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Exit transition state of endohedral X@Si20H20 complexes (X=Li+, Na+, K+, Be2+, Mg2+)
Journal of Molecular Structure: THEOCHEM 770 (2006) 145–148 www.elsevier.com/locate/theochem
Exit transition state of endohedral X@Si20H20 complexes (XZLiC, NaC, KC, Be2C, Mg2C) Cai-Yun Zhang *, Hai-Shun Wu Department of Chemistry, Shanxi Normal University, Linfen 041004, China Received 1 April 2006; received in revised form 22 May 2006; accepted 26 May 2006 Available online 8 June 2006
Abstract The kinetic stability of endohedral X@Si20H20 complexes (XZLiC, NaC, KC, Be2C, Mg2C) has been studied at the B3LYP/6-31G* level of density functional theory (DFT). The transition states (TS) are investigated by the QST3 method of Gaussian 98 package and demonstrated with Intrinsic reaction coordinate (IRC). It is found that KC@Si20H20 cluster has the most stable structure kinetically, that the exit barrier heights (Hexit) for KC expulsion from or insertion in the cage are 187.38 and 205.58 kcal/mol, respectively. However, the smallest Be2C dication is not endohedrally encapsulated and the Be2C@Si20H20 cluster is expected to be the least stable structure kinetically. By comparison, other endohedral complexes have a moderate kinetic stability. q 2006 Elsevier B.V. All rights reserved. Keywords: Exit transition state; Endohedral complexes; Exit barrier height; Kinetic stability
1. Introduction Recently, a novel metal encapsulated caged clusters of silicon has been studied theoretically and experimentally [1–8]. Among the issues of interest to Chemists are the character of the interaction between the heteroatom and the cage. Compared to the pure Si clusters, the doped clusters have higher stabilities, symmetries and size selectivities. Pichierri et al. [9] computed the endohedral complexes X@Si20H20 (XZ FK, ClK, BrK, IK) and observed the charge transfer from X into the cage. We reported [10] the structures and stabilities of the alkali and alkaline earth metal encapsulated in perhydrogenated silicon fullerene Si20H20, and revealed that X@Si20H20 complexes (XZLiC, NaC, KC, Be2C, Mg2C) had a minimum endohedral structure. However, these studies only characterized local minima for endohedral structures, the potential barriers for X expulsion from the cage are not predicted and the question of the kinetic stability of the endohedral isomers remaine open (i.e. which atoms inserted into the Si20H20 cage would result in kinetic stable species). In this paper, the dynamic calculation results provide the information about endohedral structure’s kinetic stability, and * Corresponding author. Tel./fax: C86 357 2051375. E-mail address: [email protected] (C.-Y. Zhang).
0166-1280/$ - see front matter q 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.05.053
the prediction on the structures and stabilities of these compounds may be useful guides for the preparation and the experimental realization. 2. Computations A systematic search of transition states (TS) of the endohedral to exohedral rearrangement were carried out at the B3LYP/6-31G* level using Gaussian 98 [11], the procedure, of the time-demanding optimization with recalculation of force constants at each step [optZ(ts, calcall)] and the quadratic synchronous transit (optZqst3), was used to the saddle point optimization. TS-type corresponding to the exit of the guests from the cage via a pentagonal surface was demonstrated with Intrinsic reaction coordinate (IRC), and the related exit barrier heights (Hexit)[12] were also located at the same level. Results are presented in Tables 1 and 2. The initial endohedral structures and optimized transition states (TS) geometries for the clusters are shown in Figs. 1 and 2. 3. Results and discussions As found previously [13], the parent Si20H20 cage (1, Fig. 1) in Ih symmetry is an energy minimum structure at B3LYP/ 6-31G* level, the caged Si atoms possess an electron-deficient state (qSiZC0.100) [10] and the skeletal s-bonds is weakly. Moreover, the nucleus independent chemical shifts (NICS) [14] at the center of a Si20H20 cage face is K1.5 ppm,
