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C4− carbide ligand in the trigonal prismatic environment of rheniums in [Re12CS17(CN)6]n− complexes
Polyhedron 27 (2008) 3167–3171
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C4 carbide ligand in the trigonal prismatic environment of rheniums in [Re12CS17(CN)6]n complexes Svetlana G. Kozlova a,b,c,*, Svyatoslav P. Gabuda a, Vladimir A. Slepkov a, Yuri V. Mironov a, Vladimir E. Fedorov a,c a
Nikolaev Institute of Inorganic Chemistry, Siberian Branch of Russian Academy of Sciences, 3, Akad. Lavrentiev Avenue, 630090 Novosibirsk, Russia Boreskov Institute of Catalysis, Siberian Branch of Russian Academy of Sciences, 5, Akad. Lavrentiev Avenue, 630090 Novosibirsk, Russia c Novosibirsk State University, 2, Pirogova Avenue, 630090 Novosibirsk, Russia b
a r t i c l e
i n f o
Article history: Received 12 March 2008 Accepted 10 July 2008 Available online 26 August 2008 Keywords: Carbon atom Twelve nuclear rhenium clusters ELF
a b s t r a c t The electronic state of carbon in trigonal prismatic environment in [Re12CS17(CN)6]n complexes with variable redox state n = 6 M 8 was studied by molecular orbital method and electron localization function. The state is characterized by sp2-hybridisation and oxidation state 4. A weak long-distance interaction between l6-C and l2-S in the group [(l6-C)(l2-S)3] was discovered for n = 6, the interaction disappears for n = 8. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The coordination behaviour of carbon in the carbon-centered metal complexes remains an important problem of modern theoretical chemistry. The challenge is to find the greatest number of ligands capable to form covalent bonds with carbon in organic and organoelement compounds through multicentered interactions [1,2]. A recently discovered carbon-centered tungsten complex [W6CCl18]n with changing redox states n = 0, 1, 2, 3 [3,4] is an example of such compounds which are also promising objects for molecular electronics and nanotechnologies. A lately synthesized sulfide-cyanide rhenium complex [Re12CS17(CN)6]n with variable redox states n = 6 and 8 includes carbon l6-C in trigonal prismatic environment of 6 rheniums [5]. A strong change in Re– Re and C–Re distances in the [CRe6] prisms together with the oxidation state is an unusual behaviour of the complexes (Fig. 1). In this study we investigate the complexes with different oxidation states by the methods of molecular orbitals (MO) and of electron localization function (ELF) to study the interactions of the central carbon atom l6-C with its surrounding. 2. DFT calculations The electronic structure of the diamagnetic complexes [Re12CS17(CN)6]n (n = 6, 8 with multiplicity 2S+1 = 1) of D3h * Corresponding author. Address: Nikolaev Institute of Inorganic Chemistry, Siberian Branch of Russian Academy of Sciences, 3, Akad. Lavrentiev Avenue, 630090 Novosibirsk, Russia. E-mail address: [email protected] (S.G. Kozlova). 0277-5387/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.poly.2008.07.007
point symmetry was studied by spin-restricted method using the ADF2006 program package [6]. The model Hamiltonians included the local density functional LDA (VWN [7]) and the gradient exchange functional GGA (Becke [8] and Perdew [9]). The all-electron basis set of the TZP type, as included in the ADF2006 program, has been used for all atoms. The full geometry optimization was performed for D3h point group with the quasinewtonian method [10]; relativistic effects were taken into account with the zero order relativistic approximation method n ZORA [11]. The atomic net charges for [Re12CS17(CN)6] (n = 6, 8) systems were obtained using the Hirshfeld analysis [12]. Interactions between l6-C and its surrounding were studied with the topological method of electron localization function ELF for ‘‘close-shell” systems [13,14,19]. The ELF function is an orbital independent description of the electron localization given by
ELF ¼ ð1 þ ðDr =D0r Þ2 Þ1 where Dr and D0r represent the curvature of the Fermi hole for the studied system and the homogeneous electron gas with the same density, respectively. ELF values are obviously confined within the interval between 0 and 1. The blue colour in our pictures corresponds to high electron localization, lone pairs, and strong covalent bonds (bosonic behaviour of the electronic density or shared interactions). The regions from green to red colour correspond to electron-gas-like pair probability responsible for ionic, correlation and Van der Waals interactions (unshared interactions). The chemical meaning of the ELF function has been the subject of several interpretations [13–19].
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Fig. 1. The structure of [Re12CS17(CN)6]n (n = 6,8) clusters [5]. The distance (D) between rheniums is 2.90 Å at n = 6, and 3.17 Å for n = 8.
