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Unraveling the Origin of the Relative Stabilities of Group 14 M2N22+ (M, N = C, Si, Ge, Sn, and Pb) Isomer Clusters Erik Díaz-Cervantes, Jordi Poater, Juvencio Robles, Marcel Swart, and Miquel Solà J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 04 Sep 2013 Downloaded from http://pubs.acs.org on September 5, 2013

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The Journal of Physical Chemistry

Unraveling the Origin of the Relative Stabilities of Group 14 M2N22+ (M, N = C, Si, Ge, Sn, and Pb) Isomer Clusters Erik Díaz-Cervantes,1 Jordi Poater,2,* Juvencio Robles,1 Marcel Swart,2,3 and Miquel Solà2,* 1

Departamento de Farmacia, Universidad de Guanajuato, Noria Alta s/n, Gto. 36050

Guanajuato, México. 2

Institut de Química Computacional i Catàlisi (IQCC) and Departament de Química,

Universitat de Girona, 17071 Girona, Catalonia, Spain. 3

Institució Catalana de Recerca i Estudis Avançats (ICREA), Pg. Lluís Companys 23,

08010 Barcelona, Catalonia, Spain. E-mails: [email protected], [email protected]

Abstract We analyze the molecular structure, relative stability, and aromaticity of the lowest-lying isomers of group 14 M2N22+ (M and N = C, Si, and Ge) clusters. We use the Gradient Embedded Genetic Algorithm to make an exhaustive search for all possible isomers. Group 14 M2N22+ clusters are isoelectronic with the previously studied group 13 M2N22- (M and N = B, Al, and Ga) clusters that includes Al42-, the archetypal all-metal aromatic molecule. In the two groups of clusters, the cyclic isomers present both - and -aromaticity. However, at variance with group 13 M2N22- clusters, the linear isomer of group 14 M2N22+ is the most stable for two of the clusters (C2Si22+ and C2Ge22+) and it is isoenergetic with the cyclic D4h isomer in the case of C42+. Energy decomposition analyses of the lowest-lying isomers and the calculated magnetic- and electronic-based aromaticity criteria of the cyclic isomers help to understand the nature of the bonding and the origin of the stability of the global minima. Finally, for completeness, we have also analyzed the structure and stability of the heavier Sn and Pb group 14 M2N22+ analogues.

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Keywords: Density Functional Theory, energy decomposition analysis, group 14 M2N22+ isomers, metalloaromaticity, isomers, MCI, NICS.

Introduction In 2001, Boldyrev, Wang and coworkers1 synthesized the first all-metal aromatic compound, Al42-, face-capped by a M+ cation (M = Li, Na, Cu). The analysis of the highest-lying molecular orbitals (MOs) of Al42- revealed a  filled MO formed by inphase combination of 3p out-of-plane atomic orbitals (AOs), and two filled MOS, the r (radial) and t (tangential) generated from combinations of 3p in-plane AOs.1-3 It is usually considered that the aromaticity in Al42- comes from these , r, and t orbitals containing two electrons each, and consequently, satisfying the Hückel rule4-7 for each separated set. Since then, many all-metal and semimetal aromatic clusters1,8-12 have been synthesized. The aromaticity in these species is unusual because they have not only the conventional -aromaticity of classical organic compounds, but also -,13,14 -,15-17 and aromaticity,18 thus giving rise to the so-called multifold aromaticity.9,10,19 These clusters are among the most exciting molecules produced in the beginning of the present century. In a recent study by some of us,20 the global minima of group 13 M2N22- (M and N = B, Al, and Ga) clusters were searched through an automated scanning of the potential energy surfaces, referred as gradient embedded genetic algorithm (GEGA).21 The nature of the bonding and the origin of the stability of the lowestlying in energy isomers obtained were discussed through energy decomposition and aromaticity analyses. Especial emphasis was devoted to the 1,2- (C2v) and 1,3(D2h) isomers when M and N are different. These cyclic group 13 M2N22- isomers have the same triple (r, t, and ) aromaticity of Al42-. However, we found that the most stable isomer in each case is not necessarily the one with largest aromaticity. In general, the relative stability of these isomers depends on the nature of the M and N atoms. Thus, the C2v isomer is more stable for Al2B22- and Ga2B22-, whereas Ga2Al22- favors the D2h form. In all group 13 M2N22- isomers the cyclic isomers were more stable than the linear ones.


