J Mol Model (2015) 21:143 DOI 10.1007/s00894-015-2697-y

ORIGINAL PAPER

A comprehensive analysis of P···π pnicogen bonds: substitution effects and comparison with Br···π halogen bonds Cuicui Liu 1 & Yanli Zeng 1 & Xiaoyan Li 1 & Lingpeng Meng 1 & Xueying Zhang 1

Received: 11 March 2015 / Accepted: 4 May 2015 # Springer-Verlag Berlin Heidelberg 2015

Abstract Ab initio calculations were carried out in a systematic investigation of P···π pnicogen-bonded complexes XH2P··· C2H2/C2H4 and FH2P···C2R2/C2R4 for X=H, CH3, OH, CN, Br, Cl, NO2, F, and R=F, CH3, as well as corresponding Br···π halogen-bonded complexes XBr···C2H2. Both the electronwithdrawing and electron-donating substituents in the electron acceptor have enhancing effects on the strength of P···π interactions. The electron-donating group in the electron donor leads to strengthening while the electron-withdrawing group leads to weakening of P···π interactions. The studied P···π and Br···π interactions are similar and are typically Bclosed-shell^ noncovalent character in nature. Moreover, analyses of natural bond orbital and density difference of molecular formation indicated that charge transfer and polarization also play important roles in P···π interactions. The substituents have direct effects on the molecular electrostatic potential, and the charge transfer amount and extent of polarization of the P···π interaction are also specific to each substituent. Keywords Pnicogen bond . Halogen bond . Substitution effect . Topological analysis of electron density

Introduction The realm of noncovalent interactions is extensive and covers the whole of science. Noncovalent interactions are responsible * Xueying Zhang [email protected] 1

Institute of Computational Quantum Chemistry, College of Chemistry and Material Sciences, Hebei Normal University, Shijiazhuang 050024, China

for the properties of condensed phases and the structure of biomacromolecules such as DNA and proteins. They play a key role in the molecular recognition processes that ensure extremely high fidelity in the formation of desired complexes [1–4]. Given their prominence and importance, hydrogen bonds and halogen bonds have been the subject of many experimental and theoretical investigations. Because of their crucial importance in a wide array of chemical and biochemical processes, the nature of these interactions has been studied widely over the years [5–12]. There is now another new and interesting example of a non-covalent interaction that is comparable to hydrogen and halogen bonds; the pnicogen bond. In this bond, a pnicogen atom (N, P, As, or Sb) acts as a Lewis acid and interacts with an electron donor molecule [13]. The anisotropic electronic densities of covalently bonded Group V atoms frequently give rise to regions of positive electrostatic potential (σ-holes), located approximately on the extensions of the covalent bonds to these atoms [14]. Through such positive Bσ-holes,^ atoms can interact attractively and highly directionally with negative sites (e.g., lone pairs, anions and π electrons), forming noncovalent complexes. Beginning with the landmark work of Hey-Hawkins et al. [15], who confirmed that the pnicogen bond might act as a new molecular linker in different chemical systems, the pnicogen bond has received considerable attention in recent years and has been at the forefront of studies into intermolecular interactions [16–43]. The pnicogen bond was first noticed when the lone pair of nitrogen atoms of HSN interacted with an electron deficient region on PH3 or other phosphines [16]. Experimental verification of this sort of interaction in the literature [17–19] has derived primarily from analysis of a number of crystal structures. Politzer et al. [9, 20] highlighted experimental studies on such interactions and conducted a survey of the Cambridge Structural Database for crystalline close contacts of trivalent

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nitrogen, phosphorus and arsenic with six different types of electronegative atoms in neighboring molecules. Scheiner and co-workers [13, 21–25] carried out a series of investigations on P···D interactions, in which lone pair electrons on electronegative atoms (N, O, and S) and π electrons on acetylene, ethylene, and benzene act as electron donors (D). They showed that these interactions are somewhat analogous to the hydrogen, halogen and other noncovalent bonds, along with some fundamental differences. Frontera et al. [26] also studied the behaviors of the halogen, chalcogen and pnicogen bonding interactions considering two types of Lewis bases: amines and arenes. Del Bene et al. [27, 28] stated that the sp2 hybridized P atom could participate in a P···P pnicogen bond in complexes (H2C=PX)2 and H2C=(X)P:PXH2 with a variety of substituents X. They also investigated the complexes formed between the acids O = PH3, S = PH 3, HN = PH3, H2C = PH3 and phosphorus, nitrogen bases [29]. Some pnicogen bonding interactions related to σ-hole and πhole [30–32], single electron [33], and hydride [34] were predicted and characterized. It has been demonstrated that the pnicogen bond is relevant in biological systems and can control self-assembly processes that yield the formation of macrocycles [35, 36]. The substituted groups adjoining the atoms or groups participating directly in the intermolecular interactions have an effect on the strength of those intermolecular interactions. Some related work on substituent effects in pnicogen bonds has been carried out by the groups of Scheiner and Del Bene. Scheiner studied the effects of substituents on the P···N noncovalent bond in the complexes of mono-substituted [37, 38] and the multisubstituted PH3 molecule [39] with the NH3 molecule. Del Bene et al. investigated P···P and P···N pnicogen bonds in complexes (PH2X)2 [40], H2XP:NXH2 [41], and (PHFX)2 [42], with a variety of substituents X. Li et al. [43] investigated substitution, cooperative, and solvent effects on π pnicogen bonds in FH 2 P and FH2As complexes. The present study aimed to investigate the typical P···π interactions between a variety of substituted phosphines PH2X (X=H, CH3, OH, CN, Br, Cl, NO2, and F) with ethylene, acetylene, and their derivatives C2R2/C2R4 (R=F, CH3) using quantum theory of atoms in molecules (QTAIM), natural bond orbital (NBO) and density difference of molecular formation (MFDD) analyses. The purposes of this work were to: (1) investigate the nature of this kind of P···π pnicogen bond; (2) evaluate how various substituents affect the molecular electrostatic potential, geometry, interaction strength, charge transfer, P···π bond polarization, and topological properties of the electron density; (3) determine the common features and differences between the properties of P···π and Br··· π interactions.

