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PHYSICAL ORGANIC

Yu-Tai Tao (陶雨台)

Tel: (02)27898580 E-mail: [email protected] Website:http://www.sinica.edu.tw/~ytt

Textbook: “Perspective on Structure and Mechanism in ” by F. A. Corroll, 1998, Brooks/Cole Publishing Company

References: 1. “Modern Physical Organic Chemistry” by E. V. Anslyn and D. A. Dougherty, 2005, University Science Books.

Grading: One midterm (45%) one final exam (45%) and 4 quizzes (10%) homeworks Chap.1 Review of Concepts in Organic Chemistry § Quantum number and atomic orbitals wavefunctions are associated with four quantum numbers: principle q. n. (n=1,2,3), azimuthal q.n. (m= 0,1,2,3 or s,p,d,f,..magnetic q. n. (for p, -1, 0, 1; for d, -2, -1, 0, 1, 2. spin q. n. =1/2, -1/2. § Molecular dimensions Atomic radius

, ri:size of electron cloud around an . covalent radius, rc:half of the distance between two of same element bond to each other.

van der Waal radius, rvdw:the effective size of atomic cloud around a covalently bonded atoms.

- Cl Cl2 CH3Cl measures the distance between nucleus (or the local centers of ). Bond angle measures the angle between lines connecting different nucleus.

Molecular volume and surface area can be the sum of atomic volume (or group volume) and surface area. Principle of additivity (group increment)

Physical basis of additivity law: the forces between atoms in the same or different are very “short range”. Theoretical determination of molecular size:depending on the boundary condition.

Boundary is a certain minimum value of electron density.

Molecular volume (1 au = 6.748e/Å3 ),

0.001au 0.02au expt’l

CH4 25.53 19.58 17.12

C2H6 39.54 31.10 27.34

C3H8 53.64 42.76 37.57

C4H10 67.64 44.13 47.80 § Heats of formation and reaction Heat of formation:Difference in between the compound and starting elements in their standard states obtained indirectly from other components of known

ΔHf° correct for necessary phase change (such as vaporization, sublimation) correct for ΔH at different T by heat capacity experimental measurement by calorimeter m C + n/2 H C H ΔH ° (gr) 2 (g) m n O f To calculate the heat of formation of (g) O O 6 C + 4 H + O ΔH ° (gr) 2(g) 2(g) (g) f O O + 7 O 6 CO + 4 H O (s) 2(g) 2(g) 2 (g) O ΔHcomb= -735.9 Kcal/mol

6 C(gr) + 6 O2(g) 6 CO2(g)

ΔHcomb= -94.05 (Kcal/mol C) × 6

4 H2(g) + O2(g) 4 H2O(g)

ΔHcomb= -68.32 (Kcal/mol H2) O O ΔH = 21.46 Kcal/mol (s) (g) subl O O

ΔHf°= 6 × (-94.05) + 4 × (-68.32) +735.9 +21.46 = -80.22 (Kcal/mol) Relative difference in heat of formation O OCCF3 + CF3COOH ∆H= -10.93 Kcal/mol O

OCCF3 + CF3COOH ∆H= -9.11 Kcal/mol

∆H= -1.82 Kcal/mol

H2 CH3CH=CHCH3 CH3CH2CH2CH3 ΔH=-28.6Kcal/mol cis H2 CH3CH=CHCH3 CH3CH2CH2CH3 ΔH=-27.6Kcal/mol trans The heat of is much smaller than the heat of . Both will give the difference of the stability of the two . § Bond increment calculation of heat of formation Principle of additivity:The property of a large molecule can be approximated by adding the contribution of its component. H H H H H For H H HH H (-3.83) × 10 + 3× (2.73) = -30.11 Kcal/mol § Group increment calculation of heat of formation

3 × (-10.08) + 2 × (-4.95) + 1 × (-1.90) = -42.04 Kcal/mol (obs. -41.66)

CH3 CH3 4 × (-10.08) + 2 × (-1.90) = -44.12 Kcal/mol (obs. -42.49) CH3 CH3

Further refinements correct for van der Waal strain, angle strain….

The electrostatic model for the stability of branched +1 +1 +1 +1 +1 H -10 +1 +1 H H Charge on H:0.278× 10 esu H H HH -3 -2 -2 -1 -2 -2 -2 -2 Charge on C:neutralizing charge HH H HH HH+1 HH Branched more stable +1 +1 +1 +1 +1 +1+1 +1 JACS 1975, 97, 704. Homolytic & Heterolytic

ΔH°hom:standard homolytic A-B(g) A. (g) +B. (g) bond dissociation electron transfer + - A (g)+B (g)

ΔH°het:standard heterolytic bond dissociation energy

In phase:ΔH°het >ΔH°hom

In of can lower ΔH°het, so that heterolysis becomes favorable.