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Now, in the present work, we aim to go one step further by taking into analysis the equivalent systems in group 14 M2N22+ (M and N = C, Si, and Ge). Heavier Sn and Pb analogues have been also considered. Both group 13 M2N22- and group 14 M2N22+ clusters have the same number of valence electrons and, therefore, the group 14 M2N22+ cyclic isomers are expected to have the same types of aromaticity as those present in group 13 cyclic M2N22- systems. Unlike the previous studied species, among the considered atoms we have a nonmetal atom (C) and two semimetals (Si and Ge). Since the C atoms make strong C–C bonds it is likely that the linear isomers can be particularly stabilized in isomers containing C atoms. Thus, the objectives of our study are twofold. First, to find the lowest-lying group 14 M2N22+ cyclic isomers and to investigate whether the linear isomers can be more stable than the cyclic ones in this particular group of clusters, and second, to discuss the reasons for the different stability of the isomers found. To our knowledge among the species studied here only Si42+,22,23 Ge42+ and the 1,2- (C2v) and 1,3- (D4h) isomers of Si2Ge22+ have been treated in previous works.23 It is worth noting that the aromaticity of group 14 organometallic compounds was discussed in a 2007 review by Lee and Sekiguchi.24 Even though in the present manuscript we focus on charged group 14 M 2N22+ species, several previous analyses exist related to the corresponding neutral clusters. It must be mentioned that small clusters have attracted increasing interest because they have been considered fundamental building blocks leading to metamaterials with physical and chemical properties not available in nature25-27 and of especial interest in nanodevices. The most studied clusters are those with C, with particular emphasis on fullerenes and nanotubes. Pure Si clusters28 were dismissed as equivalent candidates to form comparable structures to those of C because Si preferentially selects sp3 bonding instead of the characteristic sp2 in C clusters. However, in the binary bulk compound, silicon carbide, both elements show diamond-like tetrahedral coordination, which gives rise to its technologically important high thermal and mechanical stability; and thus being one of the most promising materials.29-31 Few works have treated germanium clusters,25,32-35 which have shown to present a similar behavior to those of Si. Nowadays SiGe nanosystems are attracting an increasing interest in the fields of energy, materials, and information and communication technologies.36 Finally, there are several


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studies that analyze the isoelectronic M2N2 and M3N- clusters with M being a group 13 and N a group 14 elements.23,37-41

Computational methods The potential energy surfaces (PESs) of the different clusters were explored at the B3LYP/3-21G level,42-45 employing the Gradient Embedded Genetic Algorithm (GEGA), developed by Alexandrova and coworkers.21 This program makes an intense search of different isomers for the specific number and type of atoms. Next, all minima were reoptimized and characterized with the Amsterdam Density Functional (ADF) program.46,47 The MOs were expanded in a large uncontracted set of Slater type orbitals (STOs) of triple-ζ quality for all atoms and two sets of polarization functions (TZ2P basis set) were included: 3d and 4f on C and Si; 4d and 4f on Ge.48 The 1s core electrons of carbon, the 1s2s2p core shells of silicon, and the 1s2s2p3s3p for germanium were treated with the frozen core approximation47 as it was shown to have a negligible effect on the obtained geometries and energetics.49 An auxiliary set of s, p, d, f, and g STOs was used to fit the molecular density and to represent the Coulomb and exchange potentials accurately for each SCF cycle. Energies and gradients were computed using the PBE functional, with the exchange and correlation corrections proposed by Perdew, Burke, and Ernzerhof.50,51 All geometry optimizations were performed with the QUILD52,53 (QUantum-regions Interconnected by Local Descriptions) program, which functions as a wrapper around the ADF program. The QUILD program constructs all input files for ADF, runs ADF, and collects all data; ADF is used only for the generation of the energy and gradients. Furthermore, the QUILD program uses improved geometry optimization techniques, such as adapted delocalized coordinates.52,53 For the heavier Sn and Pb clusters,

