Structure and Stability of M6N8 Clusters (M = Si, Ge, Sn, Ti) - The

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Structure and Stability of M6N8 Clusters (M ) Si, Ge, Sn, Ti) Elena I. Davydova,*,† Alexey Y. Timoshkin,† and Gernot Frenking‡ Inorganic Chemistry Group, Department of Chemistry, St. Petersburg State UniVersity, UniVersity pr. 26, Old Peterhoff, 198504 St. Petersburg, Russia and Philipps-UniVersita¨t Marburg, Hans-Meerwein-Strasse, D-35032 Marburg, Germany ReceiVed: NoVember 25, 2009; ReVised Manuscript ReceiVed: April 14, 2010

The structures and stabilities of the M6N8 clusters (M ) Si, Ge, Sn, Ti) have been theoretically studied at DFT and ab initio levels of theory. Two new isomers have been considered: cage-like molecules and propellerlike molecules. It is shown that only for M ) Si are both isomers true minima on the potential energy surface. The thermodynamics of the dissociation process 1/6M6N8 f 1/3M3N4 is discussed. For each M3N4 molecule, four structures with different multiplicity are considered. The thermodynamic analysis shows that independently of the multiplicity of M3N4 nitrides all M6N8 clusters are stable in the gas phase in a wide temperature range and could be potential intermediates in chemical vapor deposition of the nitride materials. 1. Introduction Silicon nitrides have attracted much interest because of their use in microelectronics. One of the leading methods for their production is chemical vapor deposition (CVD).1 In this context, considerable attention has been given to gaseous silicon-nitrogen clusters. The formation and properties of small Si-N species such as SiN, Si2N, SiN2, Si2N2, Si3N4, and others have been extensively investigated both experimentally2-17 and theoretically.11,18-34 In contrast, research about larger clusters is limited. Joseph et al.35 studied the high temperature behavior of Si3N4 using laser-induced vaporization mass spectrometry, where they observed not only gaseous Si3N4 but also Si6N8 species. The Si6N5+, Si5N7+, Si6N6+, and Si7N4+ ions were experimentally observed in mass spectra by Devienne et al.36 However, this study was limited to the mass range 0 to ca. 250 amu, which excludes the detection of Si6N8 species. Theoretical studies of the structure and properties of Si6N8 clusters were presented by Zhang et al.,37 where four possible isomers were considered. The SinNm clusters (n + m ) 20) have been studied by Jackson et al.38 Even less is known about heavier group IV element derivatives. In this report we present a detailed theoretical analysis of the structural and energetic characteristics of new isomers of M6N8 (M ) Si, Ge, Sn, Ti) clusters. Two possible structures have been optimized. The thermodynamic properties of the dissociation reaction of M6N8 clusters yielding M3N4 species in the gas phase are discussed as well. The knowledge of the structures and relative stabilities of nitride clusters can provide important information required for the formation of nitride films. 2. Computational Details The geometries of the compounds have been fully optimized with gradient-corrected density functional theory (DFT) using Becke’s three-parameter hybrid method (U)B3LYP.39,40 The calculations have been performed with all electron basis sets of DZP quality. The basis sets are (6111/41/1) for N,41 (531111/4211/1) for Si,41 (63311/5311/411) for Ge,42 and (633321/53321/531) for * To whom correspondence should be addressed. Fax: +7(812)428-6939. E-mail: [email protected]. † St. Petersburg State University. ‡ Philipps-Universita¨t Marburg.

Figure 1. Optimized structures (distances in Å and angles in degrees) of the Si6N8 clusters: (a) cage-like molecule; (b) propeller-like molecule. B3LYP/DZP level of theory.

