Electrostatic Effects
in Organic Chemistry
A guest lecture given in CHM 425 by
Jack B. Levy
March, 2003
University of North Carolina
at Wilmington
(subsequently edited by Ned H. Martin)
Outline
1.
2.
3.
4.
5.
Defining & Calculating Atomic Charges
Basis for Preferring Natural Charges
Electrostatic Effects of Alkyl Groups
Energies of Isomeric Alkanes
Understanding Conformational Energies of
Some Substituted Phenols
1. Types of Atomic Charge
Calculations in Gaussian
 Mulliken Charges
 Natural Charges
 AIM (Atoms-in-Molecules) Charges
 MK and CHELPG Charges
Concept of a Molecule
 The quantum mechanical picture of a
molecule shows a set of positive point
charges (the nuclei) imbedded in a cloud of
negative charge.
 The atomic charge model is a classical
model consisting of a set of point charges
that simulate the combined electrostatic
effects of both the atomic nuclei and the
electrons.
Various Atomic Charge
Approximations
 Mulliken charges and Natural charges
(NPA) are both based on orbital
occupancies, i.e., how much electron
density is associated with each atom’s
orbitals. The nuclear charge minus the
electron density associated with each atom
gives the atomic charge.
Various Atomic Charge
Approximations
 AIM (atoms in molecules) charges are based
on a division of the molecule into atoms
based on the topology of the electron density.
 MK and CHELPG charges are derived by a
fit to the molecule’s electrostatic potential at
a large number of grid points.
AIM (atoms in molecules)
• atomic basins (A & B)
• zero-flux surface (bold curve S)
• bond critical point (C)
ESP (electrostatic potential)
• computed potential between a point + charge
moved around the vdW surface and the
computed electron density of the molecule
Calculating Atomic Charges
in Gaussian
 Mulliken charges are automatically provided
in the output.
 Natural charges (Weinhold-Reed) require
keywords, either pop=npa or pop=nboread
(with $nbo bndidx $end at the end of the
input file to get bond orders as well).
 Pop=mk and pop=chelpg are other options.
2. Natural Charges Preferred
 In a study of a series of substituted
benzenonium ions it was found that the
natural charges correlate best with
experimental and computed 13C NMR
chemical shifts.
Levy, J. B. Structural Chemistry, 1999, 10,
121-127
Benzenonium Ion
H H
1
2
+
3
4
1
2
3
4
NPA
-0.62
-0.01
-0.24
-0.02
CHELPG
0.11
0.03
-0.13
0.16
MK
-0.07
0.12
-0.25
0.24
AIM
-0.11
-0.01
0.00
0.00
NMR (exp.)
48.9 (52.2)
173.4 (186.6)
132.0 (136.9)
166.0 (178.1
CNMR (exp.)
Benzenonium Ion
200
180
160
140
120
100
80
60
40
20
0
-0.2
-0.1
0
0.1
CHELPG Charge
0.2
R2 = 0.0041
CNMR (exp.)
Benzenonium Ion
200
180
160
140
120
100
80
60
40
20
0
-0.4
-0.2
0
MK Charge
0.2
0.4
R2 = 0.2995
CNMR (exp.)
Benzenonium Ion
200
180
160
140
120
100
80
60
40
20
0
-0.15
-0.1
-0.05
AIM Charge
0
R2 = 0.8323
CNMR (exp.)
Benzenonium Ion
200
180
160
140
120
100
80
60
40
20
0
-0.8
-0.6
-0.4
NPA Charge
-0.2
0
R2 = 0.9976
Computed NMR Chemical Shifts
(d, rel. to TMS) vs. NPA charges
250
200
CNMR
150
100
50
0
-0.8
R2 = 0.985
-0.6
-0.4
-0.2
NPA Charge
0
0.2
0.4
3. Electrostatic Effect of Alkyl Groups
 Are alkyl groups electron-donating relative
to hydrogen? (as stated in most organic texts)
 Atomic charge calculations show that the
positive carbon of a carbocation gets more
positive, not less positive, when methyls are
substituted for hydrogens!
