Hybridization and the Localized Electron Model Covalent Bonding: Orbitals A. Hybridization 1. The mixing of two or more atomic orbitals of similar energies on the same atom to produce new orbitals of equal energies. B. Hybrid Orbitals 1. Orbitals of equal energy produced by the combination of two or more orbitals on the same atom C. Evidence for hybridization of carbon Methane and sp 3 1. Four bonds of equal length and strength Carbon s isolated configuration Carbon s hybridized configuration 2. Four effective pairs of electrons surround the carbon 3. Whenever a set of equivalent tetrahedral atomic orbitals is required by an atom, this model assumes that the carbon adopts a set of sp 3 orbitals; the atom becomes hybridized D. sp 2 Hybridization 1. Trigonal planar structure, 120 o angle in ethane (ethylene) rules out sp 3 hybridization 2. sp 2 Hybridization creates three identical orbitals of intermediate energy and length and leaves one unhybridized p orbital 3. Three effective pairs of electrons surround the carbon (double bond is treated as an effective pair) 1
4. 5. Sigma bonds (σ bond) a. Bond in which the electron pair is shared in an area centered on a line running between the atoms b. Lobes of bonding orbital point toward each other c. All bonds in methane are σ bonds 6. Pi bonds (π bonds) a. Electron pair above and below the σ bond b. Created by overlapping of non-hybridized 2p orbitals on each carbon 7. Double bonds a. Double bonds always consist of one σ bond and one π bond E. sp Hybridization 1. Each atom has two hybrid orbitals and two unhybridized 2p orbitals 2. Carbon dioxide a. Oxygen atoms have 3 effective pairs of electrons (sp 2 hybrids) one double and two lone pairs b. Carbon atoms have 2 effective pairs (2 double bonds) 2
3. Notice that the sp 2 orbitals on the two oxygens are 90 o angles as are the π bond between carbon and oxygen. F. dsp 3 Hybridization 1. Five effective pairs around a central atom 2. Trigonal bipyramidal shape 3. PCl 5 is an example G. d 2 sp 3 Hybridization 1. Six effective pairs around a central atom 2. Octahedral structure 3. SF 6 is an example H. See the table below No. of effective pairs Atomic Orbitals Type of Hybridization No. of hybrid orbitals Geometry 2 s, p sp 2 Linear 3 s, p,p sp 2 3 Trigonal planar 4 s, p,p, p sp 3 4 Tetrahedral 5 s, p,p, p, d dsp 2 5 Trigonal bipyramidal 6 s, p,p, p, d,d d 2 sp 3 6 octagonal The Molecular Orbital Model A. Shortcomings of the Localized Electron Model 1. Electrons are not actually localized 2. Does not deal effectively with molecules containing unpaired electrons 3. Gives no direct information about bond energies B. Molecular Orbits 1. Can hold two electrons of opposite spins 2. The square of the orbital s wave function indicates electron probability C. The Hydrogen Molecule (H 2 ) 1. Two possible bonding orbitals, shapes determined by ψ 2 2. Bonding takes place in MO 1 (bonding MO) in which electrons achieve lower energy (greater stability), with electrons between the two nuclei 3
3. Both orbitals are in line with nuclei, so they are σ MOs 4. Higher energy orbital is designated as antibonding ( * ) 5. Electron configuration of H 2 can be written as D. A molecule is viewed on a quantum mechanical level as a collection of nuclei surrounded by delocalized molecular orbitals LCAO MO 1. Atomic wave functions are summed to obtain molecular wave functions 2. If wave functions reinforce each other, a 1 ψ bonding MO is formed (region of high = ( caϕ,1,1 ) 2 + + A s cbϕb s electron density exists between the nuclei) 3. If wave functions cancel each other, an antibonding MO is formed (a node of zero electron density occurs between the 1 ψ nuclei = ( caϕ,1,1 ) 2 + A s cbϕb s E. Bond Order 1. Bond order is the difference between the number of bonding electrons and the number of antibonding electrons, divided by