Table 1 Experimental and calculated interatomic distances, their differences (d, D) in cluster units [Re12CS17(CN)6]n. d = Rcal Rexp signifies intramolecular distances, D = R(n=8) R(n=6) signifies intermolecular calculated and experimental distances [Re12CS17(CN)6]8
Complexbond length, Å
Rein–Rein, in prism l6-C–l2-S Rein–Rein Rein–l6-C Rein–l2-S Reout–Reout Rein–Reout Reout-l3-Stop Rein–l3-Sin Reout–l3-Sout
[Re12CS17(CN)6]6 a
D
Cal
Exp
d
Cal
Expa
d
Cal
Exp
3.273 3.330 2.628 2.231 2.442 2.669 2.686 2.461 2.466 2.457
3.168 3.332 2.591 2.179 2.425 2.595 2.622 2.420 2.425 2.428
0.105 -0.002 0.037 0.052 0.017 0.074 0.064 0.041 0.041 0.029
2.974 3.454 2.739 2.171 2.391 2.664 2.687 2.460 2.464 2.448
2.901 3.438 2.692 2.126 2.378 2.600 2.630 2.424 2.422 2.405
0.073 0.016 0.047 0.045 0.013 0.064 0.057 0.036 0.042 0.043
0.299 0.124 0.111 0.060 0.051 0.069 0.001 0.001 0.002 0.009
0.267 0.106 0.101 0.053 0.047 0.005 0.008 0.004 0.003 0.023
a Since the complexes [Re12CS17(CN)6]n in the synthesized compound Cs6[Re12CS17(CN)6] 20H2O and K8[Re12CS17(CN)6] are not of the ideal point symmetry D3h, we cite only average characteristic interatomic distances [5].
3. Results Table 1 shows interatomic distances of the complexes. As is seen, both computed and experimental distances change strongly as functions of the redox state. Table 2 lists predicted charges on the atoms of complexes [Re12CS17(CN)6]n. Note that the effective charge on the l6-C atoms remains almost invariable when the redox state changes. [Re12CS17(CN)6]6 has a larger absolute bond energy (309.1 eV) than [Re12CS17(CN)6]8 (285.0 eV) and is thus more stable. This result is in a good accordance with experimental data which show that K8[Re12CS17(CN)6] is not stable in aqueous solutions and rapidly transforms into [Re12CS17(CN)6]6 anion [5].
The electronic structure of the studied systems stands out by strong redox dependence of the energy level of MO 77a00 2 (fig. 2). The splitting DE between 30a0 2 and 77a00 2 is 1.07 eV for n = 6 and 0.06 eV for n = 8. The molecular orbital 30a0 2 consists of 5d
Table 2 Calculated atomic charges in cluster units [Re12CS17(CN)6]n Complex
[Re12CS17(CN)6]8
[Re12CS17(CN)6]6
Rein Reout l6-C l2-S l3-Stop l3-Sin l3-Sout C N
0.069 0.026 0.201 0.427 0.255 0.187 0.264 0.138 0.508
0.076 0.042 0.201 0.306 0.171 0.147 0.164 0.127 0.438
Fig. 2. Energy levels of molecular orbitals for [Re12CS17(CN)6]n (n = 6, 8).
S.G. Kozlova et al. / Polyhedron 27 (2008) 3167–3171
valence orbitals of Re (20%) and 3p orbitals of l2-S (50%) 3p orbitals of l3-Sin (30%) with no contribution from the carbon l6-C. d-Orbitals of Rein atoms and 3p orbitals of l3-Sin show a weak bonding interaction between two symmetric groups {Re6S7}. MO 77a00 2 consists of valence 5d- and vacant 6d-orbitals of Re (45%), valence 3p- and vacant 4p-orbitals of l2-S (25%), valence
Fig. 3. Schematic 77a00 2 and 30a0 2 molecular orbitals for [Re12CS17(CN)6]n (n = 6, 8).
