Chapter 6. Quantum Mechanics & Molecular Structure. Chapter Outline
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1 Chater 6 Quantum Mechanic & Molecular Structure 6. Chater Outline 6. Quantum icture of the chemical bond Simlet molecule : H orn-oenheimer roximation Electronic wave function for H electronic denity in H De-localized ond: MOT and LCO linear combination of atomic orbital aroximation for H homonuclear diatomic molecule : econd eriod atom heteronuclear diatomic molecule Photoelectron ectrocoy for molecule localized bond: valence bond model wave function for electron air bond orbital hybridization for olyatomic molecule Comarion of LCO and Valence ond method
2 6. Quantum icture of the chemical bond 6.3 H molecular ion : imlet model for ingle electron molecule. exact quantum olution of H inight into chemical bonding key to more comlex molecule 6.. The Simlet molecule: H The oition of electron : r, r, φ rather than x,y,z Internal otential energy V e e πε r r 0 4πε R V V 4 0 en ttraction nn reulion between roton Schrodinger eq. ψ mol R,r, r, φ 6.. orn-oenheimer roximation , Max orn Ger and J. Oenheimer US orn-oenheimer roximation foundation for all of molecular quantum mechanic : nuclei are tationary and electron move raidly around them Frozen Nuclei, Fleeting Electron becaue nuclei are much heavier than electron Searate nuclei and electronic motion Solve Schrödinger equation for electron at fixed nuclei oition then olve Schrödinger equation for nuclei molecular orbital: one-electron molecular wave function
3 orn-oenheimer roximation 6.5 erie of calculation give the electronic wave function of electron ψ e l ; r, r, φ R Solving nuclear wave function ψ nuc R orn-oenheimer arx. End u with ψ mol R,r, r, φ ψ elr, r, φ; R ψ nuc R oundary condition: ψ e l 0 a r & r Focu firt on el wave function, then on energy change of the ytem a R 6..3 Electronic wave function for H 6.6 olution for ψ el are exact. --- firt 8 wave function
4 Electronic wave function for H 6.7 Wave function are identified with four level : integer, either or π, a ubcrit g or u, and aterik. Greek letter : how the electron robability denity ditribution around nucleu angular momentum comonent 0 π angular momentum comonent ±h/ two wave function : π u,π x u π wave function ha nodal lane y δ angular momentum comonent ±h/ a ngular momentum comonent ±3h/ Electronic wave function for H 6.8. g or u: roertie of wave f. change a we invert the oint of obervation through center of molecule g ymetric ; gerade even u antiymetric ; ungerade odd 3. aterik : antibonding orbital, higher energy g : bonding orbital, g* : antibonding orbital 4. Integer : energy level. g : the firt of g wave function.
5 6..5 Summary: Key Feature of Quantum Picture of Chemical onding 6.9. Nuclei are frozen in ecific oition and electron move fleetingly around them orn-oenheimer arox.. Molecular orbital i wave function giving amlitude of electronic motion and it quare give electron denity 3. onding orbital: decreaed otential energy and increaed electron denity between nuclei 4. ntibonding orbital: increaed otential energy and zero amlitude region i.e. node between nuclei 5. -orbital: no angular momentum and cylindrical ymmetry about internuclear axi 6. π-orbital: angular momentum ±h/π and no cylindrical ymmetry; concentrated amlitude off the axi Probability Denity Ditribution 6.0
6 6. De-localized ond: Molecular Orbital Theory & Linear Combination of tomic Orbital. MO: LCO Linear Combination of tomic Orbital eg e.g. H ion: cψ S, ψ S, electron denity i delocalized over the intire molecule to contruct arox. MO LCO: r. For H ψ MO C C C, C : relative weight, In cae of H, C C or C - C For clarification, atomic orbital i exreed with molecular orbital are with or. 6. Correlation table howing how ix of the exact H Mo correlated at large earation to um of difference of hydrogen atom orbital and at hort earation to the atomic orbital of He
