Article pubs.acs.org/JPCA
Nucleophilic Substitution: A Charge Density Perspective Travis E. Jones*,† Molecular Theory Group, Colorado School of Mines, Golden, Colorado 80401, United States ABSTRACT: A general description of nucleophilic reactions is developed using bond bundles, an extension of the quantum theory of atoms in molecules, allowing novel activating groups to be predicted for aromatic rings. Reactivity is found to be related to both the shape of the bond bundle between the substrate and leaving group and the presence of nonbonding regions. Closed bond bundles are shown to be more reactive than open ones, while nonbonding regions also increase reactivity. The advantage of this approach is that it can be employed to investigate all molecular and solid-state systems. By way of example I use this model to rationalize two anomalously reactive systems: strained heterocyclic rings and sulfideactivated aromatic rings.
N
regions on sulfur. This observation leads to the prediction that, while selenide activation of phenylflouride will be observed, oxide activation will not. QTAIM and its extensions derive structure from a quantum mechanical observable, the electron charge density, ρ(r)⃗ . The theory capitalizes on the fact that as a 3-dimensional scalar field ρ(r)⃗ possesses a topology that is partially characterized by its rank 3 critical points, CPs, the places where the charge density achieves extreme values in all three principal directions. In three-dimensional space there are four kinds of nondegenerate CP: local minima, local maxima, and two types of saddle points. In QTAIM these CPs are referred to by the (rank, signature) notation, where the signature is the number of positive curvatures minus the number of negative curvatures. For example, a minimum CP has positive curvature in three orthogonal directions; therefore it is called a (3, +3) CP. A maximum is denoted by (3, −3), because all three curvatures are negative. A saddle point with two of the three curvatures negative is denoted (3, −1), while the other saddle point is a (3, +1) CP. Through extensive studies of molecules and crystals, Bader showed that it was possible to correlate the topological properties of ρ(r)⃗ with elements of molecular structure and bonding.8,9 Nuclear sites were always found to coincide with maxima, and the (3, −3) CP was denoted an atom, or nuclear, CP. (A second type of maximum may also be present. These non-nuclear (3, −3) CP are topologically identical to atom CPs but do not coincide with the position of a nucleus.18,19) A bond path was argued to be the ridge of maximum charge density connecting two nuclei, whose existence is guaranteed by the presence of a (3, −1) CP between the two nuclei. As such, this CP is often referred to as a bond CP. The other two types of
ucleophilic substitution reactions have broad synthetic utility in organic chemistry and are ubiquitous in biochemical processes.1 However, there are a large number of systems that undergo nucleophilic substitution in which our current approaches offer little insight. While such problems have long kept solid-state phenomena, such as fracture2,3 and dislocation motion,4 out of the realm of mainstream chemistry, as synthetic chemists create new polymers5 and energetic materials,6,7 there are a growing number of reactions that resist a traditional explanation. One reason for the difficulty in predicting the behavior of many of these systems is the ambiguity associated with bonding and molecular structure. Here the unambiguous definition of molecular structure provided by a topological partitioning of the electron charge density is used to develop a new picture of nucleophilic substitution. This model is then applied to rationalize and predict the reactivity of systems that have defied traditional explanation. A key element in nucleophilic substitution is the breaking of the bond between the leaving group and substrate. The properties of that bond and those of the leaving group play a central role in determining the reactivity of a molecule. To develop a general picture of nucleophilic substitution these properties must be well-defined in all systems. An unambiguous definition of molecular structure with well-defined properties can be found in an extension of the quantum theory of atoms in molecules (QTAIM),8−12 which can be used to delineate the boundaries of atoms, bonds, and nonbonding volumes. Here I use the structures introduced through QTAIM and its extensions to show that a good leaving group is characterized by two features: a small topological bond to the substrate (a bond bundle with a small volume) and nonbonding volumes. I then show that the anomalous reactivity of 3-member rings13−17 can be explained using the topological bonds in the rings. I then go on to show that the unexplained sulfide activation of phenylflouride5 is due to topological nonbonding © 2012 American Chemical Society
Received: March 2, 2012 Revised: April 5, 2012 Published: April 5, 2012 4233
dx.doi.org/10.1021/jp302087n | J. Phys. Chem. A 2012, 116, 4233−4237
The Journal of Physical Chemistry A
Article
Figure 1. A 3-dimensional representation of the C−O BB in tert-butyl mesylate is shown on the left, with carbon black, hydrogen white, oxygen red, and sulfur yellow. The 2-ridges bounding the C−O BB are shown as the gray surfaces. A cross section of the BB in a charge density contour plot containing the C−O bond path is shown in the middle with the C−O BB shaded red, an O nonbonding region shaded green, and the edges of the 2ridges drawn in as thick black lines. The molecular graph is shown on the right.
