J . Phys. Chem. 1990, 94, 3959-3961
3959
Use of the Electrostatic Potential at the Molecular Surface To Interpret and Predict Nucleophilic Processes Per Sjoberg and Peter Politzer* Department of Chemistry, University of New Orleans, New Orleans, Louisiana 70148 (Received: August 29, 1989)
The use of the molecular electrostatic potential to analyze reactivity toward nucleophiles is not as straightforward as for electrophiles, since positive maxima are generally found only at the positions of the nuclei. We show that this problem can be avoided by computing the potential on the three-dimensionalsurface of the molecule that correspondsto a constant electronic density of 0.002 electrons/bohr3. The relative magnitudes of the positive electrostatic potentials in various regions on this surface do reveal the sites most susceptible to nucleophilic attack. This is demonstrated for several sets of examples; in each instance, the surface potential correctly predicts the observed reactive behavior. The potentials were computed at the SCF 3-21 G level, using STO-3G optimized molecular geometries.
Introduction The electrostatic potential V(r) that the electrons and nuclei .of a molecule create at each point r in the sourrounding space is given rigorously by eq 1. ZAis the charge on nucleus A, located p(r’) dr’ V(r) = A IRAzA- rl (1) Ir’ - rl
x-
s-
at R A . p ( r ) is the electronic density function of the molecule. V(r) is a real physical property, which can be determined either computationally or experimentally by diffraction methods.’ The electrostatic potential is well established as an effective tool for interpreting and predicting molecular reactive behavior toward ele~trophiles.’-~An approaching electrophile will tend initially to go to those regions in which V(r) attains its most negative values (the local minima) since these are where the effects of the molecule’s electrons are most dominant [eq 11. Unfortunately, the use of the electrostatic potential to analyze reactivity toward nucleophiles is not as straightforward. This can be understood by first recognizing that V(r) for any free neutral atom is positive everywhere, increasing to a maximum at the This simply reflects the highly concentrated nature of the nuclear charge as contrasted to the dispersed average electronic distribution. When atoms interact to form a molecule, the accompanying rearrangement of electrons normally produces one or more regions of negative electrostatic potential. Each such region has at least one minimum to which an approaching electrophile may be attracted. The positive regions, on the other hand, generally do not have maxima other than at the positions of the nuclei; these are so large in magnitude that they would mask any weaker local maxima that might indicate sites for nucleophilic attack. Thus the V(r) plots that are normally obtained provide no clearcut guidelines as to the sites most attractive to nucleophiles. In view of the considerable value of the electrostatic potential for analyzing electrophilic processes, it would be highly desirable to be able to apply it to nucleophilic ones as well. We suggested earlier that this can be done by distorting the molecular geometry in turn at each possible reactive site, so that it is in a state already somewhat amenable to interaction with a nucleophile, and comparing the potentials computed for each of these distorted structures.’ This does of course require computing a new wave function in each case. More recently, it has been proposed that (1) Politzer, P., Truhlar, D. G., Eds. Chemical Applications of Atomic and Molecular Electrostaric Potentials; Plenum Press: New York, 198 1. (2) Scrocco, E.; Tomasi, J. Adu. Quantum Chem. 1978, 11, 115. (3) Politzer, P.; Daiker, K. C. In The Force Concept in Chemistry; Deb, B. M., Ed.: Van Nostrand Reinhold: New York, 1981; p 294. (4) Politzer, P.;Parr, R. G . J . Chem. Phys. 1974, 61, 4258. (5) Weinstein, H.; Politzer, P.; Srebrenik, S. Theor. Chim. Acta 1975,38, 159. (6) Politzer, P. In Homoatomic Rings, Chains and Macromolecules of Main-Group Elements; Rheingold, A. L., Ed.; Elsevier: Amsterdam, 1977; Chapter 4.
