An Introduction to Molecular Orbital Theory

How do atoms form covalent bonds in order to form molecules The Lewis model, which shows atoms attaining a complete octet by sharing electrons, tells only part of the story. A drawback of the model is that it treats electrons like particles and does not take into account their wavelike properties. 

Molecular orbital (MO) theory combines the tendency of atoms to fill their octets by sharing electrons (the Lewis model) with their wavelike properties, assigning electrons to a volume of space called an orbital. According to MO theory, covalent bonds result when atomic orbitals combine to form molecular orbitals. Like an atomic orbital, which describes the volume of space around an atom s nucleus where an electron is likely to be found, a molecular orbital describes the volume of space around a molecule where an electron is likely to be found. And, like atomic orbitals, molecular orbitals, too, have specific sizes, shapes, and energies. 

The change in energy that occurs as two Is atomic orbitals approach each other. The internuclear distance at minimum potential energy is the length of the H — H covalent bond. 

Orbitals are conserved. In other words, the number of molecular orbitals formed must equal the number of atomic orbitals combined. In describing the formation of an H—H bond, we combined two atomic orbitals but discussed only one molecular orbital. Where is the other molecular orbital As you will see shortly, it is there it just doesn t contain any electrons. 

When two atomic orbitals overlap, two molecular orbitals are formed—one lower in energy and one higher in energy than the atomic orbitals. 

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These notes are based on lectures on molecular orbital theory that we have presented at the University of Copenhagen and Columbia University. They were designed primarily for advanced-undergraduate and first-year graduate students as an introduction to molecular orbital theory. 

McWeeny, R. Methods of Molecular Quantum Mechtmics, 2ndedn. Academic, San Diego (1992) Nakajima, T. Quantum Chemistry - An Introduction to Molecular Orbital Theory (Japanese). Shokabo, Tokyo (2009)... 

HyperChem currently supports one first-principle method ab initio theory), one independent-electron method (extended Hiickel theory), and eight semi-empirical SCFmethods (CNDO, INDO, MINDO/3, MNDO, AMI, PM3, ZINDO/1, and ZINDO/S). This section gives sufficient details on each method to serve as an introduction to approximate molecular orbital calculations. For further details, the original papers on each method should be consulted, as well as other research literature. References appear in the following sections. 

Two excellent books which offer useful background material to this chapter are An introduction to ligand fields by B. N. Figgis (published by Interscience Publishers) and Atomic and molecular orbital theory by P. O D. Offenhartz (published by the McGraw-Hill Book Co.). 

This chapter is an introduction to qualitative molecular orbital theory and pericyclic reactions. Pericyclic reactions have cyclic transition states and electron flow paths that appear to go around in a loop. The regiochemistry and stereochemistry of these reactions are usually predictable by HOMO-LUMO interactions, so to understand them we need to understand molecular orbital theory, at least on a qualitative basis. 

This book is an introduction to quantum mechanics and mathematics that leads to the solution of the Schrodinger equation. It can be read and understood by undergraduates without sacrificing the mathematical details necessary for a complete solution giving the shapes of molecular orbitals seen in every chemistry text. Readers are introduced to many mathematical topics new to the undergraduate curriculum, such as basic representation theory, Schur s lemma, and the Legendre polynomials. 

The theory of the chemical bond is one of the clearest and most informative examples of an explanatory phenomenon that probably occurs in some form or other in many sciences (psychology comes to mind) the semiautonomous, nonfundamental, fundamentally based, approximate theory (S ANFFBAT for short). Chemical bonding is fundamentally a quantum mechanical phenomenon, yet for all but the simplest chemical systems, a purely quantum mechanical treatment of the molecule is infeasible especially prior to recent computational developments, one could not write down the correct Hamiltonian and solve the Schrodinger equation, even with numerical methods. Immediately after the introduction of the quantum theory, systems of approximation began to appear. The Born Oppenheimer approximation assumed that nuclei are fixed in position the LCAO method assumed that the position wave functions for electrons in molecules are linear combinations of electronic wave functions for the component atoms in isolation. Molecular orbital theory assumed a characteristic set of position wave functions for the several electrons in a molecule, systematically related to corresponding atomic wave functions. 

At the same time as Ballhausen cultivated the scientific activity at FKI did he also found time to write his influential books. Apart from the dissertation, the first of these was Introduction to Ligand Field Theory [16]. It is probably the publication for which he is best known to the broad audience of chemists. It is a classic in the world of inorganic chemistry. It contains chapters on atomic theory and group theory, crystal-field theory, molecular orbitals, spin-orbit coupling, and vibronic interactions. Last, but not least, it also contains an actual discussion of the properties of a number of inorganic complexes. In the preface, he writes, inter alia ... 

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