Aromaticity of Some Metal Clusters: A Different View from Magnetic

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Aromaticity of Some Metal Clusters: A Different View from Magnetic Ring Current Hung Tan Pham, and Minh Tho Nguyen J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b11191 • Publication Date (Web): 09 Jan 2018 Downloaded from http://pubs.acs.org on January 10, 2018

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The Journal of Physical Chemistry

Aromaticity of Some Metal Clusters: A Different View from Magnetic Ring Current Hung Tan Phama,b and Minh Tho Nguyena,b,c,* a

Computational Chemistry Group, Ton Duc Thang University, Ho Chi Minh City, 70000

Vietnam b

Faculty of Applied Sciences, Ton Duc Thang University, Ho Chi Minh City, 70000 Vietnam

c

Department of Chemistry, KU Leuven, Celestijnenlaan 200F, B-3001 Leuven, Belgium.

(Abstract) The aromatic character of some small planar metallic clusters was revisited with an emphasis on their σ electrons. In contrast to previous reports, our approach based on magnetic ring current as an indicator for aromaticity points out that the σ electron delocalization in molecules behaves as an important contributor to their thermodynamic stability. Ring current maps were constructed using electron densities obtained from density functional theory calculations with the B3LYP functional and the 6-311G(d) basis set. Diatropic currents were further confirmed by an analysis of the symmetry of electronic excitations involved. The triatomic B3+ cycle is found to maintain a double σ and π aromaticity when it forms the [B3(NN)3]+ and [B3(CO)3]+ complexes. The planar penta-coordinated carbon clusters including C@Al5+, C@Al5-xBex1-x, C@Be5Hnn-4, C@Be5Linn-4 and C@Be5HxLi5-x+ are σ aromatic rather than π aromatic as previously assigned. The mixed copper clusters Cu3Si3+ and Cu3Ge3+ are found to be σ aromatic compounds. The copper hydrides CunHn can better be regarded as non-aromatic rather than aromatic compounds. The ring current indicator reveals the σ aromatic feature for Be2@Be5H5+ and Be2@Be6H62+ clusters, while this criterion shows a double aromaticity of Be2@B7- and Be2@B8. Overall, the present study points 1 ACS Paragon Plus Environment

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out again the importance of σ electrons in determining the bonding characteristics of metallic clusters, and they should equally be considered as a key element.

1. Introduction Aromaticity is one of the most essential and important concepts in chemistry. It has been and still is widely successful in rationalization of the unusual molecular structure, high thermodynamic stabilities and specific reactivities of many classes of chemical species, particularly in organic chemistry. It can be argued that the long history of aromaticity started in 1865 when Kekule introduced his interpretation for the structure of benzene.1,2,3 The simple (4N + 2) / 4N electron counting rule for π electrons has subsequently emerged as the most popular and most employed indicator for the aromatic character of different families of planar chemical species including organic and inorganic compounds alike. 4,5,6 More recently, the emergence and development of cluster science provided us with an unexpected expansion of the aromaticity concept to a larger range of compounds, which has extensively been reviewed in the past decade.7,8,9,10,11 Particularly, the aromatic character in metal clusters does not only involve π electrons but also other types of electrons such as the σ and δ electrons, thus establishing the emergence of multiple aromaticity.7,8 The dianion Al42- cluster was originally proposed as having a triple aromaticity involving σ-radial, σ-tangential and π-planar aromatic characters, on the basis of CMO analysis and NICS calculations.12,13,14,15,16 However, subsequent ring current calculations that evaluated the orbital contributions to the magnetic responses of its total electron density clearly demonstrated that Al42- is a σ aromatic rather than a triply aromatic compound.17,18,19,20,21

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As for prototypical multiply aromatic compounds, planar boron clusters have been found to exhibit delocalization* of both sets of π and σ electrons. A partition of the total electron density in terms of separate σ and π components points out that σ delocalization is equally important.22 The doubly aromatic character of boron-based clusters has been revealed by different methods, including the use of ring current.23,24,25,26 This ongoing debate emphasizes the need for an evaluation of the contributions of different sets of delocalized MOs when determining aromatic features. It is worth noting that δ electrons, which are formed by d-d interactions in metal clusters are also of importance in some planar cycles. On the basis of canonical MO analysis and NICS calculations, a δ aromatic nature is identified for Hf3, W32-, W3O92-, Ta3-, Ta3O- and Ta3O3-. 27,28,29,30,31

The more conventional π aromatic feature was identified for triangular cycles Zn32-,

Cd32- and Hg32- by CMO analyses, and mostly by negative NICS values involving 2 π electrons.32 Likewise, the existence of 10 delocalized π electrons confer to the [Fe(Sb)5]+ and [Fe(Bi)5]+ fivemembered rings a clear π aromatic character.33 Metal clusters containing only σ aromaticity are rather scarce. The σ aromatic character which is contributed mainly by s-AOs, was identified for different pure and doped coinage metal clusters.34,35,35,36,37,38,39,40,41,42 The trimeric cations Cu3+, Ag3+ and Au3+ were first suggested as having an σ aromatic character,38 but following studies using the ring current approaches clearly showed that these trimers are better regarded as non-aromatic, due to the existence of strong local paramagnetic currents circulating around the atomic nuclei.39 The magnetic response analysis pointed out an σ aromatic feature of Cu42-, Ag42- and Au42- planar clusters which contains each six delocalized σ electrons.40 Both planar doped Sc@Cu7 and Sc@Ag7 species containing each ten delocalized σ electrons were proved to have the sole σ aromaticity satisfying the classical (4N+2)

