Transition Metal CationâÏ Interactions: Complexes Formed by Fe2+

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Article

Transition Metal Cation–# Interactions: Complexes Formed by Fe , Co , Ni , Cu and Zn Binding with Benzene Molecules 2+

2+

2+

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Ça#la Aybüke Demircan, and U#ur Bozkaya J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b05759 • Publication Date (Web): 08 Aug 2017 Downloaded from http://pubs.acs.org on August 9, 2017

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The Journal of Physical Chemistry

Transition Metal Cation–π Interactions: Complexes Formed by Fe2+, Co2+, Ni2+, Cu2+, and Zn2+ Binding with Benzene Molecules Çağla Aybüke Demircan and Uğur Bozkaya∗ Department of Chemistry, Hacettepe University, Ankara 06800, Turkey E-mail: [email protected]

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ACS Paragon Plus Environment


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Abstract A computational investigation of the structures and interaction energies of complexes formed by Fe2+ , Co2+ , Ni2+ , Cu2+ , and Zn2+ binding with benzene (Bz) molecules is performed employing high level ab initio quantum chemical methods, such as the second-order perturbation theory (MP2), coupled-cluster singles and doubles (CCSD), and coupled-cluster singles and doubles with perturbative triples [CCSD(T)] methods, along with the 6-311++G(2d,2p) and 6-311++G(d,p) basis sets. As far as we know, the present work is the first to study the structures and energetics of Bz–M2+ and Bz–M2+ – Bz type complexes (M=Co, Ni, Cu, and Zn). Relativistic effects are also investigated via Douglas-Kroll-Hess second-order scalar relativistic computations for the complexes considered. Our results demonstrate that there are strong bindings between transition metal cations and benzene molecules. The computed interaction energies, including relativistic energy corrections, for the Bz–M2+ type complexes at the CCSD(T)/6311++G(2d,2p) level are −131.9 (Bz–Fe2+ ), −172.6 (Bz–Co2+ ), −189.8 (Bz–Ni2+ ), −181.1 (Bz–Cu2+ ), and −158.2 (Bz–Zn2+ ) kcal mol-1 . Similarly, interaction energies for the Bz–M2+ –Bz type complexes at the CCSD(T)/6-311++G(d,p) level are −206.4 (Bz–Fe2+ –Bz), −213.4 (Bz–Co2+ –Bz), −249.7 (Bz–Ni2+ –Bz), −258.6 (Bz–Cu2+ –Bz), and −235.2 (Bz–Zn2+ –Bz) kcal mol-1 . Further, our results also demonstrate that the relativistic effects are very important in accurate computations of interaction energies. The predicted relativistic energy corrections to interaction energies, using the ωB97X-D functional, are between −1.9 and −7.7 kcal mol-1 . The transition metal cation–π interactions investigated in this study prove significantly larger binding energies compared to arbitrary π–π interactions and main group cation–π interactions. We believe that the present study may open new avenues in cation–π interactions.

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1

Introduction

Cation–π interactions play prominent roles in many scientific disciplines, such as chemistry, biology, and materials science. 1–41 They have been involved in various biochemical processes, such as steroid biosynthesis, the binding of acetylcholine by various acetylcholine receptors, and ion selectivity in K+ channels. 1–3,5,6 Understanding the nature and the role of cation–π interaction in nanotechnology is of significant importance in designing new materials. 6 Understanding the nature of cation–π interactions has been of considerable interest. In early studies, it has been proposed that the cation–π interaction is basically an electrostatic interaction since a positively charged cation interacts with a negatively charged electron cloud of π systems. 2,19,42,43 However, other factors like, induction and dispersion are also important in these interactions. In recent studies, it has been proven that the induction term is as important as the electrostatic term. 5,15,16,32,34 Further, in a 2009 study, Yi et al. demonstrated that transition metal cation–π interactions are also include covalent characters due to π donations. 44 Most studies on cation–π interactions were focused on main group cations, such as Li+ , Na+ , and K+ . Transition metal cation–π interaction studies are quite limited, especially for M2+ –π-type systems. 45,46 These studies are restricted mostly to M2+ –π-type systems. 47–50 Transition metals cations are more challenging for quantum chemical methods than main group cations since most of them have open-shell electronic structures. It is also noteworthy to mention that complexes of transition metal cations with polyaromatic hydrocarbons (PAH) have been considered in various contexts. 46,51–54 Duncan and co-workers performed extensive studies of spectroscopic properties of transition metal cations–PAH complexes. 46,51–54 In this study, structures and energetics of complexes formed by 3d transition metal cations, such as Fe2+ , Co2+ , Ni2+ , Cu2+ , and Zn2+ , binding with benzene molecules were studied employing high-level ab initio methods, such as the second- and third-order perturbation theories (MP2 and MP3), the MP2.5 model, 55–60 coupled-cluster singles and doubles (CCSD), 61 and coupled-cluster singles and doubles with perturbative triples [CCSD(T)] 3



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methods. 62–65 We carry out the first scientific study, as far as we know, to report the optimized structures, harmonic vibrational frequencies, and interaction energies for the complexes formed by Co2+ , Ni2+ , Cu2+ , and Zn2+ with benzene molecules. Relativistic effects are further investigated for the complexes considered.

