PHYSICAL ORGANIC CHEMISTRY
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 Organic Chemistry” 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 Atomic orbital 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. electron spin q. n. =1/2, -1/2. § Molecular dimensions Atomic radius
ionic radius, ri:size of electron cloud around an ion. covalent radius, rc:half of the distance between two atoms 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 Bond length measures the distance between nucleus (or the local centers of electron density). 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 molecule or different molecules 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 enthalpy 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 hydrogenation is much smaller than the heat of combustion. Both will give the difference of the stability of the two isomers. § 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 butane 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 alkane +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 Dissociation Energies
homolysis ΔH°hom:standard homolytic A-B(g) A. (g) +B. (g) bond dissociation energy heterolysis electron transfer + - A (g)+B (g)
ΔH°het:standard heterolytic bond dissociation energy
In gas phase:ΔH°het >ΔH°hom
In solution: solvation of ions 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. § Polarizability 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 periodic table,
. (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 ¾alkanes are more polarizable than alkenes, may due to Electronegativity. sp2 carbons are more electronegative than sp3 carbons. § Bonding Model Valence 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 electrons in HH H-H the region H:H between two atom 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 resonance are used to describe molecules in terms of orbitals which are mainly localized between two atoms. Hybridization Theory: For carbon 1s22s22p2 3 the 2s, 2px, 2py, 2pz hybridize to form four equivalent sp 4 bonds can be formed on carbon highly directional sp3 orbital provide for more efficient overlap. + 4 methane 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 acetylene
s + p → 2sp HHor HH two p remaining H-C-C linear
No. of Hybri Geometry ligand 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 valence bond theory for molecules that more than one Lewis structure 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 covalent bond, 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 single bond 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 benzene 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:ionization 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 valence electron /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 green---neutral
-0.24 -0.17 δ δ δ F δ δ 0.09 0.36 Molecular Orbital 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 tetrahedron
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 molecular orbital theory(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 lone pair 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 ligands, steric interaction prevails § Variable Hybridization and Molecular Geometry 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 bent bond
Experimental support of variable hybridization:
NMR coupling constants J13C-1H:: cyclopropane 161, cyclobutane 134, cyclopentane 128, cyclohexane 124, cycloheptane 123, cyclooctane 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. Alkene Geometry C-C ethane 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 propene H CH H 2 H H3CC H CH2 II H CH2 H II H H I H more stable by 2Kcal/mole σ,π-formation predicts Ⅱ to be more stable, because more repulsion between double bond 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