flux boundaries,23,24 each IB is characterized by well-defined and additive properties. And because IBs are the 3-dimensional simplex of the space, they too can be glued together to form other structures, each of which also has well-defined and additive properties. In particular, the union of IBs around a common (3, +3) CP is the Bader atom, while the union of IBs sharing a common (3, −1) CP is the bond bundle (BB)the region that contains the bond’s electrons. With this rigorous definition of structure it becomes possible to investigate relationships between a molecule’s IBs and its behavior. The electron charge densities used to draw and test these correlations were obtained using the Amsterdam density functional package version 201025 with a triple-ζ single polarized basis set and the Vosko−Wilk−Nusair local density approximation.26 The calculations were also performed using the B3LYP hybrid functional; however no differences were seen between the two methods. The analysis of the charge density was performed using Tecplot and a charge density grid with 10 points per Ångstrom. To begin, consider the tert-butyl mesylate molecule shown in Figure 1. It is well-known to organic chemists that tert-butyl mesylate will readily undergo nucleophilic substitution, in part because mesylate is an excellent leaving group.27 The ease with which the C−O bond breaks is reflected in the structure of the C−O BB, Figure 1. Inspection of the 3-dimensional representation of the BB in the left pane of the figure reveals that the BB is closed in all directions, e.g., the 2-ridges converge as they move away from the bond path. This convergent behavior and its origin can be seen more clearly in the cross section of the BB shown in the middle pane. Here the red shaded region corresponds to the C−O BB. The majority of its density can be seen to lie along the carbon (black circle) and oxygen (red circle) bond line. Far from the bond path, the repulsion from the charge density in neighboring BBs (not shown) and nonbonding IBs (green shaded region) exclude the C−O BB density,28 compressing the BB into the closed shape seen in Figure 1. As the C−O internuclear distance is increased from its equilibrium value the BB will compress further as charge flows from the BB to the mesylate. Charge transfer will continue until, at a sufficient separation, the BB will be devoid of density and will collapse into a single bond path, resulting in the situation shown in Figure 2. By comparing the top pane of Figure 2 to Figure 1 it becomes clear that the nonbonding
CPs have also been correlated with features of molecular structure. A (3, +1) CP is found at the center of ring structures and is designated a ring CP. Cage structures enclose a single (3, +3) CP and are given the name cage CPs. Bader was also able to show that a molecule or solid can be partitioned into space-filling regions, called Bader atoms, in which each region contains a single nucleon bounded by a surface of zero flux in the gradient of the charge density, referred to as a zero flux surface or ZFS. By virtue of being bounded by a ZFS, the properties of these unique regions are well-defined and additive.8,9,20 That is, molecular properties, e.g. energy, can be expressed as the sum of Bader atom energiesjustifying the designation of these regions as “atoms.” Jones and Eberhart10−12 went on to note that the topology of ρ(r)⃗ can be more fully characterized through the inclusion of the charge density ridges. In 2 dimensions a ridge is a familiar topographic feature, the 1D-path (gradient path) connecting mountain passes to neighboring peaks, for example. There is only one such gradient path. It is a path of locally least steep ascent terminating at the local maximum. Consequently, it is an extremum with respect to all neighboring paths. Similarly, a valley is the gradient path connecting a saddle point to a local minimum, and because valleys and ridges differ only by the sign of the curvature along the path, they can both be denoted generically as “ridges.” In ρ(r)⃗ , a 3-dimensional field, ridges are both the gradient paths and gradient surfaces that are extrema with respect to all neighboring gradient paths and surfaces. They are denoted by an index, n − d, where n is the dimensionality of the space and d is the number of principal directions in which the charge density is extremal.21 Explicitly including ridges in the description of the topology of ρ(r)⃗ recovers bond paths and Bader atoms, while simultaneously providing a much richer picture of molecular structure by endowing space with a simplicial complex topology. The bond path is a 1-ridge and the surface of a Bader atom is composed of 2-ridges. In this topological space, however, 1- and 2-ridges represent simplicies that can be glued together to form new structures not noted in the original AIM theory. In particular, the 3-dimensional simplex in the space is the irreducible bundle (IB). It is bounded by 2-ridges and is diffeomorphic to a tetrahedron with vertices coincident with cage, ring, bond, and nuclear CPs. Its edges are 1-ridges and its faces are 2-ridges.22 Like Bader atoms, by virtue of their zero 4234
dx.doi.org/10.1021/jp302087n | J. Phys. Chem. A 2012, 116, 4233−4237
The Journal of Physical Chemistry A
Article
