CHEMPHYSCHEM ARTICLES DOI: 10.1002/cphc.201402086
Chiral Discrimination in Dimers of Diphosphines PH2PH2 and PH2PHF Luis M. Azofra,* Ibon Alkorta, and Jos Elguero[a] A theoretical study of the conformational profile of two diphosphines, PH2PH2 and PH2PHF, is carried using secondorder Møller–Plesset perturbation theory (MP2) computational methods. The chiral minima found are used to build homoand heterochiral dimers. Six minima are found for the (PH2 PH2)2 dimers and 27 for the (PH2PHF)2 dimers. Pnicogen and hydrogen bonds, the non-covalent forces that stabilize the complexes, are characterized by Atoms in Molecules (AIM) and Natural Bond Orbital (NBO) methodologies. Those with several
pnicogen bonds are more stable than those with hydrogen bonds. The chirodiastaltic energies amount to a total of 1.77 kJ mol1 for the Ra :Ra versus Ra :Sa (PH2PH2)2 dimers, 0.81 kJ mol1 for the RSa :RSa versus RSa :SRa (PH2PHF)2 dimers, and 2.93 kJ mol1 for the RRa :RRa versus RRa :SSa (PH2PHF)2 dimers. In the first and second cases, the heterochiral complex is favored whereas in the third case, the homochiral complex is favored.
1. Introduction Weak interactions, for example, hydrogen,[1–6] halogen,[7–12] and chalcogen[13–22] bonds, are known to be important in the configuration of molecules and clusters. Another kind of interaction, the pnicogen (or pnictogen) bond (ZB), has been proposed as molecular linker[23–25] and there has been a boom in its study and characterization in recent years.[26] The ZB is associated with a Lewis acid–Lewis base attractive contact in which the pnicogen atom (N, P, or As) is the interacting moiety in the Lewis acid. In some cases, it has been described that both the Lewis acid and the Lewis base could be the same molecule, and even the same group in different molecules can be responsible for the interaction.[27–35] The electrostatic nature of the pnicogen interaction has been rationalized based on the s-hole concept proposed by Politzer and Murray.[36] The term s-hole refers to the electrondeficient outer lobe of a p orbital involved in forming a covalent bond, especially if one of the atoms is highly electronegative. Chiral recognition, also known as chiral distinction,[37] is a topic of interest to both theorists and experimentalists. Of particular importance are the biological properties of chiral compounds, as optical isomers differ in their interactions with chiral receptors.[38] Chiral recognition also plays an important role in separation techniques,[39–41] supramolecular chemistry,[42] and crystallography.[43, 44] The possibility of chiral distinction in hydrogen-bonded complexes has been reviewed in the litera[a] L. M. Azofra, Prof. I. Alkorta, Prof. J. Elguero Instituto de Qumica Mdica (C.S.I.C.) Juan de la Cierva, 3, 28006 Madrid (Spain) Fax: (+ 34) 91 564 48 53 E-mail: [email protected] Homepage: http://are.iqm.csic.es Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402086.
2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
ture.[45, 46] Potential chiral distintion in pnicogen-bonded phosphines has been explored by some of us.[27, 28] However, poor energetic differences were found between homo and heterochiral dimer complexes in the cases studied. In this article, we study two diphosphine monomers, PH2PH2 (diphosphine) and PH2PHF (fluorodiphosphine), as well as the formation of dimers between different minima of the same compounds. These molecules show axial chirality along the PP bond and, in addition, the phosphine group in the PHF moiety is stereogenic because the phosphorus atom is bonded to three different groups.
Computational Methods The structures of the stationary points [minima and transition states (TSs)] of the diphosphine monomers, PH2PH2 and PH2PHF, and the minima of these dimers, were optimized using the second-order Møller–Plesset perturbation theory (MP2)[47–50] with the aug’-cc-pVTZ basis set,[51] which corresponds to the Dunning[52, 53] aug-cc-pVTZ basis set for the heavy atoms and the ccpVTZ basis set for the hydrogen atoms. In all cases, vibrational frequencies were calculated to confirm that the structures obtained corresponded to energetic minima or true TSs. All optimization calculations were carried out with the GAUSSIAN09 program.[54] The binding energy, Eb, was evaluated as the difference between the energy of the complexes and the sum of the isolated monomers in their minima configurations. The electron density of the systems was analyzed using the Atoms in Molecules (AIM)[55] methodology with the AIMAll program.[56] On the basis of this methodology, all interactions (covalent and weak interactions) were characterized by the presence of a bond critical point (BCP) and the corresponding bond path linking the two interacting nuclear attractors. The values of the electron density and its Laplacian at the BCP allow the classification of the contacts as covalent or non-covalent.[55, 57, 58] Natural bond orbital (NBO)[59] ChemPhysChem 2014, 15, 3663 – 3670
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theory at the DFT B3LYP[60, 61]/aug-cc-pVTZ computational level was also applied to the optimized MP2/aug’-cc-pVTZ geometries in order to analyze the orbital nature of the weak interactions between monomers within the NBO6.0 facilities.[62] Finally, DFT and + symmetry-adapted perturbation theory (DFT– SAPT) calculations were carried out at the PBE0[63]/aug’-cc-pVTZ computational level. The interaction energy using this methodology, EDFT–SAPT, was obtained as a sum of five terms [Eq. (1): electrostatic (Eele), exchange (Eexc), induction (Eind), dispersion (Edis), and higher-order term contributions (dHF)][64] Asymptotic corrections were included using the experimental ionization potential for the PH2PH2 molecule,[65] whereas in the PH2PHF case, the ionization potential was calculated at the MP2/aug’-cc-pVTZ computational level (vertical ionization). All of these calculations were performed using the MOLPRO program.[66] E DFTSAPT ¼ E ele þ E exc þ E ind þ E dis þ dHF
ð1Þ
2. Results and Discussion This section is divided into three parts: in the first, the stationary points (minima and TSs) of the monomers are described. The formation of the (PH2PH2)2 and (PH2PHF)2 dimers is discussed in the second and third parts, respectively. 2.1. Monomers The energetic profiles of the rotation around the PP bond in the two molecules considered in the present study are shown in Figure 1.[67, 68] In addition to the possibility of axial chirality (Ra or Sa) in these compounds, the PHF moiety in PH2PHF is stereogenic because the phosphorus atom is bonded to three different groups. Thus, only the (R)-PH2PHF system has been considered in the present article. Assuming a negligible effect of the parity violation principle, the energetic results for this system should be identical to those for (S)-PH2PHF.[37, 69] The PH2PH2 monomer presents three minima: two chiral conformations (Ra and Sa) and a meso one with C2h symmetry (see Figure 2). The ZPPZ dihedral angle, in which Z is a dummy atom bisector to the HPH group, is 78.88 in the chiral forms, and 180.08 in the meso conformation. The chiral forms are slightly more stable than the meso form; 1.39 kJ mol1 (see Table 1). The rotational barrier connecting the two chiral forms is 18.04 kJ mol1, whereas the barrier between the chiral forms and the meso conformation is only 2.86 kJ mol1. Another possible method for the interconversion of the two chiral forms is the inversion of the phosphorus atom, which has a barrier of 107.45 kJ mol1. This is in agreement with previous reports that show larger barrier for such processes:[70, 71] the barrier for inversion in PH3 is six times larger than that in NH3.[72] Experimental data for the PH2PH2 molecule is available in the literature. The photoelectron and IR spectra of this molecule in the gas phase indicate the predominance of a chiral conformation.[65, 73] However, IR and Raman spectra of the solid diphosphine are consistent with a meso conformation.[74] The chiral structure has been described by means of microwave spectroscopy[75] and electron diffraction[76] (see Table 2). The 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 1. Energy profile in kJ mol1 versus the HPPX dihedral angle, DHPPX, in degrees, at the MP2/aug’-cc-pVTZ computational level for: a) PH2PH2 (X = H) and b) PH2PHF (X = F).
