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 H-H bonding atomic orbital 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 X Y X Y Homolytic bond cleavage Heterolytic bond cleavage 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 2 as the CN is a measure of the electron density in the neighborhood of the atom in question 2 By normalization, for each MO ΣCN = 1 Thus for the only filled orbital in H2, because the molecule is symmetric |C1| = |C2| 2 Therefore C1 = C2 and C1 = 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 2 Therefore ΣCN = 1 (for each atom) For H2: 2 c1 c2 ΣC (for orbital) σ 0.707 0.707 1 * σ 0.707 -0.707 1 71 2 ΣC (for atom) 1 1 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 do 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 sp3 hybridization energy 2s 1s 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 4 1s orbitals from each hydrogen and four second shell orbitals from the carbon atom (2s, 2px, 2py, 2pz) The 8 valence electrons would need to placed in bonds formed from the combination of these atomic orbitals Each bond is a result of Where are the electrons two electrons being shared H H 3 located and what orbitals between sp hybridized C C H H H H are being used? carbon and hydrogen 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 0 nodes 1 node 1 node 1 node Molecular orbital theory predicts there are 4 bonding MOs, 1 with 0 nodes and 3 with 1 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 Molecular Orbital Theory Csp3-H MO with 1 node bond energy MO with 0 nodes Inner shell C 1s Inner shell C 1s Each sp3 hybridized orbital would thus form a The bonding MOs for methane would not bond with the 1s orbital from each hydrogen to be of identical energy form four identical energy C-H bonds How to know which model is correct if either? 75 Molecular Orbital Theory Can first compare what orbitals look like computationally (obtained with Spartan 08, DFT B3LYP 6-31G*) 0 nodes 1 node 1 node 1 node Orbitals obtained computationally are identical to those qualitatively determined If the computer theory was established using molecular orbital theory, it is not surprising the obtained MOs resemble the qualitative picture 76 Molecular Orbital Theory Is there an experimental method to test which bonding theory matches reality? Can use photoelectron spectroscopy (PES) and electron spectroscopy for chemical analysis (ESCA) which measure the ionization potential of electrons expelled from orbitals Difference between PES (<~20 eV) and ESCA (>~20 eV) is ionization potential range In short for these experiments the gas phase sample of compound under analysis is irradiated and the binding energy for an electron can be calculated by knowing the energy of ionizing irradiation and subtracting the kinetic energy of the detected emitted electrons Inner shell electrons Bonded electrons have 2 different energy levels The experiment confirms the MO description of bonding Methane does have two different energy levels for the four C-H bonds Even though valence bond theory is not correct, it is still widely used by organic chemists as a guide to predict reactions 77 Chem. Phys. Lett. (1968), 613-615 Molecular Orbital Theory Using molecular orbital theory therefore the electrons are located in regions of space on time average (orbitals) that are formed by the mixing of atomic orbitals Have already seen a simple orbital description with forming H2 MOs from mixing atomic 1s orbitals from each hydrogen atom Eσ* Eσ Remember also that Eσ* > Eσ -due to electron repulsion 78 Building Molecular Orbitals from Atomic Orbitals When forming molecular orbitals of H2 from atomic orbitals from each hydrogen atom, hydrogen only has one electron in a 1s orbital (or a 1,0,0 orbital using n,l,m designation) When building molecular orbitals from a 2nd row atom (like carbon) can use either the 2s (2,0,0) or 2p (2,1,-1; 2,1,0; or 2,1,1) atomic orbitals to form the bonds When different orbitals interact, the overlap of the orbitals changes depending upon the direction of bond formation (both in degree of overlap and symmetry of the bond) When two s orbitals interact, due to When two p orbitals interact, if lobe with symmetry of orbital the direction of approach same phase is pointing toward each other a is irrelevant bonding region can occur Overlap between orbitals of same phase leads to bonding region Bonding MO (called σ bond) 79 Building Molecular Orbitals from Atomic Orbitals Due to the unsymmetrical orientation of a p orbital, however, there are other possible orientations of approach One bonding approach direction has the p orbitals on both atoms directed opposite to the approach direction Still a bonding MO, but electron density is not symmetric about internuclear axis (called π bond) If s orbital approaches p orbital from side, however, there is no net overlap The positive overlap (blue with blue) is exactly canceled with the negative overlap (blue with red), thus there is no net overlap The orbitals are said to be “orthogonal” to each other and thus do not mix 80 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) The molecular orbital the is unoccupied that is lowest in energy Hypothetical molecule that contains is called the LUMO 6 molecular orbitals and 6 electrons Unoccupied molecular orbitals (UMOs) Would fill the orbitals by following Pauli exlusion (only 2 electrons