Theoretical methods The geometries of the monomers and the complexes were optimized and characterized by frequency computations at the MP2/aug-cc-pVDZ level, which has been shown to be of high accuracy and to provide excellent results [37]. The interaction energy was calculated as the difference between the total energy of the complexes and the sum of the isolated monomers in their minima configurations. The counterpoise procedure proposed by Boys and Bernardi [44] was used to correct the interaction energies, excluding the inherent basis set superposition error (BSSE), as well as for geometry optimization and frequency computation. All optimization and frequency calculations were carried out using the Gaussian 03 package [45]. The molecular electrostatic potential (MEP) at the 0.001 electrons Bohr−3 isodensity surfaces was calculated at the MP2/aug-cc-pVDZ level with the WFA surface analysis suite [46]. NBO analysis was performed to analyze charge transfer interactions involving occupied and unoccupied orbitals via the NBO 5.0 program [47] as implemented in Gaussian 03. In addition, the QTAIM [48, 49] was applied to find the bond critical points (BCPs) and to analyze the character of P···π/Br···π interactions, and was carried out with AIM 2000 [50]. The MFDD was analyzed at the MP2/aug-cc-pVDZ level with the Multifunctional Wavefunction Analyzer (Multiwfn) program [51].

Result and discussion Molecular electrostatic potentials The electrostatic potential [52] is a fundamentally significant feature of a molecule, and has been shown to be quite effective in analyzing and predicting noncovalent interactions. Table 1 gathers the values of the local most positive MEPs (denoted by VS,max) on the surfaces of PH2X (X=H, CH3, OH, CN, Br, Cl, NO2, and F) molecules, and the local most negative MEPs Table 1 Most positive and negative electrostatic potentials (VS,max and VS,min, kcal·mol−1) on the surfaces of PH2X, acetylene, ethylene and their derivatives, respectively Molecule

VS,max

Molecule

VS,min

PH3 PH2CH3 PH2OH PH2CN PH2Br PH2Cl PH2NO2 PH2F

14.0 9.3 29.6 41.0 35.1 37.4 54.6 44.5

C2H2 C2F2 C2(CH3)2 C2H4 C2F4 C2(CH3)4

−17.2 −2.0 −21.0 −17.4 11.6 −16.2

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(denoted by VS,min) above the C≡C/C=C bond of C2R2/C2R4 (R=H, F, CH3) molecules, respectively. For the similarity of geometry, Fig. 1 depicts contour maps of only the MEPs for PH2X and C2R2/C2R4 (X, R=H, F, CH3) computed on the 0.001 a.u. (electrons Bohr−3) contour of the electronic density. Politzer et al. [14, 53] demonstrated that covalently bonded atoms of Groups V–VII have a region of significantly positive electrostatic potential (σ-hole) on the extensions of the bonds attached to them that can form noncovalent complexes with negative sites. From Fig. 1, it can be observed that the σ-hole region is on the opposite side of the covalent P–X bond. From Table 1, for substituents in the P subunit, the electron-donating group (CH3) decreases the value of VS,max compared to the unsubstituted PH3, while the VS,max values tend to be more positive for the progressively stronger electron-withdrawing groups. Within the subset of PH2X, the VS,max values climb in

the sequence CH3 < H < OH < Br < Cl < CN < F < NO2. For the substituents in C2R2/C2R4, the electron-withdrawing F atom decreases the VS,max values greatly with respect to the H atom. As the F atom is a strong electron-withdrawing substituent that leads to a large reduction in the π electron cloud, the VS,min above the C=C bond of the C2F4 molecule becomes positive (11.6 kcal·mol−1).

