physical organic chemistry - academia sinica
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PHYSICAL ORGANIC CHEMISTRY
Yu-Tai Tao (陶雨台)
Tel: (02)27898580E-mail: [email protected]: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
Review of Concepts in Organic Chemistry
§ Molecular dimensionsAtomic radiusionic 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
§ Quantum number and atomic orbitalsAtomic 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.
Chap.1
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 ),
47.8044.1367.64C4H10
37.5742.7653.64C3H8
27.3431.1039.54C2H6
17.1219.5825.53CH4
expt’l0.02au0.001au
6 C(gr) + 4 H2(g) + O2(g) ΔHf°
+ 7 O2(g) 6 CO2(g) + 4 H2O(g)
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)
ΔHsubl= 21.46 Kcal/mol
ΔHf°= 6 × (-94.05) + 4 × (-68.32) +735.9 +21.46
= -80.22 (Kcal/mol)
§ Heats of formation and reactionHeat of formation:Difference in enthalpy between the compound and starting elements in their standard statesobtained indirectly from other components of known ΔHf°
correct for necessary phase change (such as vaporization, sublimation)correct for ΔH at different T by heat capacityexperimental measurement by calorimeter
m C(gr) + n/2 H2 (g) CmHn ΔHf°
To calculate the heat of formation of
O
O(g)
O
O(g)O
O(s)
O
O(s)
O
O(g)
Relative difference in heat of formation
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 formationPrinciple of additivity:The property of a large molecule
can be approximated by adding the contribution of its component.
+ CF3COOH ∆H= -10.93 Kcal/mol
+ CF3COOH ∆H= -9.11 Kcal/mol
OCCF3
O
OCCF3
O
∆H= -1.82 Kcal/mol
CH3CH=CHCH3 CH3CH2CH2CH3 ΔH=-28.6Kcal/molcis
CH3CH=CHCH3 CH3CH2CH2CH3 ΔH=-27.6Kcal/moltrans
H2
H2
§ Group increment calculation of heat of formation
3 × (-10.08) + 2 × (-4.95) + 1 × (-1.90) = -42.04 Kcal/mol (obs. -41.66)
4 × (-10.08) + 2 × (-1.90) = -44.12 Kcal/mol (obs. -42.49)
Further refinements correct for van der Waal strain, angle strain….
CH3
CH3
CH3
CH3
The electrostatic model for the stability of branched alkaneCharge on H:0.278× 10-10 esuCharge on C:neutralizing charge Branched more stableH H
H H
H H
H H
-2 -2-2 -2
+1
+1
+1+1+1
+1+1 +1 H H H H
-2 -2
+1 +1+1 +1
H HH
H+1
+1+1
+1
-3-1
JACS 1975, 97, 704.
e.g. CH3-H CH3. + 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
Homolytic & Heterolytic Dissociation Energies
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
Hess Law:The difference in enthalpy between products and reactants is independent of the path of the reaction.
by heat of formationΔH°r=ΣΔH°f(prd) -ΣΔH°f(pre)
= -23.7 Kcal/mol at 300℃
A-B(g) A. (g) +B. (g)
A+(g)+B-
(g)
homolysis
heterolysis electron transfer
ΔH°hom:standard homolyticbond dissociation energy
ΔH°het:standard heterolytic bond dissociation energy
§ PolarizabilityThe ability of electron cloud to distort in response to
external field, defined as the magnitude of dipole induced by one unit of field gradient.
Polarizability decreases across a row of the periodic table,. (C>N>O>F, CH4>NH3>H2O)
Polarizability increases along a column,(S>O, P>M, H2S>H2O)C-I bond is more polarizable than C-Cl
alkanes are more polarizable than alkenes, may due to Electronegativity. sp2 carbons are more electronegative thansp3 carbons.
+
§ Bonding ModelValence Bond Theory (VB) G.N. Lewis 1916Chemical bonds result from the sharing of electron pairs between two approaching atoms.
For complex molecules, hybridization and resonance are used to describe molecules in terms of orbitals which are mainly localized between two atoms.
means two bonding electrons in the region between two atom
The bond is localized.
H H H-HH:H
Cl Cl+ Cl Cl each achieve a filled shell
The region is orbital.