Sn.43 The basis sets used for the titanium compounds are identical to those that were used in the previous theoretical study of TiCl4 complex formation and ammonolysis.44 All structures correspond to minima on the respective potential energy surfaces (PES). Singlepoint energies have been evaluated at the (U)B3LYP, (U)MP2,45 and spin-projected PMP246 levels of theory based on the B3LYP/ DZP optimized geometries in conjunction with the all-electron def2TZVPP basis set47 for all atoms except tin. For Sn we employed a quasi-relativistic effective core potential (ECP) combined with a TZVPP valence basis set.48,49 The Gaussian 03 program package was used throughout.50 3. Results and Discussion The optimized structures of the M6N8 clusters are given in Figures 1-4. For each M6N8 molecule two possible structures have

10.1021/jp911209w  2010 American Chemical Society Published on Web 05/13/2010

Structure and Stability of M6N8 Clusters

J. Phys. Chem. A, Vol. 114, No. 22, 2010 6409 propeller isomer of Sn6N8 resulted either in structures that possess imaginary frequencies or in the S4 distorted structure presented in Figure 3b. It is interesting to note that the shape of the latter structure is similar to the cage compound. Moreover, the energy difference between the Sn6N8 isomers is only 35 kJ mol-1. Optimization of the Ti6N8 molecule starting both from cage and propeller isomers always resulted in the S4 distorted structure presented in Figure 4. Structures of the other type are not minima, they have two or more imaginary frequencies. To investigate the relative stability of M6N8 clusters we considered the thermodynamic characteristics of the following dissociation process of M6N8 clusters into M3N4 nitrides:

Figure 2. Optimized structure (distances in Å and angles in degrees) of the Ge6N8 cluster (propeller isomer). B3LYP/DZP level of theory. 1

/6M6N8 f 1/3M3N4

Figure 3. Optimized structures (distances in Å and angles in degrees) of the Sn6N8 clusters: (a) cage-like molecule; (b) distorted cage molecule. B3LYP/DZP level of theory.

Figure 4. Optimized structure (distances in Å and angles in degrees) of the Ti6N8 cluster (distorted cage molecule). B3LYP/DZP(ECP on Ti) level of theory.

been considered: cage-like molecules and propeller-like molecules. Both isomers of Si6N8 are true minima on the PES (Figure 1). The calculations predict that the C3V cage structure is 531 kJ mol-1 higher in energy than the S4 propeller isomer. Optimization of the Ge6N8 cage structures with symmetry higher than C1 resulted in species that possess between one and three imaginary frequencies. Lowering the symmetry to C1 converged to the more stable propeller isomer (Figure 2). For Sn6N8 the D4h cage structure is a true minimum on the PES (Figure 3a). The optimization of the

(1)

Note that for each M3N4 molecule four structures with different number of M-N double bonds, and hence different multiplicity, are possible. All M3N4 isomers possess a six-membered M3N3 ring in a chair conformation, with three metal atoms capped by an additional nitrogen atom (Figure 5). The M3N4 open cage slightly deviates from a perfect cube, the M-N-M and N-M-N angles inside the M2N2 rings are close to 90°. The M-N bond lengths in the M2N2 ring are not equivalent. M-N bond distances in M3N4 nitrides as well as in M6N8 cage compounds are intermediate between values for conventional M-N single bond distances in Cl3MNH251 and donoracceptor bond distances in MX4 · NH3.52,53 In our opinion, this indicates that M-N bonds in considered compounds have both normal single-bond and donor-acceptor characters. Similar situation was observed for Sn4N4 cage compounds.54,55 The calculated energies relative to the most stable isomer are presented in Table 1. The B3LYP/DZP calculations predict that only Ti3N4 has a singlet state as electronic ground state. For M ) Si, Ge the lowest energy isomer is a triplet, whereas for Sn3N4 it is a septet. The energy difference between the ground and singlet state is 45, 67, and 101 kJ mol-1 for Si, Ge, and Sn, respectively, with the singlet having a higher energy. Note that for the group 14 nitrides the energy difference between the ground and exited states does not exceed 164 kJ mol-1, whereas for Ti3N4 it is 207-621 kJ mol-1. Single-point energies have been also evaluated at DFT and ab initio levels of theory in conjunction with TZVPP basis set (Table 1). As can be seen, at the UMP2 level of theory the lowest energy isomer is a singlet for all M3N4 nitrides, whereas PMP2 calculations predict a triplet for Si3N4 and singlet for other nitrides as electronic ground state. Note that for open shell systems the spin contamination could lead to some errors in the calculations. The spin-squared expectation values, 〈S2〉, obtained for M3N4 nitrides by DFT and ab initio levels of theory are presented in Table 4S of the Supporting Information. Very large deviations from the expected 〈S2〉 values (2.0 for triplet, 6.0 for quintet, and 12.0 for septet) are found at UMP2 level of theory for all nitrides, leading to error in energy calculations. Thus, the UMP2 results are probably unreliable. DFT and PMP2 methods are known to give more reasonable results than UMP2.56 Indeed, the PMP2 values (except for Ge3N4) are much less influenced by spin contamination. It is less common to find significant spin contamination in DFT calculations.57 Due to the difference between B3LYP and PMP2 results, the analysis of the different electronic states of the M3N4 nitrides requires further investigation, but this lies outside the purpose of the present work.

