is readily derived and although eqn. (3.37) is too complicated, even for numerical solution, it is in principle possible to simulate the operation of H on d>. After variational minimization the calculated eigenvalues should correspond to one-electron orbital energies. However, in practice there are simply too many electrons, even in moderately-sized molecules, for this to be a viable procedure. 

Since the number of integrals to be evaluated increases rapidly with molecular size, semi-empirical calculations are more practical at present for larger molecules. The most widely used semi-empirical approach is based upon Pople s theory (22, 23) of molecular diamagnetism within the independent electron framework. All explicit two electron terms become zero in this method. Thus the necessity of evaluating many integrals is avoided and the remainder can be approximated by the methods implicit in all valence electron molecular orbital calculations. (24)... 

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