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Competition of chalcogen bond, halogen bond, and hydrogen bond in SCSHOX and SeCSeHOX (X = Cl and Br) complexes
Computational and Theoretical Chemistry 980 (2012) 56–61
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Competition of chalcogen bond, halogen bond, and hydrogen bond in SCSAHOX and SeCSeAHOX (X = Cl and Br) complexes Qing-Zhong Li ⇑, Ran Li, Ping Guo, Hui Li, Wen-Zuo Li, Jian-Bo Cheng The Laboratory of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Yantai University, Yantai 264005, PR China
a r t i c l e
i n f o
Article history: Received 13 October 2011 Received in revised form 4 November 2011 Accepted 7 November 2011 Available online 26 November 2011 Keywords: Chalcogen bond Halogen bond Hydrogen bond Competition Hypohalous acids
a b s t r a c t The competition of chalcogen bond, halogen bond, and hydrogen bond in SCSAHOX and SeCSeAHOX (X = Cl and Br) complexes have been investigated with quantum chemical calculations at the MP2/augcc-pVTZ level. The complexes have been studied with the geometrical, spectroscopic, and energetic parameters. The interaction strength is comparable for the hydrogen bond and halogen bond, which are a littler stronger than the chalcogen bond. The interaction strength depends on the nature of hypohalous acids and chalcogen atom. The nature and properties of three types of interactions have been analyzed with natural bond orbital, atoms in molecules, electrostatic potentials, and energy decomposition. The dispersion interaction plays a dominant role in three types of interactions. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction People have come to realize the key role of intermolecular interactions in molecular recognition, crystal engineering, and biomolecular systems [1,2]. The traditional research for the intermolecular interactions has focused on the more common hydrogen-bonded interactions, but a growing body of experimental and theoretical evidence confirms the importance of halogen bond [3–11]. Halogen bonding refers to the non-covalent interactions of halogen atoms in some molecules with negative sites on others [12–14]. Halogen bond belongs to r-hole interaction, which is a non-covalent interaction between a region of positive electrostatic potential on the outer surface of a Group IV, V, VI, or VII covalently-bonded atom (a r-hole) and a region of negative potential on another molecule [12–19]. It is also called chalcogen bond for Group VI atoms [20]. In complex systems with the presence of more than two types of non-covalent interactions, a competition occurs among them. A series of cocrystallization reactions can be controlled through the competition between hydrogen bonds and halogen bonds [21]. Politzer and coworkers pointed out that r-hole bonding can certainly be competitive with hydrogen bonding [22]. Alkorta et al. studied the competition of hydrogen bonds and halogen bonds in complexes of hypohalous acids with nitrogenated bases (NH3, N2, and NCH) [23]. In H2COAHOX (X = F, Cl, and Br) complex, the hydrogen bond is stronger than the halogen bond [24]. In H2SOAHOX complex, the difference in the strength of both interactions is decreased ⇑ Corresponding author. Tel./fax: +86 535 6902063. E-mail address: [email protected] (Q.-Z. Li). 2210-271X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.comptc.2011.11.019
for the Cl systems and even the Br halogen bond is stronger than the hydrogen bond [25]. Thus we think that within this research field hypohalous acids are a very interesting class of compounds because of the presence of both a proton donor and a halogen donor. Hypohalous acids are involved in stratospheric reactions that release free halogen molecules and atoms, participating in the depletion of the ozone layer [26,27]. Carbon disulfide (CS2) is a volatile liquid with a pungent smell and has been widely used for the production of viscose rayon, rubber, and other organic materials. It is an apolar aprotic solvent with a better solvability. CS2 has been used as substrate probes for enzyme activities [28]. It is known from the electrostatic potential of CS2 [20] that the C atom in CS2 has a partial negative electrostatic potential while the S atom in it exhibits anisotropic distribution of electron density. There is a region of positive electrostatic potential (r-hole) on the outermost portion of the covalentlybonded S atom while a belt of negative electrostatic potential around the central part of the S atom is found. The former can interact with an electron donor to form a noncovalent bond named chalcogen bond, whereas the latter can act as an electron donor. Andrews and coworkers studied the CS2AHF system with a matrix isolation spectroscopy [29]. Recently, we showed the theoretical evidence for the competition of hydrogen bond and r-hole interaction in CS2AHF system [30]. In this paper, we will study the competition of chalcogen bond, halogen bond, and hydrogen bond in SCSAHOX (X = Cl and Br) system with quantum chemical calculations. To the best of our knowledge, the formation of such complexes has not yet been determined theoretically or experimentally. Considering both molecules are
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present in atmosphere, we think that the study of their complexes is important in providing some useful information for understanding the interaction mechanism between them. For comparison, the SeCSeAHOX system is also considered. This work presents a detailed examination of the stabilities, electronic structure, nature, and vibrational frequencies of these complexes. We think this study can inspire experimental scientists to affirm the existence of these complexes in the future. 2. Theoretical methods The complexes of SCSAHOX and SeCSeAHOX (X = Cl and Br) have been optimized at the second-order Møller–Plesset (MP2) theory level with the Dunning’s correlation consisted basis sets aug-cc-pVTZ. This level of theory has been used to study successfully non-covalent bonded complexes [20,23–25,30]. The minimum energy nature of the optimized complexes was confirmed with the vibrational frequency calculations at the same level (there is no imaginary frequency). The interaction energy was obtained by subtracting the energies of the isolated molecules from the energy of the complex. It was corrected for the basis set superposition error (BSSE), which was estimated using the counterpoise procedure of Boys and Bernardi [31]. All calculations were carried out using the Gaussian 09 suite of programs [32]. We analyzed the bonding characteristics at the critical points in the complexes with Bader’s ‘‘atoms in molecules’’ (AIMs) theory [33]. AIM analysis was performed with the AIM2000 software package using the MP2/aug-cc-pVTZ wave functions [34]. Critical points (CPs) are extrema in the electron density or points in space where the first derivatives of electron density vanish. Hessian matrix is a matrix of second derivatives of the electron density and it is a symmetric matrix, thus it can be transformed into a diagonal matrix and the elements at main diagonal are the eigenvalues (k1, k2, and k3) of the Hessian matrix. The natural bond orbital (NBO) analyses were carried out using the NBO package [35] included in the Gaussian 09 suite of programs at the HF/aug-cc-PVTZ level. The electrostatic potentials were calculated at the MP2/aug-cc-pVTZ level with WFA surface analysis suite [36]. The symmetry adapted perturbation theory (SAPT) method was performed with the aug-cc-pVTZ basis set on the MP2/aug-cc-pVTZ geometries to unveil the nature of interactions. The SAPT calculations were performed using the SAPT2002 program [37]. A more detailed description of SAPT and some of its applications can be found in Refs. [38–43].
Fig. 1. The optimized structures of investigated complexes.
3. Results and discussion 3.1. Geometry Fig. 1 shows the optimized structures of SCSAHOX and SeCSeAHOX (X = Cl and Br) complexes. For each type of complex, there are three interaction modes. The first one is a hydrogen bond formed by the H atom in HOX with the p electrons of C@S(Se) bond and the chalcogen atom in SCS and SeCSe. The second one is a halogen bond through the X atom in HOX and the S atom in SCS or the Se atom in SeCSe. The third one is a chalcogen bond with the O atom in HOX as an electron donor and the S as well as Se atom as an electron acceptor. The formation of three types of complexes can be understood with electrostatic potentials. The latter has been proved to be a good method for predicting and charactering intermolecular interactions [44]. The electrostatic potentials of HOX, SCS, and SeCSe are shown in Fig. 2. It has been shown that there are two maxima (H and X) in the molecular electrostatic potentials of HOX and one minimum on O atom. For SCS and SeCSe, there is a positive region on the outermost portion of the chalcogen atom, while other parts on the chalcogen atom have a negative electrostatic potential.
Fig. 2. The electrostatic potentials on the molecular surface of HOCl, HOBr, SCS, and SeCSe monomers. Color ranges, in kcal/mol, are: red, greater than 12; yellow, between 12 and 6; green, between 6 and 0; blue, less than 0. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The binding distance in the complexes are presented in Table 1. For convenience, the binding distance in the hydrogen-bonded
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complexes is calculated to be the distance between the H atom in HOX and the chalcogen atom in SCS and SeCSe although there is also the interaction through the p electrons in C@S and C@Se bonds. It is shorter in the HOCl hydrogen-bonded complexes than in the HOBr counterpart. The binding distance in the Br-bonded complex is smaller than that in the Cl-bonded complex although the Br atomic radius is bigger than the Cl one. The binding distance is shorter in the SeCSe halogen-bonded complexes than in the SCS ones although the S electronegativity is larger. The binding distance in the Se O complex is larger than that in the S O complex due to the bigger Se atomic radius. The binding distance in the OBrH chalcogen-bonded complex is smaller than that in the ClOH counterpart due to the smaller electronegativity of Br atom. Upon complexation, the associated OAH bond is elongated in the hydrogen bond, while the associated OAX bond is also lengthened in the halogen bond. Furthermore, the elongation of associated OAX bond is larger than that of associated OAH bond. The distant OAX bond is contracted in the hydrogen bond, while the free OAH bond suffers almost no change in the halogen bond. An elongation is found for both OAH and OAX bonds in the chalcogen bond and their lengthening is almost same. Of course, the OAH and OAX bond elongation in the chalcogen bond is smaller than that in the hydrogen and halogen bonds.