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Davydova et al. TABLE 1: Relative Energies (kJ mol-1) for Various Electronic States of M3N4 Compounds multiplicity singlet (s ) 0)

level of theory

triplet (s ) 1)

quintet (s ) 2)

septet (s ) 3)

B3LYP/DZP//B3LYP/DZP B3LYP/TZVPP//B3LYP/DZP MP2/TZVPP//B3LYP/DZP PMP2/TZVPP//B3LYP/DZP

Si3N4 44.9 35.0 0 7.1

0 0 10.7 0

64.6 74.4 245.3 215.6

163.8 187.4 331.9 319.3


Ge3N4 66.6 60.1 0 0

0 0 68.3 33.7

30.7 38.4 252.8 202.6

77.6 95.5 351.4 321.9


Sn3N4 101.3 92.0 0 0

46.8 47.7 530.4 413.0

12.3 9.8 378.2 347.2

0 0 361.1 323.8


Ti3N4 0 0 0 0

206.6 196.9 355.3 339.9

422.0 414.8 1139.5 1105.3

620.8 620.1 1167.7 1156.6

TABLE 2: Dissociation Energies (kJ mol-1) of M6N8 Clusters M3N4 B3LYP/DZP// B3LYP/TZVPP// MP2/TZVPP// PMP2/TZVPP// multiplicity B3LYP/DZP B3LYP/DZP B3LYP/DZP B3LYP/DZP 1

singlet triplet quintet septet

61.0 46.0 67.5 100.6


149.5 134.6 156.1 189.2


97.9 75.7 85.9 101.5


90.5 72.4 60.9 56.8

/6 Si6N8 (Cage) f 1/3 Si3N4 63.8 92.0 52.1 95.6 76.9 173.8 114.6 202.7

92.0 89.7 161.5 196.1

/6Si6N8 (Propeller) f 1/3Si3N4 156.8 170.8 145.1 174.4 169.9 252.6 207.6 281.4

170.8 168.4 240.3 274.9

/6Ge6N8 (Propeller) f 1/3Ge3N4 95.9 101.3 75.9 124.1 88.7 185.6 107.7 218.5

101.3 112.6 168.9 208.6

1

1

1


Figure 5. Optimized structures (distances in Å and angles in degrees) of the M3N4 nitrides (the electronic states are given in parentheses): (a) Si3N4; (b) Ge3N4; (c) Sn3N4; (d) Ti3N4. (*) The symmetry of the exact electronic state is unidentified. (U)B3LYP/DZP(ECP on Ti) level of theory.

/6Sn6N8 (Cage) f 1/3Sn3N4 72.6 147.1 57.8 323.9 45.2 273.2 41.9 267.5

1 /6Ti6N8 (Distorted Cage) f 1/3Ti3N4 60.5 53.1 50.5 129.4 118.8 168.9 201.2 191.4 430.3 267.5 259.8 439.7

147.1 284.8 262.9 255.1 50.5 163.8 418.9 436.0

Energetic characteristics of M6N8 clusters dissociation process are summarized in Table 2. As can be seen, the dissociation reactions are endothermic for all M6N8 compounds, and this result does not depend on the multiplicity of the M3N4 species. The dissociation energies computed at the ab initio level of theory are more endothermic compared to the B3LYP values, indicating larger stability of M6N8 clusters. Thus, the B3LYP results provide a lower limit of the cluster stability. The predicted thermodynamic characteristics of the dissociation process (eq 1) are summarized in Table 3. The process (eq 1) is endothermic, but the endothermicity becomes less when entropy is considered for all M. Therefore, the M6N8 clusters are predicted to be stable with respect to the dissociation at low temperatures. It is important to note that this result does not depend on the multiplicity of the M3N4 molecules. We