Fig. 1 Electrostatic potentials on the molecular surfaces of PH2X(X=H, CH3 and F), acetylene and ethylene and their derivative C2R2/C2R4(R=F and CH3) molecules, computed on the 0.001 a.u. contour of the electronic

density. Red and blue regions represent positive and negative molecular electrostatic potential (MEP) values, respectively

Equilibrium geometries and interaction energies Based on analyses of MEPs, a total of 20 complexes XH2P··· C2H2/C2H4 and FH2P···C2R2/C2R4 were constructed and optimized at the MP2/aug-cc-pVDZ level. Table 2 presents the most important geometrical parameters, frequencies, and the interaction energies corrected for BSSE and zero-point vibrational energies. Figure 2 shows representative optimized

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Table 2 Interaction energies, bond lengths, and frequencies of XH2P···C2H2/C2H4 and FH2P···C2R2/C2R4 systems. All energies are in kJ mol−1, distances in angstroms, frequencies in cm−1, angles in degrees d(P···C) α

H3P···C2H2 H3CH2P···C2H2 HOCH2P···C2H2 NCH2P···C2H2

3.5828 3.5859 3.3397 3.4307

166.6 101.6 0.0008 171.0 113.3 −0.0003 172.5 87.5 0.0037 169.5 88.2 0.0037

BrH2P···C2H2 ClH2P···C2H2 O2NH2P···C2H2 FH2P···C2H2 FH2P···C2F2 FH2P···C2(CH3)2

3.2887 3.2653 3.2652 3.1793 3.2482 3.0351

173.9 174.5 172.5 176.0 176.3 176.9

a

β

Δr(P-X)a Δν(P-X)a ΔE

Complex

86.8 86.5 86.9 86.0 83.5 83.4

0.0098 0.0093 0.0026 0.0069 0.0020 0.0126

Complex

d(P···C) α

β

Δr(P-X)a Δν(P-X)a ΔE

0.15 1.26 −7.59 −7.02

−2.88 −4.19 −7.08 −7.60

H3P···C2H4 H3CH2P···C2H4 HOH2P···C2H4 NCH2P···C2H4

3.6435 3.5762 3.2910 3.4418

165.6 168.9 174.1 170.5

91.9 96.4 86.3 86.4

0.0017 0.0010 0.0048 0.0050

−4.19 −0.47 −11.44 −9.56

−2.62 −3.41 −7.34 −7.60

−10.43 −12.76 −2.74 −16.62 −6.81 −31.57

−8.91 −9.18 −9.96 −10.22 −5.77 −17.30

BrH2P···C2H4 ClH2P···C2H4 O2NH2P···C2H4 FH2P···C2H4 FH2P···C2F4 FH2P···C2(CH3)4

3.2276 3.2007 3.2196 3.1114 3.3374 2.9831

175.5 176.1 173.9 177.3 176.9 172.8

85.8 0.0141 85.6 0.0133 85.6 0.0053 84.7 0.0089 81.8 −0.0006 81.2 0.0160

−15.56 −19.64 −7.13 −24.04 −1.30 −41.71

−9.44 −9.70 −10.49 −11.01 −3.15 −22.81

Δr, Δν represent differences in properties between complexes and the monomer molecules

geometries of XH2P···C2H2 (X=H, CH3, OH, CN, Br, Cl, NO2, and F) and FH2P···C2R2 (R=F, CH3) complexes. All equilibrium geometries were similar, where the P–X covalent bond is in a plane with the atom C of C2R2/C2R4 and turned away from the X–P···C axis (α) by 165.6–177.3°. The P atom is located above the C≡C/C=C bond and skewed toward one C atom over the other. The two free H atoms in PH2X are located at the sides with a triple or double bond. This differs from the corresponding π-type hydrogen and halogen-bonded complexes [54, 55], which both lie perpendicular to the center of the C≡C/C=C bond and pointing toward its midpoint. Comparing the geometries reveals that the P atom deflects to the C ≡ C/C = C bond in the complex with the electronwithdrawing group (e.g., OH, CN, Br, Cl, NO2, F), while it is turned to the C–H bond in the complex with the electrondonating group (e.g., CH3). From Table 2, for the P subunit, it is apparent that the binding distances d(P···C) in almost all of the substituents are reduced in comparison with the corresponding values of unsubstituted complexes. The binding distance with the electron-withdrawing substituent is shorter than that with the electron-donating substituent. The electronwithdrawing property of the substituent causes an elongation of the P–X bond and a red shift in P–X stretching frequency. The presence of the electrondonating group has a small effect on the binding distance, P–X bond length and P–X stretching frequency. For the π subunit, the substituent effects on the binding distance, P–X bond length and P–X stretching frequency are different. The binding distance in FH2P···C2F2/C2F4 complexes become longer than in unsubstituted FH2P···C2H2/ C 2 H 4 complexes, while the presence of the electrondonating group (CH3) leads to a decrease in binding distance. The values of Δr(P–X) and Δν(P–X) in the complexes with electron-donating group are much larger than those with an electron-withdrawing group.

