Pnicogen Bonds: A Theoretical Study Based on the Laplacian of

Article pubs.acs.org/JPCA

Pnicogen Bonds: A Theoretical Study Based on the Laplacian of Electron Density K. Eskandari*,† and N. Mahmoodabadi‡ †

Department of Chemistry, Isfahan University of Technology, Isfahan 84156-83111, Iran School of Chemistry, Damghan University, Damghan 36716-41167, Iran

‡

ABSTRACT: Although, most of the authors classify the pnicogen bonds as σ-hole bonding, there are some evidence that show they do not require any positive electrostatic potential around interacting molecules. In this work, the Laplacian of electron density is used to study pnicogen bonds in different dimer and trimer complexes. It is shown that the noncovalent P···P, P···N, and N···N bonds can be categorized as lump−hole interactions; a region of charge depletion and excess kinetics energy (hole) in the valence shell charge concentration (VSCC) of pnicogen atom combines with a region of charge concentration and excess potential energy (lump) in the VSCC of another molecule and form a pnicogen bond. In fact, since the full quantum potential (according to the local statement of virial theorem) has been used in the definition of the Laplacian, the lump−hole concept is more useful than the σ-hole in which the electrostatic part of potential is only considered. It is shown that the existence of hole in the VSCC of pnicogen atom is responsible for formation and (in the absence of other interactions) geometry of pnicogen bonded complexes. Because there is (at least) one hole in their VSCC, the pnicogen atoms in PH3, PH2F, H2CPH, H2CPF, and NH2F can engage in direct pnicogen−pnicogen interactions. However, the VSCC of nitrogen atom in the NH3 is devoid of hole and hence cannot act as an electron acceptor in pnicogen-bonded complexes.

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INTRODUCTION

hydrogen bond. Similar interactions between phosphorus and nitrogen is observed, when PH3 is paired with NH3.29,33 The nature and geometry of these interactions has been also the subject of several researches. Scheiner et al.33,34 and Alkorta et al.29 showed that the complexes with P···N interactions have an almost linear X−P−N arrangement (X is the atom covalently bonded to the P) in H2XP/NXH2 complexes. Scheiner and co-workers33 also found a linear H−P−P arrangement in PH3 homodimer. In addition, they investigated the nature of pnicogen bonds and showed that these interactions are somewhat analogous to the hydrogen bonds and halogen bonds, along with some fundamental differences.19,33 Politzer et al.35 described the P···P interaction in PH2Cl dimer as a double σ-hole (a region of positive electrostatic potential in the surface of molecule) 36,37 interaction, in which the σ-hole on the extension of each Cl− P bond interacts with the negative region of the other phosphorus. Alkorta et al.38−40 and Mohajeri et al.41 also described pnicogen bonds as σ-hole bonds; however, Scheiner showed that the pnicogen bonds do not require any σ-hole around interacting molecules.19,33 Accordingly, it seems that the σ-hole, which is responsible for formation of halogen bonds

It is well-known that noncovalent interactions are of critical importance in a wide variety of chemical and biochemical systems.1−5 Although, this class of interactions encompasses different bonding types, the hydrogen bonds and halogen bonds are, without doubt, the most important ones. Because of their importance, the nature of these interactions has been widely studied over the years.6−18 Among the noncovalent interactions, there is another interesting example that is comparable with hydrogen bonds and halogen bonds; the case of pnicogen bonds. In these bonds, a pnicogen atom (N, P, or As) acts as a Lewis acid and interacts with an electron donor molecule.19 Although the pnicogen bonds have been known for several decades,20,21 it has been received immense attention in recent years.19,22−31 Hey-Hawkins et al. showed that pnicogen bonds have comparable bond strength to hydrogen bonds and might act as a molecular linker in different chemical systems. Tuononen et al.32 carried out a theoretical study of weak interactions between trivalent pnicogen centers and showed that these interactions, and P···P interactions in particular, are strong enough to be considered relevant for determining supramolecular structures in the solid state. Solimannejad and co-workers23 found an attraction between P and N atoms when HCN interacts with PH3 or other phosphines. They showed that the structure containing P···N interaction is a global minimum and more stable than the structure with a PH···N © 2013 American Chemical Society