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Table 1 ˚ ) and the radium of metal atom or metal cation (r, A ˚ ) of Selected B3LYP/6-31G* the first vibrational frequency (n1, cmK1), natural charges (q), bond lengths (R, A initial endohedral X@Si20H20 and corresponding transition state structures Structure
Sym
r(X)a
n1
qX
qSi
RbX–Si
RcSi–Si
RX-center
Li (endo) LiC(TS) NaC(endo) NaC(TS) KC(endo) KC(TS) Be2C(endo) Be2C(TS) Mg2C(endo) Mg2C(TS)
C5V C5V Ih C5V Ih C5V C5V – C5V C5V
0.68
126.4 K336.3 79.32 K235.7 141.5 K165.6 134.5 – 49.1 K144.6
0.802 0.713 0.590 0.779 0.720 0.854 1.286 – 1.721 1.448
0.015 0.044 0.083 0.664 0.081 0.131 K0.035 – K0.068 K0.003
2.590 2.216 3.354 2.425 3.368 2.815 2.200 – 2.600 2.424
2.425 2.604 2.393 2.851 2.404 3.309 2.537 – 2.494 2.830
1.082 2.604 0.000 2.617 0.000 2.660 3.066 – 1.124 2.336
C
a b c
0.97 1.33 0.35 0.66
N. N. Greenwood, A. Earnshaw, Chemistry of the Elements, second ed., Elsevier, 1997. The X–Si bond distances to the adjacent cage face. The Si–Si bond lengths of the active pentagonal surface.
compared with the NICS values at the center of benzene (K11.5 ppm) or cyclohexane (K2.1 ppm) [15], indicating a lack of cyclic electron delocalization in the five-membered ring. And the skeletal molecular orbital of Si20H20 cage does not exist conjugated p-electronic system. Therefore, the pathway for X exiting through a cage face is favorable as compared. The results further confirm that TS lie on the minimal energy pathway for expulsion of X from the cage and connect the initial endohedral structure (X@Si20H20) with the isolated components (XCSi20H20). Although all these searches are carried out without any symmetry constraints, the optimized transition structure has C5V symmetry (TS in Fig. 2). In the TS, the single imaginary frequency eigenvector is directed along the fivefold molecular axis toward the pentagonal surface.
the most favorable pathway for NaC cation exit is through the pentagonal face. In TSw2 (Fig. 2), NaC cation is fixed in the center of the broken face, and bounding to the adjacent Si atom ˚ ). However, the distances between silicon (RNa–Si: 2.425 A atoms in the active pentagonal surface have been elongated ˚ in Ih-structure (2, Fig. 1) to 2.851 A ˚ in TSw2 from 2.393 A (Fig. 2). 3.3. KC@Si20H20 As expected, the KC cation is too large to fit against a cage face, and hence the minimum structure possesses a Ih symmetry Table 2 B3LYP/6-31G* total electronic energies (Etot, a.u.) and the exit barrier heights (Hexit, kcal/mol) of initial (endo), transition state (TS) and final (iso) structures State (sym) Li (endo)(C5V) C
3.1. LiC@Si20H20 Endohedral LiC@Si20H20 structure (4, Fig. 1) is C5V symmetry and the LiC cation departs from the cage center ˚ . The calculated transition state (TSw1, Fig. 2) by 1.082 A structure converges to C5V symmetry, the corresponding exit barrier height (Hexit) for LiC expulsion from the cage is 23.66 kcal/mol. In TSw1 structure, the LiC cation is located on the fivefold axis and shifted from the initial stable point ˚ (the off-center distance is (C5V) toward a face by 1.522 A ˚ ), and formed the Li–Si bond with its bond length of 2.604 A ˚ . However, the Si–Si edges in the active pentagonal 2.216 A ˚ (4, Fig. 1) to 2.604 A ˚ in surface have elongated from 2.425 A TSw1. Although the exit barrier heights (Hexit) is not large, it is still high enough to guarantee the kinetic stability of LiC@Si20H20 cluster. 3.2. NaC@Si20H20 The initial configuration for searching transition state (TS) is the Ih symmetric structure (2, Fig. 1). The results show that the transition state (TSw2, Fig. 2) structure is larger in energy (by 99.54 kcal/mol) than that of initial structure (2, Fig. 1), and
