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Potassium orbiting in fullerene based K(C60)2 nanosystem
Journal of Molecular Structure 887 (2008) 249–252
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Potassium orbiting in fullerene based K(C60)2 nanosystem M. Sokół *, Z. Gburski, Z. Dendzik Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland
a r t i c l e
i n f o
Article history: Received 15 September 2007 Received in revised form 7 January 2008 Accepted 2 February 2008 Available online 28 March 2008 Keywords: Potassium–fullerene nanosystem Ab initio MD simulation Alkali doped fullerene Dipole moment K(C60)2
a b s t r a c t We have performed a first principle molecular dynamics (MD) simulations for the nanosystem K(C60)2, composed of two fullerene (C60) molecules and one potassium (K) atom. One can observe that at the global minimum of total energy of K(C60)2 nanosystem, the potassium atom is placed exactly between fullerene spheres. Our calculations show that a forced shift of both fullerenes closer to each other leads to substantial change of the shape of global minimum energy. The area of minimal total energy of ‘‘squeezed” K(C60)2 forms very characteristic, spatial body (torus). At low temperature (T < 50 K) the potassium atom stays at a particular place inside the minimal total energy torus and performs some small librations. When the temperature raises up to 200 K, the potassium ‘‘walks” all over the total minimum energy torus. The regular circulation of K atom over the torus-like orbit located between fullerenes results in lack of permanent dipole moment. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction In recent years, one observes an enormous activity in study of the nano-size systems. Because of the obvious difficulty of experimental preparation and measurements of nanocomposities, the molecular dynamics simulation (classical or quantum called ab initio) can be use as a valuable tool for providing an atomistically detailed description of complex molecular processes occurring in these extremely small systems. The discoveries of conducting and superconducting doped fullerides [1,2] have initiated a strong interest in experimental studding fullerene covered with alkali metals, i.e. AC60 systems (A-alkali metal atom) [3–8]. The direct motivation of our calculations was the experimental investigation (molecular deflection technique) by Rayane et al. [9] of KC60 mixture. They reported the lack of observed permanent dipole moment of KC60 sample and attributed this to the free skating of the potassium atom on the C60 surface, resulting in a statistical orientation of the electric dipole. In this note, we explore the ab initio MD technique [10] to study also the alkali metal contained nanosystem, but composed of two fullerene molecules and one potassium atom. Comparing to KC60, the K(C60)2 cluster has different symmetry and this should have the intriguing consequences as far as the motion of potassium and the dynamics of instantaneous dipole moment is concerned. We used the density-functional theory (DFT) [11,12] in its Generalized Gradient Approximation (GGA) [13–15] applying SIESTA programming code [16,17]. The core electrons were replaced by
* Corresponding author. E-mail address: [email protected] (M. Sokół). 0022-2860/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2008.02.047
normconserving pseudopotentials in their fully separable form. The non-linear exchange-correlation correction [18–20] was included for potassium atom to improve the description of the core-valence interactions. During MD run the temperature was controlled by means of Nosé thermostat. We did simulations for a several temperature: T = 50, 150, 200, 250 and 350 K. The integration time step Dt of the equation of motion was Dt = 3 fs and the MD data were collected up to 10 ps.
2. Results and discussion As mentioned in the introduction, the mixture system KC60 was studied experimentally by Rayane et al. [9]. They observed the lack of permanent dipole moment and pointed out that addition of potassium atom increases very strongly (about 20 times) the polarizability of a pure fullerene. Following their interpretation, these unusual properties of KC60 system can be explained by considering that the potassium atom (and therefore the dipole) can free move (skate) on the surface of fullerene. Our system studied K(C60)2 consists two fullerenes which determine an axial symmetry rather than the spherical one in case of single fullerene sphere in KC60. Moreover, it is known that the attractive part of fullerene–fullerene interaction potential is very strong, as a result of the high atomic density on the surface of the C60 [21]. One would like to known whether these facts would bring about some important consequences for potassium atom and dipole moment dynamics. We start by searching the equilibrium configuration of K(C60)2. We find that at the global minimum of the total energy Et of K(C60)2 nanosystem, the potassium atom is placed exactly between fullerene spheres. The distance between the centers of fullerene
250
M. Sokół et al. / Journal of Molecular Structure 887 (2008) 249–252
Fig. 1. Snapshot of simulated K(C60)2 nanosystem composed of one potassium atom (K) and two fullerene molecules (C60). Schematic view of: a) YZ plane and b) XZ plane, in which the energy map was calculated; c) schematic shape of characteristic torus formed by the area of minimal total energy of K(C60)2.
spheres in C60–K–C60 system is 13.0 Å. We were curious what happens when we shift both fullerenes closer to each other. This for example could be done with the help of carbon nanotubes, used as
a source of a squeezing force [22]. For that matter, first we find the equilibrium configuration of the pair of fullerenes only (without potassium). The distance between the centers of fullerene spheres
Fig. 2. Contour plots of Et (minimal total energy of K(C60)2) for various positions of potassium atom in YZ and XZ plains (color online).
