Frontier Molecular Orbital Theory CHEM 430 Great Books on Frontier Orbital Theory Basics of Frontier Molecular Orbital Theory Since the majority of energy gain in a reaction between two molecules is a result of the HOMO of one molecule reacting with the LUMO of a second molecule this interaction is called a Frontier Molecular Orbital (FMO) interaction A reaction is thus favored when the HOMO (nucleophile) is unusually high in energy and the LUMO (electrophile) is unusually low in energy What does unusually high HOMO or unusually low LUMO mean? Must be compared relative to something -usually compare energy levels with a known unreactive C-H (or C-C) single bond If the HOMO of a new compound is higher in energy than the HOMO of the C-H bond, then it will be more reactive as a nucleophile If the LUMO of a new compound is lower in energy than the LUMO of the C-H bond, then it will be more reactive as an electrophile How much higher or lower in energy will determine the relative rates of reactions Basics of Frontier Molecular Orbital Theory Frontier Molecular Orbitals – HOMO and LUMO It makes sense that the HOMO and LUMO are the orbitals most likely to be involved in chemical reactivity. • Chemical reactions involve the redistribution of electrons (creation and destruction of bonds, oxidation, reduction, …) • The HOMO is the orbital of highest energy that is still occupied, so energetically it is the easiest to remove electrons from this orbital. This could be simply donating electron density to form a bond (act as a Lewis base) or it could be oxidation. • The LUMO is the lowest lying orbital that is empty, so energetically it is the easiest to add more electrons into this orbital…Lewis acid; reduction. • It isn’t always the HOMO and/or LUMO involved in chemical reactivity. Symmetry plays a role, too. If the HOMO or LUMO isn’t of the correct symmetry, it might be the HOMO-1 or the LUMO+1 that is involved in the reaction. Basics of Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, therefore poor electrophile Lone pair of electrons placed in * C-H atomic orbital No electrons in atomic orbital, therefore very electrophilic Because nitrogen is more electronegative than carbon, orbital is lower in energy sp3 1s C H H+ (likewise oxygen is lower than nitrogen) :NH3 Both are very nucleophilic, :OH2 ammonia more than water C-H Very low HOMO, Factors that can adjust MO energy levels: therefore poor nucleophile 1) Unmixed valence shell atomic orbitals A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar energy levels and strong overlap, therefore high mixing Basics of Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, therefore poor electrophile *C-H Negative charge will raise the energy of orbital, therefore make compound more nucleophilic CH3 3 sp C 1s H H+ OH :NH3 :OH2 C-H Very low HOMO, Factors that can adjust MO energy levels: therefore poor nucleophile 1) Unmixed valence shell atomic orbitals A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar 2) Electric charge energy levels and strong overlap, therefore high mixing Basics of Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, therefore poor electrophile The degree of mixing of two orbitals is related to the amount *C-H of overlap between the orbitals *C-C This makes HOMO into a good nucleophile 3 2p C 2p C sp C 1s H C-C When two p orbitals overlap to form a bond, the orbitals begin higher in energy than a C-H hybridized orbital and the amount of overlap is less Very low HOMO, Factors that can adjust MO energy levels: therefore poor nucleophile 1) Unmixed valence shell atomic orbitals A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar 2) Electric charge energy levels and strong overlap, 3) Poor overlap of atomic orbitals therefore high mixing Basics of Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, therefore poor electrophile Since the oxygen 2p orbital is * C-H much lower in energy, the This makes LUMO energy match with carbon 2p is into a good worse and therefore less mixing electrophile 2p C *C-O 3 sp C 1s H 2p O C-O C-H Very low HOMO, Factors that can adjust MO energy levels: therefore poor nucleophile 1) Unmixed valence shell atomic orbitals A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar 2) Electric charge energy levels and strong overlap, 3) Poor overlap of atomic orbitals therefore high mixing 4) Poor energy match of orbitals Basics of Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, Can also use orbital energy levels to understand therefore poor electrophile differences in