Received: October 5, 2013 Revised: November 13, 2013 Published: November 18, 2013 13018

dx.doi.org/10.1021/jp4098974 | J. Phys. Chem. A 2013, 117, 13018−13024

The Journal of Physical Chemistry A

Article

However, as stated in the previous section, the distribution of the Laplacian of electron density is a powerful tool for describing noncovalent interactions despite of the nature of stabilizing forces. So, it may be useful to use the Laplacian of electron density for describing pnicogen bonds. To this end, the distribution of the L function in the VSCC of a phosphorus in an isolated PH3 has been studied. Figure 1 indicates the zero

(with few exceptions) and many other noncovalent interactions, is not useful for describing all types of pnicogen bonds. Finding a general description for all types of pnicogen bonds is the main objective of the current work. To this end, P···P, P··· N, and N···N interactions between different trivalent pnicogen centers is considered. We will characterize these interactions in terms of the Laplacian of the electron density, which has been previously shown is a powerful tool for describing different types of noncovalent interactions.13,42

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COMPUTATIONAL DETAILS

Laplacian of electron density provides a physical basis (via local statement of virial theorem)43 for the Lewis acid−base interactions. The basic regions in a molecule are, in fact, the zones where the charge is locally concentrated, and conversely, acidic regions are the zones where the charge is locally depleted. So, according to the topology of the Laplacian of electron density, the basic and acidic regions correspond to the (3,−3) and (3,+1) critical points (CPs), respectively. Usually, (3,−3) CP is called lump and (3, +1) CPs is referred to as hole.13,43 Now, an acid−base interaction can be regarded as a lump−hole interaction; a combination of a lump in the valence shell charge concentration (VSCC) of the base with a hole in the VSCC of the acid. According to local virial theorem, it is a reaction of region of excess potential energy on the based atom with a region of excess kinetic energy on the acid atom. In order to gain insight into the origin and nature of pnicogen_pnicogen interactions, homodimer and trimers of PH3 and complexes between PH3/PH2F, PH3/NH3, NH3/ NH3, and NH3/NH2F pairs have been studied. The geometry of the isolated monomers and complexes were fully optimized at second order Moller−Plesset perturbation theory (MP2) with the aug-cc-PVDZ basis set. It has been previously shown that this level of theory is of high accuracy for weak intermolecular interactions of the type of interest here.34,44−46 All of the quantum calculations were performed using the Gaussian 03 program.47 AIMAll program48 was used to find critical points of the Laplacian of electron density and calculate their properties. This package was also used to draw contour and envelope maps of the negative of the Laplacian, L = −∇2ρ, of the electron density.

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RESULTS AND DISCUSSIONS P···P Interactions in Dimers. As indicated by Scheiner,33 there are two minima on the surface of PH3 dimer. In the more stable one, the two P atoms facing one another directly form a P···P bond. Interpretations based only on the electrostatic properties of PH3 suggest that its phosphorus is not able to engage in attractive interactions with nucleophiles. In this point of view, the existence of a positive electrostatic potential (σhole) on the surface of electrophile is a necessary condition for formation of a noncovalent bond between nucleophile and electrophile. However, as indicated by Murray et al.49 and also Scheiner,33 there is no σ-hole on the surface of phosphorus in PH 3 . Consequently, the P···P interaction in the PH 3 homodimer cannot be categorized as σ-hole bonding. That is not saying much, energy decomposition analysis showed that this P···P interaction is not purely electrostatic in nature; instead there is a roughly equal contribution of electrostatic, dispersion, and induction components.19,33 The σ-hole concept is only useful when the electrostatic component plays the main role in the interaction.

Figure 1. Envelope (up) and contour (down) maps of the negative of the Laplacian of the electron density (L) for the PH3 molecule. Red and green points indicate the position of (3,+1) and (3,−3) CPs, respectively. In the contour map, red and blue lines correspond to the positive and negative values of L, respectively.

envelopes map (a set of points where L = 0) for the PH3 molecule. There are three regions of charge depletion (in which L is negative) in the VSCC of phosphorus, almost in the extension of each P−H bond. One of these holes has been also shown in a contour map of L in the Figure 1. These holes correspond to the (3,+1) CPs, which has been indicated by red points in the figures. In addition, there is a nonbonding (3,−3) CP or lump (indicated by a green point) in the VSCC of phosphorus, which corresponds to a region of charge concentration. Now the question is, can the P···P interaction in the PH3 homodimer be interpreted as a combination of a region of charge concentration in the VSCC of P in the PH3 13019



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Figure 2. Contour map of L in the H−P−P−H plane of PH3/PH3 homodimer. Red and green points are (3,+1) and (3,−3) CPs, respectively. Red and blue lines correspond to the positive and negative values of L, respectively.

