Construction of Ligand Group Orbitals for Polyatomics and Transition-Metal Complexes Using an Intuitive Symmetry-Based Approach

Abstract

A molecular orbital (MO) diagram, especially its frontier orbitals, explains the bonding and reactivity for a chemical compound. It is therefore important for students to learn how to construct one. The traditional methods used to derive these diagrams rely on linear algebra techniques to combine ligand orbitals into symmetry-adapted linear combinations or ligand group orbitals (LGOs). Over the past 10 years, I have developed and refined a simple graphical method for generating ligand group orbitals. The method is an extension of concepts that the students already know from general chemistry: VSEPR and valence bond theory, which are then used to create a generator function. LGOs are prepared by matching symmetry (nodes and phase behavior) of the generator function. The LGOs generated by this technique are qualitatively correct and sufficient for the “back-of-the-envelope” MO diagrams for which they are intended. Through a series of in-class group work and out-of-class problem sets, students learn to derive LGOs for main-group, organometallic, and coordination complexes quickly and correctly.