Etot b
Hexita
K5809.46977 23.66
LiC(TS)(C5V)c
K5809.43207
LiC(iso)d NaC(endo)(Ih)
K5809.44770 K5964.24797
NaC(TS)(C5V)
K5964.08934
NaC(iso) KC(endo)(Ih)
K5964.24427 K6401.85903
KC(TS)(C5V)
K6401.56024
KC(iso) Be2C(endo)(C5V)
K6401.88803 K5816.32112
9.81
99.54 97.22
187.38 205.58
(317.41)e 2C
Be (iso) Mg2C(endo)(C5V)
K5815.81529 K6001.60489
Mg2C(TS)(C5V)
K6001.57669
Mg2C(iso)(C5V)
K6001.39039
17.70 54.16 a b c d e
The exit barrier heights(Hexit) for X expulsion from or insertion in the cage. The initial state with the endohedral structure(X@Si20H20). Transition state (TS). The final state in possession of isolated components (Si20H20CX). Binding energy: EbindZ[E(Be2C)CE(Si20H20)]KE(Be2C@Si20H20).
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187.38 kcal/mol more than that of the other endohedral structure, and therefore the KC@Si20H20 cluster is kinetically more stable than its lighter analogues. 3.4. Be2C@Si20H20
Fig. 1. Si20H20 and various initial endohedral X@Si20H20 structures.
(2, Fig. 1). In the transition state (TSw3, Fig. 2) structure, the cage deformation changes drastically. KC cation deviates from ˚ and is located near the broken face the center by 2.660 A ˚ ). Meanwhile, K and Si are (separated Si atoms by 3.309 A ˚ in the broken face. In bonded with the bond length of 2.815 A addition, the corresponding exit barrier height (Hexit) is
Obviously, Be2C cation is small enough to avoid the steric repulsion (crowding) from the cage, which is scarcely any exit barrier for Be2C expulsion from the cage, and hence the Be2C@Si20H20 cluster is expected to be the least stable structure kinetically. Indeed, the transition state structure is impossible for Be2C due to not existing stable caged state. In order to maximize the interactions between Be2C dication and cage, Be2C prefers attachment to the cage surface, where Be2C is fixed in above the center of the broken face (separated Si ˚ ) and forming a Be2C@Si20H20 minimum atoms by 2.537 A structure based on C5V-symmetry (3, Fig. 1), the distances of ˚ and the Be2C departure from the center Be–Si is 2.200 A ˚ by 3.066 A . In addition, the binding energy (Ebind), as shown in Table 2, indicating the Be2C@Si20H20 (C5V) is 317.41 kcal/mol more than its isolated component (Be2CC Si20H20), this result further reveals that the C5V-symmetry structure (3, Fig. 1) is the only energy minimum state. 3.5. Mg2C@Si20H20 Akin to the Be2C, the Mg2C dication is also unfavorable encapsulated at the cage center due to its small radius, thus its initial configuration (4, Fig. 1) has C5V symmetry, the ˚ and Mg2C dication departures from the center by1.124 A bounds to the Si atoms of broken face (separated Si atoms ˚ ). In computed transition structure (TSw4, by 2.494 A Fig. 2), the Mg2C dication is still located inside the cage (endohedral structure). Naturally, the exit of Mg2C dication via pentagonal face is accompanied by the rupture of the ˚ and by the neighboring five Si–Si edges to 2.830 A formation of the Mg–Si bond with its bond length of ˚ in the same tier. The corresponding exit barrier 2.424 A height (Hexit) is only 17.70 kcal/mol relative to initial structure (4, Fig. 1), but 54.16 kcal/mol to isolated components, Mg2C and Si20H20. In comparison, we can see the Mg2C@Si20H20 cluster has a moderate stability. 4. Conclusions
Fig. 2. B3LYP/6-31G* optimized transition state (TS) structures. Bond lengths are given in angstroms.