M. Sokół et al. / Journal of Molecular Structure 887 (2008) 249–252
Fig. 3. The adsorption energy as a function of the distance in XZ plane between potassium atom and the center of mass of both fullerene molecules.
in C60–C60 system is 9.6 Å. Next, we construct the total energy Et map of K(C60)2 system by frizzing the fullerenes in their, previously
251
found, equilibrium positions and put the potassium atom in the chosen places. Particularly, due to the symmetry of the system, we made the total energy calculation of K(C60)2 varying the positions of potassium atom by 0.3 Å in YZ and XZ plains (see Fig. 1a and b). The contour plots of Et for various positions of potassium in YZ and XZ plains are shown in Fig. 2. One can see that the area of minimal total energy forms a spatial figure similar to torus, perpendicular to the axis connecting the centers of mass of C60 molecules (see Fig. 1c). The adsorption energy Ea is defined as the total energy gained by (C60)2 system due to addition of the potassium, Ea = Et[K(C60)2] Et[(C60)2] Et[K] (where Et[X] means total energy of molecule/atom X). The binding curve for K atom adsorbed by (C60)2 cluster is shown in Fig. 3. For the potassium atom placed in the torus at the distance 4.5 Å above the middle of the axis connecting the centers of mass of C60 molecules (equilibrium configuration for squeezed system), we obtained Ea = 1.923 ± 0.04 eV. The calculated adsorption energy of K(C60)2 in its equilibrium configuration (total energy global minimum) is smaller Ea = 2.343 ± 0.04 eV. We have rather interesting situation in this system, the adsorption energy is quite substantial, and the area of minimal total energy forms very characteristic spatial body (torus).
Fig. 4. Contour plots of charge density of: a) two fullerene molecules without potassium atom and b) two fullerene molecules with an addition of potassium atom. The potassium atom is placed at (0, 4.5 Å) coordinates in its equilibrium configuration for squeezed system K(C60)2 (color online).
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M. Sokół et al. / Journal of Molecular Structure 887 (2008) 249–252
Fig. 5. The trace of an orbital motion of the potassium atom in K(C60)2 nanosystem at temperature T = 200 K (color online).
We have also calculated the charge density, both for pure fullerene cluster (C60)2 and for K(C60)2 system (Fig. 4). The addition of potassium atom modifies only very slightly charge density distribution. This happens because the only one unbound (4s1) electron is shared between both fullerene molecules. Additionally we made the Mulliken population analysis which confirms an evenly dispersion of potassium 4s1 valence electron over both fullerenes. Losing one electron the potassium atom in practice becomes an ion (K+). Exactly speaking only the charge q = 0.131 e remains within potassium atom. The calculated electric dipole moment of the squeezed system is quite large, l=|l| = 10.7 D (Debye). Naturally, one would like to know about the dynamics of such an intriguing nanoscale system. Particularly, can the potassium atom revolve/circulate over the toruslike orbit? For that matter, we made several first principle MD simulations, beginning with the simulation at the low temperature T = 50 K. We have observed that at this low temperature the potassium stays at a particular place inside the minimal total energy torus and performs some small librations. The increasing of temperature should activate the migration (diffusion) of potassium all over the total minimum energy torus. When we increase the temperature up to T = 200 K, the potassium leaves his place and walks all over the total minimum energy torus (see Fig. 5). At this temperature, K atom has enough kinetic energy to move over the torus, but its kinetic energy is too small to allow him to leave the torus. Circulation of potassium atom (in fact K+ ion) leads to vanishing of permanent dipole moment. We have observed that at T P 250 K potassium escapes from the torus and slides randomly (skates) over the surfaces of fullerenes. In conclusion, our calculations show that at low temperatures (near 0 K) the calculated electric dipole moment of the sample is
different from zero and quite substantial (l = 10.7 D). The diffusion of potassium over the torus-like orbit located between fullerenes can be expected for T 200 K while the random skating of K atom over the surfaces of fullerenes should appear for T P 250 K. The orbiting or skating of potassium in K(C60)2 nanosystem should leads to the vanishing of the permanent dipole moment of the sample.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