0022-3654/90/2094-3959$02.50/0
nucleophilic processes can be treated by taking into account both electrostatic and polarization effects8 This poses the problem of estimating the polarization contribution to the interaction energy. In this paper, we present an approach for analyzing nucleophilic processes that requires only the electrostatic potential of the ground-state undistorted molecule. We avoid the problem associated with the very strong nuclear potentials by computing V ( r ) on a three-dimensional surface that is designed to encompass nearly all of the electronic charge of the molecule, and thus is significantly removed from all nuclear positions. In previous studies of molecular surfaces, some of which included computing the electrostatic potential, these have most commonly been defined as the outer surfaces of sets of intersecting spheres centered on the individual nuclei;”9 their radii might be, for example, the van der Waals radii of the respective atoms or some constant multiple of these. However, using such a “hard sphere” model to determine the molecular surface has the disadvantage that it does not reflect the electronic charge distribution of the molecule, but rather a superposition of those of the free atoms. This necessarily neglects such features as bond formation, lone pairs, etc., which are unique to the molecule. Accordingly, we shall define the surface in terms of a molecular property: the 0.002 electrons/bohr3 contour of the total electronic density function p(r). It has been shown, for a group of diatomic molecules and for methane, that this contour in three dimensions encompasses at least 95% of the electronic charge and yields physically reasonable molecular “dimensi~ns”.’~-~lWe will demonstrate that, when the electrostatic potential is computed on this surface, the positive regions can indeed be used to identify (7) Politzer, P.; Landry, S. J.; Warnheim, T. J . Phys. Chem. 1982, 86, 4767. (8) Francl, M . M. J . Phys. Chem. 1985, 89, 428. (9) Pullman, B.; Perahia, D.; Cauchy, D. Nucleic Acid.? Res. 1979, 6, 3821.
(IO) Weiner, P. K.; Langridge, R.; Blaney, J. M.; Schaefer, R.; Kollman, P. A Proc. Natl. Acad. Sci. U.S.A. 1982, 79, 3754. (1 1) Connolly, M. L. Science 1983, 221, 709. ( 1 2) Bash, P. A,; Pattabiraman. N.; Huang. C.; Ferrin, T. E.; Langridge, R. Science 1983, 222, 1325. (13) Francl, M. M.: Hout, R. F., Jr.; Hehre, W. J. J . A m . Chem. SOC. 1984, 106, 563. (14) Quarendon, P.; Naylor, C. B.; Richards, W. G. J . Mol. Graph. 1984, 2, 4. ( 1 5) Connolly, M . L. J . A m . Chem. SOC.1985, 107. 11 18 (16) Ritchie, J. P. J . A m . Chem. SOC.1985, 107, 1829. (17) Burridge, J. M.; Quarendon, P.; Reynolds, C. A,; Goodford, P. J. J . Mol. Graph. 1987, 5 , 165. (18) Arteca, G.A.; Jammal, V . B.; Mezey, P. G . ;Yadav, J. S.; Hermsmeier, M. A.; Gund, T. M. J . Mol. Graph. 1988, 6 , 45. (19) Kahn, S. D.: Parr, C. F.; Hehre, W. J. Int. J . Quantum Chem., Quantum Chem. Symp. 1988, 22, 575. (20) Bader, R. F. W.; Henneker, W. H.; Cade, P. E. J . Chem. Phys. 1967, 46, 3341. (21) Bader, R. F. W.; Preston, H. J. T. Theor. Chem. Acta 1970, 17, 384.
0 1990 American Chemical Society
3960 The Journal of Physical Chemistry, Vol. 94, No. 10, 1990
Sjoberg and Politzer
Figure 1. Calculated electrostatic potential on the molecular surface of acrolein (I). Hydrogens are not shown. The red region corresponds to potentials greater than
+ 10 kcal/mol;
the blue regions are negative.
Figure 3. Calculated electrostatic potentials on the molecular surfaces of fluorobenzene (IV) (top), and p-nitrofluorobenzene (V) (bottom). Hydrogens are not shown. The red regions correspond to positive potentials.
Figure 2. Calculated electrostatic potentials on the molecular surfaces of methanol, H,C-OH (top), and methyl chloride, H,C-Cl (bottom). Methyl hydrogens are not shown. The red regions correspond to potentials greater than +20 kcal/mol.
the site most susceptible to nucleophilic attack. Methods Optimized geometries were computed for all molecules with the a b initio self-consistent-fieldGAUSSIAN 82 procedure,22using the STO-3G basis set; this has been found to be effective for determining structure^.^^ Electronic densities and electrostatic potentials were then calculated at the 3-21G level. Each molecule is encompassed by a characteristic three-dimensional surface, corresponding to the contour of constant electronic density equal to 0.002 electrons/bohr3. The molecular (22) Binkley, J. S.; Frisch, M. J.; DeFrees, D. J.; Krishnan, R.; Whiteside, R. A.; Schlegel, H. B.; Fluder, E. M.; Pople, J. A. G A u s s i A N 82; CarnegieMellon Quantum Chemistry Publishing Unit; Pittsburgh, PA 15213. (23) Radom, L.; Latham, W. A.; Hehre, W. J.; Pople, J. A. J. Am. Chem. SOC.1971, 91, 5339.
