Chem 206D. A. Evans
Matthew D. Shair Wednesday, September 18, 2002
http://www.courses.fas.harvard.edu/~chem206/
a73 Reading Assignment for week:A. Carey & Sundberg: Part A; Chapter 1
B. Fleming, Chapter 1 & 2
C. Fukui,Acc. Chem. Res. 1971, 4, 57.
D. O. J. Curnow, J. Chem. Ed. 1998, 75, 910.
E. J. I. Brauman, Science, 2002, 295, 2245.
Chemistry 206
Advanced Organic Chemistry
Lecture Number 1
Introduction to FMO Theory
a73 General Bonding Considerations
a73 The H2 Molecule Revisited (Again!)
a73 Donor & Acceptor Properties of Bonding & Antibonding States
a73 Hyperconjugation and "Negative" Hyperconjugation
a73 Anomeric and Related Effects
An Introduction to Frontier Molecular Orbital Theory-1
a73 Problem of the DayThe molecule illustrated below can react through either Path A or Path B to
form salt 1 or salt 2 . In both instances the carbonyl oxygen functions as thenucleophile in an intramolecular alkylation. What is the preferred reaction path
for the transformation in question?
+
+
Br –
Br –1
2
Path A
Path B
Br NH O BrO O
BrONH
O
ONHBr
a73 Your Answer
RO
H O
C BrMeRR SN2
CR RMe Br
Me2CuLi
O
OSiR3
R3SiO
EtO
C MeRR
RO
H O
Me
H
C RRMeNu
RO
H O
H
Me
OSiR3
OSiR3
EtO2C
H2
CH3–I
A(:)
A?
B(+)
B?
2 LiH
CH3–MgBr
A B
A B
Chem 206D. A. Evans An Introduction to Frontier Molecular Orbital Theory-1
+ Br:–
minor
major
Br: –Nu:
Nonbonding interactions (Van der Waals repulsion) between substituents within a molecule or between reacting moleculesa73 Steric Effects
Universal Effects Governing Chemical ReactionsThere are three:
a73 Electronic Effects (Inductive Effects):
+SN1
rate decreases as R becomes more electronegative
Inductive Effects: Through-bond polarizationField Effects: Through-space polarization
Danishefsky, JOC 1991, 56, 387
Lewis acid
diastereoselection >94 : 6
Your thoughts on this transformation
"During the course of chemical reactions, the interaction of the highest filled (HOMO) and lowest unfilled (antibonding)
molecular orbital (LUMO) in reacting species is very important to the stabilization of the transition structure."
Geometrical constraints placed upon ground and transition statesby orbital overlap considerations.a73 Stereoelectronic Effects
Fukui Postulate for reactions:
a73 General Reaction Types
Radical Reactions (~10%): +
Polar Reactions (~90%): +
Lewis Base Lewis AcidFMO concepts extend the donor-acceptor paradigm to
non-obvious families of reactions
a73 Examples to consider
2 Li(0)+
Mg(0)+
J. I. Brauman, Science, 2002, 295, 2245.
Chem 206D. A. Evans
The H2 Molecule (again!!)
Let's combine two hydrogen atoms to form the hydrogen molecule.Mathematically, linear combinations of the 2 atomic 1s states create
two new orbitals, one is bonding, and one antibonding:
Ener
gy 1s 1s
σ? (antibonding)a73 Rule one: A linear combination of n atomic states will create n MOs.
?E
?E
Let's now add the two electrons to the new MO, one from each H atom:
Note that ?E1 is greater than ?E2. Why?
σ (bonding)
σ (bonding)
?E2
?E1
σ? (antibonding)
1s1s
ψ2
ψ2
ψ1
ψ1E
nerg
y
+C1ψ1σ = C2ψ2
Linear Combination of Atomic Orbitals (LCAO): Orbital Coefficients
Each MO is constructed by taking a linear combination of the individual atomic orbitals (AO):
Bonding MO
Antibonding MO C*2ψ2σ? =C*1ψ1–
The coefficients, C1 and C2, represent the contribution of each AO.
a73 Rule Three: (C1)2 + (C2)2 = 1
= 1antibonding(C*1)2+bonding(C1)2a73 Rule Four:
Ener
gy
pi? (antibonding)
pi (bonding)
Consider the pi -bond of a C=O function: In the ground state pi-C–Ois polarized toward Oxygen. Note (Rule 4) that the antibonding MO
is polarized in the opposite direction.
