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Quantum Mechanics and Basic Spectroscopy

by: Kylie Smitham

Quantum Mechanics and Basic Spectroscopy CHEM 163

Kylie Smitham
GPA 3.93


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This 4 page Class Notes was uploaded by Kylie Smitham on Monday September 7, 2015. The Class Notes belongs to CHEM 163 at University of California - Santa Cruz taught by Staff in Fall. Since its upload, it has received 34 views. For similar materials see /class/182239/chem-163-university-of-california-santa-cruz in Chemistry and Biochemistry at University of California - Santa Cruz.

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Date Created: 09/07/15
NOTES ON MOLECULAR ORBITAL THEORY Five major points concerning molecular orbital theories for diatomic and polyatomic molecules are summarized All of the material is covered in McQuarrie but this outline should help organize the topics which I consider important I Energybondinginteractions 1 Why don t a 2sA and 2pr interact to form a bond lt gt antibond pair 2 Will there be signi cant ls A and lsB interaction sin the 165 and 16 orbitals of F2 compared to the interactions between 2sA and 2sB in the 26S and 26 orbitals of F2 How will the energies of 16g and 16u compare to the energy ofa ls electron in F atom 3 In a coordinate system with consisten zaXis direction XA XB YA YB ZA ZB some sources use 1ncons1stent 1 W1 w p p e on 1ngorant1 on mg 3911 ZZAZZBbbd39 39b d39 What about u 2pZA 7 2pm 11 Classi cation Scheme 1 AO s used 2 Numbers of nodal planes passing through zaXis 6 11 5 etc Can you identify which d orbital components would contribute to 6bonds 11 bonds 5bonds 3 Bonding or antibonding 4 Symmetry with respect to inversion g gerade or u ungerade Notes on Molecular Orbital Theory Page 2 5 Schemes l and 3 are only approximations while 2 and 4 are rigorous classifications In complete calculations more than two ao s can interact to form mo s Thus a 263 could have in addition to 2sA and 2sB other types of 6 orbitals eg 2pm 2pBZ and classi cation 1 would only be approximate In addition if more than two ao s are esent some ao lt gt ao interactions could be bonding while others antibonding Thus classi cation 3 is only approximate The results of complex calculations therefore utilize only the inversion g or u and the plane symmetry 6 11 5 etc as in figure 915 in McQuanie III Energy ordering aufbau and molecular properties 1 Know the energy ordering appropriate for mo s from the 15 2S and 3 row ao s 2 Understand the origin of the two different schemes for porbital mo s Type II 2p 2611 y 2p26g results from a greater interaction between the 2p26 orbitals on the two atoms Type II energy ordering originates from greater 2p26A lt gt 2p26B overlap than 2p11 A lt gt 2p11B overlap at bonding intermolecular distances 9999 3 2 gtxlt 2132 Type I Notes on Molecular Orbital Theory Page 3 Type I ordering results from interactions between 25 and 2pz orbitals in forming the 256 and pzcg Although this 6u is primarily 25 lt gt 25 destructive interference there is a small 25 lt gt 2pZ constructive interference which stabilizes this of mo Although the 2p26g is primarily 2pZ lt gt 2pZ constructive interfereence destructive 25 lt gt 2pZ interference makes destabilizing energy contributions raising Ezpz g above FQpnu 25 orbitals cannot interact with 2pX or 2pg in 11 mos This interaction is especially pronounced for the larger less tightly bound 256 orbitals in the lighter diatomics The Type I scheme applies to He gt N where the type II scheme applies to 0 gt Ne Note that since the two are identical for the antibonding orbitals the Type I will give the ground state con guration for all cases ignoring shift arounds of closed shell orders 3 Understand the Aufbau principle for filling these mo 5 4 Understand how net bonding electrons and bond orders determine stability bond length etc eg see Fig 914 Application of mo theory to heteronuclear diatomics 1 When two ao 5 of ali ering energies eg B25 and F25 in BiF interact to form an mo the bonding combination will have a greater proportion of the more stable a o and the antibonding combination will contain a greater proportion of the less stable a0 2 Unequal ao contributions to the mo 5 results in dipole moments 3 For molecules having atoms with nearly the same electronegativity e g N70 CEO one can use the homonuclear energy ordering scheme with the above 2 recognition of unequal contributions of the two ao 5 or a oms 0 ea i erin e ec rone a ivi ies e ao 5 mos i e o in erac 4 F t fgr tlydff g 1 t gt t th tlklyt t t i e which interact the most are ones with the most similar energies e g H 113 136 eV from 15 F IP 1742 eV from 2p ls 46 moreHlS 1n 2p X Y quot39 E N 36 26 25 16 more 15 F2pZ H HiF F Notes on Molecular Orbital Theory Page 4 V Bonding in polyatomics 1 Most chemical approach hybrids for 6 bonds mo s delocalized for nbonds like chem lc organic Conjugated systems require delocalized orbitals 2 0 HB HF H D l CA 2PzA CBZPZB C02ch CDZPzD CE 2132B CF 2PzF One uses the variation theorem with hf which takes into account KE average repulsion of the nelectrons for one another and the attraction of CZH fragments a nd C7C framework also for g E g The variation equations are written in terms of oc s and 5 s and are solved using group theory and computers to get Cs and E s Example HQ bonds of methane IliA HD IC HB Hc CIA C1AX2s C2AX2px C3AX2py C4AX2pz CSAXIleA C7HB


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