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International Journal of Research in Engineering and Science (IJRES)
ISSN (Online): 2320-9364, ISSN (Print): 2320-9356
www.ijres.org Volume 1 Issue 1 ǁ May. 2013 ǁ PP.36-47
www.ijres.org 36 | Page
Transition from Carbon Nanoballs to Nanocapsules With
Reference To Structural and Molecular Electronic Properties
Mudassir M. Husain
Physics Section, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology,
Jamia Millia Islamia, New Delhi-110025, India.
Abstract: We have investigated theoretically the variation in energetics and electronic properties during the
gradual transition from spherical or nearly spherical form (as in case of armchair) to capsule formation. The
zigzag and armchair configurations of carbon nanostructures with different length to diameter (l/d) ratio have
been studied. Zigzag C80 and (9,0) single wall nanocapsules, armchair C70 and (5,5) carbon nanocapsules (Cncs)
system have been theoretically investigated. We have used semi-empirical molecular orbital method, at the level
of PM3 type quantum mechanical model. The geometry of these molecular systems has been suitably
optimized. The parameters studied are various molecular properties, energy values, frontier orbital (HOMO and
LUMO) energies, heats of formation, interfrontier energy gap ( gE ), density of states (DOS), electron
difference density (EDD) and electrostatic difference potential (EDP) of the capsules. The structures studied
were found to be stable with a minimum energy band gap respectively of 3.73 and 4.66 eV, in case of zigzag
and armchair configuration and exhibit insulating properties.
PACS: 31.10.+z, 31.15.-p, 31.15.bu,31.15.ae, 31.15.ap
Keywords: Carbon nanocapsule, frontier orbitals, density of states (DOS), electron difference density
(EDD), electrostatic difference potential (EDP).
I. Introduction
Since 1990, fullerene research has blossomed in a number of different directions and has attracted a
great deal of attention to the area of Carbon Science. Carbon based nano materials like fullerenes [1], nanotubes
[2], nanocones [3, 4] have enormous potential of application due to their unique physical, chemical, mechanical,
electrical and electronic properties. The term “nanocapsules” (and nanoencapsulation”) emerged in literature
for carbon encapsulating materials at the beginning of 1990s [5-9]. The study of structure and physical
properties of the nanocapsules has become important due to the increasing relevance of the field of nanoscience
and nanotechnology [10]. During the last few years, there has been intense activity in the field of nanocapsules,
both theoretical and experimental. Şakir et al. [11] applied semi-empirical method (PM3) in order to explore the
structure and electronic properties of lithium endohedral doped carbon nanocapsules. Structural and electronic
properties of nLi and nLi+
(n =1-3) doped mono-vacancy defected carbon nanocapsules systems were
investigated theoretically by semi-empirical and DFT methods [12]. Multifunctional metal-doped carbon
nanocapsules (which have applications in molecular electronics, catalysis, light harvesting and nanomechanics)
have been investitigated theoretically [13]. Suytein et al. [14] suggested that nanocapsules have an edge over
other nanostructures, for adsorption of hydrogen gas in adsorption conditions and its storage in normal
conditions. The analysis of the process responsible for nanocapsule charging with methane (storage and
desorption) has also been reported [15]. On the basis of first-principles simulation of encapsulation of molecular
hydrogen in C120 nanocapsules, Ganji [16] predicted that the hydrogen adsorptive capacity of C120
nanocapsules was higher than that of C60. Ganji et al. [17] theoretically studied the hydrogen storage capacity
of C120 nanocapsules using density functional theory (DFT), On the basis of their findings they suggested that
the C120 nanocapsules were a novel material for energy storage. It is obvious from these events that it is crucial
to explore the structure and electronic properties of different nanosized capsules. They may used for storing
different gases (hydrogen, methane and noble gases) and have other potential applications.
II. Computational technique
Initially zigzag C80, armchair C70 carbon nanoballs and zigzag (9,0), armchair (5,5) carbon
nanocapsules are constructed. Fig. 1 shows the shortest and the longest structures while Fig. 2 shows the
intermediate zigzag systems. In a related context, Fig. 3 shows the shortest and the longest structures, while
Fig. 4 shows the intermediate armchair carbon nanostructures, under investigation. These structures has been
optimized by parametric model 3 (PM3) which is a semiempirical method [18]. It may be noted that PM3 is a
very reliable method to predict the molecular geometries and estimate the heat of formation of carbon system.