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TABLE 3: Gas Phase Thermodynamic Characteristics for the Dissociation Reaction of M6N8 Clustersa M 3N 4 multiplicity

∆H°298, kJ mol-1

∆S°298, J mol-1 K-1

∆G°298, kJ mol-1

1 /6Si6N8 (Cage) f 1/3Si3N4 59.7 36.5 44.0 42.1 65.0 46.3 97.9 47.2

singlet triplet quintet septet singlet triplet quintet septet

∆G°1000, kJ mol-1

48.8 31.4 51.2 83.8

23.1 1.9 18.8 50.6

1 /6Si6N8 (Propeller) f 1/3Si3N4 146.0 30.6 136.9 130.3 36.2 119.6 151.4 40.4 139.4 184.2 41.3 171.9

115.4 94.2 111.0 142.9


/6Ge6N8 (Propeller) f 1/3Ge3N4 95.6 30.2 86.6 72.9 34.9 62.5 82.6 40.7 70.4 97.9 44.2 84.7


1 /6Sn6N8 (Cage) f 1/3Sn3N4 89.5 41.9 70.7 51.4 59.3 51.3 54.8 57.2

acknowledged. E.I.D. is grateful to the DAAD and Russian Ministry of Education and Science for a short-term fellowship (Michail-Lomonosov-Forschungsstipendien und -Aufenthalte). A.Y.T. is grateful to the Alexander von Humboldt foundation for a research fellowship. Supporting Information Available: The total energies, sum of electronic and thermal enthalpies, and standard entropies of investigated compounds; predicted vibrational frequencies and IR intensities for investigated compounds; Cartesian coordinates for optimized structures of investigated compounds at the B3LYP/DZP level of theory. This material is available free of charge via the Internet at http://pubs.acs.org.

1

65.3 38.0 41.9 53.7

77.0 55.4 44.0 37.8

47.6 19.3 8.0 -2.3

/6Ti6N8 (Distorted Cage) f 1/3Ti3N4 60.0 29.6 51.2 131.7 38.2 120.3 200.2 39.6 188.4 264.1 45.6 250.5

30.4 93.5 160.6 218.4

1

singlet triplet quintet septet a

(U)B3LYP/DZP level of theory.

believe that the endothermicity of process (eq 1) is mostly due to the unsaturated character of metal and nitrogen (except apical nitrogen) atoms in the M3N4 nitrides, which favor the dimerization. Increase of the temperature leads to decreasing ∆GT0 values (see ∆G°1000 values in Table 3). However, even at these conditions the M6N8 clusters are still predicted to be stable. Thus, our thermodynamic analysis suggests that all considered M6N8 clusters may exist in the gas phase and they might play a role as intermediates in the growth of nitrides. 4. Conclusions The structure and thermodynamic characteristics of M6N8 clusters (M ) Si, Ge, Sn, Ti) have been obtained at the B3LYP/ DZP level of theory. Two possible isomers have been considered: cage-like molecules and propeller-like molecules. It is shown that only for M ) Si both isomers are true minima on the PES with the cage structure being 531 kJ mol-1 higher in energy than the propeller isomer. For the Ge6N8 cluster, the optimization of the cage isomer resulted in the formation of the most stable propeller molecule. In contrast, Sn6N8 cluster possesses only a cage isomer. Optimization of the Ti6N8 molecule starting both from cage and propeller isomers always resulted in the distorted cage structure. For M3N4 nitrides, four structures with different multiplicity are considered. It is shown that for the group 14 nitrides the energy difference between the ground and exited states does not exceed 164 kJ mol-1, whereas for Ti3N4 it is 207-621 kJ mol-1. Analysis of the predicted thermodynamic parameters for the dissociation processes 1/6M6N8 f 1/3M3N4 shows that, independent of the multiplicity of M3N4 species, all M6N8 clusters are stable in the gas phase in a wide temperature range. The stability of M6N8 clusters makes them potential intermediates in chemical vapor deposition of solid M3N4 nitrides. Acknowledgment. Excellent service by the Hochschulrechenzentrum of the Philipps-Universita¨t Marburg is gratefully