R.C. Haddon et al., Nature (London) 350 (1991) 320. D.W. Murphy et al., J. Phys. Chem. Solids 53 (1992) 1321. S. Wehrli, E. Koch, M. Sigrist, Phys. Rev. B 68 (2003) 115412. B. Verberck, V.N. Popov, A.V. Nikolaev, D. Lamoen, J. Chem. Phys. 121 (2004) 321. A.V. Nikolaev, K.H. Michel, J. Chem. Phys. 122 (2005) 64310. A. Dawid, Z. Gburski, Phys. Rev. A 56 (1997) 3294. A. Dawid, Z. Gburski, J. Mol. Struct. 410 (1997) 507. A. Dawid, Z. Gburski, J. Mol. Struct. 704 (2004) 287. D. Rayane et al., Phys. Rev. Lett. 84 (2000) 1962. R. Car, M. Parrinello, Phys. Rev. Lett. 55 (1985) 2471. P. Hohenbergand, W. Kohn, Phys. Rev. 136 (1964) 864. W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133. A.D. Becke, Phys. Rev. A 38 (1988) 3098. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. P. Ordejón, E. Artacho, J.M. Soler, Phys. Rev. B (Rapid Commun.) 53 (1996) R10441. J.M. Soler, E. Artacho, J.D. Gale, A. García, J. Junquera, P. Ordejón, D. SánchezPortal, J. Phys. Condens. Matter 14 (2002) 2745. L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48 (1982) 1425. S.G. Louie, S. Froyen, M.L. Cohen, Phys. Rev. B 26 (1982) 1738. N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. L. Liwei, D. Bedrov, G.D. Smith, Phys. Rev. E. 71 (2005) 011502. A.G. Nasibulin, P.V. Pikhitsa, Hua Jiang, D.P. Brown, A.V. Krasheninnikov, A.S. Anisimov, P. Queipo, A. Moisala, D. Gonzalez, G. Lientschnig, A. Hassanien, S.D. Shandakov, G. Lolli, D.E. Resasco, M. Choi, D. Tománek, E.I. Kauppinen, Nat. Nanotechnol. 2 (2006) 156.
Contents lists available at ScienceDirect
Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc
Potassium orbiting in fullerene based K(C60)2 nanosystem M. Sokół *, Z. Gburski, Z. Dendzik Institute of Physics, University of Silesia, Uniwersytecka 4, 40-007 Katowice, Poland
a r t i c l e
i n f o
Article history: Received 15 September 2007 Received in revised form 7 January 2008 Accepted 2 February 2008 Available online 28 March 2008 Keywords: Potassium–fullerene nanosystem Ab initio MD simulation Alkali doped fullerene Dipole moment K(C60)2
a b s t r a c t We have performed a first principle molecular dynamics (MD) simulations for the nanosystem K(C60)2, composed of two fullerene (C60) molecules and one potassium (K) atom. One can observe that at the global minimum of total energy of K(C60)2 nanosystem, the potassium atom is placed exactly between fullerene spheres. Our calculations show that a forced shift of both fullerenes closer to each other leads to substantial change of the shape of global minimum energy. The area of minimal total energy of ‘‘squeezed” K(C60)2 forms very characteristic, spatial body (torus). At low temperature (T < 50 K) the potassium atom stays at a particular place inside the minimal total energy torus and performs some small librations. When the temperature raises up to 200 K, the potassium ‘‘walks” all over the total minimum energy torus. The regular circulation of K atom over the torus-like orbit located between fullerenes results in lack of permanent dipole moment. Ó 2008 Elsevier B.V. All rights reserved.
1. Introduction In recent years, one observes an enormous activity in study of the nano-size systems. Because of the obvious difficulty of experimental preparation and measurements of nanocomposities, the molecular dynamics simulation (classical or quantum called ab initio) can be use as a valuable tool for providing an atomistically detailed description of complex molecular processes occurring in these extremely small systems. The discoveries of conducting and superconducting doped fullerides [1,2] have initiated a strong interest in experimental studding fullerene covered with alkali metals, i.e. AC60 systems (A-alkali metal atom) [3–8]. The direct motivation of our calculations was the experimental investigation (molecular deflection technique) by Rayane et al. [9] of KC60 mixture. They reported the lack of observed permanent dipole moment of KC60 sample and attributed this to the free skating of the potassium atom on the C60 surface, resulting in a statistical orientation of the electric dipole. In this note, we explore the ab initio MD technique [10] to study also the alkali metal contained nanosystem, but composed of two fullerene molecules and one potassium atom. Comparing to KC60, the K(C60)2 cluster has different symmetry and this should have the intriguing consequences as far as the motion of potassium and the dynamics of instantaneous dipole moment is concerned. We used the density-functional theory (DFT) [11,12] in its Generalized Gradient Approximation (GGA) [13–15] applying SIESTA programming code [16,17]. The core electrons were replaced by
* Corresponding author. E-mail address: [email protected] (M. Sokół). 0022-2860/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2008.02.047
normconserving pseudopotentials in their fully separable form. The non-linear exchange-correlation correction [18–20] was included for potassium atom to improve the description of the core-valence interactions. During MD run the temperature was controlled by means of Nosé thermostat. We did simulations for a several temperature: T = 50, 150, 200, 250 and 350 K. The integration time step Dt of the equation of motion was Dt = 3 fs and the MD data were collected up to 10 ps.