C
C
O
C O
The H2 Molecular Orbitals & Antibonds
The squares of the C-values are a measure of the electron populationin neighborhood of atoms in question
In LCAO method, both wave functions must each contribute one net orbital
a73 Rule Two:
H H
HH
O
A B A
A C A C
A
Y
C
X
A C
X X X
??
lone pairHOMO σ* C–XLUMOσ* C–XLUMO
lone pairHOMO
C C C C C Si
C-SP3C-SP3C-SP3
C Si
Si-SP3
Y
C C
X
A B A B
Y
C C
B
X
Chem 206D. A. Evans Bonding Generalizations
a73 Weak bonds will have corresponding low-lying antibonds.pi Si–Si = 23 kcal/molpi C–Si = 36 kcal/molpi C–C = 65 kcal/mol
This trend is even more dramatic with pi-bonds:
σ? C–Siσ? C–C
σ C–Siσ C–C
Bond length = 1.87 ?Bond length = 1.534 ? H3C–SiH3 BDE ~ 70 kcal/molH3C–CH3 BDE = 88 kcal/mol
Useful generalizations on covalent bonding
When one compares bond strengths between C–C and C–X, where X is some other element such as O, N, F, Si, or S, keep in mind that
covalent and ionic contributions vary independently. Hence, the mapping of trends is not a trivial exercise.
Bond Energy (BDE) = Ecovalent + Eionic (Fleming, page 27)
a73 Bond strengths (Bond dissociation energies) are composed of a covalent contribution ( Ecov) and an ionic contribution ( Eionic).
better than
For example, consider elements in Group IV, Carbon and Silicon. We know that C-C bonds are considerably stronger by Ca. 20 kcal mol-1
than C-Si bonds.
a73 Overlap between orbitals of comparable energy is more effective than overlap between orbitals of differing energy.
Formation of a weak bond will lead to a corresponding low-lying antibonding orbital. Such structures are reactive as both nucleophiles & electrophiles
Better than
Better than
Case-2: Two anti sigma bonds
σ C–YHOMO
σ* C–XLUMO σ* C–XLUMO
Case-1: Anti Nonbonding electron pair & C–X bond
a73 An anti orientation of filled and unfilled orbitals leads to better overlap. This is a corrollary to the preceding generalization.
There are two common situations.
Better thanFor pi Bonds:
For σ Bonds:
a73 Orbital orientation strongly affects the strength of the resulting bond.
Better than
This is a simple notion with very important consequences. It surfaces inthe delocalized bonding which occurs in the competing anti (favored)
syn (disfavored) E2 elimination reactions. Review this situation.