Figure 2. Minima for the PH2PH2 and PH2PHF monomers calculated at the MP2/aug’-cc-pVTZ computational level (the enantiomeric minima generated by mirror inversion of those shown here are not included). The structures are ordered by their relative energies as shown in Table 1.
calculated geometry at the MP2/aug’-cc-pVTZ computational level adequately reproduces the experimental microwave data for diphosphine. ChemPhysChem 2014, 15, 3663 – 3670
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Table 1. Relative energies of the stationary points (minima and TSs) of the monomers that result from the rotation around the PP bond at the MP2/aug’-cc-pVTZ computational level.[a]
2.2.1. (PH2PH2)2 Dimers
In this section, the dimers formed by the chiral conformaSym. Erel [kJ mol1] Sym. Erel [kJ mol1] tions of the PH2PH2 molecule Ra C2 0.00 RSa C1 0.00 are considered. A total of six C2 0.00 RRa C1 5.03 Sa complexes (see Figure 3) were meso C2h 1.39 TS(RSa–RRa) C1 16.14 obtained, three formed by two C2 2.86 TS(RRa–RSa) C1 27.19 TS (Ra/Sa–meso) molecules with the same axial C2v 18.04 TS (Ra–Sa) [a] The TS connecting the minima follows the abscissa coordinate from left to right (see Figure 1). chirality (homochiral), and the other three formed by molecules with opposite chirality (heteroTable 2. Experimental and calculated geometrical parameters for the chiral). The two dimers that preschiral PH2PH2. ent a single ZB, 1 (Ra :Ra) and 2 (Ra :Sa), have lower stabilities, with binding energies of 10.75 and 10.76 kJ mol1, respecElectron diffraction[76] MP2/aug’-cc-pVTZ Parameter Microwave[75] tively (see Table 3). The most stable dimers are those that presdPP [] 2.2191 2.218 2.220 ent multiple ZBs, 3 (Ra :Ra) and 4 (Ra :Sa). Their binding energies 1.414, 1.417 1.451 1.412, 1412 dPH [] amount to 18.42 kJ mol1 for 3 and 20.19 kJ mol1 for 4. 99.1, 94.3 95.2 99.7, 94.6 APPH[8] 92.0 91.3 94.3 AHPH [8] The dimers with multiple HBs, 5 (Ra :Ra) and 6 (Ra :Sa), present 74.0 81 78.8 DHPPH [8] intermediate binding energies with values of 15.26 and PH2PH2 Stationary Point
PH2PHF Stationary Point
The (R)-PH2PHF molecule presents two diastereotopic minima, RRa and RSa. The most stable is the RSa form and the RRa form is 5.03 kJ mol1 higher in energy. Depending on the direction of rotation, two different rotational TSs are found that have energy values of 16.14 and 27.19 kJ mol1 with respect to the most stable minimum. These TSs are associated with the transformations RSa to RRa and Figure 3. (PH2PH2)2 dimer structures at the MP2/aug’-cc-pVTZ computational level. Dotted lines link those atoms with intermolecular interactions. The molecular graphs of all the complexes are gathered in Table S1. The disRRa to RSa, respectively, and tances between the atoms involved in weak interactions are shown in . follow the abscissa coordinate (DHPPF) from left to right (see Figure 1). Table 3. Relative and binding energies of the (PH2PH2)2 dimers at the Molecular electrostatic potential (MEP) on the 0.001 au elecMP2/aug’-cc-pVTZ computational level. tron density isosurface for the PH2PH2 and PH2PHF monomers shows different maxima along extensions of the PY Eb [kJ mol1] Complex Structure number Sym. Erel [kJ mol1] bonds (Y = P, H, F); this is associated with the idea of the sRa :Ra 1 C2 9.44 10.75 hole (see Figure S1 in the Supporting Information). These Ra :Sa 2 Ci 9.43 10.76 points and their surrounding areas represent candidate-bind3 D2 1.77 18.42 Ra :Ra 4 C2 0.00 20.19 Ra :Sa ing sites for interactions with the negative potentials of part:R 5 C 4.92 15.26 R a a 1 ner molecules. Ra :Sa
2.2. Dimers Two possibilities for the chiral relationship can be found in the formation of the dimers: 1) A:A and A:B homo and heterochiral dimers, in which A and B are enantiomers, allow chiral discrimination; and 2) A:C binary complexes, in which A and C are diastereoisomers. Only situation (1) is examined in the present research. 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
6
C1
5.74
14.45
14.45 kJ mol1, respectively. 1 and 2 are lineal whereas 3 to 6 are cyclic complexes. Thus, the chirodiastaltic energy in the (PH2PH2)2 dimers, that is the energy difference between the most stable configurations of the homo and heterochiral complexes, has a value of 1.77 kJ mol1, which indicates that the formation of the heterochiral dimer is favored. These results are in agreement with previous reports showing that ZBs are ChemPhysChem 2014, 15, 3663 – 3670
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Table 4. Interaction energy terms for the (PH2PH2)2 dimers, calculated using the DFT–SAPT methodology at PBE0/aug-cc-pVTZ//MP2/aug’-cc-pVTZ computational level. Dimer
Eele [kJ mol1]
Eexc [kJ mol1]
Eind [kJ mol1]
Edis [kJ mol1]
dHF [kJ mol1]
EDFT–SAPT [kJ mol1]
1 2 3 4 5 6
15.16 15.26 20.94 24.74 12.73 12.14
29.08 29.15 43.87 49.89 32.45 31.66
1.77 1.78 2.33 2.81 1.34 1.30
15.82 15.80 27.52 30.13 24.77 24.07
3.65 3.65 4.15 4.40 3.10 3.17
7.32 7.34 11.07 12.19 9.49 9.02
more stable than HBs in the (PH3)2 and (PH2F)2 homodimers.[77, 78] Evaluation of the different terms that contribute to the interaction energy, EDFT–SAPT, which was calculated with the DFT– SAPT methodology, (see Table 4), shows that the most important individual term is the repulsive exchange energy, Eexc, which outweighs the electrostatic attraction, Eele. Thus, the first-order Heitler–London interaction energy, which corresponds to the sum of the electrostatic interactions and exchange repulsion, is positive. This means that the stabilization of the complexes results from higher order attractive interactions. In all cases, the most important attractive term is the dispersion term, Edis. In the pnicogen-bonded complexes, the electrostatic term is only slightly smaller than the dispersion term, whereas in the hydrogen-bonded dimers the electrostatic term is approximately half of the dispersion term. The induction term, Eind, and the dHF term are very small in all cases. Focusing on the analysis of weak interactions, the topological analysis of the electron density using the AIM methodology (see Table S1) shows the presence of a BCP associated with a ZB between the nearest phosphorus atoms in complexes 1 and 2. Minimum 3 exhibits a total of two equidistant intermolecular ZBs (Figure 3), whereas in 4, four equidistant ZBs appear due to the cross shape that characterizes this dimer. The compromise disposition of the interacting phosphorus atoms in 3 and 4 explains the fact that the binding energies in these complexes are slightly less than twice those computed for 1 and 2. Similarly, the P···P intermolecular distances in 1 and 2 (3.426 and 3.427 ) are shorter than those found in 3 and 4 (3.528 and 3.624 ). The intermolecular BCPs at the ZBs show small values of electron density (between 0.010 and 0.007 au) and positive values of the Laplacian (between 0.024 and 0.022 au). Similar characteristics were found for the values of electron density and Laplacian corresponding to the HBs in 5 and 6 (between 0.005 and 0.007 au for the electron density and between 0.015 and 0.021 for the Laplacian). Thus, in all these systems, the weak interactions (HBs and ZBs) are within the closed-shell regime. In terms of NBO theory, the ZB can be described as a donation from Plp to s*(PX), in which X = P, H in the (PH2PH2)2 dimers, and the s* orbital refers to the orbital associated with the s-hole. Table 5 shows the analysis of the NBO interactions at the B3LYP/aug-cc-pVTZ//MP2/aug’-cc-pVTZ computational level for second-order perturbation NBO energy, E(2), values greater than 2 kJ mol1. All the bond paths present in minima 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
1–4 have NBO correspondence, with larger values of E(2) for the Plp !s*(PP) in 1 and 2, which amount to totals of 6.66 and 6.70 kJ mol1, respectively. Plp ! s*(PH) charge transfers are smaller, with values of 3.89 and 3.10 kJ mol1 for 3 and 4, respectively. Dimers supported by HBs do not exhibit E(2) quantities
Table 5. Second-order perturbation NBO energy, E(2), for the (PH2PH2)2 dimers at the B3LYP/aug-cc-pVTZ//MP2/aug’-cc-pVTZ computational level.[a] E(2) threshold greater than 2 kJ mol1. [a] Complex
Type
E(2) [kJ mol1]
1 2 3 4 5 6
Plp !s*(PP) Plp !s*(PP) Plp !s*(PH) Plp !s*(PH) Plp !s*(PH) –
6.66[b] 6.70[b] 3.89[c] 3.10[c] 2.18 –[d]
[a] E(2) threshold greater than 2 kJ mol1. [b] Two identical interactions. [c] Four identical interactions. [c] No second-order energy above 2 kJ mol1.
that exceed the cut-off, with exception of the shortest P···H bond in 5 (2.18 kJ mol1 and 3.102 ). ZBs are the main forces that hold the monomers together. In contrast with the HB acceptor monomers, which suffer a loss, the HB donor monomers in complexes 5 and 6 (C1) experience a gain in electron density. Integration of the AIM charges shows that an increase in the charge of around 0.01 e, occurs in the first monomer, and a depletion of 0.01 e occurs in the second, which is in agreement with the DFT– SAPT and NBO results in Table 4 and Table 5. Although our interest in the present article resides in the study of the homo and heterochiral dimers, the meso PH2PH2 monomer also has the possibility to form complexes supported by ZBs or HBs. Two structures of cyclic dimers have been obtained: one is supported by a single HP···PH ZB (C2), and the other by multiple HBs (Ci). For comparison purposes, the second is 8.08 kJ mol1 less stable than the first, which is 4.37 kJ mol1 less stable than the global and heterochiral minimum Ra :Sa (4). 2.2.2. (PH2PHF)2 Dimers The PH2PHF molecule contains a stereogenic phosphorus atom (the atom bonded to fluorine), which is either R or S. Additionally, the rotation around the PP bond generates another stereogenic element, which corresponds to the Ra or Sa axial dispositions. Thus, four chiral configurations can be found for this molecule: RRa, RSa, SRa, and SSa. The first and fourth, and the second and third, are enantiomer pairs. This part has been divided into two sub-sections. The first considers the RSa :RSa and RSa :SRa complexes and the second ChemPhysChem 2014, 15, 3663 – 3670
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CHEMPHYSCHEM ARTICLES the RRa :RRa and RRa :SSa dimers. Different kinds of minima are considered. These are classified based on the disposition and the interactions present, that is, complexes linked by ZBs (with unique or multiple P···P bonds) and/or by HBs.
2.2.2.1. RSa :RSa and RSa :SRa Complexes Figure 4 displays the minima obtained for the RSa :RSa and RSa :SRa (PH2PHF)2 dimers. As described for the (PH2PH2)2 dimers, the binding energies are larger in the cyclic complexes that are supported by ZBs (15 to 18, up to 27.54 kJ mol1), followed by the complexes with HBs or even F···P bonds (19 to 22, up to 17.71 kJ mol1), and finally, by the lineal complexes (7 to 14, up to 11.55 kJ mol1) (Table 6). With the exception of 10, complexes 7 to 14 present the lineal disposition characteristic of the presence of the Plp ! s*(PP) charge transfer. Specifically, for dimer 10, AIM predicts secondary F···F and F···P weak interactions, which do not have
www.chemphyschem.org Table 6. Relative and binding energies of the RSa :RSa and RSa :SRa (PH2 PHF)2 dimers at the MP2/aug’-cc-pVTZ computational level. Complex
Structure number
Sym.
Erel [kJ mol1]
Eb [kJ mol1]
RSa :RSa RSa :RSa RSa :RSa RSa :RSa RSa :SRa RSa :SRa RSa :SRa RSa :SRa RSa :RSa RSa :RSa RSa :SRa RSa :SRa RSa :RSa RSa :RSa RSa :SRa RSa :SRa
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
C2 C1 C2 C2 Ci C1 C1 C1 C2 C2 Ci C1 C1 C1 C1 C1
18.39 17.48 17.92 16.00 18.39 17.68 17.00 17.49 3.49 0.81 5.50 0.00 12.79 9.83 12.37 11.47
9.16 10.07 9.62 11.55 9.15 9.86 10.55 10.05 24.05 26.73 22.05 27.54 14.76 17.71 15.17 16.08
Figure 4. RSa :RSa and RSa :SRa (PH2PHF)2 dimer structures at the MP2/aug’-cc-pVTZ computational level. Dotted lines link those atoms with intermolecular interactions. The molecular graphs of all the complexes are gathered in Table S1. The distances between the atoms involved in weak interactions are shown in . The A and B monomers in the A:B heterochiral dimers correspond to the left and right moieties in this figure.
