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PM3 treatment of some endohedrally Mg doped C60H2 systems
Journal of Molecular Structure (Theochem) 619 (2002) 135–141 www.elsevier.com/locate/theochem
PM3 treatment of some endohedrally Mg doped C60H2 systems Lemi Tu¨rker Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey Received 2 June 2002; accepted 5 August 2002
Abstract Semiempirical quantum chemical calculations at the level of PM3 (RHF) were carried out on the regio and stereoisomers of endohedrally magnesium doped C60H2 system, Mg@C60H2. In these systems, hydrogens occupy vicinal positions at the fusion sites of five and six membered rings or at the fusion points of two hexagons. All the structures were found to be stable but endothermic. In the case of In-56Mg@C60H2 some quasi-hydride interaction occurs between the inwardly oriented hydrogens and the endohedral substituent, Mg. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Hydrofullerenes; Mg@C60H2; C60H2; Hydrogenation; PM3 treatment
1. Introduction Hydrogenation of fullerenes to fulleranes has remained an attractive field of research to many scientists since the very beginning of ‘Fullerenes era’ [1]. However, to achieve successful results in the conversion of fullerenes to partially or completely hydrogenated products most of the time is a hard task to do not only because of the technical or experimental problems confronted while the process of syntheses but also in the characterization of the products. The polyhydrofullerenes exhibit certain instability too [1]. However, a limited number of energetically favorable isomers can be expected if stoichiometrically controlled additions to just one or a few reactive double bonds of C60 (or C70) are considered. The regio and stereoisomers of C60H2 and C70H2 constitute good examples for those thermodynamically and/or kinetically favored isomers [2 – 6]. In the case of C60, the double bonds which could undergo vicinal E-mail address: [email protected] (L. Tu¨rker).
hydrogenation can be categorized as 56- and 66-type bonds. The former one is in between five- and sixmembered rings in C60 structure whereas 66-type stands for hydrogenation of a double bond located in between two hexagons. Hydrogenation of 56- and 66-type bonds engenders the regioisomers of the product, say C60H2. Theoretically all the regioisomers should have stereoisomers with endo- and exo-hydrogens (In and Out forms). Calculations at the MNDO level and ab initio involving different isomers of C60H2 and C70H2 were reported [5, 7– 9]. The most stable isomer of C60H2 is the vicinal product (1,2-addition) predicted theoretically and experimentally [10]. In the case of C60H60, the structure with 10 hydrogens inside the cage was found to be more stable than all-outside isomer [11]. On the other hand, endohedrally doped various fullerenes exist and constitute an interesting class [12]. In endohedral doping, an atom or an ion in the interior hallow core of a fullerene molecule exists (metallofullerenes or endofullerenes). The insertion of one, two and three metal species inside a fullerene
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L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
cage is common and up to four metal atoms (ions) have thus far been introduced [13]. A theoretical study at the level of AM1 type calculations revealed that endohedrally beryllium doped C60 structure (Be@C60) may accommodate hydrogen molecules endohedrally up to a certain number then a hydridic interaction occurs between Be atom and hydrogen [14]. In the light of this investigation, in the present study, some regio and stereoisomers of Mg@C60H2 system are considered for PM3 type semiempirical calculations. 2. Method
of all the structures leading to energy minima were achieved by using PM3 self-consistent fields molecular orbital (SCF MO) [16,17] method at the restricted Hartree – Fock (RHF) level [18]. The optimizations were obtained by the application of the steepest-descent method followed by conjugate gradient methods, Fletcher-Rieves and Polak-Ribiere, consecutively (convergence limit of 4.18 £ 1024 kJ/ mol (0.0001 kcal/mol) and RMS gradient of 4.18 £ 107 kJ/mmol (0.001 kcal/(A mol))). All these computations were performed by using the Hyperchem (release 5.1) and ChemPlus (2.0) package programs [15]. 3. Results and discussion
In the present treatise, the initial structure of C60 [(5,6)-fullerene-60-I h] was excerpted from the Hyperchem Library [15]. The geometry optimizations
In the present study, endohedrally Mg doped C60H2 structures having both of the hydrogens in the cage
