Hemi bonds and noncovalent interactions in the cational systems (XH2P: SHY)+

Chemical Physics Letters 659 (2016) 126–132

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Research paper

Hemi bonds and noncovalent interactions in the cational systems (XH2P: SHY)+ Xiang Li, An Yong Li ⇑ School of Chemistry and Chemical Engineering, Southwest University, Tiansheng Road No. 1, Chongqing 400715, People’s Republic of China

a r t i c l e

i n f o

Article history: Received 5 June 2016 In final form 5 July 2016 Available online 11 July 2016 Keywords: Hemi bonds Pnicogen/chalcogen bond Radical cational dimmer

a b s t r a c t Quantum chemistry ab initio MP2 and CCSD calculations were performed to investigate the P


S hemi bonds and noncovalent interactions in the radical cational systems (H3P:SH2)+, (FH2P:SH2)+ and (H3P: SHF)+. The hydride dimer (H3P:SH2)+ has a P


S hemi bonding structure and a H-bonding structure, (FH2P:SH2)+ has two hemi bonding structures and a proton-transferred H-bonding structure, (H3P: SHF)+ has two hemi bonding structures and three noncovalent structures. It is remarkable that these hemi bonds also have characters of pnicogen and chalcogen bonds. The binding energy, stability and bonding nature of the hemi bonds were presented. Ó 2016 Elsevier B.V. All rights reserved.

1. Introduction Noncovalent interactions play a critical role in many fields of science such as biochemistry, supermolecular chemistry, medicinal chemistry, materials and so on, and are responsible for properties, structures and functions of condensed systems and bio-systems [1–4]. There are enormous theoretical and experimental works on the noncovalent interactions over the last few decades [5–15]. Besides the weak van der Waals interactions, noncovalent interactions include hydrogen bonds, dihydrogen bonds, halogen bonds, chalcogen bonds, pnicogen bonds and so on, which are much stronger than the van der Waals forces and can be generally regarded as Lewis acid-base interactions. Many of the important noncovalent interactions can be interpreted in terms of the concept ‘r-hole’, and so are called r-hole bonds [8–15]. In the halogen bond the halogen atom X is covalently bonded to an electronegative group R and so has a region of positive electrostatic potential in the extension of the covalent bond RAX, which is called a r-hole. In the hydrogen, pnicogen and chalcogen bonds, there are also r-holes. The electrostatic interaction between the positive r-hole and the negative Lewis base Y is the main contribution to the r-hole bond RAX


Y. Polarization of the two subunits caused by electrostatic interaction is also important in a r-hole bond [11,12]. Charge transfer from Ln(Y) to r⁄(RAX) is a typical character of a r-hole bond [16,17]. It has

⇑ Corresponding author. E-mail addresses: [email protected] (X. Li), [email protected], ayli001@ swu.edu.cn (A.Y. Li). http://dx.doi.org/10.1016/j.cplett.2016.07.011 0009-2614/Ó 2016 Elsevier B.V. All rights reserved.

been proposed [12] that charge transfer is essentially the same thing as polarization. Covalent bond is an electron-pair-shared interaction generally between two open-shell units, but noncovalent interactions are generally interactions between two closed-shell units. Hemi bond, proposed firstly by Linus Pauling [18] in 1931, is an intermediate between the two extreme cases. It is a single-electron or threeelectron r-bond [19], often present in radical chemistry and many gas-phase processes involving radical ions. The hemi-bonds in the radical cational dimers formed by the hydrides N/P/AsH3 and O/S/SeH2 of groups V and VI have been studied extensively [20–22]. In these systems both hemi bond and noncovalent bonds can be formed [23–26]. The hemi bond usually occurs between two heavy atoms such as P


N in (H3N:PH3)+. We found that the hemibonding structure in the radical cational system (H3N:PH3)+ is very similar to the pnicogen bonding structure in the neutral system (H3N:PH3), thus the hemi bond in the radical cational complex accompanies some character of pnicogen bonds [22]. Especially, in the radical cational complex (XH2N:PH2Y)+ (X, Y = electronegative atoms or groups, F/Cl/Br and so on), the pnicogen-bonding character in the P


N hemi bonds is more remarkable [27]. A hemi bond with characters of noncovalent interactions in the radial cational complexes is very interesting. We have studied the pnicogen-bonding character of the hemi bonds in the systems (XH2N:PH2Y)+ (X, Y = F/Cl/Br/CH3/NH2/OH) [27]. In this article, we continue to study the hemi bond and pnicogen/chalcogen bonds in the radical cational systems (H3P:SH2)+, (FH2P:SH2)+, and (H3P: SHF)+. We found that these systems have two hemi-bonding structures, which have characters of pnicogen or chalcogen bond in the hemi bond. Here we present the nature of these hemi bonds.

