Molecular Orbitals Based on Inorganic Chemistry, Miessler and Tarr, 4 th edition, 2011, Pearson Prentice Hall Images from Miessler and Tarr Inorganic Chemistry 2011 obtained from Pearson Education, Inc.
Molecular Orbital theory It uses the methods of group theory to describe bonding in molecules It complements and extends the simple pictures of bonding introduced in Simple bonding theory (VSEPR) Symmetry properties and relative energy of atomic orbitales determine how they interact to form molecular orbitals (MO s) These MO s are then occupied by the available electrons according to the same rules used for atomic orbitals
Molecular orbital theory (cont.) Total energy of electrons in the MO s are then compared with the initial total energy of electrons in atomic orbitals If the total energy of the electrons in the MO s is less than in the atomic orbitals, the molecule is stable compared with the separate atoms If the total energy is not less than in the atomic orbitals, the molecule is unstable and does not form.
Formation of MO s from AO s Schrodinger equations can be written for electrons in molecules Approximate solutions to these molecular Schrodinger 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 H 2, these functions have the following form
For overlap to result in bonding Symmetry of orbitales must be such that regions with the same sign of ψ overlap Energies of atomic orbitals must be similar Distance between atoms must be short enough to provide good overlap, but not too short that repulsive forces of other electrons or nuclei interfere with overlap When these three conditions are met, the overall energy of electrons in the occupied MO s is lower in energy than the overall energy of electrons in the original AO s
MO s from s orbitals Sigma (σ) notation indicates orbitals that are symmetric to C 2 rotation about the internuclear axis
Molecular orbitals can be If the MO has a lower energy than the corresponding AO s, it is a bonding molecular orbital Electrons in bonding molecular orbitals are concentrated between the nuclei and hold them together If the MO has a higher energy than the corresponding AO s, it is an antibonding molecular orbital they have one or more nodes between the nuclei they are usually marked with an * Electrons in antibonding molecular orbitals cause a mutual repulsion between the atoms Non-bonding orbitals are also possible their energy is essentially that of an atomic orbital because the orbital on one atom has a symmetry that does not match any orbitals on the other atom
MO s from p orbitals The orientation of the atomic p orbitals is important as sigma or pi orbitals can result.
Sigma vs pi orbitals (symmetric or antisymmetric to C 2 rotation along the internuclear axis)
MO s from d orbitals Sigma, pi or delta orbitals can result Delta (δ) notation indicates a change in sign on C4 rotation about the bond axis
Energy must be considered
Homonuclear diatomic molecules Draw electron-dot Lewis diagrams for 2 nd period homonuclear molecules (Li 2, Be 2, B 2, C 2, N 2, O 2, F 2 ) Do all of them comply with the octet rule?
Homonuclear diatomic molecules Think of this oxygen Lewis structure has a double bond and all electrons paired But O 2 is paramagnetic (unpaired electrons) O O
MO theory can explain O 2 s double bond and paramagnetism Add 16 electrons (8 from each oxygen atom) Calculate bond order Notice two unpaired electrons New labels are added (u and g) to the MO s
Bond order Bond order = 1 (single bond) Bond order = 2 (double bond) Bond order = 3 (triple bond) Bond order = 2.5 (two and a half bonds?)
Orbital mixing Orbitals of appropriate energy and symmetry interact This results in a lowering of the total energy of the molecule The energy of the orbital with lower energy is lowered even more and the energy of the orbital with higher energy is raised even more Since lower energy orbitals are filled first, the energy of the total molecule is lowered
Aumento en Z*
Heteronuclear diatomic molecules A greater nuclear charge on one of the atoms will lower its atomic energy levels This lowering shifts the resulting MO energy levels The resulting wavefunctions will have different coefficients depending on the orbital which contribute In general, the atomic orbital closer in energy to an MO contributes more to the MO and the coefficient will be larger Examples are CO and HF
What orbitals are of special interest? Frontier orbitals HOMO highest occupied molecular orbital LUMO lowest unoccupied molecular orbital For example, the HOMO of CO is 3σ, with a higher electron density and a larger lobe on carbon As a result, in metal carbonyl complexes CO is bound through carbon rather than oxygen Simple electronegativity considerations would place the negative charge on oxygen
Ionic compounds and MO s Ionic compounds can be considered the limiting case of polarity in heteronuclear diatomic molecules As the atoms differ more in electronegativity, the difference in energy also increases, and the concentration of electrons shifts toward the more electronegative atom
MO s of larger molecules