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Theoretical Approach

Geometry optimizations and harmonic vibrational frequency computations for the complexes of Fe2+ , Co2+ , Ni2+ , Cu2+ , and Zn2+ with benzene molecules (Bz–M2+ and Bz–M2+ –Bz), were carried out with the MP2 method. For this purpose, Pople type polarized and diffuse triple-ζ split valence basis sets, 6-311++G(2d,2p) and 6-311G++(d,p), were used. 66–70 The former was employed for Bz–M2+ type complexes, while the latter was used for Bz–M2+ –Bz type complexes. Single point energies were computed at the optimized geometries with the MP3, MP2.5, CCSD, CCSD(T), B3LYP-D2 (where D2 is the Grimme’s empirical dispersion correction 71 ), BP86-D2, and ωB97X-D 72 methods. For Bz–M2+ and Bz–M2+ –Bz complexes considered, interaction energies were computed as follows,

∆E = Ecomplex −

Nmonomer X

Emono−i .

(1)

i=1

All intermolecular interaction energies are counterpoise corrected. 73 Further, relativistic effects were considered via Douglas-Kroll-Hess (DKH) second-order scalar relativistic computations. 74–77 Relativistic energy corrections were computed with the density-functional theory (DFT), the ωB97X-D functional were employed. For open-shell species, the unrestricted orbitals were employed, and high-spin complexes were considered. Spin multiplicities were considered are 5 (for Bz–Fe2+ and Bz–Fe2+ –Bz), 4 (Bz–Co2+ and Bz–Co2+ –Bz), 3 (Bz–Ni2+ and Bz–Ni2+ –Bz), 2 (Bz–Cu2+ and Bz–Cu2+ – Bz), and 1 (Bz–Zn2+ and Bz–Zn2+ –Bz). Hase and co-workers 45 demonstrated that for Bz– Fe2+ and Bz–Fe2+ –Bz complexes the Hund rule is valid and the low-spin (multiplicity=3) 4


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complexes correspond to excited states. Similarly, our results show that the Hund rule is valid for the complexes of Co2+ and Ni2+ , and low-spin electronic states are excited states. For the complexes of Cu2+ and Zn2+ , there are no low-lying excited states. The electronic ground states of the atomic dications are 5 D4 (Fe2+ ), 4 F9/2 (Co2+ ), 3 F4 (Ni2+ ), 2 D5/2 (Cu2+ ), and 1

S0 (Zn2+ ). All computations were performed with the Gaussian 09 program package. 78

3

Results and Discussion

3.1

The Bz–Fe2+ Complex

The optimized geometry of the Bz–Fe2+ complex, at the non-relativistic MP2/6-311++G(2d,2p) level, is depicted in Figure 1. The overall point group symmetry of the Bz–Fe2+ complex is C1 , however it is slightly deviated from the C6v symmetry. At first, upon binding to Fe2+ , the D6h symmetry of the benzene ring is distorted to a C2 geometry, as a result of the descending point group symmetry. For the benzene ring, the C–C bond lengths are 1.414 and 1.418 Å. The Fe–C distances of the complex are between 2.320–2.342 Å. The distance between Fe2+ and the center of mass (COM) of the benzene ring is 1.848 Å, which is in general agreement with values of 1.80–1.89 Å reported by Hase and co-workers 45 (from several DFT functionals with the 6-311++G(d,p) basis set). For the Bz–M2+ complexes, non-relativistic interaction energies (IE) from the MP2, MP3, MP2.5, CCSD, CCSD(T) methods with the 6-311++G(2d,2p) basis set are reported in Table 1. For the Bz–Fe2+ complex, computed IE values are −128.1 (MP2), −125.7 (MP3), −126.9 (MP2.5), −128.0 (CCSD), −129.5 [CCSD(T)], −154.8 (B3LYP-D2), −171.2 (BP86D2), and −147.2 (ωB97X-D) kcal mol-1 . The reported binding energies by Hase and coworkers 45 were between −143.1 and −160.0 kcal mol-1 (from several DFT functionals with the 6-311++G(d,p) basis set). The discrepancy between our IE values and their binding energies is attributed to the poor performance of common DFT functionals, such as B3LYP, for transition metal complexes, 79–82 and for noncovalent interaction energies (even thought 5



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-D2 and -D3 corrections were employed). Hence, our CCSD(T) value of −129.5 kcal mol-1 is a more reliable prediction for the IE value of the Bz–Fe2+ complex. The absolute error of other methods considered with respect to CCSD(T) are 1.3 (MP2), 3.8 (MP3), 2.6 (MP2.5), 1.5 (CCSD), 25.3 (B3LYP-D2), 41.7 (BP86-D2), and 17.7 (ωB97X-D) kcal mol-1 . Surprisingly, the MP2 method provides the lowest absolute error (1.3 kcal mol-1 ) with respect to CCSD(T), while results of MP2.5, and especially MP3 are in slight errors, and the DFT functionals considered are in dramatic errors. The performance of all wave function based methods considered, is significantly better than that of DFT functionals considered here and considered by Hase and co-workers, 45 where absolute errors are between 13.5 and 30.5 kcal mol-1 . For the Bz–M2+ complexes, the interaction energy including relativistic corrections at the CCSD(T)/6-311++G(2d,2p) level is reported in Table 2. For the Bz–Fe2+ complex, the relativistic energy correction for interaction energy is computed to be −2.1 kcal mol-1 , at the ωB97X-D/6-311++G(2d,2p) level. Therefore, the relativistic effects are significant and should be included in IE predictions. Hence, the predicted IE value with relativistic corrections is −131.9 kcal mol-1 at the CCSD(T)/6-311++G(2d,2p) level.