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2. Computational methods Gaussian 09 program [28] was used to optimize geometry and perform frequency calculations for the monomers and complexes at the levels MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ and CCSD/augcc-pVDZ. Single point energy calculation was done by the method CCSD(T)/aug-cc-pVTZ at the CCSD/aug-cc-pVDZ geometry. The basis set superposition error (BSSE) has been eliminated by the standard counterpoise (CP) correction method proposed by Boys and Bernardi [29]. The AIMAll program [30,31] was used to study electron density properties of the complexes at the bond critical points (BCPs). Atomic charges, spin population, WBI bond index and charge transfer were calculated using the natural bond orbital (NBO) method with the GenNBO 5.0 program [32,33]. 3. Results and discussion 3.1. Structures and vibrational frequencies The equilibrium structures of the complexes (PH3:SH2)+, (FH2P: SH2)+ and (PH3:SHF)+ have been optimized by the three methods MP2/aug-cc-pVDZ, MP2/aug-cc-pVTZ and CCSD/aug-cc-pVDZ. The hydride dimmer (PH3:SH2)+ has two isomers, a P


S hemi bonding structure PS-1 and a hydrogen bonding structure PS-2. The complexes (FH2P:SH2)+ have three isomers, two P


S hemi bonding structures FPS-1 and FPS-2, and a proton-transferred H-bonding structure FPS-3 (HPF


HASH2)+. Our calculation shows that the complexes (Cl/BrH2P:SH2)+ also have similar three isomers, as shown in Fig. S1 of the supporting materials. The complexes (H3P:SHF)+ have five isomers, two P


S hemi bonding structures PSF-1 and PSF-2, and three P


F noncovalent binding structures PSF-3/4/5. We show the structures of the five hemi bonds in Fig. 1 and list their structural parameters in Table 1, the other noncovalent structures are shown in Fig. S1 and Table S1 of supporting materials. These hemi bonds have characters of pnicogen/chalcogen bonds. In the neutral complex H3P


NH3 a large close-to-linear HAP


N angle characterizes a pnicogen bond [16]. Theoretical study on the neutral systems XH2P


SHY for a series of substituents X and Y (F, Cl, Br, H, OH, OCH3, CH3, C2H5, NH2, F, Cl, CCH, COH, CH3, OH, OCH3 and NH2) [13,14] also confirms the viewpoint that pnocogen and chalcogen bonds are characterized by large XAP


S and YAS


P angles. In PS-1 the H3P1


S5 angle (140°) has a linear tendency, much larger than the other two

HPS angles (97°). The H3P1


S5 angle (150°) in FPS-1 and F4P1


S5 (160°) in FPS-2 are also close to linearity, the H3P1


S5 angle (130°) in PSF-1 and the FS


P angle (140°) in PSF-2 are also large. These structural characters imply that in PS1, FPS-1/2 and PSF-1 there is a typical pnicogen bond, where phosphorus acting as a Lewis acid attacks sulphur along the direction of LP orbital of sulphur almost perpendicular to the SH2 or SHF plane. Similarly in PSF-2 there is a typical chalcogen bond, where phosphorus acting as a Lewis base interacts with sulphur roughly along the extension of the FS bond. These pnicogen/chalcogen bonds elongate the corresponding PH/PF/SF bonds. For example, in PS-1 the P1H3 bond is longer than the P1H2/P1H4 bonds by 0.005 Å, in FPS-1 and PSF-1 the P1H3 bond is also longer than the other PH bonds, and the PF bond in FPS-2 is longer than that in FPS-1, especially the SF bond length in PSF-2 is much larger than that in PSF-1 by 0.03 Å at the MP2/aug-cc-pVTZ level. The pnicogen/chalcogen bonds in these hemi bonds lead to a frequency red shift of the PH/PF/SF bonds participating in the pnicogen/chalcogen bonds relative to the PH/PF/SF bonds not involved in the pnicogen/chalcogen bonds. The P1H3 stretch (2501.4 cm1) in PS-1 is set apart from the two other PH bonds’ stretches (2570.8, 2589.7 cm1 for the symmetrical and antisymmetrical PH2 stretches, respectively at the level MP2/aug-ccpVTZ, see supporting Table S2) by the pnicogen bond. Similarly the P1H3 stretch (2512.0 cm1) in PSF-1 is separated from the two other PH bonds’ stretches (2567.0, 2581.7 cm1 for the symmetrical and antisymmetrical PH2 stretches, respectively). In FPS1 the symmetrical PH2 stretch degrades into the P1H3 stretch with a low frequency 2465.6 cm1, and the antisymmetrical PH2 stretch into the P1H2 stretch with a higher frequency 2561.3 cm1. The PF stretch (897.7 cm1) in FPS-2 is red shifted relative to that (918.9 cm1) in FPS-1, the SF stretch (724.3 cm1) in PSF-2 is also red shifted relative to that (833.0 cm1) in PSF-1. In these molecules the PF and SF stretches have the largest infrared intensities. The vibration mode with the smallest frequency (70–130 cm1) is the relative rotation of the two monomers about the PS bond, its large frequency implies that these structures should be also energy-minima even at higher theoretical levels. The P