The term “electron delocalization” used in this paper is not related to the valence bond theory resonance which is a ground state property and connected to energy. *



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counting rule, on the basis of both NICS values and ring current flows.34,36 The σ aromatic feature was also determined for smaller rings involving coinage metals Au6Y+, Cu6Sc+ and Cu5Sc.35,42,44 The aromatic feature of metal clusters has mainly been determined by the CMO’s, NICS values, partitions of total electron density by techniques such as the electron localization function (ELF) and the magnetic chemical shifts and ring currents. A combined CMO and NICS analysis has often been used as indicator for aromatic character. Recently, re-investigations on the aromaticity of metallic clusters pointed out that NICS values do not behave as an intrinsic indicator, due to the fact that its value is estimated at a fixed single point whereas the aromatic property is dynamically caused by freely delocalized electrons over the entire skeleton.39,40,43 In this regard, the main issue is that establishment of a σ aromatic character is not straightforward on the basis of either the shape of the CMOs or the one-point NICS value. For this purpose, the ring current density approach provides us with a better probing tool because it considers the moving electrons. Several metallic clusters have been predicted as aromatic, but due to the inherent limits on methods employed, some key characteristics are not unambiguously demonstrated yet or still controversial. In this context, it appears necessary to revisit the electron distribution of some small metallic clusters that have been investigated in previous studies using the ring current density method, which is expected to give a different perspective on electron delocalization, and thereby a more complete picture on their aromaticity. In the present theoretical investigation, the electronic structure of five series of metallic clusters including [B3(NN)3]+ and [B3(CO)3]+, Cu3Si3+ and Cu3Ge3+, C@Al5+, C@Al2Be32-, C@Be5H, C@Be5Hnn-4 and C@Be5Linn-4, Be2@Be5H5+, Be2@Be6H62+, Be2@B7- and Be2@B8, and CunHn and CunLin is reexplored making use of the ring current density method, and paying a


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particular attention to their σ electrons. Their aromatic character has previously been studied but the outcome remains a matter of debate: i) the boron ions B3-/+ have recently been identified as having a double aromaticity by us,23 whereas Cui et al.44 reported that the B3+ unit of [B3(NN)3]+ and [B3(CO)3]+ complexes is π aromatic with two π electrons; ii) the Cu3Si3+ and Cu3Ge3+ planar clusters are usually illustrated as π aromatic with two π electrons,45, while their σ electrons behavior has not been explored yet; iii) the planar penta-coordinated carbon structures including C@Al5+, C@Al2Be32-, C@Be5Hnn-4 and C@Be5Linn-4 have been reported and their chemical bonding was abundantly analyzed,46,47,48,49 but their aromatic character is still controversial; iv) the beryllium doped clusters Be2@Be5H5+, Be2@Be6H62+, Be2@B7- and Be2@B8 present with a particular geometry where two Be atoms are vertically coordinated to the Be5, Be6, B7 and B8 strings.50,51 Although their chemical bonding was carefully analyzed, their aromatic characteristics have not been well established yet, and finally v) the aromaticity of copper hydrides CunHn has been probed by NICS calculations in combination with CMO analysis.52 The reported NICS values are however small, being -8.4, -4.2, -1.4 and -0.2 ppm for Cu3H3, Cu4H4, Cu5H5 and Cu6H6, respectively. Thus, a revisit of CunHn appears necessary. In addition, the isovalent CunLin clusters are also considered in order to gain more understanding on the behavior of σ electrons. 2. Computational Methods



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The conventional theory of induced current density has been described in much detail in previous papers.53,54,55,56 Consider a closed-shell molecule in a constant uniform magnetic field B, by mean of first-order perturbation theory, the current density induced of this molecule is a sum of orbital contributions (equation (1): 𝑁 2 (1) 𝑗 (1) = ∑ 𝑗𝑛 (𝑟)

(1)

𝑛=1

where (1) 𝑗𝑛 (𝑟) = −

𝑒2 2𝑖𝑒ℏ (1) (1) 𝐵 × (𝑟 − 𝑑)𝜓𝑛2 + (𝜓𝑛 ∇𝜓𝑛 − 𝜓𝑛 ∇𝜓𝑛 ) 𝑚𝑒 𝑚𝑒

(2)

(1)

In (2), the 𝜓𝑛 is the first-order correction to orbital 𝜓𝑛 , and it is expressed as: (1)

𝜓𝑛 =

⟨𝜓𝑝 |𝑙̂(𝑑). 𝑩|𝜓𝑛 ⟩ 𝑒 ∑ 𝜓𝑝 (𝑟) 2𝑚𝑒 𝜖𝑝 − 𝜖𝑛

(3)

𝑝>𝑁/2

The exact total current density, 𝑗 (1) , is independent of choice gauge origin and the ipsocentric (1) (CTOCD-DZ) formula is resulted by treating each point r as its own gauge origin. Then, the 𝑗𝑛 (𝑟)

and the first order correction can be: (1) 𝑗𝑛 (𝑟) =

2𝑖𝑒ℏ (1) (1) (𝜓𝑛 ∇𝜓𝑛 − 𝜓𝑛 ∇𝜓𝑛 ) 𝑚𝑒

(4)


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(1)

