Molecular orbital theory uses group theory to describe the bonding in molecules ; it complements  and  extends the introductory  bonding models in   Chapter   3 .  In molecular  orbital  theory the  symmetry  properties and  relative energies  of atomic  orbitals  determine  how  these orbitals interact to form molecular orbitals. The molecular orbitals are then occupied  by the available electrons according to the same rules used for atomic orbitals as described  in  Sections  2.2.3 and  2.2.4 . The total energy of the electrons in the molecular orbitals is  compared with the initial total energy of electrons in the atomic orbitals. If the total energy  of the electrons in the molecular orbitals is less than in the atomic orbitals, the molecule is  stable relative to the separate atoms; if not, the molecule is unstable and predicted not to  form. We will first describe the bonding, or lack of it, in the first 10 homonuclear diatomic  molecules  ( H2 through   Ne2 )  and then  expand the  discussion to  heteronuclear  diatomic  molecules and molecules having more than two atoms.   A less rigorous pictorial approach is adequate to describe bonding in many small molecules and can provide clues to more complete descriptions of bonding in larger ones. A more  elaborate approach, based on symmetry and employing group theory, is essential to understand orbital interactions in more complex molecular structures. In this chapter, we describe  the pictorial approach and develop the symmetry methodology required for complex cases.  5.1 Formation of Molecular Orbitals from Atomic Orbitals  As with atomic orbitals, Schrödinger equations can be written for electrons in molecules.  Approximate solutions to these molecular Schrödinger equations can be constructed from  linear combinations of atomic orbitals (LCAO) , the sums and differences of the atomic  wave functions. For diatomic molecules such as  H2, such wave functions have the form  ­ = caca + cbcb  where  ­ is the molecular wave function,  ca and  cb are atomic wave functions for atoms  a and  b, and  ca and  cb are adjustable coefficients that  quantify the contribution  of each  atomic orbital to the molecular orbital. The coefficients can be equal or unequal, positive or  negative, depending on the individual orbitals and their energies. As the distance between  two  […]

Alkanes—An Introduction Alkanes are organic compounds that consist entirely of single-bonded carbon and hydrogen atoms and lack any other functional groups. Alkanes have the general formula \(C_nH_{2n+2}\) and can be subdivided into the following three groups: the linear straight-chain alkanes, branched alkanes, and cycloalkanes. Alkanes are also saturated hydrocarbons. Cycloalkanes are cyclic hydrocarbons, meaning that the carbons of the molecule are arranged in the form of a ring. Cycloalkanes are […]