Effects of Substituents upon the P···N Noncovalent Interaction: The

ARTICLE pubs.acs.org/JPCA

Effects of Substituents upon the P 3 3 3 N Noncovalent Interaction: The Limits of Its Strength Steve Scheiner* Department of Chemistry and Biochemistry, Utah State University, Logan, Utah 84322-0300, United States

bS Supporting Information ABSTRACT: Previous work has documented the ability of the P atom to form a direct attractive noncovalent interaction with a N atom, based in large measure on the charge transfer from the N lone pair into the σ* antibonding orbital of the P H that is turned away from the N atom. As the systems studied to date include only hydrides, the present work considers how substituents affect the interaction and examines whether P 3 3 3 N might compete with other attractive forces such as H-bonds. It is found that the addition of electron-withdrawing substituents greatly strengthens the P 3 3 3 N interaction to the point where it exceeds that of the majority of H-bonds. The highest interaction energy occurs in the FH2P 3 3 3 N(CH3)3 complex, amounting to 11 kcal/mol. A breakdown of the individual forces involved attributes the stability of the interaction to approximately equal parts electrostatic and induction energy, with a smaller contribution from dispersion.

’ INTRODUCTION Noncovalent interactions between molecules are every bit as important as the covalent forces that hold atoms together within each molecule. These intermolecular forces are primarily responsible for the properties of liquids and the three-dimensional structures adopted by crystals. Noncovalent forces are not limited to those between molecules but also contribute to the structure of single molecules via interactions between various segments that fold around such that they lie close to one another. As examples from the biological realm, such forces are largely responsible for the conformations adopted by biomolecules such as proteins, DNA, and carbohydrates. There are a range of different noncovalent forces, and various ways of classifying them.1 5 The strongest, and those of the longest range, involve the Coulombic attractions between ions of different charge, or interactions between dipole and higher molecular moments. In addition to purely electrostatic forces, there are also interactions that include a certain degree of covalent nature, which is usually taken to mean charge transfer and polarization effects. Perhaps the most widely recognized of this category are H-bonds, X H 3 3 3 Y, which classically6 12 involve a proton donor X H and acceptor Y. The definition of a H-bond has broadened in recent years13 22 to include C as a proton donor atom, and the acceptor can contribute electron density not only via its lone pair but also through π bonds, σ bonds, metal atoms, and even another H atom. Another sort of noncovalent attraction that is becoming more widely recognized is the halogen bond23 32 which involves the direct interaction between a halogen atom and another electronegative atom. The attractive nature of this interaction derives at least in part from the electrostatic potential around the halogen r 2011 American Chemical Society

atom, which is not wholly negative but contains a small positive region, which can attract an electronegative partner atom on the other molecule. Like the H-bond, the halogen bond also contains elements of induction and dispersion, in addition to Coulombic forces. The literature also contains instances of other attractive forces, between nonhalogen electronegative atoms such as S and O,33 39 although they are not yet as well understood. Recent work in this laboratory has identified a new and fundamentally different sort of noncovalent interaction. The attraction occurs directly between a trivalent P atom and the N atom on another molecule, with no intervening H atom. It was noticed first when HSN interacted with PH3 or other phosphines,40 in that the H atoms on the P rotated around to avoid the P 3 3 3 N axis, maximizing the interaction between the P and N. Further calculations41 pursued this question in more detail, seeking all minima on the potential energy surface of the heterodimer containing NH3 and PH3. The structure containing this P 3 3 3 N interaction was identified as the global minimum on the surface, more stable than a secondary minimum which encompassed a PH 3 3 3 N H-bond. A primary source of the attraction was identified as charge transfer from the N lone pair to the σ* antibond of a P H bond, the latter of which was directed away from the N atom. In addition to this charge transfer effect, there is also a sizable electrostatic attraction, as well as a large dispersion component. Subsequent work42 probed this Special Issue: Pavel Hobza Festschrift Received: April 28, 2011 Revised: June 22, 2011 Published: July 05, 2011 11202