𝜓𝑛 = −

⟨𝜓𝑝 |𝑙̂(𝑟0 ). 𝑩|𝜓𝑛 ⟩ 𝑒 (∑ 𝜓𝑝 (𝑟) ).𝑩 2𝑚𝑒 𝜖 − 𝜖 𝑝 𝑛 𝑁 𝑝>

+

2

̂|𝜓𝑛 ⟩ ⟨𝜓𝑝 |𝒑 𝑒 (𝑑 − 𝑟0 ) × ∑ 𝜓𝑝 (𝑟) 2𝑚𝑒 𝜖 𝑝 − 𝜖𝑛 𝑁 𝑝>

(

2

.𝑩

(𝑝)

(𝑑)

= 𝜓𝑛 + 𝜓𝑛

(5)

)

This formalism gives a description in which both diatropic and paratropic magnetic responses can be interpreted as the transition to the excited states generated from the first-order wave function (1)

(𝑝)

𝜓𝑛 . In equation (5), the term 𝜓𝑛

accounts for a paramagnetic contribution, and in terms of (d)

symmetry selection rules, it is determined by rotational transitions, whereas the ψn is a diatropic contribution and determined by translational transitions. The ring current maps are performed using electron densities obtained from density functional computations using the B3LYP functional in conjunction with the 6-311G(d) basis set. The magnetic response is carried out using the SYSMO package,56,57 which is linked to the GAMESS-UK program.58 Most geometrical structures used in this study have been taken from previous reports in the literature, except for the lithium series C@Be5H5-xLix+ and CunLin. All structures considered are re-optimized or optimized using the B3LYP/311G(d) level. For the C@Be5H5-xLix+ and CunLin series, their geometries are generated in replacing H atoms by Li atoms, without additional search for the possible isomers. All geometry optimizations are performed with the aid of the Gaussian 09 package.59 The electronic structure of clusters is further examined using the electron localization function (ELF) which is a partition of the total electron density into basins. The ELF 7 ACS Paragon Plus Environment


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maps often provide a complementary view to results obtained from ring current calculations.60 In each current density map, the contour and shading show the modulus of induced current density and narrows display its projection onto the plotting plane. As for a convention, anticlockwise and clockwise circulations correspond to diatropic and paratropic magnetic current, respectively. The diatropic current density corresponds to an aromatic character, whereas the paratropic current indicates an antiaromatic behavior. 3. Results and Discussion In the following sections, the aromatic feature of each series of compounds mentioned above will be presented. 3.1 The boron trimeric cation B3+ and its complexes are doubly aromatic Both [B3(NN)3]+ and [B3(CO)3]+ complexes, containing each a D3h B3+ cycle, were experimentally synthesized, and geometrically characterized as having a planar form in which each B atom is bonded to a NN or CO ligand.44 The authors concluded that either the free cation B3+ or the ring within these complexes satisfies the (4N + 2) Hückel count exhibiting two delocalized π electrons (N = 0). Therefore, both [B3(NN)3]+ and [B3(CO)3]+ were claimed as the smallest aromatic compounds with two π electrons. This conclusion has also been further supported by negative NICS(1) values. The authors44 also claimed that [B3(NN)3]+ and [B3(CO)3]+ are somewhat σ aromatic due to the donation of NN and CO ligands to the LUMO of B3+. As stated above, there have been recent investigations demonstrating that the NICS value is not a good indicator for aromaticity of all-metal cycles.21,39,40,61 Additionally, the aromatic character of σ electrons in small boron-based clusters is confirmed by different indicators including the CMO and NBO,62 ELF,63 TRE64 and ring current maps.23 Recently we characterized the B3+ 8 ACS Paragon Plus Environment

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cation as a doubly aromatic trimer.23 We demonstrate again here this aromatic feature of B3+ and both [B3(NN)3]+ and [B3(CO)3]+ complexes by performing induced magnetic ring currents, not only for all electrons but also from both separate sets of π and σ electrons. Our present calculations provide an additional support for the doubly aromatic feature of B3+. As shown in Figure 1, the π orbital of the B3+ cycle and those in [B3(NN)3]+ and [B3(CO)3]+ complexes significantly raise the diatropic current density. The strongly diatropic currents are equally observed for σ electrons of the naked cation B3+ and that in both complexes (Figure 1). In contrast to previous report,44 the ring current maps uniformly indicate the double σ and π aromatic character of the triatomic boron cation and both [B3(NN)3]+ and [B3(CO)3]+ complexes, rather than the sole π aromatic species. Calculated orbital contributions clearly show that the doubly degenerate HOMO-1,1’ are the main contributor to the σ ring current map of both [B3(NN)3]+ and [B3(CO)3]+ complexes, thus constitute the main source of their intrinsic σ aromaticity. The electronic transitions responsible for magnetic current density of both B3(NN)3+ and B3(CO)3+ are schematically illustrated in Figure 3. Under D3h point group for both B3(NN)3+ and B3(CO)3+, the excitation is occurred from the HOMO (A2”) to the LUMO (A”), where Г(T(x,y)) = A2” x A” is of allowed translational transition and responsible for diatropic current density of π electrons. Additionally, the allowed translational transition from the HOMO-1,1’ (E’) to the LUMO+1,1’ (E’), in which Г(T(x,y)) = E’ x E’, raises the diatropic ring current maps for σ electrons of B3(NN)3+ and B3(CO)3+ complexes. Overall, the doubly aromatic feature of the boron cation B3+ is firmly maintained when it interacts with either N2 or CO molecules. 3.2 Si3Cu3+ and Ge3Cu3+ are σ aromatic