The interaction energies span the range of −2.62 kJ·mol−1 for the H3P···C2H4 complex up to −22.81 kJ·mol−1 for the FH2P···C2(CH3)4 complex. It was found that all substituents in the P subunit, whether electron-donating or electronwithdrawing groups, enhance the strength of the interaction relative to that of unsubstituted systems. Regarding substituents in the P subunit, electron-withdrawing groups (OH, CN, Br, Cl, NO2, F) greatly enhance the interaction with respect to the H atom, while an electron-donating group (CH 3 ) strengthens it only slightly. The strength of the interaction energies increases in the order of X = CH3 < OH < CN < Br < Cl < NO2 < F, which differs from the order of the maximum magnitude of the σ-hole potential. Interestingly, the enhancing effect of the Cl and Br atoms is greater than that of the CN group, while the VS,max value of PH 2 Cl and PH 2 Br is smaller than that of PH 2 CN. Another interesting piece of data is that the interaction forces of FH2P···C2H2/C2H4 are stronger than those of O 2 NH 2 P···C 2 H 2 /C 2 H 4 , although the V S,max value of PH2NO2 is much larger than that of PH2F. For substituents in the π subunit, the electronwithdrawing F atom weakens the strength of the interaction relative to that of the unsubstituted FH2P···C2H2/ C 2 H 4 systems. Specially, the interaction energy of FH2P···C2F4 is very small, which is coincident with the positive VS,min value above the C=C bond in C2F4 molecule. The methyl group in the π subunit (electron donor) exhibits a much bigger contribution to the P···π bond than that in the P subunit (electron acceptor). Analyses of natural bond orbitals NBO analysis stresses the role of intermolecular orbital interactions in the complex, particularly to charge transfer. This is carried out by considering all possible interactions between filled donor and empty acceptor NBOs

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Fig. 2 Optimized geometries of the representative complexes XH2P···C2H2(X=H, CH3, OH, CN, Br, Cl, NO2, and F) and FH2P···C2R2(R=F and CH3)

[56]. Table 3 reports the second-order perturbation energies E(2) for the stabilizing intermolecular charge transitions, the amount of charge transferred (Δq) due to

the interaction of donor and acceptor orbital, and the change in occupancy of the pertinent antibonding orbital Δocc. The amount of charge transferred from a donor

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Table 3

Natural bond orbital (NBO) analyses for XH2P···C2H2/C2H4 and FH2P···C2R2/C2R4 systems. E(2) is in kcal mol−1, Δq and Δocc in me

Complex

E(2)PXa E(2)CCb ΔqPXa ΔqCCb ΔoccPXc ΔoccCCd Complex

E(2)PX E(2)CC ΔqPX ΔqCC ΔoccPX ΔoccCC

H3P···C2H2 H3CH2P···C2H2 HOCH2P···C2H2 NCH2P···C2H2 BrH2P···C2H2 ClH2P···C2H2 O2NH2P···C2H2 FH2P···C2H2 FH2P···C2F2 FH2P···C2(CH3)2

0.47 0.36 2.24 1.68 3.21 3.31 3.76 3.87 3.01 5.34

0.80 0.90 3.35 2.09 4.89 5.01 5.29 5.80 2.31 6.61

a

0.32 0.29 0.98 0.57 0.94 1.05 0.94 1.51 0.71 1.60

0.8 0.7 4.9 3.3 8.4 8.2 9.2 8.2 6.2 12.1

0.5 0.5 1.9 1.0 1.7 1.8 1.6 2.7 1.4 2.9

1.7 1.7 7.4 5.2 11.6 11.6 9.1 13.2 8.4 20.1

2.1 1.9 4.3 2.1 3.9 4.4 3.2 6.8 2.9 8.3

H3P···C2H4 H3CH2P···C2H4 HOH2P···C2H4 NCH2P···C2H4 BrH2P···C2H4 ClH2P···C2H4 O2NH2P···C2H4 FH2P···C2H4 FH2P···C2F4 FH2P···C2(CH3)4