As far as speed is concerned, it is a fast computational method as compared to ab initio and DFT techniques
Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular
www.ijres.org 37 | Page
[19]. This method applied to ground state conformations of nitrogen and boron substituted fullerenes shows
good agreement with ab initio results [20]. The dimensions of the systems studied have been indicated in the
relevant figures. Initially, the geometry of all the systems was optimized classically, using molecular mechanics
(MM) method [21] taking into consideration mm+ force field [22]. This initial steps makes it easier to perform
full optimization by quantum mechanical methods. The next step is to subject these classically optimized
systems to geometry optimization using self-consistent field molecular orbital at Parametic Method (PM3)
level, in restricted Harte-Fock (RHF) formalism [23]. The Polak-Ribiere optimizer was used in geometry
optimization. The convergence criterion employed was that the gradient magnitude should become less than
3
100.1 
 kcal/Å mol . The entire calculation was performed in ground state of the system in its singlet state
configuration. The calculations were done using HyperChem 7.51 [24 ] package program. Quantumwise
Atomistics program [25] is used for calculating the density of states (DOS), Electron difference density (EDD)
and electrostatic difference potential (EDP).
Fig. 1. Optimized structure of zzC80 and zzCnc4.
0.82 nm
0.82 nm
0.79 nm
1.65 nm
Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular
www.ijres.org 38 | Page
Fig. 2. Optimized structures of zigzag carbon nanocapsules.
Table 1. Calculated Energy (in kcal/mol unless otherwise stated) of zzC80 and(9,0) zigzag carbon nanocapsules
.
Quantity zzC80 zzCnc-1 zzCnc-2 zzCnc-3 zzCnc-4
Total no. of atoms 80 100 120 140 160
l/d 1.00 1.23 1.53 1.79 2.10
Total energy -217943.00 -272479.34 -327063.03 -381678.22 -436442.85
Binding energy -1237.00 -15971.83 -19254.03 -22567.71 -26030.84
Isolated atomic energy -205206.00 -256507.50 -307809.00 -359110.50 -410412.00
Electronic energy -
3617915.00
-5147180.22 -
6845360.50
-
8695216.00
-10646513.81
Core-core interaction 3399972.03 4874700.88 6518297.35 8313541.53 10210070.96
Heat of formation 934.200 1117.165 1252.772 1356.89 1311.55
HOMO (eV) -9.098 -8.385 -8.311 -8.2136 -8.957
LUMO (eV) -3.36 -4.516 -4.525 -4.482 -3.060
ΔEg(eV) 5.73 3.87 3.79 3.73 5.89
l/d: length to diameter ratio
i) zzCnc-1
ii) zzCnc-2
iii) zzCnc-3
iv) End cap view of zzCnc
0.81 nm
1.00 nm
1.23 nm
0.80 nm
0.79 nm
1.42 nm
Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular
www.ijres.org 39 | Page
Fig. 3. Optimized structure of acC70 and acCnc-4.
Fig. 4. Optimized structures of armchair carbon nanocapsules (PM3 results).
i) acCnc-1
ii) acCnc-2
iii) acCnc-3
iv) End cap view of acCnc
0.70 nm
0.92 nm
1.19 nm
0.68 nm
1.41 nm
0.67 nm
0.73 nm
0.83 nm
0.62 nm
1.35 nm
Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular
www.ijres.org 40 | Page
Table 2. Calculated Energy (in kcal/mol unless otherwise stated) of acC70 and (5,5) armchair carbon
nanocapsules .