relativistic

effects

have

been

incorporated

through

the

ZORA

approximation.54,55 Benchmark calculations have been performed with the Gaussian 09 package56 at the CCSD(T)/6-311G* and CAS(6,8)/6-311+G* levels of theory.57-59 To gain more insight into the nature of the bonding in these clusters, an energy decomposition analysis (EDA)60-63 was performed as implemented in the ADF package46,47 at the same PBE/TZ2P level. The overall bond energy, E,


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corresponding to the formation of a molecule from two fragments is divided into two major components (see Eq. 1) E = Eprep + Eint

(1)

The preparation energy, Eprep, corresponds to the energy required to deform the separated fragments from their equilibrium structures to the geometries they acquire into the molecule. The interaction energy, Eint, corresponds to the actual energy generated when the deformed fragments are combined to generate the final molecule. This energy can be divided into three physical meaningful terms: the Pauli repulsion (EPauli), the classical electrostatic interaction, Velsat, and the orbital interaction energy, Eoi (see Eq. 2). The orbital interaction energy term can be decomposed into the contributions from each irreducible representationof the interacting system (Eq. 3). In particular, in planar systems the / separation is possible. Eint = EPauli + Velstat + Eoi



∑ 

(2) (3)

Results and Discussion We discuss first the structure, stability, and aromaticity of the clusters that involve C, Si, and Ge. These clusters are compared to the isoelectronic analogous M2N22species of group 13.20 Clusters containing Sn and Pb are commented at the end. All systems treated in this work have a closed-shell singlet ground state, with the triplet state being higher in energy. The six possible M2N22+ (M, N = C, Si, and Ge) combinations under analysis have been optimized at the PBE/TZ2P level of theory. The homoatomic species show a preference for the D4h symmetry (see Table 1 and Figure 1). For C42+, the clusters with D∞h and D4h symmetries are almost isoenergetic, and C3v is the highest in energy (42.3 kcal mol-1). For Si42+ and Ge42+, C3v is more stable than D∞h, being the former 22.8 and 6.7 kcal mol-1 higher than D4h for Si and Ge, respectively. On the other hand, for C2Si22+ and C2Ge22+, the linear form appears to be the most stable


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geometry, with an energy difference with respect to D4h bigger than 100 kcal mol-1. It must be mentioned that the lowest-lying equilibrium structure of neutral C2Si2 is controversial and the most recent analyses consider the linear Si-C-C-Si in its triplet state as the most stable.35 Finally, for Si2Ge22+, the C2v geometry is the most stable, 2.1 and 18.9 kcal mol-1 lower than the D2h and D∞h, respectively. It has to be pointed out that for C2Si22+ and C2Ge22+, the C2v form is not found. These energy differences are in good agreement with the corresponding benchmark values calculated at the CCSD(T)/6-311G* (values also enclosed in Table 1) with the same optimized PBE/TZ2P geometries. The only difference is for Si2Ge22+, for which the D2h geometry is more stable than C2v by 1.6 kcal mol-1. A previous study at the MP2/6-31G(d) also found the 1,3- (D2h) isomer more stable than the 1,2- (C2v) by 3.2 kcal mol-1.23 To discuss the possible multideterminantal character of these species, CASSCF(6,8)/6-311+G* calculations for C42+ in the D4h and D∞h symmetry have been performed. Results at the CASSCF(6,8)/6-311+G* level show that the linear isomer is more stable than the cyclic by 5.0 kcal mol-1. With respect to the weight of the first configuration, it is around 80% for the D∞h form and 65% for the D4h isomer. More important, the second most important configuration in the CAS wave function has a weight that is lower than 6% in the two cases. This means that these species can be safely treated with a monodeterminantal approach since the static correlation seems to be not particularly important for these clusters. Table 1 and Figure 1 here To understand the preference of a given cluster for the cyclic or linear arrangements, we have performed the decomposition of the corresponding interaction energies in their different components. In particular, we have considered two equivalent MN+··· fragments at their lowest-lying quadruplet state, with two unpaired  and one unpaired  electrons; one fragment with the three unpaired electrons with spin , and the second with spin , in order to build the suitable bonds. With these equivalent fragments in the quadruplet state we have built the clusters with D4h/D2h and D∞h symmetries. In the former we are generating two separated  bonds (the r and t) plus one delocalized , whereas for the latter we are forming a somehow localized triple bond (one and two