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The Journal of Physical Chemistry A issue further, investigating whether such an interaction is limited to P or represents a broader phenomenon. It was learned that the first-row N congener was incapable of engaging in a direct N 3 3 3 N interaction of this type. On the other hand, secondrow atoms, i.e., S and Cl, could also participate in a X 3 3 3 N interaction with an N lone pair, as could the third row congener As. Intriguingly, the strength of this interaction was surprisingly insensitive to the nature of the atom involved.42 Interaction energies and intermolecular equilibrium distances for X = P, S, Cl, and As spanned fairly narrow ranges, as did various components of the interaction, such as electrostatic, induction, and dispersion energies. The previous investigations have been limited to the simple hydrides of each of the atoms above. Many other noncovalent interactions, such as H and halogen bonds, are strongly influenced by the presence of substituents on the partner molecules. H-bond proton donor molecules, for example, are greatly strengthened by electron-withdrawing substituents. The present work thus focuses on the question of how various substituents affect the ability of the P atom to form a P 3 3 3 N interaction. It goes on to probe the limits of this interaction: just how strong can the noncovalent P 3 3 3 N force become? Can it compete with other well-known intermolecular forces such as H-bonds, and under what conditions might the P 3 3 3 N attraction be favored?

’ COMPUTATIONAL METHODS Calculations were carried out using the Gaussian 03 package.43 Geometries were optimized at the ab initio MP2 level, using the aug-cc-pVDZ basis set, designed specifically44 for correlated calculations, and which has been shown to be of high accuracy, and to provide excellent results, especially when combined with MP2 correlation. For example, a recent study45 of weak intermolecular interactions found MP2/aug-cc-pVDZ results within 0.04 kcal/mol of CCSD(T) data. And another very recent work46 demonstrated that this same theoretical approach matched experimental binding energetics almost perfectly. As a further check on the computational methods, additional calculations were carried out using the larger aug-cc-pVTZ basis set,44 applying not only the MP2 procedure but also the higher-level CCSD(T).47 49 The MP2 computations employed the frozencore approximation. Minima were identified using a range of starting points for geometry optimizations; structures were verified as minima by having all real vibrational frequencies. Interaction energies were computed as the difference in energy between the dimer, and the sum of the optimized energies of the isolated monomers. These quantities were corrected for basis set superposition error by the counterpoise procedure,50 and by zero-point vibrational energies. Natural bond orbital (NBO) analysis51,52 was carried out via the procedures contained within Gaussian 03. The interaction energy was decomposed by the symmetry-adapted perturbation theory (SAPT) procedure,53,54 implemented via the MOLPRO set of codes,55 using its HF variant with the aug-cc-pVDZ basis set. ’ RESULTS NH3 was paired with a variety of substituted phosphines XPH2, with X = CH3, NH2, CF3, HO, Cl, F, and NO2. The geometries optimized for the X P 3 3 3 N complexes are illustrated in Figure 1 for all substituents examined. The structures are all rather similar, with the P X covalent bond turned away from the P 3 3 3 N axis by 163 173°. In most cases the N lone pair

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Figure 1. Optimized geometries of the XP 3 3 3 N complexes with NH3 for X = (a) CH3, (b) H, (c) NH2, (d) CF3, (e) OH, (f) Cl, (g) F, and (h) NO2. Distances in Å and angles in degrees.

points directly at the P atom, with the exceptions of CH3PH2 and PH3 in Figure 1a,b where the lone pair is oriented upward, toward one of the HP atoms. In addition to facilitating a PH 3 3 3 N H-bond, one of the NH3 H atoms is 161 163° away from the P 3 3 3 N axis, which facilitates a certain amount of reciprocal Plp f σ*(NH) charge transfer. It might be noted that including counterpoise correction directly into the geometry optimization procedure had little effect. In the case of FH2P 3 3 3 NH3, for example, there is a slight lengthening of the intermolecular separation, by 0.09 Å, but the θ(FP 3 3 3 N) angle was unchanged. More importantly, the interaction energy was altered by less than 0.1 kcal/mol. Some of the most important properties of these complexes are summarized in Table 1. The counterpoise-corrected interaction energies, ΔECC, span the range of 1.33 kcal/mol for the methyl substituent up to a maximum of 6.59 kcal/mol for NO2. The columns of Table 1 are arranged in order of increasingly negative ΔECC and show that the methyl group slightly weakens the interaction with respect to an H atom, but the various substituents progressively add to the attraction in the order NH2 < CF3 < HO < Cl < F < NO2. The intermolecular R(P 3 3 3 N) distances come down from a maximum of 3.35 Å for the methyl substituent to 2.62 Å for F, more or less in close correspondence with the interaction energy. To ensure that the energetics are reliable, computations were also carried out with the larger triple valence aug-cc-pVTZ basis set. The binding energies are reported in the next row of Table 1, where a small but uniform enhancement is observed with the larger set. Applying the CCSD(T) approach, again with the larger aug-cc-pVTZ basis, leads to a very small change as well, in this case a slight reduction in the binding energy. In sum, these augmentations of basis set or method of including correlation leave the energetics essentially unchanged and have no effect upon the trends. 11203