σ C–YHOMO
Chem 206D. A. Evans Donor-Acceptor Properties of Bonding and Antibonding States
a73 σ?CSP3-CSP2 is a better acceptor orbital than σ?CSP3-CSP3
C-SP3
C-SP3
σ* C–C
σ C–C
C-SP3
σ C–C
σ* C–C
C-SP2
Donor Acceptor Properties of CSP3-CSP3 & CSP3-CSP2 Bonds
a73 The greater electronegativity of CSP2 lowers both the bonding & antibonding C–C states. Hence:a73 σ C
SP3-CSP3 is a better donor orbital than σ CSP3-CSP2
a73 σ?C–O is a better acceptor orbital than σ?C–Ca73 σ C–C is a better donor orbital than σ C–O
a73 The greater electronegativity of oxygen lowers both the bonding & antibonding C-O states. Hence:
Consider the energy level diagrams for both bonding & antibonding orbitals for C–C and C–O bonds.Donor Acceptor Properties of C-C & C-O Bonds
O-SP3
σ* C-O
σ C-O
C-SP3
σ C-C
σ* C-C
better donor
better acceptor
decreasing donor capacity
Nonbonding States
poorest donor
The following are trends for the energy levels of nonbonding states of several common molecules. Trend was established by photoelectron spectroscopy. best acceptor
poorest donor
Increasing -acceptor capacity
σ-anti-bonding States: (C–X)
σ-bonding States: (C–X)
decreasing -donor capacity
Following trends are made on the basis of comparing the bonding and antibonding states for the molecule CH3–X where X = C, N, O, F, & H.Hierarchy of Donor & Acceptor States
CH3–CH3 CH3–H
CH3–NH2 CH3–OH
CH3–F
CH3–H CH3–CH3
CH3–NH2 CH3–OH
CH3–F
HCl:H2O:H3N:
H2S:H3P:
2
2.5
3
3.5
4
4.5
5
Pauling Electronegativity
20 25 30 35 40 45 50 55
% S-Character
C
SP3
C
SP2
C
SP
N
SP3
N
SP2
N
SP
25
30
35
40
45
50
55
60
Pka of Carbon Acid
20 25 30 35 40 45 50 55
% S-Character
CH
4
(56)
C
6
H
6
(44)
PhCC-H (29)
CSP3 CSPCSP2
1 S Orbital
2 S Orbital
3 S Orbital
2 S Orbital
2 P Orbital
3 P Orbital
Chem 206D. A. Evans
This becomes apparent when the radial probability functions for S and P-states are examined: The radial probability functions for the
hydrogen atom S & P states are shown below.
Electrons in 2S states "see" a greater effective nuclear charge than electrons in 2P states.
Above observation correctly implies that the stability of nonbonding electron pairs is directly proportional to the % of S-character in the doubly occupied orbital
Least stable Most stable
The above trend indicates that the greater the % of S-character at a given atom, the greater the electronegativity of that atom.
There is a direct relationship between %S character & hydrocarbon acidity
There is a linear relationship between %S character & Pauling electronegativity
Hybridization vs Electronegativity
?
Radi
al Pr
obab
ility
100 %100 %
Radi
al Pr
obab
ility
?
S-states have greater radial penetration due to the nodal properties of the wave function. Electrons in S-states "see" a higher nuclear charge.
+
+ +
+
C C
R
HH H
H
C HH
R
C HHCH
H
C HH
Me
Me
Me
H
[F5Sb–F–SbF5]–
Me
Me
Me
C
Chem 206D. A. Evans
The Adamantane Reference(MM-2)
T. Laube, Angew. Chem. Int. Ed. 1986, 25, 349
First X-ray Structure of an Aliphatic Carbocation
110 °
100.6 °
1.530 ?
1.608 ?
1.528 ?
1.431 ?
a73 Bonds participating in the hyperconjugative interaction, e.g. C–R, will be lengthened while the C(+)–C bond will be shortened.
Physical Evidence for Hyperconjugation
The new occupied bonding orbital is lower in energy. When you stabilize the electrons is a system you stabilize the system itself.
a73 Take a linear combination of σ C–R and CSP2 p-orbital:
σ C–R
σ? C–R
σ C–R
σ? C–R
The Molecular Orbital Description
Syn-planar orientation between interacting orbitalsStereoelectronic Requirement for Hyperconjugation:
The graphic illustrates the fact that the C-R bonding electrons can "delocalize" to stabilize the electron deficient carbocationic center.
Note that the general rules of drawing resonance structures still hold:the positions of all atoms must not be changed.
+
a73 The interaction of a vicinal bonding orbital with a p-orbital is referred to as hyperconjugation.
Hyperconjugation: Carbocation Stabilization
This is a traditional vehicle for using valence bond to denote charge delocalization.