 The more substituted carbocations are more
stable because of an electrostatic effect.
Charges and 13C NMR of Simple
Carbocations (MP2/6-31G*)
1
CH3 2 CH3
C +
3
CH3 4 CH3
C +
CH3
H
NPA
5
7 8
CH3 6 CH2CH3
C +
H
CHELPG
MK
AIM
NMR
1 -0.80
-0.43
-0.52
-0.11
51.7
2
0.35
0.58
0.57
0.025
3 -0.79
-0.43
-0.56
-0.11
4
0.52
0.67
0.71
0.031
5 -0.79
-0.45
-0.52
-0.11
6
0.30
0.44
0.42
0.014
7 -0.55
-0.05
-0.03
-0.09
70.5
8 -0.69
-0.28
-0.40
-0.05
18.6
315.1
47.5
331.9
43.3
310.5
Charges and 13C NMR of Simple
Carbocations (MP2/6-31G* Calculations)
H
C
H
+
H3C
CH3
C+
CH3
H3C
CH3
C
H2
C
H3C
+
CH3
NPA
0.35
0.30
0.52
CHELPG
0.58
0.44
0.67
MK
0.57
0.42
0.71
AIM
0.025
0.014
0.031
13C
315.1
310.5
331.9
NMR
Graph of Charges vs. CNMR shifts
Charge on carbocation C
0.8
0.7
0.6
npa
0.5
ChelpG
0.4
M-K
0.3
AIM
0.2
Linear (npa)
0.1
0
300
310
320
330
CNMR chemical shift
340
Electrostatic Stabilization of
Carbocations by Alkyl Groups
d+
H
d+
H
d+H
d+
C
dC
d-
C d+
d+
H
dC
H
H
d+
H d+
H d+
H d+
Effect of Adjacent Charges
d+
H
d+
d+H
3º
H
C
d-
d+
d- C dC
d+
d+
H
C
H d+
H
H
d+
adjacent positive
charges
H
d+
H
d+
C
d+ H
H
H
d-
dH
H
d+
d+
d+ H
C
d+
H
dC
H
d+
2º
H
C d+
C
d+ d+
2º
adjacent positive
charges
H
d+
d+
C
H
d+
d+
C d+
d-
H
Only 3º carbocations have
NO adjacent positively
charged atoms!
d+
H
H
d+ H
d+
dH
adjacent negative charges
d+
Bond Order
(Hyperconjugation) Effects
CH 3
CH 3
C
+
H3C
H+
C
H
H3C
C
H2
CH 2
3º
C-C Bond Order = 1.09
H
C
H3C
H
+
H
C
H2
H+
C
H3C
2º
C-C Bond Order = 1.16
CH 2
Calculating Electrostatic Energies
Electrostatic energy = Si j(qiqj /er)
(in atomic units)
The e in the above equation, called the permitivity
of free space, is just a scaling factor. Remember that
the atomic charges are being treated as point charges.
This approximation can work well if the charges are
appropriately scaled by the use of standards, as will be
shown.
4. Energies of Isomeric Alkanes
Highly branched alkanes are more stable than less branched
isomers; this phenomenon can be explained in terms of the
electrostatic interactions that result from the significant polarity
of C-H bonds. Benson and Luria (1975) presented a model for
alkanes in which each H had an effective point charge of 0.0581
and each carbon a balancing negative charge. This model leads
to a formula that successfully predicts heats of formation to ±0.2
kcal/mol for all the n-alkanes to n-C7H16 and for the branched
alkanes up to C5H12 :
DHfo298(CnH2n+2 gas) = -2.0(n + 1) – 0.5 + Eel (CnH2n+2)
(kcal/mol)
Isomeric Alkane Energies
Benson’s formula can be further improved by accounting
for steric effects, such as gauche interactions, that are not
primarily electrostatic in nature. The electrostatic energy is
calculated from Coulomb’s law.