Table 2 Interaction energy (DE, kJ/mol) corrected for BSSE and frequency shifts of stretch vibrations (Dv, cm1) in the complexes at the MP2/aug-cc-pVTZ level. Complexes
DE
DvOH
DvOX
SCSAHOCl SCSAClOH SCSAOClH SCSAHOBr SCSABrOH SCSAOBrH SeCSeAHOCl SeCSeAClOH SeCSeAOClH SeCSeAHOBr SeCSeABrOH SeCSeAOBrH
9.88 9.29 6.33 10.03 12.23 6.68 12.06 9.88 7.34 12.15 13.55 7.74
73 0 9 70 1 10 111 1 11 112 1 12
1 21 1 3 26 1 0 35 2 4 41 1
Table 3 The most positive electrostatic potentials (Vmax, kcal/mol) and the most negative electrostatic potential (Vmin, kcal/mol) calculated at the MP2/aug-cc-pVTZ level.
HOCl HOBr SCS
3.2. Interaction energy and frequency shifts Table 2 presents the interaction energies corrected for BSSE in the complexes. For each type of complex, the interaction energy is smallest in the chalcogen-bonded complex, the Cl bond shows smaller interaction energy than the hydrogen bond, but the Br bond presents larger interaction energy than the hydrogen bond. One also sees that the interaction energies in three types of complexes have not a great difference, thus we think three interaction modes can compete each other. For the hydrogen bond, the interaction energy in the HOBr complex is close to that in the HOCl counterpart, while it is more negative in the SeCSe complex than in the SCS counterpart. The negative charge on C atom is 0.2739 e in SCS and 0.5159 e in SeCSe. The energy is 0.4754 eV for the p orbital of C@S bond and 0.4413 eV for the p orbital of C@Se bond. It is thus difficult for SCS to form a hydrogen bond with hypohalous acids. For the halogen bond, the Br bond is stronger than the Cl bond, while the interaction energy in the SeCSe complex is more negative than that in the SCS counterpart. Table 3 presents the most positive electrostatic potential (Vmax) associated with the halogen atom and the most negative electrostatic potential (Vmin) associated with the chalcogen atom. The Vmax value is 26.0 and 35.4 kcal/mol for the Cl and Br atoms, respectively, while the Vmin value is 2.2 and 2.4 kcal/mol for the S and Se atoms, respectively. The results
Table 1 Binding distance (R, Å) and change of bond lengths (Dr, Å) in the complexes at the MP2/aug-cc-pVTZ level. Complexes
R
DrOH
DrOX
SCSAHOCl SCSAClOH SCSAOClH SCSAHOBr SCSABrOH SCSAOBrH SeCSeAHOCl SeCSeAClOH SeCSeAOClH SeCSeAHOBr SeCSeABrOH SeCSeAOBrH
2.484 3.168 3.090 2.487 3.097 3.064 2.566 3.155 3.097 2.569 3.106 3.074
0.003 0.000 0.001 0.003 0.000 0.001 0.005 0.000 0.001 0.005 0.000 0.001
0.002 0.006 0.001 0.002 0.011 0.001 0.002 0.011 0.001 0.003 0.017 0.001
SeCSe
Vmax
Vmin
26.0(Cl) 62.1(H) 35.4(Br) 59.6(H) 17.9(S) 6.9(C) 21.9(Se) 3.5(C)
21.2(O) 23.2(O) 2.2(S) 2.4(Se)
are consistent with the interaction energy of halogen bond, indicating the contribution of electrostatic interaction in the formation of halogen bond. For the chalcogen bond, the interaction energy in the HOBr complex is close to that in the HOCl counterpart, and it is larger in the SeCSe complex than that in the SCS counterpart. The Vmax value is 17.9 kcal/mol for the S atom and 21.9 kcal/mol for the Se atom. The Vmin value is 21.2 and 23.2 kcal/mol for the O atom in HOCl and OHBr, respectively. The results also support the change of the interaction energy of chalcogen bond. The frequency shifts of some bond stretch vibrations are also given in Table 2. In the hydrogen-bonded complexes, the associated OAH bond stretch shows a red shift, while the distant OAX bond stretch displays a small blue shift. The OAH stretch shift in the SeCSe complex is larger than that in the SCS counterpart. This is consistent with the change of the bond length. Such distant blue shift was also observed in other complexes [23–25]. In the halogen-bonded complexes, the associated OAX bond stretch exhibits a red shift, while the distant OAH bond stretch has a negligible shift. The OAX stretch shift in the SeCSe complex is also larger than that in the SCS counterpart. The red shift of OAX stretch vibration in the halogen-bonded complex is smaller than that of OAH stretch vibration in the hydrogen-bonded complex although the bond elongation in the former is larger than that in the latter. This is due to the larger atomic mass of halogen. In the chalcogen-bonded complexes, a red shift is found for both OAH and OAX stretch vibrations, and the shift is larger for the former than for the latter.
3.3. NBO analyses NBO theory can present an analysis for the formation of complexes in view of orbital interaction. The types of orbital interactions and the corresponding stabilization energies in the complexes are given in Table 4. In the hydrogen-bonded complexes, there are three types of orbital interactions: r(CAS) or r(CASe) ? r⁄(OAH), LP(S)
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or LP(Se) ? r⁄(OAH), and r⁄(CAS) or r⁄(CASe) ? r⁄(OAH). The respective stabilization energy is increased in the order r(CAS) ? r⁄(OAH) < r⁄(CAS) ? r⁄(OAH) < LP(S) ? r⁄(OAH) in SCSAHOCl and SCSAHOBr complexes, r⁄(CASe) ? r⁄(OAH) < r(CASe) ? r⁄(OAH) < LP(Se) ? r⁄(OAH) in SeCSe-HOCl complex, LP(Se) ? r⁄(OAH) < r⁄(CASe) ? r⁄(OAH) r(CASe) ? r⁄(OAH) < ⁄ (OAH) < r⁄(CASe) ? r⁄(OAH) r(CASe) ? r⁄(OAH) < LP(Se) in SeCSe-HOBr complex. We checked the occupancy of r⁄C@S(Se) orbital in the monomer and found that it is large enough to donate electrons. It is 0.4618 and 0.4819 e in SCS and SeCSe monomers, respectively. In the complexes, however, it is decreased. For example, it is 0.4776 e in SeCSeAHOCl complex. Thus such orbital interaction is also a stabilizing force in SCSAHOX and SeCSeAHOX complexes. In NBO orbital interaction analysis, we have not found LP(C) ? r⁄(OAH) orbital interaction in SCSAHOX and SeCSeAHOX (X = Cl and Br) complexes. This indicates that there is not an interaction between the C atom and the HAO group although the H atom is closer to the C atom than the S(Se) atom in Fig. 1. In the halogenbonded complexes, there are two types of orbital interactions: LP(S) or LP(Se) ? r⁄(OAX) and r⁄(CAS) or r⁄(CASe) ? r⁄(OAX). The stabilization energy due to the LP(S) or LP(Se) ? r⁄(OAX) orbital interaction is much larger than that due to the r⁄(CAS) or r⁄(CASe) ? r⁄(OAX) one. In the chalcogen-bonded complexes, only LP(O) ? r⁄(CAS) or r⁄(CASe) orbital interaction is present. The orbital interaction is strongest in the halogen-bonded complexes, followed by the hydrogen-bonded complexes, and the chalcogen-bonded complexes present the weakest orbital interaction. Accompanied with the orbital interactions, the charge transfer occurs between both molecules. They are obtained by calculating the sum of atom charge in the electron acceptor molecule for each type of complex. The charge transfer in these complexes is not prominent and it increases as follows: hydrogen-bonded complexes < chalcogen-bonded complexes < halogen-bonded complexes. This sequence is not completely consistent with the interaction energy. Thus the charge transfer plays a minor role in the formation of complexes. The three orbital interactions in the hydrogen-bonded complexes cause an increase in the electron density of r⁄(OAH) and a decrease in the electron density of r(OAH). Of course, the latter is very small. The former is mainly responsible for the elongation of OAH bond. A similar result is also found for the electron density of r⁄(OAX) in the halogen-bonded complexes although the electron density of r(OAX) has a different change. The electron density in the distant r(OAH) and r(OAX) is decreased, while it is increased for the corresponding r⁄(OAH) and r⁄(OAX) in the halogen and
hydrogen bonds. A similar result is also observed in the chalcogen-bonded complexes. 3.4. AIM analyses The formation of complexes can also be analyzed with topological analyses of the electron density. Fig. 3 shows the molecular graphs of complexes of SeCSe and HOBr as well as another three hydrogen-bonded complexes. The presence of intermolecular bond critical points (BCPs) in all the complexes confirms the formation of complexes. It locates in the line between the Br atom and Se atom in SeCSeABrOH complex, while it locates in the curve between the H atom and C(S) atom in the hydrogen-bonded complexes. Actually, the path of BCP in the latter should be from the H atom to the C@S(Se) bond in some complexes. Table 5 presents the electron density and its Laplacian at the intermolecular bond critical point (BCP) in the complexes. It has been suggested that both parameters for closed-shell interactions as H-bonds are positive and should be within the following ranges: 0.002–0.04 au for the electron density and 0.02–0.15 au for its Laplacian [45]. One can see that all electron density values and the corresponding Laplacians are within the range proposed by Koch and Popelier for closed-shell interactions. Both topological parameters are good descriptors of interaction strength since they correlate well with the interaction energy. Fig. 4 shows the linear relationship between the electron density and the interaction energy. The linear correlation coefficient for this dependence amounts to 0.956, whereas this coefficient for the relationship between the Laplacian of electron density and the interaction energy is equal to 0.924. Three eigenvalues (k1, k2 and k3) of the Hessian of the electron density are also shown in Table 5. With them ellipticity is calculated with formulas of e = k1/k2 1. The ellipticity of the electron density provides a measure of the deviation of the electron density distribution from cylindrical symmetry [46]. It is 0.6–1.4 for the hydrogen bond, 0.1–0.2 for the halogen bond, and 0.05–0.1 for the chalcogen bond. The larger ellipticity in the hydrogen bond is consistent with the bond path of critical point as shown in Fig. 3, while the smaller ellipticity in the chalcogen bond means that the bond angle CAS(Se) O is close to 180°. 3.5. SAPT calculations To have a further understanding the nature of interaction in the complexes, we performed a SAPT calculation for the SCS system at the MP2/aug-cc-pVTZ level on the MP2/aug-cc-pVTZ geometry.