Our DFT calculation on the exit transition states of X@Si20H20 (XZLiC, NaC, KC, Be2C, Mg2C) complexes indicates that endohedral structures are dynamically stable except Be2C dication, and that the most favorable exit path for endohedral-isolated structure rearrangement is the migration of the X through a pentagonal cage face. Among the species, Be2C guest is not endohedrally encapsulated due to its small radius, and its exit transition state (TS) is actually not expected to be observable. While the KC cation, with the maximum caged state radius, has the most exit barrier height (Hexit) and corresponds to the most stable endohedral structure in dynamics. In comparison, other endohedral complexes have
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the moderate kinetic stabilities. The corresponding exit barrier heights (Hexit), for Mg2C, LiC, NaC and KC, are 17.70, 23.66, 99.54 and 187.38 kcal/mol, respectively, and increase with the increase of X radius. In transition states (TS) structures, the univalent cation series guests (LiC, NaC, KC) stretch the active pentagonal face roughly in proportion to their radii, their increased steric repulsion is compensated by increased the Si–Si bond lengths ˚ [LiC(TS)] to 3.309 A ˚ [KC(TS)]. However, the from 2.604 A ˚ ) is trend is somewhat different for Mg2C, its radius (0.66 A C ˚ smaller than that of Li (0.68 A), whereas the Si–Si distance ˚ ) is larger than that of LiC(2.604 A ˚ ). This can be (2.830 A ascribed to the electron transfer from the cage framework to the X guests. As shown in Table 1, the Mg2C dication accepts more electron (0.552 e) from the cage than those of cation series guests (0.287 e/LiC, 0.221 e/NaC and 0.146 e/KC, respectively), as indicated by the partial positive charges (1.448/Be, 0.713/Li, 0.779/Na and 0.854/K). This charge transfer reduces the electron density of adjacent Si atoms, namely, from K0.068/endo to K0.003/TS for Mg2C@Si20H20, and thus the Si–Si bonds become weaker and longer.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12]
Acknowledgements This work was supported by the Natural Science Foundation of China (20341005), and by the Natural Science Foundation of Shanxi Province (20011015) China.
[13] [14] [15]
K. Jackson, B. Nellermoe, Chem. Phys. Lett. 254 (1996) 249. V. Kumar, Y. Kawazoe, Phys. Rev. Lett. 87 (2001) 045503. V. Kumar, Y. Kawazoe, Phys. Rev. B 65 (2002) 073404. V. Kumar, C. Majumder, Y. Kawazoe, Chem. Phys. Lett. 363 (2002) 319. V. Kumar, Eur. Phys. J. D. 24 (2003) 227. V. Kumar, Y. Kawazoe, Appl. Phys. Lett. 80 (2002) 859. M. Ohara, K. Koyasu, A. Nakajima, K. Kaya, Chem. Phys. Lett. 371 (2003) 490. J. Lu, S. Nagase, Chem. Phys. Lett. 372 (2003) 394. F. Pichierri, V. Kumar, Y. Kawazoe, Chem. Phys. Lett. 406 (2005) 341. C.Y. Zhang, H.S. Wu, H. Jiao, Chem. Phys. Lett. 410 (2005) 457. M.J. Frish, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, Jr. R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, GAUSSIAN 98, Gaussian, Inc., Pittsburgh, PA, 1998. O.P. Charkin, N.M. Klimenko, D. Moran, A.M. Mebel, D.O. Charkin, P.v.R. Schleyer, Inorg. Chem. 40 (2001) 6913. C.W. Earley, J. Phys. Chem. A 104 (2000) 6622. H. Jiao, P.v.R. Schleyer, Y. Mo, M.A. Mcallister, T.T. Tidwell, J. Am. Chem. Soc. 119 (1997) 7075. H. Jiao, R. Nagelkerke, H.A. Kurtz, R.V. Williams, W.T. Borden, P.v.R. Schleyer, J. Am. Chem. Soc. 119 (1997) 5921.