Rather than assuming a constant charge for hydrogen, one
can now use the results of quantum mechanics. In our work
we use natural charges and geometries computed at the
MP2/6-311+G** level of theory.
Benson, S. W.; Luria, M. J. Am Chem. Soc., 97, 704-709
(1975)
Heats of Formation (Lange’s, 4th Ed.) and Quantum
Chemically Calculated Energy Differences
DHfo
Butane
2-Methylpropane
DDHfo
MP2/6-311+G**
-125.6
-8.6
-8.4
-154.0
-7.1
-6.5
2,2-Dimethylpropane -168.3
-21.4
-22.9
Pentane
2-Methylbutane
-134.2
-146.9
Gauche Interaction Energy
MP2/6-311+G**
(au; kJ/mol, rel.)
Scaled
Electrostatic Energy
(kJ/mol; kJ/mol, rel.)
Butane (anti)
-157.9626605; 0.0
-803/9.9; 0.0
2-Methylpropane
-157.9658348; -8.4
-886/9.9; -8.4
Butane (gauche)
-157.9618318; 2.2
-811/9.9; -0.8
H
H
CH3
H
H
H
H
CH3
anti
CH3
H
CH3
H
2-methylpropane
H
H
CH3
CH3
H
H
gauche
5. Understanding Conformational Energies
of a Series of Substituted Phenols
 A series of analogous nitrogen, phosphorus
and arsenic derivatives of phenol has been
investigated by
ab initio and
classical electrostatic calculations.
Use of a Common
Isodesmic Reaction
OH
O M(CH 3)2
OH
+
+
O M(CH 3)2
DHrxn = interaction energy
Interaction Energies (MP2/6-31G**,
kJ/mol) of Phenol Derivatives
O
O
H
H
O
O
N
M
CH 3
H3C
-52.3
H3C
CH 3
M = N -49.0
M = P -34.8
M = As -45.2
Bond Distances, Å (MP2/6-31G**)
1.336 O
1.341 O 1.045
H
H
1.454
1.458
O
O
1.486 N
H3C
1.036
1.492 N
1.401
CH 3
H3C
1.353 O 0.988
1.397
CH 3
1.350 O
H
H
1.680
1.722
O
O
1.803 P 1.521
H3C
0.999
CH 3
1.897 As
H3C
1.666
CH 3
Comparison of Bond Lengths to
those in Parent Structures
1.341 O 1.045
1.336 O
H
H
1.454
1.458
O
O
1.486 N
H3C
1.036
1.401
CH 3
1.492 N
H3C
1.397
CH 3
1.374 O 0.965
H
1.497
N
H3C
O
1.363
CH 3
Structures Investigated:
M = N, P, or As
H
O
O
M
N
O
M
H3C
CH 3
O
CH 3
O
O
H3C
O
H
H
H
CH 3
CH 3
CH 3
M
O
H3C
H
H
O
O
O
CH 3
H3C
M
CH 3
H
H
O
CH 3
M
O
H
O
M
H3C
H
CH 3
CH 3
M
O
O
O
OH
O M(CH 3)2
H3C
H3C
M
O
H3C
H3C
M
O
CH 3
O
Potential Energy
(Rel., kJ/mol)
MP2/6-31G** Potential Energy vs Scaled Atomic Point
Charge (NPA) Electrostatic Energy of
Dimethylaminophenol Oxides and Related P and As
Compounds
100
50
0
-50
-100
-150
-100
-50
0
50
Electrostatic Energy (Rel., kJ/mol)
100
Summary
1.
2.
3.
4.
5.
Calculating Atomic Charges
Basis for Preferring Natural Charges
Electrostatic Effects of Alkyl Groups
Energies of Isomeric Alkanes
Understanding Conformational Energies of
Some Substituted Phenols
Acknowledgements
 Thanks to our Department of
Chemistry and the (former) North
Carolina Supercomputing Center for
computing facilities used in this work.