+
NMR Spectroscopya73 Greater e-density at R
a73 Less e-density at X NMR Spectroscopy
a73 Longer C–R bond X-ray crystallography
Infrared Spectroscopya73 Weaker C–R bond
a73 Stronger C–X bond Infrared Spectroscopy
X-ray crystallographya73 Shorter C–X bond
Spectroscopic ProbeChange in StructureThe Expected Structural Perturbations
As the antibonding C–R orbital decreases in energy, the magnitude
of this interaction will increase σ C–R
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σ? C–R
The Molecular Orbital Description
a73 Delocalization of nonbonding electron pairs into vicinal antibonding orbitals is also possible
"Negative" HyperconjugationD. A. Evans Chem 206
X
Since nonbonding electrons prefer hybrid orbitals rather that P orbitals, this orbital can adopt either a syn or anti relationship
to the vicinal C–R bond.
C XRHH HH X HHCHHR
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This decloalization is referred to as "Negative" hyperconjugation antibonding σ? C–R
a73 Overlap between two orbitals is better in the anti orientation as stated in "Bonding Generalizations" handout.
+
–
Anti Orientation
filled hybrid orbital
filled hybrid orbital
antibonding σ? C–RSyn Orientation
–
+C XHH
C XHHCH
CHHR X
H
R X
C XHH
C XHHR:
R:
Nonbonding e– pair
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Note that σ C–R is slightly destabilized
R
R
NF N
N NF
N NF F
F
(HOMO)
N FNF
A
A B
B
F
A
A B
B
Chem 206
The cis Isomer
a73 Note that two such interactions occur in the molecule even though only one has been illustrated.
a73 Note that by taking a linear combination of the nonbonding and antibonding orbitals you generate a more stable bonding situation.
σ? N–F
filled N-SP2antibonding σ? N–Ffilled N-SP
2
In fact the cis isomer is favored by 3 kcal/ mol at 25 °C.
Let's look at the interaction with the lone pairs with the adjacent C–Fantibonding orbitals.
This molecule can exist as either cis or trans isomers
The interaction of filled orbitals with adjacent antibonding orbitals canhave an ordering effect on the structure which will stabilize a particular
geometry. Here are several examples:
D. A. Evans Lone Pair Delocalization: N2F2
Case 1: N2F2
The trans Isomer Now carry out the same analysis with the same 2 orbitals present in the trans isomer.
filled N-SP2
antibonding σ? N–F
a73 In this geometry the "small lobe" of the filled N-SP2 is required to overlap with the large lobe of the antibonding C–F orbital. Hence, when
the new MO's are generated the new bonding orbital is not as stabilizingas for the cis isomer.
filled N-SP2
(HOMO)
σ? N–F
Conclusions
a73 Lone pair delocalization appears to override electron-electron and dipole-dipole repulsion in the stabilization of the cis isomer.
(LUMO)
(LUMO)
.. .. .. ..
There are two logical reasons why the trans isomer should be more stable than the cis isomer.
a73 The nonbonding lone pair orbitals in the cis isomer will be destabilizing due to electron-electron repulsion.
a73 The individual C–F dipoles are mutually repulsive (pointing in same direction) in the cis isomer.
a73 This HOMO-LUMO delocalization is stronger in the cis isomer due to better orbital overlap.
Important Take-home Lesson
Orbital orientation is important for optimal orbital overlap.
forms stronger pi-bond than
forms stronger sigma-bond than
This is a simple notion with very important consequences. It surfaces inthe delocalized bonding which occurs in the competing anti (favored)
syn (disfavored) E2 elimination reactions. Review this situation.
N NMeN N
Me H
N HNMe N NMe
O
H
OMe O H
OMe
CH CR RR
Cl
HO O OHCl H
Cl
H
OMe
OMe
HO
H
OMe
OMe
H
O
H
H
CR OH
Chem 206
a73 We now conclude that this is another example of the vicinal lone pair effect.
D. A. Evans The Anomeric Effect and Related Issues
filled N-SP2
Infrared evidence for lone pair delocalization into vicinal antibonding orbitals.
ν N–H = 2188 cm -1
ν N–H = 2317 cm -1
filled N-SP2
antibonding σ? N–H
..
antibonding σ? N–H
The N–H stretching frequency of cis-methyl diazene is 200 cm-1 lower than the trans isomer.