Exit transition state of endohedral X@Si20H20 complexes (XZLiC, NaC, KC, Be2C, Mg2C) Cai-Yun Zhang *, Hai-Shun Wu Department of Chemistry, Shanxi Normal University, Linfen 041004, China Received 1 April 2006; received in revised form 22 May 2006; accepted 26 May 2006 Available online 8 June 2006
Abstract The kinetic stability of endohedral X@Si20H20 complexes (XZLiC, NaC, KC, Be2C, Mg2C) has been studied at the B3LYP/6-31G* level of density functional theory (DFT). The transition states (TS) are investigated by the QST3 method of Gaussian 98 package and demonstrated with Intrinsic reaction coordinate (IRC). It is found that KC@Si20H20 cluster has the most stable structure kinetically, that the exit barrier heights (Hexit) for KC expulsion from or insertion in the cage are 187.38 and 205.58 kcal/mol, respectively. However, the smallest Be2C dication is not endohedrally encapsulated and the Be2C@Si20H20 cluster is expected to be the least stable structure kinetically. By comparison, other endohedral complexes have a moderate kinetic stability. q 2006 Elsevier B.V. All rights reserved. Keywords: Exit transition state; Endohedral complexes; Exit barrier height; Kinetic stability
1. Introduction Recently, a novel metal encapsulated caged clusters of silicon has been studied theoretically and experimentally [1–8]. Among the issues of interest to Chemists are the character of the interaction between the heteroatom and the cage. Compared to the pure Si clusters, the doped clusters have higher stabilities, symmetries and size selectivities. Pichierri et al. [9] computed the endohedral complexes X@Si20H20 (XZ FK, ClK, BrK, IK) and observed the charge transfer from X into the cage. We reported [10] the structures and stabilities of the alkali and alkaline earth metal encapsulated in perhydrogenated silicon fullerene Si20H20, and revealed that X@Si20H20 complexes (XZLiC, NaC, KC, Be2C, Mg2C) had a minimum endohedral structure. However, these studies only characterized local minima for endohedral structures, the potential barriers for X expulsion from the cage are not predicted and the question of the kinetic stability of the endohedral isomers remaine open (i.e. which atoms inserted into the Si20H20 cage would result in kinetic stable species). In this paper, the dynamic calculation results provide the information about endohedral structure’s kinetic stability, and * Corresponding author. Tel./fax: C86 357 2051375. E-mail address: [email protected] (C.-Y. Zhang).
0166-1280/$ - see front matter q 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.theochem.2006.05.053
the prediction on the structures and stabilities of these compounds may be useful guides for the preparation and the experimental realization. 2. Computations A systematic search of transition states (TS) of the endohedral to exohedral rearrangement were carried out at the B3LYP/6-31G* level using Gaussian 98 [11], the procedure, of the time-demanding optimization with recalculation of force constants at each step [optZ(ts, calcall)] and the quadratic synchronous transit (optZqst3), was used to the saddle point optimization. TS-type corresponding to the exit of the guests from the cage via a pentagonal surface was demonstrated with Intrinsic reaction coordinate (IRC), and the related exit barrier heights (Hexit)[12] were also located at the same level. Results are presented in Tables 1 and 2. The initial endohedral structures and optimized transition states (TS) geometries for the clusters are shown in Figs. 1 and 2. 3. Results and discussions As found previously [13], the parent Si20H20 cage (1, Fig. 1) in Ih symmetry is an energy minimum structure at B3LYP/ 6-31G* level, the caged Si atoms possess an electron-deficient state (qSiZC0.100) [10] and the skeletal s-bonds is weakly. Moreover, the nucleus independent chemical shifts (NICS) [14] at the center of a Si20H20 cage face is K1.5 ppm,
146
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Table 1 ˚ ) and the radium of metal atom or metal cation (r, A ˚ ) of Selected B3LYP/6-31G* the first vibrational frequency (n1, cmK1), natural charges (q), bond lengths (R, A initial endohedral X@Si20H20 and corresponding transition state structures Structure