The previous discussion suggests that two features of a molecule’s IBs mediate its susceptibility to nucleophilic substitution, the first of these is the size and shape of its substrate-leaving group BB. Because this BB must collapse to break the leaving group-substrate bond, it should be small and closed. The second requirement is the presence of nonbonding IBs to accommodate the excess charge that is transferred as the BB collapses. Now that possible topological and geometric structures of ρ(r)⃗ mediating nucleophilic susceptibility have been identified, we can examine systems that have resisted traditional explanations. Two such systems will be explored here: the first, ring-opening nucleophilic reactions, shows how changing the structure of the molecule leads to a change in the substrate leaving group BB and corresponding changes in reactivity, while the second, sulfide activated nucleophilic aromatic substitution, is an example of how differences in nonbonding regions lead to different reactivities. It has long been known that ring-opening nucleophilic reactions in strained rings show rate enhancement relative to their unstrained analogues and that the magnitude of the enhancement is not solely due to the release of strain energy.15−17 The increase in reactivity of three member heterocyclic rings even permits reactions to be performed with extremely poor leaving groups, such as amines and thioethers.16 While being of broad synthetic utility, there is no clear explanation of the origin of the increase in reactivity of these molecules. Their IBs offer such an explanation. To take but one example, consider the 3- and 4-member heterocyclic rings phosphirane and phosphetane shown in Figure 3. Under nucleophilic addition with methylphosphine
Figure 2. The topology after the C−O BB collapses to a bond line in tert-butyl (top). The energy as a function of separation (bottom). The dashed line indicates the point at which the BB becomes too small to resolve.
region on the mesylate grows as the group leaves. This increase in volume is due to the excess charge from the C−O BB accumulating in the nonbonding region on the leaving group. This assertion is confirmed by the fact that at equilibrium the C−O BB contains approximately 1.5 valence electrons. After the bond is broken the charge on the Bader oxygen is approximately −1. The transformation of the BB to a bond path can be associated with the breaking of the C−O bond. When the C−O internuclear axis is lengthened from its equilibrium value, the energy of the system increases rapidly, i.e., lower pane of Figure 2, as the density in the C−O BB is transferred to the mesylate nonbonding volume. When the internuclear axis is stretched to 4 Å, the C−O BB has nearly vanished29 as an occupied and unoccupied orbital become nearly degenerate.30 At this point charge transfer between the substrate and BB is reduced and there is a corresponding reduction in the change in energy as a function of separation, Figure 2. When the charge transfer is complete the 2-ridges bounding the BB will coalesce with the bond path and the C−O bond will be broken. (As a side note, the observation that the energy change of the system is small when the C−O bond is stretched beyond the point at which the BB collapses may offer insight into the role of bond points, and their BBs, in what are typically considered to be nonbonding interactions, such as hydrogen−hydrogen bonds.31 If the bundles in these nonbonding interactions are vanishingly small, they will offer little or no stabilization. While such an investigation may be fruitful, it is beyond the scope of this work.)
Figure 3. Cross section of the C−P bond in phosphirane (left) and phosphetane (right).
the rings will open by cleavage of the C−P bond. The activation energy of phosphetane in this reaction is 2 times higher than the activation energy of phosphirane, but the difference in strain energy only accounts for 10% of the difference in activation energy.15 When the BBs of phosphirane and phosphetane are investigated the differences in reactivity become apparent. Because the C−P bond is being broken and the nonbonding regions are identical in phosphirane and phosphetane, we can focus on the C−P BB. In phosphirane (Figure 3 left) the BB is closed, while in phosphetane (Figure 3 right) it is open in one direction, suggesting that the 3-member ring is more reactive. 4235
dx.doi.org/10.1021/jp302087n | J. Phys. Chem. A 2012, 116, 4233−4237
The Journal of Physical Chemistry A
Article
make the σ -complex intermediate these IBs can accommodate the excess charge, allowing bis(4-fluorophenyl)sulfide to undergo nucleophilic aromatic substitution. Other reasonable candidate molecules for arylfluoride substitution can be easily be envisioned. The simplest of these would be bis(4-fluorophenyl)oxide and bis(4fluorophenyl)selenide, where the sulfur atom has been replaced by an oxygen or selenium atom. These three systems might be expected to behave in a similar fashion because all three are (valence) isoelectronic. However, within the IB picture of reactivity they are not. Oxide activation in bis(4-fluorophenyl)oxide should not be observed because the oxygen atom in bis(4-fluorophenyl)oxide does not have nonbonding IBs to accommodate excess charge. The only bond paths terminating at the oxygen atom in the molecule are paths connected to its nearest neighbor carbon atoms, resulting in a single 2-ridge passing through the oxygen atom as shown in Figure Figure 6. While not shown, bis(4-
Another area of anomalous reactivity is the sulfide activation of aromatic rings toward nucleophilic aromatic substitution.5 Knauss and Edson have shown that poly(aryl ether sulfide)s can be produced through the nucleophilic aromatic substitution of bis(4-fluorophenyl)sulfide with bisphenol A and bisphenol AF, Figure 4.