0.41 0.53 1.39 0.68 1.36 1.54 1.29 2.28 0.46 1.54

1.6 1.8 7.6 4.3 14.4 13.6 13.9 13 44 15.7

0.8 1.1 2.8 1.3 2.7 3.1 2.5 4.6 1.1 3.2

2.4 3.2 11.7 7.5 18.8 18.8 15.5 20.7 5.7 26.2

1.5 2.2 6.2 2.5 5.8 6.7 4.6 10.4 −2.5 10.5

π(C≡C/C=C)→σ*(P-X) charge transfer

b

LP(P)→π*(C≡C/C=C) charge transfer

c

Change of occupation of the P-X σ* orbital

d

Change of occupation of the C-C π* orbital

orbital to a given orbital of an acceptor may be estimated using the following approximation:
 Fi j 2 Δq ¼ qi ε j −εi Where qi is the orbital occupancy, εi, εj are diagonal elements and Fij is the off-diagonal NBO Fock matrix element. The NBO analyses indicate that charge transfer stabilizes the P···π interaction. The dominant charge-transfer interaction is reported as E(2)PX and ΔqPX in Table 3 occurs between πelectrons of donor species and σ*(P–X) antibonding orbitals of PH 2 X [π(C ≡ C/C = C) → σ*(P–X)]. Unlike the P···N pnicogen bond [37], there is back-donation in the reverse direction from the P lone pairs into π*(C≡C/C=C) antibonding orbitals [LP(P)→π*(C≡C/C=C)]. As an index to judge the relevant measures of this shift, E(2)CC, this phenomenon is significant, amounting to 24–44% of the dominant π(C≡C/ C=C)→σ*(P–X) quantities. This second factor may account for the P···π interaction being stronger than that of the corresponding hydrogen bond [54]. From Tables 2 and 3, the E(2)PX between the π electrons of the C≡C/C=C bond and σ* of the P–X bond correlates well to the binding distance d(P···C). The linear correlation coefficients showing the dependency of E(2)PX on d(P···C) for XH2P···C2R2 and XH2P···C2R4 were found to be 0.986 and 0.967, respectively. The accumulation of density in the antibonding orbital causes a stretch in the P–X bond; the shorter binding distance in the complex allows the PH2X molecule to withdraw electron density more effectively from the π-system, increasing the charge transfer. It can be seen from the values of E(2), Δq, and Δocc that the transferred charge of electron-withdrawing groups in the

PH2X subunit is much greater than that of electron-donating groups, while the reverse is true for substituents in the π subunit. The presence of electron-withdrawing substituents decreases the electron cloud around the P atom in PH2X, so more π-electrons are transferred to the P–X σ* antibonding orbital. The nature of the substituent affects charge transfer due to the interaction of the donor and acceptor orbital, and the sequence according to the quantity of E(2) is CH3 < CN < OH < Br < Cl < NO2 < F. From Table 1, the CN group is a stronger electronwithdrawing substituent that leads to more positive electrostatic potential than Cl and Br atoms. From Table 3, the E(2) of the CN group occurring from the C≡C/C=C π bond to the P–X σ* antibonding orbital or from the P lone pairs to the π*(C≡C/C=C) antibonding orbital was much smaller than that of the Cl and Br groups. The Δocc of the P-X σ* orbital and C≡C/C=C π* orbital in NCH2P···C2H2/C2H4,, ClH2P··· C2H2/C2H4 and BrH2P···C2H2/C2H4 complexes also shows that the antibonding orbitals of NCH2P···C2H2/C2H4 suffer lesser augment of population than the latter two. The sequences of both E(2) and Δocc are consistent with that of the interaction energies, indicating that charge transfer from the negative site to the σ* and π* antibonding orbitals plays an important role in formation of the P···π bond. The values of E(2) and Δocc of the F and NO2 groups also highlight the important role of charge transfer in the interaction energy. Analyses of electron density difference One can achieve a more thorough overview by examining the results of density difference of molecular formation (MFDD) analysis [53, 57–59]. A detailed picture can be obtained by plotting the difference between the electron density of the

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complex and the sum of the electron density of free monomers, placed at the same positions that they occupy in the complex. Such a density difference map provides information on charge shifts occurring within each monomer, i.e., polarizations resulting from the electric field of its partner in the dimer. Figure 3a–j shows how the charge redistributions of PH2X (X=H, CH3, OH, CN, Br, Cl, NO2, and F) and C2R2 (R=H, F, CH3) occur when they interact to form XH2P···C2H2 and FH2P···C2R2. It can be seen that the electron donor C2R2 (R=H, F, CH3) exerts a significant electric field on the σhole of PH2X (X=H, CH3, OH, CN, Br, Cl, NO2, and F) and, as a consequence, causes rearrangement of the electron density of PH2X: a decrease in electron density outside the P atom at the region of the σ-hole and an increase in the P–X internuclear region near the nucleus of substituent groups. Moreover, due to the electric field of the positive σ-hole and lone pairs of the phosphor atom of PH2X, the redistribution of electronic charge of C2R2 (R=H, F, CH3) shows a buildup in electron density above the C2R2 molecules and the C–R internuclear region located at the P side. The conclusions are consistent with the physical interpretation of noncovalent interactions made by Politzer [60]. Here, our attention is focused on the region of electron density difference outside the phosphorus atom of PH2X, and its negative internal charges, which are shown in Table 4. It is clear that the substituents have an effect on polarization. In the case of XH2P···C2H2, with the order X= CH3, OH, CN, Br, Cl, NO2, F, the electric field of the π electron becomes more and more stronger, while the electron density difference outside the P atom becomes more and more

Page 7 of 12 143 Table 4 Integral charges (e) of the density difference region outside the P atom in P···π interactions Complex

