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Reduction of carbon and nitrogen centered trigonal prismatic tungsten clusters: Bonding patterns as viewed by ELF and AIM methods
Polyhedron 173 (2019) 114131
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Reduction of carbon and nitrogen centered trigonal prismatic tungsten clusters: Bonding patterns as viewed by ELF and AIM methods Maxim R. Ryzhikov a,b,⇑, Svetlana G. Kozlova a,b,c a
Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, Academician Lavrentiev Avenue 3, Novosibirsk 630090, Russian Federation Novosibirsk State University, Pirogova Street 2, Novosibirsk 630090, Russian Federation c Belgorod State Technological University named after V.G. Shukhov, Kostukov Avenue 46, Belgorod 308012, Russian Federation b
a r t i c l e
i n f o
Article history: Received 8 June 2019 Accepted 24 August 2019 Available online 31 August 2019 Keywords: Trigonal prismatic clusters Bonding pattern Topological methods DFT Reduction
a b s t r a c t WAW and WAX bonds in a series of trigonal prismatic [X@W6Cl18]n (n = 0, 2, 4 for X = C; n = 1, 1, 3 for X = N) clusters were studied using the methods of Electron Localization Function (ELF) and the Atoms In Molecules (AIM) along with the molecular orbital (MO) approach. The [X@W6Cl18]n clusters contain two {W3} fragments which form a trigonal prism. Each {W3} fragment is characterized by a three-center bond and three two-center bonds. The carbon or the nitrogen atom encapsulated in the center of the trigonal prism influence intertriangular WAW bonds. The bonding pattern of {W3} fragments are preserved even in four-electron reduced clusters. The inter-triangular bonding is mainly due to the interactions of two tungsten atoms with the central C or N atom and is associated with the formation of a heteroatomic three-center bond. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Transition metal clusters are a broad class of compounds with metal–metal bonds [1], which makes them interesting from the practical viewpoint as luminescent, catalytic, and electronic materials [2–5]. Of special interest are the clusters with trigonal prismatic cores, since their structures belong to quite a rare type. The cavities of prismatic fragments usually contain a hypercoordinated non-metal atom. For example, atom-centered trigonal prisms are formed in the following series of hexanuclear cluster anions with encapsulated atoms: [X@W6Cl18]n (X = C, N, n = 0, 1, 2, 3) [6–8], [X@Nb6Br17]3 (X = S) [9], polymeric chalcohalides of niobium {X@Nb6I9}1 (X = S) [10]; a family of twelvenuclear rhenium clusters based on the [X@Re12S17(CN)6]n (X = C; n = 6, 8) complexes possessing a unique structure [11–19]. It was shown that the structural changes in [X@Re12S17(CN)6]n clusters in different oxidation states are mainly due to the changes occurring in the prismatic fragment {X@Re6}. The side edges (Reintra– Reintra) of the prism in [X@Re12S17(CN)6]6 are 0.3 Å smaller than in the doubly reduced cluster [X@Re12S17(CN)6]8 [11]. The changes in the distances are accompanied by profound changes in 13C NMR chemical shifts on l6-C and in the Electron Localization Function (ELF) distribution of the prismatic fragment [13–17]. ⇑ Corresponding author at: Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, Academician Lavrentiev Avenue 3, Novosibirsk 630090, Russian Federation. E-mail address: [email protected] (M.R. Ryzhikov). https://doi.org/10.1016/j.poly.2019.114131 0277-5387/Ó 2019 Elsevier Ltd. All rights reserved.
These results allow considering [X@Re12S17(CN)6]n complexes as hypothetical electronic nanodevices [13]. In [X@W6Cl18]n (X = C, n = 0, 2, 4; X = N, n = 1, 1, 3) complexes, like in twelvenuclear rhenium clusters, bond lengths depend on the oxidation states [6,8,20–24]. The mechanism responsible for the changes in the distances in [X@W6Cl18]n clusters are interesting in terms of using these clusters as nanodevice building blocks. Based on the analysis of molecular orbitals and interatomic distances, a concept of electronic structure was proposed for [X@W6Cl18]n clusters [25]. The tungsten atoms of the [W3Cl13]3 building block are connected by eight WAW bonding states, whereas the {W3} fragments in [X@W6Cl18]n clusters interact with each other through the central atom by the WAX covalent bonding [25]. The analysis of NMR chemical shifts indicates sp2 hybridization of the carbon atom in [C@W6Cl18]n clusters [6]. The presence of antibonding WAW interactions between {W3} fragments was discovered in the highest occupied molecular orbital (HOMO) of the [N@W6Cl18]1 cluster [8]. Even though [X@W6Cl18]n clusters have been studied in quite detail by different methods (including quantum chemical methods), the bonding pattern and the changes in the electronic structure during the reduction still remain unclear. In this work, we present a detailed study of trigonal prismatic tungsten clusters [X@W6Cl18]n (X = C, n = 0, 2, 4; X = N, n = 1, 1, 3) using topological methods of quantum chemistry such as Atoms In Molecules (AIM) and Electron Localization Function (ELF) along with the Molecular Orbital (MO) analysis to study the bonding pattern of these clusters [26,27].