H Cl+ H Cl
σ bond from S and P σ bond by P and P
σ :cylindrical symmetry
For carbon 1s22s22p2
the 2s, 2px, 2py, 2pz hybridize to form four equivalent sp3
4 bonds can be formed on carbonhighly directional sp3 orbital provide for more efficient overlap.
acetylene
ethene
methane CH4
HC≡CH, CO2, HCN, H2C=C=CH2
linearsp2
CH2=CH2, H2C=O, C6H6, CO3
=, CH3.Trigonalsp23
CH4, CCl4, CH3OH,Tetrahedral
sp34
GeometryHybrid
No. of ligand
C
+ 43s p sp3
H
HH
H
109.5° C
H
H H
H
H H o r H H
HHHH
1 2 0 °H H
H Ho r
π bond, plane sym.s + 2p → 3sp2
one p remaining
s + p → 2sptwo p remaining
H-C-C linear
Hybridization Theory:
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 3 CC CH 2
H 2 C
H 3 CC CH 2
H 2 C
H 3 CC O
H 2 C
H 3 CC O
H 2 C
H CCH
CH
H
H
H CCH
CH
H
H
HH
HH
HC
HC
CH
O
H
HC
HC
CH
O
H
HC
HC
CH
O
H
more stable
major minorsignificant
two equivalent structurecharge located equally on two C’sthe allyl cation is planar for maximum p interaction
restricted rotation around single bond
§ Dipole moment:the vector quantity that measures the separation of charges.
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.
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
% ionic character = × 100 %
HCl +0.17 electron charge on H.
- 0.17 electron charge on Cl. λ = 0.45
λ2
(1 +λ2)
e.g. CH3F μ= 1.81 DH
CHH
F
1.385Å
Cl
μ= 1.61 D
For dichlorobenzene μ= 2.30, 1.55, 0
Cl Cl ClCl
ClCl
q = = 0.27 e-1.81× 10-18
1.385× 4.8× 10-10
+q -q 1 electron charge = 4.8x10-10 esu0.1 e 0.1e
d = 1.5x10-8cm
§ Electronegativity & Bond PolarityElectronegativity: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 other scale of electronegativity,
more related to atomic properties.
χM = I:ionization potential of atom
A:e- affinity of atom
χspec:based on the average I.P.of all of the valence P and S electrons.
χα:based on atomic polarizability
VX:no. of valence electron /covalent radii
A-A + B-B2
I + A2
Mulliken1934
Allen 1989Nagle 1990
Benson 1988
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 potentialblue --- positive potentialgreen---neutral
Fδ
δ
δ
δ
δ
0.36
-0.17
0.09
-0.24
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
1s
σ*
σ
1s
For H2, 2e- For HHe+, 2e-
He 1s
1s
For CO, 10e-
2Px,2Py,2Pz
σ’*
2Px,2Py,2Pz
σ’
π x*, π
y*
π x, π y
σ’*
σC O
2s2s
MO for methane
First approach
ψsp31= (C2s + C2px
+ C2py+ C2pz
)
ψsp32= (C2s + C2px
- C2py- C2pz
)
ψsp33= (C2s - C2px
+ C2py- C2pz
)
ψsp34= (C2s - C2px
- C2py+ C2pz
)
1212
12
12
each sp3 overlap with a 1s of H to form CH4
bond angle 109.5°
This implies identical bonds for the bonding electrons.
But ESCA data of methane shows
The M.O. formed above is symmetry incorrect.
each of these has a shape of , pointing to the corner of a tetrahedron
1s
290eV 23.0eV 12.7eV
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 2 = 0.545 C2px+ 0.272 (H1 + H2 - H3 - H4)
ψ3 = 0.545 C2py+ 0.272 (H1 - H2 + H3 - H4)
ψ4 = 0.545 C2pz+ 0.272 (H1 - H2 - H3 + H4)
The energy of on M.O. increase with the no. of nodes in the M.O.