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3p- and vacant 4p-orbitals of l3-Sout (17%) and with considerable contribution (10%) of 2p and 3p orbitals from l6-C, but no direct overlap of atomic shells between Rein in two symmetrical groups {Re6S7} (fig. 3). Comparison of measured and computed interatomic distances suggests that the singularity in interatomic interactions on the redox state changes is ‘‘localized” in the vicinity of l6-C (Table 1). However, the structure of the molecular orbitals alone cannot clarify the behaviour of interatomic interactions with l6-C. Therefore we studied the electronic density in [Re12CS17(CN)6]n (n = 6, 8) by the method of electron localisation function. Figs. 4 and 5 show the results of the topological analysis of the electron density in [Re12CS17(CN)6]n (n = 6, 8) in the vicinity of l6-C. At ELF 0.78, the l6-C atom has three identical attractors (lone pairs) in the [(l6-C)(l2-S)3] plane for both complexes [Re12CS17(CN)6]n (n = 6, 8). The monosynaptic attractors are directed from the centre l6-C of the triangle towards its apexes made by l2-S atoms to form the angles 120o. In the vicinity of l6-C along the triad axis in the plane perpendicular to the [(l6-C)(l2-S)3] plane there is yet another region of electron localization (ELF 0.78) that can be also interpreted as a lone pair. The observed pattern of electron localization suggests that the electron configuration of l6-C is made by sp2-hybrids. Since ELF is close to 0.8 at each of the four attractors corresponding to the three sp2 hybrid orbitals and the remaining nonhybrid p orbital, the redox state is close to 4 in both complexes (this is in general agreement with the invariant charges of l6-C, Table 2). When the redox state of [Re12CS17(CN)6]n changes, the only result is the change in interaction within the systems [(l6-C)(l2-S)3] and [(l6-C){Re6}2]. A bonding attractor, or V(Re,Re) disynaptic basin, is seen between each pair of Re atoms at ELF 0.5. Though ELF is not so high here, it is known that low ELF values associated with covalent bonding between d elements are explained by the fact that electron localization is greatly reduced due the Pauli repulsion exerted by the electron density concentrated in core
Fig. 4. ELF distribution maps for [Re6CS17(CN)6]6 complex: (a) cutting plane Re(l2-S)Re(l6-C), the Re atoms belong to different symmetry groups {Re6S7}; (b) cutting plane through three atoms l2-S and the atom l6-C; (c) cutting plane through the atoms Re(l6-C)Re (the rheniums belong to the same group {Re6S7}). Arrows 1 point to the attractors of sp2-hybridization, arrows 2 point to the bonding between l6-C and l2-S, arrows 3 point to the disynaptic V(Re,Re) basins of covalent bond Re–Re.
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Fig. 5. ELF distribution maps for [Re6CS17(CN)6]8 complex: (a) the plane crossing the atoms Re(l2-S)Re(l6-C), the Re atoms belong to different symmetric groups {Re6S7}; (b) the plane crossing three atoms l2-S and the atom l6-C; (c) the plane crossing the atoms Re(l6-C)Re (the rheniums belong to the same group {Re6S7}). Arrows 1 point to the attractors of sp2-hybridization, arrow 3 point to the disynaptic V(Re,Re) basins of covalent bond Re–Re.
Fig. 6. Isosurfaces ELF = 0.3 for [Re12CS17(CN)6]6 (a) and [Re12CS17(CN)6]8 (b). The arrow depicts the bonding between l6-C and l2-S in [Re12CS17(CN)6]6, the bonding disappears in [Re12CS17(CN)6]8.
Fig. 7. ELF distribution maps for W6CCl18 molecule: (a) cutting plane through W(l6-C)W atoms; (b) cutting plane through Cl atoms and the atom l6-C; (c) cutting plane crossing the atoms W(l6-C)W (the W belong to the same fragment [W3]). Arrows 1 point to the attractors of sp2-hybridization, arrows 2 point to the region between W, arrow 3 points to the disynaptic V(W,W) basins of the covalent bond W–W.
S.G. Kozlova et al. / Polyhedron 27 (2008) 3167–3171
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regions [16,18]. The bonding between l6-C and Rein in the fragments [(l6-C){Re6}2] results from electron exchange that binds the valent area l6-C with the V(Re,Re) associated with different levels of electron density localization (ELF 0.36 for [Re12CS17(CN)6]6 and ELF 0.32 for [Re12CS17(CN)6]8). We characterize this interaction as a multicentered shared electron interaction. At [Re12CS17(CN)6]6 an unexpected bonding (ELF 0.3) is seen between l6-C and l2-S in the group [(l6-C)(l2-S)3] which is not observed in [Re12CS17(CN)6]8 (Figs. 4–6). To compare our results for [Re12CS17(CN)6]n with the analysis of the carbon l6-C in trigonal prismatic environment of tungsten atoms in [W6CCl18]n [3], we studied the electron localization function in diamagnetic W6CCl18 (n = 0 and 2S + 1 = 1) in the vicinity of l6-C with ELF function (all quantum-chemical calculations were made in the same manner as for [Re12CS17(CN)6]n). In isolated molecular clusters W6CCl18, the atom C was hypothesized to be characterized by sp2pz-state with the sp2 lobes directed to the prism edges, increasing the Cl–Cl distances of the bridges [3]. As is seen in Fig. 7 of the ELF distribution map, the attractors of the lone pairs of l6-C atom are indeed directed to the prism edges.