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localized bonds). The values obtained for such analysis are enclosed in Table 2 for all isomers. Table 2 here We first focus on the C42+, Si42+, and Ge42+ clusters. C42+ isomers present the largest Pauli repulsion, and more importantly, this is larger for D∞h than D4h, opposite to the other two systems. This observation could be attributed to the short bond length of the central C‒C in the linear C42+ (1.259 Å), very close to that of a triple bond in HC≡CH (1.206 Å at the same PBE/TZ2P level). As can be seen in Chart 1, the central C‒C bond length is expected to be close to that of the triple bond (resonant structure a with the two positive charges more separated has the largest contribution), but somewhat larger than the typical triple bond in acetylene due to the influence of resonant structure b. This view is further supported by the Voronoi charges of the terminal and central carbon atoms of +0.73 and +0.27, respectively. Despite the higher Pauli repulsion, the D∞h C42+ isomer presents more favorable electrostatic and orbital interactions, which compensate the larger Pauli repulsion, and thus cyclic and linear isomers are isoenergetic at the end. As said before, the generation of the triple bond in the linear isomer implies the formation of one  and two  bonds, whereas in the cyclic isomer we are forming two bonds (r and t) and one delocalized  bond. Not unexpectedly, the absolute value of the  component of the Eoi term is higher in the cyclic form with two  bonds, whereas the  component is more stabilizing in the linear one with two  bonds. The fact that the differences are not huge is attributed to the more favorable overlap in the formation of the  bond in the linear form and the contribution of aromaticity to the stabilization of the  bond in the cyclic form. On the other hand, when we move from C42+ to Si42+ and Ge42+, the bonding energy of all isomers becomes less stabilizing and in some cases it is even positive. In this latter case it means that these clusters are metastable, i.e., the system is energetically stabilized by dissociation into two MN+··· fragments in their lowestlying quadruplet state but with a Coulombic barrier for the dissociation, as found for instance in the N22+ compound.64,65 In the cyclic isomer of Si42+, the larger Pauli repulsion of D4h is compensated by more favorable orbital interactions (both and  but especially the interactions), which makes this isomer the most stable. An


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important difference with C42+ is that the linear isomer of Si42+ has a much less  stabilizing contribution as a result of less effective overlap due to the longer bond lengths and the more diffuse character of the 3p orbitals. Ge42+ presents a similar behavior to that of Si42+, although for this system both isomers are metastable.

