Molecule orbitals are formed when atomic orbitals overlap. Mathematically, this is represented by a linear combination of atomic orbitals (as in the LCAOMO method). Some possible classifications of orbitals are bonding and antibonding and  and symmetry. This Demonstration shows the basic characteristics for a set of six molecules: the label, the description, the number of electrons in the chosen molecular orbital, and a 3D view of the probability density (with boundary surface, phasecoloring included) and also a ball and stick model for each example.
The atomic orbitals used in this Demonstration are the following Slatertype orbitals: , , , . For ethene, the LCAOMO method gives two normalized molecule orbitals: , . The formula for the distance of two points in threedimensional space can be used to rewrite the wavefunctions with the corresponding Slater orbital ( … interatomic distance): , . The diagrams for the molecular orbitals for dihydrogen, ethyne, and allene can also be written using the separationdependent formula. The simple Hückel method (SMO) is a rudimentary method for energies and orbitals of electron systems. An essential step is solving the secular equations. For cyclobutadiene, the secular equations are: , . Taking symmetry into account, one can factorize this secular determinant into two separate determinants: yielding the solutions , and . The four corresponding LCAO molecular orbitals are found using cofactors: , , , . An alternative set for cyclobutadiene is: , , , . Similarly for benzene, from the secular determinant, can be factorized to give the wavefunctions: , , , , , . Cyclic sytems (such as cyclobutadiene and benzene) can be rewritten with the corresponding Slater orbitals in the complex exponential form: , with . ChemSpider [1] is the source for the ball and stick figures. The ChemSpider IDs for each structure used are listed in the code for the Demonstration. [2] H. E. Zimmerman, Quantum Mechanics for Organic Chemists, London: Academic Press, 1975. [3] A. Rauk, Orbital Interaction Theory of Organic Chemistry (2nd ed.), New York: John Wiley & Sons, 2000.