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Table 1. Energetic (kcal/mol), Geometric, and Electronic Aspects of XP 3 3 3 N Complexes, All with NH3 as Proton Acceptora H3CPH2

HPH2

H2NPH2

F3CPH2

HOPH2

ClPH2

FPH2

O2NPH2

ΔE

2.16

2.05

3.19

4.58

4.90

6.99

7.89

8.30

ΔECC MP2/aug-cc-pVDZb

1.33

1.43

2.09

3.40

3.58

5.35

6.19

6.59

ΔECC MP2/aug-cc-pVTZ

1.58

1.66

2.38

3.66

4.17

5.62

6.59

7.46

ΔECC CCSD(T)/ aug-cc-pVTZ

1.53

1.58

2.28

3.60

3.87

5.17

6.09

7.23

ΔECC+ZPEc

0.61

0.41

1.12

2.36

2.18

3.66

4.22

4.78

R(X 3 3 3 N), Å Δq,d me

3.353

3.302

3.090

3.034

2.870

2.697

2.624

2.645

1.4

2.0

7.1

8.8

16.5

34.6

33.3

40.6

E(2),e kcal/mol Δr(X P), mÅ

0.76 0.2

1.18 2.7

4.19 7.0

4.93 4.2

9.20 15.2

16.51 42.8

18.18 26.5

20.05 21.9

a Data computed at the MP2/aug-cc-pVDZ level except where indicated otherwise. b CC = counterpoise corrected. c Zero-point vibrational energy correction, computed at the MP2/aug-cc-pVDZ level. d Nlp f σ*(X P) charge transfer. e NBO perturbation energy corresponding to Nlp f σ*(X P).

Figure 2. Variation of second-order energy and amount of charge transferred from N lone pair to σ*(XP) antibonding orbital as a function of total interaction energy, ΔE.

Zero-point vibrational energies are added to the MP2/aug-ccpVDZ values in the next row of Table 1. The additional vibrational modes in the complexes, as compared to the separated monomers, lead to a general reduction in the binding energies by an amount that varies between 0.7 and 2.0 kcal/mol. But all complexes remain bound and the trends from one substituent to the next remain unchanged. The next few rows of Table 1 are associated with the charge that is transferred from the N lone pair to the X P σ* antibond. NBO analysis of this phenomenon yields the magnitude of this transfer, Δq, and a second-order perturbation energy E(2), which is associated with it. This accumulation of density in the antibonding orbital causes a stretch in the X P bond, which is reported as Δr in the last row of Table 1. The two NBO measures of charge transfer, Δq and E(2), are plotted against the full interaction energy in Figure 2 where it may be seen that they are both correlated rather closely with ΔE. The main exception is the charge transfer Δq for Cl is a bit larger than that of F, although the former substituent results in a somewhat weaker total interaction. And, indeed, this larger charge transfer into the P Cl σ* antibond is reflected in a disproportionately long bond stretch