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2. Computational details The electronic structure of the clusters was calculated with the Density Functional Theory (DFT) method using the ADF2017 code [28,29]. Full geometry optimization and frequency calculations were performed using the standard core double zeta, valence triple zeta, single polarized basis set (TZP) and the VWN + BP86 density functional [30–33]. Scalar relativistic effects were accounted for by the Zero Order Regular Approximation (ZORA) [34]. The geometries of [X@W6Cl18]n (X = C, n = 0, 2, 4 and X = N, n = 1, 1, 3) clusters were searched within the C1 symmetry. Clusters [C@W6Cl18]4 and [N@W6Cl18]1+ are hypothetical, but they are interesting from the theoretical viewpoint. All optimized geometries exhibited no imaginary frequencies to confirm the local minima for the studied clusters. ELF and AIM analysis was performed using the dgrid4.6 program with a 0.05 a.u. (0.026 Å) mesh step [35–39]. 3. Results and discussion 3.1. Structure of [X@W6Cl18]n complexes Tungsten atoms in [X@W6Cl18]n clusters are located in the vertexes of top ({W3}T) and bottom ({W3}B) triangular fragments (the terms ‘‘top” and ‘‘bottom” are used here conditionally). Triangles {W3}T and {W3}B and the atom X form a {X@W6} prism with a non-metal atom X in the central (l6) position. The {X@W6} prism is surrounded by terminal and bridging chlorine ligands (Fig. 1). The optimized distances in these clusters agree well with experimental data (Table 1). Since the [C@W6Cl18]4 cluster is hypothetical, no experimental structural data are available for its structure; however, the optimized distances correspond well to the tendency observed in the distances as they are changed during the reduction from [C@W6Cl18]2 to [C@W6Cl18]3. Even though all clusters were calculated within the C1 symmetry, the resulting geometry of [X@W6Cl18]n (X = C, n = 0, 2 and X = N, n = +1, 1) clusters has an idealized D3h symmetry, whereas [X@W6Cl18]n (X = C, n = -4 and X = N, n = -3) clusters acquire a less symmetrical geometry within idealized C2v symmetry. 3.2. Basic clusters [C@W6Cl18] and [N@W6Cl18]1+ When considering the clusters in different oxidation states, [C@W6Cl18] and [N@W6Cl18]1+ will be referred to as basic clusters. Consequently, the oxidation states of other clusters will be counted with respect to the basic clusters. [C@W6Cl18] and [N@W6Cl18]1+
Table 1 Mean calculated and experimental distances in [X@W6Cl18]n clusters (Å). WTAWT/ WBAWB are interatomic distances between W atoms of the same fragment {W3}T or {W3}B; WTAWB are interatomic distances between W atoms of different fragments {W3}T and {W3}B; WTAX/WBAX are interatomic distances between atoms W and X. The digits after the symbol x show the number of almost identical distances. The experimental distances in the table are taken from the XRD structural data reported earlier [6–8].
[C@W6Cl18]0 [C@W6Cl18]0 [6] [C@W6Cl18]2 [C@W6Cl18]2 [7] [C@W6Cl18]3 [7] [C@W6Cl18]4 [N@W6Cl18]1+ [N@W6Cl18]1 [N@W6Cl18]1 [8] [N@W6Cl18]3 [N@W6Cl18]3 [8]
WTAWT/WBAWB
WTAWB
WTAX/WBAX
2.774 6 2.743 6 2.674 6 2.667 6 2.635 2 2.742 4 2.563 2 2.792 4 2.789 6 2.679 6 2.652 6 2.572 2 2.792 2 2.599 2 2.733 4
2.952 3 2.930 3 3.094 3 3.028 3 2.850 1 3.018 2 2.719 1 3.168 2 2.975 3 3.119 3 3.071 3 2.733 1 3.187 2 2.803 1 3.095 2
2.178 6 2.157 6 2.186 6 2.159 6 2.114 2 2.174 4 2.162 4 2.215 2 2.188 6 2.196 6 2.168 6 2.167 4 2.226 2 2.147 4 2.183 2
are isoelectronic and differ by the type of the encapsulated atom (C or N). According to the ELF analysis, there is an unusual bonding pattern in the trigonal prismatic cluster [C@W6Cl18]. Each of {W3}T and {W3}B fragments demonstrates a three-center (3c) bond and three two-center (2c) bonds with V(WT,WT,WT)/V(WB,WB,WB) and V(WT,WT)/V(WB,WB) basins, respectively (Fig. 2 a and Table 2). The bonding between {W3}T and {W3}B fragments is formed by three WTACAWB heteroatomic 3c bonds with a trisynaptic basin V(WT,C, WB) (Fig. 2a and Table 2). The central carbon atom is characterized by sp2 hybridization promoting the formation of WTACAWB bonds and by a non-bonding lone pair pz with a V(C) basin. The hybridization on the C atom agrees with previously reported NMR data [6]. Thus, the bonding pattern in the {C@W6} fragment of the [C@W6Cl18] cluster can be represented as a set of three 2c bonds WTAWT/WBAWB and one 3c bond WTAWTAWT/WBAWBAWB in both {W3}T and {W3}B fragments, three 3c bonds WTACAWB between {W3}T and {W3}B, and a lone pair p on the C atom (Fig. S1). The difference between