action between them can be characterized only as an exchangecorrelation interaction between closed-shell atoms [20]. We think that the weak electron bonding between l6-C and l2-S is responsible for shortened Rein–Rein distances in the system [Re12CS17(CN)6]6. This interaction seems to be substantially weakened when the antibonding MO 77a00 2 in [Re12CS17(CN)6]8 is filled by two electrons and is absent at ELF = 0.3 (Fig. 6) which results in a strong increase of interatomic distances Rein–Rein and a significant change in MO 77a00 2 energy (Fig. 2). The obtained results appear to have important implications for the carbon coordination behaviour in the complexes of transition metals.
4. Conclusion
[1] P. Chini, J. Organomet. Chem. 2000 (1) (1980) 37. [2] V.I. Minkin, R.M. Minyaev, Mendeleev Commun. 2 (2004) 43. [3] Y.-Q. Zheng, H.G. von Schnering, J.-H. Chang, Y. Grin, G. Engelhardt, G. Heckmann, Z. Anorg. Allg. Chem. 629 (2003) 1256. [4] E.J. Welch, N.R.M. Crawford, R.G. Bergman, J.R. Long, J. Am. Chem. Soc. 125 (2003) 11464. [5] Yu.V. Mironov, N.G. Naumov, S.G. Kozlova, S.G. Sung-Jin Kim, V.E. Fedorov, Angew. Chem., Int. Ed. 44 (2005) 6867. [6] Amsterdam Density Functional (ADF) Program, Release 2006.02; Vrije Universteit: Amsterdam, The Netherlands, 2006. [7] S.H. Vosko, L. Wilk, M. Nusair. Can. J. Phys. 58 (1980) 1200. [8] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [9] J.P. Perdew, Phys. Rev. B 33 (N12) (1986) 8822. [10] L. Versluis, T. Ziegler, J. Chem. Phys. 88 (1988) 322. [11] E. Van Lenthe, A.E. Ehlers, E.J. Baerends, J. Chem. Phys. 110 (1999) 8943. [12] F.L. Hirshfeld, Theor. Chim. Acta 44 (1977) 129. [13] A.D. Becke, K.E. Edgecombe, J. Chem. Phys. 92 (1990) 5387. [14] A. Savin, O. Jepsen, J. Flad, O.K. Andersen, H. Preuss, H.G. von Schnering, Angew. Chem. 31 (1992) 187. [15] B. Silvi, A. Savin, Nature 371 (1994) 683. [16] S. Berski, G.L. Gutsev, M.D. Mochena, J. Andrés, J. Phys. Chem. A 108 (2004) 6025. [17] S. Noury, B. Silvi, R.J. Gillespie, Inorg. Chem. 41 (8) (2002) 2164–2172. [18] B. Silvi, C. Gatti, J. Phys. Chem. A 104 (2000) 947. [19] M. Kohout, A. Savin, Int. J. Quant. Chem. 60 (1996) 875. [20] P. Pyykko, Chem. Rev. 97 (1997) 597.
The obtained results indicate that the electronic state of l6-C in the trigonal-prismatic environment can be interpreted as the one formed by filled sp2 hybrid orbitals and having the oxidation state 4 independently on the redox state of the complexes. It is thus shown that C4 carbide anion can be viewed as a strong electron donor ligand in the trigonal prismatic environment of transition metals, which is in agreement with [3]. The obtained evidence of very weak long-distant (3.454 Å) interactions between l6-C and l2-S (ELF 0.3) in the [(l6-C)(l2-S)3] of [Re12CS17(CN)6]6 and the absence of such interactions in [Re12CS17(CN)6]8 is an unexpected result. The discovered interaction between l6-C and l2-S cannot be of covalent nature since it occurs at the distance 3.454 Å in complex [Re12CS17(CN)6]6- and disappears at shorter distances 3.330 Å in [Re12CS17(CN)6]8- (a disynaptic attractor could be expected to appear at a covalent bonding when the interatomic distance decreases). According to the classification [13] the observed bonding belongs to the unshared electron interaction. Since the charges on l6-C and l2-S are negative (Table 2), the inter-
Acknowledgements The study was supported by Russian Foundation for Basic Research (Grants 07-03-00912 and 08-03-00826).