of more than 0.04 Å, the largest bond elongation of any of the systems considered here. Source of Stability. A decomposition of each total complexation energy provides a valuable aid in understanding the source of the bonding. The SAPT components are reported in Table 2, again in the same order of increasing total binding energy from left to right. The various terms follow the same trend as the full ΔE, in that they all increase in magnitude from left to right. The only exception is a very small dip in IND and DISP on going from F to NO2, with the increase in ES making up the difference. The close correspondence between the three attractive terms with each other, and with the total energy, is exhibited in Figure 3. The growth in each term is not quite linear but approximately so. It is worth noting that the ES and IND terms are very nearly equal to one another, making comparable contributions to the total. Smaller in magnitude, but certainly not unimportant, is the dispersion. The latter grows more slowly than do ES and IND as the substituent becomes more electron-withdrawing. While DISP is approximately equal to ES and IND for X = H and CH3, it is only about one-third their magnitude for X = F. One might note that there is a great deal of similarity between the IND term in Table 2 and the E(2) quantity in Table 1. In most cases, they are within less than 1 kcal/mol of each other. Because the induction energy includes in principle not only that which corresponds to the Nlp f σ*(X P) interaction but also any other contributions, this similarity speaks to the dominance of this particular charge transfer element in the context of the full electron density shifts between the two molecules. Although of obvious importance, the Nlp f σ*(X P) charge transfer is not the only electronic rearrangement that occurs upon the formation of each complex. In addition to shifts from one molecule to another, there are also internal rearrangements within each monomer. The full panoply of total electron density redistribution is on display in Figure 4 for each of the complexes, where yellow regions represent charge buildup and depletion of density is indicated by brown. There is a pattern commonality in all of these dimers, first in that a yellow increase occurs on the N lone pair, in concert with a larger area of charge loss immediately to the right of the P atom. Buildup is observed also within the P X bond, as well as on the far (left) side of most of the substituents. The far right, on the remote side of the N atom, suffers a substantial loss of charge as indicated by the large brown area. While the patterns are very much the same for all substituents, there is a general enlargement of the magnitudes as one progresses from the weakest (CH3) to the strongest (NO2) substituent. 11204

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Table 2. SAPT Decompositions (kcal/mol) of the Complexation Energies of the XP 3 3 3 N Bonded Complexes, All with NH3 as Partner Molecule H3CPH2

HPH2

H2NPH2

F3CPH2

HOPH2

ClPH2

FPH2

O2NPH2

ES

2.40

2.68

4.84

7.55

9.45

15.62

18.21

19.25

EX IND

3.00 1.43

3.16 1.68

5.97 3.86

7.45 5.37

11.27 8.63

19.04 16.21

22.07 19.91

21.41 19.80

IND+EXIND

0.27

0.34

0.76

1.26

1.71

3.41

4.08

4.52

DISP

2.09

2.04

3.06

3.27

4.35

5.89

6.39

6.17

DISP+EXDISP

1.77

1.72

2.49

2.63

3.43

4.53

4.90

4.74

TOTAL

1.44

1.59

2.12

3.99

3.32

4.51

5.11

7.11

Figure 3. Variation of SAPT electrostatic, induction, and dispersion energies as a function of total interaction energy, ΔE, for various substituents on the P atom of PH3.

Given the rather large contribution of electrostatics to the stability of these complexes, it is important to consider the root of this force. One would expect that the negatively charged N atom and its lone pair would be most attracted by a positive electrostatic potential as it approaches the P atom. The electrostatic potentials of the various monomers are illustrated in Figure 5 where red and blue regions correspond respectively to negative and positive regions of potential. A broken magenta line is provided in each figure to indicate the direction of approach of the N atom toward the P. When approaching the CH3PH2 molecule, this N would experience first a negative potential and then a positive area as it penetrates more closely to the P. For the other substituents, however, the approach line is completely surrounded by a blue positive potential, facilitating the complexation. While helpful in understanding the source of the electrostatic attraction, there is no obvious quantitative correlation between the extent of the blue contour and the magnitude of the electrostatic attraction. Of course, the ES term is guided not only by the extent of the positive region but also by how closely the N atom can penetrate as it achieves its equilibrium separation from P, so a strict correlation is not necessarily to be expected. It is worth noting as well that, while electrostatics certainly play a key role in the geometry adopted by each complex, there are other important factors as well. That is, if the geometry were

Figure 4. Density shifts occurring in the indicated XP 3 3 3 N complexes upon formation of each complex. Yellow regions indicate density increase, brown a decrease. Contours are shown at the 0.0005 au level.