Figure 3. Contour map of L in the PH2F/PH3 (up) and PH2F/PH2F (down) complexes. Lumps and holes are indicated by green and red points, respectively.

with a region of charge depletion in the second PH3? In other words, can it be regarded as a lump−hole interaction? The positions of lump and holes in the PH3 monomers and also the geometry of PH3 homodimer may help us to find the answer. In fact, lump−hole interactions are highly directional; the geometry of the complexes is determined by the positions of lumps and hole in the monomers. Consequently, for the current case, if the P···P bond is a result of a lump−hole interaction, the H−P−P angle in the complex should be

determined by the position of the hole in the PH3. The H−P− hole angle in the PH3 monomer is about 140°, and hence, according to the lump−hole prediction, an H−P−P angle near to this value is expected for PH3 homodimer. However, the optimized geometry of this complex indicates that this angle is about 178°, considerably greater than the H−P−hole angle. Although this geometry is not in agreement with our primary prediction, considering the distribution of the Laplacian of electron density of PH3 dimer (Figure 2) reveals another 13020



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Figure 4. L contours in the molecular plane of H2CPF (left) and H2CPH (right). Lumps and holes are indicated by green and red points, respectively.

hole on the surface of PH2F at the extension of F−P bond, which may be responsible for formation of P···P bonds. So, the fact that the lump−hole could characterize the P···P bonds in both PH2F/PH3 and PH3/PH3 dimers shows that the distribution of the Laplacian of electron density is a powerful tool for describing pnicogen bonds despite of the nature of stabilizing forces. There is another example that confirms that the lump−hole is better than σ-hole in defining the pnicogen bonds. In a recent work, Del Bene and co-workers38 showed that the molecules with SP2 hybridized P atoms could form complexes stabilized with pnicogen bonds. For example, they found P···P interactions in (H2CPF)2 and (H2CPH)2 complexes. Although, there is a σ-hole on the surface of H2CPF, which may be responsible for formation of (H2C PF)2 complex, the σ-hole on phosphorus in the H2CPH monomer is not well-defined. Conversely, the Laplacian of electron density provides an identical definition for P···P bonds in both complexes. As indicated in Figure 4, both monomers have a hole in the VSCC of P atom, and consequently, the P···P interactions in the both complexes can be categorized as lump− hole interactions. Indeed, the local statement of virial theorem is behind of this advantage of the lump−hole concept; according to this theorem, the L function at a given point, L(r), is related to the potential energy density, V(r), and kinetics energy density, G(r), by43

feature of its P···P interaction. Each PH3 has a hole in the extension of its P−H bond, which can interact with the lump on the other PH3. The P···P interaction in this complex is a result of simultaneous interactions of two holes and two lumps. The H−P−P angle is almost linear because holes (lumps) on the both PH3 are completely identical and have equal tendency to combine with lumps (holes). So, the molecules will be oriented in such a way to provide two simultaneous lump−hole interactions with equal contribution in the P···P interaction. Indeed, P···P in PH3 homodimer is an example of a double lump−hole interaction. To gain a deeper understanding of P···P interaction, one of the hydrogens of PH3 has been replaced with fluorine. Again, the phosphorus of PH2F has three holes in its VSCC; two along the extension of H−P bond and the third along the F−P bond. Obviously, these holes, unlike those of PH3, are not identical and have different L values. The value of L at the CP along F−P bond is about −0.085 au and is more negative than those of H−P bonds (which are about −0.04 au). This means that the hole in the extension of F−P bond has more propensity to combine with a lump than the other two holes. So, one can predict that a P···P bond is forming along the F−P bond, if PH2F interacts with PH3; a predication that is confirmed by geometry optimization of PH2F/PH3 heterodimer. Once more, we deal with a double lump−hole interaction, but unlike PH3 homodimer, the involved holes are not identical. The hole of the PH2F is a better lump acceptor (more negative) than that is of PH3 and plays the main role in the P···P interaction and therefore, the P···P interaction in the PH2F/PH3 complex results from a single lump−hole combination (Figure 3). It is reflected in the geometry of PH2F/PH3 complex; the F−P−P angle deviates from linearity and becomes about 170°. The H− P−P angle shows more deviation and is about 140°, comparable with the 120° of H−P−lump angle in the PH3 monomer. Clearly, a double lump−hole interaction is expected if PH2F interacts with another PH2F (Figure 3). In this case, the holes are identical and hence have equal contribution in the interaction. It should be mentioned that the P···P interactions in the PH2F/PH3 and PH2F/PH2F complexes, unlike in the PH3 homodimer, could also be described according to the σ-hole concept. As indicated by Alkorta et al.,40 there is a positive σ-

