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# Physical Chemistry CHEM 3510

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This 7 page Class Notes was uploaded by Mr. Clementine Gottlieb on Wednesday October 21, 2015. The Class Notes belongs to CHEM 3510 at Tennessee Tech University taught by Scott Northrup in Fall. Since its upload, it has received 42 views. For similar materials see /class/225693/chem-3510-tennessee-tech-university in Chemistry at Tennessee Tech University.

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Date Created: 10/21/15

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 7 bond in this simple molecule first Each carbon has a sz orbital perpendicular to plane of molecule Use LCAOMO to get two MO s which gives rise to 2x2 secular determinant O A Etrial 3 Etrial S l5 Etrial 5 0H3 Etrial HMO approx Set all overlap integrals S O Recognize the oc integrals are equal This gives quadratic oc E2 32 O ROOtSEoc3 ocS 27139 05 13 Total 7 bond energy 2 oc 3 Stabilization due to bond formation 23 28 3 is intrinsically negative and 24 eV for CC bond 230 kJmol 2 Butadiene C C C Treat sigma bonding framework using VB theory as follows MN cw 39 92 mg 4 C QM L7cr wwkf Still have an unused p orbital available on each C perpendicular to plane of molecule Edge on view o do wcw c c I 3941 19 These extensively overlap to form a deocaized Tl system P0 Z 4 Ml O 39 Treat Tl 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 a overlap integrals S O 29 2 Set all resonance integrals between nonneighbors 0 B13 B14 524 etc O 3 Set all other resonance integrals 5 equal to one another Resulting Sec detm xE 5 o o 5 xE 5 o o O B xE B o o 5 x E Generates a quartic polynomial in E which has four roots Therefore 4 J39sorbital MO 4 energies roots of secular determinant They are E on I 162 5 on I 062 5 Energy diagram 1 4 W a 1623 377 39 C2p a 0623 2 a 0623 Jv 7739 a 1623 Figure 1139 Atkins Physical Chemiszry Eighth Editinn o 2006 Peter Atkins and Julio de Paula 30 Spectroscopic transition HOMO a LUMO called frontier orbitals HOMO highest occupied molecular orbital here MO 211 LUMO lowest unoccupied molecular orbital here MO 3n AEtrams LUMO HOMO o 062 3 0L 062 3 1243 Compare wave functions with particle in box l Delocalized system have extra stability deloc energy DE Calculate it DE Energy of cc39c39c Energy of cccc Allow electrons 2 separate To delocalize Tl bonds like in ethene 2a 162 3 2a 062 3 22a 2p 40i4483 40L43 048B 110 kJmol of stabilization 31 Benzene cyclic delocalized system 6X6 secular determinant ocE 5 o o o 5 5 ocE 5 o o o o 5 ocE 5 o o o O O 5 ocE 5 0 o o o 5 ocE 5 5 o o o 5 ocE fclue to cyclic connection Energy eigenvalues are E on i 23a i Ba i B k xll j J 819 2 K Figure 1 1 41 Atkins Physical Chemistry Eighth Edm39an 2006 Peter Atkins and Julio de Paula Calculate delocalization energy DE Total pi electron energy 2a 26 4a B6a 86 Energy of three CC in ethane 2a 26 DE difference 26 460 kJmol 32 C 4 Solids are extreme case of delocalization Graphite is like benzene stretching to infinity Modern Computational Chemistry 1 Falls in three categories a b C semiempirical 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 AMl 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 ab initio methods actually solve these integrals numerically To make it easier they replace the hydrogenic atom orbitals with Gaussianlike atomic orbitals which are quicker to evaluate integrals Example HF321G HartreeFock method with 321G 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 density functional theories DFF 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 Ep 33 Calculations generally take less time than HartreeFock and are as accurate Example names DFFB3LYP321G 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 Problem in Atkins Use it to treat a hypothetical molecule H3 H3 0 Q G 15A 153 15C The secular determinant would be OPE BAB39E SAB BAC39E SAC BEAE SBA OL39E BBCE SBC 0 BCA39E SCA BCB39E SCB OPE 34

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