Electrostatic Effects in Organic Chemistry

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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)

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Outline

• 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

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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 atoms
  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
  molecules 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 popnpa or popnboread (with nbo bndidx
  end at the end of the input file to get bond
  orders as well).
• Popmk and popchelpg 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
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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Computed NMR Chemical Shifts (d,
rel. to TMS) vs. NPA charges
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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)
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)
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 NMR 315.1 310.5 331.9
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Graph of Charges vs. CNMR shifts
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Electrostatic Stabilization of Carbocations by
Alkyl Groups
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Effect of Adjacent Charges
Only 3º carbocations have NO
adjacent positively charged atoms!
3º
2º
2º
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Bond Order (Hyperconjugation) Effects
3º
2º
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Calculating Electrostatic Energies
Electrostatic energy Si ¹j(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.
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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  DHfo298(CnH2n2 gas) -2.0(n
1) 0.5 Eel (CnH2n2) (kcal/mol)
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Isomeric Alkane Energies
Bensons 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 Coulombs 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 MP2/6-311G
level of theory.  Benson, S. W. Luria, M. J.
Am Chem. Soc., 97, 704-709 (1975)
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Heats of Formation (Langes, 4th Ed.) and Quantum
Chemically Calculated Energy Differences
DHfo DDHfo
MP2/6-311G 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
MP2/6-311G 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
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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
DHrxn interaction energy
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Interaction Energies (MP2/6-31G, kJ/mol) of
Phenol Derivatives
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Bond Distances, Å (MP2/6-31G)
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Comparison of Bond Lengths to those in Parent
Structures
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Structures Investigated M N,
P, or As
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Summary

• Calculating Atomic Charges
• Basis for Preferring Natural Charges
• Electrostatic Effects of Alkyl Groups
• Energies of Isomeric Alkanes
• 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.