2. Results and discussion As mentioned in the introduction, the mixture system KC60 was studied experimentally by Rayane et al. [9]. They observed the lack of permanent dipole moment and pointed out that addition of potassium atom increases very strongly (about 20 times) the polarizability of a pure fullerene. Following their interpretation, these unusual properties of KC60 system can be explained by considering that the potassium atom (and therefore the dipole) can free move (skate) on the surface of fullerene. Our system studied K(C60)2 consists two fullerenes which determine an axial symmetry rather than the spherical one in case of single fullerene sphere in KC60. Moreover, it is known that the attractive part of fullerene–fullerene interaction potential is very strong, as a result of the high atomic density on the surface of the C60 [21]. One would like to known whether these facts would bring about some important consequences for potassium atom and dipole moment dynamics. We start by searching the equilibrium configuration of K(C60)2. We find that at the global minimum of the total energy Et of K(C60)2 nanosystem, the potassium atom is placed exactly between fullerene spheres. The distance between the centers of fullerene
250
M. Sokół et al. / Journal of Molecular Structure 887 (2008) 249–252
Fig. 1. Snapshot of simulated K(C60)2 nanosystem composed of one potassium atom (K) and two fullerene molecules (C60). Schematic view of: a) YZ plane and b) XZ plane, in which the energy map was calculated; c) schematic shape of characteristic torus formed by the area of minimal total energy of K(C60)2.
spheres in C60–K–C60 system is 13.0 Å. We were curious what happens when we shift both fullerenes closer to each other. This for example could be done with the help of carbon nanotubes, used as
a source of a squeezing force [22]. For that matter, first we find the equilibrium configuration of the pair of fullerenes only (without potassium). The distance between the centers of fullerene spheres
Fig. 2. Contour plots of Et (minimal total energy of K(C60)2) for various positions of potassium atom in YZ and XZ plains (color online).
M. Sokół et al. / Journal of Molecular Structure 887 (2008) 249–252
Fig. 3. The adsorption energy as a function of the distance in XZ plane between potassium atom and the center of mass of both fullerene molecules.
in C60–C60 system is 9.6 Å. Next, we construct the total energy Et map of K(C60)2 system by frizzing the fullerenes in their, previously
251
found, equilibrium positions and put the potassium atom in the chosen places. Particularly, due to the symmetry of the system, we made the total energy calculation of K(C60)2 varying the positions of potassium atom by 0.3 Å in YZ and XZ plains (see Fig. 1a and b). The contour plots of Et for various positions of potassium in YZ and XZ plains are shown in Fig. 2. One can see that the area of minimal total energy forms a spatial figure similar to torus, perpendicular to the axis connecting the centers of mass of C60 molecules (see Fig. 1c). The adsorption energy Ea is defined as the total energy gained by (C60)2 system due to addition of the potassium, Ea = Et[K(C60)2] Et[(C60)2] Et[K] (where Et[X] means total energy of molecule/atom X). The binding curve for K atom adsorbed by (C60)2 cluster is shown in Fig. 3. For the potassium atom placed in the torus at the distance 4.5 Å above the middle of the axis connecting the centers of mass of C60 molecules (equilibrium configuration for squeezed system), we obtained Ea = 1.923 ± 0.04 eV. The calculated adsorption energy of K(C60)2 in its equilibrium configuration (total energy global minimum) is smaller Ea = 2.343 ± 0.04 eV. We have rather interesting situation in this system, the adsorption energy is quite substantial, and the area of minimal total energy forms very characteristic spatial body (torus).
Fig. 4. Contour plots of charge density of: a) two fullerene molecules without potassium atom and b) two fullerene molecules with an addition of potassium atom. The potassium atom is placed at (0, 4.5 Å) coordinates in its equilibrium configuration for squeezed system K(C60)2 (color online).