governed by electrostatics alone, then the nucleophile NH3 would not approach along the magenta lines in Figure 5 but would rather take a different path that would lie directly along the main blue positive lobes. Thus, instead of the θ(X P 3 3 3 N) angles that are near 180° in these complexes, electrostatic considerations alone would lead to much smaller angles of perhaps 120° or so. The nearly linear geometries can be ascribed in large part to the maximization of the overlap between the N lone pair and the P X σ* orbital. Secondary Minima. Given the perhaps unexpected structures of the dimers in Figure 1, it would be natural to wonder whether these geometries represent true minima on the potential energy surface, and if so, are they the global minimum. All of the complexes in Figure 1 are in fact true minima, with all positive vibrational frequencies. In most cases, they are also the global minimum, lower in energy than other minima that exist on the surface. One obvious exception is the complex of NH3 with HOPH2: an alternate geometry that contains a strong OH 3 3 3 N H-bond is lower in energy than the P 3 3 3 N minimum, with a counterpoise-corrected interaction energy of 7.9 kcal/mol vs 3.6 kcal/mol for P 3 3 3 N. (This, and all minima not displayed 11205

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case of ClPH2 the interaction energy of this secondary minimum is only half of that in Figure 1; the ratio is closer to 1/3 for FPH2. There is an alternate minimum on the surface of the complex pairing NH3 with F3CPH2, which contains three H-bonds: two NH 3 3 3 F and one PH 3 3 3 N. However, even these three attractions in sum are less of a binding force than the single P 3 3 3 N interaction in Figure 1, weaker by 0.5 kcal/mol in total. Another minimum, containing a pair of NH 3 3 3 F H-bonds is still more weakly bound. One might anticipate that the powerful proton-accepting ability of the O atoms in O2NPH2 could form reasonably strong NH 3 3 3 O H-bonds with the NH3. Such bonds do in fact occur, but the complexes in which they are present are considerably less stable than the global minimum, which relies purely on the P 3 3 3 N interaction for its stability. There is, for example, a complex that combines a NH 3 3 3 O H-bond with another of the PH 3 3 3 N type, but this structure has a binding energy roughly half that of the global minimum. Another structure has a pair of NH 3 3 3 O H-bonds but is even less stable, bound by less than 1 kcal/mol after ZPE corrections are included. In the case of the CH3PH2 molecule, the weakness of the CP 3 3 3 N interaction opens the possibility that other structures might be competitive in energy. And, indeed, the switching of the methyl group with one of the PH hydrogens replaces the CP 3 3 3 N bond with its HP 3 3 3 N counterpart. While the latter is weaker than the former, the structure in which it appears also contains a CH 3 3 3 N H-bond, which is reinforced by the rotation of the NH3 lone pair toward the pertinent methyl H atom. Together, these two forces are competitive with the single CP 3 3 3 N attraction, making the two minima essentially identical in energy. Like PH3, CH3PH2 also forms a second, and much weaker, complex with NH3, which contains a PH 3 3 3 N H-bond.

Figure 5. Electrostatic potentials of substituted monomers of PH3. Red and blue colors denote negative and positive potential, respectively, all at the (0.005 au contour. Magenta broken line indicates projection of X P bond to right of P atom.

in Figure 1, are reported graphically in the Supporting Information.) Another parallel exception arises in the context of the NH2 substituent. The potency of this group as a proton donor leads to a number of NH 3 3 3 N H-bonded complexes, some of which contain a secondary H-bond. But the halogen atoms of the other substituents obviously cannot act as strong proton donors to the N lone pair, as can OH. Nor are the halogens potent enough proton acceptors to form a NH 3 3 3 X H-bond strong enough to compete effectively with the P 3 3 3 N attraction. For example, both FPH2 and ClPH2 engage in a secondary complex with NH3, in which the halogen atom switches places with one of the phosphine H atoms. The F/Cl atom is thus in position to form a weak and angularly distorted NH 3 3 3 X H-bond with the NH3, which supplements the remaining HP 3 3 3 N interaction. But even taken together, these two attractive interactions amount to less stabilization than the single X P 3 3 3 N interaction in the primary minima of Figure 1. In the