Chart 1

With respect to the orbital interactions present in these systems, Figure 2 depicts the MOs of all systems considered. It can be seen that whereas for C42+ the tangential (T) is the HOMO, followed by the radial (R) and the , for both Si and Ge systems, the HOMO is the , followed by the radial and the tangential ones. As already discussed, the MOs found for these systems are equivalent to those for group 13 metal clusters (B42-, Al42-, Ga42-, and their combinations), previously studied by us.20 Both series of clusters are isoelectronic in the valence space, and thus similar electronic characteristics are expected. Thus, for both B42- and C42+, the  orbital is more stable than the tangential and the radial, whereas the  is the HOMO for the heaviest members of the series (Al42-, Ga42-, Si42+, Ge42+) systems. This different ordering of the MOs is justified by the overlaps of the MOs of the two fragments involved in the EDA analysis (see Table 3). Thus, the higher stability of the  orbital in C42+ is in line with the fact that the corresponding overlap is higher (0.255) than for Si42+ and Ge42+ (0.232 and 0.203, respectively). This is in part due to the smaller size of the C4 ring, but also to the more diffuse character of the 3p and 4p orbitals. Figure 2 and Table 3 here Now, for the rest of the systems in Table 2, C2Si22+ and C2Ge22+ present a similar behavior to that of C42+, although now the linear is much more stable than the D2h


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isomer. Thus again the linear isomer has a larger Pauli repulsion that is largely compensated by more favorable electrostatic and orbital interactions. Not unexpectedly, the , and the total orbital interactions in the linear isomers of C2Si22+ and C2Ge22+ are almost the same as those found in C42+ (formation of the same C≡C bond), whereas those of the cyclic isomers are much less. Moreover, the electrostatic stabilization is larger in the linear C2Si22+ and C2Ge22+ as compared to that of the analogous C42+ cluster, thus making linear C2Si22+ and C2Ge22+ species particularly stable (they have the largest bonding energy). Finally, in the case of Si2Ge22+ the two isomers are metastable with the D2h being more favorable than the linear D∞h with a GeSi–SiGe bond (that having a SiGe–GeSi is somewhat less stable). The cyclic isomer presents a higher Pauli repulsion, but the more favorable orbital interactions make this isomer more stable than the linear. The Eoi term in both linear and cyclic Si2Ge22+ isomers is particularly low, especially that of the linear isomer that is similar to the Eoi found in Si42+. Overall, from the results above we observe that the C‒C bond plays a determinant role in the preference of the linear geometry for both C2Si22+ and C2Ge22+. These two systems also present a short C‒C bond (1.245 and 1.249 Å), a bond length that must be assigned to a triple C≡C bond. Such bond causes an extra stabilization in the systems where it is present. In addition, in both C2Si22+ and C2Ge22+, such triple bond character avoids finding the C2v geometry as an equilibrium structure. Geometry optimization starting from C2v structures of C2Si22+ and C2Ge22+ leads to the linear isomers. In fact, this structure is only present in the case of the Si2Ge22+ species. This behavior is similar to that previously found for group 13 clusters, 20 where we showed that the B‒B bond had an important stabilization role and the isomers that present this bond are more stable than the alternated systems, despite being less aromatic than higher symmetric systems. This hypothesis can be further supported by the calculation of how much energy is necessary to break double C‒C, Si‒Si, and Ge‒Ge bonds in H2C=CH2, H2Si=SiH2, and H2Ge=GeH2 systems, respectively, as an homolytic breaking (fragments in triplet state). The obtained values are 188.5, 101.3 and 91.3 kcal mol-1 for C=C, Si=Si and Ge=Ge, respectively (see Supporting Information; values for the dissociation of the triple bond in HC≡CH, HSi≡SiH, and HGe≡GeH are also enclosed). It must be pointed out


