3-MO theory

Molecular Orbital Theory Valence Bond Theory: Electrons are located in discrete pairs between specific atoms Molecular Orbital Theory: Electrons are located in the molecule, not held in discrete regions between two bonded atoms Thus the main difference between these theories is where the electrons are located, in valence bond theory we predict the electrons are always held between two bonded atoms and in molecular orbital theory the electrons are merely held “somewhere” in molecule Mathematically can represent molecule by a linear combination of atomic orbitals (LCAO) ΨMOL = c1 φ1 + c2 φ2 + c3 φ3 + cn φn Where Ψ2 = spatial distribution of electrons If the ΨMOL can be determined, then where the electrons are located can also be determined 66   Building Molecular Orbitals from Atomic Orbitals Similar to a wave function that can describe the regions of space where electrons reside on time average for an atom, when two (or more) atoms react to form new bonds, the region where the electrons reside in the new molecule are described by a new wave function This new wave function describes molecular orbitals instead of atomic orbitals Mathematically, these new molecular orbitals are simply a combination of the atomic wave functions (e.g LCAO) Hydrogen 1s atomic orbital H-H bonding molecular orbital 67   Building Molecular Orbitals from Atomic Orbitals An important consideration, however, is that the number of wave functions (molecular orbitals) resulting from the mixing process must equal the number of wave functions (atomic orbitals) used in the mixing In the case of H2, in addition to the new bonding molecular orbital obtained by adding the two atomic 1s orbitals, an antibonding orbital is obtained by subtracting the two atomic orbitals node H-H antibonding molecular orbital 68   Electronic Configuration for H2 Each Hydrogen 1s atomic orbital has one electron When two atomic orbitals mix, they produce two molecular orbitals As the number of nodes increases, the energy of the orbital increases The molecule has a total of two electrons and follow Aufbau principle and Pauli principle to fill electrons in molecule 69   Bond Strength Eσ* > Eσ -due to electron repulsion Called the bond dissociation energy (BDE) The bond strength for H2 is considered the amount of energy required to break the bond and produce two hydrogen atoms X Y X Y Homolytic bond cleavage X Y X Heterolytic bond cleavage Y 70   Molecular Orbital Theory The σ and σ* orbitals can be written mathematically thus as a combination of atomic orbitals Ψσ = c1φ1 + c2φ2 Ψσ* = c1φ1 - c2φ2 The size of coefficients (c1 and c2) is related to the electron density as the CN2 is a measure of the electron density in the neighborhood of the atom in question By normalization, for each MO ΣCN2 = Thus for the only filled orbital in H2, because the molecule is symmetric |C1| = |C2| Therefore C1 = C2 and C12 = 1/2 C1 = C2 = 1/√2 = 0.707 Also if all the MOs are filled, there must be one electron in each spin state on each atom Therefore ΣCN2 = (for each atom) For H2: σ σ* ΣC2 (for atom) c1 c2 0.707 0.707 0.707 -0.707 ΣC2 (for orbital) 1 71   Molecular Orbital Theory The electron location in H2 is identical between valence bond theory and molecular orbital theory (due to there only being one bond in H2 and thus the electrons must be located on the two atoms) What happens however if there is more than one bond in the molecule, how the bonding theories differ in describing the location of electrons? Consider methane Valence bond theory predicts four identical C-H bonds in methane formed by the carbon hybridizing to an sp3 hybridization 2p energy 2s 1s sp3 hybridization 1s Each sp3 hybridized orbital would thus form a bond with the 1s orbital from each hydrogen to form four identical energy C-H bonds 72   Molecular Orbital Theory Molecular orbital theory would not use the concept of hybridization (hybridization is entirely a concept developed with valence bond theory) Instead of hybridizing the atomic orbitals first before forming bonds, molecular orbital theory would instead treat the molecular orbitals used to form the bonds as a result of mixing the atomic orbitals themselves For methane thus would have 1s orbitals from each hydrogen and four second shell orbitals from the carbon atom (2s, 2px, 2py, 2pz) The valence electrons would need to placed in bonds formed from the combination of these atomic orbitals Each bond is a result of two electrons being shared between sp3 hybridized carbon and hydrogen Where are the electrons located and what orbitals are being used? H C H H H H C H H H Valence Bond Theory Molecular Orbital Theory 73   Molecular Orbital Theory To visualize where the electrons are located and what molecular orbitals the electrons are located, consider the four hydrogen 1s orbitals and the four outer shell orbitals of carbon H 1s C 2s C 2px C 2py C 2pz Then mix the outer shell atomic orbitals to find the bonding patterns nodes node node node Molecular orbital theory predicts there are bonding MOs, with nodes and with node (therefore they must be at different energy levels if different number of nodes!) 74   Molecular Orbital Theory The bonding pattern in methane is thus different using either valence bond or molecular orbital theory Valence Bond Theory energy Csp3-H bond Inner shell C 1s Each sp3 hybridized orbital would thus form a bond with the 1s orbital from each hydrogen to form four identical energy C-H bonds Molecular Orbital Theory MO with node MO with nodes Inner shell C 1s The bonding MOs for methane would not be of identical energy How to know which model is correct if either? 