Announcements • Today (11/20): • Chap 14: Molecular Orbitals • Chap 14: Spectroscopy
• Thursday (11/22): Happy Thanksgiving
• Dinner: 11/26 - Stay tuned for an email with details over Thanksgiving break
• Next week (11/26): There will be a quiz this week • Tuesday: Chap 14: Spectroscopy Chap 15: Chemical Kinetics • Thursday: Chap 15: Chemical Kinetics Practice Exam 3 posted
• Saturday (12/1): Review Session for Exam 3 (Date/Location TBA)
• Following week (12/3): • Tuesday: Chap 15: Chemical Kinetics • Thursday: Exam 3 Announcements • Final Exam: 12/20, 4:10-7 PM, 209 Hav
• Study Week: Tues, 12/11, and Thurs, 12/13, 11:40- 12:55 PM—Please keep these dates and times open on your calendars
• Homework • Read Chap 15: Chemical Kinetics • Do even problems at the end of Chap 15 • Read J Chem Ed article posted on Courseworks • Install 30-day trial version of MATLAB on your laptop …but, “how” are electrons shared?
Electron pair Molecular orbital (MO) Covalent bonds Valence bond theory repulsions, bonding theory and linear and sharing of and hybridization of geometries, and the combinations of atomic electrons orbitals shapes of molecules orbitals (LCAOs)
•Shapes of molecules •Energy Levels •Bond orders •Predicting unpaired e− Valence-bond theory and hybridization of orbitals
Orbital Combination Hybrids Arrangement Unused Orbitals s + p 2 sp linear 2 p
s + 2p 3 sp2 trigonal (120˚) 1 p
s + 3p 4 sp3 t et r ahedr al none
NOTES
• The n superscript in spn indicates the number of p orbitals that have been combined with one s orbital.
• The number of hybrid orbitals equals the number of atomic orbitals combined.
• Don't forget the orbitals that are not involved in the hybridization.
• Hybridization is not a physical phenomenon—it is purely mathematical. MO theory and LCAOs—Molecular orbitals of H2 Molecular Orbital Diagrams • The interaction between two atomic orbitals is typically represented by a molecular orbital diagram, which links atomic orbitals to the MOs. s*–orbital (antibonding)
1ss* • Note that the number of molecular orbitals equals the sum of atomic orbitals. • Note that the number of 1s 1s electrons in molecular orbitals equals the sum of H H 1ss the number of electrons in atomic orbitals.
s–orbital (bonding) H2
# e in bonding orbitals - # e antibonding orbitals 2 - 0 Bond order = = = 1 2 2 MO theory and LCAOs—Bond order, bond energy, and bond length
For similar systems, • bond energy increases with increase in bond order, and • bond length decreases with increase in bond order. MO theory and LCAOs—Other homonuclear diatomic molecules
General Guidelines for Construction of Molecular Orbital Diagrams
(1)Identify all orbitals in the valence shell.
(2) Combine pairs of atomic orbitals of appropriate symmetry to give bonding and antibonding orbitals.
(3) Atomic orbitals combine most effectively with other atomic orbitals of the same or similar energy.
(4) The effectiveness with which two orbitals combine is proportional to their overlap.
(5) Note how many electrons are present in each atom and adjust for the charge.
(6) Accommodate the electrons in order of increasing energy.
(7) When MOs have the same energy, electrons enter different orbitals with the same spin before pairing the spins. MO theory and LCAOs The homonuclear diatomic molecules: O2 and F2 as examples
• The four valence orbitals of each atom are 2s, 2px, 2py and 2pz. • These may combine to form eight molecular orbitals.
2s + 2s s2s + s*2s
2pz + 2pz s2p + s*2p
2px + 2px p2p + p*2p
2py + 2py p2p + p*2p MO theory and LCAOs—Overlap of p orbitals
Two orbitals can only interact if they have appropriate symmetry.
± no interaction
± no interaction
constructive overlap constructive overlap = destructive overlap, i.e., the orbitals remain nonbonding.
destructive overlap
Molecular orbitals are classified as either bonding, nonbonding or antibonding. MO theory and LCAOs—Overlap of p orbitals
s*2p node
2pz ± 2pz s2p
p*2p node
2px ± 2px p2p
p*2p node
2py ± 2py p2p
Note that colors are often used to indicate phase (+/–) MO theory and LCAOs—Overlap of p orbitals
• For a given distance, end-to-end overlap is greater than side-to-side overlap.
• Thus, s2p will be more stable, i.e., lower in energy, than p2p.
end-to-end s2p
side-to-side p2p MO theory and LCAOs The homonuclear diatomic molecules O2 and F2 as examples
NOTE • 8 atomic orbitals give 8 molecular orbitals.
• s2p is more
stable than p2p MO theory and LCAOs The homonuclear diatomic molecules: O2
• Oxygen has 6 valence electrons, i.e., there are 12 electrons in MOs.
• Two electrons in p* orbitals are unpaired, i.e., O2 is paramagnetic.
• The electron configuration is: 2 2 2 4 2 (s2s) (s*2s) (s2p) (p2p) (p*2p) .