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that Robles et al. already pointed out the stronger character of C‒C bonds compared to Si‒C and Si‒Si,29 in C4, Si2C2, and Si4 clusters. For comparison to previously analyzed group 13 clusters, we have also undertaken the analysis of the aromaticity of the cyclic clusters of group 14 by means of the electronic multicenter index MCI,66-69 and their corresponding  and  components together with a scan of the magnetic NICSzz and NICSzz indices70,71 along the outof-plane z-coordinate and starting from the center of the ring. Both indices have been calculated at the B3LYP/6-311+G* level at the previously optimized PBE/TZ2P geometries by means of ESI-3D72-74 and APOST-3D74,75 programs for MCI, and Gaussian 0956 for NICS. From Figure 3 it is observed how all systems present a similar NICSzz scan, with C42+ showing the most diatropic response that has probably to be attributed to the ring-size dependence of NICS values. This behavior is equivalent to that of group 13 clusters, although NICS(0)zz is somehow higher (around -10 ppm compared to -8 ppm for group 13). Moreover, the NICSzz are almost identical between group 13 and 14 clusters. On the other hand, with respect to calculated MCI values (see Table 4), Ge42+ presents higher aromaticity than Si42+ and C42+, and also among the mixed clusters, those with Ge present higher aromaticity. Again, the values obtained are really close to those of group 13. In Si2Ge22+, the most stable D2h isomer is found to be marginally more aromatic than the C2v form. As for the group 13 clusters,20 NICS results indicate that the aromaticity is much more important than the -one in the systems analyzed, whereas the MCI descriptor gives similar weights to the - and -aromaticities. Finally, it is worth noting that the energy difference between the linear and the cyclic isomers could be taken as a measure of the aromaticity of these systems. However, we consider that this energy difference does not contain only the energetic gain due to aromaticity because the number of  and  electrons change when going from cyclic to linear M2N22+ clusters. As discussed previously, it is quite difficult to find good references for the calculation of the resonance energy in the case of inorganic clusters.76 Table 4 and Figure 3 here


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For the sake of completeness, the clusters with Sn and Pb have also been analyzed (see Figure 4). When these two heavier atoms are taken into account, the D4h/D2h/C2v cyclic conformations are more stable in all cases, except for Si2Pb22+ and Ge2Pb22+, for which the linear one is more stable. Particularly interesting are the D2h isomers of C2Sn22+ and C2Pb22+. In this case, somewhat unexpectedly from the previous results, the linear conformation is not the most stable form. Instead a D2h isomer in which there is formally a C22- unit (isoelectronic with N2) interacting with two dications (Sn+2 or Pb+2) becomes the most stable structure. In fact, the C– C bond length (1.265 and 1.266 Å) in C2Sn22+ and C2Pb22+ resembles that of the C22unit (C–C bond length of 1.292 Å at PBE/TZ2P level). The Voronoi charge on the C22- unit is –0.3 e for C2Sn22+ and –0.35 e for C2Pb22+, which is far from the formally expected but still negative for a dication. Thus, for the most electropositive atoms of the series the C2M22+ (M = Si, Ge, Sn, Pb) adopts a D2h form, while for the less electropositive the linear form is preferred. The geometry of these two D2h systems resemble that of Li2O2 and Na2O2 species77 and that of Sc2C2 in [email protected]

Conclusion In this work we have analyzed the molecular structure, relative stability, and aromaticity of the lowest-lying isomers of group 14 M2N22+ (M and N = C, Si, and Ge) clusters. Heavier clusters containing Sn and Pb have been also considered. We have found that the Ge42+ and Si2Ge22+ clusters are metastable with respect to dissociation to two equivalent MN+··· fragments in their lowest-lying quadruplet state. Moreover the linear Si42+ and the cyclic C2Ge22+ are also metastable. The cyclic and linear forms of the rest of the systems studied are stable with respect to dissociation into MN+··· fragments. Generation of the linear isomer from two identical MN+··· fragments implies the formation of one  and two  more or less localized bonds, whereas in the cyclic isomer two delocalized  and one bonds are formed. Interestingly, the linear isomer is the most stable for the C2Si22+ and C2Ge22+ clusters and it is isoenergetic with the cyclic D4h isomer in the case of C42+. For the remaining clusters, the cyclic D4h/D2h isomer is the most stable. The reason for the stability of the linear forms in C42+, C2Si22+, and C2Ge22+ clusters is attributed to the strong C–C bond formed in all these species. Finally, NICS results indicate


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that the -aromaticity is much more important than the -one in the systems analyzed, whereas the MCI descriptor gives similar weights to the - and aromaticities. For C2Sn22+ and C2Pb22+, the D2h isomer in which there is a C22- unit interacting with two dications (Sn+2 or Pb+2) is the most stable structure instead of the expected linear conformation.