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In continuing with the aromatic character of three-membered rings, the Si3Cu3+ and Ge3Cu3+ clusters are reexplored with use of ring currents. Geometrically, both Si3Cu3+ and Ge3Cu3+ are located as having a planar shape in which each of the three Cu atoms is attached to a Si-Si and GeGe vertex of Si3 and Ge3 three-membered cycle, respectively, resulting in D3h adducts.45 Subsequent chemical bonding analysis suggested that both can be regarded as π aromatic compounds with 2 π electrons. Our present ring current density analysis does not support such a view point. Figure 4a) displays the total, σ and π ring current densities for both Si3Cu3+ and Ge3Cu3+ clusters. It is clear that the total ring current maps, in terms of magnetic response resulting from all electrons, are strongly diatropic indicating a total aromatic feature for both. The σ electrons of either Si3Cu3+ or Ge3Cu3+ equally produce strongly diatropic ring current densities. Ring current flows raised by π electrons are not found, corresponding thus to a π non-aromaticity. As a consequence, both Si3Cu3+ and Ge3Cu3+ clusters should be classified into the class of single σ aromatic rather than π aromatic compounds. In order to further understand this issue, ring current densities of σ as well as of π orbitals are performed and displayed in Figure 4b. It is illustrative that the doubly degenerate HOMO-0,0’ for Si3Cu3+ and HOMO-1,1’ for Ge3Cu3+, deliver the main contribution to the σ current density. As given in Figure 5, the doubly degenerate HOMO-1,1’ of Ge3Cu3+ and HOMO-0,0’ of Si3Cu3+ (both having E’ symmetry) are involved in the electronic transitions to the LUMO-2,2’, and allowed under the translational selection rule, with Г(T(x,y))= E’ x E’. Combining with two σ electrons occupied on the HOMO-2, there is thus agreement between the (4N + 2) counting rule and ring current indicator in predicting the σ-aromaticity for both Si3Cu3+ and Ge3Cu3+ clusters. Together


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with ScCu7 and ScAg7 clusters, this property of Si3Cu3+ and Ge3Cu3+ again illustrates that σ electron delocalization in coinage metal clusters is of importance, and cannot be ignored. 3.3 Planar pentacoordinated carbon clusters In this section, the aromaticity of some planar penta-coordinated carbon (ppC) clusters is explored in some detail. Obtained results point out that σ electron delocalization should be considered when designing planar poly-coordinated carbon compounds. 3.3.1 C@Al5+ and C@Al2Be32- are σ aromatic A planar penta-coordinated carbon structure in which a C atom is located at the central position of a Al5 pentagonal cycle was established by both theoretical calculations and experiment.46 Motivated by the planar shape of C@Al5+ cluster, Merino et al. carefully explored the geometry of isoelectronic CAl5-xBex1-x systems with x = 1-3, and the ppC was found for them.47 Subsequent electronic structure analysis on the basis of both NICS and CMO results suggested that both ppC’s C@Al5+ and C@Al5-xBex1-x could be considered as doubly σ and π aromatic species. The present ring current indicator gives however a different view on the CAl5-xBex1-x clusters in which the sole σ aromaticity is now identified. Figure 6 displays the total, σ and π ring current maps of C@Al5+ and isoelectronic C@Al5-xBex1-x systems with x = 1-3. In agreement with previous results, the total ring current maps are strongly diatropic in terms of magnetic response, clearly indicating their overall aromaticity. Remarkably, the ring current densities calculated for separate π and σ electrons, displayed in Figure 6, indicate that both C@Al5+ and C@Al5-xBex1-x cannot be regarded as doubly aromatic. The strongly diatropic current flow is only observed for σ electrons of each ppC structure considered, whereas their π counterparts are basically empty. This 11 ACS Paragon Plus Environment


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result suggests that the isoelectronic C@Al5+ and C@Al5-xBex1-x clusters are solely σ aromatic in contrast with results derived from previous CMO and NICS analyses. The σ-aromatic feature of ppC compounds considered can be understood upon exploration of the ring current maps of σ orbitals. For the C@Al5+, previous CMO-NICS analysis pointed out that both degenerate HOMO-0,0’ are the main contributor to the σ aromaticity, whereas the HOMO-1,1’ are less important. As given in Figure 7a, the σ ring current map of C@Al5+ receives significant contributions by the degenerate HOMO-1,1’, whereas the degenerate HOMO-0,0’ turn out to be inactive with respect to magnetic response. Similarly, it is illustrative that the HOMO-3 of C@Al5-xBex1-x structure, which has the same irreducible representation as the HOMO-1,1’ of C@Al5+, also delivers an important contribution to the σ current density. Electronic transitions from these HOMOs to the respective LUMO again correspond to allowed translational transitions. 3.3.2 C@Be5Hnn-4 and C@Be5Linn-4 are σ aromatic The ppC structural motif is also found for two isoelectronic series involving C@Be5Hnn-4 and C@Be5Linn-4.