Quantity acC70 acCnc-1 acCnc-2 acCnc-3 acCnc-4
Total no. of atoms 70 80 100 120 130
l/d 1.11 1.30 1.75 2.10 2.19
Total energy -190667.31 -217920.38 -272508.91 -327097.13 -354483.09
Binding energy -11112.07 -12714.38 -16001.41 -19255.11 -21023.34
Isolated atomic energy -179555.25 -205206.00 -256507.50 -307809.00 -333459.75
Electronic energy -2938431.88 -
3632786.25
-5151395.50 -
6628044.50
-
7697149.38
Core-core interaction 2747764.57 3414865.83 4878886.88 6500947.21 7342666.29
Heat of formation 850.23 956.819 1087.587 1218.69 1192.35
HOMO (eV) -9.74 -8.37 -8.44 -8.24 -9.41
LUMO (eV) -2.72 -3.7098 -3.395 -3.065 -2.52
ΔEg(eV) 7.02 4.66 5.05 5.18 6.89
l/d: length to diameter ratio
(i)
Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular
www.ijres.org 41 | Page
(ii)
Fig. 5. Variation of the energy band gap (i) and heat of formation (ii) on moving from spherical to
capsule formation.
(i)
Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular
www.ijres.org 42 | Page
(ii)
Fig. 6. Variation of the energy band gap (i) and heat of formation (ii) on moving from spherical to
capsule formation in armchair configuration
III. Results and discussion
To investigate the structural and electronic properties of single wall carbon nanocapsules (SWCncs),
both zigzag and armchair configurations were constructed. These structures were then optimized using PM3
method; the advantages of choosing this method and the details of calculation have already been discussed
above. The length to diameter ( )/ dl ratio for these zigzag and armchair systems lies in the range 1.00 - 2.10,
and 1.11 - 2.19 respectively. These ranges are chosen because they exhibit the variation of structural and
electronic parameters when the carbon nanostructures undergo shape (spherical to capsule) and size
transformation.
3.1. Zigzag naostructures
We have considered zzC80 as the smallest zigzag nanostructure, then gradually increase its length, by
adding successively one unit of single wall carbon nanotube (9,0), so as to form a nanocapsule. The various
carbon nanocapsule systems in zigzag configuration are denoted by zzCnc-1(100), zzCnc-2 (120), zzCnc-3
(140) and zzCnc-4 (160); the value inside the brackets denotes the number of atoms in that particular system.
The PM3 optimized geometry of the shortest (zzC80) and the longest (zzCnc-4) zigzag nanostuctrues; and the
intermediate structures between these two extremes of this class are illustrated in figures (Fig. 1-2). The
dimensions of the systems are also mentioned in these figures. The length to diameter ( )/ dl ratio for these
nanostructure systems lies in the range 1.00-2.10. A ratio of 1.00 characterises zzC80 which is spherical in shape.
The different molecular properties calculated for these five zigzag nanostructures, alongwith some
thermodynamical properties of the systems such as total energy, binding energy, isolated atomic energy,
electronic energy, core-core interaction and heat of formation are presented, in Table 1. Fig. 5 (i) shows the
variation of energy band gap with the size of the systems. The smallest system zzC80 has a band gap of 5.73
eV. The gap decreases rapidly as the system undergoes structural change and forms a capsule. For zzCnc-3 the
energy band gap has the lowest value of 3.73 eV. This value is the minimum as compared other members and
shows that this system is most reactive. The energy band gap then again rises for zzCnc-4 and exceeds that of
zzC80. The heat of formation )( fH for these systems is positive, indicating that the process of formation is
endothermic. Fig. 5(ii) shows the plot of heat of formation for various zigzag structures, the heat of formation is
Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular
www.ijres.org 43 | Page
least for zzC80 i.e. 934.20 kcal/mol. It then increases and reaches its maximum value for zzCnc-3 and further
shows a decreasing trend. The carbon nanocapsule zzCnc-3 (which has smallest gE energy band gap) has the
maximum value of fH . Fig. 7 shows a comparison of the density of states for spherical and capsule form.
The 2-D plot of electron density difference and electrostatic difference potential are shown in Fig. 8 (a,b) and
(c,d) respectively. These plots shows some interesting features, the negative charge is developed along the walls
and the a positive charge on the ends of the capsules.