75   Building New Molecular Orbitals from Molecular Orbitals In addition to building new molecular orbitals from adding atomic orbitals, new molecular orbitals can result from combining orbitals from two different molecules using their molecular orbitals (the result of a reaction between two molecules) For a given molecule there might be a multitude of molecular orbitals (the total number are due to the number of atoms in the molecule) Hypothetical molecule that contains molecular orbitals and electrons The molecular orbital the is unoccupied that is lowest in energy is called the LUMO Unoccupied molecular orbitals (UMOs) Would fill the orbitals by following Pauli exlusion (only electrons per orbital) and filling the lowest energy orbitals first Occupied molecular orbitals (OMOs) The orbitals are classified by whether they are “filled” or “unfilled” In addition the molecular orbital that is occupied that is highest in energy is called the HOMO 81   Building New Molecular Orbitals from Molecular Orbitals When two molecules react (each with their own set of molecular orbitals) it is important to recognize which molecular orbital interaction determines the reaction (if a chemist knows this then they can predict reactions) Each molecular orbital in compound A however will react with each molecular orbital in compound B Whenever any two nonorthogonal orbitals interact they will create two new MOs, one higher in energy and one lower in energy When two UMOs react, there is no change in energy as there are no electrons in the orbitals Compound A Compound B When two OMOs react, there is an increase in energy due to the two higher energy electrons outweighing any energy gain The number of OMOs and UMOs and energy placement of orbitals is dependent upon the There is only an energy gain when a OMO of compound one molecule interacts with an UMO on the other molecule 82   Building New Molecular Orbitals from Molecular Orbitals The amount of energy gain is also dependent upon how close in energy the two orbitals are before mixing Consider mixing of two orbitals, one filled (OMO) and one unfilled (UMO) ΔE ΔE If the OMO is identical in energy to the UMO there will be the maximum energy gain due to the best possible mixing of the orbitals As the OMO has a greater difference in energy to the UMO, the mixing will be less and the energy gain will thus be lower Thus the energy gain is greatest in a reaction when the HOMO of one compound is closest in energy to the LUMO of the second compound 83   Building New Molecular Orbitals from Molecular Orbitals When mixing any two orbitals therefore the two important considerations are the overlap between the two orbitals and the match in energy of the two orbitals before mixing Considerations between mixing of orbitals are therefore: -when two nonorthogonal orbitals overlap and mix, they generate two new orbitals (one higher in energy and one lower in energy) -the amount of energy shift upon mixing is greater with more overlap of the orbitals and lower the further apart in energy the orbitals are before mixing -average energy of two new orbitals is slightly higher than average of original orbitals (partly an artifact of electron-electron repulsion in higher energy orbital) Consider the original hypothetical compound A reacting with compound B The most important interaction to consider is the HOMO of A reacting with the LUMO of B (largest energy gain) The energy gain from this interaction must be large enough to overcome the energy loss of each OMO mixing with another OMO (which causes an energy loss) Compound A Compound B 84   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 85   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 σ*C-H atomic orbital No electrons in atomic orbital, therefore very electrophilic sp3C 1s H H+ Because nitrogen is more electronegative than carbon, orbital is lower in energy (likewise oxygen is lower than nitrogen) :NH σC-H Very low HOMO, therefore poor nucleophile Both are very nucleophilic, ammonia more than water A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar energy levels and strong overlap, therefore high mixing :OH2 Factors that can adjust MO energy levels: 1) Unmixed valence shell atomic orbitals 86   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 Negative charge will raise the energy of orbital, σ*C-H therefore make compound more nucleophilic CH3 sp3C 1s H H+ OH :NH3 :OH2 σC-H Very low HOMO, therefore poor nucleophile A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar energy levels and strong overlap, therefore high mixing Factors that can adjust MO energy levels: 1) Unmixed valence shell atomic orbitals 2) Electric charge 87   Frontier Molecular Orbital Theory We can compare the placement of HOMO and LUMO levels relative to placement of C-H bonds Very high LUMO, The degree of mixing of two therefore poor electrophile orbitals is related to the amount σ*C-H of overlap between the orbitals π*C-C sp3C 1s H 2p C This makes HOMO into a good nucleophile 2p C πC-C When two p orbitals overlap to form a π bond, the orbitals begin higher in energy than a hybridized orbital and the amount of overlap is less σC-H Very low HOMO, therefore poor nucleophile A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar energy levels and strong overlap, therefore high mixing Factors that can adjust MO energy levels: 1) Unmixed valence shell atomic orbitals 2) Electric charge 3) Poor overlap of atomic orbitals 88   Frontier Molecular Orbital Theory sp3C 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 σ*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 π*C-O 1s H 2p O πC-O σC-H Very low HOMO, therefore poor nucleophile A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar energy levels and strong overlap, therefore high mixing Factors that can adjust MO energy levels: 1) Unmixed valence shell atomic orbitals 2) Electric charge 3) Poor overlap of atomic orbitals 4) Poor energy match of orbitals 89   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 σ*C-H σ*C-Mg A C-Cl bond is good electrophile sp3C 1s H sp3C ο*C-Cl spMg sp3C σC-Mg sp3Cl σC-H Very low HOMO, therefore poor nucleophile A sp3 hybridized carbon atom and a 1s orbital of hydrogen have similar energy levels and strong overlap, therefore high mixing σC-Cl A C-Mg bond is good nucleophile Factors that can adjust MO energy levels: 1) Unmixed valence shell atomic orbitals 2) Electric charge 3) Poor overlap of atomic orbitals 4) Poor energy match of orbitals 90   ... -0.707 ΣC2 (for orbital) 1 71   Molecular Orbital Theory The electron location in H2 is identical between valence bond theory and molecular orbital theory (due to there only being one bond in H2... bonds 72   Molecular Orbital Theory Molecular orbital theory would not use the concept of hybridization (hybridization is entirely a concept developed with valence bond theory) Instead of hybridizing... and what orbitals are being used? H C H H H H C H H H Valence Bond Theory Molecular Orbital Theory 73   Molecular Orbital Theory To visualize where the electrons are located and what molecular