7 6.3 LCO molecular orbital for H aroximate molecular orbital MO [ [ g g g R C R C * * [ u u u R C 6.4 LCO molecular orbital for H ditribution of electron robability denity [ [ g g C C * [ [ [ u u C [ di t ib ti f l t b bilit d it f i t ti t ditribution of electron robability denity of non-interacting ytem obtained by averaging the robabilitie for H H and H H [ 3. i n C ψ C 3 0.5
8 6.5 reduced robability to find electron with node betw nuclei --antibonding Increaed electron denity with node betw nuclei -- bonding Indeendent O -- noninteracting Energy of H in LCO aroximation 6.6 otential energy of for H Force between nuclei in antibonding - everywhere reulive in bonding tate, nuclei are attracted to form a bound tate at ditance R e corre. to lowet otential energy bond diociation energy :D e R e : attractive & reulive force balance equilibrium bond length Predicted: D e redicted.76 ev at tr redicted.3 d ctual: D e.79 ev at R meaured.060 Correlation diagram for H in LCO a. onding orbital i tabilized by the energy difference
9 6.. Homonuclear diatomic molecule: Firt-Period tom 6.7 MO equation for He & He by LCO C He He C g * u C g [ g [ u [ He He C [ u Weak bond for He but No bond for He due to energy diff. ond Order / x # electron in bonding MO - # electron in antibonding MO.O. : He / & He 0 Homonuclear diatomic molecule 6.8 Higher.O. higher bond energy horter bond length.
10 6..3 Homonuclear diatomic molecule: Second-Period tom 6.9 N : at leat 7 a. MO by combination of,, ψ MO C C [ C[ C3[ x x [ C [ 4 y y 5 imlified way to contruct MO for multi-electron atom. Two O contribute t ignificantly ifi to bond formation only if their atomic energy level are very cloe can ignor mixing between and valence hell,. Two O on different atom contribute ignificantly to bond formation only if they overla ignificantly. onding: ame hae - contructive interference ntibonding: ooite hae - detructive interference Nonbonding: no overla or bonding-antibonding cancellation z z Overla of orbital 6.0 Sigma bond reult from the end-on overla of orbital. overla between and orbital : overla between and orbital : only by end-on aroache of orbital to orbital Combination of O : ame a orbital C g * u C g u [ [
11 Overla of orbital 6. Combination of the orbital -- igma bond [ z z [ g C z g * u C z u z z π ond : ide to ide overla 6. electron denity of bonding orbital & nonbonding orbital x and y direction both. π C π π π u x u [ x x [ C x g x * g x [ y y [ u Cu y C y g y * g y π & π u u x y are degenerate
12 Order of Energy of MO 6.3 orbital barely overla little net effect on bonding Since bonding & antibonding orbital are all occuied. energy of π orbital contant, E or orbital fall raidly. : from N O orbital of oxygen fall below π orbital aramagnetic 6.4 N F
13 Paramagnetic v. diamagnetic 6.5 Paramagnetim of oxygen reult from the unaired electron in the molecular orbital. Lewi tructure how limitation but MO how evidence. Pro. of econd-eriod diatomic molecule 6.6
14 6..4 Heteronuclear Diatomic Molecule 6.7 Diatomic molecule : O, CO, NO MO for thee, no ymmetry dro g, u * C C ' C C ' : if i more electronegative than C >C for bonding. O * π 4 z MO of HF In the cae of NO, V electron * π 4 z π * nb π nb x, π nb y bond order : 8-3/ aramagnetic In the cae of HF, 8 V electron : E of & of F << E of H : overla of H: F: begligible : overla of H: F: x of F: y no only H: F: z remainder denoted with nb, π nb nonbonding no contribution in bonding bond order : -0/
15 Photoelectron Sectrocoy for Molecule PES confirm the MO decrition of bonding and meaure energy for individual MO. radiate hν.ev, nm to diatomic ga meaure KE of emitted hotoelectron by ubtracting KE from light E meauring IE IE-ε, by Kooman however, ome of E can be conumed to excite vibrational tate of molecular ion E vib vib h ν hoton mev ε i Ei IE i hν hoton m v e ε nhν i vib n 0,,..
