Huckel molecular Orbital Theory - Lecture Notes | CHEM 3510, Study notes of Physical Chemistry

Download Huckel molecular Orbital Theory - Lecture Notes | CHEM 3510 and more Study notes Physical Chemistry in PDF only on Docsity! 28 B. Huckel Molecular Orbital theory (HMO theory). An approximate theory that gives us a very quick picture of the MO energy diagram and MO’s of molecules without doing a lot of work. Structure and bonding in highly conjugated systems nicely treated by HMO. Look at examples: 1. Ethene – look at the π bond in this simple molecule first. Each carbon has a 2pz orbital perpendicular to plane of molecule. Use LCAO-MO to get two MO’s, which gives rise to 2x2 secular determinant: HMO approx: Set all overlap integrals S = 0 Recognize the α integrals are equal This gives quadratic (α - E)2 - β2 = 0 Roots E = α + β, α - β Total π bond energy = 2 (α + β ) Stabilization due to bond formation = 2β 29 β is intrinsically negative and ~ -2.4 eV for C-C bond (~ -230 kJ/mol) 2. Butadiene. Treat sigma bonding framework using VB theory as follows: Still have an unused p orbital available on each C, perpendicular to plane of molecule. Edge on view: These extensively overlap to form a delocalized π system. Treat π system by HMO as follow: a. basis set is composed of four 2pz orbitals (perpendicular to plane). Therefore will get 4 x 4 matrix or secular determinant b. HMO approx: 1) Set all overlap integrals S = 0 C C C C 32 3. Benzene – cyclic delocalized system. 6x6 secular determinant = α-E β 0 0 0 β β α-E β 0 0 0 0 β α-E β 0 0 = 0 0 0 β α-E β 0 0 0 0 β α-E β β 0 0 0 β α-E due to cyclic connection =Energy eigenvalues are E = α + 2β, α + β, α + β Calculate delocalization energy DE: Total pi electron energy = 2(α + 2β) + 4( α + β ) = 6α + 8β Energy of three C=C in ethane = 2α + 2β DE = difference = 2β = −460 kJ/mol 33 4. Solids are extreme case of delocalization. Graphite is like benzene stretching to infinity. C. Modern Computational Chemistry. 1. Falls in three categories: a) semi-empirical methods – don’t actually evaluate the integrals giving rise to S (overlaps), a (coulomb), or b (resonance). Many integrals set to zero and others are parameterized to give good fit to experimental data. First example, CNDO (complete neglect of differential overlap). MNDO = moderate neglect of differential overlap. AM1 = Austin Model 1 (more advanced, fewer integrals set to zero). Are able to treat systems of 100’s of atoms because the size of the calculation increases as ~N2. b) ab initio methods – actually solve these integrals numerically. To make it easier, they replace the hydrogenic atom orbitals with Gaussian-like atomic orbitals which are quicker to evaluate integrals. Example: HF/3-21G = Hartree-Fock method with 3-21G basis set, meaning 3 Gaussians are added together to give each atomic orbital. Are able to treat systems of only 10’s of atoms because the size of the calculation increases as ~N4. c) density functional theories (DFT). focuses on the electron density rather than the wavefunction. Energy is seen as a function of the density (function of a function is a functional). E( ρ ) 34 Calculations generally take less time than Hartree-Fock and are as accurate. Example names: DFT/B3LYP/3-21G 2. Properties of molecules that can be calculated using computational software. (see HyperChem demonstration and do your own calculations) a) Structural properties like optimum bond lengths, bond angles, etc. b) Shape of potential surface vs nuclear coordinates, which allows calculation of vibrational (IR) spectra. c) Electron density surfaces (isodensity surface) = surface of constant electron density. d) Electrostatic potential surface – use hot and cool colors to map the electrostatic potential onto the electron density surface. e) Dipole moments. f) Energy diagrams and transition energies. g) Shapes of HOMO and LUMO, which indicate where the molecule would be most susceptible to attack from electrophile, nucleophile. D. Problem in Atkins: Use it to treat a hypothetical molecule H3. H3 The secular determinant would be: α-E βAB-E SAB βAC-E SAC βBA-E SBA α-E βBC-E SBC = 0 βCA-E SCA βCB-E SCB α-E 1sA 1sB 1sC