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NBO correspondence greater than the threshold imposed. In addition, case 14 has a F···P bond, with a Flp !s*(PP) charge transfer that amounts to 2.30 kJ mol1. All the Plp !s*(PP) E(2) values in these complexes are greater than those in the lineal (PH2PH2)2 dimers, at between 3.18 and 5.73 kJ mol1, due to the presence of the F atoms. In general, E(2) increases following the trend FHP H2P···PHFPH2, FHPH2P···PH2 PHF, and PH2FHP···PHFPH2, despite the higher value corresponding to dimer 8. Minima 15 to 22 have cyclic dispositions, and are divided into two main groups: 1) dimers 15 to 18, linked solely by one or many ZBs; and 2) dimers 19 to 22, linked by many HBs (P···H and in 19–21 F···H type) and F···P bonds. Focusing on group (1) (Table 7), the P···P bonds have much larger E(2) values and shorter distances than those in the lineal complexes. The ZB in 16 is notable, with identical values for donation and retrodonation orbital interactions of 39.99 kJ mol1 and an inter-phosphorus distance of 2.902 . The effect of the presence of F atoms attached to the P atom is more prominent in group (1), and FP···PF bonds thus result in
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Table 7. Second-order perturbation NBO energy E(2) for the cyclic RSa :RSa and RSa :SRa (PH2PHF)2 dimers 15 to 18 at the B3LYP/aug-cc-pVTZ//MP2/ aug’-cc-pVTZ computational level.[a] Complex
Donor/Acceptor[b]
Type
E(2) [kJ mol1]
A to B Plp !s*(PH) 7.33 13.48 A to B Plp !s*(PF) 15 B to A Plp !s*(PH) 7.33 13.48 B to A Plp !s*(PF) A to B Plp !s*(PF) 39.99 16 39.99 B to A Plp !s*(PF) A to B Plp !s*(PF) 14.19 17 14.19 B to A Plp !s*(PF) 2.93 A to B Plp !s*(PH) 17.63 A to B Plp !s*(PF) 18 B to A s(PP)!s*(PF) 3.68 20.10 B to A Plp !s*(PF) B to A Plp !s*(PH) 3.14 [a] E(2) threshold greater than 2 kJ mol1. [b] Fragments A and B refer to the A and B moieties in the A:B complexes (see Figure 4).
more bonded moieties than HP···PF and HP···PH bonds. This fact can be confirmed, for instance, in 15, by the E(2) quantities of 13.48 and 7.33 kJ mol1. The FP···PF bond in 18 has Plp ! s*(PF) donation and retro-donation charge transfers that amount to 17.63 and 20.10 kJ mol1, even though the geometrical disposition of the phosphine groups is not optimal. Dimer 18 is the most stable structure of all the complexes described for the (PH2PHF)2 dimer. The energetic results show that the chirodiastaltic energy for the RSa :RSa versus RSa :SRa (PH2PHF)2 dimers has a value of 0.81 kJ mol1, which means that the formation of the heterochiral complex is favored. As for the (PH2PH2) dimers, the most important term derived from the DFT–SAPT analysis is the exchange term, Eexc. The electrostatic, Eele, and dispersion, Edis, terms have similar values, the second higher than the first in all cases, with exception of complexes 15–18. The induction term, Eind, and dHF have small values in all cases (see Table S3).
Table 8. Relative[a] and binding energies of the RRa :RRa and RRa :SSa (PH2 PHF)2 dimers at the MP2/aug’-cc-pVTZ computational level. Complex
Structure number
Sym.
Erel [kJ mol1]
Eb [kJ mol1]
RRa :RRa RRa :RRa RRa :RRa RRa :RRa RRa :SSa RRa :SSa RRa :SSa RRa :SSa RRa :RRa RRa :RRa RRa :SSa
23 24 25 26 27 28 29 30 31 32 33
C2 C1 C2 C2 Ci C1 C1 C1 C2 C2 C1
27.20 26.89 27.74 25.64 27.16 26.44 25.75 27.23 24.09 19.48 16.55
10.40 10.71 9.86 11.95 10.44 11.16 11.84 10.37 13.50 18.11 21.05
[a] Complex 18 is used as reference to calculate the relative energies.
are observed in Table 8 for the lineal and cyclic complexes, respectively. Binding energies for the lineal dimers appear to be in the range of 10–12 kJ mol1 in absolute terms. Based on the energetic results, the chirodiastaltic energy for the RRa :RRa versus RRa :SSa (PH2PHF)2 dimers has a value of 2.93 kJ mol1, which means that the formation of the heterochiral complex is favored. As mentioned previously, the most important term derived from the DFT–SAPT analysis is the exchange term, Eexc. The electrostatic, Eele, and dispersion, Edis, terms have similar values, with the second higher than the first in all cases, with excep-
2.2.2.2. RRa :RRa and RRa :SSa Complexes Figure 5 displays the (PH2PHF)2 complexes formed by monomers with the same chirality in the stereogenic phosphorus and the axial PP covalent bond, that is, RRa :RRa and RRa :SSa. With the exception of 26, minima 23 to 30 correspond to lineal complexes linked by P···P bonds, and have only weak secondary F···F and F···P interactions. Minimum 30 has an F···P bond in addition to the P···P bond. Due to the disposition of the atoms in the phosphine groups, cyclic dimers 31 to 33 do not have solely ZBs or HBs as described for the RSa :RSa and RSa :SRa cases. The energetic values show that the RRa :RRa and RRa :SSa (PH2PHF)2 dimers are less stable than the RSa :RSa and RSa :SRa dimers. Using complex 18 as reference, relative energies between 25.64 and 27.74 kJ mol1 and between 24.09 and 16.55 kJ mol1 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 5. RRa :RRa and RRa :SSa (PH2PHF)2 dimer structures at the MP2/aug’-cc-pVTZ computational level. Dotted lines link those atoms with intermolecular interactions. The molecular graphs of all the complexes are gathered in Table S1. The distances between the atoms involved in weak interactions are shown in . The A and B monomers in the A:B heterochiral dimers correspond to the left and right moieties in this figure.
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tion of complexes 29 and 33. The induction term, Eind, and dHF have small values in all cases (see Table S3).
3. Conclusions The conformational profiles of the PH2PH2 and PH2PHF diphosphines have been studied using the MP2/aug’-cc-pVTZ computational method. Three minima were found for PH2PH2, two with axial chirality, Ra and Sa, and a meso form. In the case of the PH2PHF molecule, two minima were found on rotation of the PP bond. As the phosphorus atom in the PHF group is already stereogenic, four minima are possible for this molecule, RRa, RSa, SRa, and SSa. Six minima were characterized for the dimers formed between chiral monomers of PH2PH2. They are stabilized by ZBs or HBs. The complexes stabilized by ZBs are more stable than those stabilized by HBs. The most stable structure corresponds to a heterochiral dimer that shows two ZB interactions. The chirodiastaltic energy in this system is 1.77 kJ mol1. In the case of the PH2PHF molecule, two sets of dimers were considered. On one hand, the RSa :RSa and RSa :SRa dimers were studied, and on the other hand, the RRa :RRa and RRa :SSa dimers. A total of 16 and 11 minima were found for the two sets. The minima of the first set are more stable than those of the second set. The most stable of all the minima have two ZBs between the lone pair of the phosphorus atom of one molecule and the s*(PF) orbital of the other. The chirodiastaltic energies of the two sets are 0.81 and 2.93 kJ mol1, respectively.