S distance in FPS-2(PSF-2) is much shorter than that in FPS-1(PSF-1) by 0.12 Å (0.25–0.34 Å), which implies the P


S interacting in FPS-2(PSF-2) stronger than that in FPS-1(PSF-1). Moreover, the pnicogen bond in FPS-2 is stronger than that in FPS-1, and the chalcogen bond in PSF-2 is stronger than the pnicogen bond in PSF-1.

FPS-1 C 1

FPS-2 Cs

PSF-1 C 1

PSF-2 C1

PS-1 Cs

Fig. 1. AIM molecular maps for the hemi-bonding structures of the complexes (PH3:SH2)+, (FH2P:SH2)+, and (PH3:SHF)+ optimized at the level MP2/aug-cc-pVDZ.

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Table 1 Geometrical parameters (length: Å; angle: °) of the hemi-bonding structures PS-1, FPS-1/2 and PSF-1/2, calculated at the three levels, (A) MP2/aug-cc-pVTZ, (B) MP2/aug-cc-pVDZ, and (C) CCSD/aug-cc-pVDZ. Structures

Terms

A

B

C

Structures

Terms

A

B

C

PS-1 Cs

P(1)-S(5) P(1)-H(2,4) P(1)-H(3) S(5)-H(6,7) h(H3-P1-S5) P(1)-F(4) P(1)-H(2) P(1)-H(3) P(1)-S(5) S(5)-H(6) S(5)-H(7) h(H3P1S5) h(F4-P1-S5) P(1)-F(4) P(1)-H(2,3) P(1)-S(5) S(5)-H(6,7) h(F4-P1-S5)

2.715 1.397 1.405 1.344 143.6 1.564 1.399 1.409 2.638 1.344 1.345 152.0 86.5 1.570 1.397 2.520 1.345 159.8

2.786 1.411 1.416 1.357 138.9 1.614 1.414 1.422 2.699 1.358 1.358 149.8 86.4 1.620 1.411 2.568 1.358 158.6

2.808 1.415 1.420 1.361 138.0 1.613 1.418 1.425 2.724 1.361 1.362 148.2 86.9 1.615 1.415 2.598 1.361 156.9

PSF-1 C1

P(1)-S(5) P(1)-H(2) P(1)-H(3) P(1)-H(4) S(5)-F(7) S(5)-H(6) h(H3-P1-S5) h(P1-S5-F7) P(1)-S(5) P(1)-H(2) P(1)-H(3) P(1)-H(4) S(5)-F(7) S(5)-H(6) h(F7-S5-P1) h(H2-P1-S5)

2.710 1.398 1.403 1.399 1.591 1.348 134.4 86.4 2.369 1.403 1.398 1.397 1.630 1.344 142.6 121.5

2.791 1.411 1.414 1.412 1.640 1.362 125.8 84.0 2.451 1.416 1.411 1.410 1.671 1.359 142.8 120.5

2.820 1.415 1.417 1.415 1.638 1.365 126.4 84.0 2.549 1.419 1.414 1.413 1.657 1.362 139.5 124.0

FPS-1 C1

FPS-2 Cs

PSF-2 C1

3.2. The nature of the bonding

(PS) MO, respectively, for FPS-2. So in the structures PS-1, FPS1/2 and PSF-1/2, the a spin describes a noncovalent interaction — a pnicogen bond or chalcogen bond, but the b spin expresses a hemi bond. The a spin hyperconjugations Lp(S) ? r⁄(PF) in FPS2 and Lp(P) ? r⁄(SF) in PSF-2 are quite large, which lead to large charge transfer from the lone orbital to the antibonding r orbital, therefore the pnicogen bond in FPS-2 and chalcogen bond in PSF-2 are stronger than the pnicogen bonds in PS-1, FPS-1 and PSF-1. The differences between the a and b spins for the hemi bonds are further described by the Laplacian of electron density. Fig. S2 in supporting material shows the Laplacian contour maps of the a and b spin electron densities and the total electron density for all the hemi-bonding and noncovalent structures. Fig. 3 gives the contour maps of FPS-2 as an example. For the noncovalent bonds PS-2, FPS-3 and PSF-3/4/5, the Laplacian contours of the a and b spin and the total electron densities are quite similar to each other, there is no area of negative Laplacian between the two interacting subunits. But for the hemi bonds PS-1, FPS-1/2 and PSF-1/2, the b spin Laplacian contour has a region of negative Laplacian between P


S, which denotes electron density accumulation between P


S, different from that of the a spin (and the total spin) which has no region of negative Laplacian between the two subunits. This is a typical character of the hemi bond.