Use bond dissociation energy to calculate reaction ΔH°r e.g. CH3-HCH3.+H.ΔH°r= +104 Kcal/mol

Cl-Cl Cl.+Cl.ΔH°r= +58 Kcal/mol

Cl.+CH3. CH3Cl ΔH°r= -84 Kcal/mol

+) Cl.+H. H-Cl ΔH°r= -103 Kcal/mol

CH3-H + Cl-Cl CH3Cl + HCl ΔH°r= -25 Kcal Hess Law:The difference in enthalpy between products and reactants is independent of the path of the reaction. by heat of formation

ΔH°r=ΣΔH°f(prd) -ΣΔH°f(pre) = -23.7 Kcal/mol at 300℃ § Bond length and bond energy Bond length is nearly a constant property between molecules. § The ability of electron cloud to distort in response to external field, defined as the magnitude of dipole induced by one unit of field gradient.

¾Polarizability decreases across a row of the ,

. (C>N>O>F, CH4>NH3>H2O) ¾ Polarizability increases along a column,(S>O, P>M, H2S>H2O) C-I bond is more polarizable than C-Cl ¾ are more polarizable than , may due to . sp2 are more electronegative than sp3 carbons. § Bonding Model Bond Theory (VB) G.N. Lewis 1916 Chemical bonds result from the sharing of electron pairs between two approaching atoms. The bond is localized. means two + bonding in HH H-H the region H:H between two The region is orbital.

Cl+ Cl Cl Cl each achieve a filled shell HCl+ H Cl

σ bond from S and P σ bond by P and P σ:cylindrical symmetry

For complex molecules, hybridization and are used to describe molecules in terms of orbitals which are mainly localized between two atoms. Hybridization Theory: For 1s22s22p2 3 the 2s, 2px, 2py, 2pz hybridize to form four sp 4 bonds can be formed on carbon highly directional sp3 orbital provide for more efficient overlap. + 4 CH4 3 sp sp3 H H H 109.5° C C H H H H H ethene π bond, plane sym. H H HHs + 2p → 3sp2 120° or H H HHone p remaining

s + p → 2sp HHor HH two p remaining H-C-C linear

No. of Hybri Geometry d 3 4 sp Tetrahedr CH4, CCl4, CH3OH, al 2 3 sp Trigonal CH2=CH2, H2C=O, C6H6, = CO3 , CH3.

2 sp linear HC≡CH, CO2, HCN, H2C=C=CH2 Resonance Theory: An extension of for molecules that more than one can be written. Useful in describing electron delocalization, in conjugate system and reactive intermediates. (a)If more than one Lewis structure can be written, which has nuclear positions constant, but differ in assignment of electrons, the molecule is described by a combination of these structure (a hybrid of all). (b)The most favorable (lowest energy) resonance structure makes the greatest contribution to the true structure. determining energy:maximum number of , minimum separation of unlike charge, placement of negative charge on most electronegative atom (vice versa). (c)Those with delocalized electrons are usually more stable than single localized structure.

H 2 C H 2 C H 2 C H 2 C CCH2 CCH2 CO CO H 3 C H 3 C H 3 C H 3 C more stable two equivalent structure H H H H charge located equally on two C’s C C C C H C H H C H H H the allyl cation is planar for maximum p interaction H H H H restricted rotation around H H H H C O H C O H C O C C C C C C H H H H H H majorsignificant minor § Dipole moment:the vector quantity that measures the separation of charges. 0.1 e 0.1e +q -q 1 electron charge = 4.8x10-10 esu d = 1.5x10-8cm bond dipole = q × d = 0.1× (4.8× 10-10esu) × 1.5× 10-8 cm = 0.72× 10-18esu.cm = 0.72 D (1 Debye = 10-18esu.Cm) Molecular dipole is the vector sum of various “bond dipoles”. It provides information about molecular structure and bonding.

e.g. CH3F μ= 1.81 D H 1.81× 10-18 H C F q = = 0.27 e- -10 H 1.385× 4.8× 10 1.385Å For dichlorobenzene

Cl μ= 2.30, 1.55, 0 Cl Cl Cl μ= 1.61 D Cl

Cl Cl From trigonometry, the calculated angles between two bond “dipole moment” are 89° , 122° , 180°. support the concept that is planar. The dipole moment results from unequal sharing of the electron. due to different attraction for electron electronegativity Polar bond = [covalent bond] +λ [ionic bond] λ= weighing factor 2 % ionic character = λ × 100 % (1 +λ2) HCl +0.17 electron charge on H. - 0.17 electron charge on Cl. λ = 0.45 § Electronegativity & Bond Polarity Electronegativity:The power of an atom in a molecule to attract electrons to itself. Pauline 1932

