Review of VB and MO theory Lecture 7, Chemistry 312

Brief history of VB theory After Gilbert Newton Lewis published “The Atom and the Molecule” in 1916, in which he introduced the idea of a covalent bond, chemists wanted to gain a better and more mathematical description of what the chemical bond actually was. In 1926, Erwin Schrodinger published the quantum mechanical interpretation of energy levels in an atom (Schrodinger’s equation), and the next year, Walter Heitler and Fritz London use it to come up with a mathematical model for the H2 molecule – this is the forerunner of valence bond theory.

VB theory Linus Pauling combined Lewis’s ideas of covalent bondng (shared electron pairs) with the Heitler-London calculation to expand VB theory to a larger group of molecules, published in a 1927 paper “The Shared-Electron Chemical Bond”. He added the ideas of resonance and orbital hybridization later, and in 1936, published The Nature of the Chemical Bond. Because of his insistence on the supremacy of the analysis of VB theory, Pauling did not embrace molecular orbital theory.

Formation of σ and π (covalent) bonds

The road to MO theory Molecular orbital theory began nearly at the same time as VB theory. Friedrich Hund and Robert Mulliken (electron delocalization over a whole molecule), John C Slater (linear combination of atomic orbitals), John Lennard-Jones (potential between two noble gas atoms), all published papers on these topics in 1927-1928. Mulliken coined the word “orbital” in 1932, but it was not until Douglas Hartree then Vladimir Fock refined self-consistent field theory (1940s) that MO theory became useful as a quantitative tool.

Linear combin-ations of AOs By adding together adjacent atoms’ electronic wavefunctions with the same or different phases, you can generate areas of overlap between these orbitals There can be constructive interference between the orbitals, in which case an area of enhanced electron density is created There can be destructive interference between the orbitals, in which case a node is created

Combining AOs into MOs The left column (except for the last row) are bonding MOs The right column (except for the last row) are antibonding Mos – note the presence of an extra nodal plane (what does this imply about the energy of these types of orbitals?) The last row contains non-bonding orbitals – they retain the localization and other attributes of the AOs

What do both theories try to do? Both theories explain the formation of the covalent bond A covalent bond (VB theory) or a molecular orbital (MO theory) is formed when two atomic orbitals having the same symmetry and the same energy overlap with each other Both theories predict that there is an increase in electron density between the two bonding nuclei, and this enhanced density is the bond

So what is the difference between VB and MO theories? VB theory MO theory Consider a molecule as a set of individual bonds between pairs of atoms (localized electrons) Resonance and hybridization help explain molecular shape Only half-filled orbitals in valence shell take part in bonding – filled orbitals are non-bonding Consider a molecule as held together by electronic orbitals that span the molecule (delocalized e-) Resonance and hybridization play no role in shape All atomic orbitals (filled, half-filled, empty) overlap to form molecular orbitals, given symmetry rules

Which one is “right”? Both! VB theory is great for predicting molecular shapes, and energies of bonds in simple non-metallic compounds, whereas MO theory is in general better at predicting bond energies of more complex molecules, especially those with delocalized electrons (conjugated systems).

O2 paramagnetism For instance, MO theory correctly predicts the paramagnetism of the oxygen molecule whereas VB theory does not Note that the bond order = (1/2) (# of e– in bonding orbitals – # of e– in antibonding orbitals) Higher bond order = stronger (higher energy) bond = shorter bond

One other key difference Note below that ϕ is an LCAO of similar symmetry atomic orbitals The symmetry needed for VB theory is simple: recognizing cylindrical symmetry, nodal (mirror) planes, center of inversion The symmetry needed for MO theory is the sophisticated group theory version used in chapter 6 – need point groups at the very least Consider the water molecule and its MOs – water is in the C2v point group

Constructing the MO diagram Treat the central atom as one unit and the side (ligand) atoms as another, then determine what symmetry species (irreducible representation) they belong to: the symmetry of the oxygen’s 2s orbital is A1 (it remains unchanged under any operation). This is also true of the oxygen’s pz orbital (defining the z axis as the principal C2 axis), so this orbital is A1. Similarly, you can show that the oxygen’s px atomic orbital has B1 symmetry and the py atomic orbital has B2 symmetry.

Symmetry-adapted linear combinations The hydrogens also act as a unit. Note that there are only two possible combinations how these two 1s orbitals can interact: in-phase or out of phase. The in-phase combined wavefunction (top) has A1 symmetry; the out of phase combined wavefunction (bottom) has B2 symmetry. These are called SALCs.

Constructing the MO diagram A combination of the A1 symmetry hydrogen 1s orbitals and the A1 symmetry oxygen 2s and 2pz orbitals will overlap, and these new MOs will be called a1 orbitals (lower case, but same letter and subscript as the AO designation). Mathematically, then, Φa1 = c1 ψH1s + c2 ψO2s + c3 ψO2pz By altering the signs on the c’s, you get a bonding (lowest), an intermediate and an antibonding orbital.

Constructing the MO diagram The B2 symmetry species are the B2 hydrogen 1s orbital combination and the oxygen 2py orbital; these combine to give Φb2 = c4 ψH1s + c5 ψO2py By adjusting the signs of the c’s, you get the two b2 MOs: a bonding and an antibonding orbital. Finally, the B1 symmetry 2px does not have a counterpart in the hydrogen orbitals – this orbital “comes across” on the diagram, retaining its energy, and is a non-bonding orbital.