Fig. 1. The geometry optimized three-dimensional structures of the molecules considered.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
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Table 1 Some calculated properties of the structures considered Mg@C60
In-56
In-66
Out-56
Out-66
Area Volume Polarizability Dipole moment Charge on Mg C –H bond lengths
545.72 1207.03 113.81 0.0000 20.1306 –
Molecular point group
C1
545.11 1201.63 110.73 0.8905 20.4074 3.20 3.29 C2V
548.05 1209.81 110.73 0.1768 20.1495 1.17 1.17 C2
552.30 1222.96 112.91 7.0714 20.1316 1.11 1.11 C1
548.93 1220.55 110.73 8.0187 20.1310 1.11 1.11 C2V
Area, volume, polarizability, dipole moment values and bond lengths are in the order of 10220 m2, 10230 m3, 10230 m3, 10230 C m and 10 m, respectively. 210
and out of the cage have been considered. These structures exhibit regioisomerism such that the vicinal hydrogenation should have taken place at the fusion points of five- and six-membered rings or at the fusion points of two six-membered rings. All these structural variations are formulated as In-56Mg@C 60 H 2, Out-56Mg@C60H 2, OutIn-66Mg@C 60H 2, 66Mg@C60H2. The geometry optimized three-dimensional structures of these molecules are shown in Fig. 1. As seen in the figure, the carbon – hydrogen bonds in the case of In-56Mg@C60H2 structure are highly elongated (3.29 and 3.20 £ 10210 m). This implies that the C –H bonds are almost broken but some quasihydridic interaction with magnesium atom occurs. However, in the case of In-66Mg@C60H2 structure such kind of occurrence is not expected (both C –H bonds are 1.17 £ 10210 m, respectively). On the other hand, the charges on Mg atoms are 2 0.4073 and 2 0.1495 unit of charge, respectively, for In-56 and In-66 forms. Negative charge accumulation on Mg atom (see Table 1) indicates that C60 cage ligands to
Mg atom using its empty atomic orbitals. Table 1 shows C –H bond lengths of the other isomers as well as some other calculated properties of these structures. Note that Out-type isomers have rather high dipole moments as compared to their In-type analogous. Various energies of the systems of consideration are shown in Table 2. As seen in the table, all these structures are stable (the total and binding energies) but endothermic in nature (the heats of formation data). Of the various isomeric structures considered, In-56Mg@C60H2 is the most stable and the least endothermic one which also indicates that certain stabilizing interactions occur between the hydrogens in In-56 isomer and Mg atom. On the other hand, In-66Mg@C60H2 structure is the least stable and the most endothermic among the isomeric systems considered. This observation could be tried to be explained by means of the ‘isolated pentagon rule’ (IPR) [1]. It is known that among the various isomeric structures having the empirical formula, C60, the one in which all the pentagons surrounded by hexagons
Table 2 Various energies of the systems of interest Energy
Mg@C60
In-56
In-66
Out-56
Out-66
Total Binding Isolated atomic Electronic Core–core repulsion Heat of formation
2684,507 238,394 2646,113 29,794,736 9,110,229 4652.58
2688,104 239,468 2648,635 210,003,149 9,315,044 4013.88
2686,888 238,253 2648,635 299,522,732 9,265,843 5229.51
2687,546 238,911 2648,635 29,913,551 9,226,005 4571.57
2687,620 238,985 2648,635 29,915,710 9,228,090 4497.59
Energies in kJ/mol. In-56 (66) and Out-56 (66) stand for In and Out forms of Mg@C60H2.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
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seems to be more stable and less endothermic than the former one. Thus these results of calculations cannot be explained merely on the basis of violated IPR concept. Hence, one has to consider the influence of endohedrally substituted Mg atom. The violation to IPR and perturbational effect of endohedral atom on p-electron cloud of C60H2 cage overall should be responsible for the energetics of these isomeric structures such that In-56 is favored over In-66 isomer but on the contrary Out-66 is more favorable than Out-56 isomer. Fig. 2 shows three-dimensional electrostatic potential field maps for the isomers considered. Table 3 shows the HOMO, LUMO energies and the interfrontier energy gaps (DE ) for these systems. As seen there, although Out-56 and Out66 isomers have comparable HOMO, LUMO and DE values as compared to Mg@C60 system, In-56 and especially In-66 isomers have quite different respective values than of Mg@C60. The HOMO, LUMO energies, and DE values of the isomers follow the order of Fig. 2. Three-dimensional electrostatic field maps for the isomers considered.