Table 4 Stabilization energy (E, kcal/mol), charge transfer (CT, e), and differences between NBO electron density (ED) in the complexes and the isolated HOX in OAH and OAX sigma bonding (Dr) and sigma antibonding (Dr⁄) orbitals in the complexes at the HF/aug-cc-pVTZ level.
a b c d e f
Complexes
E
CT
Dr(OAH)
Dr⁄(OAH)
Dr(OAX)
Dr⁄(OAX)
SCSAHOCl SCSAClOH SCSAOClH SCSAHOBr SCSABrOH SCSAOBrH SeCSeAHOCl SeCSeAClOH SeCSeAOClH SeCSeAHOBr SeCSeABrOH SeCSeAOBrH
0.30a, 1.65b, 0.84c 2.75d, 0.28e 1.45f 0.40a, 1.45b, 0.97c 6.53d, 0.48e 1.24f 1.60a, 1.65b, 1.42c 4.35d, 0.38e 1.52f 1.89a, 1.48b, 1.52c 10.65d, 0.67e 2.58f
0.004 0.008 0.006 0.003 0.018 0.007 0.007 0.016 0.010 0.006 0.035 0.010
0.0011 0.0002 0.0002 0.0014 0.0000 0.0001 0.0021 0.0002 0.0003 0.0025 0.0001 0.0002
0.0071 0.0001 0.0000 0.0067 0.0000 0.0001 0.0093 0.0001 0.0001 0.0093 0.0000 0.0001
0.0076 0.0014 0.0022 0.0065 0.0020 0.0021 0.0076 0.0013 0.0034 0.0066 0.0003 0.0030
0.0001 0.0121 0.0001 0.0004 0.0264 0.0004 0.0004 0.0200 0.0002 0.0008 0.0405 0.0005
The r(CAS) or r(CASe) ? r⁄(OAH) orbital interaction. LP(S) or LP(Se) ? r⁄(OAH) orbital interaction. The r⁄(CAS) or r⁄(CASe) ? r⁄(OAH) orbital interaction. The LP(S) or LP(Se) ? r⁄(OAX) (X = Cl and Br) orbital interaction. The r⁄(CAS) or r⁄(CASe) ? r⁄(OAX) (X = Cl and Br) orbital interaction. The LP(O) ? r⁄(CAS) or r⁄(CASe) orbital interaction.
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Q.-Z. Li et al. / Computational and Theoretical Chemistry 980 (2012) 56–61 Table 6 The SAPT analysis of the interaction energy of the complexes at the MP2/aug-cc-pVTZ level. All are in kJ/mol. Complexes
Eelst
Eexch
Eind
Edisp
dEHF int;r
ESAPT2 int
SCSAHOCl SCSAClOH SCSAOClH SCSAHOBr SCSABrOH SCSAOBrH
8.78 12.96 8.36 10.03 23.83 10.45
29.26 33.44 16.30 33.44 57.27 20.90
7.11 2.51 0.84 7.11 6.69 1.25
19.23 20.90 12.12 21.74 28.42 14.21
3.34 5.43 1.25 3.76 8.78 1.67
9.20 7.94 6.69 9.20 10.45 6.69
ESAPT2 ¼ Eelst þ Eexch þ Eind þ Edisp þ dEHF int int;r .
Fig. 3. The molecular graphs of complexes of SeCSe and HOBr as well as the hydrogen-bonded complexes. Small red balls indicate the bond critical points. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 5 Electron density (q, au), its Laplacian (r2q, au), eigenvalues of Hessian (k), and ellipticity (e) at the intermolecular bond critical point (BCP) in the complexes at the MP2/aug-cc-pVTZ level. Complexes
q
r2q
k1
k2
k3
e
SCSAHOCl SCSAClOH SCSAOClH SCSAHOBr SCSABrOH SCSAOBrH SeCSeAHOCl SeCSeAClOH SeCSeAOClH SeCSeAHOBr SeCSeABrOH SeCSeAOBrH
0.0158 0.0125 0.0084 0.0162 0.0172 0.0093 0.0179 0.0151 0.0096 0.0185 0.0199 0.0105
0.0459 0.0465 0.0384 0.0478 0.0537 0.0413 0.0495 0.0493 0.0402 0.0517 0.0531 0.0429
0.0173 0.0070 0.0065 0.0178 0.0095 0.0072 0.0199 0.0082 0.0072 0.0209 0.0106 0.0079
0.0106 0.0058 0.0061 0.0098 0.0085 0.0065 0.0086 0.0067 0.0068 0.0088 0.0095 0.0073
0.0738 0.0593 0.0510 0.0755 0.0716 0.0552 0.0779 0.0642 0.0542 0.0814 0.0732 0.0581
0.6219 0.2084 0.0664 0.8238 0.1130 0.1096 1.3146 0.2177 0.0516 1.3793 0.1161 0.0787
followed by that in the hydrogen bond, and that in the chalcogen bond is smallest. The electrostatic force plays a secondary role in these complexes. For the chalcogen bond, the induction energy and dEHF int;r are relatively small, while the electrostatic term corresponds to 69% of Edisp in SCSAOClH complex and 73% in SCSAOBrH complex. For the halogen bond, the contribution from the induction energy is increased from SCSAClOH complex to SCSABrOH one and the electrostatic contribution is also prominent. For the hydrogen bond, the induction term is close to the electrostatic one, both having an increase from SCSAHOCl complex to SCSAHOBr one. The dEHF int;r term is larger in the halogen bond than in the hydrogen bond. 4. Conclusions We performed a theoretical study of the SCSAHOX and SeCSeAHOX (X = Cl and Br) complexes with quantum chemical calculations at the MP2/aug-cc-pVTZ level. Three minimum configurations were found for each type of complex: one hydrogen bond, one halogen bond, and one chalcogen bond. The SeCSe complex is more stable than the SCS counterpart. The hydrogen bond is close to the halogen bond in strength; both are stronger than the chalcogen bond. The vibrational analysis of the studied complexes shows a significant red shift of the OH bond in complexes with a hydrogen bond, while a small red shift is found for the OX bond in the halogen-boned complexes. Additionally, a small blue shift in the stretching frequency in the bond in the hypohalous acid not involved in the interactions is observed for three types of complexes. The dispersion energy plays a dominant contribution in the three types of interactions. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 20973149), the Outstanding Youth Natural Science Foundation of Shandong Province (JQ201006), and the Program for New Century Excellent Talents in University. References
Fig. 4. The relationship of the interaction energy and the electron density at the intermolecular bond critical point in the complexes.
The results are presented in Table 6. The interaction energy was separated into five parts: electrostatic energy (Eelst), exchange energy (Eexch), induction energy (Eind), dispersion energy (Edisp), and dEHF int;r , which collects the contributions to supermolecular Hartree–Fock energy beyond the second-order of intermolecular operator [47]. One sees that the value of ESAPT2 agrees reasonably with int the MP2 interaction energy. The dispersion energy plays a dominant contribution to the three types of interactions. It is largest in the halogen bond,
[1] S. Scheiner, Hydrogen Bonding: A Theoretical Perspective, Oxford University Press, New York, 1997. [2] G.A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997. [3] J.S. Murray, K.E. Riley, P. Politzer, T. Clark, Aust. J. Chem. 63 (2010) 1598–1607. [4] P. Metrangolo, F. Meyer, T. Pilati, G. Resnati, G. Terraneo, Halogen bonding in supramolecular chemistry, Angew. Chem. Int. Ed. 47 (2008) 6114–6127. [5] A. Farina, S.V. Meille, M.T. Messina, P. Metrangolo, G. Resnati, G. Vecchio, Resolution of racemic 1,2-dibromohexafluoropropane through halogenbonded supramolecular helices, Angew. Chem. Int. Ed. 38 (1999) 2433–2436. [6] P. Metrangolo, Y. Carcenac, M. Lahtinen, T. Pilati, K. Rissanen, A. Vij, G. Resnati, Science 323 (2009) 1461–1464. [7] P. Auffinger, F.A. Hays, E. Westhof, P.S. Ho, Halogen bonds in biological molecules, Proc. Natl. Acad. Sci. USA 101 (2004) 16789–16794. [8] R. Voth, F.A. Hays, P.S. Ho, Directing macromolecular conformation through halogen bonds, Proc. Natl. Acad. Sci. USA 104 (2007) 6188–6193.
