* 1s. --- if the sign does change it is called ungerade or u
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1 Chapter Qualitative Theory of Chemical Bondin Backround: We have briefly mentioned bondin but it now time to talk about it for real. In this chapter we will delocalied orbitals and introduce Hückel MOT. * More MO Theory time to talk formally about and - The MO -- is completely symmetric about internuclear axis -- there are two possible combos: --- bondin, : sa + sb s --- antibondin, * : sa + sb * s -- symmetry arument: --- when the sin of the MO does not chane with respect to its center of inversion it is even and we would call it erade (German word for even) or s s s s S A B --- if the sin does chane it is called unerade or u s s s s S A B u -- only AOs with similar eneries are combined in this way otherwise there will be very little overlap btwn them --- the combs btwn s orbitals are very similar to s: sa sb s sa sb us --- the primary bondin axis is the -axis which is where the p bonds p p p p p p A B A B u
2 - The MO -- for px and py they are perpendicular to each other and p so there is no net overlap between them --- they only have overlap with each other --- pxa pxb upx pxa pxb px ---- this delineation is based on a center of inversion arument ---- when we invert across the center for u we have a sin chane btwn the lobes --- we et the same result for py combos - Enery Orderin of MOs
3 * Bond Order and molecular electronic confiurations - Bond Order no. of bondin e ' s no. of antibondin e ' s Species No. of e - s Ground State Electron Confi Bond Order Bond Lenth (pm) Bindin E (kj/mol) H H He 3 s us He 4 s us s << - Pauli Exclusion Principle -- placement of e- s in MOs follows the PEP and the orderin follows Hund s rules -- e.. O s us s us p upx upy px py or KKs us p upx upy px py where KK is the filled n = shell B.O. = so oxyen is predicted to have a double bond * Heteronuclear Diatomics and Molecular Orbital Theory - we can extend MOT to heteronuclear diatomic molecules - the difference is that the J, S, and K interals are dependent on how close in enery the atomic orbitals on adjacent atoms are - the more EN an atom is the lower the AOs -- e.. CO is close enouh so that the orbital overlaps occur btwn the same AOs on each atom -- e.. for HF the s AO on hydroen overlaps with the p orbital on F to ive rise to the sinle bond btwn the two species * Molecular Term Symbols for Linear Molecules - we start by evaluatin the total anular momentum of e- s in the MOs: e.. ml = 0 for and ml = for - we use capitalied Greek symbols to specify term symbols for our linear molecules
4 - the term symbol is represented by: S M L Symbol 0 3 M L -- where MS is aain the sum of spin and S is the total spin - Examples: -- H round state: --- our only ML is 0 so is our symbol --- in the round state our e- s are paired so Ms 0 S --- so our round state is a sinlet sima: -- B round state: u u u u --- everythin is paired up until we et to the orbitals so these are the only e-s we need to consider --- ml = ML = = -, 0, or + for --- ms = ½ ML = +, 0, or -, L0 S, L0 S, L S 0, L S 0, L0 S 0, L0 S we follow the same rules we used to determine the atomic term symbols ---- the larest L = so and S + = S(0) + = ---- next L = 0 with S + = lastly, L = 0 with S + = --- the larest spin state is the round state or 3 * Symmetry and term symbols - when both MOs are erade then for the overall symmetry - when both MOs are unerade then uu for the overall symmetry - when the MOs are opposite symmetry then u ufor the overall symmetry - e.. the term symbol for B is then 3 - Plane of Inversion and term symbols -- for obitals the reflection thru a plane is always + -- with orbitals the reflection thru a plane will be either + or dependin upon the plane we use to define our system
5 -- for our x the sin will be and for y the sin will be + -- e.. the complete term symbol for B is then 3 since we have an e- in each of these MOs -- Table.3 summaries the complete term symbols for all the possible diatomics up to F -- We can also apply these same steps to determine excited states for our diatomics * Pi Bondin - ethene, CH4 -- let s say the p orbitals are responsible for the pi MOs is formed c c pa pb -- we can solve this system usin variational methods
6 H ES H ES H Hˆ d ij pi p j 0 H ES H ES Sij p i p jd where H = H since the C-atoms on ethene are equivalent --- the diaonal elements of the Hamiltonian operator are the Coulomb interals --- the off-diaonal ones are the Exchane interals/resonance interals - Hückel Molecular Orbital Theory -- this is an approximation method that simplifies the secular determinant for pi systems -- the method: --- the overlap interals, Sij, are set to the Kroenecker delta: ij 0 i j Sij ij i j --- the Coulomb interals are the same for all C-atoms and are denoted by --- the resonance/exchane interals represent nearest neihbor interactions and are assumed to be the same and are denoted by --- all remainin resonance interals are set to ero -- applied to ethene our secular determinant becomes: E 0 E 0 E E E --- where E and E are the bondin and antibondin MOs, respectively --- the experimental value of is -75 kj/mol --- now we can use HMOT to obtain our wavefunctions ---- we start by rewrittin the secular determinant as two equations with the two unknown coefficients c Ec 0 c c E next we plu in our enery, E c c 0c c 0c c0c c nb cp A p B p A pb ---- for E c c 0c c 0c c nb cp A p B p A pb
7 -- butadiene time for a delocalied pi-system, c 4 i ij p i j --- our secular determinant H ES H ES H ES H ES H ES H ES H ES H ES H ES H ES H ES H ES H ES H ES H ES H ES applyin our HMOT approximation our determinant becomes: E 0 0 x 0 0 E 0 E 4 x 0 0 if we let x then 0 0 E 0 x 0 0 E 0 0 x this leads to a secular equation of: x.68, x 3x 0 x therefore, --- the total pi-electronic enery is: E now, if we compare this enery to double the enery we obtained for ethene we will see there is a stabiliation enery which results from our delocaliation E kj 35 kj deloc E but E eth Edeloc mol mol -- we can solve for our coefficients and derive wavefunctions for our MOs: 0.377p E 0.605p E 0.605p E p p3 p E 4 * Sections.7-.8 Skip!
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