’ CONCLUSIONS AND DISCUSSION The replacement of one H atom of PH3 by various substituents has a strengthening effect upon the P 3 3 3 N interaction, which varies in the order CH3 ∼ H < NH2 < CF3 < OH < Cl < F < NO2. The counterpoise-corrected interaction energy climbs from a minimum of 1.3 kcal/mol to 6.6 kcal/mol for the strongest O2NPH2 electron acceptor. Along with this bond strengthening, one sees a concomitant contraction of the intermolecular separation. Also running parallel to the interaction energy are its component terms: The electrostatic and induction energies are very nearly equal to one another throughout the series, whereas the dispersion energy rises less quickly and varies from equal contributor for X = H and CH3 to only about 30% the magnitude of ES and IND for the NO2 substituent. A large portion of the induction energy can be associated with the transfer of charge from the N lone pair to the P X σ* antibonding orbital. Both the amount of NBO charge transferred and the second-order perturbation energy E(2) run parallel to the induction energy, and E(2) is rather similar in magnitude to the total induction energy. Another indicator of this charge transfer to the P X antibond is the lengthening that this bond undergoes as a result of the complex formation, which is also roughly proportional to the total interaction energy. The favorable electrostatic component can be understood on the basis of the electrostatic potential around each electron acceptor molecule. The chosen direction of approach, roughly antipodal to the P X bond, lies along a positive region of the potential. At the same time, this direction is not the most favored from a purely 11206

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The Journal of Physical Chemistry A electrostatic perspective, which would tend toward a more acute angle of approach. It is concluded then that the angular characteristics arise from a combination of electrostatic and n f σ* charge transfer effects. Mapping of total density shifts show similar features for all complexes, although the magnitudes of the shifts rise along with the interaction energy. The patterns appear to be a fingerprint of these P 3 3 3 N interactions, as they differ from those of H-bonds and halogen bonds.41 In all cases, electron density is gained in the lone pair region of the N, and lost immediately to its left, near the P atom. There is a shift of density away from the H atoms of NH3, and toward the X substituent on the P atom. The parallel behavior of the total interaction energy with the ES, IND, and DISP components of the interaction energy, as well as other markers such as E(2) and Δq, is auspicious for attempts to predict interaction energy based on simpler quantities. For example, prior work56,57 has indicated that the evaluation of the magnitude of the electrostatic potential at one particular point in the vicinity of the electron acceptor atom correlates well with the total interaction energy in complexes related to those described here. Likewise, one could imagine markers that would correlate with induction energy and the capability to engage in n f σ* transfer. And, indeed, it is noted that the stronger complexes are associated with XPH2 molecules that have a lower σ* energy, closer in energy to the lone pair of NH3, and so better able to interact with one another. It is perhaps remarkable that a direct interaction between the P and N atoms, with no intervening H, is as strong as it is. This interaction is a prominent feature of the global minimum in most cases, stronger than the various H-bonds that participate in the secondary minima. This P 3 3 3 N interaction is clearly stronger than PH 3 3 3 N H-bonds that are possible for each pair. This superiority of P 3 3 3 N over PH 3 3 3 N is especially notable in view of the strongly electron-withdrawing substituents, such as F, CF3, and NO2, that would normally be expected to amplify the proton-donating potential of the PH. The P 3 3 3 N interaction is also more powerful than other sorts of H-bonds with which it competes, such as NH 3 3 3 F or NH 3 3 3 Cl H-bonds, and even surpasses the NH 3 3 3 O H-bonds that are possible for the OH and NO2 substituents. Indeed, the only sort of H-bond that is stronger than P 3 3 3 N is the OH 3 3 3 N H-bond in the H2POH 3 3 3 NH3 complex, or NH 3 3 3 N for X = NH2. One can place the P 3 3 3 N interaction in perspective by comparison with the prototypical H-bond of the water dimer. The counterpoisecorrected OH 3 3 3 O H-bond energy in that system, at the same theoretical level as applied here, amounts to 4.43 kcal/mol, which is surpassed by the XP 3 3 3 N interaction energy with three substituents: X = Cl, F, and NO2. And indeed, while the counterpoise-corrected interaction energies between 6 and 7 kcal/mol for the complexes of NH3 with FH2P and O2NPH2 are quite large, they do not represent the maximum attainable for this sort of interaction. Just as substitutions on the electron acceptor phosphine are capable of enhancing the interaction, the same is true of the electron donor. When the NH3 molecule of the FH2P 3 3 3 NH3 complex was replaced by the trialkylated N(CH3)3, the interaction energy grew from 6.2 to 10.9 kcal/mol, between 2 and 3 times the magnitude of the H-bond energy in the water dimer. Commensurate with this strong interaction is a short R(P 3 3 3 N) of only 2.325 Å. There are a handful of previous computational data that might serve as a point of comparison. Murray et al.58 had surmised that

