Substituent Effects on the Properties of Pnicogen-Bonded Complexes

Article pubs.acs.org/JPCA

Substituent Effects on the Properties of Pnicogen-Bonded Complexes H2XP:PYH2, for X, Y = F, Cl, OH, NC, CCH, CH3, CN, and H Janet E. Del Bene,*,† Ibon Alkorta,*,‡ and José Elguero‡ †

Department of Chemistry, Youngstown State University, Youngstown, Ohio 44555, United States Instituto de Química Médica (IQM-CSIC), Juan de la Cierva, 3, E-28006 Madrid, Spain

‡

S Supporting Information *

ABSTRACT: Ab initio MP2/aug′-cc-pVTZ calculations have been carried out on the pnicogen-bonded homodimers (PH2X)2 and the binary complexes H2XP:PYH2, for X, Y = F, Cl, OH, NC, CCH, CH3, CN, and H. The binding energies of these complexes are influenced by the nature of the X,Y pair, the intermolecular distance, the relative orientation of the interacting molecules, and the charge-transfer energies from the lone pair of one P to the σ-hole of the other. Binary complexes with X,Y = F, Cl, OH, and NC, as well as the homodimers, have a trans arrangement of the P−A and P−A′ bonds with respect to the P···P bond, with A and A′, the atoms of X and Y, respectively, bonded to the P atoms. The trendlines for the homodimers in plots of the binding energy versus the P−P distance, and the binding energy versus the total charge-transfer energy, exhibit better correlations than the trendlines for the binary complexes. The trendlines for the homodimers mark the boundary of the region in which points for the binary complexes appear. Pnicogen-bond radii for P in PH2X molecules have been determined from the P−P distances in the homodimers. The sum of these radii provides an excellent approximation to the P−P distance in the corresponding binary complex. EOM-CCSD spin−spin coupling constants 1pJ(P−P) have also been computed for all complexes. Coupling constants for the dimers and binary complexes exhibit a similar linear increase as the P−P distance decreases.

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INTRODUCTION The pnicogen bond, an intermolecular bond involving a group 15 atom as an electron-pair acceptor, has been a topic of interest in the recent literature. A number of studies have indicated the presence of this interaction in solid-state crystal structures.1−7 Most theoretical studies of the pnicogen bond have examined the P atom as the electron-pair acceptor, with emphasis on PH3 and its substituted derivatives.8−20 In some of our previous studies, we have focused on P···P pnicogen bonds in dimers (PH2X)221 and (H2CPX)2,22 and some mixed binary complexes including H 2 XP:P(X)CH 2 23 and H2XP:PCX,24 for X = F, Cl, OH, NC (bonded at both C and N), CCH, CH3, and H. By optimizing structures of the (PH2X)2 and (H2CPX)2 dimers in which P···P−A could approach linearity, with A the atom of X directly bonded to P, we have made the two molecules equivalent, thereby ensuring that there is no net charge transfer between them. While these studies have yielded a significant amount of new information about the pnicogen bond, more could be learned about this bond by removing this restriction. In the present study, we have investigated the binary complexes H2XP:PYH2, with X and Y the same substituents defined above. The dimers (PH2X)2 have C2h symmetry, while the binary complexes have Cs symmetry, both having P−P−A and P−P−A′ lying in the symmetry plane and having the opportunity to approach linearity if energetically favorable. A and A′ are the atoms of X and Y which are bonded to Px and Py, © XXXX American Chemical Society

respectively. We have determined the structures, binding energies, charge-transfer energies, bonding properties, and spin−spin coupling constants of these complexes, and we have compared them with the properties of the corresponding homodimers (PH2X)2. In this paper, we report the results of this investigation.

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METHODS The structures of the isolated monomers and the complexes H2XP:PYH2, for X,Y = F, Cl, OH, NC (bonded at both C and N), CCH, CH3, and H were optimized at second-order Møller−Plesset perturbation theory (MP2)25−28 with the aug′cc-pVTZ basis set.29 This basis set is derived from the Dunning aug-cc-pVTZ basis set by removing diffuse functions from H atoms.30,31 Frequencies were computed to establish that the optimized structures correspond to equilibrium structures on their potential surfaces. The binding energies of these complexes were computed as the difference between the total energy of the complex and the sum of the energies of the optimized monomers. All calculations were performed using the Gaussian 09 program.32 The electron densities of the complexes have been analyzed using the Atoms in Molecules (AIM) methodology33−36 and Received: November 24, 2014 Revised: December 3, 2014