3.2

The Bz–Fe2+ –Bz Complex

The optimized geometry of the Bz–Fe2+ –Bz complex, at the MP2/6-311G++(d,p) level, is depicted in Figure 2. The overall point group symmetry of the Bz–Fe2+ –Bz complex is D6d . The C–C bond lengths in the benzene rings are 1.414 Å, while the Fe–C distances of the complex are 2.418 Å. The distance between Fe2+ and the COM of the benzene ring is 1.963 Å, which is in general agreement with values of 1.91–2.03 Å reported by Hase and co-workers 45 (from several DFT functionals with the 6-311++G(d,p) basis set). For the Bz–M2+ –Bz complexes, non-relativistic interaction energies from the MP2, MP3, MP2.5, CCSD, CCSD(T) methods with the 6-311++G(d,p) basis set are reported in Table 3. For the Bz–Fe2+ –Bz complex, computed IE values are −203.1 (MP2), −195.5 (MP3), 6


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−199.3 (MP2.5), −198.7 (CCSD), −202.0 [CCSD(T)], −235.6 (B3LYP-D2), −256.7 (BP86D2), and −235.7 (ωB97X-D) kcal mol-1 . The reported binding energies by Hase and coworkers 45 were between −225.5 and −246.6 kcal mol-1 (from several DFT functionals with the 6-311++G(d,p) basis set). The discrepancy between our IE values and their binding energies is again attributed to the poor performance of common DFT functionals, such as B3LYP, for transition metal complexes, 79–82 and for noncovalent interaction energies. Hence, our CCSD(T) value of −202.0 kcal mol-1 is a more reliable prediction for the IE value of the Bz–Fe2+ –Bz complex. The absolute error of other methods considered with respect to CCSD(T) are 1.1 (MP2), 6.5 (MP3), 2.7 (MP2.5), 3.2 (CCSD), 33.6 (B3LYP-D2), 54.7 (BP86-D2), and 33.7 (ωB97X-D) kcal mol-1 . The MP2 method again provides the lowest absolute error (1.1 kcal mol-1 ) with respect to CCSD(T), while results of CCSD, MP2.5, and especially MP3 are in significant errors, and the DFT functionals considered are in dramatic errors. However, the performance of post Hartree–Fock (HF) methods considered, is dramatically better than that of DFT functionals considered here and considered by Hase and co-workers, 45 where absolute errors are between 23.5 and 44.6 kcal mol-1 . For the Bz–M2+ –Bz complexes, the interaction energy including relativistic corrections at the CCSD(T)/6-311++G(d,p) level is reported in Table 4. For the Bz–Fe2+ –Bz complex, the relativistic energy correction for interaction energy is computed to be −3.1 kcal mol-1 , at the ωB97X-D/6-311++G(d,p) level. Therefore, the relativistic effects are even more significant for the Bz–Fe2+ –Bz complex compared to Bz–Fe2+ , and should be considered in IE predictions. Hence, the predicted IE value with relativistic corrections is −206.4 kcal mol-1 at the CCSD(T)/6-311++G(d,p) level.

3.3

The Bz–Co2+ Complex

The optimized geometry of the Bz–Co2+ complex, at the MP2/6-311++G(2d,2p) level, is depicted in Figure 3. The overall point group symmetry of the Bz–Co2+ complex is C2v , however it is slightly deviated from the C6v symmetry. Upon binding to Co2+ , the D6h 7



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symmetry of the benzene ring is distorted to a C2v geometry, as a result of the descending point group symmetry. For the benzene ring, the C–C bond lengths are 1.416 and 1.419 Å. The Co–C distances of the complex are 2.267 and 2.286 Å. Further, the distance between Co2+ and the COM of the benzene ring is 1.777 Å. For the Bz–Co2+ complex, non-relativistic interaction energies from the MP2, MP3, MP2.5, CCSD, CCSD(T) methods with the 6-311++G(2d,2p) basis set are reported in Table 1. Computed IE values are −182.2 (MP2), −177.5 (MP3), −179.8 (MP2.5), −176.5 (CCSD), −170.7 [CCSD(T)], −150.0 (B3LYP-D2), −189.1 (BP86-D2), and −219.8 (ωB97X-D) kcal mol-1 . The absolute error of other methods considered with respect to CCSD(T) are 11.5 (MP2), 6.8 (MP3), 9.1 (MP2.5), 5.8 (CCSD), 20.7 (B3LYP-D2), 18.4 (BP86-D2), and 49.1 (ωB97X-D) kcal mol-1 . Hence, performances of MP2.5, MP3, and CCSD are in significant errors, while the DFT functionals considered are in dramatic errors. For the Bz–Co2+ complex, the interaction energy including relativistic corrections at the CCSD(T)/6-311++G(2d,2p) level is reported in Table 2. For the Bz–Co2+ complex, the relativistic energy correction for interaction energy is computed to be −2.4 kcal mol-1 , at the ωB97X-D/6-311++G(2d,2p) level. Therefore, the relativistic effects are not negligible, as in the case of iron cation– benzene complexes. Hence, the predicted IE value with relativistic corrections is −172.6 kcal mol-1 at the CCSD(T)/6-311++G(2d,2p) level.