Figure 4. Polymerization of bis(4-fluorophenyl)sulfide with bisphenol A.
In the traditional picture of nucleophilic aromatic substitution a strong electron withdrawing substituent, such as a nitro group, is required on the aromatic ring to stabilize the σcomplex intermediate. However, the reaction reported by Knauss and Edson is novel because it lacks such an activating group. While this synthetic breakthrough suggests there are new possible activating groups that will yield new potentially useful materials, there has been no way to predict which groups are good choices, until now. The way in which bis(4-fluorophenyl)sulfide stabilizes the σcomplex intermediate can be seen by examining its IBs. Figure 5 shows a 3-dimensional representation of the 2-ridges terminating at the sulfur nuclear site in the top pane. Notice that there is a region that does not contain a bond path to any atom in the molecule. This region is the nonbonding volume on sulfur, which is shown by way of green shading in the middle pane. When the nucleophile attaches to the ipso carbon to
Figure 6. The single 2-ridge dividing the oxygen atom in bis(4fluorophenyl)oxide (top) and the molecular graph of bis(4fluorophenyl)oxide (bottom).
fluorophenyl)selenide does have nonbonding IBs on the selenium atom. Thus, selenide activation is expected. An identical argument can also be applied to show that the more geometrically complex 2,7-difluorothianthrene and 2,7-difluoroselenanthrene will will also undergo nucleophilic aromatic substitution, the former has been shown experimentally.32 In conclusion, a picture of nucleophilic reactivity based on the topology and geometry of the electron charge density was presented. It suggests that a closed leaving group substrate BB will be more reactive than an open one, while the presence of nonbonding IBs is required to accommodate the charge transfer during the reaction. The advantage of this model over traditional pictures of nucleophilic substitution is that it is general. It can be used in systems that have defied traditional explanation, as was shown by rationalizing the anomalous reactivity of 3 member heterocyclic rings and predicting novel ring activating substituents for nucleophilic aromatic substitutions. Although this work focused on molecular systems, because it is based on a quantum mechanical observable, the IB picture of reactivity can also be applied to the solid state, which is the subject of an ongoing investigation.
Figure 5. The nonbonding bundle on sulfur in and bis(4fluorophenyl)sulfide. A 3D representation is shown in the top frame, a 2D cross section though the sulfur atom in the middle frame, and a molecular graph in the lower pane. 4236
dx.doi.org/10.1021/jp302087n | J. Phys. Chem. A 2012, 116, 4233−4237
The Journal of Physical Chemistry A
■
Article
(19) Jones, T. E.; Eberhart, M. E. Acta Cryst. A 2009, 65, 141−144. (20) Martín Pendás, A.; Blanco, M.; Francisco, E. Chem. Phys. Lett. 2006, 417, 16−21. (21) Eberly, D.; Gardner, R.; Morse, B.; Pizer, S.; Scharlach, C. J. Math Imaging Vis. 1994, 4, 353−373. (22) Cage and ring points will not be present for every IB in molecules. However, the 2-ridges making up the faces of the IB can still be identified. (23) Nasertayoob, P.; Shahbazian, S. Int. J. Quantum Chem. 2009, 109, 726. (24) Heidarzadeh, F.; Shahbazian, S. Int. J. Quantum Chem. 2011, 111, 2788. (25) te Velde, G.; Bickelhaupt, F. M.; van Gisbergen, S. J. A.; Fonseca Guerra, C.; Baerends, E. J.; Snijders, J. G.; Ziegler, T. J. Comput. Chem. 2001, 22, 931. (26) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200− 1211. (27) Carey, F. A.; Sundber, R. J. Advanced Organic Chemistry, 4th ed.; Springer: New York, 2006. (28) Liu, S. J. Chem. Phys. 2007, 126, 244103. (29) When the internuclear separation reaches 4 Å, the C−O BB can only be resolved when the charge density grid spacing is less than 0.1 Å. (30) Jones, T. E.; Eberhart, M. E.; Clougherty, D. P. Phys. Rev. Lett. 2010, 105, 265702. (31) Matta, C.; Hernandez-Trujillo, J.; Tang, T.; Bader, R. Chem.− Eur. J. 2003, 9, 1885−1885. (32) Robb, M. J.; Knauss, D. M. J. Polym. Sci., Part A: Polym. Chem. 2009, 47, 2453−2461.