References
Contents lists available at ScienceDirect
Polyhedron journal homepage: www.elsevier.com/locate/poly
C4 carbide ligand in the trigonal prismatic environment of rheniums in [Re12CS17(CN)6]n complexes Svetlana G. Kozlova a,b,c,*, Svyatoslav P. Gabuda a, Vladimir A. Slepkov a, Yuri V. Mironov a, Vladimir E. Fedorov a,c a
Nikolaev Institute of Inorganic Chemistry, Siberian Branch of Russian Academy of Sciences, 3, Akad. Lavrentiev Avenue, 630090 Novosibirsk, Russia Boreskov Institute of Catalysis, Siberian Branch of Russian Academy of Sciences, 5, Akad. Lavrentiev Avenue, 630090 Novosibirsk, Russia c Novosibirsk State University, 2, Pirogova Avenue, 630090 Novosibirsk, Russia b
a r t i c l e
i n f o
Article history: Received 12 March 2008 Accepted 10 July 2008 Available online 26 August 2008 Keywords: Carbon atom Twelve nuclear rhenium clusters ELF
a b s t r a c t The electronic state of carbon in trigonal prismatic environment in [Re12CS17(CN)6]n complexes with variable redox state n = 6 M 8 was studied by molecular orbital method and electron localization function. The state is characterized by sp2-hybridisation and oxidation state 4. A weak long-distance interaction between l6-C and l2-S in the group [(l6-C)(l2-S)3] was discovered for n = 6, the interaction disappears for n = 8. Ó 2008 Elsevier Ltd. All rights reserved.
1. Introduction The coordination behaviour of carbon in the carbon-centered metal complexes remains an important problem of modern theoretical chemistry. The challenge is to find the greatest number of ligands capable to form covalent bonds with carbon in organic and organoelement compounds through multicentered interactions [1,2]. A recently discovered carbon-centered tungsten complex [W6CCl18]n with changing redox states n = 0, 1, 2, 3 [3,4] is an example of such compounds which are also promising objects for molecular electronics and nanotechnologies. A lately synthesized sulfide-cyanide rhenium complex [Re12CS17(CN)6]n with variable redox states n = 6 and 8 includes carbon l6-C in trigonal prismatic environment of 6 rheniums [5]. A strong change in Re– Re and C–Re distances in the [CRe6] prisms together with the oxidation state is an unusual behaviour of the complexes (Fig. 1). In this study we investigate the complexes with different oxidation states by the methods of molecular orbitals (MO) and of electron localization function (ELF) to study the interactions of the central carbon atom l6-C with its surrounding. 2. DFT calculations The electronic structure of the diamagnetic complexes [Re12CS17(CN)6]n (n = 6, 8 with multiplicity 2S+1 = 1) of D3h * Corresponding author. Address: Nikolaev Institute of Inorganic Chemistry, Siberian Branch of Russian Academy of Sciences, 3, Akad. Lavrentiev Avenue, 630090 Novosibirsk, Russia. E-mail address: [email protected] (S.G. Kozlova). 0277-5387/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.poly.2008.07.007
point symmetry was studied by spin-restricted method using the ADF2006 program package [6]. The model Hamiltonians included the local density functional LDA (VWN [7]) and the gradient exchange functional GGA (Becke [8] and Perdew [9]). The all-electron basis set of the TZP type, as included in the ADF2006 program, has been used for all atoms. The full geometry optimization was performed for D3h point group with the quasinewtonian method [10]; relativistic effects were taken into account with the zero order relativistic approximation method n ZORA [11]. The atomic net charges for [Re12CS17(CN)6] (n = 6, 8) systems were obtained using the Hirshfeld analysis [12]. Interactions between l6-C and its surrounding were studied with the topological method of electron localization function ELF for ‘‘close-shell” systems [13,14,19]. The ELF function is an orbital independent description of the electron localization given by
ELF ¼ ð1 þ ðDr =D0r Þ2 Þ1 where Dr and D0r represent the curvature of the Fermi hole for the studied system and the homogeneous electron gas with the same density, respectively. ELF values are obviously confined within the interval between 0 and 1. The blue colour in our pictures corresponds to high electron localization, lone pairs, and strong covalent bonds (bosonic behaviour of the electronic density or shared interactions). The regions from green to red colour correspond to electron-gas-like pair probability responsible for ionic, correlation and Van der Waals interactions (unshared interactions). The chemical meaning of the ELF function has been the subject of several interpretations [13–19].