3.2. Armchair nanostuctures
The members of this group are denoted by acC70 , acCnc-1(80), acCnc-2(100), acCnc-3(120) and
acCnc-4(130). Table 2 displays the PM3 calculated values of structural, electronic and thermodynamic
properties of armchair carbon nanostructures. The smallest member of this group is acC70 , for which dl / ratio
is 1.11; and it is not completely spherical. Fig 6(i) shows the plot of gE of these structures. It is observed that
the energy band gap for acC70 is the maximum (7.02 eV). As the system undergoes shape transformation and
forms a capsule, the energy band immediately becomes a minimum (4.66 eV) for acCnc-1. Then it again
increases as the length of the capsules increases and for the longest capsule (acCnc-4), the energy band gap
becomes 6.89eV. In this configuration, as the capsule is formed from nearly spherical structure; there is a sharp
dip in energy band gap which is different from the zigzag case. In zigzag, the energy attains a minimum value
for zzCnc-3 and not for zzCnc-1. The more reactive member in this case is acCnc-1. The process of armchair
structure formation here is again endothermic, as the heat of formation is positive; although the values are lower
as compared to zigzag structures. The trend of heat of formation for armchair Fig. 6(ii) is similar to that of
zigzag structures, it first increases, reaches a maximum and then decreases. Fig. 8 shows a comparison of the
density of states for spherical and capsule form in case of armchair configuration. The 2-D plot of electron
density difference and electrostatic difference potential are shown in Fig. 10 (a,b) and (c,d) respectively.
Fig. 7. Density of states (DOS) of zizzag spherical and capsule structures.
Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular
www.ijres.org 44 | Page
Fig. 9. Density of states (DOS) of armchair spherical and capsule structures.
(a) (b)
Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular
www.ijres.org 45 | Page
(c) (d)
Fig. 8. Electron difference density (a,b) and electrostatic difference potential (c,d) of zigzag structures
(a) (b)
Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular
www.ijres.org 46 | Page
(b) (d)
Fig. 10. Electron difference density (a,b) and electrostatic difference potential (c,d) of armchair structures
IV. Conclusions
To summarize, we have carried out theoretical investigations by performing PM3 semi-empirical
molecular orbital calculations, in the context of RHF type quantum chemical treatment. The purpose has been
to explore the variation in structural, electronic and thermodynamical properties; when these systems undergo
shape and size transformation. We have observed that the energy band gap and heat of formation follow definite
trends; as size is varied; both in zigzag and armchair configurations. The band gap in case of armchair carbon
nanocapsules is greater than that in zigzag form; establishing that zigzag form of fullerenes or capsules are more
reactive.
References
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H2 molecules and B-, N- and Si doped C60. Physica E 2009, 41, 1406-1409.
[17] Ganji, M. D.; Valizadeh, G.; Jahan-tigh, M. Hydrogen storage capacity of C120 nanocapsules:
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Transition from Carbon Nanoballs to Nanocapsules

  • 1. International Journal of Research in Engineering and Science (IJRES) ISSN (Online): 2320-9364, ISSN (Print): 2320-9356 www.ijres.org Volume 1 Issue 1 ǁ May. 2013 ǁ PP.36-47 www.ijres.org 36 | Page Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular Electronic Properties Mudassir M. Husain Physics Section, Department of Applied Sciences and Humanities, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi-110025, India. Abstract: We have investigated theoretically the variation in energetics and electronic properties during the gradual transition from spherical or nearly spherical form (as in case of armchair) to capsule formation. The zigzag and armchair configurations of carbon nanostructures with different length to diameter (l/d) ratio have been studied. Zigzag C80 and (9,0) single wall nanocapsules, armchair C70 and (5,5) carbon nanocapsules (Cncs) system have been theoretically investigated. We have used semi-empirical molecular orbital method, at the level of PM3 type quantum mechanical model. The geometry of these molecular systems has been suitably optimized. The parameters studied are various molecular properties, energy values, frontier orbital (HOMO and LUMO) energies, heats of formation, interfrontier energy gap ( gE ), density of states (DOS), electron difference density (EDD) and electrostatic difference potential (EDP) of the capsules. The structures studied were found to be stable with a minimum energy band gap respectively of 3.73 and 4.66 eV, in case of zigzag and armchair configuration and exhibit insulating properties. PACS: 31.10.