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neither PH3 nor P(CH3)3 would engage in such a bond on the basis of their analysis of their electrostatic potentials and so did not pursue the matter further. They did, however, consider complexes of the trisubstituted PF3 and P(CN)3 molecules with the N lone pair of HCN, which were both predicted to be stable. Both structures resembled the P 3 3 3 N complexes considered here in that the X P 3 3 3 N angles were close to linearity. In terms of monosubstitution, a strongly electron-withdrawing NO2 group enabled59 NO2PH2 to form a complex with the N lone pair of HCN. The binding energy was computed at the MP2/6311++G(3df,2p) level to be 5.5 kcal/mol. This quantity is apt to be inflated by basis set superposition, which was not addressed, and so would probably be closer to 4 kcal/mol, following counterpoise correction. Crystal structure analyses provide support for some of the ideas expressed here. When PBr3 was paired with 1,4-dimethylpiperazine, the two molecules were oriented60 such that one of the Br atoms of PBr3 lies directly opposite the N atom, with a θ(BrP 3 3 3 N) angle of 179.5°, and the N lone pair points directly toward the P atom. Moreover, the pertinent P Br bond was stretched by 0.08 Å relative to the other two P Br bonds that are not involved in the charge transfer into a σ*(P Br) antibond, confirming an important tenet of the proposed source of the bonding. A later work61 likewise identified a P 3 3 3 N noncovalent interaction in the structure of a hypercoordinate acetylene phosphorus molecule. One P-bonded acetylene group lies directly opposite the N atom, θ(CP 3 3 3 N) = 177°, whose P C bond length is longer by 13.4 mÅ than the other P C bond. Short P 3 3 3 N distances (2.44 2.57 Å) were also identified62 in an intramolecular contact involving three separate molecules, wherein P was covalently bonded to 2 Cl atoms, and N bonded to three methyl groups. In all cases, the alignment was nearly linear, with θ(ClP 3 3 3 N) = 172 174° and once again, there was a significant stretch, by 0.08 Å, of the P Cl bond that lay opposite the N atom. Earlier calculations41 had indicated that a pair of P atoms can engage in an interaction very much like the P 3 3 3 N noncovalent bonding considered here. And indeed, the recent literature also contains evidence of a comparable P 3 3 3 P covalent interaction. For example, structure determination63 of a series of diphosphafunctionalized naphthalenes found R(P 3 3 3 P) distances of 2.77 2.81 Å. The structure of 1,2-(diphenylphosphino)-1,2dicarba-closo-dodecaborane64 and related molecules65 contained interphosphorus distances in the range between 3.15 and 3.22 Å. In agreement with the ideas expressed here for P 3 3 3 N, the authors attributed this close approach to electron donation from the lone pair of one P to the antibonding P C orbital of the other. A more recent work66 found short P 3 3 3 P distances in a series of closo-dicarbaboranes, for which some degree of noncovalent bonding was further indicated by through-space coupling. Calculations confirmed Plp f σ*(P C) charge transfer as a contributing factor. Calculations were also applied to P 3 3 3 P interactions67 with a variety of different substituents on each P atom; the data confirm our own finding in the P 3 3 3 N case that the strongest interaction involves F-substitution (NO2 was not considered). In conclusion, the addition of electron-withdrawing substituents exerts a powerful strengthening influence upon the P 3 3 3 N interaction, capable of bringing its interaction energy up higher than the majority of H-bonds. Indeed, most of the complexes examined here forego the possibility of any of several sorts of H-bonds so as to engage in a P 3 3 3 N interaction, which is favored 11207

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The Journal of Physical Chemistry A energetically. This sort of noncovalent force should therefore be entitled to take its rightful place in the pantheon of molecular interactions.

’ ASSOCIATED CONTENT

bS

Supporting Information. Graphical descriptions of all minima not illustrated in Figure 1. This information is available free of charge via the Internet at http://pubs.acs.org/.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

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