the bonding patterns in [N@W6Cl18]1+ and its isoelectronic counterpart [C@W6Cl18] is that the former has three extra bonds WTAWB with a low populated V(WT,WB) basin (Table 2). There is also some redistribution of electrons between V(WT,N,WB) and V(N) basins. The bonding pattern can be represented as a set of six 2c bonds WAW (WTAWT and WBAWB) and two 3c bonds WAWAW (WTAWTAWT and WBAWBAWB) in {W3}T and {W3}B fragments, three 2c bonds WTAWB, three 3c bonds WTANAWB between {W3}T and {W3}B and the p lonepair on the N atom (Fig. 2d, S4). According to the AIM analysis which represents chemical interactions as pairwise bonds, the bonding graphs of both basic clusters are formed by two tetrahedra with one common vertex so that {W3}T and {W3}B fragments are linked to each other by the non-metal atom without forming WTAWB bonds. The parameters of Bond Critical Points (BCPs) indicate that WTAWT/WBAWB bonds in the fragments {W3}T and {W3}B and WTAC/CAWB bonds are intermediate type interactions (1 < |V|/G < 2; H < 0) (Fig. 3, Table S1). 3.3. Doubly reduced clusters [C@W6Cl18]2 and [N@W6Cl18]1
Fig. 1. Typical structure of [X@W6Cl18]n clusters.
The doubly reduced cluster [C@W6Cl18]2 is characterized by a bonding pattern similar to that of the basic [C@W6Cl18]. The difference is due to the presence of two electrons on the Highest
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Fig. 2. ELF isosurface corresponding to the isovalue 0.5 (the parts of the isosurface corresponding to V(WT,WT)/V(WB,WB) basins are colored green, the parts corresponding to V(WT,WT,WT)/V(WB,WB,WB) basins are colored red, the parts corresponding V(WT,WB) basins are colored cyan and the parts corresponding to C/N valence electrons are colored grey), WAXAW slice planes of ELF, and molecular orbitals of clusters [C@W6Cl18]n (n = 0 (a), 2 (b) 4 (c)) and [N@W6Cl18]n (n = +1 (d), 1 (e), 3 (f)). Only the regions related to the {X@W6} fragment are shown for clarity.
Table 2 Populations of ELF basins in [X@W6Cl18]n clusters. V(WT,WT)/V(WB,WB) are disynaptic basins between W atoms within {W3}T or {W3}B fragments; V(WT,WB) are disynaptic basins between the nearest W atoms of different fragments {W3}T and {W3}B; V(WT,WT,WT)/V(WB,WB,WB) are trisynaptic basins between atoms W within {W3}T or {W3}B fragments; V (WT,X,WB) are trisynaptic basins between W atoms of different {W3}T and {W3}B fragments and X atom; V(WT,X)/V(WB,X) are disynaptic basins between atoms W and X; V(X) are the monosynaptic basins of atoms X (X = C, N). The number of equivalent basins is shown after the x symbol. Notable increase or decrease of the basin populations during reduction are marked by " or ; arrows, respectively. [C@W6Cl18]0
[C@W6Cl18]2
[C@W6Cl18]4
[N@W6Cl18]1+
[N@W6Cl18]1
[N@W6Cl18]3
V(WT,WT)/V(WB,WB)
0.492 6
"0.657 6
0.479 6
"0.667 6
V(WT,WB) V(WT,WT,WT)/V(WB,WB,WB) V(WT,X,WB) V(WT,X)/V(WB,X) V(X)
n/a 0.730 2 1.386 3 n/a 1.443 2
n/a "0.765 2 n/a 0.848 6 ;0.781 2
;0.591 4 "0.694 2 0.575 1 ;0.730 2 1.458 1 1.276 4 n/a
0.202 3 0.778 2 2.202 3 n/a 0.090 2
n/a 0.773 2 n/a 1.163 6 n/a
;0.603 4 "0.701 2 "0.611 1 ;0.730 2 1.700 1 1.291 4 n/a
Occupied Molecular Orbital (HOMO) of [C@W6Cl18]2 (Lowest Unoccupied Molecular Orbital (LUMO) in the basic [C@W6Cl18] cluster). The HOMO is a bonding orbital with respect to the atoms within {W3} fragments, an antibonding orbital with respect to the interaction between the fragments {W3}T and {W3}B, and a bonding orbital with respect to the interactions WTAC/CAWB (Fig. 2b). In this case, WTAWT/WBAWB and WTAWTAWT/WBAWBAWB bonds become stronger and the population of disynaptic and trisynaptic basins increases as compared to the basic cluster. 3c WTACAWB bonds are divided into the pairs of 2c WTAC and CAWB bonds. The contribution of Cl atoms into the HOMO is small and is mainly due to the terminal Cl ligands. According to the ELF analysis, the
bonding pattern in the [C@W6Cl18]2 cluster can be represented as a set of three 2c bonds WTAWT/WBAWB and one 3c bond WTAWTAWT/WBAWBAWB in each fragment {W3}T and {W3}B, six 2c bonds WTAC/CAWB, and a lone pair p of the carbon atom (Fig. S2). The [N@W6Cl18]1 cluster is similar to [C@W6Cl18]2. The occupation of the LUMO by two electrons in [N@W6Cl18]1+ (or the HOMO in [N@W6Cl18]1) makes WTAWB bonds disappear, while 3c bonds WTANAWB transform into 2c WTAN and NAWB bonds (Fig. 2e). In this case, the interactions are characterized by three 2c bonds WTAWT/WBAWB, one 3c bond WTAWTAWT/ WBAWBAWB in each fragment {W3}T and {W3}B, and six 2c bonds WTAN/NAWB (Fig. S5).