8 – 4 • Bond order = = 2 2 Bond order corresponds to the double bond predicted by simple valence considerations with oxygen having 6 valence electrons. MO theory and LCAOs The homonuclear diatomic molecules: F2
• Fluorine has 7 valence electrons, i.e., there are 14 electrons in MOs.
• Electrons in p* orbitals are paired, i.e., F2 is diamagnetic.
• The electron configuration is: 2 2 2 4 4 (s2s) (s*2s) (s2p) (p2p) (p*2p) .
8 – 6 • Bond order = = 1 2 Bond order corresponds to the single bond predicted by simple valence considerations with fluorine having 7 valence electrons. MO theory and LCAOs MO diagrams for homonuclear diatomic molecules in the second period MO theory and LCAOs MO diagrams for homonuclear diatomic molecules in the second period MO theory and LCAOs Bond properties of homonuclear diatomic molecules in the second period MO theory and LCAOs MO diagrams for heteronuclear diatomic molecules A more complex molecule: Benzene (C6H6)
30 valence e−s total
Each C-H moiety is associated with 5 valence e−s
Number of “effective electron pairs” around each C, or the “steric number” of each C is three A more complex molecule: Benzene (C6H6) Valence bond theory, hybridized orbital view
• 30 valence e−s total • How many valence e−s in sp2 orbitals? • 24 valence e−s in sp2 hybrid orbitals • Where are the remaining valence e−s? A more complex molecule: Benzene (C6H6) Valence bond theory, hybridized orbital view A more complex molecule: Benzene (C6H6) Valence bond theory, hybridized orbital view à Molecular orbital view
• Resonance structures: Two valid Lewis structures are averaged to describe reality. Often related by symmetry, as in this case, so they’re equally valid and averaged with equal weight. • Conjugated: Alternating double and single bonds.
• Delocalized: Molecular orbital spread over many atoms. Potentially have color (visible chromophores) and/or electrical conductivity.
• Aromatic: Planar cyclic conjugated and/or delocalized. A more complex molecule: Benzene (C6H6) Molecular orbital view
• 30 valence e−s total p6* • 6 2s atomic orbitals combine
to form 6 s orbitals (3 s2s and 3 s*2s) p *, p * 4 5 • s2s and s*2s molecular orbitals are full: 12 valence − e s in s2s molecular orbitals − and 12 valence e s in s*2s molecular orbitals
p , p 2 3 • 6 p orbitals combine to form 6 p orbitals (3 p and 3 p*)
− • 6 valence e s in p2p p1 molecular orbitals A more complex molecule: Benzene (C6H6) Molecular orbital view
p6*
p *, p * Lowest Unoccupied Molecular 4 5 Orbitals (LUMO)
p , p Highest Occupied Molecular 2 3 Orbitals (HOMO)
p1 Spectroscopy Spectroscopy
• Fortunately, a lot of structural information can be obtained by using a variety of spectroscopic techniques, such as UV- visible (UV-vis) spectroscopy, infrared (IR) spectroscopy, microwave spectroscopy, and nuclear magnetic resonance (NMR) spectroscopy.
• These techniques are capable of identifying the types of functional groups that are present in a molecule and the relative positions of these functional groups, as well as the bond lengths, the bond angles, and, in some cases, the three-dimensional structure of a molecule.
• As such, spectroscopy encompasses a set of techniques that are invaluable to a chemist and provides a link between an “invisible” molecule and its structure. Spectroscopy Spectroscopy Absorption versus emission spectroscopy Spectroscopy Atomic spectroscopy
• In atomic spectroscopy, the frequencies of the light absorbed or emitted are related to the difference in energies between the various electronic states.
1 Infrared – 9 R H 1 – 4 R H
Ultraviolet Spectroscopy Molecular spectroscopy • An additional feature for molecules, because of their three-dimensional nature, is that the energy does not only depend on the electronic state, but also depends on their rotational and vibrational states.
• To a good approximation, the energy of a molecule may be expressed as:
Etot = Eel + Evib + Erot
• For a given electronic state, the molecule can be in a multitude of vibrational levels and, in each vibrational level, the molecule can be in a multitude of rotational levels. Electronic Spectroscopy Promotion of electrons (Ultraviolet and visible)
• Electronic spectroscopy involves transferring an electron from one molecular orbital to another.
• For example, the lowest energy transition for ethylene (C2H4) involves the transfer of an electron from the p molecular orbital to the p* molecular orbital. This transition occurs in the UV region. Electronic Spectroscopy A simple electronic spectroscopy experiment
• Absorption spectra are typically recorded by spectrophotometers, which record intensity of a signal as a function of wavelength or frequency (i.e., the “spectrum”).
• The intensity of the light transmitted through the sample cell (IS) is typically measured relative to that of a reference cell (IR) that contains no sample. Doing so removes, to the best extent possible, any spectroscopic features of the solvent in which the sample is dissolved or suspended and/or of the cell. Electronic Spectroscopy A simple electronic spectroscopy experiment
• Spectra can be presented in either transmittance (T = IS/IR) or absorbance (A = ln(IR/IS) = –lnT) modes.
• At any given wavelength, the absorption of a sample may be expressed by the Beer-Lambert Law:
A = cell where c is the concentration
el is the molar extinction coefficient at l l is the cell length
• Note that absorbance and transmittance are dimensionless quantities.