Q.-Z. Li et al. / Computational and Theoretical Chemistry 980 (2012) 56–61 [9] Y.X. Lu, T. Shi, Y. Wang, H.Y. Yang, X.H. Yan, X.M. Luo, H.L. Jiang, W.L. Zhu, Halogen bondings – a novel interaction for rational drug design?, J Med. Chem. 52 (2009) 2854–2862. [10] P. Metrangolo, H. Neukirch, T. Pilati, G. Resnati, Halogen bonding based recognition processes: a world parallel to hydrogen bonding, Acc. Chem. Res. 38 (2005) 386–395. [11] K.E. Riley, P. Hobza, Branching ratios of aliphatic amines + OH gas-phase reactions: a variational transition-state theory study, J. Chem. Theory Comput. 4 (2008) 232–242. [12] T. Clark, M. Hennemann, J.S. Murray, P. Politzer, Halogen bonding: the r-hole, J. Mol. Model. 13 (2007) 291–296. [13] P. Politzer, P. Lane, M.C. Concha, Y. Ma, J.S. Murray, An overview of halogen bonding, J. Mol. Model. 13 (2007) 305–311. [14] P. Politzer, J.S. Murray, M.C. Concha, Halogen bonding and the design of new materials: organic bromides, chlorides and perhaps even fluorides as donors, J. Mol. Model. 13 (2007) 643–650. [15] J.S. Murray, M.C. Concha, P. Lane, P. Hobza, P. Politzer, Blue shifts vs red shifts in r-hole bonding, J. Mol. Model. 14 (2008) 699–704. [16] J.S. Murray, P. Lane, P. Politzer, A predicted new type of directional noncovalent interaction, Int. J. Quant. Chem. 107 (2007) 2286–2292. [17] Z.P. Shields, J.S. Murray, P. Politzer, Directional tendencies of halogen and hydrogen bonds, Int. J. Quant. Chem. 110 (2010) 2823–2832. [18] K.E. Riley, J.S. Murray, P. Politzer, M.C. Concha, P. Hobza, Br O complexes as probes of factors affecting halogen bonding: interactions of bromobenzenes and bromopyrimidines with acetone, J. Chem. Theor. Comput. 5 (2009) 155–163. [19] P. Politzer, J.S. Murray, T. Clark, Halogen bonding: an electrostatically-driven highly directional noncovalent interaction, Phys. Chem. Chem. Phys. 12 (2010) 7748–7757. [20] W.Z. Wang, B.M. Ji, Y. Zhang, Chalcogen bond: a sister noncovalent bond to halogen bond, J. Phys. Chem. A 113 (2009) 8132–8135. [21] C.B. Aakeröy, M. Fasulo, N. Schultheiss, J. Desper, C. Moore, Structural competition between hydrogen bonds and halogen bonds, J. Am. Chem. Soc. 129 (2007) 13772–13773. [22] P. Politzer, J.S. Murray, P. Lane, r-Hole bonding and hydrogen bonding: competitive interactions, Int. J. Quant. Chem. 107 (2007) 3046–3052. [23] Alkorta, F. Blanco, M. Solimannejad, J. Elguero, Competition of hydrogen bonds and halogen bonds in complexes of hypohalous acids with nitrogenated bases, J. Phys. Chem. A 112 (2008) 10856–10863. [24] Q.Z. Li, X.S. Xu, T. Liu, B. Jing, W.Z. Li, J.B. Cheng, B.A. Gong, J.Z. Sun, Competition between hydrogen bond and halogen bond in complexes of formaldehyde with hypohalous acids, Phys. Chem. Chem. Phys. 12 (2010) 6837–6843. [25] Q.Z. Li, B. Jing, R. Li, Z.B. Liu, W.Z. Li, F. Luan, J.B. Cheng, B.A. Gong, J.Z. Sun, Some measures for making halogen bonds stronger than hydrogen bonds in H2CSAHOX (X = F, Cl, and Br) complexes, Phys. Chem. Chem. Phys. 13 (2011) 2266–2271. [26] M.J. Molina, T.L. Tso, L.T. Molina, F.C. Wang, Antarctic stratospheric chemistry of chlorine nitrate, hydrogen chloride, and ice: release of active chlorine, Science 238 (1987) 1253–1257. [27] M.A. Tolbert, M.J. Rossi, R. Malhotra, D.M. Golden, Reaction of chlorine nitrate with hydrogen chloride and water at antarctic stratospheric temperatures, Science 238 (1987) 1258–1260. [28] V.S. Haritos, G. Dojchinov, Carbonic anhydrase metabolism is a key factor in the toxicity of CO2 and COS but CS2 toward the flour beetle Tribolium castaneum, J. Catal. Today 98 (2004) 633–638.
61
[29] L. Andrews, R.B. Bohn, R.T. Arlinghaus, R.D. Hunt, Matrix infrared spectra of HF complexes with N2O, OCS and CS2, Chem. Phys. Lett. 158 (1989) 564–570. [30] Q.Z. Li, B. Jing, Z.B. Liu, W.Z. Li, J.B. Cheng, B.A. Gong, J.Z. Sun, Competition and cooperativity between hydrogen bond and r-hole bond in SCSA(HF)n (n = 1 and 2) systems, J. Mol. Struct. Theochem 952 (2010) 90–95. [31] S.F. Boys, F. Bernardi, The calculation of small molecular interactions by the difference of separate total energies. Some procedures with reduced errors, Mol. Phys. 19 (1970) 553–566. [32] M.J. Frisch, et al., GAUSSIAN 09, Revision A.02, Gaussian, Inc., Wallingford, CT, 2009. [33] R.F.W. Bader, Atoms in Molecules: A Quantum Theory, Clarendon, Oxford, UK, 1990. [34] F. Biegler-König, AIM2000 University of Applied Sciences, Bielefeld, Germany, 2000. [35] E.D. Glendening, A.E. Reed, J.E. Carpenter, F. Weinhold, NBO Version 3.1. [36] F.A. Bulat, A. Toro-Labbé, T. Brinck, J.S. Murray, P. Politzer, Quantitative analysis of molecular surfaces: areas, volumes, electrostatic potentials and average local ionization energies, J. Mol. Model. 16 (2010) 1679–1691. [37] R. Bukowski, W. Cencek, P. Jankowski, B. Jeziorski, M. Jeziorska, S.A. Kucharski, A.J. Misquitta, R. Moszynski, K. Patkowski, S. Rybak, K. Szalewicz, H.L. Williams, P.E.S. Wormer, SAPT2002: an ab initio program for many-body symmetryadapted perturbation theory calculations of intermolecular interaction energies, Sequential and Parallel Versions, 2003. [38] R. Bukowski, K. Szalewicz, C.F. Chabalowski, Ab initio interaction potentials for simulations of dimethylnitramine solutions in supercritical carbon dioxide with cosolvents, J. Phys. Chem. A 103 (1999) 7322–7340. [39] Milet, R. Moszynski, P.E.S. Wormer, A. van der Avoird, Hydrogen bonding in water clusters: pair and many-body interactions from symmetry-adapted perturbation theory, J. Phys. Chem. A 103 (1999) 6811–6819. [40] K. Dongwook, P. Shaowen Hu, S.K. Tarakeshwar, S.K. Kwang, Cation-p interactions: a theoretical investigation of the interaction of metallic and organic cations with alkenes, arenes, and heteroarenes, J. Phys. Chem. A 107 (2003) 1228–1238. [41] P.E.S. Wormer, A. van der Avoird, Intermolecular potentials, internal motions, and spectra of van der Waals and hydrogen-bonded complexes, Chem. Rev. 100 (2000) 4109–4143. [42] A.L. Ringer, M.S. Figgs, M.O. Sinnokrot, C.D. Sherrill, Aliphatic CAH/p interactions: methane–benzene, methane–phenol, and methane–indole complexes, J. Phys. Chem. A 110 (2006) 10822–10828. [43] J.Y. Wu, J.C. Zhang, Z.X. Wang, W.L. Cao, Theoretical investigations of the nature of interaction of ClF with HF, H2O, and NH3, J. Chem. Theory Comput. 3 (2007) 95–102. [44] P. Politzer, J.S. Murray, Z. Peralta-Inga, Molecular surface electrostatic potentials in relation to noncovalent interactions in biological systems, Int. J. Quant. Chem. 85 (2001) 676–684. [45] U. Koch, P.L.A. Popelier, Characterization of CAHAO hydrogen bonds on the basis of the charge density, J. Phys. Chem. A 99 (1995) 9747–9754. [46] K. Kobayashi, S. Nagase, Bonding features in endohedral metallofullerenes. Topological analysis of the electron density distribution, Chem. Phys. Lett. 302 (1999) 312–316. [47] J. Cukras, J. Sadlej, Symmetry-adapted perturbation theory interaction energy decomposition for some noble gas complexes, Chem. Phys. Lett. 459 (2008) 44–48.