Acknowledgements L.M.A. thanks the MICINN for a PhD grant (No. BES-2010-031225). We also thank the MINECO (Project No. CTQ2012-35513-C02-02) and the Comunidad Autnoma de Madrid (Project MADRIDSOLAR2, ref. S2009/PPQ-1533) for continuing support and CTI (C.S.I.C.) and CESGA for an allocation of computer time. Keywords: axial chirality · computational chemistry conformational analysis · hydrogen bonds · pnicogens
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Received: March 4, 2014 Published online on May 18, 2014
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Chiral Discrimination in Dimers of Diphosphines PH2PH2 and PH2PHF Luis M. Azofra,* Ibon Alkorta, and Jos Elguero[a] A theoretical study of the conformational profile of two diphosphines, PH2PH2 and PH2PHF, is carried using secondorder Møller–Plesset perturbation theory (MP2) computational methods. The chiral minima found are used to build homoand heterochiral dimers. Six minima are found for the (PH2 PH2)2 dimers and 27 for the (PH2PHF)2 dimers. Pnicogen and hydrogen bonds, the non-covalent forces that stabilize the complexes, are characterized by Atoms in Molecules (AIM) and Natural Bond Orbital (NBO) methodologies. Those with several
pnicogen bonds are more stable than those with hydrogen bonds. The chirodiastaltic energies amount to a total of 1.77 kJ mol1 for the Ra :Ra versus Ra :Sa (PH2PH2)2 dimers, 0.81 kJ mol1 for the RSa :RSa versus RSa :SRa (PH2PHF)2 dimers, and 2.93 kJ mol1 for the RRa :RRa versus RRa :SSa (PH2PHF)2 dimers. In the first and second cases, the heterochiral complex is favored whereas in the third case, the homochiral complex is favored.
1. Introduction Weak interactions, for example, hydrogen,[1–6] halogen,[7–12] and chalcogen[13–22] bonds, are known to be important in the configuration of molecules and clusters. Another kind of interaction, the pnicogen (or pnictogen) bond (ZB), has been proposed as molecular linker[23–25] and there has been a boom in its study and characterization in recent years.[26] The ZB is associated with a Lewis acid–Lewis base attractive contact in which the pnicogen atom (N, P, or As) is the interacting moiety in the Lewis acid. In some cases, it has been described that both the Lewis acid and the Lewis base could be the same molecule, and even the same group in different molecules can be responsible for the interaction.[27–35] The electrostatic nature of the pnicogen interaction has been rationalized based on the s-hole concept proposed by Politzer and Murray.[36] The term s-hole refers to the electrondeficient outer lobe of a p orbital involved in forming a covalent bond, especially if one of the atoms is highly electronegative. Chiral recognition, also known as chiral distinction,[37] is a topic of interest to both theorists and experimentalists. Of particular importance are the biological properties of chiral compounds, as optical isomers differ in their interactions with chiral receptors.[38] Chiral recognition also plays an important role in separation techniques,[39–41] supramolecular chemistry,[42] and crystallography.[43, 44] The possibility of chiral distinction in hydrogen-bonded complexes has been reviewed in the litera[a] L. M. Azofra, Prof. I. Alkorta, Prof. J. Elguero Instituto de Qumica Mdica (C.S.I.C.) Juan de la Cierva, 3, 28006 Madrid (Spain) Fax: (+ 34) 91 564 48 53 E-mail: [email protected] Homepage: http://are.iqm.csic.es Supporting Information for this article is available on the WWW under http://dx.doi.org/10.1002/cphc.201402086.
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ture.[45, 46] Potential chiral distintion in pnicogen-bonded phosphines has been explored by some of us.[27, 28] However, poor energetic differences were found between homo and heterochiral dimer complexes in the cases studied. In this article, we study two diphosphine monomers, PH2PH2 (diphosphine) and PH2PHF (fluorodiphosphine), as well as the formation of dimers between different minima of the same compounds. These molecules show axial chirality along the PP bond and, in addition, the phosphine group in the PHF moiety is stereogenic because the phosphorus atom is bonded to three different groups.
Computational Methods The structures of the stationary points [minima and transition states (TSs)] of the diphosphine monomers, PH2PH2 and PH2PHF, and the minima of these dimers, were optimized using the second-order Møller–Plesset perturbation theory (MP2)[47–50] with the aug’-cc-pVTZ basis set,[51] which corresponds to the Dunning[52, 53] aug-cc-pVTZ basis set for the heavy atoms and the ccpVTZ basis set for the hydrogen atoms. In all cases, vibrational frequencies were calculated to confirm that the structures obtained corresponded to energetic minima or true TSs. All optimization calculations were carried out with the GAUSSIAN09 program.[54] The binding energy, Eb, was evaluated as the difference between the energy of the complexes and the sum of the isolated monomers in their minima configurations. The electron density of the systems was analyzed using the Atoms in Molecules (AIM)[55] methodology with the AIMAll program.[56] On the basis of this methodology, all interactions (covalent and weak interactions) were characterized by the presence of a bond critical point (BCP) and the corresponding bond path linking the two interacting nuclear attractors. The values of the electron density and its Laplacian at the BCP allow the classification of the contacts as covalent or non-covalent.[55, 57, 58] Natural bond orbital (NBO)[59] ChemPhysChem 2014, 15, 3663 – 3670
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theory at the DFT B3LYP[60, 61]/aug-cc-pVTZ computational level was also applied to the optimized MP2/aug’-cc-pVTZ geometries in order to analyze the orbital nature of the weak interactions between monomers within the NBO6.0 facilities.[62] Finally, DFT and + symmetry-adapted perturbation theory (DFT– SAPT) calculations were carried out at the PBE0[63]/aug’-cc-pVTZ computational level. The interaction energy using this methodology, EDFT–SAPT, was obtained as a sum of five terms [Eq. (1): electrostatic (Eele), exchange (Eexc), induction (Eind), dispersion (Edis), and higher-order term contributions (dHF)][64] Asymptotic corrections were included using the experimental ionization potential for the PH2PH2 molecule,[65] whereas in the PH2PHF case, the ionization potential was calculated at the MP2/aug’-cc-pVTZ computational level (vertical ionization). All of these calculations were performed using the MOLPRO program.[66] E DFTSAPT ¼ E ele þ E exc þ E ind þ E dis þ dHF
ð1Þ
2. Results and Discussion This section is divided into three parts: in the first, the stationary points (minima and TSs) of the monomers are described. The formation of the (PH2PH2)2 and (PH2PHF)2 dimers is discussed in the second and third parts, respectively. 2.1. Monomers The energetic profiles of the rotation around the PP bond in the two molecules considered in the present study are shown in Figure 1.[67, 68] In addition to the possibility of axial chirality (Ra or Sa) in these compounds, the PHF moiety in PH2PHF is stereogenic because the phosphorus atom is bonded to three different groups. Thus, only the (R)-PH2PHF system has been considered in the present article. Assuming a negligible effect of the parity violation principle, the energetic results for this system should be identical to those for (S)-PH2PHF.[37, 69] The PH2PH2 monomer presents three minima: two chiral conformations (Ra and Sa) and a meso one with C2h symmetry (see Figure 2). The ZPPZ dihedral angle, in which Z is a dummy atom bisector to the HPH group, is 78.88 in the chiral forms, and 180.08 in the meso conformation. The chiral forms are slightly more stable than the meso form; 1.39 kJ mol1 (see Table 1). The rotational barrier connecting the two chiral forms is 18.04 kJ mol1, whereas the barrier between the chiral forms and the meso conformation is only 2.86 kJ mol1. Another possible method for the interconversion of the two chiral forms is the inversion of the phosphorus atom, which has a barrier of 107.45 kJ mol1. This is in agreement with previous reports that show larger barrier for such processes:[70, 71] the barrier for inversion in PH3 is six times larger than that in NH3.[72] Experimental data for the PH2PH2 molecule is available in the literature. The photoelectron and IR spectra of this molecule in the gas phase indicate the predominance of a chiral conformation.[65, 73] However, IR and Raman spectra of the solid diphosphine are consistent with a meso conformation.[74] The chiral structure has been described by means of microwave spectroscopy[75] and electron diffraction[76] (see Table 2). The 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 1. Energy profile in kJ mol1 versus the HPPX dihedral angle, DHPPX, in degrees, at the MP2/aug’-cc-pVTZ computational level for: a) PH2PH2 (X = H) and b) PH2PHF (X = F).