APPENDIX Liu has shown that the steric potential of the electron charge density can be defined as the functional derivative of the Weizsäcker kinetic energy with respect to the total electron density 28
vs( r ⃗) =
1 |∇ρ( r ⃗)|2 1 ∇2 ρ( r ⃗) − 8 ρ2( r ⃗) 4 ρ( r ⃗)
(1)
If we examine the behavior of the steric potential on the 2ridges we find that across the face of an IB the first term vanishes, owing to the zero-flux condition, while the second term is extremal.11 In particular, the Laplacian of ρ(r)⃗ , ∇2ρ(r)⃗ , reaches a maximum in the direction normal to the 2-ridges bounding a BB or nonbonding region. These surfaces are then the boundaries at which the steric repulsion from neighboring volumes reaches its minimum value, and the BB is the volume over which the steric potential is perturbed due to the presence of the bond path.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest. † Also at School of Physics, The University of Sydney, Sydney, New South Wales 2006, Australia CNR-IOM Democritos, SISSA, via Bonomea 265 I-34136, Trieste, Italy.
■ ■
ACKNOWLEDGMENTS I gratefully acknowledge support of this work by ONR under Grant No. N00014-10-1-0838 and ARO under 421-20-18. REFERENCES
(1) Doudna, J.; Cech, T. R. Nature 2002, 418, 222−228. (2) Whitesides, G. Relations between Fracture and Coordination Chemistry. In Atomistics of Fracture; Latanision, R., Pickens, J., Eds.; Plenum Press: New York, 1983. (3) Jones, T. E.; Sauer, M. A.; Eberhart, M. E. Phys. Rev. B 2008, 78, 092104. (4) Jones, T. E.; Eberhart, M. E.; Clougherty, D. P.; Woodward, C. Phys. Rev. Lett. 2008, 101, 085505. (5) Knauss, D. M.; Edson, J. B. Polymer 2006, 47, 3996−4003. (6) Rice, B.; Hare, J. J. Phys. Chem. A 2002, 106, 1770−1783. (7) Rice, B.; Sahu, S.; Owens, F. THEOCHEM 2002, 583, 69−72. (8) Bader, R. F. W. Atoms in Molecules. A Quantum Theory; Clarendon Press: Oxford, UK: 1990. (9) The Quantum Theory of Atoms in Molecules: From Solid State to DNA and Drug Design; Matta, C., Boyd, R., Becke, A., Eds.; WileyVCH: 2007. (10) Jones, T.; Eberhart, M. Int. J. Quantum Chem. 2010, 110, 1500− 1505. (11) Jones, T. E.; Eberhart, M. E. J. Chem. Phys. 2009, 130, 204108. (12) Jones, T. E.; Eberhart, M. E.; Imlay, S.; Mackey, C. J. Phys. Chem. A 2011, 115, 12582−12585. (13) L., C. J. Org. Chem. 1988, 53, 1733−1736. (14) Di Vona, M.; Illuminati, G.; Lillocci, C. J. Chem. Soc., Perkin Trans. 1985, 2, 380−381. (15) Wolk, J.; Hoz, T.; Basch, H.; Hoz, S. J. Org. Chem. 2001, 66, 915−918. (16) Banks, H. J. Org. Chem. 2003, 68, 2639−2644. (17) Wolk, J.; Rozental, E.; Basch, H.; Hoz, S. J. Org. Chem. 2006, 71, 3876−3879. (18) Pendás, A. M.; Blanco, M. A.; Costales, A.; Sánchez, P. M.; Luaña, V. Phys. Rev. Lett. 1999, 83, 1930−1933. 4237
dx.doi.org/10.1021/jp302087n | J. Phys. Chem. A 2012, 116, 4233−4237