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Computational and Theoretical Chemistry journal homepage: www.elsevier.com/locate/comptc
Competition of chalcogen bond, halogen bond, and hydrogen bond in SCSAHOX and SeCSeAHOX (X = Cl and Br) complexes Qing-Zhong Li ⇑, Ran Li, Ping Guo, Hui Li, Wen-Zuo Li, Jian-Bo Cheng The Laboratory of Theoretical and Computational Chemistry, School of Chemistry and Chemical Engineering, Yantai University, Yantai 264005, PR China
a r t i c l e
i n f o
Article history: Received 13 October 2011 Received in revised form 4 November 2011 Accepted 7 November 2011 Available online 26 November 2011 Keywords: Chalcogen bond Halogen bond Hydrogen bond Competition Hypohalous acids
a b s t r a c t The competition of chalcogen bond, halogen bond, and hydrogen bond in SCSAHOX and SeCSeAHOX (X = Cl and Br) complexes have been investigated with quantum chemical calculations at the MP2/augcc-pVTZ level. The complexes have been studied with the geometrical, spectroscopic, and energetic parameters. The interaction strength is comparable for the hydrogen bond and halogen bond, which are a littler stronger than the chalcogen bond. The interaction strength depends on the nature of hypohalous acids and chalcogen atom. The nature and properties of three types of interactions have been analyzed with natural bond orbital, atoms in molecules, electrostatic potentials, and energy decomposition. The dispersion interaction plays a dominant role in three types of interactions. Ó 2011 Elsevier B.V. All rights reserved.
1. Introduction People have come to realize the key role of intermolecular interactions in molecular recognition, crystal engineering, and biomolecular systems [1,2]. The traditional research for the intermolecular interactions has focused on the more common hydrogen-bonded interactions, but a growing body of experimental and theoretical evidence confirms the importance of halogen bond [3–11]. Halogen bonding refers to the non-covalent interactions of halogen atoms in some molecules with negative sites on others [12–14]. Halogen bond belongs to r-hole interaction, which is a non-covalent interaction between a region of positive electrostatic potential on the outer surface of a Group IV, V, VI, or VII covalently-bonded atom (a r-hole) and a region of negative potential on another molecule [12–19]. It is also called chalcogen bond for Group VI atoms [20]. In complex systems with the presence of more than two types of non-covalent interactions, a competition occurs among them. A series of cocrystallization reactions can be controlled through the competition between hydrogen bonds and halogen bonds [21]. Politzer and coworkers pointed out that r-hole bonding can certainly be competitive with hydrogen bonding [22]. Alkorta et al. studied the competition of hydrogen bonds and halogen bonds in complexes of hypohalous acids with nitrogenated bases (NH3, N2, and NCH) [23]. In H2COAHOX (X = F, Cl, and Br) complex, the hydrogen bond is stronger than the halogen bond [24]. In H2SOAHOX complex, the difference in the strength of both interactions is decreased ⇑ Corresponding author. Tel./fax: +86 535 6902063. E-mail address: [email protected] (Q.-Z. Li). 2210-271X/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.comptc.2011.11.019
for the Cl systems and even the Br halogen bond is stronger than the hydrogen bond [25]. Thus we think that within this research field hypohalous acids are a very interesting class of compounds because of the presence of both a proton donor and a halogen donor. Hypohalous acids are involved in stratospheric reactions that release free halogen molecules and atoms, participating in the depletion of the ozone layer [26,27]. Carbon disulfide (CS2) is a volatile liquid with a pungent smell and has been widely used for the production of viscose rayon, rubber, and other organic materials. It is an apolar aprotic solvent with a better solvability. CS2 has been used as substrate probes for enzyme activities [28]. It is known from the electrostatic potential of CS2 [20] that the C atom in CS2 has a partial negative electrostatic potential while the S atom in it exhibits anisotropic distribution of electron density. There is a region of positive electrostatic potential (r-hole) on the outermost portion of the covalentlybonded S atom while a belt of negative electrostatic potential around the central part of the S atom is found. The former can interact with an electron donor to form a noncovalent bond named chalcogen bond, whereas the latter can act as an electron donor. Andrews and coworkers studied the CS2AHF system with a matrix isolation spectroscopy [29]. Recently, we showed the theoretical evidence for the competition of hydrogen bond and r-hole interaction in CS2AHF system [30]. In this paper, we will study the competition of chalcogen bond, halogen bond, and hydrogen bond in SCSAHOX (X = Cl and Br) system with quantum chemical calculations. To the best of our knowledge, the formation of such complexes has not yet been determined theoretically or experimentally. Considering both molecules are
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present in atmosphere, we think that the study of their complexes is important in providing some useful information for understanding the interaction mechanism between them. For comparison, the SeCSeAHOX system is also considered. This work presents a detailed examination of the stabilities, electronic structure, nature, and vibrational frequencies of these complexes. We think this study can inspire experimental scientists to affirm the existence of these complexes in the future. 2. Theoretical methods The complexes of SCSAHOX and SeCSeAHOX (X = Cl and Br) have been optimized at the second-order Møller–Plesset (MP2) theory level with the Dunning’s correlation consisted basis sets aug-cc-pVTZ. This level of theory has been used to study successfully non-covalent bonded complexes [20,23–25,30]. The minimum energy nature of the optimized complexes was confirmed with the vibrational frequency calculations at the same level (there is no imaginary frequency). The interaction energy was obtained by subtracting the energies of the isolated molecules from the energy of the complex. It was corrected for the basis set superposition error (BSSE), which was estimated using the counterpoise procedure of Boys and Bernardi [31]. All calculations were carried out using the Gaussian 09 suite of programs [32]. We analyzed the bonding characteristics at the critical points in the complexes with Bader’s ‘‘atoms in molecules’’ (AIMs) theory [33]. AIM analysis was performed with the AIM2000 software package using the MP2/aug-cc-pVTZ wave functions [34]. Critical points (CPs) are extrema in the electron density or points in space where the first derivatives of electron density vanish. Hessian matrix is a matrix of second derivatives of the electron density and it is a symmetric matrix, thus it can be transformed into a diagonal matrix and the elements at main diagonal are the eigenvalues (k1, k2, and k3) of the Hessian matrix. The natural bond orbital (NBO) analyses were carried out using the NBO package [35] included in the Gaussian 09 suite of programs at the HF/aug-cc-PVTZ level. The electrostatic potentials were calculated at the MP2/aug-cc-pVTZ level with WFA surface analysis suite [36]. The symmetry adapted perturbation theory (SAPT) method was performed with the aug-cc-pVTZ basis set on the MP2/aug-cc-pVTZ geometries to unveil the nature of interactions. The SAPT calculations were performed using the SAPT2002 program [37]. A more detailed description of SAPT and some of its applications can be found in Refs. [38–43].
Fig. 1. The optimized structures of investigated complexes.
3. Results and discussion 3.1. Geometry Fig. 1 shows the optimized structures of SCSAHOX and SeCSeAHOX (X = Cl and Br) complexes. For each type of complex, there are three interaction modes. The first one is a hydrogen bond formed by the H atom in HOX with the p electrons of C@S(Se) bond and the chalcogen atom in SCS and SeCSe. The second one is a halogen bond through the X atom in HOX and the S atom in SCS or the Se atom in SeCSe. The third one is a chalcogen bond with the O atom in HOX as an electron donor and the S as well as Se atom as an electron acceptor. The formation of three types of complexes can be understood with electrostatic potentials. The latter has been proved to be a good method for predicting and charactering intermolecular interactions [44]. The electrostatic potentials of HOX, SCS, and SeCSe are shown in Fig. 2. It has been shown that there are two maxima (H and X) in the molecular electrostatic potentials of HOX and one minimum on O atom. For SCS and SeCSe, there is a positive region on the outermost portion of the chalcogen atom, while other parts on the chalcogen atom have a negative electrostatic potential.
Fig. 2. The electrostatic potentials on the molecular surface of HOCl, HOBr, SCS, and SeCSe monomers. Color ranges, in kcal/mol, are: red, greater than 12; yellow, between 12 and 6; green, between 6 and 0; blue, less than 0. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
The binding distance in the complexes are presented in Table 1. For convenience, the binding distance in the hydrogen-bonded
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complexes is calculated to be the distance between the H atom in HOX and the chalcogen atom in SCS and SeCSe although there is also the interaction through the p electrons in C@S and C@Se bonds. It is shorter in the HOCl hydrogen-bonded complexes than in the HOBr counterpart. The binding distance in the Br-bonded complex is smaller than that in the Cl-bonded complex although the Br atomic radius is bigger than the Cl one. The binding distance is shorter in the SeCSe halogen-bonded complexes than in the SCS ones although the S electronegativity is larger. The binding distance in the Se O complex is larger than that in the S O complex due to the bigger Se atomic radius. The binding distance in the OBrH chalcogen-bonded complex is smaller than that in the ClOH counterpart due to the smaller electronegativity of Br atom. Upon complexation, the associated OAH bond is elongated in the hydrogen bond, while the associated OAX bond is also lengthened in the halogen bond. Furthermore, the elongation of associated OAX bond is larger than that of associated OAH bond. The distant OAX bond is contracted in the hydrogen bond, while the free OAH bond suffers almost no change in the halogen bond. An elongation is found for both OAH and OAX bonds in the chalcogen bond and their lengthening is almost same. Of course, the OAH and OAX bond elongation in the chalcogen bond is smaller than that in the hydrogen and halogen bonds.