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dx.doi.org/10.1021/jp5117504 | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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Table 1. MEP Maxima and Minima [V(Smax) and V(Smin), au] at P on the 0.001 au Electron Density Isosurfaces of PH2X Molecules

a

PH2X, X =

F

Cl

OH

NCa

CCH

CH3

CNa

H

V(Smax) V(Smin)

+0.0597 −0.0191

+0.0534 −0.0148

+0.0395 −0.0240

+0.0682 −0.0047

+0.0341 −0.0222

+0.0128 −0.0343

+0.0577 −0.0029

+0.0205 −0.0257

The atom written first is the atom bonded to P.

the Electron Localization Function (ELF),37 employing the AIMAll38 and Topmod39 programs. The topological analysis of the electron density produces the molecular graph of each complex. This graph identifies the location of electron density features of interest, including the electron density (ρ) maxima associated with the various nuclei, saddle points which correspond to bond critical points (BCPs), and ring critical points which indicate a minimum electron density within a ring. The zero gradient line which connects a BCP with two nuclei is the bond path. The electron density at the BCP (ρBCP), the Laplacian of the electron density at the BCP (∇2ρBCP), and the total energy density (HBCP) are additional useful quantities for characterizing interactions.40 The Natural Bond Order (NBO)41 method has been used to analyze the stabilizing charge-transfer interactions using the NBO-6 program.42 Because MP2 orbitals are nonexistent, the charge-transfer interactions have been computed using the B3LYP functional43,44 with the aug′-cc-pVTZ basis set at the MP2/aug′-cc-pVTZ complex geometries, so that at least some electron correlation effects could be included. Spin−spin coupling constants were evaluated using the equation-of-motion coupled cluster singles and doubles (EOMCCSD) method in the CI(configuration interaction)-like approximation,45,46 with all electrons correlated. For these calculations, the Ahlrichs47 qzp basis set was placed on 13C, 15 N, 17O, and 19F, and the qz2p basis set on 31P and 35Cl. The Dunning cc-pVDZ basis set was placed on all hydrogen atoms. The EOM-CCSD calculations were performed using ACES II48 on the IBM Cluster 1350 (Glenn) at the Ohio Supercomputer Center.

Figure 1. Molecular electrostatic potential of PH2Cl showing regions of positive and negative charge. The color code is the following: red > 0.035 > yellow > 0.017 > green > 0.00 > blue. The positions of local minima and maxima are indicated with light blue and black dots, respectively.

The data of Tables 1 and 2 show that (PH2F)2 has the greatest binding energy of −34.0 kJ mol−1 at the shortest P−P distance of 2.471 Å, while (PH3)2 has the smallest binding energy of −7.1 kJ mol−1 at the longest P−P distance of 3.589 Å. Figure 2 presents two plots of these variables, one for the homodimers which has a correlation coefficient R2 of 0.982, and the other for the binary complexes which has a reduced correlation coefficient of 0.840. In Figure 2, it can be seen that most of the points for the binary complexes lie above the trendline for the homodimers, which indicates that at the same P−P distance, the binary complexes are usually more stable than the homodimer. Why is the correlation coefficient of the trendline relating the binding energy to the intermolecular distance for binary complexes relatively low, certainly compared to that of the homodimers? An examination of Table 2 shows that the nature of X itself influences the binding energy of its complex with Y, as evident from the following orderings of binding energies.

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RESULTS AND DISCUSSION Monomers. As is well-known, molecules containing phosphorus atoms can form intermolecular P···P pnicogen bonds as one P acts as an electron-pair donor to the σ-hole of the other. Table 1 presents the maxima and minima molecular electrostatic potential (MEP) values on the 0.001 au electron density isosurfaces of the monomers PH2X, and Figure 1 illustrates the MEP for the PH2Cl molecule. Potential donation by P of a lone pair is evidenced by the values of V(Smin), and lone-pair acceptance by the values of V(Smax). Structures, Binding Energies, and Charge-Transfer Energies of Complexes H2XP:PYH2. The structures, total energies, and molecular graphs of complexes H2XP:PYH2 are reported in Table S1 of the Supporting Information. The binding energies of complexes H2XPx:PyYH2 are reported in Table 2. These are arranged according to decreasing binding energy of the homodimers (PH2X)2, which appears on the diagonal. The homodimers have C2h symmetry, while the remaining binary complexes have Cs symmetry. The structures of these complexes are described by the P−P distances in Table 3 and the Py-Px-A and Px-Py-A′ angles in Table 4, with A and A′ the atoms of X and Y, respectively, which are directly bonded to Px and Py.