16 PES of H ion 6.3 H aroache diociation limit n0 n0 5.5eV, IE with no vib excitation E increae toward 8 ev, the amount of vib excitation of H ion increae, & acing bet vib level become maller. H aroache diociation limit Vibrational eak & MO 6.3 Cae : removal of hotoelectron from bonding orbital,.o.of oitive ion will be maller than that of arent molecule. bond become le tiff vib ν become lower PES : ν 6.78x0 3 / for H ion v.84x0 3 / for H Cae : removal of hotoelectron from antibonding orbital.o.of oitive ion will be larger. bond become tiffer vib ν become higher PES Cae C : removal of hotoelectron from nonbonding orbital, no change in.o. & vib ν
17 PES of HCl 6.33 ~ 3 ev: from nonbonding orbital few eak ~ 6 ev: numerou eak from bonding orbital 6.34 PES of N and O N O
18 6.4 Localized ond: Valence ond Model 6.35 Valence ond Theory ond are formed by the overla of atomic orbital. Stronger covalent bond are the reult of more overla. Smaller orbital overla more than larger orbital. Orbital with imilar ize overla more than orbital with mimatched ize. Valence ond Theory exlain bond length and bond energie better than VSEPR or Lewi dot tructure. V theory doe not exlain bond angle in molecule a better model i needed 6.4. Wave function for electron-air bond 6.36 ingle bond -- bond conider Hydrogen molecule, l a the two atom aroach each other, bond formation el ψ, r ; R C R r r r - the atom interact, we can not ditinguih electron which belong to which atom. then, wave function become el ψ, r ; R C R r r r C R r r at large ditance then imly ψ el g C [ two atom aroach
19 6.37 Simle valence bond model for H valence bond model for F & HF 6.38 ψ For F, bond g C [z z z z For HF, ψ bond F H F C [ z z H
20 valence bond model for multile bond 6.39 multile bond In cae of N, - head-on overla in z axi z bond bond ψ C [ z z z z - ide by ide overla in x, y axi x, y π bond bond ψ π, ; R x x C R [ C R [ x x valence bond model for olyatomic molecule 6.40 Polyatomic molecule : check with VSEPR S.N.: linear from VSEPR e : no unaired electron to overla with of H VT failed S.N.3: triangular from VSEPR : only one unaired electron to overla with of H VT failed New concet wa needed : Hybridization of orbital
21 6.4. Orbital Hybridization for Polyatomic Molecule 6.4 Hybridization :mixo of central atom to form ame number of new hybrid O SP hybrid atomic orbital : eh molecule mix and z orbital of e to form new hybrid orbital wave function of hybrid orbital : χ χ r [ z χ r [ z Hybridization: 6.4
22 6.43 Hybriidization of eh hybrid O form on the central atom, e: χ χ bond H H ψ, C [ χ χ bond H H ψ 3,4 C [ χ 3 4 χ χ Hybridization of 6.44 SP hybrid atomic orbital :H 3 molecule mix and x, y orbital of to form new hybrid orbital / χ r y 3 / / χ r x y 3 / / χ3 r x y
23 6.45 Hybridization of 6.46 Hybridization of 3 SP 3 hybrid atomic orbital :CH molecule [ z y x r χ : CH 4 molecule mix and x, y, z orbital of C [ [ 3 z y x z y x r r χ χ [ 4 z y x r χ
24 Hybridization of Hybridization of Lone air electron occuy hybrid orbital. : NH 3, H O
25 Hybridization of d Hybridization of d
26 Samle Problem 6.5 What i the hybridization of the central atom in: CH 3 Cl, H S, CS, PCl 5? 3 5 CH 3 3 Cl carbon i hybridized H S ulfur i 3 hybridized CS C i hybridized PCl 5 P i 3 d hybridized 6.5 Comarion of LCO & V method 6.5 LCO : contruct MO delocalized over molecule by taking linear combination of O. V : quantum mechanical decrition of localized chemical bond Comarion for H LCO for H : [ g ψ el MO g g [ [ el V for H : ψ V by comaring both method for H el ψ [ [ MO el ψ - - V ψ ionic from H H & H H LCO include an ionic contribution to the bond. no evidence. but LCO good for olar HF. true chemical bond and molecular tructure: between LCO-V
27 Homework 6.53, 4, 8,, 8, 3, 4,48, 5, 5, 54, 56
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