Δne

Complex

Δne

H3P···C2H2 H3CH2P···C2H2 HOCH2P···C2H2 NCH2P···C2H2

−0.0063 −0.0011 −0.0158 −0.0171

H3P···C2H4 H3CH2P···C2H4 HOH2P···C2H4 NCH2P···C2H4

−0.0158 −0.0115 −0.0218 −0.0182

BrH2P···C2H2 ClH2P···C2H2 O2NH2P···C2H2 FH2P···C2H2 FH2P···C2F2 FH2P···C2(CH3)2

−0.0194 −0.0194 −0.0198 −0.0221 −0.0068 −0.0308

BrH2P···C2H4 ClH2P···C2H4 O2NH2P···C2H4 FH2P···C2H4 FH2P···C2F4 FH2P···C2(CH3)4

−0.0220 −0.0223 −0.0224 −0.0258 −0.0069 −0.0273

negative, which is consistent with the sequence of the interaction energies. On the other hand, for the three complexes shown in Fig. 3h–j, with the same electron acceptor PH2F, the negative internal charges outside the phosphor atom of PH2X are computed to be −0.0221, −0.0068, and −0.0308e, respectively. The presence of the electron-donating CH3 group causes the greatest decrease in electron density outside the P atom. These results are basically in agreement with the conclusions drawn from NBO analyses. Analyses of the topological properties of electron density In the framework of Bader’s QTAIM [48, 49], atom–atom interactions, such as intermolecular contacts or valence bonds, can be characterized by analyzing the topological properties of

Fig. 3 Computed density difference plots for the representative complexes XH2P···C2H2(X=H, CH3, OH, CN, Br, Cl, NO2, and F) and FH2P···C2R2(R=F, CH3)

J Mol Model (2015) 21:143 −0.0016 −0.0015 −0.0009 −0.0011 0.0011 −0.0022 1.13 1.15 1.13 1.13 1.16 1.02 0.0006 0.0007 0.0006 0.0007 0.0006 0.0002 a

ΔρC(P-X) represents the difference in electron density at the P-X bond critical points (BCPs) between the complexes and the monomer molecules

−0.0046 −0.0047 −0.0045 −0.0056 −0.0038 −0.0084 0.0052 0.0054 0.0051 0.0063 0.0044 0.0086 0.0232 0.0240 0.0232 0.0280 0.0200 0.0348 BrH2P···C2H4 ClH2P···C2H4 O2NH2P···C2H4 FH2P···C2H4 FH2P···C2F4 FH2P···C2(CH3)4 0.0084 0.0087 0.0087 0.0097 0.0090 0.0138 BrH2P···C2H2 ClH2P···C2H2 O2NH2P···C2H2 FH2P···C2H2 FH2P···C2F2 FH2P···C2(CH3)2

0.0216 0.0224 0.0220 0.0256 0.0240 0.0340

0.0046 0.0048 0.0047 0.0055 0.0051 0.0076

−0.0038 −0.0039 −0.0039 −0.0047 −0.0043 −0.0068

0.0008 0.0009 0.0008 0.0008 0.0008 0.0008

1.21 1.23 1.21 1.17 1.19 1.12

−0.0010 −0.0011 −0.0005 −0.0008 0.0004 −0.0019

0.0102 0.0107 0.0102 0.0121 0.0081 0.0171

−0.0004 0.0000 −0.0004 −0.0010 1.19 1.17 1.18 1.20 0.0004 0.0004 0.0007 0.0006 −0.0021 −0.0023 −0.0039 −0.0030 0.0025 0.0027 0.0046 0.0036 0.0112 0.0128 0.0208 0.0168 0.0049 0.0052 0.0087 0.0069 H3P···C2H4 H3CH2P···C2H4 HOH2P···C2H4 NCH2P···C2H4 −0.0001 0.0004 −0.0003 −0.0008 0.0049 0.0049 0.0074 0.0065 H3P···C2H2 H3CH2P···C2H2 HOCH2P···C2H2 NCH2P···C2H2

0.0124 0.0140 0.0192 0.0168

0.0026 0.0027 0.0041 0.0035

−0.0021 −0.0020 −0.0033 −0.0029

0.0005 0.0007 0.0008 0.0006

1.24 1.35 1.24 1.21

Complex ρC

∇2ρC

GC

VC

HC

-GC/VC

ΔρC(P-X)a

ρC

∇2ρC

GC

VC

HC

-GC/VC

ΔρC(P-X)a

Page 8 of 12

Complex

Table 5 Topological properties at P···π bond critical points for XH2P···C2H2/C2H4 and FH2P···C2R2/C2R4 systems (a.u.). ρC Electron density, ∇2ρC the Laplacian of the electron density, GC local kinetic electron energy density, VC potential electron energy density, HC total electron energy density