48,49

A doubly aromatic character was previously assigned for them according to

NICS and CMO analyses. Additionally, the aromatic feature of C@Be5Linn-4 structures was explored using the Bz method, and as a result, each cluster contains two apart electron delocalization systems, namely π and σ. More importantly, these authors illustrated that σ orbitals significantly contribute, whereas π electrons participate by ~10% to the aromaticity as indicated by the Bz values. This consequently emphasizes a dominant σ delocalization. We now revisit these structures in examining their ring current densities. For a more complete understanding, as well as emphasizing the different effects of the Li atoms on the aromatic character, the ring current densities of the Li-H mixed C@Be5HxLi5-x+ systems are also


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considered. Figures 8, 9 and 10 display the total, σ and π ring current maps of C@Be5Hnn-4, C@Be5Linn-4 and C@Be5H5Li5-x+ species. The diatropic current flows are clearly observed for the total density of these systems. Exploration of ring current densities of both sets of σ and π orbitals, as displayed in Figures 9 and 10, also shows that σ electrons invariably raise a strong diatropic current density, whereas the π-current flows appear to be almost negligible. It is internally consistent that σ electrons provide the largest, if not the sole, contribution to the total diatropic ring current maps. In other words, the C@Be5Hnn-4, C@Be5Linn-4 and C@Be5H5Li5-x+ planar cycles should be classified, in contrary with previous report, in the group of single σ aromatic species. The σ ring current densities of the hydrides C@Be5Hnn-4 and the lithium derivatives C@Be5Linn-4 contain a different aspect, even though they exhibit diatropic magnetic responses. The current flows of C@Be5Linn-4 systems (Figures 8b and 10b) move over the whole cluster skeleton including regions located between Be and Li atoms. In contrast, only C@Be5H3- and C@Be5H22- produce ring current maps (Figure 8a and 10a), which also circulate around the whole molecular geometry, while those of C@Be5H5+ and C@Be5H4 are limited in regions between C and Be atoms. Li atoms appear to consequently generate the aromaticity whereas H atoms do not. In order to clarify this point, the current density of the series C@Be5H5-xLix+ with x = 1-4 are performed, and shown in Figures 8c, 9c and 10c. Increase of the number Li atoms induces the clearer molecular ring current maps for C@Be5H5-xLix+ systems. This result emphasizes the different effects of H and Li atoms where Li atoms, using their ability to donate one electron per Li atom, turn the aromatic character on whereas H atoms turn it off. Electron delocalization of the cycles C@Be5Hnn-4, C@Be5Linn-4 and C@Be5H5-xLix+ and their electronic structure are also examined by means of electron localization function (ELF). This 13 ACS Paragon Plus Environment


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technique is a partition of the total electron density in terms of local basins. At the bifurcation value of ELF = 0.85, a localization domain located in regions between C and five Be atoms are found for all the cases considered (Figure 11). The C atoms turns out to bear a delocalized bonding with Be atoms. In the ELF map of C@Be5Li5+, a localization domain is located in the whole region between Li and Be, whereas in C@Be5H5+ this domain is divided into five smaller basins concentrated on H nuclei. A comparison of the ELF iso-surface of C@Be5Li4H+ with C@Be5LiH4+ shows an interesting effect of Li and H atoms on the cyclic delocalization. At the bifurcation value of ELF = 0.85, two localization domains are observed for C@Be5Li4H+, one being located around H nuclei and the other over the entire domain between Li and Be atoms. In contrast, C@Be5LiH4+ produces an ELF map consisting of five localization domains, at the same bifurcation value, in which four domains are related to H nuclei. Thus, valence electrons tend to be concentrated around H nuclei, while Li atoms allow them to move more freely. A consistent picture emerges between ELF and ring current maps of C@Be5Hnn-4, C@Be5Linn-4 and C@Be5H5-xLix+. In all cases, a diatropic current flow is found for the C@Be5 moiety and a corresponding localization domain is observed in region between the C and five Be atoms. Due to the fact that valence electrons are favorably located around H nuclei, the presence of H atoms does not induce additional ring current density. On the contrary, Li atoms, upon electron donation, prefer to allow the electrons to circulate more freely, and thereby produce ring current maps delocalized over the entire molecular skeletons. The above analysis emphasizes that the σ aromaticity is apparently a dominant contributor to the total aromaticity of the clusters considered, and should be regarded as an important factor governing the stability of planar carbon molecules. Generally, in order to stabilize a planar hyper14 ACS Paragon Plus Environment

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coordinated carbon species, on a perspective of electronic structure, the ligands must produce σdonating / π-accepting interactions with the C center.65,66 In the situation of ppC clusters considered here, the pz lone pair of C atom enjoys a delocalized π bonding, however resulting in MOs that do not induce a π aromaticity. The σ-donating interaction between the five-membered ring and the C center raise a strong σ aromaticity, which is a dominant contributor to the aromatic character of ppC. The planar carbon compound was theoretically discovered long ago,67,68 and their electronic structure is rationalized by the importance of π delocalization.65,66,69,70 In the planar penta-coordinated C systems examined in the present work, a σ delocalization can specially be highlighted, whereas a π aromaticity is proved to be insignificant. 3.4 Be2@Be5H5+ and Be2@Be6H62+ are σ aromatic while Be2B7- and Be2B8 are doubly aromatic The bimetallic boron cycle, a structural motif in which two metal atoms are vertically located to a boron ring, has been found as a general tendency for 3d atoms,71 while those of Group 2 metals is rather scarce. Recently, the doubly Be doped Be2@B7- and Be2@B8 are characterized as new members of this class in which two Be atoms are vertically coordinated but on two opposite sides to the B7 and B8 strings, respectively.50 Also the beryllium hydrides Be7H5+ and Be8H62+ were recently found to form bimetallic cycles in which two Be atoms are vertically placed to Be5 and Be6 cycles and H atoms are attached to each of the Be-Be edges.51 Previous analysis using the AdNDP method pointed out that both species Be7H5+ and Be8H62+ could be classified as doubly aromatic, exhibiting each 6σ and 2π electrons, according to the classical (4N + 2) counting rule.54 A doubly aromatic character has also been predicted for both Be2B7- and Be2B8 on the basis of their 6σ and 6π electrons. 15 ACS Paragon Plus Environment