References and Notes (1) Pierson, H. O., Ed. Handbook of Chemical Vapor Deposition: Principles, Technology and Applications, 2nd ed.; William Andrew Publishing, LLC: New York, 1999; 482 pp. (2) Zmbov, K. F.; Margrave, J. L. J. Am. Chem. Soc. 1967, 89, 2492. (3) Benninghoven, A.; Sichtermann, W.; Storp, S. Thin Solid Films 1975, 28, 59. (4) Lembke, R. R.; Ferrante, R. F.; Weltner, W. J. Am. Chem. Soc. 1977, 99, 416. (5) Hemment, P. L. F.; Peart, R. F.; Yao, M. F.; Stephens, K. G.; Chater, R. J.; Kilner, J. A.; Meekison, D.; Booker, G. R.; Arrowsmith, R. P. Appl. Phys. Lett. 1985, 46, 952. (6) Manabe, Y.; Mitsuyu, T. J. Appl. Phys. 1989, 66, 2475. (7) Naulin, C.; Costes, M.; Moudden, Z.; Ghamen, N.; Dorthe, G. Chem. Phys. Lett. 1993, 202, 452. (8) Ito, H.; Suzuki, K.; Kondow, T.; Kuchitsu, K. Chem. Phys. Lett. 1993, 208, 328. (9) Iraqi, M.; Goldberg, N.; Schwarz, H. J. Phys. Chem. 1993, 97, 11371. (10) Marine, W.; Tokarev, V.; Gerri, M. Thin Solid Films 1994, 241, 103. (11) Goldberg, N.; Iraqi, M.; Schwarz, H. J. Chem. Phys. 1994, 101, 2871. (12) Takigawa, Y.; Hemminger, J. C. Appl. Surf. Sci. 1994, 79/80, 146. (13) Yoshimoto, M.; Takubo, K.; Komoda, M.; Matsunami, H. Appl. Surf. Sci. 1994, 79/80, 264. (14) Viswanathan, R.; Schmude, R. W.; Gingerich, K. A. J. Chem. Thermodyn. 1995, 27, 1303. (15) Wang, S. L.; Ledingham, K. W. D.; Jia, W. J.; Singhal, R. P. Appl. Surf. Sci. 1995, 93, 205. (16) Rocabois, P.; Chatillon, C.; Bernard, C. J. Am. Ceram. Soc. 1996, 79, 1351. (17) Gingerich, K. A.; Viswanathan, R.; Schmude, R. W. J. Chem. Phys. 1997, 106, 6016. (18) DeKock, R. L.; Grev, R. S.; Schaefer, H. F. J. Chem. Phys. 1988, 89, 3016. (19) Cai, Z.-L.; Wang, Y.-F.; Xiao, H.-M. J. Chem. Soc. Faraday Trans. 1992, 88, 1611. (20) Dixon, D. A.; DeKock, R. L. J. Chem. Phys. 1992, 97, 1157. (21) Ignatyev, I. S.; Schaefer, H. F. J. Phys. Chem. 1992, 96, 7632. (22) Murray, C. W.; Laming, G. J.; Handy, N. C.; Amos, R. D. J. Phys. Chem. 1993, 97, 1868. (23) Wang, J.; Eriksson, L. A.; Boyd, R. J.; Shi, Z. J. Phys. Chem. 1994, 98, 1844. (24) Chong, D. P. Chem. Phys. Lett. 1994, 229, 102. (25) Ornellas, F. R.; Iwata, S. J. Phys. Chem. 1996, 100, 10919. (26) Ornellas, F. R.; Iwata, S. J. Phys. Chem. 1996, 100, 16155. (27) Cai, Z.-L.; Martin, J. M. L.; Francois, J. P.; Gijbels, R. Chem. Phys. Lett. 1996, 252, 398. (28) Davy, R. D.; Schaefer, H. F. Chem. Phys. Lett. 1996, 255, 171. (29) Borin, A. C. Chem. Phys. Lett. 1996, 262, 80. (30) Ornellas, F. R.; Ueno, L. T.; Iwata, S. J. Chem. Phys. 1997, 106, 151. (31) Maier, G.; Reisenauer, H. P.; Glatthaar, J. Organometallics 2000, 19, 4775. (32) Jungnickel, G.; Frauenheim, T.; Jackson, K. A. J. Chem. Phys. 2000, 112, 1295. (33) Ueno, L. T.; Ornellas, F. R. J. Braz. Chem. Soc. 2001, 12, 99. (34) Puyad, A. L.; Raghunath, P.; Chaitanya, G. K.; Ramakrishna, K.; Bhanuprakash, K. J. Mol. Struct.: THEOCHEM 2007, 807, 73. (35) Joseph, M.; Sivakumar, N.; Manoravi, P. Int. J. Mass Spectrom. 1998, 176, 237. (36) Devienne, F. M.; Barnabe, C.; Couderc, M.; Ourisson, G. C. R. Acad. Sci. Paris, Ser. IIc 2000, 3, 341.