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the cluster is subjected to reduction, the changes in this fragment are small, so that the same bonding pattern of three 2c bonds and one 3c bond is shared by all oxidation states. A similar bonding pattern was previously reported in triangular clusters [Mo3S4Cl3 (PH3)6]+ and in the {Mo3} faces of [Mo6X8]n clusters (X = S, Se, and Te; n = 0 and 4) [40,41]. Thus, the bonding pattern with 2c and 3c bonds seems to be typical of {M3} fragments of molybdenum and tungsten. The whole prismatic construction is held together primarily due to the central non-metal atom, which agrees with the results reported previously [25]. In nitrogen containing clusters, more electrons are localized on the shared heteroatomic WAN or WANAW bonds with V(WT,N)/V(WB,N) or V (WT,N,WB) basins, respectively, whereas carbon containing clusters are characterized by higher populations of V(C) lone pairs, but the distances in these isoelectronic clusters are similar. Note that the AIM topological analysis, which represents chemical bonding in terms of pairwise interactions, does not show any intertriangular bonds WTAWB in most of the studied structures. Weak pairwise interactions occur only in quadruply reduced clusters [C@W6Cl18]4 and [N@W6Cl18]3, as is indicated by both topological methods. The change of the population of ELF basins correlates with the bonding/antibonding character of the MO that is occupied during the reduction. More specifically, if a MO is bonding or antibonding relative to some interatomic interactions, the population of corresponding ELF basins increases or decreases, respectively. Thus, ELF can be used to analyze bond strengthening or weakening as a result of reduction or oxidation. The WTAWB distances are increased by 0.15 Å as the basic clusters undergo two-electron reduction, but the clusters maintain the idealized D3h symmetry. Four-electron reduction of basic clusters leads to the distortion of the trigonal prism, and the idealized symmetry is C2v. Due to dramatic changes in the electronic structure and geometry, trigonal prismatic clusters of tungsten may be considered as single-molecule switches similar to twelvenuclear rhenium clusters [13]. Acknowledgments Fig. 3. AIM molecular graphs for {X@W6} fragments of [X@W6Cl18]n clusters.