3.4

The Bz–Co2+ –Bz Complex

The optimized geometry of the Bz–Co2+ –Bz complex, at the MP2/6-311G++(d,p) level, is depicted in Figure 4. The overall point group symmetry of the Bz–Co2+ –Bz complex is C3 (approximately D6d ). The C–C bond lengths in the benzene rings are 1.415 Å, while the Co–C distances of the complex are 2.279 Å. The distance between Co2+ and the COM of the benzene ring is 1.785 Å. For the Bz–Co2+ –Bz complex, non-relativistic interaction energies from the MP2, MP3, MP2.5, CCSD, CCSD(T) methods with the 6-311++G(d,p) basis set are reported in Table 8


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3. The computed IE values are −209.5 (MP2), −189.1 (MP3), −199.3 (MP2.5), −202.4 (CCSD), −209.3 [CCSD(T)], −271.2 (B3LYP-D2), −277.8 (BP86-D2), and −239.5 (ωB97XD) kcal mol-1 . The absolute error of methods considered with respect to CCSD(T) are 0.2 (MP2), 20.2 (MP3), 10.0 (MP2.5), 6.9 (CCSD), 61.9 (B3LYP-D2), 68.5 (BP86-D2), and 30.2 (ωB97X-D) kcal mol-1 . The MP2 method provides the lowest absolute error (0.2 kcal mol-1 ) with respect to CCSD(T), while results of CCSD, MP2.5, and especially MP3 are in significant errors, and the DFT functionals considered are again in dramatic errors. Hence, it appears that the effect of triple excitation corrections are very important for the Bz–Co2+ – Bz complex. For the Bz–Co2+ –Bz complex, the interaction energy including relativistic corrections at the CCSD(T)/6-311++G(d,p) level is reported in Table 4. The relativistic energy correction for interaction energy is computed to be −4.4 kcal mol-1 , at the ωB97XD/6-311++G(d,p) level. Therefore, the relativistic effects are quite important for the Bz– Co2+ –Bz complex. Hence, the predicted IE value with relativistic corrections is −213.4 kcal mol-1 at the CCSD(T)/6-311++G(d,p) level.

3.5

The Bz–Ni2+ Complex

The optimized geometry of the Bz–Ni2+ complex, at the MP2/6-311++G(2d,2p) level, is depicted in Figure 5. The overall point group symmetry of the Bz–Ni2+ complex is C6v . Upon binding to Ni2+ , the D6h symmetry of the benzene ring is distorted to a C6v geometry. For the benzene ring, the C–C bond lengths are 1.416 Å. The Ni–C distances of the complex are 2.205 Å. Further, the distance between Ni2+ and the COM of the benzene ring is 1.686 Å. For the Bz–Ni2+ complex, non-relativistic interaction energies from the MP2, MP3, MP2.5, CCSD, CCSD(T) methods with the 6-311++G(2d,2p) basis set are reported in Table 1. Computed IE values are −193.5 (MP2), −184.1 (MP3), −188.8 (MP2.5), −191.6 (CCSD), −187.7 [CCSD(T)], −223.3 (B3LYP-D2), −214.4 (BP86-D2), and −219.8 (ωB97XD) kcal mol-1 . The absolute error of other methods considered with respect to CCSD(T) 9



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are 5.8 (MP2), 3.6 (MP3), 1.1 (MP2.5), 3.9 (CCSD), 35.6 (B3LYP-D2), 26.7 (BP86-D2), and 32.1 (ωB97X-D) kcal mol-1 . Hence, the CCSD and MP2.5 methods provide the lowest errors with respect to CCSD(T), while the results of MP3, MP2, and the DFT functionals considered are in dramatic errors. For the Bz–Ni2+ complex, the interaction energy including relativistic corrections at the CCSD(T)/6-311++G(2d,2p) level is reported in Table 2. For the Bz–Ni2+ complex, the relativistic energy correction for interaction energy is computed to be −2.6 kcal mol-1 , at the ωB97X-D/6-311++G(2d,2p) level. Therefore, the relativistic effects are significant for reliable predictions of IE, as in the case of previous metal cation– benzene complexes. Hence, the predicted IE value with relativistic corrections is −189.8 kcal mol-1 at the CCSD(T)/6-311++G(2d,2p) level.