reactivity for C-X bonds *C-H A C-Cl bond is good *C-Mg electrophile spMg *C-Cl 3 3 3 sp C 1s H sp C sp C C-Mg A C-Mg bond is sp3 Cl good nucleophile C-Cl C-H Very low HOMO, Factors that can adjust MO energy levels: therefore poor nucleophile 1) Unmixed valence shell atomic orbitals A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar 2) Electric charge energy levels and strong overlap, 3) Poor overlap of atomic orbitals therefore high mixing 4) Poor energy match of orbitals Basics of Frontier Molecular Orbital Theory Frontier molecular orbital (FMO) theory allows a chemist to make predictions about a reaction by knowing the placement of the HOMO and LUMO energy levels A high HOMO level represents a compound that is a good nucleophile Anything that will raise CH3 > NH2 > OH energy level of HOMO will increase nucleophilicity A low LUMO level represents a compound that is a good electrophile R Anything that will lower CO H3C Cl energy level of LUMO will R increase electrophilicity The energy level of the HOMO and LUMO can be predicted by knowing that when two atomic orbitals mix they form two new molecular orbitals, one lower in energy and one higher in energy The amount of mixing is dependent upon: 1) The amount of overlap between the mixing orbitals (e.g., the overlap for a bond is greater than the overlap for a bond) 2) The closer in energy are two orbitals, the greater the amount of mixing that occurs Basics of Frontier Molecular Orbital Theory FMO will also allow prediction about where a reaction will occur (regiochemistry) and direction of approach (stereochemistry) Consider a reaction with a carbonyl compound FMO predicts that a carbonyl should react as an electrophile due to the low energy LUMO The regio- and stereochemistry can also be predicted by considering the interacting frontier orbital (the LUMO) The coefficient on carbon is rotate larger than the coefficient on oxygen, therefore nucleophile reacts at carbon LUMO of formaldehyde Basics of Frontier Molecular Orbital Theory What direction should a nucleophile approach the carbonyl? NUC NUC Direction appears better, Optimal interaction but still not optimal interaction (best overlap of interacting orbitals) NUC Expect this direction to be highly disfavored due to orthogonal interaction with orbitals Could there possibly be a method to test the angle of approach of nucleophile to carbonyl? X-ray structures come to the solution once again! Basics of Frontier Molecular Orbital Theory What direction should a nucleophile approach the carbonyl? Studied a variety of X-ray NUC structures where a N Optimal interaction reacts with a carbonyl (best overlap of intramolecularly interacting orbitals) As the N came closer to carbonyl, the C-O bond lengthened and the carbonyl carbon becomes pyramidalized Called the “Bürgi-Dunitz” angle The angle of <N-C-O averaged 107˚ ( ) Could there possibly be a method to test the angle of approach of nucleophile to carbonyl? X-ray structures come to the solution once again! Bürgi, H.B., Dunitz, J.D., Shefter,E., J. Am. Chem. Soc. (1973), 95, 5065-5067 Basics of Frontier Molecular Orbital Theory What about the stereochemistry for a reaction with an alkyl halide? Since alkyl halide is reacting as the electrophile, need to look at the LUMO Largest coefficient is on the backside of the carbon Nucleophile thus reacts with a NUC methyl halide in a SN2 reaction with backside attack So called “inversion of configuration” LUMO of methyl halide Bonds that break base Base thus reacts by abstracting hydrogen anticoplanar to The base will abstract the leaving group and form new hydrogen that is anticoplanar bond in E2 reaction to leaving group New bond LUMO of 2˚ alkyl halide Steric, Inductive & Stereoelectronic Effects General Reviews Stereoelectronic Effects Fleming, I. Frontier Orbitals and Organic Chemical Reactions Geometrical constraints placed upon ground and transition states by orbital overlap considerations. Fukui, Acc. Chem. Res. 1971, 4, 57. Kirby, A. J. Stereoelectronic Effects. Fukui Postulate for reactions: During the course of chemical reactions, the interaction of Universal Effects Governing all Chemical Reactions the highest filled (HOMO) and lowest unfilled (antibonding) molecular orbital (LUMO) in reacting species is very important Steric Effects to the stabilization of the transition structure. Nonbonding interactions (van der Waals repulsion) between substituents within a molecule or between reacting molecules General Reaction Types Me Me SN2 – Nu: CBr Nu C R Br: R Radical Reactions