According to the AIM analysis, the bonding pattern in doubly reduced clusters is similar to that in the basic clusters. The only difference is BCP parameters which indicate the strengthening or the weakening of the bonds due to the influence of two additional electrons (Fig. 3, Table S1). 3.4. Quadruply reduced clusters [C@W6Cl18]
4
3
and [N@W6Cl18]
The [C@W6Cl18]4 cluster has an idealized C2v symmetry. As a result, ELF basins V(WT,WT,WT)/V(WB,WB,WB) are shifted from the geometrical center in both fragments {W3}T and {W3}B. Moreover, since the HOMO is a strongly bonding orbital with respect to one of WTAWB interactions, one intertriangular WTAWB bond is formed in quadruply reduced clusters (Fig. 2c). In this case, the bonding pattern in [C@W6Cl18]4 can be represented as a set of three 2c bonds WTAWT (or WBAWB), one 3c bond WTAWTAWT (or WBAWBAWB) in both {W3}T and {W3}B, one bond WTAWB, and five 3c bonds WTACAWB between {W3}T and {W3}B (Fig. S3). As far as the number of basins and their populations, the bonding in the [N@W6Cl18]3 cluster is similar to that in the [C@W6Cl18]4 cluster (Fig. 2f and S6). 4. Conclusion The data of the topological analysis indicate that the W3 fragment is quite a stable part of trigonal-prismatic clusters. When
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Reduction of carbon and nitrogen centered trigonal prismatic tungsten clusters: Bonding patterns as viewed by ELF and AIM methods Maxim R. Ryzhikov a,b,⇑, Svetlana G. Kozlova a,b,c a
Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, Academician Lavrentiev Avenue 3, Novosibirsk 630090, Russian Federation Novosibirsk State University, Pirogova Street 2, Novosibirsk 630090, Russian Federation c Belgorod State Technological University named after V.G. Shukhov, Kostukov Avenue 46, Belgorod 308012, Russian Federation b
a r t i c l e
i n f o
Article history: Received 8 June 2019 Accepted 24 August 2019 Available online 31 August 2019 Keywords: Trigonal prismatic clusters Bonding pattern Topological methods DFT Reduction
a b s t r a c t WAW and WAX bonds in a series of trigonal prismatic [X@W6Cl18]n (n = 0, 2, 4 for X = C; n = 1, 1, 3 for X = N) clusters were studied using the methods of Electron Localization Function (ELF) and the Atoms In Molecules (AIM) along with the molecular orbital (MO) approach. The [X@W6Cl18]n clusters contain two {W3} fragments which form a trigonal prism. Each {W3} fragment is characterized by a three-center bond and three two-center bonds. The carbon or the nitrogen atom encapsulated in the center of the trigonal prism influence intertriangular WAW bonds. The bonding pattern of {W3} fragments are preserved even in four-electron reduced clusters. The inter-triangular bonding is mainly due to the interactions of two tungsten atoms with the central C or N atom and is associated with the formation of a heteroatomic three-center bond. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Transition metal clusters are a broad class of compounds with metal–metal bonds [1], which makes them interesting from the practical viewpoint as luminescent, catalytic, and electronic materials [2–5]. Of special interest are the clusters with trigonal prismatic cores, since their structures belong to quite a rare type. The cavities of prismatic fragments usually contain a hypercoordinated non-metal atom. For example, atom-centered trigonal prisms are formed in the following series of hexanuclear cluster anions with encapsulated atoms: [X@W6Cl18]n (X = C, N, n = 0, 1, 2, 3) [6–8], [X@Nb6Br17]3 (X = S) [9], polymeric chalcohalides of niobium {X@Nb6I9}1 (X = S) [10]; a family of twelvenuclear rhenium clusters based on the [X@Re12S17(CN)6]n (X = C; n = 6, 8) complexes possessing a unique structure [11–19]. It was shown that the structural changes in [X@Re12S17(CN)6]n clusters in different oxidation states are mainly due to the changes occurring in the prismatic fragment {X@Re6}. The side edges (Reintra– Reintra) of the prism in [X@Re12S17(CN)6]6 are 0.3 Å smaller than in the doubly reduced cluster [X@Re12S17(CN)6]8 [11]. The changes in the distances are accompanied by profound changes in 13C NMR chemical shifts on l6-C and in the Electron Localization Function (ELF) distribution of the prismatic fragment [13–17]. ⇑ Corresponding author at: Nikolaev Institute of Inorganic Chemistry, Siberian Branch of the Russian Academy of Sciences, Academician Lavrentiev Avenue 3, Novosibirsk 630090, Russian Federation. E-mail address: [email protected] (M.R. Ryzhikov). https://doi.org/10.1016/j.poly.2019.114131 0277-5387/Ó 2019 Elsevier Ltd. All rights reserved.
These results allow considering [X@Re12S17(CN)6]n complexes as hypothetical electronic nanodevices [13]. In [X@W6Cl18]n (X = C, n = 0, 2, 4; X = N, n = 1, 1, 3) complexes, like in twelvenuclear rhenium clusters, bond lengths depend on the oxidation states [6,8,20–24]. The mechanism responsible for the changes in the distances in [X@W6Cl18]n clusters are interesting in terms of using these clusters as nanodevice building blocks. Based on the analysis of molecular orbitals and interatomic distances, a concept of electronic structure was proposed for [X@W6Cl18]n clusters [25]. The tungsten atoms of the [W3Cl13]3 building block are connected by eight WAW bonding states, whereas the {W3} fragments in [X@W6Cl18]n clusters interact with each other through the central atom by the WAX covalent bonding [25]. The analysis of NMR chemical shifts indicates sp2 hybridization of the carbon atom in [C@W6Cl18]n clusters [6]. The presence of antibonding WAW interactions between {W3} fragments was discovered in the highest occupied molecular orbital (HOMO) of the [N@W6Cl18]1 cluster [8]. Even though [X@W6Cl18]n clusters have been studied in quite detail by different methods (including quantum chemical methods), the bonding pattern and the changes in the electronic structure during the reduction still remain unclear. In this work, we present a detailed study of trigonal prismatic tungsten clusters [X@W6Cl18]n (X = C, n = 0, 2, 4; X = N, n = 1, 1, 3) using topological methods of quantum chemistry such as Atoms In Molecules (AIM) and Electron Localization Function (ELF) along with the Molecular Orbital (MO) analysis to study the bonding pattern of these clusters [26,27].