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S.G. Kozlova et al. / Polyhedron 27 (2008) 3167–3171
Fig. 1. The structure of [Re12CS17(CN)6]n (n = 6,8) clusters [5]. The distance (D) between rheniums is 2.90 Å at n = 6, and 3.17 Å for n = 8.
Table 1 Experimental and calculated interatomic distances, their differences (d, D) in cluster units [Re12CS17(CN)6]n. d = Rcal Rexp signifies intramolecular distances, D = R(n=8) R(n=6) signifies intermolecular calculated and experimental distances [Re12CS17(CN)6]8
Complexbond length, Å
Rein–Rein, in prism l6-C–l2-S Rein–Rein Rein–l6-C Rein–l2-S Reout–Reout Rein–Reout Reout-l3-Stop Rein–l3-Sin Reout–l3-Sout
[Re12CS17(CN)6]6 a
D
Cal
Exp
d
Cal
Expa
d
Cal
Exp
3.273 3.330 2.628 2.231 2.442 2.669 2.686 2.461 2.466 2.457
3.168 3.332 2.591 2.179 2.425 2.595 2.622 2.420 2.425 2.428
0.105 -0.002 0.037 0.052 0.017 0.074 0.064 0.041 0.041 0.029
2.974 3.454 2.739 2.171 2.391 2.664 2.687 2.460 2.464 2.448
2.901 3.438 2.692 2.126 2.378 2.600 2.630 2.424 2.422 2.405
0.073 0.016 0.047 0.045 0.013 0.064 0.057 0.036 0.042 0.043
0.299 0.124 0.111 0.060 0.051 0.069 0.001 0.001 0.002 0.009
0.267 0.106 0.101 0.053 0.047 0.005 0.008 0.004 0.003 0.023
a Since the complexes [Re12CS17(CN)6]n in the synthesized compound Cs6[Re12CS17(CN)6] 20H2O and K8[Re12CS17(CN)6] are not of the ideal point symmetry D3h, we cite only average characteristic interatomic distances [5].
3. Results Table 1 shows interatomic distances of the complexes. As is seen, both computed and experimental distances change strongly as functions of the redox state. Table 2 lists predicted charges on the atoms of complexes [Re12CS17(CN)6]n. Note that the effective charge on the l6-C atoms remains almost invariable when the redox state changes. [Re12CS17(CN)6]6 has a larger absolute bond energy (309.1 eV) than [Re12CS17(CN)6]8 (285.0 eV) and is thus more stable. This result is in a good accordance with experimental data which show that K8[Re12CS17(CN)6] is not stable in aqueous solutions and rapidly transforms into [Re12CS17(CN)6]6 anion [5].
The electronic structure of the studied systems stands out by strong redox dependence of the energy level of MO 77a00 2 (fig. 2). The splitting DE between 30a0 2 and 77a00 2 is 1.07 eV for n = 6 and 0.06 eV for n = 8. The molecular orbital 30a0 2 consists of 5d
Table 2 Calculated atomic charges in cluster units [Re12CS17(CN)6]n Complex
[Re12CS17(CN)6]8
[Re12CS17(CN)6]6
Rein Reout l6-C l2-S l3-Stop l3-Sin l3-Sout C N
0.069 0.026 0.201 0.427 0.255 0.187 0.264 0.138 0.508
0.076 0.042 0.201 0.306 0.171 0.147 0.164 0.127 0.438
Fig. 2. Energy levels of molecular orbitals for [Re12CS17(CN)6]n (n = 6, 8).
S.G. Kozlova et al. / Polyhedron 27 (2008) 3167–3171
valence orbitals of Re (20%) and 3p orbitals of l2-S (50%) 3p orbitals of l3-Sin (30%) with no contribution from the carbon l6-C. d-Orbitals of Rein atoms and 3p orbitals of l3-Sin show a weak bonding interaction between two symmetric groups {Re6S7}. MO 77a00 2 consists of valence 5d- and vacant 6d-orbitals of Re (45%), valence 3p- and vacant 4p-orbitals of l2-S (25%), valence
Fig. 3. Schematic 77a00 2 and 30a0 2 molecular orbitals for [Re12CS17(CN)6]n (n = 6, 8).