In-66 , In-56 , Out-56 , Out-66
represents the most stable structure. In the case of hydrogenation of such a structure, the rule is violated because of the imported sp3 type carbon atom bearing the hydrogens. Thus, certain pentagons are not wholly circumferred by hexagons. In the case of In-56 isomer, only one pentagon but in the case of In-66 isomer two pentagons suffer from this effect. Consequently, In-66Mg@C60H2 structure should be thought to be less stable and more endothermic than the other regioisomer, In-56Mg@C60H2. However, when the energetics of Out-56Mg@C60H2, and Out-66Mg@C60H2 are inspected, the latter one
The coordinates of Mg atom varies from structure to structure; thus different extents of interaction with the cage occurs causing such kind of order to appear. Fig. 3 shows the HOMO and LUMO of the structures considered. In the case of Mg@C60, In-66Mg@C 60 H2 , Out-56Mg@C60H 2 and Out66Mg@C60H2 the HOMO is concentrated in the cage. Whereas in all the structures, the cage highly contribute to the LUMO. The molecular orbital energy spectra for these structures are shown in Fig. 4. There, In-56 isomer is distinguishable from the other isomers by having rather discrete upper occupied energy levels.
Table 3 The HOMO, LUMO energies and the interfrontier energy gaps (DE ) for the presently considered structures Energy
Mg@C60
In-56
In-66
Out-56
Out-66
LUMO HOMO DE
24.6625 (AU) 213.8705 (AU) 9.2080
216.5966 (A1) 216.6174 (B2) 0.0208
226.5226 (A) 226.6301 (B) 0.1075
24.7911 (A) 213.6240 (A) 8.8329
24.5374 (A1) 213.5910 (A1) 9.0536
Energies in the order of 10219 J. In-56 (66) and Out-56 (66) stand for In and Out forms of Mg@C60H2.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
Fig. 3. The HOMO and LUMO of the structures considered.
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L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
Fig. 4. The molecular orbital energy spectra for the systems considered.
4. Conclusion The present PM3 (RHF) type semiempirical calculations on endohedrally magnesium doped C60H2 isomers (the regio and stereoisomers of Mg@C60H2) reveal that they are all stable but
endothermic structures. In-56 isomer is especially interesting indicating that some quasi-hydride formation in between the Mg atom and inwardly located hydrogens. Thus, this system although nonexistent yet, could be exploited in future as some sort of hydrogen storage device at the molecular level.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
References [1] A. Hirsch, The Chemistry of the Fullerenes, Verlag, Stuttgart, 1994. [2] C.C. Henderson, P.A. Cahill, Science 259 (1993) 1885. [3] S. Ballenweg, R. Gleiter, W. Kratschmer, Tetrahedron Lett. 34 (1993) 3737. [4] T.F. Guarr, M.S. Meier, V.K. Vance, M. Clayton, J. Am. Chem. Soc. 115 (1993) 9862. [5] A. Hirsch, A. Soi, H.R. Karfunkel, Angew. Chem. 104 (1992) 808. [6] A. Hirsch, T. Gro¨sser, A. Skiebe, A. Soi, Chem. Berr. 126 (1993) 1061. [7] N. Matsuzawa, D.A. Dixon, T. Fukunaga, J. Phys. Chem. 96 (1992) 7594.
141
[8] C.C. Henderson, C.M. Rofling, P.A. Cahill, Chem. Phys. Lett. 213 (1993) 383. [9] H.R. Karfunkel, A. Hirsch, Angew. Chem. 104 (1992) 1529. [10] N. Matsuzawa, T. Fukunaga, D.A. Dixon, J. Phys. Chem. 96 (1992) 10747. [11] M. Saunders, Science 253 (1991) 330. [12] M.S. Dresselhause, G. Dresselhause, P.C. Eklund, Science of Fullerenes and Carbon Nanotubes, Academic Press, New York, 1995. [13] R.E. Smalley, Mater. Sci. Engng B19 (1993) 1. [14] L. Tu¨rker, J. Mol. Struct. (Theochem) 577 (2002) 205. [15] Hyperchem, Hypercube Inc., Gainesville, FL, USA. [16] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209. [17] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 221. [18] A.R. Leach, Molecular Modelling, Longman, Essex, 1997.