The nature of chemical bonding can be quantitatively analyzed by use of electron density properties at BCPs and Wiberg bond indexes (WBIs) which are defined as bond orders. In PS-1, FPS1/2 and PSF-1/2, the P


S bond orders are in the range 0.28–0.6, electron density at the P


S BCP is larger than 0.05 a.u., and local electron energy density H at the P


S BCP is a nonignorable negative value, as shown in Table 2. In contrast, PS-2, FPS-3 and PSF3/4/5 have small bond order, and small BCP electron density and ignorable H values at the intermolecular bonds, see Table S3 in supporting materials. These data imply that in PS-1, FPS-1/2 and PSF-1/2, the P


S bonds are typical hemi bonds and have some covalent character, but in PS-2, FPS-3 and PSF-3/4/5 the intermolecular bonds are typically noncovalent interactions. The hemi bonds and noncovalent interactions have distinct differences on the a and b spin Lewis structures, charger transfer and hyperconjugation. The a and b spin Lewis structures for the noncovalent structures PS-2, FPS-3 and PSF-3/4/5 have the same covalent bonding styles except that the a-spin has one more lone electron on phosphor or sulphur than the b spin. For the hydrogen bonds PS-2 and FPS-3 the a and b spins also have the same charge transfer except for the magnitudes having small differences. However, for the hemi bonds PS-1, FPS-1/2 and PSF-1/2, the a and b spins have different electronic structures. In the a spin, phosphorus has three PAH/F covalent bonds and one lone electron, sulphur has two SAH/F covalent bonds and two lone electrons. But in the b spin besides those covalent bonds also occurring in the a spin there is one more PAS covalent bond, and only one lone electron on sulphur. Fig. 2(a) and (b) shows the a and b spin Lewis structures of FPS-2 as an example. The a spin has a charge transfer from Lp(S) to r⁄(PF/PH), or from Lp(P) to r⁄(SF), and the b spin r(PS) MO is constructed from hybrids of P and S, see Table 2. Fig. 2 (c) and (d) shows the a spin hyperconjugation and the b spin r

3.3. Interaction energies In our calculated systems the hemi-bonds have different nature from noncovalent bonds. The hemi bond has one shared electron and so has some covalent character, but the noncovalent bond has no shared electron. The hemi bond is much stronger and more stable than the noncovalent bond. The interaction energies of the hemi bonds and noncovalent bonds are calculated using the supermolecular method. For these radical cational systems, in order to calculate the interaction energy using this method, we need to

Table 2 WBIs, and electron density q, Laplacian r2q and local electron energy density H at the P


S BCPs for the hemi bonds PS-1, FPS-1/2 and PSF-1/2, the second-order orbital interaction energies E(2) (kcal/mol) and orbital occupancy for a spin, the r(PS) bond for the b spin, calculated at MP2/aug-cc-pVTZ, h is hybrid orbital. Structures PS-1 FPS-1 FPS-2 PSF-1 PSF-2

WBI 0.281 0.310 0.389 0.288 0.602

q 0.050 0.057 0.065 0.053 0.093

r2q 0.025 0.013 0.003 0.022 0.039

H

E(2)

0.011 0.015 0.022 0.012 0.037

E [Lp(S) ? r (P1H4)] = 5.6 E(2)[Lp(S) ? r⁄(P1H3)] = 7.3 E(2)[Lp(S) ? r⁄(PF)] =18.3 E(2)[Lp(S) ? r⁄(P1H3)] = 4 E(2)[Lp(P) ? r⁄(SF)] =34.4 (2)

⁄

r⁄

r(PS)

r⁄(P1H4) = 0.015e r⁄(P1H3) = 0.027e r⁄(PF) = 0.056e r⁄(P1H3) = 0.012e r⁄(SF) = 0.060e

0.623h(P) + 0.782h(S) 0.621h(P) + 0.784h(S) 0.567h(P) + 0.824h(S) 0.640h(P) + 0.768h(S) 0.691h(P) + 0.723h(S)

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H

F P H

H

F

H

S

P H

H

(a) α spin Lewis structure

(c) α spin hyperconjugation between LP(S) and σ*(PF)

H

S

H (b) β spin Lewis structure

(d) β spin σ(PS) MO

Fig. 2. a and b spin NBO analysis for FPS-2.