two. 2. Larger bond order = a. greater bond strength b. greater bond energy c. shorter bond length Bonding in Homonuclear Diatomic Molecles A. In order to participate in MOs, AOs must overlap in space B. Larger bond order is favored C. When MOs are formed from p orbitals, σ orbitals are favored over π orbitals (σ interactions are stronger than π interactions) 1. Electrons are closer to the nucleus = lower energy 2 σ 1s D. Magnetism 1. Magnetism can be induced in some nonmagnetic materials when in the presence of a magnetic field a. Paramagnetism causes the substance to be attracted into the inducing magnetic field (1) associated with unpaired electrons b. Diamagnetism causes the substance to be repelled from the inducing magnetic field (1) associated with paired electrons 4
Relative MO energy levels for Period 2 homonuclear diatomic molecules Z 8 Z 7 5
Bonding in Heteronuclear Diatomic Molecules A. Similar but not identical atoms 1. Use MO diagrams for homonuclear molecules B. Significantly different atoms 1. Each molecule must be examined individually 2. There is no universally accepted MO energy order Putting our bonding models together The VSEPR / hybridization approach is good at explaining shapes around a central atom in a molecule BUT, since it depends on keeping electrons in pairs at all times, it is not so good at predicting electron distributions (like in oxygen!) Is there a way to bring them together? Let s go back to RESONANCE Combining our two bonding models σ bonds can be described as being localized. π bonding must be treated as being delocalized. The ozone molecule, O 3 VAL: 18 e σ bond network VB theory 2 σ bonds: 2 O(sp 2 ) [central O] + (2 x 1 O(sp 2 )): 4σ bonding electrons Left for π bonding MO theory 18 val 4σ bonding electrons (5x2) sp 2 electrons: We construct LCAO-MO ψ MO = caφ A, 2 p + c z BφB,2 p + c z CφC, 2 p z Ozone is symmetrical. ψ 1 = caφ A,2 p + c z BφB,2 p + c z CφC, 2 p, ψ ( ) z 2 = ca φa,2 p φ z C, 2 p, z ψ = φ + c φ c 3 ca A,2 p z B B,2 pz CφC, 2 p z 6
Conjugated Systems A. Conjugated double bonds are separated by one single bond. Example: 1,3-pentadiene. B. Isolated double bonds are separated by two or more single bonds. 1,4-pentadiene. C. Cumulated double bonds are on adjacent carbons. Example: 1,2-pentadiene D. 1,3-Butadiene 1. Single bond is shorter than 1.54 Å. 2. Electrons are delocalized over molecule. Constructing Molecular Orbitals A. π molecular orbitals are the sideways overlap of p orbitals. B. p orbitals have 2 lobes. Plus (+) and minus (-) indicate the opposite phases of the wave function, not electrical charge. C. When lobes overlap constructively, (+ and +, or - and -) a bonding MO is formed. D. When + and - lobes overlap, waves cancel out and a node forms; antibonding MO. E. 7
F. Allylic Systems: Carbon adjacent to C=C is allylic. H 2 C H C + CH 2 + H 2 C H C CH 2 MOs for Allylic Systems G. Benzene 1. σ bonds ( C- H and C C) are sp 2 hybridized a. Localized model 2. π bonds are a result of remaining p orbitals above and below the plane of the benzene ring 3. 4. σ bond framework 8
5. π bonds Ultraviolet Spectroscopy A. Absorption of correct energy photon will promote an electron to an energy level that was previously unoccupied. B. HOMO=Highest occupied molecular orbital LUMO=Lowest occupied molecular orbital 9
C. 200-400 nm photons excite electrons from a π bonding orbital to a π* antibonding orbital. D. Conjugated dienes have MO s that are closer in energy. E. A compound that has a longer chain of conjugated double bonds absorbs light at a longer wavelength. F. π π* for ethylene and butadiene Photoelectron Spectroscopy A. Can be used to determine the relative energies of electrons in individual atoms and molecules. B. High-energy photons are directed at the sample, and the kinetic energies of the ejected electrons are measured. 10