Acknowledgments The authors are grateful to the Research Executive Agency of the European Research Council for financial support through the PIRSES-GA-2009-247671 project of the FP7-PEOPLE-2009-IRSES program. We also thank the following organizations for financial support: the Ministerio de Ciencia e Innovación (MICINN, projects number CTQ2011-23156/BQU and CTQ2011-25086), the DIUE of the Generalitat de Catalunya (projects number 2009SGR637, 2009SGR528, and XRQTC), and the FEDER fund (European Fund for Regional Development) for the grant UNGI08-4E-003. Excellent service by the Centre de Supercomputació de Catalunya (CESCA) is gratefully acknowledged. Support for the research of M.S. was received through the ICREA Academia 2009 prize for excellence in research funded by the DIUE of the Generalitat de Catalunya. J.R. is grateful for support from CONACYT grant number CB-2011-168474. E.D. acknowledges support from a partial scholarship to fund his travel expenses from CONACYT.

Supporting Information Cartesian coordinates of all optimized structures and homolytic bond dissociation energies for a series of reference systems. This material is available free of charge via the Internet at http://pubs.acs.org.


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(75) Salvador, P.; Ramos-Cordoba, E. In APOST-3D; Institute of Computational Chemistry and Catalysis, University of Girona: Girona, Catalonia, Spain, 2011. (76) Boldyrev, A. I.; Kuznetsov, A. E. On the Resonance Energy in New All-Metal Aromatic Molecules. Inorg. Chem. 2002, 41, 532-537. (77) El-Hamdi, M.; Poater, J.; Bickelhaupt, F. M.; Solà, M. X2Y2 Isomers: Tuning Structure and Relative Stability through Electronegativity Differences (X = H, Li, Na, F, Cl, Br, I; Y = O, S, Se, Te). Inorg. Chem. 2013, 52, 2458-2465. (78) Wang, C.-R.; Kai, T.; Tomiyama, T.; Yoshida, T.; Kobayashi, Y.; Nishibori, E.; Takata, M.; Sakata, M.; Shinohara, H. A Scandium Carbide Endohedral Metallofullerene: (Sc2C2)@C84. Angew. Chem. Int. Ed. 2001, 40, 397-399.


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Table 1. Relative energies (in kcal mol-1) of the isomers calculated both at the PBE/TZ2P and CCSD(T)/6-311G*//PBE/TZ2P levels.

PBE/TZ2P

CCSD(T)/6-311G*//PBE/TZ2P

D∞h

D4h/D2h

C3v/C2v

D∞h

D4h/D2h

C3v/C2v

C42+

0.0

0.1

42.3

2.4

0.0

49.4

Si42

34.4

0.0

22.8

30.2

0.0

17.4

Ge42+

18.0

0.0

6.7

28.1

0.0

15.9

C2Si22+

0.0

103.0

D∞h

0.0

111.3

D∞h

C2Ge22+

0.0

144.4

D∞h

0.0

133.8

D∞h

Si2Ge22+

18.9

2.1

0.0

26.4

0.0

1.6


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47


Table 2. PBE/TZ2P energy decomposition analysis for the linear and cyclic molecules. Energies are in kcal mol-1.