143

the electron density distribution. In a comprehensive survey of experimental densities derived from X-ray diffraction for 83 complexes, Espinosa et al. [61] demonstrated that essentially all hydrogen bonds exhibit the same topological features. The QTAIM has been applied widely and successfully to the study of the properties of various conventional and unconventional hydrogen bonds [62], halogen bonds [62, 63], as well as pnicogen bonds [30]. Table 5 lists the QTAIM topological results, including electron density (ρC), the Laplacian of the electron density (∇2ρC), and the local kinetic (GC), potential (VC), and total (HC) electron energy density. The electron densities at the P···π BCPs span the range of 0.0049–0.0171 a.u., the maximum electron density is observed for the CH3 substituent in the FH2P···C2(CH3)4 complex, which can be attributed to the greatest strength of the studied P···π interactions. For substituents in the P subunit, the values of ρC, ∇2ρC, and GC for the electron-donating groups are smaller than those for the electron-withdrawing groups. The reverse is true in the π subunit. The results of ρ C (NCH 2 P···C 2 H 2 /C 2 H 4 ) < ρ C (BrH 2 P···C 2 H 2 /C 2 H 4 ), ρC(2ONH2P···C2H2/C2H4)0 and HC 0, HC >0, and −GC/VC >1. Hence, the studied pnicogen bonding interactions are typically Bclosed-shell^ non-covalent in character.

Comparison of P···π with Br···π interactions

Fig. 4a–c Exponential relationships between the topological properties at the P···π BCPs (ρC, ∇2ρC, GC, and VC) and the binding distance [d(P···C)] for the studied complexes. a Electron density ρC versus the binding distance d(P···C). b Laplacian of the electron density ∇2ρC versus the binding distance d(P···C). c Local kinetic GC and potential VC energy versus the binding distance d(P···C)

BCP designates the concentration of the electron charge in the region between the nuclei of the interacting atoms and is

We computed geometric, energetic, and electronic properties of the complexes formed by BrX (X=H, CH3, OH, CN, Br, Cl, NO2, and F) with C2H2 at the same level, to explicitly identify common as well as unique features between P···π and Br···π interactions. The results are listed in Table 6. The dependence on the identity of substituent of the most positive electrostatic potentials (VS,max) on the surfaces of PH2X and BrX (σ-hole) is illustrated graphically in Fig. 5a. Most of them are reasonably close, but with differences being observed for the NO2 and F substituents. In the former case, P serves as the stronger electron acceptor than Br, but the situation is reversed for F, where the Br atom forms the tightest interaction with C2H2. Figure 5b shows a comparison of the interaction energies of P···π pnicogen bonds and Br···π halogen bonds. It can be seen that the strength of the Br···π interaction is stronger than that of P···π interaction for electron-withdrawing substituents with the exception of the NO2 group. From Table 6, the electron density (ρC), its Laplacian (∇2ρC), and total electron energy density (HC) at the Br···π BCPs are larger than those at the P···π BCPs. The topological analyses of electron density (∇2ρC >0, HC >0, −GC/VC >1) show that the studied halogen bonding interactions can also be classified as Bclosed-shell^ weak interactions. Similar Br···π interactions in NCBr/HBr··· C6H6 complexes were investigated by Riley et al. [68], who also found that dispersion plays a pronounced role in Br···π interactions. From the values of Δr(Br–X), Δν(Br–X), and Δρb(Br–X) in Table 6, it can be seen that the behavior of the NO2 substituent is different from that of the other substituents and pnicogen-bonded complexes in a number of ways. In the formation of O2NBr···C2H2, the Br–N bond length is shortened, the Br–N stretching vibration moves to high frequency (blue shift), and the electron density at the Br–N BCP decreases in comparison to those of monomer BrNO2.

143 Table 6

J Mol Model (2015) 21:143

Page 10 of 12

Analyses of geometries, energies, quantum theory of atoms in molecules (QTAIM) and natural bond orbital (NBO) for XBr···C2H2 complexes

VS,max/kcal mol−1 ΔE/kJ mol−1 d(Br···C)/Å ν(Br···π)/cm−1 Δr(Br-X)/Å Δν(Br-X)/cm−1 ΔρC(Br-X)/a.u. ρC/a.u. ∇2ρC/a.u. HC/a.u. -GC/VC E(2)BrX/kcal mol−1 E(2)CC/kcal mol−1 ΔqBrX/me ΔqCC/me ΔoccBrX/me ΔoccCC/me

H

CH3

OH

CN

Br

Cl

NO2

F

16.1 −2.36 3.6007 55.64 0.0015 −9.61 −0.0002 0.0051 0.0144 0.0030 1.30 0.60 0.24 1.3 0.5 1.9 0.7

3.9 −3.41 3.5992 53.12 0.0005 −0.63 0.0005 0.0053 0.0144 0.0030 1.20 0.67 0.31 1.6 0.7 1.8 1.0

32.3 −10.75 3.1214 85.71 0.0089 −17.4 −0.0016 0.0115 0.0364 0.0074 1.30 5.01 1.58 13.6 3.6 16.9 5.1