For X = F:

Y = F > OH > Cl > CN > NC ≈ CCH > H > CH3

For X = NC: X = CN:

Y = CN > F > OH > Cl ≈ CCH > H > NC > CH3

Y = F > NC ≈ Cl > OH ≈ CH3 > H ≈ CCH > CN

Thus, for X = F, the homodimer (PH2F)2 has a higher binding energy than any other binary complex containing F. In contrast, when X is NC or CN, the binding energies of the homodimers [PH2(CN)]2 and [PH2(NC)]2 are relatively low, while the corresponding mixed binary complex H2(NC)P:P(CN)H2 has a high binding energy. From the P−P distances in Table 3, it is possible to deduce pnicogen-bond radii for each PH2X molecule, which are analogous to previously developed radii for molecules involved in hydrogen bonds.49−51 The pnicogen-bond radius for P in each PH2X molecule can be assigned as half of the P−P distance in the corresponding homodimer. Using these values, the complete matrix of intermolecular distances can be predicted for the H2XP:PYH2 complexes. The largest deviations B



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Table 2. MP2/aug′-cc-pVTZ Binding Energies (ΔE, kJ mol−1) of Complexes H2XP:PYH2

a

H2XP =

H2FP

H2ClP

H2(OH)P

H2(NC)Pa

H2(CCH)P

H2(CH3)P

H2(CN)Pa

H3P

PYH2 = PFH2 PClH2 P(OH)H2 P(NC)H2a P(CCH)H2 P(CH3)H2 P(CN)H2a PH3

−34.0 −26.8 −28.6 −21.5 −21.3 −16.4 −25.0 −19.2

−22.1 −22.8 −17.8 −17.9 −13.6 −21.3 −16.2

−20.6 −20.1 −15.3 −14.6 −15.8 −12.9

−13.8 −17.5 −11.0 −21.8 −16.8

−12.2 −12.6 −11.8 −9.8

−8.9 −15.4 −8.1

−8.4 −12.1

−7.1

The atom written first is the atom bonded to P.

Table 3. P−P Distances (R, Å) in Complexes H2XP:PYH2 H2XP =

H2FP

H2ClP

H2(OH)P

H2(NC)P

H2(CCH)P

H2(CH3)P

H2(CN)P

H3P

PYH2 = PFH2 PClH2 P(OH)H2 P(NC)H2 P(CCH)H2 P(CH3)H2 P(CN)H2 PH3

2.471 2.620 2.631 2.771 2.955 2.994 2.931 3.060

2.768 2.777 2.929 3.084 3.127 3.050 3.188

2.851 2.934 3.139 3.141 3.168 3.255

3.040 3.217 3.239 3.158 3.268

3.353 3.387 3.405 3.471

3.481 3.397 3.529

3.375 3.490

3.589

Table 4. P···P−A and P···P−A′ Angles in Complexes H2XP:PYH2a,b Cl > OH > NC, which is the same order as decreasing binding energies. Between the points for (PH2F)2 and (PH2Cl)2 in Figure 7 are four points at 175 kJ mol−1 which belong to two binary complexes with X,Y equal to F,Cl and F,OH. Above and below the point for (PH2Cl)2 at about 125 kJ mol−1 are four points which belong to the binary complexes with X,Y equal to F,NC

Figure 2. Negative binding energies of the homodimers and the binary complexes versus the intermolecular P−P distance.

Figure 3. Predicted versus computed P−P distances for complexes H2XP:PYH2.

the atoms of X and Y, respectively, that are directly bonded to the corresponding P atoms. When the value of the Py−Px−A angle is less than 180°, the Px−A and Py−A′ bonds are trans with respect to the P···P bond. The trans and cis orientations are illustrated by (PH2F)2 and H2FP:PH3, respectively, in Figure 4. The two P−A bonds in the homodimers are trans with respect to the P−P bond in complexes with C2h symmetry. The data of Table 4 also indicate that a group of complexes, H2XP:PYH2 in which X and Y are the more electronegative substituents F, Cl, OH, and NC, also have trans structures. All other binary complexes have a cis arrangement of P−A and P− A′ bonds except for H2FP:P(CN)H2 and H2(OH)P:P(CCH)H2, in which the P−A bond is collinear with the P−P bond, and H2ClP:P(CN)H2 and H2(OH)P:P(CN)H2, which have trans structures. How does the cis or trans arrangement of P−A and P−A′ bonds influence the binding energies of these complexes?