Figure 4. Calculated electrostatic potentials on the molecular surfaces of acetyl fluoride (VI) (top), and acetamide (VII) (bottom). Methyl hydrogens are not shown. The red regions correspond to potentials greater than +32 kcal/mol; the blue regions are less than +IO kcal/mol.
The Journal of Physical Chemistry, Vol. 94, No. 10, 1990 3961
Prediction of Nucleophilic Processes electrostatic potentials were computed and plotted on these surfaces. These potentials can of course be shown at whatever degree of resolution is desired, just as for planar surfaces;'-3 however, since our present objective is the purely qualitative one of simply identifying the most likely sites for nucleophilic attack, we will limit the plots to showing just two or three ranges of potential values.
Results and Discussion 1. Acrolein. Acrolein, I, is an example of an a,@-unsaturated carbonyl compound, 11. These are known to undergo nucleophilic "\
/
h a l ~ g e n . ~ However, ~**~ the reactivity of the halogen is greatly increased by the presence of the electron-withdrawing NO2 group in an ortho or para position. Our surface electrostatic potentials are fully consistent with these experimental observations. Figure 3 shows the potential to be negative above all of the carbons in fluorobenzene (IV), making the aromatic ring clearly unattractive for an approaching nucleophile. In p-nitrofluorobenzene (V), however, there is a positive region above (only) the fluorinated carbon, indicating increased reactivity to nucleophilic attack (Figure 3). F
H
F
6
HF=c\ c=o /
Iv
H
I1
I
attack at the carbonyl and the 0 ~ a r b o n s ; in ~ ~the J ~particular case of acrolein, this occurs primarily at the carbonyl carbon.24 We showed earlier that electrostatic potential plots in planes through the ground-state acrolein molecule reveal no features that indicate the carbonyl carbon to be the favored site for nucleophilic attack? However, this preference is brought out quite clearly when the potential is plotted on the molecular surface (Figure 1). No distortion of the structure or polarization need be considered; the molecule is in its equilibrium ground state. 2. Methanol and Methyl Chloride. In aliphatic systems, the s N 2 replacement of a group X by a nucleophile z: proceeds through the transition state 111 and thus involves inversion of c o n f i g ~ r a t i o n . For ~ ~ ~a ~given ~ Z, this substitution proceeds more
NO2 V
4 . Acetyl Fluoride and Acetamide. Acetyl halides, VI, are quite reactive toward nucleophilic substitution at the carbonyl carbon; for example, they decompose in ~ a t e r . ~ Acetamide, ~ * ~ ~ , ~ ~ VII, on the other hand, is considerably less active and is stable in water. H3C
0 II
-C -X
VI X = halogen
0 II
HSC-C-NH, VI1
These differences in behavior are exactly what would be predicted from our calculated surface potentials for acetyl fluoride and acetamide, shown in Figure 4. The former has, overall, much stronger positive regions than the latter, and these focus upon the carbonyl carbon. Summary
I11
readily for H3C-CI than for H3C-OH. This could not be predicted from electrostatic potential plots in planes through these two molecules in their ground state^,^ but it follows immediately from an examination of the potentials on the methyl sides of the H3C-Cl and H3C-OH surfaces (Figure 2), where the former is distinctly more positive. 3. Fluorobenzene and p-Nitrofuorobenzene. Aryl halides show very little susceptibility to nucleophilic ( s N 2 ) replacement of the (24) Morrison, R. T.; Boyd, R. N. Organic Chemistry, 3rd ed.; Allyn and Bacon: Boston. MA. 1973. (25) Stowell; J. C: Carbanions in Organic Synthesis; Wiley-Interscience: New York, 1979; pp 31-35. (26) Kemp, D. S.;Vellaccio, F. Organic Chemistry, Worth Publishers: New York, 1980.
Our results show that the electrostatic potential plotted on the molecular surface as here defined can be used effectively for interpreting and predicting nucleophilic processes. This approach requires only p ( r ) and V(r) for the ground-state molecule; both of these are rigorously defined physical observables. In each case examined, the conclusions reached on the basis of the surface potential were in full agreement with experimental observations.
Acknowledgment. We thank Dr. Jane S. Murray for very helpful comments and discussions. We greatly appreciate the partial support of this work by the Office of Naval Research, through contract NOOO14-85-K-0217. Registry No. I, 107-02-8; IV, 462-06-6; V, 350-46-9; VI, 557-99-3; VII, 60-35-5; H,COH, 67-56-1; H3CC1, 74-87-3.
~
(27) Windholz, M., Ed. The Merck Index, 10th ed.; Merck & Co.: Rahway, NJ, 1983.