3.6

The Bz–Ni2+ –Bz Complex

The optimized geometry of the Bz–Ni2+ –Bz complex, at the MP2/6-311G++(d,p) level, is depicted in Figure 6. The overall point group symmetry of the Bz–Ni2+ –Bz complex is C2 (approximately D6d ). The C–C bond lengths in the benzene rings are 1.414 Å, while the Ni–C distances of the complex are 2.259 Å. The distance between Ni2+ and the COM of the benzene ring is 1.760 Å. For the Bz–Ni2+ –Bz complex, non-relativistic interaction energies from the MP2, MP3, MP2.5, CCSD, CCSD(T) methods with the 6-311++G(d,p) basis set are reported in Table 3. The computed IE values are −241.4 (MP2), −217.8 (MP3), −229.6 (MP2.5), −238.1 (CCSD), −246.5 [CCSD(T)], −277.1 (B3LYP-D2), −313.3 (BP86-D2), and −278.1 (ωB97XD) kcal mol-1 . The absolute error of methods considered with respect to CCSD(T) are 0.7 (MP2), 36.3 (MP3), 18.5 (MP2.5), 9.8 (CCSD), 26.4 (B3LYP-D2), 62.6 (BP86-D2), and 27.4 (ωB97X-D) kcal mol-1 . 5.2 (MP2), 28.8 (MP3), 17.0 (MP2.5), 8.4 (CCSD), 30.6 (B3LYP-D2), 66.8 (BP86-D2), and 31.6 (ωB97X-D) kcal mol-1 . The MP2 method again provides the lowest absolute error (5.2 kcal mol-1 ) with respect to CCSD(T), whereas results of MP3, MP2.5, and the DFT functionals considered are in dramatic errors. The failure of CCSD indicates that 10


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the effect of triple excitation corrections are very important for the Bz–Ni2+ –Bz complex. The interaction energy including relativistic corrections at the CCSD(T)/6-311++G(d,p) level is reported in Table 4. The relativistic energy correction for interaction energy is computed to be −4.7 kcal mol-1 , at the ωB97X-D/6-311++G(d,p) level. The magnitude of the relativistic energy correction indicates that relativistic effects have important roles in accurate description of the Bz–Ni2+ –Bz complex. Hence, the predicted IE value with relativistic corrections is −249.7 kcal mol-1 at the CCSD(T)/6-311++G(d,p) level.

3.7

The Bz–Cu2+ Complex

The optimized geometry of the Bz–Cu2+ complex, at the MP2/6-311++G(2d,2p) level, is depicted in Figure 7. The overall point group symmetry of the Bz–Cu2+ complex is C2v , however it is slightly deviated from the C6v symmetry. Upon binding to Cu2+ , the D6h symmetry of the benzene ring is distorted to a C2v geometry. For the benzene ring, the C–C bond lengths are 1.405 and 1.426 Å. The Cu–C distances of the complex are 2.167 and 2.249 Å. Further, the distance between Cu2+ and the COM of the benzene ring is 1.708 Å. For the Bz–Cu2+ complex, non-relativistic interaction energies from the MP2, MP3, MP2.5, CCSD, CCSD(T) methods with the 6-311++G(2d,2p) basis set are reported in Table 1. Computed IE values are −165.6 (MP2), −154.4 (MP3), −160.0 (MP2.5), −174.0 (CCSD), −178.5 [CCSD(T)], −206.4 (B3LYP-D2), −226.4 (BP86-D2), and −201.9 (ωB97X-D) kcal mol-1 . The absolute error of other methods considered with respect to CCSD(T) are 12.9 (MP2), 24.1 (MP3), 18.5 (MP2.5), 4.5 (CCSD), 27.9 (B3LYP-D2), 47.9 (BP86-D2), and 23.4 (ωB97X-D) kcal mol-1 . Hence, the CCSD method provides the lowest errors with respect to CCSD(T), whereas the results of MP2, MP3, MP2.5, and the DFT functionals considered are in dramatic errors. For the Bz–Cu2+ complex, the interaction energy including relativistic corrections at the CCSD(T)/6-311++G(2d,2p) level is reported in Table 2. For the Bz– Cu2+ complex, the relativistic energy correction for interaction energy is computed to be −1.9 kcal mol-1 , at the ωB97X-D/6-311++G(2d,2p) level. Although, the magnitude of the 11



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relativistic energy correction is smaller compared to the other Bz–M2+ complexes considered, relativistic effects are still significant and can not be neglected. Hence, the predicted IE value with relativistic corrections is −181.1 kcal mol-1 at the CCSD(T)/6-311++G(2d,2p) level.

3.8

The Bz–Cu2+ –Bz Complex

The optimized geometry of the Bz–Cu2+ –Bz complex, at the MP2/6-311G++(d,p) level, is depicted in Figure 8. The overall point group symmetry of the Bz–Cu2+ –Bz complex is C2h . The C–C bond lengths in the benzene rings are between 1.399–1.421 Å, while the Cu–C distances of the complex are between 2.222–2.465 Å. The distance between Cu2+ and the COM of the benzene ring is 1.842 Å. For the Bz–Cu2+ –Bz complex, non-relativistic interaction energies from the MP2, MP3, MP2.5, CCSD, CCSD(T) methods with the 6-311++G(d,p) basis set are reported in Table 3. Computed IE values are −248.4 (MP2), −227.3 (MP3), −237.9 (MP2.5), −247.0 (CCSD), −254.0 [CCSD(T)], −287.3 (B3LYP-D2), −314.9 (BP86-D2), and −285.0 (ωB97XD) kcal mol-1 . The absolute error of methods considered with respect to CCSD(T) are 5.6 (MP2), 26.7 (MP3), 16.1 (MP2.5), 7.0 (CCSD), 33.3 (B3LYP-D2), 60.9 (BP86-D2), and 31.0 (ωB97X-D) kcal mol-1 . The MP2 method again provides the lowest absolute error (5.6 kcal mol-1 ) with respect to CCSD(T), while the results of MP2.5, MP3, and the DFT functionals considered are in dramatic errors. The failure of CCSD indicates that the effect of triple excitation corrections are essential for the Bz–Cu2+ –Bz complex. The interaction energy including relativistic corrections at the CCSD(T)/6-311++G(d,p) level is reported in Table 4. The relativistic energy correction for interaction energy is computed to be −4.1 kcal mol-1 , at the ωB97X-D/6-311++G(d,p) level. The magnitude of the relativistic energy correction indicates that relativistic effects have important roles in accurate description of the Bz–Cu2+ –Bz complex. Hence, the predicted IE value with relativistic corrections is −258.6 kcal mol-1 at the CCSD(T)/6-311++G(d,p) level.