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2. Computational details The electronic structure of the clusters was calculated with the Density Functional Theory (DFT) method using the ADF2017 code [28,29]. Full geometry optimization and frequency calculations were performed using the standard core double zeta, valence triple zeta, single polarized basis set (TZP) and the VWN + BP86 density functional [30–33]. Scalar relativistic effects were accounted for by the Zero Order Regular Approximation (ZORA) [34]. The geometries of [X@W6Cl18]n (X = C, n = 0, 2, 4 and X = N, n = 1, 1, 3) clusters were searched within the C1 symmetry. Clusters [C@W6Cl18]4 and [N@W6Cl18]1+ are hypothetical, but they are interesting from the theoretical viewpoint. All optimized geometries exhibited no imaginary frequencies to confirm the local minima for the studied clusters. ELF and AIM analysis was performed using the dgrid4.6 program with a 0.05 a.u. (0.026 Å) mesh step [35–39]. 3. Results and discussion 3.1. Structure of [X@W6Cl18]n complexes Tungsten atoms in [X@W6Cl18]n clusters are located in the vertexes of top ({W3}T) and bottom ({W3}B) triangular fragments (the terms ‘‘top” and ‘‘bottom” are used here conditionally). Triangles {W3}T and {W3}B and the atom X form a {X@W6} prism with a non-metal atom X in the central (l6) position. The {X@W6} prism is surrounded by terminal and bridging chlorine ligands (Fig. 1). The optimized distances in these clusters agree well with experimental data (Table 1). Since the [C@W6Cl18]4 cluster is hypothetical, no experimental structural data are available for its structure; however, the optimized distances correspond well to the tendency observed in the distances as they are changed during the reduction from [C@W6Cl18]2 to [C@W6Cl18]3. Even though all clusters were calculated within the C1 symmetry, the resulting geometry of [X@W6Cl18]n (X = C, n = 0, 2 and X = N, n = +1, 1) clusters has an idealized D3h symmetry, whereas [X@W6Cl18]n (X = C, n = -4 and X = N, n = -3) clusters acquire a less symmetrical geometry within idealized C2v symmetry. 3.2. Basic clusters [C@W6Cl18] and [N@W6Cl18]1+ When considering the clusters in different oxidation states, [C@W6Cl18] and [N@W6Cl18]1+ will be referred to as basic clusters. Consequently, the oxidation states of other clusters will be counted with respect to the basic clusters. [C@W6Cl18] and [N@W6Cl18]1+
Table 1 Mean calculated and experimental distances in [X@W6Cl18]n clusters (Å). WTAWT/ WBAWB are interatomic distances between W atoms of the same fragment {W3}T or {W3}B; WTAWB are interatomic distances between W atoms of different fragments {W3}T and {W3}B; WTAX/WBAX are interatomic distances between atoms W and X. The digits after the symbol x show the number of almost identical distances. The experimental distances in the table are taken from the XRD structural data reported earlier [6–8].
[C@W6Cl18]0 [C@W6Cl18]0 [6] [C@W6Cl18]2 [C@W6Cl18]2 [7] [C@W6Cl18]3 [7] [C@W6Cl18]4 [N@W6Cl18]1+ [N@W6Cl18]1 [N@W6Cl18]1 [8] [N@W6Cl18]3 [N@W6Cl18]3 [8]
WTAWT/WBAWB
WTAWB
WTAX/WBAX
2.774 6 2.743 6 2.674 6 2.667 6 2.635 2 2.742 4 2.563 2 2.792 4 2.789 6 2.679 6 2.652 6 2.572 2 2.792 2 2.599 2 2.733 4
2.952 3 2.930 3 3.094 3 3.028 3 2.850 1 3.018 2 2.719 1 3.168 2 2.975 3 3.119 3 3.071 3 2.733 1 3.187 2 2.803 1 3.095 2
2.178 6 2.157 6 2.186 6 2.159 6 2.114 2 2.174 4 2.162 4 2.215 2 2.188 6 2.196 6 2.168 6 2.167 4 2.226 2 2.147 4 2.183 2
are isoelectronic and differ by the type of the encapsulated atom (C or N). According to the ELF analysis, there is an unusual bonding pattern in the trigonal prismatic cluster [C@W6Cl18]. Each of {W3}T and {W3}B fragments demonstrates a three-center (3c) bond and three two-center (2c) bonds with V(WT,WT,WT)/V(WB,WB,WB) and V(WT,WT)/V(WB,WB) basins, respectively (Fig. 2 a and Table 2). The bonding between {W3}T and {W3}B fragments is formed by three WTACAWB heteroatomic 3c bonds with a trisynaptic basin V(WT,C, WB) (Fig. 2a and Table 2). The central carbon atom is characterized by sp2 hybridization promoting the formation of WTACAWB bonds and by a non-bonding lone pair pz with a V(C) basin. The hybridization on the C atom agrees with previously reported NMR data [6]. Thus, the bonding pattern in the {C@W6} fragment of the [C@W6Cl18] cluster can be represented as a set of three 2c bonds WTAWT/WBAWB and one 3c bond WTAWTAWT/WBAWBAWB in both {W3}T and {W3}B fragments, three 3c bonds WTACAWB between {W3}T and {W3}B, and a lone pair p on the C atom (Fig. S1). The difference between