Orbital Theory and Methods

The concepts of electronegativity, hardness, and polarizability are all interrelated. For the kind of qualitative applications we will make in discussing reactivity, the concept that initial interactions between reacting molecules can be dominated by either partial electron transfer by bond formation (soft reactants) or by electrostatic interaction (hard reactants) is a useftxl generalization. 

Another broad approach to the description of molecular structure that is of importance in organic chemistry is molecular orbital theory. Molecular orbital (MO) theory pictures electrons as being distributed among a set of molecular orbitals of discrete 

In order to make the mathematics tractable, approximations must be made. The choice of approximations has produced a variety of MO methods, the judicious application of which can provide valuable insight into questions of bonding, structure, dynamics, and reactivity. The discussion that follows will not be sufficiently detailed or complete for the reader to understand how the calculations are performed or the details of the approximations. Instead, the nature of the information that is obtained will be described, and the ways in which organic chemists have applied the results of MO theoiy will be illustrated. Several excellent books are available which provide detailed treatment of various aspects of MO methods. 

There is a trade-off between the accuracy of the calculation and the amount of computation required. In general, the more severe the approximations, the more limited is the range of applicability of the particular calculation. An organic chemist who wishes to make use of the results of MO calclulations must therefore make a judgment about the suitability of the various methods to the particular problem. The rapid increases that have occurred in computer speed and power have made the application of sophisticated methods practical for increasingly larger molecules. 

Mathematically, the molecular orbitals are treated as linear combinations of atomic orbitals, so that the wave function, is expressed as a sum of individual atomic orbitals multiplied by appropriate weighting factors (atomic coefficients)  

The individual MOs are described as linear combinations of the atomic orbitals cpj (LCAO)  

The atomic orbitals that are used constitute was is known as the basis set and a minimum basis set for compounds of second-row elements is made up of the 2s, 2p, 2py, and 2p orbitals of each atom, along with the 1 orbitals of the hydrogen atoms. In MO calculations, an initial molecular structure and a set of approximate MOs are chosen and the molecular energy is calculated. Iterative cycles of calculation of a self-consistent electrical field (SCF) and geometry optimization are then repeated until a 

The output of an MO calculation includes atomic positions and the fractional contribution of each basis set orbital to each MO, that is, the values of Qp. The energy of each MO is calculated, and the total binding energy of the molecule is the sum of the binding energies of the fdled MOs  

The electronic charge at any particular atom can be calculated by the equation 

The second broad approach to the description of molecular structure that is of importance in organic chemistry is molecular orbital theory. Molecular orbital (MO) theory discards the idea that bonding electron pairs are localized between specific atoms in a molecule and instead pictures electrons as being distributed among a set of molecular orbitals of discrete energies. In contrast to the orbitals described by valence bond theory, which are usually concentrated between two specific atoms, these orbitals can extend over the entire molecule. Molecular orbital theory is based on the Schrodinger equation, 

The coefficients indicate the contribution of each atomic orbital to the molecular orbital. This method of representing molecular orbital wave functions in terms of combinations of atomic orbital wave functions is known as the linear combination of atomic orbitals (LCAO) approximation. The combination of atomic orbitals chosen is called the basis set. A minimum basis set for molecules containing C, H, O, and N would consist of 2s, Ip, 2py, and 2p orbitals for each C, N, and O and a Is orbital for each hydrogen. The basis sets are mathematical expressions describing the properties of the atomic orbitals. 

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