1. 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)

2. Outline 1.Defining & Calculating Atomic Charges 2.Basis for Preferring Natural Charges 3.Electrostatic Effects of Alkyl Groups 4.Energies of Isomeric Alkanes 5.Understanding Conformational Energies of Some Substituted Phenols

3. 1. Types of Atomic Charge Calculations in Gaussian  Mulliken Charges  Natural Charges  AIM (Atoms-in-Molecules) Charges  MK and CHELPG Charges

4. 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.

5. 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.

6. 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.

7. AIM (atoms in molecules) atomic basins ( A & B ) zero-flux surface (bold curve S ) bond critical point ( C )

8. ESP (electrostatic potential) computed potential between a point + charge moved around the vdW surface and the computed electron density of the molecule

9. 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.

10. 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 13 C NMR chemical shifts. Levy, J. B. Structural Chemistry, 1999, 10, 121-127

11. 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

16. Computed NMR Chemical Shifts ( , rel. to TMS) vs. NPA charges

17. 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.

18. Charges and 13 C NMR of Simple Carbocations (MP2/6-31G*) NPA CHELPG MKAIM NMR 1 -0.80 -0.43-0.52-0.11 51.7 2 0.35 0.58 0.57 0.025315.1 3 -0.79 -0.43-0.56-0.11 47.5 4 0.52 0.67 0.71 0.031331.9 5 -0.79 -0.45-0.52-0.11 43.3 6 0.30 0.44 0.42 0.014310.5 7 -0.55 -0.05-0.03-0.09 70.5 8 -0.69 -0.28-0.40-0.05 18.6

19. Charges and 13 C NMR of Simple Carbocations (MP2/6-31G* Calculations) NPA0.35 0.300.52 CHELPG0.58 0.440.67 MK0.57 0.420.71 AIM0.025 0.0140.031 13 C NMR315.1 310.5331.9

20. Graph of Charges vs. CNMR shifts

21. Electrostatic Stabilization of Carbocations by Alkyl Groups

22. Effect of Adjacent Charges 3º 2º Only 3º carbocations have NO adjacent positively charged atoms!

23. Bond Order (Hyperconjugation) Effects 3º 2º

24. Calculating Electrostatic Energies Electrostatic energy =  i  j (q i q j /  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.

25. 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-C 7 H 16 and for the branched alkanes up to C 5 H 12 :  H f o 298 (C n H 2n+2 gas) = -2.0(n + 1) – 0.5 + E el (C n H 2n+2 ) (kcal/mol)

26. 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)

27. Heats of Formation (Lange’s, 4 th Ed.) and Quantum Chemically Calculated Energy Differences  H f o  H f 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

28. 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

29. 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.

30. Use of a Common Isodesmic Reaction  H rxn = interaction energy

31. Interaction Energies (MP2/6-31G**, kJ/mol) of Phenol Derivatives

32. Bond Distances, Å (MP2/6-31G**)

33. Comparison of Bond Lengths to those in Parent Structures

34. Structures Investigated: M = N, P, or As

36. Summary 1.Calculating Atomic Charges 2.Basis for Preferring Natural Charges 3.Electrostatic Effects of Alkyl Groups 4.Energies of Isomeric Alkanes 5.Understanding Conformational Energies of Some Substituted Phenols

37. Acknowledgements  Thanks to our Department of Chemistry and the (former) North Carolina Supercomputing Center for computing facilities used in this work.