Figure 4. trans and cis structures of complexes (PH2F)2 and H2FP:PH3, respectively. D



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Figure 5. ELF isosurfaces for (PH2F)2 and H2FP:PH3. The ELF basins associated with lone pairs are indicated in red.

Table 5. NBO Py(lp) → σ*Px−A Charge-Transfer Energies (kJ mol−1) for Complexes H2XP:PYH2a

a

H2XP =

H2FP

H2ClP

H2(OH)P

H2(NC)P

H2(CCH)P

H2(CH3)P

H2(CN)P

H3P


131.8 87.5 104.6 62.4 50.0 57.6 38.9 38.2

59.9 73.9 38.7 37.6 45.0 26.9 28.5

46.6 29.4 24.9 26.8 20.1 20.0

31.6 31.1 37.5 24.4 26.7

11.3 12.1 6.5 9.9

11.3 17.1 5.1

11.5 12.9

5.6

Px is the P of H2XP, and Py is the P of H2YP; A is the atom of X directly bonded to Px.

Table 6. NBO Px(lp) → σ*Py−A′ Charge-Transfer Energies (kJ mol−1) for Complexes H2XP:PYH2a

a

H2XP =

H2FP

H2ClP

H2(OH)P

H2(NC)P

H2(CCH)P

H2(CH3)P

H2(CN)P

H3P


131.8 91.0 67.4 60.3 19.6 16.0 23.5 13.1

59.9 45.6 42.3 14.2 11.5 17.4 9.0

46.6 51.6 16.5 10.5 21.7 9.7

31.6 6.7 7.4 10.8 6.0

11.3 6.5 15.7 6.4

11.3 4.2 6.9

11.5 3.6

5.6

Px is the P of H2XP, and Py is the P of H2YP; A′ is the atom of Y directly bonded to Py.

Figure 6. Negative of the binding energy versus the total chargetransfer energy for the dimers (PH2X)2 and the binary complexes H2XP:PYH2.

Figure 7. Total charge-transfer energies versus the P−P−A and P−P− A′ angles for complexes H2XP:PYH2.

and Cl,OH. Finally between the points for [PH2(CN)]2 and [PH2(OH)]2 are four points with charge-transfer energies of about 75 kJ mol−1. They belong to the binary complexes with Cl,NC and OH,NC. Values of the P−P−A angle for these binary complexes lie between 162 and 173°, while values of the

P−P−A′ angle are between 157 and 175°. Thus, all of these complexes have a trans arrangement of P−A and P−A′ bonds across the P···P pnicogen bond. E



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There are six remaining complexes which have trans arrangements of P−A and P−A′ bonds, including the four homodimers with X = CCH, CH3, CN, and H, and the binary complexes with X,Y = Cl,CN and OH,CN, but these have significantly reduced charge-transfer energies. Except for the complex H2(OH)P:P(CN)H2, they also have significantly longer P−P distances than other complexes with trans structures. As observed previously, the charge-transfer energy in pnicogen-bonded complexes has a strong dependence on the P−P distance. The second-order trendline for dimers and binary complexes in Figure 8 has a correlation coefficient of 0.979.