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3.9

The Bz–Zn2+ Complex

The optimized geometry of the Bz–Zn2+ complex, at the MP2/6-311++G(2d,2p) level, is depicted in Figure 9. The overall point group symmetry of the Bz–Zn2+ complex is C6v . Upon binding to Zn2+ , the D6h symmetry of the benzene ring is distorted to a C6v geometry, as a result of the descending point group symmetry. For the benzene ring, the C–C bond lengths are 1.422 Å. The Zn–C distances of the complex are 2.258 Å. Further, the distance between Zn2+ and the COM of the benzene ring is 1.754 Å. For the Bz–Zn2+ complex, non-relativistic interaction energies from the MP2, MP3, MP2.5, CCSD, CCSD(T) methods with the 6-311++G(2d,2p) basis set are reported in Table 1. Computed IE values are −156.4 (MP2), −148.8 (MP3), −152.6 (MP2.5), −150.9 (CCSD), −152.4 [CCSD(T)], −166.6 (B3LYP-D2), −172.6 (BP86-D2), and −165.2 (ωB97XD) kcal mol-1 . The absolute error of other methods considered with respect to CCSD(T) are 4.0 (MP2), 3.6 (MP3), 0.2 (MP2.5), 1.4 (CCSD), 14.2 (B3LYP-D2), 20.2 (BP86-D2), and 12.8 (ωB97X-D) kcal mol-1 . Hence, the results of MP2.5 and CCSD(T) are nearly identical. This remarkable performance of MP2.5 is not surprising. The scaling parameters of MP2.5 are among optimal choices, 55–57 it can be considered as a scaled MP3 method, for closed-shell molecular systems. The failure of MP2.5 for other complexes, which have open-shell electronic configurations, indicates that one needs to revise the scaling parameter for open-shell systems. The DFT functionals considered are again in dramatic errors. For the Bz–Zn2+ complex, the interaction energy including relativistic corrections at the CCSD(T)/6-311++G(2d,2p) level is reported in Table 2. The relativistic energy correction for interaction energy is computed to be −5.8 kcal mol-1 , at the ωB97X-D/6-311++G(2d,2p) level. The magnitude of the relativistic energy correction indicates that relativistic effects are quite important and should not be neglected. Hence, the predicted IE value with relativistic corrections is −158.2 kcal mol-1 at the CCSD(T)/6-311++G(2d,2p) level.

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3.10

The Bz–Zn2+ –Bz Complex

The optimized geometry of the Bz–Zn2+ –Bz complex, at the MP2/6-311G++(d,p) level, is depicted in Figure 10. The overall point group symmetry of the Bz–Zn2+ –Bz complex is C1 (approximately Cs ). The benzene rings are in the parallel displaced position in contrast to other complexes, where they are staggered. The C–C bond lengths in the benzene rings are between 1.403–1.436 Å, while the Zn–C distances of the complex are between 2.167–3.071 Å. The distances between Zn2+ and the COM of the benzene rings are 1.880 and 2.252 Å. The one of the angle between C–COM-Zn2+ is 51.0◦ , while others are about 90.0◦ . In all other complexes, the C–COM-M2+ angle is about 90.0◦ . For the Bz–Zn2+ –Bz complex, non-relativistic interaction energies from the MP2, MP3, MP2.5, CCSD, CCSD(T) methods with the 6-311++G(d,p) basis set are reported in Table 3. The computed IE values are −235.4 (MP2), −221.9 (MP3), −228.7 (MP2.5), −224.5 (CCSD), −227.5 [CCSD(T)], −251.0 (B3LYP-D2), −260.8 (BP86-D2), and −249.3 (ωB97XD) kcal mol-1 . The absolute error of methods considered with respect to CCSD(T) are 7.9 (MP2), 5.6 (MP3), 1.2 (MP2.5), 3.0 (CCSD), 23.5 (B3LYP-D2), 33.3 (BP86-D2), and 21.8 (ωB97X-D) kcal mol-1 . Hence, the performance of MP2.5 is again noteworthy, while IE values of MP2 and MP3 are in significant errors, and the DFT functionals considered are in dramatic errors. The interaction energy including relativistic corrections at the CCSD(T)/6311++G(d,p) level is reported in Table 4. The relativistic energy correction for IE is computed to be −7.7 kcal mol-1 , at the ωB97X-D/6-311++G(d,p) level. The magnitude of the relativistic energy correction indicates that relativistic effects are indispensable in accurate description of the Bz–Zn2+ –Bz complex. It is also remarkable to note that the relativistic correction for the Bz–Zn2+ –Bz complex is significantly larger (about 2-fold compare to other Bz–M2+ –Bz complexes) than other complexes considered, which indicates that Bz–Zn2+ –Bz is more prone to such effects. The final IE value with relativistic corrections is −235.2 kcal mol-1 at the CCSD(T)/6-311++G(d,p) level.