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3p- and vacant 4p-orbitals of l3-Sout (17%) and with considerable contribution (10%) of 2p and 3p orbitals from l6-C, but no direct overlap of atomic shells between Rein in two symmetrical groups {Re6S7} (fig. 3). Comparison of measured and computed interatomic distances suggests that the singularity in interatomic interactions on the redox state changes is ‘‘localized” in the vicinity of l6-C (Table 1). However, the structure of the molecular orbitals alone cannot clarify the behaviour of interatomic interactions with l6-C. Therefore we studied the electronic density in [Re12CS17(CN)6]n (n = 6, 8) by the method of electron localisation function. Figs. 4 and 5 show the results of the topological analysis of the electron density in [Re12CS17(CN)6]n (n = 6, 8) in the vicinity of l6-C. At ELF 0.78, the l6-C atom has three identical attractors (lone pairs) in the [(l6-C)(l2-S)3] plane for both complexes [Re12CS17(CN)6]n (n = 6, 8). The monosynaptic attractors are directed from the centre l6-C of the triangle towards its apexes made by l2-S atoms to form the angles 120o. In the vicinity of l6-C along the triad axis in the plane perpendicular to the [(l6-C)(l2-S)3] plane there is yet another region of electron localization (ELF 0.78) that can be also interpreted as a lone pair. The observed pattern of electron localization suggests that the electron configuration of l6-C is made by sp2-hybrids. Since ELF is close to 0.8 at each of the four attractors corresponding to the three sp2 hybrid orbitals and the remaining nonhybrid p orbital, the redox state is close to 4 in both complexes (this is in general agreement with the invariant charges of l6-C, Table 2). When the redox state of [Re12CS17(CN)6]n changes, the only result is the change in interaction within the systems [(l6-C)(l2-S)3] and [(l6-C){Re6}2]. A bonding attractor, or V(Re,Re) disynaptic basin, is seen between each pair of Re atoms at ELF 0.5. Though ELF is not so high here, it is known that low ELF values associated with covalent bonding between d elements are explained by the fact that electron localization is greatly reduced due the Pauli repulsion exerted by the electron density concentrated in core
Fig. 4. ELF distribution maps for [Re6CS17(CN)6]6 complex: (a) cutting plane Re(l2-S)Re(l6-C), the Re atoms belong to different symmetry groups {Re6S7}; (b) cutting plane through three atoms l2-S and the atom l6-C; (c) cutting plane through the atoms Re(l6-C)Re (the rheniums belong to the same group {Re6S7}). Arrows 1 point to the attractors of sp2-hybridization, arrows 2 point to the bonding between l6-C and l2-S, arrows 3 point to the disynaptic V(Re,Re) basins of covalent bond Re–Re.
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Fig. 5. ELF distribution maps for [Re6CS17(CN)6]8 complex: (a) the plane crossing the atoms Re(l2-S)Re(l6-C), the Re atoms belong to different symmetric groups {Re6S7}; (b) the plane crossing three atoms l2-S and the atom l6-C; (c) the plane crossing the atoms Re(l6-C)Re (the rheniums belong to the same group {Re6S7}). Arrows 1 point to the attractors of sp2-hybridization, arrow 3 point to the disynaptic V(Re,Re) basins of covalent bond Re–Re.
Fig. 6. Isosurfaces ELF = 0.3 for [Re12CS17(CN)6]6 (a) and [Re12CS17(CN)6]8 (b). The arrow depicts the bonding between l6-C and l2-S in [Re12CS17(CN)6]6, the bonding disappears in [Re12CS17(CN)6]8.
Fig. 7. ELF distribution maps for W6CCl18 molecule: (a) cutting plane through W(l6-C)W atoms; (b) cutting plane through Cl atoms and the atom l6-C; (c) cutting plane crossing the atoms W(l6-C)W (the W belong to the same fragment [W3]). Arrows 1 point to the attractors of sp2-hybridization, arrows 2 point to the region between W, arrow 3 points to the disynaptic V(W,W) basins of the covalent bond W–W.
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regions [16,18]. The bonding between l6-C and Rein in the fragments [(l6-C){Re6}2] results from electron exchange that binds the valent area l6-C with the V(Re,Re) associated with different levels of electron density localization (ELF 0.36 for [Re12CS17(CN)6]6 and ELF 0.32 for [Re12CS17(CN)6]8). We characterize this interaction as a multicentered shared electron interaction. At [Re12CS17(CN)6]6 an unexpected bonding (ELF 0.3) is seen between l6-C and l2-S in the group [(l6-C)(l2-S)3] which is not observed in [Re12CS17(CN)6]8 (Figs. 4–6). To compare our results for [Re12CS17(CN)6]n with the analysis of the carbon l6-C in trigonal prismatic environment of tungsten atoms in [W6CCl18]n [3], we studied the electron localization function in diamagnetic W6CCl18 (n = 0 and 2S + 1 = 1) in the vicinity of l6-C with ELF function (all quantum-chemical calculations were made in the same manner as for [Re12CS17(CN)6]n). In isolated molecular clusters W6CCl18, the atom C was hypothesized to be characterized by sp2pz-state with the sp2 lobes directed to the prism edges, increasing the Cl–Cl distances of the bridges [3]. As is seen in Fig. 7 of the ELF distribution map, the attractors of the lone pairs of l6-C atom are indeed directed to the prism edges.