0.035 au for H2ClP:P(CH3)H2, and then once again, the value decreases. When X = OH, maximum values of the Laplacian of 0.035 au are found for [PH2(OH)]2 and H2(OH)P:P(NC)H2, while the maximum value for X = NC is 0.034 au for [PH2(NC)]2. These data are indicative of the changing nature of the pnicogen bond, from a weak intermolecular bond at long distances, to a bond with some covalent character at intermediate distances, and finally at short distances to one that has a much higher degree of covalency. By comparison, the (FH)n:(PH2F)2 clusters with n = 1−3 have P−P distances which are shorter than the P−P distance in (PH2F)2, and these clusters do exhibit negative values of the Laplacian.63 The evolution of the Laplacian contours in the intermolecular P···P region with decreasing P−P distance and increasing covalency of the P···P bond is illustrated in Figure 10 for the complexes (PH3)2, H2FP:PH3, (PH2F)2, and FH: (PH2F)2. The Laplacian contours in the intermolecular regions are positive for both (PH3)2 and H2FP:PH3, although the extent of the negative region of PH3 into the intermolecular space in H2FP:PH3 is greater than it is in (PH3)2. As the P−P distance decreases and the covalency of the P···P bond increases in (PH2F)2, the Laplacian contours become negative in most of the intermolecular region, although the Laplacian at the BCP is positive because it is found in a very narrow region of positive contours. Finally, in FH:(PH2F)2, the Lapacian contours are continuously negative in the intermolecular region, and the Laplacian at the BCP in this region is also negative. In these complexes, as the P−P distance decreases, the covalency of the P···P bond increases in the order (PH3)2 < H2FP:PH3 < (PH2F)2 < FH:(PH2F)2. Values of the energy density can also be used to assess the degree of covalency of the P···P bonds. Energy densities are negative for all complexes with X = F, Cl, and OH, except for H2(OH)P:PH3. Values between −0.005 and −0.021 au are found for the bonds in complexes H2FP:PYH2 for Y = F, Cl, OH, NC; (PH2Cl)2 and H2ClP:P(OH)H2; and [PH2(OH)]2, which are indicative of their partial covalent character. Energydensity values between −0.002 and −0.004 au are found for the remaining complexes with X = F; H2ClP:PYH2 for Y = NC, CCH, and CH3; H2(OH)P:P(NC)H2; and [PH2(NC)]2, indicating a reduced covalency relative to the first set of complexes. The remaining complexes have values of the energy density between ±0.001 au, indicating that these intermolecular bonds have little if any covalent character. Spin−Spin Coupling Constants. It has been demonstrated previously that spin−spin coupling constants for P···P bonds in the homodimers are dominated by the Fermi contact (FC) terms, which are excellent approximations to total 1pJ(P− P) values.20 The values of the FC terms and 1pJ(P−P) for these complexes and the binary complexes H2FP:PYH2 are reported in Table 7. From these data, it is apparent that the FC term is an excellent approximation to the total coupling constant in the binary complexes as well, so it is the FC terms which are denoted 1pJ(P−P) and are discussed below. Table 8 reports the coupling constants 1pJ(P−P) for the homodimers and binary complexes. The largest coupling constants which vary from 638 to 1152 Hz, are found for complexes with X,Y = F, Cl, OH, and NC. The remaining coupling constants vary between 130 and 605 Hz. 1pJ(P−P) values for the homodimers and binary complexes are plotted against the P−P distance in Figure 11. These coupling constants correlate linearly with the P−P distance, with correlation coefficients R2 of 0.905 for the homodimers, and

Figure 8. Total charge-transfer energy versus the intermolecular P−P distance for complexes H2XP:PYH2.

AIM Results. Tables S2, S3, and S4 of the Supporting Information report values of the electron density at the bondcritical point (ρBCP), the Laplacian of the electron density at the BCP (∇ 2ρBCP), and the total energy density (H BCP), respectively, of complexes H2XP:PYH2. As is usually the case, electron densities at bond critical points correlate exponentially with P−P distances, with a correlation coefficient R2 of 0.998.54−62 The Laplacians of the electron densities are always positive and show an interesting distance dependence in Figure 9. Values of the Laplacian increase dramatically for complexes H2FP:PYH2, from 0.009 au for (PH2F)2 to a maximum of 0.037 au for H2FP:P(CH3)H2, and then decrease. For complexes with X = Cl, the Laplacian increases from 0.031 au for (PH2Cl)2 to

Figure 9. Laplacian of the electron density versus the P−P distance for complexes H2XP:PYH2. The third-order trendline has a correlation coefficient of 0.963. F



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Figure 10. Laplacian contours and molecular graphs in the symmetry planes of (PH3)2, H2FP:PH3, (PH2F)2, and FH:(PH2F)2, showing the evolution of contours in the intermolecular regions. Negative values of the Laplacians are indicated by dashed lines.