C42+

Si42+

Ge42+

C2Si22+

C2Ge22+

Si2Ge22+

D∞h

D4h

D∞h

D4h

D∞h

D4h

D∞h

D2h

D∞h

D2h

D∞h

D2h

ΔEPauli

515.48

442.71

143.69

184.52

117.96

139.05

494.74

345.97

476.82

245.00

137.39

161.07

ΔEelstat

-34.45

53.54

31.49

33.75

30.25

-16.71 -100.78

9.81

32.04

34.42

37.30 -113.32

ΔEoiσ

-409.80 -442.60 -120.41 -183.74

-97.52 -133.93 -409.93 -296.65 -407.15 -205.60 -120.76 -156.00

ΔEoiπ

-108.17

-23.06

ΔEoi

-517.97 -532.10 -150.94 -227.48 -120.58 -166.61 -518.44 -362.93 -516.51 -250.31 -152.23 -193.76

-89.51

-30.53

-43.73

ΔEint

-36.94

-35.85

24.24

-9.21

27.62

ΔEdef

3.30

2.28

1.44

0.56

0.80

-33.64

-33.57

25.68

-8.65

28.42

ΔE

-32.69 -108.50

9.74 -137.02 0.70

6.86

10.44 -130.16

-66.28 -109.36

-33.67 -140.47

-44.71

-31.47

-37.76

4.50

17.20

1.74

6.28

5.72

1.96

0.64

-27.07 -134.19

10.22

19.16

2.38

6.60


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Table 3. Overlap integrals between MN+··· fragment  orbitals of the cyclic D4h/D2h M2N22+ clusters.

C42+ Si42+ Ge42+ C2Si22+ C2Ge22+ Si2Ge22+

0.255 0.232 0.203 0.270 0.225 0.216


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Table 4. B3LYP/6-311+G*//PBE/TZ2P MCI, MCI and MCI values (in a.u.) of the cyclic D4h/D2h M2N22+ clusters.

C42+ Si42+ Ge42+ C2Si22+ C2Ge22+ Si2Ge22+ Si2Ge22+ (C2v)

MCI 0.270 0.333 0.384 0.119 0.216 0.357 0.347

MCI 0.188 0.188 0.187 0.084 0.133 0.187 0.181


MCI 0.083 0.146 0.197 0.035 0.083 0.170 0.166

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Figure 1. PBE/TZ2P optimized geometries of lowest-lying group 14 M2N22+ clusters. Bond lengths in Å and CCSD(T)/6-311G*//PBE/TZ2P relative energies in kcal mol-1.

1.451 1.467

C42+

1.442 1.259 E = 0.0 kcal mol-1, D4h

E = 2.4 kcal mol-1, D∞h

E = 49.4 kcal mol-1, C3v

2.313

Si42+

2.384 2.339 2.181 E = 0.0 kcal mol-1, D4h



2.528

Ge4

2+

2.510

2.542 2.337

E = 0.0 kcal mol-1, D4h

C2Si2

2+


1.829

1.881 1.245 E = 0.0 kcal mol-1, D∞h

C2Ge22+

E = 111.3 kcal mol-1, D2h 2.000

2.037 1.249 E = 0.0 kcal mol-1, D∞h

Ge2Si22+


2.424

E = 133.8 kcal mol-1, D2h 2.275 2.426 2.590

E = 0.0 kcal mol-1, D2h



2.321 2.424 E = 26.4 kcal mol-1, D∞h

22

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Figure 2. Molecular orbital pictures for the cyclic isomers of the M2N22+ clusters.


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Figure 3. B3LYP/6-311+G*//PBE/TZ2P NICSzz (top) and NICSzz (bottom) (in ppm) components plotted along the principal axis (in Å) perpendicular to the molecular plane of the cyclic D4h/D2h M2N22+ molecules.


24

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Figure 4. PBE/TZ2P optimized geometries of lowest-lying group 14 M2N22+ clusters with M or N = Sn or Pb. Bond lengths in Å and PBE/TZ2P relative energies in kcal mol-1.


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Figure 4 cont.


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TOC Graphic


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Isomer Clusters - American Chemical Society

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