Total electron density

α electron density

β electron density

Fig. 3. Molecular graphs and Laplacian contour maps of the total electron density and the a and b spin electron densities in the symmetry plane for the structure FPS-2. BCPs are marked as green dots. Green solid isolines correspond to the positive Laplacian values, and red ones correspond to the negative values. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

determine the two monomers of the whole complex using the interacting distance, bond order, BCP electron density, spin density and charge population. The spin density and charge population have been calculated by use of the NBO, AIM and Mulliken methods, the results of the three methods are qualitatively consistent with each other. Here we only list the spin density and charge population of the NBO method in Table S4. The spin density and charge population show that the noncovalent structures PS-2, FPS-3 and PSF-3/4/5 can be completely divided into two subunits, H3P+ + SH2 for PS-2, HFP + SH+3 for FPS-3, H4P+ + FS for PSF-3, and H3P+ + FSH for PSF-4/5. But the hemi bonding structures PS-1, FPS-1/2 and PSF-1/2 cannot be unambiguously separated into two parts. This is also a remarkable difference between the hemi bond and noncovalent bond. For the hemi bonding structures, the following two divisions can be used. (a) The positive charge and unpaired electron are located at the subunit of phosphorus, the two subunits are H3P+ + SH2 for PS-1, H2FP+ + SH2 for FPS-1/2, and H3P+ + SFH for PSF-1/2. (b) The positive charge and unpaired electron are located at the subunit þ of sulphur, the two subunits are H3P + SHþ 2 for PS-1, H2FP + SH2 + for FPS-1/2, and H3P + HFS for PSF-1/2. Therefore, for the noncovalent structures we obtained one value of the interaction energy, listed in supporting Table S5; but for the hemi bonds we obtained two interacting energies, which are listed in Table 3. Here the BSSE has been corrected. The binding energy of the hemi bond is much larger than that of the noncovalent bond for the same system. For a hemi bond, the energy of division (b) is larger than that of division (a). This means that PH3/PH2F loses an electron easier than SH2/SHF. This can be

Table 3 BSSE-corrected interaction energies (kJ/mol) for the hemi bonds calculated at the levels (A) MP2/aug-cc-pVTZ, (B) MP2/aug-cc-pVDZ, (C) CCSD/aug-cc-pVDZ and (D) CCSD(T)/aug-cc-pVTZ//CCSD/aug-cc-pVDZ. Structures

B

C

D

Hemibonds-division (a) PS-1 98.28 FPS-1 106.19 FPS-2 116.48 PSF-1 86.47 PSF-2 91.78

A

90.11 102.29 110.73 71.77 69.98

88.88 102.24 107.16 69.86 61.81

101.29 110.13 118.48 88.98 91.90

Hemibonds-division (b) PS-1 166.91 FPS-1 158.54 FPS-2 168.92 PSF-1 141.44 PSF-2 146.50

154.77 134.40 142.93 138.06 135.69

139.71 117.27 122.44 127.89 120.87

166.91 158.54 168.92 141.44 146.50

understood by the fact that the first ionization energy of H2S is larger than that of PH3 (the ionization energy of H2S and PH3 calculated at the level MP2/aug-cc-pVTZ are 10.39 and 9.68 eV respectively, their difference is about 68 kJ/mol). Therefore the spin density and positive charge in the complex are mainly distributed on the subunit of phosphorus, as shown in Table S4. The binding energy of FPS-2 is larger than that of FPS-1, their difference is about 10 kJ/mol at the level MP2/aug-cc-pVTZ, which is just the energy difference of the pnicogen bonds in FPS-1 and FPS-2. Similarly, the binding energy of PSF-2 is larger than that of PSF-1, their difference is about 5 kJ/mol at the level MP2/augcc-pVTZ, which is just the energy difference of the chalcogen bond

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Table 4 Energies E(kJ/mol) without BSSE correction of the various structures relative to the energy of the most stable structure calculated at the levels (A) MP2/aug-cc-pVTZ, (B) MP2/aug-cc-pVDZ, (C) CCSD/aug-cc-pVDZ, (D) CCSD(T)/aug-cc-pVTZ//CCSD/aug-ccpVDZ and G4, enthalpies and free energies H and G (kJ/mol) relative to the most stable structure at ambient condition (298.15 K, 1 atm) calculated by MP2/aug-cc-pVTZ. In the hydride dimer PS-1 is the most stable structure, in the F systems FPS-2 is the most stable. Structures

E(A)

E(B)

E(C)

E(D)

E(G4)

H(A)

G(A)

PS-1 PS-2 FPS-2 FPS-1 FPS-3 PSF-3 PSF-2 PSF-1 PSF-5 PSF-4

0 54.50 0 11.44 44.54 161.98 172.07 178.24 220.91 221.57

0 48.51 0 10.34 15.63 135.36 164.45 164.85 193.42 193.50

0 49.38 0 6.92 3.41 119.45 158.20 153.28 181.07 181.13

0 53.35 0 9.37 33.45 146.28 162.19 165.51 208.60 209.43

0 – 0 7.70 34.41 153.64 160.34 164.84 229.82 231.07

0.00 48.57 0.00 9.91 40.04 162.18 170.39 174.78 215.88 216.54

0.00 41.30 0.00 7.94 22.10 153.58 169.41 169.40 205.77 205.85

in PSF-2 and the pnicogen bond in PSF-1. Here we note that the large basis set aug-cc-pVTZ is more reliable than the smaller double zeta basis set aug-cc-pVDZ for predicting the interacting energy of the hemi bonds. It is notable that the purely noncovalent pnicogen and chalcogen bonds in neutral systems XH2P