Sym
r(X)a
n1
qX
qSi
RbX–Si
RcSi–Si
RX-center
Li (endo) LiC(TS) NaC(endo) NaC(TS) KC(endo) KC(TS) Be2C(endo) Be2C(TS) Mg2C(endo) Mg2C(TS)
C5V C5V Ih C5V Ih C5V C5V – C5V C5V
0.68
126.4 K336.3 79.32 K235.7 141.5 K165.6 134.5 – 49.1 K144.6
0.802 0.713 0.590 0.779 0.720 0.854 1.286 – 1.721 1.448
0.015 0.044 0.083 0.664 0.081 0.131 K0.035 – K0.068 K0.003
2.590 2.216 3.354 2.425 3.368 2.815 2.200 – 2.600 2.424
2.425 2.604 2.393 2.851 2.404 3.309 2.537 – 2.494 2.830
1.082 2.604 0.000 2.617 0.000 2.660 3.066 – 1.124 2.336
C
a b c
0.97 1.33 0.35 0.66
N. N. Greenwood, A. Earnshaw, Chemistry of the Elements, second ed., Elsevier, 1997. The X–Si bond distances to the adjacent cage face. The Si–Si bond lengths of the active pentagonal surface.
compared with the NICS values at the center of benzene (K11.5 ppm) or cyclohexane (K2.1 ppm) [15], indicating a lack of cyclic electron delocalization in the five-membered ring. And the skeletal molecular orbital of Si20H20 cage does not exist conjugated p-electronic system. Therefore, the pathway for X exiting through a cage face is favorable as compared. The results further confirm that TS lie on the minimal energy pathway for expulsion of X from the cage and connect the initial endohedral structure (X@Si20H20) with the isolated components (XCSi20H20). Although all these searches are carried out without any symmetry constraints, the optimized transition structure has C5V symmetry (TS in Fig. 2). In the TS, the single imaginary frequency eigenvector is directed along the fivefold molecular axis toward the pentagonal surface.
the most favorable pathway for NaC cation exit is through the pentagonal face. In TSw2 (Fig. 2), NaC cation is fixed in the center of the broken face, and bounding to the adjacent Si atom ˚ ). However, the distances between silicon (RNa–Si: 2.425 A atoms in the active pentagonal surface have been elongated ˚ in Ih-structure (2, Fig. 1) to 2.851 A ˚ in TSw2 from 2.393 A (Fig. 2). 3.3. KC@Si20H20 As expected, the KC cation is too large to fit against a cage face, and hence the minimum structure possesses a Ih symmetry Table 2 B3LYP/6-31G* total electronic energies (Etot, a.u.) and the exit barrier heights (Hexit, kcal/mol) of initial (endo), transition state (TS) and final (iso) structures State (sym) Li (endo)(C5V) C
3.1. LiC@Si20H20 Endohedral LiC@Si20H20 structure (4, Fig. 1) is C5V symmetry and the LiC cation departs from the cage center ˚ . The calculated transition state (TSw1, Fig. 2) by 1.082 A structure converges to C5V symmetry, the corresponding exit barrier height (Hexit) for LiC expulsion from the cage is 23.66 kcal/mol. In TSw1 structure, the LiC cation is located on the fivefold axis and shifted from the initial stable point ˚ (the off-center distance is (C5V) toward a face by 1.522 A ˚ ), and formed the Li–Si bond with its bond length of 2.604 A ˚ . However, the Si–Si edges in the active pentagonal 2.216 A ˚ (4, Fig. 1) to 2.604 A ˚ in surface have elongated from 2.425 A TSw1. Although the exit barrier heights (Hexit) is not large, it is still high enough to guarantee the kinetic stability of LiC@Si20H20 cluster. 3.2. NaC@Si20H20 The initial configuration for searching transition state (TS) is the Ih symmetric structure (2, Fig. 1). The results show that the transition state (TSw2, Fig. 2) structure is larger in energy (by 99.54 kcal/mol) than that of initial structure (2, Fig. 1), and
Etot b
Hexita
K5809.46977 23.66
LiC(TS)(C5V)c
K5809.43207
LiC(iso)d NaC(endo)(Ih)
K5809.44770 K5964.24797
NaC(TS)(C5V)
K5964.08934
NaC(iso) KC(endo)(Ih)
K5964.24427 K6401.85903
KC(TS)(C5V)
K6401.56024
KC(iso) Be2C(endo)(C5V)
K6401.88803 K5816.32112
9.81
99.54 97.22
187.38 205.58
(317.41)e 2C
Be (iso) Mg2C(endo)(C5V)
K5815.81529 K6001.60489
Mg2C(TS)(C5V)
K6001.57669
Mg2C(iso)(C5V)
K6001.39039
17.70 54.16 a b c d e
The exit barrier heights(Hexit) for X expulsion from or insertion in the cage. The initial state with the endohedral structure(X@Si20H20). Transition state (TS). The final state in possession of isolated components (Si20H20CX). Binding energy: EbindZ[E(Be2C)CE(Si20H20)]KE(Be2C@Si20H20).