Table 7. FC Terms and 1pJ(P−P) (Hz) for Homodimers (PH2X)2 and Binary Complexes H2FP:PYH2 (PH2Y)2 FC Y=F Cl OH NC CCH CH3 CN H

1p

1008 1117 642 638 281 160 299 130

H2FP:PYH2 J(P−P)

FC

999 1120 644 640 282 161 300 131

1p

J(P−P)

1152 832 894 601 557 605 481

1150 829 894 600 556 606 481

0.894 for the binary complexes, and the two trendlines are nearly superimposable. The largest deviations from the trendlines for both sets of complexes are found at short P−P distances. The three points that lie above the trendlines at short P−P distances belong to complexes containing the substituent Cl and include H2FP:PClH2, (PH2Cl)2, and H2ClP:P(NC)H2. These coupling constants appear to be too large for their intermolecular distances. The three points which are found below the trendlines at these distances belong to the dimers (PH2F)2 and [PH2(OH)]2, and the corresponding mixed

Figure 11. Spin−spin coupling constants for complexes H2XP:PYH2 versus the P−P distance.

binary complex H2FP:P(OH)H2. These complexes have 1pJ(P− P) values that appear to be too small for their P−P distances. Figure 12 presents an interesting plot of 1pJ(P−P) for complexes H2XP:PYH2 for fixed X as a function of Y, versus 1p J(P−P) for complexes H2FP:PYH2. The points which show the largest deviations from the trendlines are those with large

Table 8. [1pJ(P−P), Hz] for Complexes H2XP:PYH2 H2XP =

H2FP

H2ClP

H2(OH)P

H2(NC)P

H2(CCH)P

H2(CH3)P

H2(CN)P

H3P


1008 1152 832 894 601 557 605 481

1117 887 817 565 549 538 440

642 662 424 375 439 324

638 424 432 419 361

281 228 290 203

160 267 146

299 225

130

G



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energy, mark the boundary of the region in which points for the binary complexes appear. 6. Spin−spin coupling constants 1pJ(P−P) for homodimers and binary complexes correlate linearly with the P−P distance, with correlation coefficients of 0.9.

ASSOCIATED CONTENT

S Supporting Information *

Geometries, total energies, and molecular graphs of complexes H2XP:PYH2; values of electron densities, Laplacians, and energy densities at P−P bond critical points; full refs 32 and 48. This material is available free of charge via the Internet at http://pubs.acs.org. Figure 12. 1pJ(P−P) for complexes H2XP:PYH2 versus complexes H2FP:PYH2.

1p

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J(P−P) for

*E-mail: [email protected]. Tel.: +1 330-609-5593. *E-mail: [email protected]. Tel.: +34 915622900.

values of 1pJ(P−P) in complexes with Y = F and Cl. The correlation coefficients vary from 0.902 for X = CN to 0.988 for X = OH. Starting with the largest values on the 1pJ(P−P) for H2XP:PYH2 axis, the 1pJ(P−P) trendlines are ordered with respect to X as

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AUTHOR INFORMATION

Corresponding Authors

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was carried out with financial support from the Ministerio de Economiá y Competitividad (Project No. CTQ2012-35513-C02-02) and Comunidad Autónoma de Madrid (Project FOTOCARBON, ref S2013/MIT-2841). Thanks are also given to the Ohio Supercomputer Center and CTI (CSIC) for their continued computational support.

Cl > OH ≈ NC > CCH ≈ CN > CH3 > H

CONCLUSIONS Ab initio MP2/aug′-cc-pVTZ calculations have been performed to determine the structures, binding energies, and bonding properties of pnicogen-bonded binary complexes H2XP:PYH2, and EOM-CCSD calculations have been carried out to determine coupling constants 1pJ(P−P) for these complexes. The following statements are supported by the results of these calculations. 1. (PH2X)2 homodimers have equilibrium C2h structures, while the binary complexes H 2 XP:PYH 2 have C s structures. Although the binding energies of the homodimers correlate well with the P−P distance, the binding energies of binary complexes show some scatter. 2. Intermolecular P−P distances in binary complexes may be approximated as the sum of the pnicogen-bond radii, determined as 1/2 the P−P distances in the corresponding homodimers (PH2X)2. 3. In addition to the intermolecular distance, other factors which influence the binding energies of H2XP:PYH2 complexes are the nature of the particular X,Y pair; the relative orientation of the interacting molecules as described by the P−P−A and P−P−A′ angles, where A and A′ are the atoms of X and Y, respectively, that are directly bonded to the P atoms; and the charge-transfer energies from the lone pair of one P to the σ-hole of the other. 4. Binary complexes H2XP:PYH2 in which X,Y are F, Cl, OH, and NC, and the homodimers (PH2X)2 have trans arrangements of the P−A and P−A′ bonds with respect to the P···P bond. 5. The nature of the P···P bond evolves from a weak intermolecular bond at long distances to one with varying degrees of covalency at shorter distances. 6. The trendlines for the homodimers in plots of the binding energy versus the intermolecular distance and the binding energy versus the total charge-transfer

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