Approximate methods for solving the secular determinant

The secular determinant gives us a general method for calculating the energy. This approximate method is really only a starting point since we need to ensure that the solution for each electron is consistent with all of the other electrons. However, before we treat the problem of the self-consistent field, it is useful to discuss approximate methods that are so simple that we can do the calculations by hand. This way we can understand the process and appreciate the significance of the results obtained by the use of computers. The simplest method is known as Huckel theory. In the presentation below the rules of Huckel theory are presented and the application to both ethene and butadiene are given.

Huckel theory application to anti-aromaticity

One test of Huckel theory is to compare butadiene with its cyclic counterpart cyclobutadiene. The rule of aromaticity (4n + 2) and anti-aromaticity (4n) are well known in the study of pi systems. Aromatic pi systems are more stable as a cyclic molecule than as a lienar molecule and anti-aromatic systems are more stable as the linear polyene. We examine the prediction of Hucke theory in the presentation below. This is a critical test of Huckel theory.