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(37) Zhang, C.-R.; Chen, H.-S.; Xu, G.-J.; Chen, Y.-H.; Zhang, H.-L. J. Mol. Struct.: THEOCHEM 2007, 807, 161. (38) Jackson, K.; Jungnickel, G.; Frauenhaim, T. Chem. Phys. Lett. 1998, 292, 235. (39) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (40) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B. 1988, 37, 785. (41) Dunning, T. H.; Hay, P. J. In Modern Theoretical Chemistry; Schaefer, H. F., Ed.; Plenum: New York, 1976; Vol. 3, p 1. (42) Scha¨fer, A.; Horn, H.; Ahlrichs, R. J. Chem. Phys. 1992, 97, 2571. (43) Godbout, N.; Salahub, D. R.; Andzelm, J.; Wimmer, E. Can. J. Chem. 1992, 70, 560. (44) Timoshkin, A. Y.; Siodmiak, M.; Korkin, A. A.; Frenking, G. Comput. Mater. Sci. 2003, 27, 109. (45) Møller, C.; Plesset, S. Phys. ReV. 1934, 46, 618. (46) Schlegel, H. B. J. Phys. Chem. 1988, 92, 3075. (47) Weigend, F.; Ahlrichs, R. Phys. Chem. Chem. Phys. 2005, 7, 3297. (48) Metz, B.; Stoll, H.; Dolg, M. J. Chem. Phys. 2000, 113, 2563. (49) Basis sets were obtained from the Extensible Computational Chemistry Environment Basis Set Database, Version 7/29/02, as developed and distributed by the Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory which is part of the Pacific Northwest Laboratory, P.O. Box 999, Richland, Washington 99352, USA, and funded by the U.S. Department of Energy. The Pacific Northwest Laboratory is a multi-program laboratory operated by Battelle Memorial Institue for the U.S. Department of Energy under contract DE-AC06-76RLO 1830. Contact David Feller or Karen Schuchardt for further information. (50) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, Jr., J. A.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.;

Davydova et al. Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A.; Gaussian 03, reVision D.01; Gaussian, Inc.: Wallingford, CT, 2004. (51) Davydova, E. I.; Timoshkin, A. Y.; Sevastianova, T. N.; Suvorov, A. V.; Frenking, G. Mol. Phys. 2009, 107, 899. (52) Siodmiak, M.; Frenking, G.; Korkin, A. J. Mol. Model. 2000, 6, 413. (53) Davydova, E. I.; Timoshkin, A. Y.; Sevastianova, T. N.; Suvorov, A. V.; Frenking, G. J. Mol. Struct.: THEOCHEM 2006, 767, 103. (54) Veith, M.; Recktenwald, O. Z. Naturforsch. B. 1983, 38, 1054. (55) Veith, M. Chem. ReV. 1990, 90, 3. (56) Wong, M. W.; Radom, L. J. Phys. Chem. 1995, 99, 8582. (57) Young, D. Computational Chemistry: A Practical Guide for Applying Techniques to Real-World Problems; Wiley-Interscience: New York, 2001.

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Structure and Stability of M6N8 Clusters (M = Si, Ge, Sn, Ti) - The

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