C.-Y. Zhang, H.-S. Wu / Journal of Molecular Structure: THEOCHEM 770 (2006) 145–148
147
187.38 kcal/mol more than that of the other endohedral structure, and therefore the KC@Si20H20 cluster is kinetically more stable than its lighter analogues. 3.4. Be2C@Si20H20
Fig. 1. Si20H20 and various initial endohedral X@Si20H20 structures.
(2, Fig. 1). In the transition state (TSw3, Fig. 2) structure, the cage deformation changes drastically. KC cation deviates from ˚ and is located near the broken face the center by 2.660 A ˚ ). Meanwhile, K and Si are (separated Si atoms by 3.309 A ˚ in the broken face. In bonded with the bond length of 2.815 A addition, the corresponding exit barrier height (Hexit) is
Obviously, Be2C cation is small enough to avoid the steric repulsion (crowding) from the cage, which is scarcely any exit barrier for Be2C expulsion from the cage, and hence the Be2C@Si20H20 cluster is expected to be the least stable structure kinetically. Indeed, the transition state structure is impossible for Be2C due to not existing stable caged state. In order to maximize the interactions between Be2C dication and cage, Be2C prefers attachment to the cage surface, where Be2C is fixed in above the center of the broken face (separated Si ˚ ) and forming a Be2C@Si20H20 minimum atoms by 2.537 A structure based on C5V-symmetry (3, Fig. 1), the distances of ˚ and the Be2C departure from the center Be–Si is 2.200 A ˚ by 3.066 A . In addition, the binding energy (Ebind), as shown in Table 2, indicating the Be2C@Si20H20 (C5V) is 317.41 kcal/mol more than its isolated component (Be2CC Si20H20), this result further reveals that the C5V-symmetry structure (3, Fig. 1) is the only energy minimum state. 3.5. Mg2C@Si20H20 Akin to the Be2C, the Mg2C dication is also unfavorable encapsulated at the cage center due to its small radius, thus its initial configuration (4, Fig. 1) has C5V symmetry, the ˚ and Mg2C dication departures from the center by1.124 A bounds to the Si atoms of broken face (separated Si atoms ˚ ). In computed transition structure (TSw4, by 2.494 A Fig. 2), the Mg2C dication is still located inside the cage (endohedral structure). Naturally, the exit of Mg2C dication via pentagonal face is accompanied by the rupture of the ˚ and by the neighboring five Si–Si edges to 2.830 A formation of the Mg–Si bond with its bond length of ˚ in the same tier. The corresponding exit barrier 2.424 A height (Hexit) is only 17.70 kcal/mol relative to initial structure (4, Fig. 1), but 54.16 kcal/mol to isolated components, Mg2C and Si20H20. In comparison, we can see the Mg2C@Si20H20 cluster has a moderate stability. 4. Conclusions
Fig. 2. B3LYP/6-31G* optimized transition state (TS) structures. Bond lengths are given in angstroms.