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Let us now have another look at the aromatic character of these Be-containing clusters considering the magnetic ring current density. The corresponding total, σ and π ring current maps of these Be species are displayed in Figure 12. The total ring current densities of Be7H5+ and Be8H62+ are of diatropic nature in terms of magnetic response. In other words, these Be-based clusters are aromatic. However, the current density maps performed respectively for σ and π orbitals indicate that both Be7H5+ and Be8H62+ structures are solely active σ aromatic species, due to the fact that only σ electrons raise strongly diatropic current density. A current density produced by π electrons is basically non-existent, indicating a π non-aromatic feature. In other words, both Be7H5+ and Be8H62+ cycles are σ aromatic. The ring current density maps indicate a doubly aromatic nature for the boron Be2B7- and Be2B8 cycles. Indeed, both sets of σ and π electrons in each cycle (Figure 13) contribute to the creation of diatropic magnetic responses. The orbital contributions to ring current densities of Be structures are examined in Figure 13. For σ orbitals, each Be cluster contains three delocalized σ orbitals thus populated by 6 electrons, and of the latter MOs, the doubly degenerate HOMO, except for the case of Be2@B6H62+ being the HOMO-1,1’, delivers the predominant contribution to the σ ring current density. An agreement between the (4N + 2) count and ring current indicator is thus found for this series. Either Be2@Be5H5+ or Be2@Be6H62+ has only one π orbital occupied by 2 electrons, and it does not produce any significant current density, and therefore they cannot be classified as π aromatic. On the contrary, the doubly degenerate HOMO-1,1’ of Be2@B7- and Be2@B8 produces strongly diatropic ring current flows, and thus gives the main contribution to π ring current densities. According to this indicator, both Be2@B7- and Be2@B8 boron cycles are doubly aromatic. 16 ACS Paragon Plus Environment

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3.5 CunHn and CunLin The planar copper hydrides Dnh CunHn with n = 3-6 were predicted by Tsipis et al.52 As supported by negative NICS values, the authors determined their aromatic character as the driving force for the planar shape. We explore here the ring current maps of CunHn and its isovalent lithium derivatives CunLin. Ring current density maps of planar copper hydrides CunHn, displayed in Figure 14, are indicative for their non-aromatic character. The current flows actually stay around Cu and H nuclei rather than moving around the whole cluster. Turning back to the results of Tsipis et al., the NICS values obtained for CunHn amount to around -2 ppm, and in fact these values are apparently too small for this purpose. In total contrast with CunHn, the lithium CunLin systems, as in the case described in a previous section, present both strongly diatropic and paratropic current densities according to the (4N + 2) or 4N number of electrons. Both Cu3Li3 and Cu5Li5, which possess 6 and 10 valence electrons, respectively, produce diatropic current maps. Possessing 8 and 12 valence electrons, both Cu4Li4 and Cu6Li6 induce as expected paratropic ring current maps, and thereby behave as anti-aromatic species. While CunLin structures are either aromatic or anti-aromatic, the hydrides CunHn clusters are uniformly nonaromatic. This result emphasizes again the basically different effects of Li and H atoms on the aromatic character. As for another typical example, the possible transitions of Cu5Li5 are performed and given in Figure 15. Within D5h point group, the excitation from the HOMO-0,0’ (E2’) to the LUMO+1,1’ (E1’) is under in-plane selection rule, where the transition Г(T(x,y)) = E2’ x E1’ in allowed by



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translational selection rule, and subsequently produce the diatropic current density for Cu5Li5 cluster. We analyze further the electronic structure of CunXn with X = H and Li using the electron localization function. At the bifurcation value of ELF = 0.7, the ELF maps of CunLin (Figure 16) show that each Li atom exhibits two basins in which electrons are fully delocalized over the whole cluster, in contrast, localization domains of CunHn appear at H centers rather than distributed in two domains as Li atoms. On the other hand, Li atoms give more electrons to the delocalized pattern than H dopants, and as a result, the aromatic/anti-aromatic character is identified for CunLin series, but a non-aromaticity is found for the copper hydride clusters. 4. Concluding Remarks In this theoretical investigation, the aromatic character of five series of small metallic clusters was revisited by using the magnetic ring current approach, in which their σ aromaticity was emphasized. A number of new results, that disagree with previously reported studies, emerge as follows: i) The double aromaticity involving both σ and π electrons of the B3+ cycle is found to be maintained in both [B3(NN)3]+and [B3(CO)3]+ complexes. ii) Both Cu3Si3+ and Cu3Ge3+ clusters are illustrated as σ aromatic species by diatropic current densities, rather than as π aromatic compounds with 2 π electrons. iii) Reexamination on the aromatic feature of CunHn illustrates that these cooper hydrides should be regarded as non-aromatic rather than aromatic compounds.