ψ1
ψ2 ψ3 ψ4
+-
+
+
++
+
+
+
+
++
ψ1
+
--
-
--
++
Group orbitals from qualitative molecular orbital theory(QMOT)planar methyl
pyramidal methyl Walsh diagram
Valence Shell Electron Pair Repulsion Theory (VSEPR)
In predicting the shape of molecules, bonds are treated asrepulsive 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
CH
HH
H109.5°
CH
HH
C
H
HH
∠H-C-H =109.5° ∠H-C-H = 109.3°
NH
HH
∠H-N-H = 107°
OH H
∠H-O-H = 104.5°
Cl
CH
H H
Cl
CH
H H
∠H-C-H = 110°52'∠H-C-Cl = 108°0'
predicted ∠H-C-H = 109.5° ∠H-C-Cl = 109.5°
Bonding electron polarized toward Cl, 1.76Å
1.09Å
1.781Å
1.096Å
Effect of lone pair on bond angleRepulsion:lone pair occupies larger domainlone pair:lone pair>lone pair:bond pair>bond pair:bond pair
Effect of lone pair on bond lengthThe closer and larger domain of lone pair prevents a
bonding pair getting closer. The adjacent bond longer
Effect of electronegativity on bond angle
98.2OSBr2101.0PBr3
96.2OSCl2100.3PCl3
92.3OSF297.8PF3
∠XSX(° )OSX2∠XPX(° )PX3
Increasing electronegativity, the bonding pair shifts further away from the central atom. angle decreases
PF
FF
120.2° > 109.5°
96.9° < 109.5°
BrF
F
F
FF
1.79Å
1.68Å
SO O
H3CO OCH3
Multiple bond domain ≣ > = > -
SO O
SO O
SO O> >
H
B
H
H
HB
H
H
122°
109°
98°122°
122°
97°
Multi-center bond occupies less domain than a single bondMulti-center bond
Trigonal bipyramidal molecules
5 points are non-equivalent
(1) the axial bond is longer than eq. bond rax/req = 1~1.4
(2) larger domain electron pair (lone pair, multiple bond) occupies equatorial position
(3) more electronegative atom occupies axial position
eg. PF3Cl2, PF2Cl3PCl5
Limitations:- not applicable to ionic comp’d- for localized bonding/non-bonding pair, not for
delocalized- for sufficiently large ligands, steric interaction prevails
90°
120°
√2 r
√3 r
C l
PC l
C l
C l
C lF
S
FF
FF
S
FF
FO
F
Kr
F
F
Xe
F
OO
O
F
PF
Cl
F
FF
PCl
Cl
F
FF
PCl
Cl
F
ClF
PCl
Cl
Cl
Cl
1.2
1.05
1.01
0.91
0.96
0.9
§ Variable Hybridization and Molecular GeometryFor carbon bonded to different atom, different
hybridizations are proposed.For CH4, CCl4:sp3 hybridization % S = 25
% P = 75
For spn, define λ 2 = n ,λ:hybridization parameter
% S = , % P =
sum of P-fraction Σ = n,
sum of S-fraction Σ = 1
Interorbital angle θab , 1+ λa λb cosθab = 0if a = b,1+ λa
2 cosθaa = 0, cosθaa =
λ2
(1 +λ2)1
(1 +λ2)
-1λa
2
hybridization index
sp3 → θaa = 109.5 °sp2 → θaa = 120 °sp → θaa = 180 °
3sin2 θab = 2 (1- cosθaa )from θab = 108° , θaa = 110.5 °from θaa = 110.5° , λa
2 = 2.86∴sp2.86 for C-H
from 3 ( ) + = 1, λb2 = 3.51
1 +λb2
11 + 2.86
the S character↑ , λ↓
λi2
(1 +λi2)i
i1
(1 +λi2)
C
a b
Cl
CH
H
H
b
aa
a
θab
108°
110.5°
sp3.5
sp2.86
more S-character
more P
For CA3B
For CH2Cl2 λCl
2 = = 2.69
∴sp2.69 for C-Cl
from 2 ( ) + 2 ( ) = 1
λH2 = 3.37, sp3.37 for C-H
-1cos111°47
′
11 +λH
21
1 + 2.69
from cosθHH = , θHH = 107° ≠-1λH
2 112 ° (expt’l)
λHH2 = 2.67,
λCl2 = 3.39,
θClCl = 107°
the inter-orbital bond angle smaller than the inter nuclear bond angle
H
C
Cl
ClH
111.47°112°
1.082Å 1.772Å
Cl
CH
HH
F
CH
H
H
F
C
HH
H
108.0°
110.52°
108.9°
109.54°
106.7°
(by inter nuclear)bent bond
H
C
Cl
ClH
Experimental support of variable hybridization:NMR coupling constants J13C-1H:: cyclopropane 161, cyclobutane 134, cyclopentane 128, cyclohexane 124, cycloheptane 123, cyclooctane 122
Cyclopropane
bent bond from sp3 hybridization (or variable hybridization)
H
H
H
H
H
H
115 ° 1
H
H
Sp3.94
sp2.36
Walsh orbital:from sp2 hybridization
θcc=105°
H
CHHC
H
H
HC
HC
HCH C
Prediction of Physical Properties with diff. Bonding model1. 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:
C-C distance 1.32Å
C-C distance 1.18Å
2. Acidity
ethane 10-42 sp3
ethene 10-36.5 sp2
ethyne 10-25 sp
bent bond formulation
HC
H HC
H
CH C H
1.54Å
1.54Å
1.54Å
only sp3
hybridization
S character increase greater e--pulling power for the orbital better stabilization of the anion
decreased repulsionfurther decrease in repulsion
conformation of propene
σ,π-formation predicts Ⅱ to be more stable, because more repulsion between double bond and the C-H bond in IBent bond formulation:
The bent bond (Ω bond ) is agreed in cyclopropaneproposed or shown to more suitable than σ,π description in CF2=CF2, CO2, CO, benzene
Conclusion
H
H
H
CH2 H CH2H
H
H
H3C C
CH2
H
H
H CH2
H
H
HH CH2
H
H
more stable by 2Kcal/mole
more stable
IIIII