252
M. Sokół et al. / Journal of Molecular Structure 887 (2008) 249–252
Fig. 5. The trace of an orbital motion of the potassium atom in K(C60)2 nanosystem at temperature T = 200 K (color online).
We have also calculated the charge density, both for pure fullerene cluster (C60)2 and for K(C60)2 system (Fig. 4). The addition of potassium atom modifies only very slightly charge density distribution. This happens because the only one unbound (4s1) electron is shared between both fullerene molecules. Additionally we made the Mulliken population analysis which confirms an evenly dispersion of potassium 4s1 valence electron over both fullerenes. Losing one electron the potassium atom in practice becomes an ion (K+). Exactly speaking only the charge q = 0.131 e remains within potassium atom. The calculated electric dipole moment of the squeezed system is quite large, l=|l| = 10.7 D (Debye). Naturally, one would like to know about the dynamics of such an intriguing nanoscale system. Particularly, can the potassium atom revolve/circulate over the toruslike orbit? For that matter, we made several first principle MD simulations, beginning with the simulation at the low temperature T = 50 K. We have observed that at this low temperature the potassium stays at a particular place inside the minimal total energy torus and performs some small librations. The increasing of temperature should activate the migration (diffusion) of potassium all over the total minimum energy torus. When we increase the temperature up to T = 200 K, the potassium leaves his place and walks all over the total minimum energy torus (see Fig. 5). At this temperature, K atom has enough kinetic energy to move over the torus, but its kinetic energy is too small to allow him to leave the torus. Circulation of potassium atom (in fact K+ ion) leads to vanishing of permanent dipole moment. We have observed that at T P 250 K potassium escapes from the torus and slides randomly (skates) over the surfaces of fullerenes. In conclusion, our calculations show that at low temperatures (near 0 K) the calculated electric dipole moment of the sample is
different from zero and quite substantial (l = 10.7 D). The diffusion of potassium over the torus-like orbit located between fullerenes can be expected for T 200 K while the random skating of K atom over the surfaces of fullerenes should appear for T P 250 K. The orbiting or skating of potassium in K(C60)2 nanosystem should leads to the vanishing of the permanent dipole moment of the sample.
References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
R.C. Haddon et al., Nature (London) 350 (1991) 320. D.W. Murphy et al., J. Phys. Chem. Solids 53 (1992) 1321. S. Wehrli, E. Koch, M. Sigrist, Phys. Rev. B 68 (2003) 115412. B. Verberck, V.N. Popov, A.V. Nikolaev, D. Lamoen, J. Chem. Phys. 121 (2004) 321. A.V. Nikolaev, K.H. Michel, J. Chem. Phys. 122 (2005) 64310. A. Dawid, Z. Gburski, Phys. Rev. A 56 (1997) 3294. A. Dawid, Z. Gburski, J. Mol. Struct. 410 (1997) 507. A. Dawid, Z. Gburski, J. Mol. Struct. 704 (2004) 287. D. Rayane et al., Phys. Rev. Lett. 84 (2000) 1962. R. Car, M. Parrinello, Phys. Rev. Lett. 55 (1985) 2471. P. Hohenbergand, W. Kohn, Phys. Rev. 136 (1964) 864. W. Kohn, L.J. Sham, Phys. Rev. 140 (1965) A1133. A.D. Becke, Phys. Rev. A 38 (1988) 3098. C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. P. Ordejón, E. Artacho, J.M. Soler, Phys. Rev. B (Rapid Commun.) 53 (1996) R10441. J.M. Soler, E. Artacho, J.D. Gale, A. García, J. Junquera, P. Ordejón, D. SánchezPortal, J. Phys. Condens. Matter 14 (2002) 2745. L. Kleinman, D.M. Bylander, Phys. Rev. Lett. 48 (1982) 1425. S.G. Louie, S. Froyen, M.L. Cohen, Phys. Rev. B 26 (1982) 1738. N. Troullier, J.L. Martins, Phys. Rev. B 43 (1991) 1993. L. Liwei, D. Bedrov, G.D. Smith, Phys. Rev. E. 71 (2005) 011502. A.G. Nasibulin, P.V. Pikhitsa, Hua Jiang, D.P. Brown, A.V. Krasheninnikov, A.S. Anisimov, P. Queipo, A. Moisala, D. Gonzalez, G. Lientschnig, A. Hassanien, S.D. Shandakov, G. Lolli, D.E. Resasco, M. Choi, D. Tománek, E.I. Kauppinen, Nat. Nanotechnol. 2 (2006) 156.