the bonding patterns in [N@W6Cl18]1+ and its isoelectronic counterpart [C@W6Cl18] is that the former has three extra bonds WTAWB with a low populated V(WT,WB) basin (Table 2). There is also some redistribution of electrons between V(WT,N,WB) and V(N) basins. The bonding pattern can be represented as a set of six 2c bonds WAW (WTAWT and WBAWB) and two 3c bonds WAWAW (WTAWTAWT and WBAWBAWB) in {W3}T and {W3}B fragments, three 2c bonds WTAWB, three 3c bonds WTANAWB between {W3}T and {W3}B and the p lonepair on the N atom (Fig. 2d, S4). According to the AIM analysis which represents chemical interactions as pairwise bonds, the bonding graphs of both basic clusters are formed by two tetrahedra with one common vertex so that {W3}T and {W3}B fragments are linked to each other by the non-metal atom without forming WTAWB bonds. The parameters of Bond Critical Points (BCPs) indicate that WTAWT/WBAWB bonds in the fragments {W3}T and {W3}B and WTAC/CAWB bonds are intermediate type interactions (1 < |V|/G < 2; H < 0) (Fig. 3, Table S1). 3.3. Doubly reduced clusters [C@W6Cl18]2 and [N@W6Cl18]1
Fig. 1. Typical structure of [X@W6Cl18]n clusters.
The doubly reduced cluster [C@W6Cl18]2 is characterized by a bonding pattern similar to that of the basic [C@W6Cl18]. The difference is due to the presence of two electrons on the Highest
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Fig. 2. ELF isosurface corresponding to the isovalue 0.5 (the parts of the isosurface corresponding to V(WT,WT)/V(WB,WB) basins are colored green, the parts corresponding to V(WT,WT,WT)/V(WB,WB,WB) basins are colored red, the parts corresponding V(WT,WB) basins are colored cyan and the parts corresponding to C/N valence electrons are colored grey), WAXAW slice planes of ELF, and molecular orbitals of clusters [C@W6Cl18]n (n = 0 (a), 2 (b) 4 (c)) and [N@W6Cl18]n (n = +1 (d), 1 (e), 3 (f)). Only the regions related to the {X@W6} fragment are shown for clarity.
Table 2 Populations of ELF basins in [X@W6Cl18]n clusters. V(WT,WT)/V(WB,WB) are disynaptic basins between W atoms within {W3}T or {W3}B fragments; V(WT,WB) are disynaptic basins between the nearest W atoms of different fragments {W3}T and {W3}B; V(WT,WT,WT)/V(WB,WB,WB) are trisynaptic basins between atoms W within {W3}T or {W3}B fragments; V (WT,X,WB) are trisynaptic basins between W atoms of different {W3}T and {W3}B fragments and X atom; V(WT,X)/V(WB,X) are disynaptic basins between atoms W and X; V(X) are the monosynaptic basins of atoms X (X = C, N). The number of equivalent basins is shown after the x symbol. Notable increase or decrease of the basin populations during reduction are marked by " or ; arrows, respectively. [C@W6Cl18]0
[C@W6Cl18]2
[C@W6Cl18]4
[N@W6Cl18]1+
[N@W6Cl18]1
[N@W6Cl18]3
V(WT,WT)/V(WB,WB)
0.492 6
"0.657 6
0.479 6
"0.667 6
V(WT,WB) V(WT,WT,WT)/V(WB,WB,WB) V(WT,X,WB) V(WT,X)/V(WB,X) V(X)
n/a 0.730 2 1.386 3 n/a 1.443 2
n/a "0.765 2 n/a 0.848 6 ;0.781 2
;0.591 4 "0.694 2 0.575 1 ;0.730 2 1.458 1 1.276 4 n/a
0.202 3 0.778 2 2.202 3 n/a 0.090 2
n/a 0.773 2 n/a 1.163 6 n/a
;0.603 4 "0.701 2 "0.611 1 ;0.730 2 1.700 1 1.291 4 n/a
Occupied Molecular Orbital (HOMO) of [C@W6Cl18]2 (Lowest Unoccupied Molecular Orbital (LUMO) in the basic [C@W6Cl18] cluster). The HOMO is a bonding orbital with respect to the atoms within {W3} fragments, an antibonding orbital with respect to the interaction between the fragments {W3}T and {W3}B, and a bonding orbital with respect to the interactions WTAC/CAWB (Fig. 2b). In this case, WTAWT/WBAWB and WTAWTAWT/WBAWBAWB bonds become stronger and the population of disynaptic and trisynaptic basins increases as compared to the basic cluster. 3c WTACAWB bonds are divided into the pairs of 2c WTAC and CAWB bonds. The contribution of Cl atoms into the HOMO is small and is mainly due to the terminal Cl ligands. According to the ELF analysis, the
bonding pattern in the [C@W6Cl18]2 cluster can be represented as a set of three 2c bonds WTAWT/WBAWB and one 3c bond WTAWTAWT/WBAWBAWB in each fragment {W3}T and {W3}B, six 2c bonds WTAC/CAWB, and a lone pair p of the carbon atom (Fig. S2). The [N@W6Cl18]1 cluster is similar to [C@W6Cl18]2. The occupation of the LUMO by two electrons in [N@W6Cl18]1+ (or the HOMO in [N@W6Cl18]1) makes WTAWB bonds disappear, while 3c bonds WTANAWB transform into 2c WTAN and NAWB bonds (Fig. 2e). In this case, the interactions are characterized by three 2c bonds WTAWT/WBAWB, one 3c bond WTAWTAWT/ WBAWBAWB in each fragment {W3}T and {W3}B, and six 2c bonds WTAN/NAWB (Fig. S5).