+z, 31.15.-p, 31.15.bu,31.15.ae, 31.15.ap Keywords: Carbon nanocapsule, frontier orbitals, density of states (DOS), electron difference density (EDD), electrostatic difference potential (EDP). I. Introduction Since 1990, fullerene research has blossomed in a number of different directions and has attracted a great deal of attention to the area of Carbon Science. Carbon based nano materials like fullerenes [1], nanotubes [2], nanocones [3, 4] have enormous potential of application due to their unique physical, chemical, mechanical, electrical and electronic properties. The term “nanocapsules” (and nanoencapsulation”) emerged in literature for carbon encapsulating materials at the beginning of 1990s [5-9]. The study of structure and physical properties of the nanocapsules has become important due to the increasing relevance of the field of nanoscience and nanotechnology [10]. During the last few years, there has been intense activity in the field of nanocapsules, both theoretical and experimental. Şakir et al. [11] applied semi-empirical method (PM3) in order to explore the structure and electronic properties of lithium endohedral doped carbon nanocapsules. Structural and electronic properties of nLi and nLi+ (n =1-3) doped mono-vacancy defected carbon nanocapsules systems were investigated theoretically by semi-empirical and DFT methods [12]. Multifunctional metal-doped carbon nanocapsules (which have applications in molecular electronics, catalysis, light harvesting and nanomechanics) have been investitigated theoretically [13]. Suytein et al. [14] suggested that nanocapsules have an edge over other nanostructures, for adsorption of hydrogen gas in adsorption conditions and its storage in normal conditions. The analysis of the process responsible for nanocapsule charging with methane (storage and desorption) has also been reported [15]. On the basis of first-principles simulation of encapsulation of molecular hydrogen in C120 nanocapsules, Ganji [16] predicted that the hydrogen adsorptive capacity of C120 nanocapsules was higher than that of C60. Ganji et al. [17] theoretically studied the hydrogen storage capacity of C120 nanocapsules using density functional theory (DFT), On the basis of their findings they suggested that the C120 nanocapsules were a novel material for energy storage. It is obvious from these events that it is crucial to explore the structure and electronic properties of different nanosized capsules. They may used for storing different gases (hydrogen, methane and noble gases) and have other potential applications. II. Computational technique Initially zigzag C80, armchair C70 carbon nanoballs and zigzag (9,0), armchair (5,5) carbon nanocapsules are constructed. Fig. 1 shows the shortest and the longest structures while Fig. 2 shows the intermediate zigzag systems. In a related context, Fig. 3 shows the shortest and the longest structures, while Fig. 4 shows the intermediate armchair carbon nanostructures, under investigation. These structures has been optimized by parametric model 3 (PM3) which is a semiempirical method [18]. It may be noted that PM3 is a very reliable method to predict the molecular geometries and estimate the heat of formation of carbon system. As far as speed is concerned, it is a fast computational method as compared to ab initio and DFT techniques
