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Electrostatic Effects in Organic Chemistry
A guest lecture given in CHM 425 byJack B. LevyMarch, 2003
University of North Carolina at Wilmington
(subsequently edited by Ned H. Martin)
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Outline
1. Defining & Calculating Atomic Charges2. Basis for Preferring Natural Charges3. Electrostatic Effects of Alkyl Groups4. Energies of Isomeric Alkanes5. Understanding Conformational Energies of
Some Substituted Phenols
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1. Types of Atomic Charge Calculations in Gaussian
Mulliken Charges Natural Charges AIM (Atoms-in-Molecules) Charges MK and CHELPG Charges
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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.
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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.
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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.
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AIM (atoms in molecules)
• atomic basins (A & B) • zero-flux surface (bold curve S)• bond critical point (C)
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ESP (electrostatic potential)
• computed potential between a point + charge moved around the vdW surface and the computed electron density of the molecule
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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.
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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
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Benzenonium Ion
H H
+
12
34
NPA CHELPG MK AIM NMR (exp.)1 -0.62 0.11 -0.07 -0.11 48.9 (52.2)2 -0.01 0.03 0.12 -0.01 173.4 (186.6)3 -0.24 -0.13 -0.25 0.00 132.0 (136.9)4 -0.02 0.16 0.24 0.00 166.0 (178.1
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Benzenonium Ion
R2 = 0.0041
020406080
100120140160180200
-0.2 -0.1 0 0.1 0.2
CHELPG Charge
CNM
R (e
xp.)
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Benzenonium Ion
R2 = 0.2995
020406080
100120140160180200
-0.4 -0.2 0 0.2 0.4
MK Charge
CNM
R (e
xp.)
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Benzenonium Ion
R2 = 0.8323
020406080
100120140160180200
-0.15 -0.1 -0.05 0
AIM Charge
CNM
R (e
xp.)
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Benzenonium Ion
R2 = 0.9976
020406080
100120140160180200
-0.8 -0.6 -0.4 -0.2 0
NPA Charge
CNM
R (e
xp.)
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Computed NMR Chemical Shifts (, rel. to TMS) vs. NPA charges
R2 = 0.985
0
50
100
150
200
250
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4
NPA Charge
CNM
R
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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.
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Charges and 13C NMR of Simple Carbocations (MP2/6-31G*)
+CCH3 CH2CH3
H
56
7 82
1
C CH3 CH3
H
+ +CCH3 CH3
CH3
34
NPA CHELPG MK AIM NMR
1 -0.80 -0.43 -0.52 -0.11 51.7
2 0.35 0.58 0.57 0.025 315.1
3 -0.79 -0.43 -0.56 -0.11 47.5
4 0.52 0.67 0.71 0.031 331.9
5 -0.79 -0.45 -0.52 -0.11 43.3
6 0.30 0.44 0.42 0.014 310.5
7 -0.55 -0.05 -0.03 -0.09 70.5
8 -0.69 -0.28 -0.40 -0.05 18.6
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Charges and 13C NMR of Simple Carbocations (MP2/6-31G* Calculations)
H
CH3C CH3
+ CH3C C
H2
CH3
H
+
CH3
CH3C 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 0.03113C NMR 315.1 310.5 331.9
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Graph of Charges vs. CNMR shifts
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
300 310 320 330 340
CNMR chemical shift
Cha
rge
on c
arbo
catio
n C
npaChelpGM-KAIMLinear (npa)
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Electrostatic Stabilization of Carbocations by Alkyl Groups
C
C
CC
H
H
H
H
H
H H
H
H
+
-
- -+
+++
+
+
+
+
+
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Effect of Adjacent Charges
C
C
CC
H
H
H
H
H
H H
H
H
C
H
CCH
H
H H
H
H
C
H
CCH
H
H H
H
C
H
H
H
+
-
- -+
+++
+
+
+
+
+
+
++
+++
+
+
++
++
+
+
+
++
+ -
- -
adjacent positivecharges
adjacent positivecharges
adjacent negative charges
- -
3º
2º2º
Only 3º carbocations have NO adjacent positively charged atoms!
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Bond Order (Hyperconjugation) Effects
H
CH3C C
H2
+
CH3
CH3C C
H2
+
H
CH3C CH2
H +H
CH3
CH3C CH2
+H H
C-C Bond Order = 1.09
C-C Bond Order = 1.16
3º
2º
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Calculating Electrostatic Energies
Electrostatic energy = ij(qiqj /r) (in atomic units)
The 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.
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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 :
Hfo298(CnH2n+2 gas) = -2.0(n + 1) – 0.5 + Eel (CnH2n+2)
(kcal/mol)
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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)
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Heats of Formation (Lange’s, 4th Ed.) and Quantum
Chemically Calculated Energy Differences
Hfo Hf
o MP2/6-311+G**
Butane -125.6
2-Methylpropane -134.2 -8.6 -8.4
Pentane -146.9
2-Methylbutane -154.0 -7.1 -6.5 2,2-Dimethylpropane -168.3 -21.4 -22.9
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Gauche Interaction Energy
Scaled MP2/6-311+G** Electrostatic Energy (au; kJ/mol, rel.) (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 CH3CH3
HHCH3
H HCH3
HHH
H HCH3
CH3H
anti gauche2-methylpropane
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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.
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Use of a Common Isodesmic Reaction
OH M(CH3)2O
+
OH
M(CH3)2O
+
Hrxn = interaction energy
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Interaction Energies (MP2/6-31G**, kJ/mol) of Phenol Derivatives
OH
MO
H3C CH3
OH
NO
H3CCH3
M = N -49.0 M = P -34.8 M = As -45.2
-52.3
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Bond Distances, Å (MP2/6-31G**)
O
H
N
O
H3C CH3
1.454
1.036
1.397
1.336O
H
N
O
H3CCH3
1.492
1.341 1.045
1.458
1.4011.486
O
H
P
O
H3C CH3
O
H
As
O
H3C CH3
0.988
1.722
1.521
0.999
1.680
1.666
1.353
1.803
1.350
1.897
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Comparison of Bond Lengths to those in Parent Structures
O
H
N
O
H3C CH3
1.454
1.036
1.397
1.336O
H
N
O
H3CCH3
1.492
1.341 1.045
1.458
1.4011.486
N
O
H3C CH3
O
H
0.965
1.363
1.374
1.497
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Structures Investigated: M = N, P, or As
OH
MO
H3C CH3
O
M
H
CH3
CH3
O
O
M
H
CH3
O
H3C
OH
NO
H3CCH3
MO
H3C CH3
O H
MO
H3C CH3
OH
M
CH3
CH3
O
O H
M
CH3
CH3
O
OH
OH
M
H3C
H3CO
OH
M
H3C
H3CO
OH
M(CH3)2O
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MP2/6-31G** Potential Energy vs Scaled Atomic Point Charge (NPA) Electrostatic Energy of
Dimethylaminophenol Oxides and Related P and As Compounds
-150-100
-500
50100
-100 -50 0 50 100Electrostatic Energy (Rel., kJ/mol)
Pote
ntia
l Ene
rgy
(Rel
., kJ
/mol
)
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Summary
1. Calculating Atomic Charges2. Basis for Preferring Natural Charges3. Electrostatic Effects of Alkyl Groups4. Energies of Isomeric Alkanes5. Understanding Conformational Energies of
Some Substituted Phenols
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Acknowledgements
Thanks to our Department of Chemistry and the (former) North Carolina Supercomputing Center for computing facilities used in this work.