Table 2 Interaction energy (DE, kJ/mol) corrected for BSSE and frequency shifts of stretch vibrations (Dv, cm1) in the complexes at the MP2/aug-cc-pVTZ level. Complexes
DE
DvOH
DvOX
SCSAHOCl SCSAClOH SCSAOClH SCSAHOBr SCSABrOH SCSAOBrH SeCSeAHOCl SeCSeAClOH SeCSeAOClH SeCSeAHOBr SeCSeABrOH SeCSeAOBrH
9.88 9.29 6.33 10.03 12.23 6.68 12.06 9.88 7.34 12.15 13.55 7.74
73 0 9 70 1 10 111 1 11 112 1 12
1 21 1 3 26 1 0 35 2 4 41 1
Table 3 The most positive electrostatic potentials (Vmax, kcal/mol) and the most negative electrostatic potential (Vmin, kcal/mol) calculated at the MP2/aug-cc-pVTZ level.
HOCl HOBr SCS
3.2. Interaction energy and frequency shifts Table 2 presents the interaction energies corrected for BSSE in the complexes. For each type of complex, the interaction energy is smallest in the chalcogen-bonded complex, the Cl bond shows smaller interaction energy than the hydrogen bond, but the Br bond presents larger interaction energy than the hydrogen bond. One also sees that the interaction energies in three types of complexes have not a great difference, thus we think three interaction modes can compete each other. For the hydrogen bond, the interaction energy in the HOBr complex is close to that in the HOCl counterpart, while it is more negative in the SeCSe complex than in the SCS counterpart. The negative charge on C atom is 0.2739 e in SCS and 0.5159 e in SeCSe. The energy is 0.4754 eV for the p orbital of C@S bond and 0.4413 eV for the p orbital of C@Se bond. It is thus difficult for SCS to form a hydrogen bond with hypohalous acids. For the halogen bond, the Br bond is stronger than the Cl bond, while the interaction energy in the SeCSe complex is more negative than that in the SCS counterpart. Table 3 presents the most positive electrostatic potential (Vmax) associated with the halogen atom and the most negative electrostatic potential (Vmin) associated with the chalcogen atom. The Vmax value is 26.0 and 35.4 kcal/mol for the Cl and Br atoms, respectively, while the Vmin value is 2.2 and 2.4 kcal/mol for the S and Se atoms, respectively. The results
Table 1 Binding distance (R, Å) and change of bond lengths (Dr, Å) in the complexes at the MP2/aug-cc-pVTZ level. Complexes
R
DrOH
DrOX
SCSAHOCl SCSAClOH SCSAOClH SCSAHOBr SCSABrOH SCSAOBrH SeCSeAHOCl SeCSeAClOH SeCSeAOClH SeCSeAHOBr SeCSeABrOH SeCSeAOBrH
2.484 3.168 3.090 2.487 3.097 3.064 2.566 3.155 3.097 2.569 3.106 3.074
0.003 0.000 0.001 0.003 0.000 0.001 0.005 0.000 0.001 0.005 0.000 0.001
0.002 0.006 0.001 0.002 0.011 0.001 0.002 0.011 0.001 0.003 0.017 0.001
SeCSe
Vmax
Vmin
26.0(Cl) 62.1(H) 35.4(Br) 59.6(H) 17.9(S) 6.9(C) 21.9(Se) 3.5(C)
21.2(O) 23.2(O) 2.2(S) 2.4(Se)
are consistent with the interaction energy of halogen bond, indicating the contribution of electrostatic interaction in the formation of halogen bond. For the chalcogen bond, the interaction energy in the HOBr complex is close to that in the HOCl counterpart, and it is larger in the SeCSe complex than that in the SCS counterpart. The Vmax value is 17.9 kcal/mol for the S atom and 21.9 kcal/mol for the Se atom. The Vmin value is 21.2 and 23.2 kcal/mol for the O atom in HOCl and OHBr, respectively. The results also support the change of the interaction energy of chalcogen bond. The frequency shifts of some bond stretch vibrations are also given in Table 2. In the hydrogen-bonded complexes, the associated OAH bond stretch shows a red shift, while the distant OAX bond stretch displays a small blue shift. The OAH stretch shift in the SeCSe complex is larger than that in the SCS counterpart. This is consistent with the change of the bond length. Such distant blue shift was also observed in other complexes [23–25]. In the halogen-bonded complexes, the associated OAX bond stretch exhibits a red shift, while the distant OAH bond stretch has a negligible shift. The OAX stretch shift in the SeCSe complex is also larger than that in the SCS counterpart. The red shift of OAX stretch vibration in the halogen-bonded complex is smaller than that of OAH stretch vibration in the hydrogen-bonded complex although the bond elongation in the former is larger than that in the latter. This is due to the larger atomic mass of halogen. In the chalcogen-bonded complexes, a red shift is found for both OAH and OAX stretch vibrations, and the shift is larger for the former than for the latter.
3.3. NBO analyses NBO theory can present an analysis for the formation of complexes in view of orbital interaction. The types of orbital interactions and the corresponding stabilization energies in the complexes are given in Table 4. In the hydrogen-bonded complexes, there are three types of orbital interactions: r(CAS) or r(CASe) ? r⁄(OAH), LP(S)
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or LP(Se) ? r⁄(OAH), and r⁄(CAS) or r⁄(CASe) ? r⁄(OAH). The respective stabilization energy is increased in the order r(CAS) ? r⁄(OAH) < r⁄(CAS) ? r⁄(OAH) < LP(S) ? r⁄(OAH) in SCSAHOCl and SCSAHOBr complexes, r⁄(CASe) ? r⁄(OAH) < r(CASe) ? r⁄(OAH) < LP(Se) ? r⁄(OAH) in SeCSe-HOCl complex, LP(Se) ? r⁄(OAH) < r⁄(CASe) ? r⁄(OAH) r(CASe) ? r⁄(OAH) < ⁄ (OAH) < r⁄(CASe) ? r⁄(OAH) r(CASe) ? r⁄(OAH) < LP(Se) in SeCSe-HOBr complex. We checked the occupancy of r⁄C@S(Se) orbital in the monomer and found that it is large enough to donate electrons. It is 0.4618 and 0.4819 e in SCS and SeCSe monomers, respectively. In the complexes, however, it is decreased. For example, it is 0.4776 e in SeCSeAHOCl complex. Thus such orbital interaction is also a stabilizing force in SCSAHOX and SeCSeAHOX complexes. In NBO orbital interaction analysis, we have not found LP(C) ? r⁄(OAH) orbital interaction in SCSAHOX and SeCSeAHOX (X = Cl and Br) complexes. This indicates that there is not an interaction between the C atom and the HAO group although the H atom is closer to the C atom than the S(Se) atom in Fig. 1. In the halogenbonded complexes, there are two types of orbital interactions: LP(S) or LP(Se) ? r⁄(OAX) and r⁄(CAS) or r⁄(CASe) ? r⁄(OAX). The stabilization energy due to the LP(S) or LP(Se) ? r⁄(OAX) orbital interaction is much larger than that due to the r⁄(CAS) or r⁄(CASe) ? r⁄(OAX) one. In the chalcogen-bonded complexes, only LP(O) ? r⁄(CAS) or r⁄(CASe) orbital interaction is present. The orbital interaction is strongest in the halogen-bonded complexes, followed by the hydrogen-bonded complexes, and the chalcogen-bonded complexes present the weakest orbital interaction. Accompanied with the orbital interactions, the charge transfer occurs between both molecules. They are obtained by calculating the sum of atom charge in the electron acceptor molecule for each type of complex. The charge transfer in these complexes is not prominent and it increases as follows: hydrogen-bonded complexes < chalcogen-bonded complexes < halogen-bonded complexes. This sequence is not completely consistent with the interaction energy. Thus the charge transfer plays a minor role in the formation of complexes. The three orbital interactions in the hydrogen-bonded complexes cause an increase in the electron density of r⁄(OAH) and a decrease in the electron density of r(OAH). Of course, the latter is very small. The former is mainly responsible for the elongation of OAH bond. A similar result is also found for the electron density of r⁄(OAX) in the halogen-bonded complexes although the electron density of r(OAX) has a different change. The electron density in the distant r(OAH) and r(OAX) is decreased, while it is increased for the corresponding r⁄(OAH) and r⁄(OAX) in the halogen and
hydrogen bonds. A similar result is also observed in the chalcogen-bonded complexes. 3.4. AIM analyses The formation of complexes can also be analyzed with topological analyses of the electron density. Fig. 3 shows the molecular graphs of complexes of SeCSe and HOBr as well as another three hydrogen-bonded complexes. The presence of intermolecular bond critical points (BCPs) in all the complexes confirms the formation of complexes. It locates in the line between the Br atom and Se atom in SeCSeABrOH complex, while it locates in the curve between the H atom and C(S) atom in the hydrogen-bonded complexes. Actually, the path of BCP in the latter should be from the H atom to the C@S(Se) bond in some complexes. Table 5 presents the electron density and its Laplacian at the intermolecular bond critical point (BCP) in the complexes. It has been suggested that both parameters for closed-shell interactions as H-bonds are positive and should be within the following ranges: 0.002–0.04 au for the electron density and 0.02–0.15 au for its Laplacian [45]. One can see that all electron density values and the corresponding Laplacians are within the range proposed by Koch and Popelier for closed-shell interactions. Both topological parameters are good descriptors of interaction strength since they correlate well with the interaction energy. Fig. 4 shows the linear relationship between the electron density and the interaction energy. The linear correlation coefficient for this dependence amounts to 0.956, whereas this coefficient for the relationship between the Laplacian of electron density and the interaction energy is equal to 0.924. Three eigenvalues (k1, k2 and k3) of the Hessian of the electron density are also shown in Table 5. With them ellipticity is calculated with formulas of e = k1/k2 1. The ellipticity of the electron density provides a measure of the deviation of the electron density distribution from cylindrical symmetry [46]. It is 0.6–1.4 for the hydrogen bond, 0.1–0.2 for the halogen bond, and 0.05–0.1 for the chalcogen bond. The larger ellipticity in the hydrogen bond is consistent with the bond path of critical point as shown in Fig. 3, while the smaller ellipticity in the chalcogen bond means that the bond angle CAS(Se) O is close to 180°. 3.5. SAPT calculations To have a further understanding the nature of interaction in the complexes, we performed a SAPT calculation for the SCS system at the MP2/aug-cc-pVTZ level on the MP2/aug-cc-pVTZ geometry.