SHY [13,14], with large interacting distances r(P


S) 2.5–3.6 Å and small interacting energies 1.5–10 kcal/mol, are much weaker than the hemi bond plus chalcogen/pnicogen bond of the hemi bonding structures PS-1, FPS-1/2 and PSF-1/2, even also weaker than the noncovalent bonds of the noncovalent structures PS-2, FPS-3 and PSF-3/4/5, in the radical cational systems studied here. 3.4. Stability For the system (PH3:SH2)+ the hemi-bonding structure PS-1 is much more stable than the H-bonding structure PS-2 by

Fig. 4. Energy paths without BSSE correction from FPS-2 to FPS-3 and from PSF-2 to PSF-3 calculated at the MP2/aug-cc-pVTZ level. (a) FPS-2 (FPH2


SH2)+ ? (FPH2)+ + SH2 ? FPH + H+ + SH2 ? FPH + SH+3 ? FPS-3 (HPF


HASH2)+ (b) PSF-2 (PH3


SFH)+ ? H3P + HFS+ ? H3P + H+ + (SF)  ? H4P+ + (SF)  ? PSF-3 (H4P


SHF)+.

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50 kJ/mol. For the systems (FPH2:SH2)+ and (PH3:SHF)+, the hemibonding structure FPS-2 is the most stable one, the stability order is FPS-2 > FPS-1 > FPS-3  PSF-3 > PSF-2 > PSF-1 > PSF-5 > PSF-4. The energies of the structures PSF-4 and PSF-5 are very close to each other. Table 4 lists the relative energies without BSSE correction of the various structures for the systems (PH3:SH2)+, (FPH2: SH2)+ and (PH3:SHF)+, where the energy of the most stable structure for each system is set to zero. We also listed the enthalpies and free energies of the various structures relative to the most stable structure at ambient condition (298.15 K, 1 atm). The thermodynamic stability order is consistent with the energy stability order, thus for each system the reaction from a structure with a higher energy to a structure with a lower energy is exothermal and spontaneous. Here we note that the double zeta basis set aug-cc-pVDZ are quite unreliable for predicting the energy, the triple zeta basis set aug-cc-pVTZ is more reasonable. Especially the method CCSD/aug-cc-pVDZ gives wrong energy order. It predicts the proton-transferred H-bond FPS-3 more stable than the hemi bond FPS-1 and the hemi bond PSF-2 less stable than the hemi bond PSF-1. It is notable that the structures of (FPH2:SH2)+ are much more stable than the structures of (PH3:SHF)+. The reason is that the negativity of P is smaller than that of S, so the PAF bond is stronger than the SAF bond, but the PAH bond is weaker than the SAH bond. The energy difference E(PSF)  E(FPS) between PSF and FPS is roughly equal to the bonding energy difference of the PAF and SAF bonds plus the bonding energy difference of the SAH and PAH bonds. The theoretical bond energies calculated at the level MP2/aug-cc-pVTZ and the experimental bond energies for the PAF, S-F, P-H and SAH bonds are listed in Table S6 [34]. The theoretical bond energy differences BE(PF)  BE(SF) and BE(SH)  BE (PH) are about 120 and 40 kJ/mol, respectively, so the energy difference E(PSF)  E(FPS) is about 160 kJ/mol, consistent with the data in Table 4. The relative energies further confirm the hemi bonding structures are more stable than the noncovalent structures for each system, and the hemi bonds FPS-2 (PSF-2) is more stable than FPS-1 (PSF-1). For (FPH2:SH2)+, the two hemi-bonding structures FPS1/2 are more stable than the proton-transferred H-bonding structure FPS-3. But for (PH3:SHF)+, the proton-transferred structure PSF-3 is more stable than the hemi-bonding structures PSF-1/2. This difference can be understood by the energy paths from FPS2 to FPS-3 and from PSF-2 to PSF-3. FPS-2 can be transferred to FPS-3 through the path FPS-2 (FPH2


SH2)+ ? (FPH2)+ + SH2 ? FPH + H+ + SH2 ? FPH + SH+3 ? FPS-3 (HPF


HASH2)+, as shown in Fig. 4(a). PSF-2 can be transferred to PSF-3 through the path PSF-2 (PH3


SFH)+ ? H3P + HFS+ ? H3P + H+ + (SF) ? H4P+ +  (SF) ? PSF-3 (H4P


SHF)+, as shown in Fig. 4(b). In each process the energies of the first and last steps are just the binding energies of FPS-2(PSF-2) and FPS-3(PSF-3), the binding energy differences of FPS-2 and PSF-2 and of FPS-3 and PSF-3 are about 30 and 17 kJ/mol, respectively. The second step is deprotonation of (FPH2)+ or HFS+, their energy difference is only about 18 kJ/mol. The third step is protonation of SH2 or H3P, their energy difference is large, 80 kJ/mol. So it is just the large protonation energy of PH3 relative to H2S leading to PSF-3 more stable than PSF-1/2 for (PH3:SHF)+, opposite to the case of (FPH2:SH2)+.