χp:based on the difference in bond energy of AB and A-A + B-B other scale of electronegativity, 2 more related to atomic properties. Mulliken χ = I + A I: potential of atom 1934 M 2 A:e- affinity of atom Allen χspec:based on the average I.P.of all of the valence P 1989 and S electrons. Nagle 1990 χα:based on atomic polarizability Benson VX:no. of /covalent radii 1988 Third Dimension of Periodic Table J. Am. Chem. Soc. 1989, 111, 9004. In complex molecules with many polar bonds involved, electrostatic potential surfaces (from quantum mechanic calculation) are used to view the charge distribution in the whole molecule.

red ----negative potential blue --- positive potential ---neutral

-0.24 -0.17 δ δ δ F δ δ 0.09 0.36 Method Electrons are distributed among a set of molecular orbitals of discrete energies. The orbitals extend over the entire molecule. First Approximation: the MO is a linear combination of contributing atomic orb.

Ψ = c1ψ1 + c2 ψ2 + ‥‥‥ + cn ψn

ψ’S are basis set

c’S coefficient, reflect contribution The no. of MO’s (bonding + non-bonding +antibonding) = total no. of a.o.’s

- - For H2, 2e For HHe+, 2e σ*

1s 1s 1s He 1s

σ

σ’* For CO, 10e- π x*, π y* 2Px,2Py,2Pz σ’ 2Px,2Py,2Pz

π x, π y σ’* 2s 2s σ C O MO for methane First approach 1 ψsp3 = (C2s + C2p + C2p + C2p ) 1 2 x y z 1 ψsp3 = (C2s + C2p - C2p - C2p ) 2 2 x y z 1 ψsp3 = (C2s - C2p + C2p - C2p ) 3 2 x y z 1 ψ 3 = (C - C - C + C ) sp 4 2 2s 2px 2py 2pz each sp3 overlap with a 1s of each of these has a shape H to form CH4 of , pointing to the bond angle 109.5° corner of a

This implies identical bonds for the bonding electrons.

But ESCA data of methane shows

1s

290eV 23.0eV 12.7eV

The M.O. formed above is symmetry incorrect. The symmetry of the M.O. must conform to the symmetry of the molecule in such a way that the M.O.’s are either symmetric or antisymmetric to all the symmetry elements of the molecule. Solution:form the delocalized methane M.O. directly form

unhybridized orbitals:1C2s, 3C2p’s, 4H1s

ψ1 = 0.545 C2s + 0.272 (H1 + H2 + H3 + H4) ψ = 0.545 C + 0.272 (H + H - H - H ) 2 2px 1 2 3 4 ψ = 0.545 C + 0.272 (H - H + H - H ) 3 2py 1 2 3 4 ψ = 0.545 C + 0.272 (H - H - H + H ) 4 2pz 1 2 3 4

ψ2 ψ3 ψ4

ψ1

The energy of on M.O. increase with the no. of nodes in the M.O.

+ - - + + + + + + + + + + + - - + - + -

ψ1 Group orbitals from qualitative (QMOT) planar methyl

pyramidal methyl Walsh diagram Building larger molecule from group orbitals Valence Shell Electron Pair Repulsion Theory (VSEPR)

In predicting the shape of molecules, bonds are treated as repulsive points and the repulsive points made as far apart as possible. - counting the number of electron groups:unshared pair is a group, each bond is a group, whether single or multiple. - 2 groups linear 3 groups trigonal 4 groups tetrahedral - non-bonding electron pair more repulsive - bonding pair to electronegative groups less repulsive

H H H H N O H C H H C C H H 109.5° H H H H H H ∠H-C-H =109.5° ∠H-C-H = 109.3° ∠H-N-H = 107° ∠H-O-H = 104.5° Bonding electron polarized toward Cl Cl 1.76Å 1.781Å Cl,

H C 1.09Å H C 1.096Å H H H H predicted ∠H-C-H = 109.5° ∠H-C-H = 110°52' ∠H-C-Cl = 109.5° ∠H-C-Cl = 108°0' Effect of on bond angle Repulsion:lone pair occupies larger domain lone pair:lone pair>lone pair:bond pair>bond pair:bond pair

120.2° > 109.5° P F F F 96.9° < 109.5° Effect of lone pair on bond length The closer and larger domain of lone pair prevents a bonding pair getting closer. The adjacent bond longer

F 1.68Å 1.79Å F F Br F F Effect of electronegativity on bond angle

PX3 ∠XPX(° ) OSX2 ∠XSX(° )