Table 4 Stabilization energy (E, kcal/mol), charge transfer (CT, e), and differences between NBO electron density (ED) in the complexes and the isolated HOX in OAH and OAX sigma bonding (Dr) and sigma antibonding (Dr⁄) orbitals in the complexes at the HF/aug-cc-pVTZ level.
a b c d e f
Complexes
E
CT
Dr(OAH)
Dr⁄(OAH)
Dr(OAX)
Dr⁄(OAX)
SCSAHOCl SCSAClOH SCSAOClH SCSAHOBr SCSABrOH SCSAOBrH SeCSeAHOCl SeCSeAClOH SeCSeAOClH SeCSeAHOBr SeCSeABrOH SeCSeAOBrH
0.30a, 1.65b, 0.84c 2.75d, 0.28e 1.45f 0.40a, 1.45b, 0.97c 6.53d, 0.48e 1.24f 1.60a, 1.65b, 1.42c 4.35d, 0.38e 1.52f 1.89a, 1.48b, 1.52c 10.65d, 0.67e 2.58f
0.004 0.008 0.006 0.003 0.018 0.007 0.007 0.016 0.010 0.006 0.035 0.010
0.0011 0.0002 0.0002 0.0014 0.0000 0.0001 0.0021 0.0002 0.0003 0.0025 0.0001 0.0002
0.0071 0.0001 0.0000 0.0067 0.0000 0.0001 0.0093 0.0001 0.0001 0.0093 0.0000 0.0001
0.0076 0.0014 0.0022 0.0065 0.0020 0.0021 0.0076 0.0013 0.0034 0.0066 0.0003 0.0030
0.0001 0.0121 0.0001 0.0004 0.0264 0.0004 0.0004 0.0200 0.0002 0.0008 0.0405 0.0005
The r(CAS) or r(CASe) ? r⁄(OAH) orbital interaction. LP(S) or LP(Se) ? r⁄(OAH) orbital interaction. The r⁄(CAS) or r⁄(CASe) ? r⁄(OAH) orbital interaction. The LP(S) or LP(Se) ? r⁄(OAX) (X = Cl and Br) orbital interaction. The r⁄(CAS) or r⁄(CASe) ? r⁄(OAX) (X = Cl and Br) orbital interaction. The LP(O) ? r⁄(CAS) or r⁄(CASe) orbital interaction.
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Q.-Z. Li et al. / Computational and Theoretical Chemistry 980 (2012) 56–61 Table 6 The SAPT analysis of the interaction energy of the complexes at the MP2/aug-cc-pVTZ level. All are in kJ/mol. Complexes
Eelst
Eexch
Eind
Edisp
dEHF int;r
ESAPT2 int
SCSAHOCl SCSAClOH SCSAOClH SCSAHOBr SCSABrOH SCSAOBrH
8.78 12.96 8.36 10.03 23.83 10.45
29.26 33.44 16.30 33.44 57.27 20.90
7.11 2.51 0.84 7.11 6.69 1.25
19.23 20.90 12.12 21.74 28.42 14.21
3.34 5.43 1.25 3.76 8.78 1.67
9.20 7.94 6.69 9.20 10.45 6.69
ESAPT2 ¼ Eelst þ Eexch þ Eind þ Edisp þ dEHF int int;r .
Fig. 3. The molecular graphs of complexes of SeCSe and HOBr as well as the hydrogen-bonded complexes. Small red balls indicate the bond critical points. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Table 5 Electron density (q, au), its Laplacian (r2q, au), eigenvalues of Hessian (k), and ellipticity (e) at the intermolecular bond critical point (BCP) in the complexes at the MP2/aug-cc-pVTZ level. Complexes
q
r2q
k1
k2
k3
e
SCSAHOCl SCSAClOH SCSAOClH SCSAHOBr SCSABrOH SCSAOBrH SeCSeAHOCl SeCSeAClOH SeCSeAOClH SeCSeAHOBr SeCSeABrOH SeCSeAOBrH
0.0158 0.0125 0.0084 0.0162 0.0172 0.0093 0.0179 0.0151 0.0096 0.0185 0.0199 0.0105
0.0459 0.0465 0.0384 0.0478 0.0537 0.0413 0.0495 0.0493 0.0402 0.0517 0.0531 0.0429
0.0173 0.0070 0.0065 0.0178 0.0095 0.0072 0.0199 0.0082 0.0072 0.0209 0.0106 0.0079
0.0106 0.0058 0.0061 0.0098 0.0085 0.0065 0.0086 0.0067 0.0068 0.0088 0.0095 0.0073
0.0738 0.0593 0.0510 0.0755 0.0716 0.0552 0.0779 0.0642 0.0542 0.0814 0.0732 0.0581
0.6219 0.2084 0.0664 0.8238 0.1130 0.1096 1.3146 0.2177 0.0516 1.3793 0.1161 0.0787
followed by that in the hydrogen bond, and that in the chalcogen bond is smallest. The electrostatic force plays a secondary role in these complexes. For the chalcogen bond, the induction energy and dEHF int;r are relatively small, while the electrostatic term corresponds to 69% of Edisp in SCSAOClH complex and 73% in SCSAOBrH complex. For the halogen bond, the contribution from the induction energy is increased from SCSAClOH complex to SCSABrOH one and the electrostatic contribution is also prominent. For the hydrogen bond, the induction term is close to the electrostatic one, both having an increase from SCSAHOCl complex to SCSAHOBr one. The dEHF int;r term is larger in the halogen bond than in the hydrogen bond. 4. Conclusions We performed a theoretical study of the SCSAHOX and SeCSeAHOX (X = Cl and Br) complexes with quantum chemical calculations at the MP2/aug-cc-pVTZ level. Three minimum configurations were found for each type of complex: one hydrogen bond, one halogen bond, and one chalcogen bond. The SeCSe complex is more stable than the SCS counterpart. The hydrogen bond is close to the halogen bond in strength; both are stronger than the chalcogen bond. The vibrational analysis of the studied complexes shows a significant red shift of the OH bond in complexes with a hydrogen bond, while a small red shift is found for the OX bond in the halogen-boned complexes. Additionally, a small blue shift in the stretching frequency in the bond in the hypohalous acid not involved in the interactions is observed for three types of complexes. The dispersion energy plays a dominant contribution in the three types of interactions. Acknowledgments This work was supported by the National Natural Science Foundation of China (Grant No. 20973149), the Outstanding Youth Natural Science Foundation of Shandong Province (JQ201006), and the Program for New Century Excellent Talents in University. References
Fig. 4. The relationship of the interaction energy and the electron density at the intermolecular bond critical point in the complexes.
The results are presented in Table 6. The interaction energy was separated into five parts: electrostatic energy (Eelst), exchange energy (Eexch), induction energy (Eind), dispersion energy (Edisp), and dEHF int;r , which collects the contributions to supermolecular Hartree–Fock energy beyond the second-order of intermolecular operator [47]. One sees that the value of ESAPT2 agrees reasonably with int the MP2 interaction energy. The dispersion energy plays a dominant contribution to the three types of interactions. It is largest in the halogen bond,
[1] S. Scheiner, Hydrogen Bonding: A Theoretical Perspective, Oxford University Press, New York, 1997. [2] G.A. Jeffrey, An Introduction to Hydrogen Bonding, Oxford University Press, New York, 1997. [3] J.S. Murray, K.E. Riley, P. Politzer, T. Clark, Aust. J. Chem. 63 (2010) 1598–1607. [4] P. Metrangolo, F. Meyer, T. Pilati, G. Resnati, G. Terraneo, Halogen bonding in supramolecular chemistry, Angew. Chem. Int. Ed. 47 (2008) 6114–6127. [5] A. Farina, S.V. Meille, M.T. Messina, P. Metrangolo, G. Resnati, G. Vecchio, Resolution of racemic 1,2-dibromohexafluoropropane through halogenbonded supramolecular helices, Angew. Chem. Int. Ed. 38 (1999) 2433–2436. [6] P. Metrangolo, Y. Carcenac, M. Lahtinen, T. Pilati, K. Rissanen, A. Vij, G. Resnati, Science 323 (2009) 1461–1464. [7] P. Auffinger, F.A. Hays, E. Westhof, P.S. Ho, Halogen bonds in biological molecules, Proc. Natl. Acad. Sci. USA 101 (2004) 16789–16794. [8] R. Voth, F.A. Hays, P.S. Ho, Directing macromolecular conformation through halogen bonds, Proc. Natl. Acad. Sci. USA 104 (2007) 6188–6193.