action between them can be characterized only as an exchangecorrelation interaction between closed-shell atoms [20]. We think that the weak electron bonding between l6-C and l2-S is responsible for shortened Rein–Rein distances in the system [Re12CS17(CN)6]6. This interaction seems to be substantially weakened when the antibonding MO 77a00 2 in [Re12CS17(CN)6]8 is filled by two electrons and is absent at ELF = 0.3 (Fig. 6) which results in a strong increase of interatomic distances Rein–Rein and a significant change in MO 77a00 2 energy (Fig. 2). The obtained results appear to have important implications for the carbon coordination behaviour in the complexes of transition metals.
4. Conclusion
[1] P. Chini, J. Organomet. Chem. 2000 (1) (1980) 37. [2] V.I. Minkin, R.M. Minyaev, Mendeleev Commun. 2 (2004) 43. [3] Y.-Q. Zheng, H.G. von Schnering, J.-H. Chang, Y. Grin, G. Engelhardt, G. Heckmann, Z. Anorg. Allg. Chem. 629 (2003) 1256. [4] E.J. Welch, N.R.M. Crawford, R.G. Bergman, J.R. Long, J. Am. Chem. Soc. 125 (2003) 11464. [5] Yu.V. Mironov, N.G. Naumov, S.G. Kozlova, S.G. Sung-Jin Kim, V.E. Fedorov, Angew. Chem., Int. Ed. 44 (2005) 6867. [6] Amsterdam Density Functional (ADF) Program, Release 2006.02; Vrije Universteit: Amsterdam, The Netherlands, 2006. [7] S.H. Vosko, L. Wilk, M. Nusair. Can. J. Phys. 58 (1980) 1200. [8] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [9] J.P. Perdew, Phys. Rev. B 33 (N12) (1986) 8822. [10] L. Versluis, T. Ziegler, J. Chem. Phys. 88 (1988) 322. [11] E. Van Lenthe, A.E. Ehlers, E.J. Baerends, J. Chem. Phys. 110 (1999) 8943. [12] F.L. Hirshfeld, Theor. Chim. Acta 44 (1977) 129. [13] A.D. Becke, K.E. Edgecombe, J. Chem. Phys. 92 (1990) 5387. [14] A. Savin, O. Jepsen, J. Flad, O.K. Andersen, H. Preuss, H.G. von Schnering, Angew. Chem. 31 (1992) 187. [15] B. Silvi, A. Savin, Nature 371 (1994) 683. [16] S. Berski, G.L. Gutsev, M.D. Mochena, J. Andrés, J. Phys. Chem. A 108 (2004) 6025. [17] S. Noury, B. Silvi, R.J. Gillespie, Inorg. Chem. 41 (8) (2002) 2164–2172. [18] B. Silvi, C. Gatti, J. Phys. Chem. A 104 (2000) 947. [19] M. Kohout, A. Savin, Int. J. Quant. Chem. 60 (1996) 875. [20] P. Pyykko, Chem. Rev. 97 (1997) 597.
The obtained results indicate that the electronic state of l6-C in the trigonal-prismatic environment can be interpreted as the one formed by filled sp2 hybrid orbitals and having the oxidation state 4 independently on the redox state of the complexes. It is thus shown that C4 carbide anion can be viewed as a strong electron donor ligand in the trigonal prismatic environment of transition metals, which is in agreement with [3]. The obtained evidence of very weak long-distant (3.454 Å) interactions between l6-C and l2-S (ELF 0.3) in the [(l6-C)(l2-S)3] of [Re12CS17(CN)6]6 and the absence of such interactions in [Re12CS17(CN)6]8 is an unexpected result. The discovered interaction between l6-C and l2-S cannot be of covalent nature since it occurs at the distance 3.454 Å in complex [Re12CS17(CN)6]6- and disappears at shorter distances 3.330 Å in [Re12CS17(CN)6]8- (a disynaptic attractor could be expected to appear at a covalent bonding when the interatomic distance decreases). According to the classification [13] the observed bonding belongs to the unshared electron interaction. Since the charges on l6-C and l2-S are negative (Table 2), the inter-
Acknowledgements The study was supported by Russian Foundation for Basic Research (Grants 07-03-00912 and 08-03-00826).
References