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the cluster is subjected to reduction, the changes in this fragment are small, so that the same bonding pattern of three 2c bonds and one 3c bond is shared by all oxidation states. A similar bonding pattern was previously reported in triangular clusters [Mo3S4Cl3 (PH3)6]+ and in the {Mo3} faces of [Mo6X8]n clusters (X = S, Se, and Te; n = 0 and 4) [40,41]. Thus, the bonding pattern with 2c and 3c bonds seems to be typical of {M3} fragments of molybdenum and tungsten. The whole prismatic construction is held together primarily due to the central non-metal atom, which agrees with the results reported previously [25]. In nitrogen containing clusters, more electrons are localized on the shared heteroatomic WAN or WANAW bonds with V(WT,N)/V(WB,N) or V (WT,N,WB) basins, respectively, whereas carbon containing clusters are characterized by higher populations of V(C) lone pairs, but the distances in these isoelectronic clusters are similar. Note that the AIM topological analysis, which represents chemical bonding in terms of pairwise interactions, does not show any intertriangular bonds WTAWB in most of the studied structures. Weak pairwise interactions occur only in quadruply reduced clusters [C@W6Cl18]4 and [N@W6Cl18]3, as is indicated by both topological methods. The change of the population of ELF basins correlates with the bonding/antibonding character of the MO that is occupied during the reduction. More specifically, if a MO is bonding or antibonding relative to some interatomic interactions, the population of corresponding ELF basins increases or decreases, respectively. Thus, ELF can be used to analyze bond strengthening or weakening as a result of reduction or oxidation. The WTAWB distances are increased by 0.15 Å as the basic clusters undergo two-electron reduction, but the clusters maintain the idealized D3h symmetry. Four-electron reduction of basic clusters leads to the distortion of the trigonal prism, and the idealized symmetry is C2v. Due to dramatic changes in the electronic structure and geometry, trigonal prismatic clusters of tungsten may be considered as single-molecule switches similar to twelvenuclear rhenium clusters [13]. Acknowledgments Fig. 3. AIM molecular graphs for {X@W6} fragments of [X@W6Cl18]n clusters.
According to the AIM analysis, the bonding pattern in doubly reduced clusters is similar to that in the basic clusters. The only difference is BCP parameters which indicate the strengthening or the weakening of the bonds due to the influence of two additional electrons (Fig. 3, Table S1). 3.4. Quadruply reduced clusters [C@W6Cl18]
4
3
and [N@W6Cl18]
The [C@W6Cl18]4 cluster has an idealized C2v symmetry. As a result, ELF basins V(WT,WT,WT)/V(WB,WB,WB) are shifted from the geometrical center in both fragments {W3}T and {W3}B. Moreover, since the HOMO is a strongly bonding orbital with respect to one of WTAWB interactions, one intertriangular WTAWB bond is formed in quadruply reduced clusters (Fig. 2c). In this case, the bonding pattern in [C@W6Cl18]4 can be represented as a set of three 2c bonds WTAWT (or WBAWB), one 3c bond WTAWTAWT (or WBAWBAWB) in both {W3}T and {W3}B, one bond WTAWB, and five 3c bonds WTACAWB between {W3}T and {W3}B (Fig. S3). As far as the number of basins and their populations, the bonding in the [N@W6Cl18]3 cluster is similar to that in the [C@W6Cl18]4 cluster (Fig. 2f and S6). 4. Conclusion The data of the topological analysis indicate that the W3 fragment is quite a stable part of trigonal-prismatic clusters. When
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