PF3 97.8 OSF2 92.3

PCl3 100.3 OSCl2 96.2

PBr3 101.0 OSBr2 98.2 Increasing electronegativity, the bonding pair shifts further away from the central atom. angle decreases Multiple bond domain ≣>=>- O O >>O O O O 122° S S S O O S 109° H H H Multi-center bond 97° H3CO OCH3 122° B B occupies less domain 98° H H H than a single bond Multi-center bond 122° Trigonal bipyramidal molecules 5 points are non-equivalent (1) the axial bond is longer than

eq. bond rax/req = 1~1.4

√3 r (2) larger domain electron pair 90° (lone pair, multiple bond) 120° occupies equatorial position √2 r (3) more electronegative atom occupies axial position

eg. PF3Cl2, PF2Cl3 PCl5

Cl F 1.2 1.01 0.96 F Cl F F Cl P S O S Cl F F Cl F F 1.05 0.91 F F 0.9 O Kr O Xe O F F

F F F F F F Cl Cl Cl P Cl P Cl P Cl P F Cl Cl Cl F F F Cl Limitations: - not applicable to ionic comp’d - for localized bonding/non-bonding pair, not for delocalized - for sufficiently large , steric interaction prevails § Variable Hybridization and For carbon bonded to different atom, different hybridizations are proposed. 3 For CH4, CCl4:sp hybridization % S = 25 % P = 75 hybridization index For spn, define λ 2 = n , λ:hybridization parameter 2 % S = 1 , % P = λ (1 +λ2) (1 +λ2) 2 sum of P-fraction Σ λi = n, 2 i (1 +λi ) sum of S-fraction Σ 1 = 1 2 i (1 +λi )

Interorbital angle θab ,1+ λa λb cosθab = 0 if a = b, C 2 -1 1+ λa cosθaa = 0, cosθaa = 2 a b λa θab

sp3 →θ = 109.5 ° For CA B aa the S character↑ , λ↓ 3 2 sp →θaa = 120 ° 3.5 sp sp →θaa = 180 ° more P Cl b 2 108° 3sin θ = 2 (1- cosθ ) 2.86 ab aa sp C H H from θab = 108° , θaa = 110.5 ° a a from θ = 110.5° , λ 2 = 2.86 more S-character H 110.5° aa a a ∴sp2.86 for C-H 1 1 2 from 3 ( ) +2 = 1, λb = 3.5 1 + 2.86 1 +λb For CH Cl 2 2 -1 λ 2 = = 2.69 1.082Å 1.772Å Cl cos111°47 H Cl ′ ∴sp2.69 for C-Cl

112° C 111.47° 1 1 from 2 ( ) + 2 ( 2 ) = 1 1 + 2.69 1 +λH H Cl 2 3.37 λH = 3.37, sp for C-H

-1 from cosθHH =,2 θHH = 107°≠112 ° (expt’l) λH 2 λHH = 2.67, λ 2 H Cl Cl = 3.39, θ = 107° C ClCl H Cl

the inter-orbital bond angle smaller than the inter nuclear bond angle Cl F F 108.9° 106.7° 108.0° C C C H H H H 109.54° H 110.52° H H H (by inter nuclear) H

Experimental support of variable hybridization:

NMR coupling constants J13C-1H:: 161, 134, 128, 124, 123, 122 H Cyclopropane

H H H 115 ° 1 H H bent bond from sp3 hybridization (or variable hybridization) Sp3.94 θcc=105°

H

sp2.36 H

Walsh orbital: from sp2 hybridization Prediction of Physical Properties with diff. Bonding model 1. Geometry C-C ethene ethyne bond length 1.54Å 1.34Å 1.20Å by σ,πformulation: sp3 hybrid. % S = 25 in ethene sp2 hybrid. % S = 33.3 S↑bond legth dec. addition π bond, shorter bond in ethyne sp hybrid. % S = 50, no quantitative prediction by bent bond formulation: H 1.54Å H 3 only sp C C C-C distance 1.32Å hybridization HH1.54Å

H C C H C-C distance 1.18Å 1.54Å 2. Acidity

ethane 10-42 sp3 S character increase greater e--pulling -36.5 2 ethene 10 sp power for the orbital ethyne 10-25 sp better stabilization of the anion bent bond formulation H H H H H H C C C C H C C H H further decrease in decreased repulsion repulsion conformation of H CH H 2 H H3CC H CH2 II H CH2 H II H H I H more stable by 2Kcal/ σ,π-formation predicts Ⅱ to be more stable, because more repulsion between and the C-H bond in I Bent bond formulation: H H

H CH2 H CH H 2

H H more stable The bent bond (Ω bond ) is agreed in cyclopropane proposed or shown to more suitable than σ,π description

in CF2=CF2, CO2, CO, benzene

Conclusion