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iv) The ring current indicator proves a σ aromatic feature for Be2@Be5H5+ and Be2@Be6H62+ clusters, while this criterion shows that Be2@B7- and Be2@B8 are doubly σ and π aromatic compounds. v) Magnetic ring current maps point out a σ-aromatic nature of planar penta-coordinated carbon compounds including C@Al5+, C@Al5-xBex1-x, C@Be5Hnn-4, C@Be5Linn-4 and C@Be5HxLi5-x+ systems. Overall, the present study emphasizes that when considering the thermodynamic stability of cluster having planar shape, all types of electron delocalization need to be considered rather than exploring only the set of π electrons. For this purpose, the magnetic responses of the total electron density and different components, expressed in terms of ring currents, emerge as a valuable approach. In many compounds assigned as aromatic by this approach, the classical (4N + 2) electron count is not obeyed. Finally, rapid developments in cluster science are leading to discovery of a plethora of novel structural motifs, and an appropriate examination on their electronic structure and chemical bonding is certainly of crucial importance in the rationalization and establishment of relationships between their geometry and thermodynamic stability. Although the classical concepts remain important for understanding, they can possibly lead us to miss some novel key factors and phenomena such as the σ aromaticity. Acknowledgements This paper is dedicated to our colleagues and friends, Manuel Yanez and Otila Mo, who for many years coordinated with much dedication and enthusiasm the Erasmus Mundus European Master in Theoretical Chemistry and Computational Modeling (TCCM). This program has been, and still is, 19 ACS Paragon Plus Environment


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educating generation of computational chemists worldwide. We are indebted to KU Leuven Research Council (GOA program) and FWO-Vlaanderen. We also thank Ton Duc Thang University (Demasted) for support. We are grateful to Dr. Remco Havenith at Groningen University, The Netherlands, for assistance with the SYSMO program. Authors Information. *

Minh Tho Nguyen, Email: [email protected], [email protected]. ORCID:

000-0002-3803-0569 Hung Tan Pham, Email: [email protected]. ORCID: 0000-0001-6356-3167


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Figures:

Structure

(σ+π) electrons

π electrons

σ electrons

[B3-(NN)3]+

[B3-(CO)3]+

B3+

Figure 1. The total, π and σ ring current maps of [B3(NN)3]+, [B3(CO)3]+ and B3+ (B3LYP/6311G(d)).



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HOMO

HOMO-1,1’ σ-orbitals π-orbital [B3(NN)3]+

π-orbitals

σ-orbitals [B3(CO)3]+


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Figure 2. The ring current maps of π and σ orbitals of [B3(NN)3]+ and [B3(CO)3]+ complexes (B3LYP/6-311G(d)).



e'

e'

e”

e”

T(x,y)

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T(x,y)

a2”

a2”

e'

e'

B3(NN)3+

B3(CO)3+

Figure 3. Presentation of the electronic transitions of B3(NN)3+ and B3(CO)3+ which produce the diatropic current density and are allowed by transition selection rule.


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Cu3Si3+

Cu3Ge3+

a)

HOMO-0,0’

HOMO-2 Si3Cu3+

HOMO-1

HOMO-1,1’

HOMO-2 Ge3Cu3+

HOMO

b)



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Figure 4. a) total, σ and π ring current densities of Cu3Si3+,Cu3Ge3+, Si3H3+-slide and Si3H3+-tail; b) ring current density of σ and π orbitals (B3LYP/6-311G(d)).


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e'

e'

T(x,y) T(x,y)

e'

e'

Cu3Si3+

Cu3Ge3+

Figure 5. Electronic transitions producing the ring currents for Cu3Si3+ and Cu3Ge3+ clusters and allowed by transition selection rule. .

π+σ

σ

π 27

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Figure 6. The total (σ+π), σ and π ring current maps of C@Al5-xBex1-x with x = 0-3 (B3LYP/6311G(d)).


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HOMO


HOMO-1

HOMO-4 HOMO-3

HOMO’

HOMO-1’

HOMO-5 HOMO-4’

C@Al5+

a)

HOMO

HOMO-1

HOMO-2

HOMO-3

HOMO-5

C@Al4Be



HOMO

HOMO-1

HOMO-2

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HOMO-3

HOMO-5

HOMO-3

HOMO-5

C@Al3Be2-

HOMO

HOMO-1

HOMO-2 C@Al2Be32-

b) Figure 7. The ring current maps of σ orbitals of a) C@Al5+, and b) C@Al5-xBex1-x (B3LYP/6311G(d))


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C@Be5Li5+

C@Be5Li4

C@Be5Li3-

C@Be5Li22-

C@Be5H3-

C@Be5H22-

C@Be5Li2H3+

C@Be5Li1H4+

a)

C@Be5H5+

C@Be5H4 b)

C@Be5Li4H+

C@Be5Li3H2+ c)



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Figure 8. The total ring current maps of a) C@Be5Linn-4, b) C@Be5Hnn-4 and c) C@Be5LixHn+ with x + n = 5 (B3LYP/6-311G(d))


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C@Be5H5+

C@Be5H4

C@Be5H3-

C@Be5H22-

C@Be5Li3-

C@Be5Li22-

C@Be5Li2H3+

C@Be5Li1H4+

a)

C@Be5Li5+

C@Be5Li4 b)

C@Be5Li4H+

C@Be5Li3H2+

c)



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Figure 9. The π ring current maps of a) C@Be5Linn-4, b) C@Be5Hnn-4 and c) C@Be5LixHn+ with x + n = 5 (B3LYP/6-311G(d)).