N. C. Craig & co-workers JACS 1979, 101, 2480.
ν C–H = 3050 cm -1ν C–H = 2730 cm -1
Aldehyde C–H Infrared Stretching Frequencies
The IR C–H stretching frequency for aldehydes is lower than the closely related olefin C–H stretching frequency. For years this observation has
gone unexplained.
The Anomeric Effect
It is not unexpected that the methoxyl substituent on a cyclohexane ring prefers to adopt the equatorial conformation.
? G° = +0.6 kcal/mol
? G° = –0.6 kcal/mol
What is unexpected is that the closely related 2-methoxytetrahydropyranprefers the axial conformation:
a73 That effect which provides the stabilization of the axial OR conformerwhich overrides the inherent steric bias of the substituent is referred to as
the anomeric effect.
axial O lone pair?σ? C–H axial O lone pair?σ? C–O
Principal HOMO-LUMO interaction from each conformation is illustrated below:
a73 Since the antibonding C–O orbital is a better acceptor orbital than the antibonding C–H bond, the axial OMe conformer is better stabilized by
this interaction which is worth ca 1.2 kcal/mol.Other electronegative substituents such as Cl, SR etc. also participate in
anomeric stabilization.
This conformer preferred by 1.8 kcal/mol 1.819 ?
1.781 ?
Why is axial C–Cl bond longer ?
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a73 The low-frequency N–H shift in the cis isomer is a result of N–Hbond weakening due to presence of the anti lone par on the vicinal
nitrogen which is interacting with the N–H antibonding orbital.Note that the orbital overlap is not nearly as good from the trans
isomer
N N N N
N NHH HH H NH
H
H
(HOMO) (HOMO)
(HOMO)
H
H
N HH
(HOMO)
O HOH H
(HOMO)
O H
H
O H
(HOMO)
(LUMO) σ? N–H
Chem 206
In fact, the gauche conformation is favored. Hence we have neglected an important stabilization feature in the structure.
Hydrazine can exist in either gauche or anticonformations (relative to lone pairs).
The interaction of filled orbitals with adjacent antibonding orbitals canhave an ordering effect on the structure which will stabilize a particular
conformation. Here are several examples of such a phenomon called the gauche effect:
D. A. Evans Lone Pair Delocalization: The Gauche Effect
There is a logical reason why the anti isomer should be more stable than the gauche isomer. The nonbonding lone pair orbitals in the gauche
isomer should be destabilizing due to electron-electron repulsion.
Hydrazine
H σ? N–H
(LUMO)filled N-SP3 (LUMO) σ? N–H
H
filled N-SP3
σ N–H
H
σ N–H
HOMO-LUMO InteractionsOrbital overlap between filled (bonding) and antibonding states is
best in the anti orientation. HOMO-LUMO delocalization is possible between: (a) N-lone pair ? σ? N–H; (b) σ N–H ? σ? N–H
better stabilization
The closer in energy the HOMO and LUMO the better the resulting stabilization through delocalization.
a73 Hence, N-lone pair ? σ? N–H delocalization better than σ N–H ? σ? N–H delocalization.
a73 Hence, hydrazine will adopt the gauche conformation where both N-lone pairs will be anti to an antibonding acceptor orbital.
The trend observed for hydrazine holds for oxygen derivatives as well
Hydrogen peroxide
gaucheanti
anti gauche
H2O2 can exist in either gauche or anti conformations (relative to hydrogens).
The gauche conformer is prefered.
a73 Major stabilizing interaction is the delocalization of O-lone pairs intothe C–H antibonding orbitals (Figure A). Note that there are no such
stabilizing interactions in the anti conformation while there are 2 in the gauche conformation.
observed HOOH dihedral angle Ca 90°
observed HNNH dihedral angle Ca 90°
(LUMO)
σ? O–H
filled O-SP3 filled O-SP3
a73 Note that you achieve no net stabilization of the system by generating molecular orbitals from two filled states (Figure B).
Figure A Figure B
Problem: Consider the structures XCH2–OH where X = OCH3 and F. What is the most favorable conformation of each molecule? Illustrate the
dihedral angle relationship along the C–O bond.
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