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. 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

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

+

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

Benzenonium Ion

R2 = 0.0041

020406080

100120140160180200

-0.2 -0.1 0 0.1 0.2

CHELPG Charge

CN

MR

(e

xp

.)

Benzenonium Ion

R2 = 0.2995

020406080

100120140160180200

-0.4 -0.2 0 0.2 0.4

MK Charge

CN

MR

(e

xp

.)

Benzenonium Ion

R2 = 0.8323

020406080

100120140160180200

-0.15 -0.1 -0.05 0

AIM Charge

CN

MR

(e

xp

.)

Benzenonium Ion

R2 = 0.9976

020406080

100120140160180200

-0.8 -0.6 -0.4 -0.2 0

NPA Charge

CN

MR

(e

xp

.)

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

CN

MR

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*)

+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

Charges and 13C NMR of Simple Carbocations (MP2/6-31G* Calculations)

H

C

H3C CH3

+C

H3C CH2

CH3

H

+

CH3

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 NMR 315.1 310.5 331.9

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

Ch

arg

e o

n c

arb

oc

ati

on

C

npa

ChelpG

M-K

AIM

Linear (npa)

Electrostatic Stabilization of Carbocations by Alkyl Groups

C

C

CC

H

H

H

H

H

H H

H

H

+

-

- -+

+

++

+

+

+

+

+

Effect of Adjacent Charges

C

C

CC

H

H

H

H

H

H H

H

H

C

H

CC

H

H

H H

H

H

C

H

CC

H

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!

Bond Order (Hyperconjugation) Effects

H

C

H3C CH2

+

CH3

C

H3C CH2

+

H

C

H3C CH2

H +H

CH3

C

H3C CH2

+H H

C-C Bond Order = 1.09

C-C Bond Order = 1.16

3º

2º

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.

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 :

 Hfo

298(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

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

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 CH3

CH3

HHCH3

H HCH3

HHH

H HCH3

CH3H

anti gauche2-methylpropane

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 M(CH3)2O

+

OH

M(CH3)2O

+

Hrxn = interaction energy

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

OH

MO

H3C CH3

OH

NO

H3C

CH3

M = N -49.0 M = P -34.8 M = As -45.2

-52.3

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

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

Structures Investigated: M = N, P, or As

O

H

M

O

H3C CH3

O

M

H

CH3

CH3

O

O

M

H

CH3

O

H3C

O

H

N

O

H3CCH3

M

O

H3C CH3

O H

M

O

H3C CH3

OH

M

CH3

CH3

O

OH

M

CH3

CH3

O

OH

OH

M

H3C

H3CO

OH

M

H3C

H3CO

OH

M(CH3)2O

MP2/6-31G** Potential Energy vs Scaled Atomic Point Charge (NPA) Electrostatic Energy of

Dimethylaminophenol Oxides and Related P and As Compounds

-150

-100

-50

0

50

100

-100 -50 0 50 100

Electrostatic Energy (Rel., kJ/mol)

Po

ten

tia

l E

ne

rgy

(Re

l.,

kJ/m

ol)

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

Acknowledgements

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