Figure 2. Minima for the PH2PH2 and PH2PHF monomers calculated at the MP2/aug’-cc-pVTZ computational level (the enantiomeric minima generated by mirror inversion of those shown here are not included). The structures are ordered by their relative energies as shown in Table 1.
calculated geometry at the MP2/aug’-cc-pVTZ computational level adequately reproduces the experimental microwave data for diphosphine. ChemPhysChem 2014, 15, 3663 – 3670
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Table 1. Relative energies of the stationary points (minima and TSs) of the monomers that result from the rotation around the PP bond at the MP2/aug’-cc-pVTZ computational level.[a]
2.2.1. (PH2PH2)2 Dimers
In this section, the dimers formed by the chiral conformaSym. Erel [kJ mol1] Sym. Erel [kJ mol1] tions of the PH2PH2 molecule Ra C2 0.00 RSa C1 0.00 are considered. A total of six C2 0.00 RRa C1 5.03 Sa complexes (see Figure 3) were meso C2h 1.39 TS(RSa–RRa) C1 16.14 obtained, three formed by two C2 2.86 TS(RRa–RSa) C1 27.19 TS (Ra/Sa–meso) molecules with the same axial C2v 18.04 TS (Ra–Sa) [a] The TS connecting the minima follows the abscissa coordinate from left to right (see Figure 1). chirality (homochiral), and the other three formed by molecules with opposite chirality (heteroTable 2. Experimental and calculated geometrical parameters for the chiral). The two dimers that preschiral PH2PH2. ent a single ZB, 1 (Ra :Ra) and 2 (Ra :Sa), have lower stabilities, with binding energies of 10.75 and 10.76 kJ mol1, respecElectron diffraction[76] MP2/aug’-cc-pVTZ Parameter Microwave[75] tively (see Table 3). The most stable dimers are those that presdPP [] 2.2191 2.218 2.220 ent multiple ZBs, 3 (Ra :Ra) and 4 (Ra :Sa). Their binding energies 1.414, 1.417 1.451 1.412, 1412 dPH [] amount to 18.42 kJ mol1 for 3 and 20.19 kJ mol1 for 4. 99.1, 94.3 95.2 99.7, 94.6 APPH[8] 92.0 91.3 94.3 AHPH [8] The dimers with multiple HBs, 5 (Ra :Ra) and 6 (Ra :Sa), present 74.0 81 78.8 DHPPH [8] intermediate binding energies with values of 15.26 and PH2PH2 Stationary Point
PH2PHF Stationary Point
The (R)-PH2PHF molecule presents two diastereotopic minima, RRa and RSa. The most stable is the RSa form and the RRa form is 5.03 kJ mol1 higher in energy. Depending on the direction of rotation, two different rotational TSs are found that have energy values of 16.14 and 27.19 kJ mol1 with respect to the most stable minimum. These TSs are associated with the transformations RSa to RRa and Figure 3. (PH2PH2)2 dimer structures at the MP2/aug’-cc-pVTZ computational level. Dotted lines link those atoms with intermolecular interactions. The molecular graphs of all the complexes are gathered in Table S1. The disRRa to RSa, respectively, and tances between the atoms involved in weak interactions are shown in . follow the abscissa coordinate (DHPPF) from left to right (see Figure 1). Table 3. Relative and binding energies of the (PH2PH2)2 dimers at the Molecular electrostatic potential (MEP) on the 0.001 au elecMP2/aug’-cc-pVTZ computational level. tron density isosurface for the PH2PH2 and PH2PHF monomers shows different maxima along extensions of the PY Eb [kJ mol1] Complex Structure number Sym. Erel [kJ mol1] bonds (Y = P, H, F); this is associated with the idea of the sRa :Ra 1 C2 9.44 10.75 hole (see Figure S1 in the Supporting Information). These Ra :Sa 2 Ci 9.43 10.76 points and their surrounding areas represent candidate-bind3 D2 1.77 18.42 Ra :Ra 4 C2 0.00 20.19 Ra :Sa ing sites for interactions with the negative potentials of part:R 5 C 4.92 15.26 R a a 1 ner molecules. Ra :Sa
2.2. Dimers Two possibilities for the chiral relationship can be found in the formation of the dimers: 1) A:A and A:B homo and heterochiral dimers, in which A and B are enantiomers, allow chiral discrimination; and 2) A:C binary complexes, in which A and C are diastereoisomers. Only situation (1) is examined in the present research. 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
6
C1
5.74
14.45
14.45 kJ mol1, respectively. 1 and 2 are lineal whereas 3 to 6 are cyclic complexes. Thus, the chirodiastaltic energy in the (PH2PH2)2 dimers, that is the energy difference between the most stable configurations of the homo and heterochiral complexes, has a value of 1.77 kJ mol1, which indicates that the formation of the heterochiral dimer is favored. These results are in agreement with previous reports showing that ZBs are ChemPhysChem 2014, 15, 3663 – 3670
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Table 4. Interaction energy terms for the (PH2PH2)2 dimers, calculated using the DFT–SAPT methodology at PBE0/aug-cc-pVTZ//MP2/aug’-cc-pVTZ computational level. Dimer
Eele [kJ mol1]
Eexc [kJ mol1]
Eind [kJ mol1]
Edis [kJ mol1]
dHF [kJ mol1]
EDFT–SAPT [kJ mol1]
1 2 3 4 5 6
15.16 15.26 20.94 24.74 12.73 12.14
29.08 29.15 43.87 49.89 32.45 31.66
1.77 1.78 2.33 2.81 1.34 1.30
15.82 15.80 27.52 30.13 24.77 24.07
3.65 3.65 4.15 4.40 3.10 3.17
7.32 7.34 11.07 12.19 9.49 9.02
more stable than HBs in the (PH3)2 and (PH2F)2 homodimers.[77, 78] Evaluation of the different terms that contribute to the interaction energy, EDFT–SAPT, which was calculated with the DFT– SAPT methodology, (see Table 4), shows that the most important individual term is the repulsive exchange energy, Eexc, which outweighs the electrostatic attraction, Eele. Thus, the first-order Heitler–London interaction energy, which corresponds to the sum of the electrostatic interactions and exchange repulsion, is positive. This means that the stabilization of the complexes results from higher order attractive interactions. In all cases, the most important attractive term is the dispersion term, Edis. In the pnicogen-bonded complexes, the electrostatic term is only slightly smaller than the dispersion term, whereas in the hydrogen-bonded dimers the electrostatic term is approximately half of the dispersion term. The induction term, Eind, and the dHF term are very small in all cases. Focusing on the analysis of weak interactions, the topological analysis of the electron density using the AIM methodology (see Table S1) shows the presence of a BCP associated with a ZB between the nearest phosphorus atoms in complexes 1 and 2. Minimum 3 exhibits a total of two equidistant intermolecular ZBs (Figure 3), whereas in 4, four equidistant ZBs appear due to the cross shape that characterizes this dimer. The compromise disposition of the interacting phosphorus atoms in 3 and 4 explains the fact that the binding energies in these complexes are slightly less than twice those computed for 1 and 2. Similarly, the P···P intermolecular distances in 1 and 2 (3.426 and 3.427 ) are shorter than those found in 3 and 4 (3.528 and 3.624 ). The intermolecular BCPs at the ZBs show small values of electron density (between 0.010 and 0.007 au) and positive values of the Laplacian (between 0.024 and 0.022 au). Similar characteristics were found for the values of electron density and Laplacian corresponding to the HBs in 5 and 6 (between 0.005 and 0.007 au for the electron density and between 0.015 and 0.021 for the Laplacian). Thus, in all these systems, the weak interactions (HBs and ZBs) are within the closed-shell regime. In terms of NBO theory, the ZB can be described as a donation from Plp to s*(PX), in which X = P, H in the (PH2PH2)2 dimers, and the s* orbital refers to the orbital associated with the s-hole. Table 5 shows the analysis of the NBO interactions at the B3LYP/aug-cc-pVTZ//MP2/aug’-cc-pVTZ computational level for second-order perturbation NBO energy, E(2), values greater than 2 kJ mol1. All the bond paths present in minima 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
1–4 have NBO correspondence, with larger values of E(2) for the Plp !s*(PP) in 1 and 2, which amount to totals of 6.66 and 6.70 kJ mol1, respectively. Plp ! s*(PH) charge transfers are smaller, with values of 3.89 and 3.10 kJ mol1 for 3 and 4, respectively. Dimers supported by HBs do not exhibit E(2) quantities
Table 5. Second-order perturbation NBO energy, E(2), for the (PH2PH2)2 dimers at the B3LYP/aug-cc-pVTZ//MP2/aug’-cc-pVTZ computational level.[a] E(2) threshold greater than 2 kJ mol1. [a] Complex
Type
E(2) [kJ mol1]
1 2 3 4 5 6
Plp !s*(PP) Plp !s*(PP) Plp !s*(PH) Plp !s*(PH) Plp !s*(PH) –
6.66[b] 6.70[b] 3.89[c] 3.10[c] 2.18 –[d]
[a] E(2) threshold greater than 2 kJ mol1. [b] Two identical interactions. [c] Four identical interactions. [c] No second-order energy above 2 kJ mol1.
that exceed the cut-off, with exception of the shortest P···H bond in 5 (2.18 kJ mol1 and 3.102 ). ZBs are the main forces that hold the monomers together. In contrast with the HB acceptor monomers, which suffer a loss, the HB donor monomers in complexes 5 and 6 (C1) experience a gain in electron density. Integration of the AIM charges shows that an increase in the charge of around 0.01 e, occurs in the first monomer, and a depletion of 0.01 e occurs in the second, which is in agreement with the DFT– SAPT and NBO results in Table 4 and Table 5. Although our interest in the present article resides in the study of the homo and heterochiral dimers, the meso PH2PH2 monomer also has the possibility to form complexes supported by ZBs or HBs. Two structures of cyclic dimers have been obtained: one is supported by a single HP···PH ZB (C2), and the other by multiple HBs (Ci). For comparison purposes, the second is 8.08 kJ mol1 less stable than the first, which is 4.37 kJ mol1 less stable than the global and heterochiral minimum Ra :Sa (4). 2.2.2. (PH2PHF)2 Dimers The PH2PHF molecule contains a stereogenic phosphorus atom (the atom bonded to fluorine), which is either R or S. Additionally, the rotation around the PP bond generates another stereogenic element, which corresponds to the Ra or Sa axial dispositions. Thus, four chiral configurations can be found for this molecule: RRa, RSa, SRa, and SSa. The first and fourth, and the second and third, are enantiomer pairs. This part has been divided into two sub-sections. The first considers the RSa :RSa and RSa :SRa complexes and the second ChemPhysChem 2014, 15, 3663 – 3670
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CHEMPHYSCHEM ARTICLES the RRa :RRa and RRa :SSa dimers. Different kinds of minima are considered. These are classified based on the disposition and the interactions present, that is, complexes linked by ZBs (with unique or multiple P···P bonds) and/or by HBs.
2.2.2.1. RSa :RSa and RSa :SRa Complexes Figure 4 displays the minima obtained for the RSa :RSa and RSa :SRa (PH2PHF)2 dimers. As described for the (PH2PH2)2 dimers, the binding energies are larger in the cyclic complexes that are supported by ZBs (15 to 18, up to 27.54 kJ mol1), followed by the complexes with HBs or even F···P bonds (19 to 22, up to 17.71 kJ mol1), and finally, by the lineal complexes (7 to 14, up to 11.55 kJ mol1) (Table 6). With the exception of 10, complexes 7 to 14 present the lineal disposition characteristic of the presence of the Plp ! s*(PP) charge transfer. Specifically, for dimer 10, AIM predicts secondary F···F and F···P weak interactions, which do not have
www.chemphyschem.org Table 6. Relative and binding energies of the RSa :RSa and RSa :SRa (PH2 PHF)2 dimers at the MP2/aug’-cc-pVTZ computational level. Complex
Structure number
Sym.
Erel [kJ mol1]
Eb [kJ mol1]
RSa :RSa RSa :RSa RSa :RSa RSa :RSa RSa :SRa RSa :SRa RSa :SRa RSa :SRa RSa :RSa RSa :RSa RSa :SRa RSa :SRa RSa :RSa RSa :RSa RSa :SRa RSa :SRa
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
C2 C1 C2 C2 Ci C1 C1 C1 C2 C2 Ci C1 C1 C1 C1 C1
18.39 17.48 17.92 16.00 18.39 17.68 17.00 17.49 3.49 0.81 5.50 0.00 12.79 9.83 12.37 11.47
9.16 10.07 9.62 11.55 9.15 9.86 10.55 10.05 24.05 26.73 22.05 27.54 14.76 17.71 15.17 16.08
Figure 4. RSa :RSa and RSa :SRa (PH2PHF)2 dimer structures at the MP2/aug’-cc-pVTZ computational level. Dotted lines link those atoms with intermolecular interactions. The molecular graphs of all the complexes are gathered in Table S1. The distances between the atoms involved in weak interactions are shown in . The A and B monomers in the A:B heterochiral dimers correspond to the left and right moieties in this figure.