4. Conclusions In this article we theoretically presented the structures, stability, binding energies and bonding nature of the P


S hemi bonds and the noncovalent interactions in the radical cational dimers (PH3:H2S)+, (FPH2:SH2)+ and (PH3:SHF)+. We note that the hemi bond is much stronger than the noncovalent interactions in these

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systems. It is remarkable that in the hemi bonding structures of these systems the hemi bond also has characters of a pnicogen or chalcogen bond. In the hemi bonds the a and b spins describe a pnicogen/chalcogen bond and a two-center-one-electron covalent bond, respectively. For (FPH2:SH2)+ the hemi-bond structure with a strong FAP


S pnicogen bond is the most stable, but for (PH3: SHF)+ the proton-transferred structure is the most stable.

Appendix A. Supplementary material Fig. S1 shows molecular graphs of the structures PS-2, FPS-3 and PSF-3/4/5, and ClPS-1/2/3 and BrPS-1/2/3 of the complexes (XH2P: SH2)+ (X = Cl/Br). Table S1 lists geometrical parameters of the noncovalent structures. Table S2 lists the frequencies of some vibrational modes related to the intermolecular interactions. Table S3 lists properties of the intermolecular bonds for the noncovalent structures. Fig. S2 gives the Laplacian contour of the electron densities. Table S4 lists spin density and charge population of the NBO method. Table S5 lists the BSSE-corrected interaction energies of the noncovalent structures. Table S6 lists the theoretical and experimental bond energies of the PAF/H and SAF/H bonds. Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.cplett.2016.07.011.

References [1] P. Auffinger, F.A. Hays, E. Westhof, P.S. Ho, Halogen bonds in biological molecules, Proc. Natl. Acad. Sci. USA 101 (2004) 16789–16794. [2] M. Raynal, P. Ballester, A. Vidal-Ferran, P.W. van Leeuwen, Supramolecular catalysis. Part 1: Non-covalent interactions as a tool for building and modifying homogeneous catalysts, Chem. Soc. Rev. 43 (2014) 1660–1733. [3] P. Metrangolo, F. Meyer, T. Pilati, G. Resnati, G. Terraneo, Halogen bonding in supramolecular chemistry, Angew. Chem. Int. Ed. 47 (2008) 6114–6127. [4] A.J. Parker, J. Stewart, K.J. Donald, C.A. Parish, Halogen bonding in DNA base pairs, J. Am. Chem. Soc. 134 (2012) 5165–5172. [5] G.C. Maitland, Intermolecular Forces: Their Origin and Determination, Oxford University Press, 1981. [6] A. Stone, The Theory of Intermolecular Forces, Oxford University Press, 2013. [7] Y. Fang, A.Y. Li, F.Y. Ma, A comparative study of the chalcogen bond, halogen bond and hydrogen bond S


O/Cl/H formed between SHX and HOCl, J. Mol. Model. 21 (2015) 61. [8] P. Politzer, P. Lane, M.C. Concha, Y. Ma, J.S. Murray, An overview of halogen bonding, J. Mol. Model. 13 (2007) 305–311. [9] P. Politzer, J.S. Murray, M.C. Concha, R-hole bonding between like atoms; a fallacy of atomic charges, J. Mol. Model. 14 (2008) 659–665. [10] P. Politzer, J.S. Murray, A Unified View of Halogen Bonding, Hydrogen Bonding and Other r-Hole Interactions, Noncovalent Forces, Springer, 2015, pp. 291– 321. [11] J.S. Murray, P. Lane, T. Clark, K.E. Riley, P. Politzer, R-Holes, p-holes and electrostatically-driven interactions, J. Mol. Model. 18 (2012) 541–548. [12] P. Politzer, J.S. Murray, T. Clark, Halogen bonding and other r-hole interactions: a perspective, Phys. Chem. Chem. Phys. 15 (2013) 11178–11189. [13] M.D. Esrafili, N. Mohammadirad, An ab initio study on tunability of r-hole interactions in XHS:PH2Y and XH2P:SHY complexes (X = F, Cl, Br; Y = H, OH, OCH3, CH3, C2H5, and NH2), J. Mol. Model. 21 (2015) 176. [14] M.D. Esrafili, H. Akhgarpour, An ab initio study on competition between pnicogen and chalcogen bond interactions in binary XHS:PH2X complexes (X = F, Cl, CCH, COH, CH3, OH, OCH3 and NH2), Mol. Phys. 114 (2016) 1847– 1855. [15] P. Politzer, D.G. Truhlar, Chemical applications of atomic and molecular electrostatic potentials: reactivity, structure, scattering, and energetics of organic, inorganic, and biological systems, Springer Science & Business Media, 2013. [16] S. Scheiner, A new noncovalent force: Comparison of P