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4

Conclusions

In this research, we have investigated the structures and interaction energies for complexes formed by Fe2+ , Co2+ , Ni2+ , Cu2+ , and Zn2+ binding with benzene molecules employing high level ab initio quantum chemical methods. As far as we know, the present work is the first to study the structures and energetics of Bz–M2+ and Bz–M2+ –Bz type complexes (M = Co, Ni, Cu, and Zn). Relativistic effects are also investigated via Douglas-Kroll-Hess second-order scalar relativistic computations for the complexes considered. The computed interaction energies (IEs), including relativistic energy corrections, for the Bz–M2+ type complexes at the CCSD(T)/6-311++G(2d,2p) level are −131.9 (Bz–Fe2+ ), −172.6 (Bz–Co2+ ), −189.8 (Bz–Ni2+ ), −181.1 (Bz–Cu2+ ), and −158.2 (Bz–Zn2+ ) kcal mol-1 , which indicate strong binding between transition metal cations and benzene molecules. The relativistic energy corrections, at the ωB97X-D/6-311++G(d,p) level, to interaction energies are computed to be −2.1 (Bz–Fe2+ ), −2.4 (Bz–Co2+ ), −2.6 (Bz–Ni2+ ), −1.9 (Bz–Cu2+ ), and −5.8 (Bz–Zn2+ ) kcal mol-1 . Hence, these effects can not be neglected in interaction energy predictions. It is also noteworthy that the Bz–Zn2+ complex appears to be more sensitive against relativistic effects than other transition metal cations considered. The computed interaction energies, including relativistic energy corrections, for the Bz– M2+ –Bz type complexes at the CCSD(T)/6-311++G(d,p) level are −206.4 (Bz–Fe2+ –Bz), −213.4 (Bz–Co2+ –Bz), −249.7 (Bz–Ni2+ –Bz), −258.6 (Bz–Cu2+ –Bz), and −235.2 (Bz–Zn2+ – Bz) kcal mol-1 , which indicate very strong binding between transition metal cations and benzene molecules. The magnitude of IEs are 1.2–1.5 times larger compared to the Bz–M2+ type complexes. The relativistic energy corrections, at the ωB97X-D/6-311++G(d,p) level, to interaction energies are computed to be −3.1 (Bz–Fe2+ –Bz), −4.4 (Bz–Co2+ –Bz), −4.7 (Bz–Ni2+ –Bz), −4.1 (Bz–Cu2+ –Bz), and −7.7 (Bz–Zn2+ –Bz) kcal mol-1 . Hence, these effects are very important in accurate computations of interaction energies. The transition metal cation–π interactions investigated in this study produce larger binding energies compared to arbitrary π–π interactions, and these interactions are an order of 15



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magnitude stronger than π–π interactions. 83 Further, the computed interaction energies for metal cations considered, are significantly more stronger (∼ 4–11 times) compared with main group metal cations, such as Li+ , Na+ , and K+ . 5 Overall, the present study may open new avenues in cation–π interactions. Finally, we would like to note that complexes considered might be metastable with respect to charge transfer dissociation. The metal ions might steal an electron from the benzene molecule, forming two singly charged ions, which will then dissociate via coulomb repulsion, as in the case of dication-water complexes. 84,85 The ground spin multiplicities of Bz+ –M+ complexes are different than that of Bz–M2+ complexes. Hence, this situation requires forbidden electronic state crossings. However, in some cases, the electronic state crossing might happen efficiently and the Bz–M2+ complexes may not form. Therefore, this situation should be considered in experimental studies that aim to generate these complexes.

Supporting Information Available (1) Optimized geometries of all species considered. (2) Harmonic vibrational frequencies of all species considered. (3) Interaction energies without CP corrections. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement This research was supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK-114Z786) and the European Cooperation in Science and Technology (CM1405). U.B. also acknowledge support from the Turkish Academy of Sciences, Outstanding Young Scientist Award (TÜBA-GEBİP 2015).

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(78) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Mennucci, B.; Petersson, G. A.; et al., Gaussian 09. Gaussian, Inc.: Wallingford, CT, 2009. (79) Cramer, C. J.; Truhlar, D. G. Density Functional Theory for Transition Metals and Transition Metal Chemistry. Phys. Chem. Chem. Phys. 2009, 11, 10757–10816. (80) Cohen, A. J.; Mori-Sanchez, P.; Yang, W. Challenges for Density Functional Theory. Chem. Rev. 2012, 112, 289–320. (81) Jiang, W.; Laury, M. L.; Powell, M.; Wilson, A. K. Comparative Study of Single and Double Hybrid Density Functionals for the Prediction of 3d Transition Metal Thermochemistry. J. Chem. Theory Comput. 2012, 8, 4102–4111. (82) Luo, S.; Averkiev, B.; Yang, K. R.; Xu, X.; Truhlar, D. G. Density Functional Theory of Open-Shell Systems. The 3d-Series Transition-Metal Atoms and Their Cations. J. Chem. Theory Comput. 2014, 10, 102–121. (83) Sinnokrot, M. O.; Sherrill, C. D. High-Accuracy Quantum Mechanical Studies of π–π Interactions in Benzene Dimers. J. Phys. Chem. A 2006, 110, 10656–10668. (84) Wu, B.; Duncombe, B. J.; Stace, A. J. Fragmentation Pathways of [Mg(NH3 )n ]2+ Complexes: Electron Capture versus Charge Separation. J. Phys. Chem. A 2006, 110, 8423–8432. (85) Duncombe, B. J.; Duale, K.; Buchanan-Smith, A.; Stace, A. J. The Solvation of Cu2+ with Gas-Phase Clusters of Water and Ammonia. J. Phys. Chem. A 2007, 111, 5158– 5165.