PM3 treatment of some endohedrally Mg doped C60H2 systems Lemi Tu¨rker Department of Chemistry, Middle East Technical University, 06531 Ankara, Turkey Received 2 June 2002; accepted 5 August 2002
Abstract Semiempirical quantum chemical calculations at the level of PM3 (RHF) were carried out on the regio and stereoisomers of endohedrally magnesium doped C60H2 system, Mg@C60H2. In these systems, hydrogens occupy vicinal positions at the fusion sites of five and six membered rings or at the fusion points of two hexagons. All the structures were found to be stable but endothermic. In the case of In-56Mg@C60H2 some quasi-hydride interaction occurs between the inwardly oriented hydrogens and the endohedral substituent, Mg. q 2002 Elsevier Science B.V. All rights reserved. Keywords: Hydrofullerenes; Mg@C60H2; C60H2; Hydrogenation; PM3 treatment
1. Introduction Hydrogenation of fullerenes to fulleranes has remained an attractive field of research to many scientists since the very beginning of ‘Fullerenes era’ [1]. However, to achieve successful results in the conversion of fullerenes to partially or completely hydrogenated products most of the time is a hard task to do not only because of the technical or experimental problems confronted while the process of syntheses but also in the characterization of the products. The polyhydrofullerenes exhibit certain instability too [1]. However, a limited number of energetically favorable isomers can be expected if stoichiometrically controlled additions to just one or a few reactive double bonds of C60 (or C70) are considered. The regio and stereoisomers of C60H2 and C70H2 constitute good examples for those thermodynamically and/or kinetically favored isomers [2 – 6]. In the case of C60, the double bonds which could undergo vicinal E-mail address: [email protected] (L. Tu¨rker).
hydrogenation can be categorized as 56- and 66-type bonds. The former one is in between five- and sixmembered rings in C60 structure whereas 66-type stands for hydrogenation of a double bond located in between two hexagons. Hydrogenation of 56- and 66-type bonds engenders the regioisomers of the product, say C60H2. Theoretically all the regioisomers should have stereoisomers with endo- and exo-hydrogens (In and Out forms). Calculations at the MNDO level and ab initio involving different isomers of C60H2 and C70H2 were reported [5, 7– 9]. The most stable isomer of C60H2 is the vicinal product (1,2-addition) predicted theoretically and experimentally [10]. In the case of C60H60, the structure with 10 hydrogens inside the cage was found to be more stable than all-outside isomer [11]. On the other hand, endohedrally doped various fullerenes exist and constitute an interesting class [12]. In endohedral doping, an atom or an ion in the interior hallow core of a fullerene molecule exists (metallofullerenes or endofullerenes). The insertion of one, two and three metal species inside a fullerene
0166-1280/02/$ - see front matter q 2002 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 6 - 1 2 8 0 ( 0 2 ) 0 0 5 6 8 - 7
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L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
cage is common and up to four metal atoms (ions) have thus far been introduced [13]. A theoretical study at the level of AM1 type calculations revealed that endohedrally beryllium doped C60 structure (Be@C60) may accommodate hydrogen molecules endohedrally up to a certain number then a hydridic interaction occurs between Be atom and hydrogen [14]. In the light of this investigation, in the present study, some regio and stereoisomers of Mg@C60H2 system are considered for PM3 type semiempirical calculations. 2. Method
of all the structures leading to energy minima were achieved by using PM3 self-consistent fields molecular orbital (SCF MO) [16,17] method at the restricted Hartree – Fock (RHF) level [18]. The optimizations were obtained by the application of the steepest-descent method followed by conjugate gradient methods, Fletcher-Rieves and Polak-Ribiere, consecutively (convergence limit of 4.18 £ 1024 kJ/ mol (0.0001 kcal/mol) and RMS gradient of 4.18 £ 107 kJ/mmol (0.001 kcal/(A mol))). All these computations were performed by using the Hyperchem (release 5.1) and ChemPlus (2.0) package programs [15]. 3. Results and discussion
In the present treatise, the initial structure of C60 [(5,6)-fullerene-60-I h] was excerpted from the Hyperchem Library [15]. The geometry optimizations
In the present study, endohedrally Mg doped C60H2 structures having both of the hydrogens in the cage