N interaction with hydrogen and halogen bonds, J. Chem. Phys. 134 (2011) 094315, http://dx.doi. org/10.1063/1.3562209. [17] U. Adhikari, S. Scheiner, Effects of charge and substituent on the S


N chalcogen bond, J. Phys. Chem. A 118 (2014) 3183–3192. [18] L. Pauling, The nature of the chemical bond. IV. The energy of single bonds and the relative electronegativity of atoms, J. Am. Chem. Soc. 54 (1932) 3570– 3582. [19] L. Pauling, The Nature of the Chemical Bond, Cornell University Press, Ithaca, NY, 1960. [20] R. Joshi, T.K. Ghanty, T. Mukherjee, S. Naumov, Hydrogen bonding in neutral and cation dimers of H2Se with H2O, H2S, and H2Se, J. Phys. Chem. A 116 (2012) 11965–11972.

132

X. Li, A.Y. Li / Chemical Physics Letters 659 (2016) 126–132

[21] T. Stein, C.A. Jiménez-Hoyos, G.E. Scuseria, Stability of hemi-bonded vs protontransferred structures of (H2O)+2, (H2S)+2, and (H2Se)+2 studied with projected Hartree-Fock methods, J. Phys. Chem. A 118 (2014) 7261–7266. [22] L.F. Ji, A.Y. Li, Z.Z. Li, Structures and stabilities of hemi-bonded vs protontransferred isomers of dimer radical cation systems (XH3YH3)+ (X, Y = N, P, As), Chem. Phys. Lett. 619 (2015) 115–121. [23] M. Marín-Luna, I. Alkorta, J. Elguero, A computational study on [(PH2X)2]+ homodimers involving intermolecular two-center three-electron bonds, Struct. Chem. 27 (2016) 753–762. [24] R. Joshi, T.K. Ghanty, S. Naumov, T. Mukherjee, Structural investigation of asymmetrical dimer radical cation system (H2O–H2S)+: proton-transferred or hemi-bonded?, J Phys. Chem. A 111 (2007) 2362–2367. [25] P.-R. Pan, Y.-S. Lin, M.-K. Tsai, J.-L. Kuo, J.-D. Chai, Assessment of density functional approximations for the hemibonded structure of the water dimer radical cation, Phys. Chem. Chem. Phys. 14 (2012) 10705–10712. [26] H. Do, N.A. Besley, Proton transfer or hemibonding? The structure and stability of radical cation clusters, Phys. Chem. Chem. Phys. 15 (2013) 16214–16219. [27] L.F. Ji, A.Y. Li, Z.Z. Li, Z.X. Ge, Substituent effects on the properties of the hemibonded complexes (XH2P


NH2Y)(+) (X, Y = H, F, Cl, Br, NH2, CH3, OH), J. Mol. Model. 22 (2016), http://dx.doi.org/10.1007/s00894-015-2876-x. 1-1.

[28] M. Frisch, G. Trucks, H.B. Schlegel, G. Scuseria, M. Robb, J. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. Petersson, Gaussian 09, Revision A. 02, Gaussian Inc., Wallingford, CT, 200 (2009). [29] S.F. Boys, F.D. Bernardi, The calculation of small molecular interactions by the differences of separate total energies. Some procedures with reduced errors, Mol. Phys. 19 (1970) 553–566. [30] R.F. Bader, Atoms in Molecules: A Quantum Theory, International Series of Monographs on Chemistry 22, Oxford University Press, Oxford, G. Henkelman, A. Arnaldsson, H. Jónsson (2006), A fast and robust algorithm for Bader decomposition of charge density, Computation Materials Science, 36 (1990) 354–360. [31] T. Keith, AIMAll (Version 13.10. 19) TK Gristmill Software, Overland Park KS, USA, 2013. [32] F. Weinhold, Discovering Chemistry with Natural Bond Orbitals, John Wiley & Sons, 2012. [33] E. Glendening, J. Badenhoop, A. Reed, J. Carpenter, J. Bohmann, F. Weinhold, GenNBO5.0W, Theoretical Chemistry Institute, University of Wisconsin, Madison, WI, 1996. 2001. [34] Y.-R. Luo, Comprehensive handbook of chemical bond energies, CRC Press, 2007.