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Complex Bz–Fe2+ Bz–Co2+ Bz–Ni2+ Bz–Cu2+ Bz–Zn2+

MP2 −128.1 −182.2 −193.5 −165.6 −156.4

MP3 MP2.5 CCSD −125.7 −126.9 −128.0 −177.5 −179.8 −176.5 −184.1 −188.8 −191.6 −154.4 −160.0 −174.0 −148.8 −152.6 −150.9

CCSD(T) −129.5 −170.7 −187.7 −178.5 −152.4

B3LYP-D2 −154.8 −150.0 −223.3 −206.4 −166.6

BP86-D2 −171.2 −189.1 −214.4 −226.4 −172.6

ωB97X-D −147.2 −219.8 −219.8 −201.9 −165.2

Multiplicity 5 4 3 2 1

Table 1: Counterpoise corrected non-relativistic interaction energies (in kcal mol-1 ) from the MP2, MP3, MP2.5, CCSD, CCSD(T), B3LYP-D2, BP86-D2, and ωB97X-D methods (with the 6-311++G(2d,2p) basis set) and multiplicities for the Bz–M2+ complexes.

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Table 2: Interaction energies (in kcal mol-1 ) including relativistic corrections at the CCSD(T)/6-311++G(2d,2p) level for the Bz–M2+ complexes. Relativistic energy corrections are computed at the ωB97X-D/6-311++G(2d,2p) level. Complex CCSD(T) Bz–Fe2+ −131.9 2+ Bz–Co −172.6 Bz–Ni2+ −189.8 2+ Bz–Cu −181.1 2+ Bz–Zn −158.2

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Complex Bz–Fe2+ –Bz Bz–Co2+ –Bz Bz–Ni2+ –Bz Bz–Cu2+ –Bz Bz–Zn2+ –Bz

MP2 −203.1 −209.5 −241.4 −248.4 −235.4

MP3 MP2.5 CCSD −195.5 −199.3 −198.7 −189.1 −199.3 −202.4 −217.8 −229.6 −238.1 −227.3 −237.9 −247.0 −221.9 −228.7 −224.5

CCSD(T) −202.0 −209.3 −246.5 −254.0 −227.5

B3LYP-D2 −235.6 −271.2 −277.1 −287.3 −251.0

BP86-D2 −256.7 −277.8 −313.3 −314.9 −260.8

ωB97X-D −235.7 −239.5 −278.1 −285.0 −249.3

Multiplicity 5 4 3 2 1

Table 3: Counterpoise corrected non-relativistic interaction energies (in kcal mol-1 ) from the MP2, MP3, MP2.5, CCSD, CCSD(T), B3LYP-D2, BP86-D2, and ωB97X-D methods (with the 6-311++G(d,p) basis set) and multiplicities for the Bz– M2+ –Bz complexes.

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Table 4: Interaction energies (in kcal mol-1 ) including relativistic corrections at the CCSD(T)/6-311++G(d,p) level for the Bz–M2+ –Bz complexes. Relativistic energy corrections are computed at the ωB97X-D/6-311++G(d,p) level. Complex CCSD(T) Bz–Fe2+ –Bz −206.4 2+ Bz–Co –Bz −213.4 Bz–Ni2+ –Bz −249.7 2+ Bz–Cu –Bz −258.6 2+ Bz–Zn –Bz −235.2

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Figure 1: The optimized geometry of the Bz–Fe2+ complex at the MP2/6-311++G(2d,2p) level

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Figure 2: The optimized geometry of the Bz–Fe2+ –Bz complex at the MP2/6-311++G(d,p) level

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Figure 3: The optimized geometry of the Bz–Co2+ complex at the MP2/6-311++G(2d,2p) level

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Figure 4: The optimized geometry of the Bz–Co2+ –Bz complex at the MP2/6-311++G(d,p) level

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Figure 5: The optimized geometry of the Bz–Ni2+ complex at the MP2/6-311++G(2d,2p) level

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Figure 6: The optimized geometry of the Bz–Ni2+ –Bz complex at the MP2/6-311++G(d,p) level

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Figure 7: The optimized geometry of the Bz–Cu2+ complex at the MP2/6-311++G(2d,2p) level

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Figure 8: The optimized geometry of the Bz–Cu2+ –Bz complex at the MP2/6-311++G(d,p) level

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Figure 9: The optimized geometry of the Bz–Zn2+ complex at the MP2/6-311++G(2d,2p) level

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Figure 10: The optimized geometry of the Bz–Zn2+ –Bz complex at the MP2/6-311++G(d,p) level

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Transition Metal CationâÏ Interactions: Complexes Formed by Fe2+

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