Fig. 1. The geometry optimized three-dimensional structures of the molecules considered.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
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Table 1 Some calculated properties of the structures considered Mg@C60
In-56
In-66
Out-56
Out-66
Area Volume Polarizability Dipole moment Charge on Mg C –H bond lengths
545.72 1207.03 113.81 0.0000 20.1306 –
Molecular point group
C1
545.11 1201.63 110.73 0.8905 20.4074 3.20 3.29 C2V
548.05 1209.81 110.73 0.1768 20.1495 1.17 1.17 C2
552.30 1222.96 112.91 7.0714 20.1316 1.11 1.11 C1
548.93 1220.55 110.73 8.0187 20.1310 1.11 1.11 C2V
Area, volume, polarizability, dipole moment values and bond lengths are in the order of 10220 m2, 10230 m3, 10230 m3, 10230 C m and 10 m, respectively. 210
and out of the cage have been considered. These structures exhibit regioisomerism such that the vicinal hydrogenation should have taken place at the fusion points of five- and six-membered rings or at the fusion points of two six-membered rings. All these structural variations are formulated as In-56Mg@C 60 H 2, Out-56Mg@C60H 2, OutIn-66Mg@C 60H 2, 66Mg@C60H2. The geometry optimized three-dimensional structures of these molecules are shown in Fig. 1. As seen in the figure, the carbon – hydrogen bonds in the case of In-56Mg@C60H2 structure are highly elongated (3.29 and 3.20 £ 10210 m). This implies that the C –H bonds are almost broken but some quasihydridic interaction with magnesium atom occurs. However, in the case of In-66Mg@C60H2 structure such kind of occurrence is not expected (both C –H bonds are 1.17 £ 10210 m, respectively). On the other hand, the charges on Mg atoms are 2 0.4073 and 2 0.1495 unit of charge, respectively, for In-56 and In-66 forms. Negative charge accumulation on Mg atom (see Table 1) indicates that C60 cage ligands to
Mg atom using its empty atomic orbitals. Table 1 shows C –H bond lengths of the other isomers as well as some other calculated properties of these structures. Note that Out-type isomers have rather high dipole moments as compared to their In-type analogous. Various energies of the systems of consideration are shown in Table 2. As seen in the table, all these structures are stable (the total and binding energies) but endothermic in nature (the heats of formation data). Of the various isomeric structures considered, In-56Mg@C60H2 is the most stable and the least endothermic one which also indicates that certain stabilizing interactions occur between the hydrogens in In-56 isomer and Mg atom. On the other hand, In-66Mg@C60H2 structure is the least stable and the most endothermic among the isomeric systems considered. This observation could be tried to be explained by means of the ‘isolated pentagon rule’ (IPR) [1]. It is known that among the various isomeric structures having the empirical formula, C60, the one in which all the pentagons surrounded by hexagons
Table 2 Various energies of the systems of interest Energy
Mg@C60
In-56
In-66
Out-56
Out-66
Total Binding Isolated atomic Electronic Core–core repulsion Heat of formation
2684,507 238,394 2646,113 29,794,736 9,110,229 4652.58
2688,104 239,468 2648,635 210,003,149 9,315,044 4013.88
2686,888 238,253 2648,635 299,522,732 9,265,843 5229.51
2687,546 238,911 2648,635 29,913,551 9,226,005 4571.57
2687,620 238,985 2648,635 29,915,710 9,228,090 4497.59
Energies in kJ/mol. In-56 (66) and Out-56 (66) stand for In and Out forms of Mg@C60H2.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
138
seems to be more stable and less endothermic than the former one. Thus these results of calculations cannot be explained merely on the basis of violated IPR concept. Hence, one has to consider the influence of endohedrally substituted Mg atom. The violation to IPR and perturbational effect of endohedral atom on p-electron cloud of C60H2 cage overall should be responsible for the energetics of these isomeric structures such that In-56 is favored over In-66 isomer but on the contrary Out-66 is more favorable than Out-56 isomer. Fig. 2 shows three-dimensional electrostatic potential field maps for the isomers considered. Table 3 shows the HOMO, LUMO energies and the interfrontier energy gaps (DE ) for these systems. As seen there, although Out-56 and Out66 isomers have comparable HOMO, LUMO and DE values as compared to Mg@C60 system, In-56 and especially In-66 isomers have quite different respective values than of Mg@C60. The HOMO, LUMO energies, and DE values of the isomers follow the order of Fig. 2. Three-dimensional electrostatic field maps for the isomers considered.