Our DFT calculation on the exit transition states of X@Si20H20 (XZLiC, NaC, KC, Be2C, Mg2C) complexes indicates that endohedral structures are dynamically stable except Be2C dication, and that the most favorable exit path for endohedral-isolated structure rearrangement is the migration of the X through a pentagonal cage face. Among the species, Be2C guest is not endohedrally encapsulated due to its small radius, and its exit transition state (TS) is actually not expected to be observable. While the KC cation, with the maximum caged state radius, has the most exit barrier height (Hexit) and corresponds to the most stable endohedral structure in dynamics. In comparison, other endohedral complexes have
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the moderate kinetic stabilities. The corresponding exit barrier heights (Hexit), for Mg2C, LiC, NaC and KC, are 17.70, 23.66, 99.54 and 187.38 kcal/mol, respectively, and increase with the increase of X radius. In transition states (TS) structures, the univalent cation series guests (LiC, NaC, KC) stretch the active pentagonal face roughly in proportion to their radii, their increased steric repulsion is compensated by increased the Si–Si bond lengths ˚ [LiC(TS)] to 3.309 A ˚ [KC(TS)]. However, the from 2.604 A ˚ ) is trend is somewhat different for Mg2C, its radius (0.66 A C ˚ smaller than that of Li (0.68 A), whereas the Si–Si distance ˚ ) is larger than that of LiC(2.604 A ˚ ). This can be (2.830 A ascribed to the electron transfer from the cage framework to the X guests. As shown in Table 1, the Mg2C dication accepts more electron (0.552 e) from the cage than those of cation series guests (0.287 e/LiC, 0.221 e/NaC and 0.146 e/KC, respectively), as indicated by the partial positive charges (1.448/Be, 0.713/Li, 0.779/Na and 0.854/K). This charge transfer reduces the electron density of adjacent Si atoms, namely, from K0.068/endo to K0.003/TS for Mg2C@Si20H20, and thus the Si–Si bonds become weaker and longer.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11]
[12]
Acknowledgements This work was supported by the Natural Science Foundation of China (20341005), and by the Natural Science Foundation of Shanxi Province (20011015) China.
[13] [14] [15]
K. Jackson, B. Nellermoe, Chem. Phys. Lett. 254 (1996) 249. V. Kumar, Y. Kawazoe, Phys. Rev. Lett. 87 (2001) 045503. V. Kumar, Y. Kawazoe, Phys. Rev. B 65 (2002) 073404. V. Kumar, C. Majumder, Y. Kawazoe, Chem. Phys. Lett. 363 (2002) 319. V. Kumar, Eur. Phys. J. D. 24 (2003) 227. V. Kumar, Y. Kawazoe, Appl. Phys. Lett. 80 (2002) 859. M. Ohara, K. Koyasu, A. Nakajima, K. Kaya, Chem. Phys. Lett. 371 (2003) 490. J. Lu, S. Nagase, Chem. Phys. Lett. 372 (2003) 394. F. Pichierri, V. Kumar, Y. Kawazoe, Chem. Phys. Lett. 406 (2005) 341. C.Y. Zhang, H.S. Wu, H. Jiao, Chem. Phys. Lett. 410 (2005) 457. M.J. Frish, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery, Jr. R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, GAUSSIAN 98, Gaussian, Inc., Pittsburgh, PA, 1998. O.P. Charkin, N.M. Klimenko, D. Moran, A.M. Mebel, D.O. Charkin, P.v.R. Schleyer, Inorg. Chem. 40 (2001) 6913. C.W. Earley, J. Phys. Chem. A 104 (2000) 6622. H. Jiao, P.v.R. Schleyer, Y. Mo, M.A. Mcallister, T.T. Tidwell, J. Am. Chem. Soc. 119 (1997) 7075. H. Jiao, R. Nagelkerke, H.A. Kurtz, R.V. Williams, W.T. Borden, P.v.R. Schleyer, J. Am. Chem. Soc. 119 (1997) 5921.