  • 2. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 37 | Page [19]. This method applied to ground state conformations of nitrogen and boron substituted fullerenes shows good agreement with ab initio results [20]. The dimensions of the systems studied have been indicated in the relevant figures. Initially, the geometry of all the systems was optimized classically, using molecular mechanics (MM) method [21] taking into consideration mm+ force field [22]. This initial steps makes it easier to perform full optimization by quantum mechanical methods. The next step is to subject these classically optimized systems to geometry optimization using self-consistent field molecular orbital at Parametic Method (PM3) level, in restricted Harte-Fock (RHF) formalism [23]. The Polak-Ribiere optimizer was used in geometry optimization. The convergence criterion employed was that the gradient magnitude should become less than 3 100.1   kcal/Å mol . The entire calculation was performed in ground state of the system in its singlet state configuration. The calculations were done using HyperChem 7.51 [24 ] package program. Quantumwise Atomistics program [25] is used for calculating the density of states (DOS), Electron difference density (EDD) and electrostatic difference potential (EDP). Fig. 1. Optimized structure of zzC80 and zzCnc4. 0.82 nm 0.82 nm 0.79 nm 1.65 nm
  • 3. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 38 | Page Fig. 2. Optimized structures of zigzag carbon nanocapsules. Table 1. Calculated Energy (in kcal/mol unless otherwise stated) of zzC80 and(9,0) zigzag carbon nanocapsules . Quantity zzC80 zzCnc-1 zzCnc-2 zzCnc-3 zzCnc-4 Total no. of atoms 80 100 120 140 160 l/d 1.00 1.23 1.53 1.79 2.10 Total energy -217943.00 -272479.34 -327063.03 -381678.22 -436442.85 Binding energy -1237.00 -15971.83 -19254.03 -22567.71 -26030.84 Isolated atomic energy -205206.00 -256507.50 -307809.00 -359110.50 -410412.00 Electronic energy - 3617915.00 -5147180.22 - 6845360.50 - 8695216.00 -10646513.81 Core-core interaction 3399972.03 4874700.88 6518297.35 8313541.53 10210070.96 Heat of formation 934.200 1117.165 1252.772 1356.89 1311.55 HOMO (eV) -9.098 -8.385 -8.311 -8.2136 -8.957 LUMO (eV) -3.36 -4.516 -4.525 -4.482 -3.060 ΔEg(eV) 5.73 3.87 3.79 3.73 5.89 l/d: length to diameter ratio i) zzCnc-1 ii) zzCnc-2 iii) zzCnc-3 iv) End cap view of zzCnc 0.81 nm 1.00 nm 1.23 nm 0.80 nm 0.79 nm 1.42 nm
  • 4. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 39 | Page Fig. 3. Optimized structure of acC70 and acCnc-4. Fig. 4. Optimized structures of armchair carbon nanocapsules (PM3 results). i) acCnc-1 ii) acCnc-2 iii) acCnc-3 iv) End cap view of acCnc 0.70 nm 0.92 nm 1.19 nm 0.68 nm 1.41 nm 0.67 nm 0.73 nm 0.83 nm 0.62 nm 1.35 nm
  • 5. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 40 | Page Table 2. Calculated Energy (in kcal/mol unless otherwise stated) of acC70 and (5,5) armchair carbon nanocapsules . Quantity acC70 acCnc-1 acCnc-2 acCnc-3 acCnc-4 Total no. of atoms 70 80 100 120 130 l/d 1.11 1.30 1.75 2.10 2.19 Total energy -190667.31 -217920.38 -272508.91 -327097.13 -354483.09 Binding energy -11112.07 -12714.38 -16001.41 -19255.11 -21023.34 Isolated atomic energy -179555.25 -205206.00 -256507.50 -307809.00 -333459.75 Electronic energy -2938431.88 - 3632786.25 -5151395.50 - 6628044.50 - 7697149.38 Core-core interaction 2747764.57 3414865.83 4878886.88 6500947.21 7342666.29 Heat of formation 850.23 956.819 1087.587 1218.69 1192.35 HOMO (eV) -9.74 -8.37 -8.44 -8.24 -9.41 LUMO (eV) -2.72 -3.7098 -3.395 -3.065 -2.52 ΔEg(eV) 7.02 4.66 5.05 5.18 6.89 l/d: length to diameter ratio (i)
  • 6. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 41 | Page (ii) Fig. 5. Variation of the energy band gap (i) and heat of formation (ii) on moving from spherical to capsule formation. (i)
  • 7. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 42 | Page (ii) Fig. 6. Variation of the energy band gap (i) and heat of formation (ii) on moving from spherical to capsule formation in armchair configuration III. Results and discussion To investigate the structural and electronic properties of single wall carbon nanocapsules (SWCncs), both zigzag and armchair configurations were constructed. These structures were then optimized using PM3 method; the advantages of choosing this method and the details of calculation have already been discussed above. The length to diameter ( )/ dl ratio for these zigzag and armchair systems lies in the range 1.00 - 2.10, and 1.11 - 2.19 respectively. These ranges are chosen because they exhibit the variation of structural and electronic parameters when the carbon nanostructures undergo shape (spherical to capsule) and size transformation. 