In-66 , In-56 , Out-56 , Out-66
represents the most stable structure. In the case of hydrogenation of such a structure, the rule is violated because of the imported sp3 type carbon atom bearing the hydrogens. Thus, certain pentagons are not wholly circumferred by hexagons. In the case of In-56 isomer, only one pentagon but in the case of In-66 isomer two pentagons suffer from this effect. Consequently, In-66Mg@C60H2 structure should be thought to be less stable and more endothermic than the other regioisomer, In-56Mg@C60H2. However, when the energetics of Out-56Mg@C60H2, and Out-66Mg@C60H2 are inspected, the latter one
The coordinates of Mg atom varies from structure to structure; thus different extents of interaction with the cage occurs causing such kind of order to appear. Fig. 3 shows the HOMO and LUMO of the structures considered. In the case of Mg@C60, In-66Mg@C 60 H2 , Out-56Mg@C60H 2 and Out66Mg@C60H2 the HOMO is concentrated in the cage. Whereas in all the structures, the cage highly contribute to the LUMO. The molecular orbital energy spectra for these structures are shown in Fig. 4. There, In-56 isomer is distinguishable from the other isomers by having rather discrete upper occupied energy levels.
Table 3 The HOMO, LUMO energies and the interfrontier energy gaps (DE ) for the presently considered structures Energy
Mg@C60
In-56
In-66
Out-56
Out-66
LUMO HOMO DE
24.6625 (AU) 213.8705 (AU) 9.2080
216.5966 (A1) 216.6174 (B2) 0.0208
226.5226 (A) 226.6301 (B) 0.1075
24.7911 (A) 213.6240 (A) 8.8329
24.5374 (A1) 213.5910 (A1) 9.0536
Energies in the order of 10219 J. In-56 (66) and Out-56 (66) stand for In and Out forms of Mg@C60H2.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
Fig. 3. The HOMO and LUMO of the structures considered.
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L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
Fig. 4. The molecular orbital energy spectra for the systems considered.
4. Conclusion The present PM3 (RHF) type semiempirical calculations on endohedrally magnesium doped C60H2 isomers (the regio and stereoisomers of Mg@C60H2) reveal that they are all stable but
endothermic structures. In-56 isomer is especially interesting indicating that some quasi-hydride formation in between the Mg atom and inwardly located hydrogens. Thus, this system although nonexistent yet, could be exploited in future as some sort of hydrogen storage device at the molecular level.
L. Tu¨rker / Journal of Molecular Structure (Theochem) 619 (2002) 135–141
References [1] A. Hirsch, The Chemistry of the Fullerenes, Verlag, Stuttgart, 1994. [2] C.C. Henderson, P.A. Cahill, Science 259 (1993) 1885. [3] S. Ballenweg, R. Gleiter, W. Kratschmer, Tetrahedron Lett. 34 (1993) 3737. [4] T.F. Guarr, M.S. Meier, V.K. Vance, M. Clayton, J. Am. Chem. Soc. 115 (1993) 9862. [5] A. Hirsch, A. Soi, H.R. Karfunkel, Angew. Chem. 104 (1992) 808. [6] A. Hirsch, T. Gro¨sser, A. Skiebe, A. Soi, Chem. Berr. 126 (1993) 1061. [7] N. Matsuzawa, D.A. Dixon, T. Fukunaga, J. Phys. Chem. 96 (1992) 7594.
141
[8] C.C. Henderson, C.M. Rofling, P.A. Cahill, Chem. Phys. Lett. 213 (1993) 383. [9] H.R. Karfunkel, A. Hirsch, Angew. Chem. 104 (1992) 1529. [10] N. Matsuzawa, T. Fukunaga, D.A. Dixon, J. Phys. Chem. 96 (1992) 10747. [11] M. Saunders, Science 253 (1991) 330. [12] M.S. Dresselhause, G. Dresselhause, P.C. Eklund, Science of Fullerenes and Carbon Nanotubes, Academic Press, New York, 1995. [13] R.E. Smalley, Mater. Sci. Engng B19 (1993) 1. [14] L. Tu¨rker, J. Mol. Struct. (Theochem) 577 (2002) 205. [15] Hyperchem, Hypercube Inc., Gainesville, FL, USA. [16] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 209. [17] J.J.P. Stewart, J. Comput. Chem. 10 (1989) 221. [18] A.R. Leach, Molecular Modelling, Longman, Essex, 1997.