1 − L(r ) = 2G(r ) + V (r ) 4

The potential energy density contains the virial of Ehrenfest force and involves the full quantum potential. The electrostatic potential (which is used to define the σ-hole) is only one component of this total potential. In fact, charge depletion in the VSCC of an atom in a molecule does not always result in a positive electrostatic potential and a σ-hole around it. PH3 Trimers. Adhikari and Scheiner50 showed that PH3 molecule can form homotrimers (and even homotetramers) in addition to homodimer. Their calculations indicate that there are eight minima on the surface of trimer, which are stabilized by one, two, or three P···P interactions. The most stable minimum is a nearly equilateral triangle with three P···P bonds. The P···P interactions in this structure are longer than that of 13021



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PH3 homodimer. In addition, the total binding energy of this trimer is slightly less than the three times the binding energy of the dimer. Again, the distribution of the Laplacian of electron density can be used for justification of the existence and geometry of these interactions. Figure 5 indicates the contour

Figure 6. L contours of NH3 (up) and NH2F (down). Black point in the VSCC of NH3 indicates a (3,+1) CP with a positive L. Figure 5. Contour map of L in the symmetry plane of PH3 homotrimer. Lumps and holes are indicated by green and red points, respectively.

formed because both (3,+1) and (3,−3) critical points are regions of excess potential energy density and the Laplacian is negative. However, replacement of one H atom of NH3 with a F atom changes the shape of the VSCC of nitrogen; the Laplacian at the (3,+1) CP becomes positive, and a region of excess kinetics energy density appears in the VSCC of nitrogen atom at the extension of F−N bond (Figure 6). Now, this hole could combine with the lump of NH3 and form a N···N noncovalent bond (Figure 7). However, the optimized geometry of NH3/NH2F complex shows that this lump−hole interaction is not the only stabilizing force, and another interaction such as N···H hydrogen bonds may have an impact in the geometry of the complex. In a same way, the P···N interaction of PH3/NH3 heterodimer can be interpreted based on the lump−hole combination; a lump in the VSCC of nitrogen atom combines with a hole in the VSCC of phosphorus (Figure 7).

map of L in the P−P−P surface of the trimer. It is clear from the figure that all of P···P interactions result from lump−hole attractions. However, in contrast to PH3 homodimer, in which a double lump−hole interaction is responsible for P···P bond formation, there is a single lump−hole interaction between each pair of phosphorus in the trimer. This is maybe the reason why the P···P bonds in trimer are longer and weaker than those of the dimer. In addition, the H−P−P angle in the trimer is 158°, smaller than the same angle in the dimer and closer to the H−P−hole angle of PH3 monomer. In a same way, the P···P interactions in other stable structures of PH3 homotrimer can be interpreted based on lump−hole interaction. Furthermore, the P···P bonds in the cyclic trimers of PH2X (X is a halogen) can be described in terms of lump−hole combination; however, one can categorize them as σ-hole bonds because there is a positive σ-hole on the surface of PH2X.31 N···N and P···N Bonds. As stated in the introduction, previous works showed that when PH3 is paired with NH3 the P and N atoms face one another directly and form a P···N bond.33 In addition, Scheiner51 showed that, although, the two N atom of a pair of NH3 molecules will not interact attractively, the replacement of one H with a F atom results in a N···N interaction. In this part of article, we will see how these observations can be explained by the distribution of the Laplacian of electron density. The distribution of the L for NH3 is shown in Figure 6. As indicated, although there is a (3,+1) CP in the VSCC of nitrogen atom, the Laplacian at this CP is negative (L is positive), and hence, it cannot act as a good partner for the lump of the other NH3, for which the Laplacian is also negative. In other words, N···N bond between a pair of NH3 is not