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NBO correspondence greater than the threshold imposed. In addition, case 14 has a F···P bond, with a Flp !s*(PP) charge transfer that amounts to 2.30 kJ mol1. All the Plp !s*(PP) E(2) values in these complexes are greater than those in the lineal (PH2PH2)2 dimers, at between 3.18 and 5.73 kJ mol1, due to the presence of the F atoms. In general, E(2) increases following the trend FHP H2P···PHFPH2, FHPH2P···PH2 PHF, and PH2FHP···PHFPH2, despite the higher value corresponding to dimer 8. Minima 15 to 22 have cyclic dispositions, and are divided into two main groups: 1) dimers 15 to 18, linked solely by one or many ZBs; and 2) dimers 19 to 22, linked by many HBs (P···H and in 19–21 F···H type) and F···P bonds. Focusing on group (1) (Table 7), the P···P bonds have much larger E(2) values and shorter distances than those in the lineal complexes. The ZB in 16 is notable, with identical values for donation and retrodonation orbital interactions of 39.99 kJ mol1 and an inter-phosphorus distance of 2.902 . The effect of the presence of F atoms attached to the P atom is more prominent in group (1), and FP···PF bonds thus result in
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Table 7. Second-order perturbation NBO energy E(2) for the cyclic RSa :RSa and RSa :SRa (PH2PHF)2 dimers 15 to 18 at the B3LYP/aug-cc-pVTZ//MP2/ aug’-cc-pVTZ computational level.[a] Complex
Donor/Acceptor[b]
Type
E(2) [kJ mol1]
A to B Plp !s*(PH) 7.33 13.48 A to B Plp !s*(PF) 15 B to A Plp !s*(PH) 7.33 13.48 B to A Plp !s*(PF) A to B Plp !s*(PF) 39.99 16 39.99 B to A Plp !s*(PF) A to B Plp !s*(PF) 14.19 17 14.19 B to A Plp !s*(PF) 2.93 A to B Plp !s*(PH) 17.63 A to B Plp !s*(PF) 18 B to A s(PP)!s*(PF) 3.68 20.10 B to A Plp !s*(PF) B to A Plp !s*(PH) 3.14 [a] E(2) threshold greater than 2 kJ mol1. [b] Fragments A and B refer to the A and B moieties in the A:B complexes (see Figure 4).
more bonded moieties than HP···PF and HP···PH bonds. This fact can be confirmed, for instance, in 15, by the E(2) quantities of 13.48 and 7.33 kJ mol1. The FP···PF bond in 18 has Plp ! s*(PF) donation and retro-donation charge transfers that amount to 17.63 and 20.10 kJ mol1, even though the geometrical disposition of the phosphine groups is not optimal. Dimer 18 is the most stable structure of all the complexes described for the (PH2PHF)2 dimer. The energetic results show that the chirodiastaltic energy for the RSa :RSa versus RSa :SRa (PH2PHF)2 dimers has a value of 0.81 kJ mol1, which means that the formation of the heterochiral complex is favored. As for the (PH2PH2) dimers, the most important term derived from the DFT–SAPT analysis is the exchange term, Eexc. The electrostatic, Eele, and dispersion, Edis, terms have similar values, the second higher than the first in all cases, with exception of complexes 15–18. The induction term, Eind, and dHF have small values in all cases (see Table S3).
Table 8. Relative[a] and binding energies of the RRa :RRa and RRa :SSa (PH2 PHF)2 dimers at the MP2/aug’-cc-pVTZ computational level. Complex
Structure number
Sym.
Erel [kJ mol1]
Eb [kJ mol1]
RRa :RRa RRa :RRa RRa :RRa RRa :RRa RRa :SSa RRa :SSa RRa :SSa RRa :SSa RRa :RRa RRa :RRa RRa :SSa
23 24 25 26 27 28 29 30 31 32 33
C2 C1 C2 C2 Ci C1 C1 C1 C2 C2 C1
27.20 26.89 27.74 25.64 27.16 26.44 25.75 27.23 24.09 19.48 16.55
10.40 10.71 9.86 11.95 10.44 11.16 11.84 10.37 13.50 18.11 21.05
[a] Complex 18 is used as reference to calculate the relative energies.
are observed in Table 8 for the lineal and cyclic complexes, respectively. Binding energies for the lineal dimers appear to be in the range of 10–12 kJ mol1 in absolute terms. Based on the energetic results, the chirodiastaltic energy for the RRa :RRa versus RRa :SSa (PH2PHF)2 dimers has a value of 2.93 kJ mol1, which means that the formation of the heterochiral complex is favored. As mentioned previously, the most important term derived from the DFT–SAPT analysis is the exchange term, Eexc. The electrostatic, Eele, and dispersion, Edis, terms have similar values, with the second higher than the first in all cases, with excep-
2.2.2.2. RRa :RRa and RRa :SSa Complexes Figure 5 displays the (PH2PHF)2 complexes formed by monomers with the same chirality in the stereogenic phosphorus and the axial PP covalent bond, that is, RRa :RRa and RRa :SSa. With the exception of 26, minima 23 to 30 correspond to lineal complexes linked by P···P bonds, and have only weak secondary F···F and F···P interactions. Minimum 30 has an F···P bond in addition to the P···P bond. Due to the disposition of the atoms in the phosphine groups, cyclic dimers 31 to 33 do not have solely ZBs or HBs as described for the RSa :RSa and RSa :SRa cases. The energetic values show that the RRa :RRa and RRa :SSa (PH2PHF)2 dimers are less stable than the RSa :RSa and RSa :SRa dimers. Using complex 18 as reference, relative energies between 25.64 and 27.74 kJ mol1 and between 24.09 and 16.55 kJ mol1 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
Figure 5. RRa :RRa and RRa :SSa (PH2PHF)2 dimer structures at the MP2/aug’-cc-pVTZ computational level. Dotted lines link those atoms with intermolecular interactions. The molecular graphs of all the complexes are gathered in Table S1. The distances between the atoms involved in weak interactions are shown in . The A and B monomers in the A:B heterochiral dimers correspond to the left and right moieties in this figure.
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tion of complexes 29 and 33. The induction term, Eind, and dHF have small values in all cases (see Table S3).
3. Conclusions The conformational profiles of the PH2PH2 and PH2PHF diphosphines have been studied using the MP2/aug’-cc-pVTZ computational method. Three minima were found for PH2PH2, two with axial chirality, Ra and Sa, and a meso form. In the case of the PH2PHF molecule, two minima were found on rotation of the PP bond. As the phosphorus atom in the PHF group is already stereogenic, four minima are possible for this molecule, RRa, RSa, SRa, and SSa. Six minima were characterized for the dimers formed between chiral monomers of PH2PH2. They are stabilized by ZBs or HBs. The complexes stabilized by ZBs are more stable than those stabilized by HBs. The most stable structure corresponds to a heterochiral dimer that shows two ZB interactions. The chirodiastaltic energy in this system is 1.77 kJ mol1. In the case of the PH2PHF molecule, two sets of dimers were considered. On one hand, the RSa :RSa and RSa :SRa dimers were studied, and on the other hand, the RRa :RRa and RRa :SSa dimers. A total of 16 and 11 minima were found for the two sets. The minima of the first set are more stable than those of the second set. The most stable of all the minima have two ZBs between the lone pair of the phosphorus atom of one molecule and the s*(PF) orbital of the other. The chirodiastaltic energies of the two sets are 0.81 and 2.93 kJ mol1, respectively.
Acknowledgements L.M.A. thanks the MICINN for a PhD grant (No. BES-2010-031225). We also thank the MINECO (Project No. CTQ2012-35513-C02-02) and the Comunidad Autnoma de Madrid (Project MADRIDSOLAR2, ref. S2009/PPQ-1533) for continuing support and CTI (C.S.I.C.) and CESGA for an allocation of computer time. Keywords: axial chirality · computational chemistry conformational analysis · hydrogen bonds · pnicogens
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Received: March 4, 2014 Published online on May 18, 2014
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