Q.-Z. Li et al. / Computational and Theoretical Chemistry 980 (2012) 56–61 [9] Y.X. Lu, T. Shi, Y. Wang, H.Y. Yang, X.H. Yan, X.M. Luo, H.L. Jiang, W.L. Zhu, Halogen bondings – a novel interaction for rational drug design?, J Med. Chem. 52 (2009) 2854–2862. [10] P. Metrangolo, H. Neukirch, T. Pilati, G. Resnati, Halogen bonding based recognition processes: a world parallel to hydrogen bonding, Acc. Chem. Res. 38 (2005) 386–395. [11] K.E. Riley, P. Hobza, Branching ratios of aliphatic amines + OH gas-phase reactions: a variational transition-state theory study, J. Chem. Theory Comput. 4 (2008) 232–242. [12] T. Clark, M. Hennemann, J.S. Murray, P. Politzer, Halogen bonding: the r-hole, J. Mol. Model. 13 (2007) 291–296. [13] P. Politzer, P. Lane, M.C. Concha, Y. Ma, J.S. Murray, An overview of halogen bonding, J. Mol. Model. 13 (2007) 305–311. [14] P. Politzer, J.S. Murray, M.C. Concha, Halogen bonding and the design of new materials: organic bromides, chlorides and perhaps even fluorides as donors, J. Mol. Model. 13 (2007) 643–650. [15] J.S. Murray, M.C. Concha, P. Lane, P. Hobza, P. Politzer, Blue shifts vs red shifts in r-hole bonding, J. Mol. Model. 14 (2008) 699–704. [16] J.S. Murray, P. Lane, P. Politzer, A predicted new type of directional noncovalent interaction, Int. J. Quant. Chem. 107 (2007) 2286–2292. [17] Z.P. Shields, J.S. Murray, P. Politzer, Directional tendencies of halogen and hydrogen bonds, Int. J. Quant. Chem. 110 (2010) 2823–2832. [18] K.E. Riley, J.S. Murray, P. Politzer, M.C. Concha, P. Hobza, Br O complexes as probes of factors affecting halogen bonding: interactions of bromobenzenes and bromopyrimidines with acetone, J. Chem. Theor. Comput. 5 (2009) 155–163. [19] P. Politzer, J.S. Murray, T. Clark, Halogen bonding: an electrostatically-driven highly directional noncovalent interaction, Phys. Chem. Chem. Phys. 12 (2010) 7748–7757. [20] W.Z. Wang, B.M. Ji, Y. Zhang, Chalcogen bond: a sister noncovalent bond to halogen bond, J. Phys. Chem. A 113 (2009) 8132–8135. [21] C.B. Aakeröy, M. Fasulo, N. Schultheiss, J. Desper, C. Moore, Structural competition between hydrogen bonds and halogen bonds, J. Am. Chem. Soc. 129 (2007) 13772–13773. [22] P. Politzer, J.S. Murray, P. Lane, r-Hole bonding and hydrogen bonding: competitive interactions, Int. J. Quant. Chem. 107 (2007) 3046–3052. [23] Alkorta, F. Blanco, M. Solimannejad, J. Elguero, Competition of hydrogen bonds and halogen bonds in complexes of hypohalous acids with nitrogenated bases, J. Phys. Chem. A 112 (2008) 10856–10863. [24] Q.Z. Li, X.S. Xu, T. Liu, B. Jing, W.Z. Li, J.B. Cheng, B.A. Gong, J.Z. Sun, Competition between hydrogen bond and halogen bond in complexes of formaldehyde with hypohalous acids, Phys. Chem. Chem. Phys. 12 (2010) 6837–6843. [25] Q.Z. Li, B. Jing, R. Li, Z.B. Liu, W.Z. Li, F. Luan, J.B. Cheng, B.A. Gong, J.Z. Sun, Some measures for making halogen bonds stronger than hydrogen bonds in H2CSAHOX (X = F, Cl, and Br) complexes, Phys. Chem. Chem. Phys. 13 (2011) 2266–2271. [26] M.J. Molina, T.L. Tso, L.T. Molina, F.C. Wang, Antarctic stratospheric chemistry of chlorine nitrate, hydrogen chloride, and ice: release of active chlorine, Science 238 (1987) 1253–1257. [27] M.A. Tolbert, M.J. Rossi, R. Malhotra, D.M. Golden, Reaction of chlorine nitrate with hydrogen chloride and water at antarctic stratospheric temperatures, Science 238 (1987) 1258–1260. [28] V.S. Haritos, G. Dojchinov, Carbonic anhydrase metabolism is a key factor in the toxicity of CO2 and COS but CS2 toward the flour beetle Tribolium castaneum, J. Catal. Today 98 (2004) 633–638.
61
[29] L. Andrews, R.B. Bohn, R.T. Arlinghaus, R.D. Hunt, Matrix infrared spectra of HF complexes with N2O, OCS and CS2, Chem. Phys. Lett. 158 (1989) 564–570. [30] Q.Z. Li, B. Jing, Z.B. Liu, W.Z. Li, J.B. Cheng, B.A. Gong, J.Z. Sun, Competition and cooperativity between hydrogen bond and r-hole bond in SCSA(HF)n (n = 1 and 2) systems, J. Mol. Struct. Theochem 952 (2010) 90–95. [31] S.F. Boys, F. Bernardi, The calculation of small molecular interactions by the difference of separate total energies. Some procedures with reduced errors, Mol. Phys. 19 (1970) 553–566. [32] M.J. Frisch, et al., GAUSSIAN 09, Revision A.02, Gaussian, Inc., Wallingford, CT, 2009. [33] R.F.W. Bader, Atoms in Molecules: A Quantum Theory, Clarendon, Oxford, UK, 1990. [34] F. Biegler-König, AIM2000 University of Applied Sciences, Bielefeld, Germany, 2000. [35] E.D. Glendening, A.E. Reed, J.E. Carpenter, F. Weinhold, NBO Version 3.1. [36] F.A. Bulat, A. Toro-Labbé, T. Brinck, J.S. Murray, P. Politzer, Quantitative analysis of molecular surfaces: areas, volumes, electrostatic potentials and average local ionization energies, J. Mol. Model. 16 (2010) 1679–1691. [37] R. Bukowski, W. Cencek, P. Jankowski, B. Jeziorski, M. Jeziorska, S.A. Kucharski, A.J. Misquitta, R. Moszynski, K. Patkowski, S. Rybak, K. Szalewicz, H.L. Williams, P.E.S. Wormer, SAPT2002: an ab initio program for many-body symmetryadapted perturbation theory calculations of intermolecular interaction energies, Sequential and Parallel Versions, 2003. [38] R. Bukowski, K. Szalewicz, C.F. Chabalowski, Ab initio interaction potentials for simulations of dimethylnitramine solutions in supercritical carbon dioxide with cosolvents, J. Phys. Chem. A 103 (1999) 7322–7340. [39] Milet, R. Moszynski, P.E.S. Wormer, A. van der Avoird, Hydrogen bonding in water clusters: pair and many-body interactions from symmetry-adapted perturbation theory, J. Phys. Chem. A 103 (1999) 6811–6819. [40] K. Dongwook, P. Shaowen Hu, S.K. Tarakeshwar, S.K. Kwang, Cation-p interactions: a theoretical investigation of the interaction of metallic and organic cations with alkenes, arenes, and heteroarenes, J. Phys. Chem. A 107 (2003) 1228–1238. [41] P.E.S. Wormer, A. van der Avoird, Intermolecular potentials, internal motions, and spectra of van der Waals and hydrogen-bonded complexes, Chem. Rev. 100 (2000) 4109–4143. [42] A.L. Ringer, M.S. Figgs, M.O. Sinnokrot, C.D. Sherrill, Aliphatic CAH/p interactions: methane–benzene, methane–phenol, and methane–indole complexes, J. Phys. Chem. A 110 (2006) 10822–10828. [43] J.Y. Wu, J.C. Zhang, Z.X. Wang, W.L. Cao, Theoretical investigations of the nature of interaction of ClF with HF, H2O, and NH3, J. Chem. Theory Comput. 3 (2007) 95–102. [44] P. Politzer, J.S. Murray, Z. Peralta-Inga, Molecular surface electrostatic potentials in relation to noncovalent interactions in biological systems, Int. J. Quant. Chem. 85 (2001) 676–684. [45] U. Koch, P.L.A. Popelier, Characterization of CAHAO hydrogen bonds on the basis of the charge density, J. Phys. Chem. A 99 (1995) 9747–9754. [46] K. Kobayashi, S. Nagase, Bonding features in endohedral metallofullerenes. Topological analysis of the electron density distribution, Chem. Phys. Lett. 302 (1999) 312–316. [47] J. Cukras, J. Sadlej, Symmetry-adapted perturbation theory interaction energy decomposition for some noble gas complexes, Chem. Phys. Lett. 459 (2008) 44–48.