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C@Be5H5+

C@Be5H4

C@Be5H3-

C@Be5H22-

C@Be5Li3-

C@Be5Li22-

C@Be5Li2H3+

C@Be5Li1H4+

a)

C@Be5Li5+

C@Be5Li4 b)

C@Be5Li4H+

C@Be5Li3H2+ c)



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Figure 10. The σ ring current maps of a) C@Be5Linn-4, b) C@Be5Hnn-4 and c) C@Be5LixHn+ with x + n = 5 (B3LYP/6-311G(d)).


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.

C@Be5H5+

C@Be5H4

C@Be5H3-

C@Be5H22-

C@Be5Li4H+

C@Be5Li3H2+

C@Be5Li2H3+

C@Be5LiH4+

C@Be5Li5+

C@Be5Li4

C@Be5Li3-

C@Be5Li22-

Figure 11. ELF maps of C@Be5Hnn-4, C@Be5Linn-4 and C@Be5H5-xLix+ at the bifurcation value of 0.85 (B3LYP/6-311G(d))



Total

σ

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π

Be2@Be5H5+

Be2@Be6H62+

Be2B7-

Be2@B8


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Figure 12. The total, σ and π ring current maps of Be2@Be5H5+, Be2@Be6H6+, Be2@B7- and Be2@B7 clusters.



HOMO-0,0’

HOMO-2

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HOMO-1

Be2@Be5H5+

HOMO-1,1’

HOMO-2

HOMO

Be2@B6H62+


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HOMO-0,0’

HOMO-3

HOMO-1,1’

HOMO-4

Be2@B7-

HOMO-0,0’

HOMO-3

HOMO-1,1’

HOMO-4

Be2@B8

Figure 13. The ring current maps of σ and πorbitals of Be2@Be5H5+, Be2@Be6H62+, Be2@B7- and Be2@B8 (B3LYP/6-311G(d)).



total

σ electrons

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total

σ electrons

Cu3H3

C@Cu3Li3

Cu4H4

Cu4Li4

Cu5H5

Cu5Li5


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Cu6H6

Cu6Li6

Figure 14. The total and σ ring current maps of CunHn and CunLin planar clusters (B3LYP/6311G(d)). .



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e1'

T(x,y)

e2'

Figure 15. The electronic excitation of the Cu5Li5 cluster which is allowed by symmetry (transitional transition).


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Cu3H3

C@Cu3Li3

Cu5H5

Cu5Li5

Cu4H4

Cu4Li4

Cu6H6

Cu6Li6

Figure 16. The ELF iso-surfaces plotting at the bifurcation value of 0.75 of CunHn and CunLin systems (B3LYP/6-311G(d)).



Page 46 of 52

References

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(15) Islas, R.; Poater, J.; Matito, E.; Solà, M. Molecular Structures of M2N22− (M and N = B, Al, and Ga) Clusters Using the Gradient Embedded Genetic Algorithm, Phys. Chem. Chem. Phys. 2012, 14, 1485014859. (16) Nejad, C. F.; Shahbazian, S.; Feixas, F.; Ranjbar, P. R.; Solà, M.; A Dissected Ring Current Model for Assessing Magnetic Aromaticity: A General Approach for both Organic and Inorganic Rings. J. Comput. Chem. 2011, 32, 2422-2431. (17) Foroutan-Nejad, C. Al42−; the Anion–π Interactions and Aromaticity in the Presence of Counter Ions. Phys. Chem. Chem. Phys. 2012, 14, 9738-9748. (18) Poater, J.; Feixas, F.; Bickelhaupt, F. M.; Solà, M. All-metal Aromatic Clusters M42− (M = B, Al, and Ga). Are π-electrons Distortive or Not? Phys. Chem. Chem. Phys. 2011, 13, 20673-20681. (19) Fowler, P. W.; Havenith R. W. A.; Steiner, E. Unconventional Ring Currents in an `All-Metal Aromatic', Al42− , Chem. Phys. Lett. 2001, 342, 85-90. (20) Havenith, R. W. A.; Fowler, P. The Origin of the Ring Current in the All-metal Aromatic, Al42−, Phys. Chem. Chem. Phys., 2006, 8, 3383-3386. (21) Tam, N. M.; Pham, T. H.; Nguyen, M. T. Ring Currents in Silicon Tetramer (Si4, Si42+) and Planar Tetracoordinate Carbon Doped Cluster Si4C2+: σ versus π Aromaticity. Chem. Phys. Lett., 2014, 608, 255263. (22) Rincon, L.; Almeida, R.; Alvarellos, J. E.; Aldea, D. G.; Hasmy, A.; Gonzalez, C. The σ Delocalization In Planar Boron Clusters. Dalton Trans., 2009, 3328- 3333. (23) Pham, H. T.; Lim, K. Z.; Havenith, R. W. A.; Nguyen, M. T. Aromatic Character of Planar Boron-Based Clusters Revisited by Ring Current Calculations, Phys. Chem. Chem. Phys., 2016, 18, 11919-11931 . (24) Pham, H. T.; Tam, N. M.; Pham-Ho, M. P.; Nguyen, M. T. Stability and Bonding of The Multiply Coordinated

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DELOCALIZATION

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