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CONCLUSIONS The distribution of the Laplacian of electron density has been used to investigate the noncovalent P···P, P···N, and N···N pnicogen bonds. It has been shown that in all of these interactions, a region of charge depletion and excess kinetics energy (hole) in the VSCC of pnicogen atom combines with a region of charge concentration and excess potential energy (lump) on another molecule and forms a pnicogen bond. So, resembling halogen bonds, the pnicogen bonds can be categorized as lump−hole interactions. In describing these interactions, the lump−hole concept is more useful than the σhole because the full quantum potential has been used in the definition of the Laplacian, in contrast to the σ-hole concept in which the electrostatic part of potential is merely considered. In addition, it has been shown that the existence of hole (with positive value of L) in the VSCC of pnicogen atom is a necessary condition for formation of pnicogen bonds (however, 13022



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Figure 7. Contour map of L in the NH3/NH2F (up) and PH3/NH3 (down) complexes. (6) Scheiner, S. Hydrogen Bonding. A Theoretical Perspective; Oxford University Press: New York, 1997. (7) Grabowski, S. J. Hydrogen Bonding: New Insights; Springer: Dordrecht, The Netherlands, 2006; Vol. 3. (8) Gilli, G.; Gilli, P. The Nature of the Hydrogen Bond: Outline of a Comprehensive Hydrogen Bond Theory; Oxford University Press: Oxford, U.K., 2009. (9) Jeffrey, G. A. An Introduction to Hydrogen Bonding; Oxford University Press: New York, 1997. (10) Arman, H. H. D.; Metrangolo, P.; Resnati, G. Halogen Bonding: Fundamentals and Applications; Springer: New York, 2008; Vol. 126. (11) Politzer, P.; Lane, P.; Concha, M. C.; Ma, Y.; Murray, J. S. An Overview of Halogen Bonding. J. Mol. Model. 2007, 13, 305−311. (12) Metrangolo, P.; Neukirch, H.; Pilati, T.; Resnati, G. Halogen Bonding Based Recognition Processes: a World Parallel to Hydrogen Bonding. Acc. Chem. Res. 2005, 38, 386−395. (13) Eskandari, K.; Zariny, H. Halogen Bonding: A Lump−Hole Interaction. Chem. Phys. Lett. 2010, 492, 9−13. (14) Jahromi, H.; Eskandari, K. Halogen Bonding: a Theoretical Study Based on Atomic Multipoles Derived from Quantum Theory of Atoms in Molecules. Struct. Chem. 2013, 24, 1281−1287. (15) Riley, K. E.; Hobza, P. Investigations into the Nature of Halogen Bonding Including Symmetry Adapted Perturbation Theory Analyses. J. Chem. Theor. Comput. 2008, 4, 232−242. (16) Del Bene, J. E.; Alkorta, I.; Elguero, J. Spin− Spin Coupling Across Intermolecular F−Cl···N Halogen Bonds. J. Phys. Chem. A 2008, 112, 7925−7929. (17) Solimannejad, M.; Malekani, M.; Alkorta, I. Substituent Effects on the Cooperativity of Halogen Bonding. J. Phys. Chem. A 2013, 117, 5551−5557. (18) Scheiner, S. Sensitivity of Noncovalent Bonds to Intermolecular Separation: Hydrogen, Halogen, Chalcogen, and Pnicogen Bonds. CrystEngComm 2013, 15, 3119−3124.

this charge depletion in the VSCC of pnicogen does not always result in a σ-hole around it). For example, the phosphorus atoms in PH3, PH2F, H2CPH, and H2CPF can engage in direct P···P or P···N interactions because there is at least one hole in their VSCC. However, since there is no hole in the VSCC of nitrogen atom of NH3, it cannot interact with electron donor species and form a pnicogen bond. However, when one H atom of ammonia replaces with a fluorine atom, a hole appears in the nitrogen VSCC, which could combine with a lump on another molecule and form a pnicogen bond.

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AUTHOR INFORMATION

Corresponding Author

*(K.E.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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REFERENCES

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Pnicogen Bonds: A Theoretical Study Based on the Laplacian of

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