44.8 −9.18 3.3537 74.16 0.0040 −6.96 −0.0009 0.0079 0.0224 0.0047 1.27 1.88 0.59 4.0 1.3 5.4 1.4

31.9 −11.27 3.1504 81.44 0.0135 −12.5 −0.0018 0.0112 0.0340 0.0069 1.33 5.02 1.27 16.6 2.8 19.6 3.5

37.2 −13.11 3.0743 89.58 0.0163 −19.49 −0.0029 0.0127 0.0392 0.0080 1.29 6.56 1.65 20.5 3.7 24.6 4.6

37.2 −6.82 3.3138 66.53 −0.0243 17.76 0.0084 0.0089 0.0248 0.0051 1.28 3.85 0.72 15.5 1.7 −19.2 1.8

56.4 −19.66 2.8436 111.30 0.0210 −40.91 −0.0047 0.0189 0.0616 0.0129 1.25 14.56 3.80 39.7 8.7 49.3 11.4

The last six rows in Table 6 show the NBO analyses of Br··· π interactions. As in the P···π interactions, charge transfer also occurs from π electrons of donor species to the σ*(Br–X) antibonding orbital of BrX [π(C≡C)→σ*(Br–X)] and from the Br lone pairs into the π*(C≡C) antibonding orbital of C2H2. It was found that the stabilization energy E(2)BrX and the amount of charge transfer qBrX of Br···π interactions were considerable more favorable than those of P···π interactions, especially for the F substituent. This observation indicates that charge transfer also plays an important role in Br···π interactions. NBO analyses aid in understanding why the interaction energy between BrNO2 and C2H2 is the smallest of all the complexes with electron-withdrawing groups. From Table 6,

the negative value of ΔoccBrNO2 indicates that the Br–N antibond actually suffers a loss of population. While some charge is transferred into the Br–N σ* orbital, it does not remain there. A good deal of charge moves onto the O lone pairs of the NO2 group. A lone pair on each of these two oxygens shows a charge increase of 19.6 me, for a total of 39.2 me, which exceeds the 15.5 me originally deposited into the Br−N σ* orbital. It is this diminished occupation of this antibond that is the origin of the shortening of the Br−N bond length and blue-shift of Br−N stretching frequency when the O2NBr···C2H2 complex is formed, contrary to the usual observation in other complexes. There was no such effect for the O2NH2P···C2H2 complex. The results were similar with ntype halogen and pnicogen bonds [24].

Fig. 5a,b Comparison of P···π and Br···π interactions for various substituents X. Electron acceptor atoms are as indicated (P and Br). a The most positive electrostatic potentials (VS,max). b Interaction energies (−ΔE)

J Mol Model (2015) 21:143

Conclusions In this work, the P···π interactions between PH2X and C2R2/ C2R4 were investigated using high-level ab initio calculations, where R=H, F, CH3 and X=H, CH3, OH, CN, Br, Cl, NO2, and F. Substitutent effects on the MEP, geometry, strength of intermolecular interactions, properties of charge transfer and electron density were studied. The computed properties of the pnicogen-bonded complexes were compared with those of the corresponding halogen-bonded complexes XBr···C2H2 (X= H, CH3, OH, CN, Br, Cl, NO2, and F). The results of these calculations support the following statements: (1) The studied P···π and Br···π interactions are similar, both have a typical Bclosed-shell^ non-covalent character. (2) Substitution of the H atoms by electron-donating groups in both P and π subunits enhances the strength of the interaction. The electron-withdrawing groups in the P subunit play an enhancing role, while those in the π subunit have a weakening effect. (3) MEP, NBO, and MFDD analyses indicated that electrostatics, charge transfer, and polarization play important roles in the P···π interactions. The substituents adjoined with the P atom have different effects on the MEP, the amount of charge transferred from a donor orbital to an acceptor orbital, and the negative integral charges of the density difference region outside the P atom. (4) The greatest divergence of substituent effect on P···π and Br···π interactions occurs for the NO2 group, where the strength of the O2NBr···C2H2 interaction is the weakest of the complexes with electron-withdrawing groups. Upon complexation, the Br−N bond is shortened and the respective stretch exhibits a blue shift. The NBO values of the orbital occupation and natural charge show that a good deal of the new density bypasses the Br and N atoms and winds up on the lone pairs of the two O atoms.

Page 11 of 12 143 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32.

Acknowledgments This work was supported by the National Natural Science Foundation of China (Contract No. 21371045, 21372062), the Natural Science Foundation of Hebei Province (Contract No. B2014205109), the Education Department Foundation of Hebei Province (Contract No. ZH2012106, ZD20131037), and Doctor Foundation of Hebei Normal University (Contract No. L2011B09).

33. 34. 35. 36.

Compliance with Ethical Standards The manuscript has full control of all primary data, and the authors agree to allow the journal to review their data if requested. The authors declare no competing financial interest.

37. 38. 39. 40. 41.

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