3.1. Zigzag naostructures We have considered zzC80 as the smallest zigzag nanostructure, then gradually increase its length, by adding successively one unit of single wall carbon nanotube (9,0), so as to form a nanocapsule. The various carbon nanocapsule systems in zigzag configuration are denoted by zzCnc-1(100), zzCnc-2 (120), zzCnc-3 (140) and zzCnc-4 (160); the value inside the brackets denotes the number of atoms in that particular system. The PM3 optimized geometry of the shortest (zzC80) and the longest (zzCnc-4) zigzag nanostuctrues; and the intermediate structures between these two extremes of this class are illustrated in figures (Fig. 1-2). The dimensions of the systems are also mentioned in these figures. The length to diameter ( )/ dl ratio for these nanostructure systems lies in the range 1.00-2.10. A ratio of 1.00 characterises zzC80 which is spherical in shape. The different molecular properties calculated for these five zigzag nanostructures, alongwith some thermodynamical properties of the systems such as total energy, binding energy, isolated atomic energy, electronic energy, core-core interaction and heat of formation are presented, in Table 1. Fig. 5 (i) shows the variation of energy band gap with the size of the systems. The smallest system zzC80 has a band gap of 5.73 eV. The gap decreases rapidly as the system undergoes structural change and forms a capsule. For zzCnc-3 the energy band gap has the lowest value of 3.73 eV. This value is the minimum as compared other members and shows that this system is most reactive. The energy band gap then again rises for zzCnc-4 and exceeds that of zzC80. The heat of formation )( fH for these systems is positive, indicating that the process of formation is endothermic. Fig. 5(ii) shows the plot of heat of formation for various zigzag structures, the heat of formation is
  • 8. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 43 | Page least for zzC80 i.e. 934.20 kcal/mol. It then increases and reaches its maximum value for zzCnc-3 and further shows a decreasing trend. The carbon nanocapsule zzCnc-3 (which has smallest gE energy band gap) has the maximum value of fH . Fig. 7 shows a comparison of the density of states for spherical and capsule form. The 2-D plot of electron density difference and electrostatic difference potential are shown in Fig. 8 (a,b) and (c,d) respectively. These plots shows some interesting features, the negative charge is developed along the walls and the a positive charge on the ends of the capsules. 3.2. Armchair nanostuctures The members of this group are denoted by acC70 , acCnc-1(80), acCnc-2(100), acCnc-3(120) and acCnc-4(130). Table 2 displays the PM3 calculated values of structural, electronic and thermodynamic properties of armchair carbon nanostructures. The smallest member of this group is acC70 , for which dl / ratio is 1.11; and it is not completely spherical. Fig 6(i) shows the plot of gE of these structures. It is observed that the energy band gap for acC70 is the maximum (7.02 eV). As the system undergoes shape transformation and forms a capsule, the energy band immediately becomes a minimum (4.66 eV) for acCnc-1. Then it again increases as the length of the capsules increases and for the longest capsule (acCnc-4), the energy band gap becomes 6.89eV. In this configuration, as the capsule is formed from nearly spherical structure; there is a sharp dip in energy band gap which is different from the zigzag case. In zigzag, the energy attains a minimum value for zzCnc-3 and not for zzCnc-1. The more reactive member in this case is acCnc-1. The process of armchair structure formation here is again endothermic, as the heat of formation is positive; although the values are lower as compared to zigzag structures. The trend of heat of formation for armchair Fig. 6(ii) is similar to that of zigzag structures, it first increases, reaches a maximum and then decreases. Fig. 8 shows a comparison of the density of states for spherical and capsule form in case of armchair configuration. The 2-D plot of electron density difference and electrostatic difference potential are shown in Fig. 10 (a,b) and (c,d) respectively. Fig. 7. Density of states (DOS) of zizzag spherical and capsule structures.
  • 9. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 44 | Page Fig. 9. Density of states (DOS) of armchair spherical and capsule structures. (a) (b)
  • 10. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 45 | Page (c) (d) Fig. 8. Electron difference density (a,b) and electrostatic difference potential (c,d) of zigzag structures (a) (b)
  • 11. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 46 | Page (b) (d) Fig. 10. Electron difference density (a,b) and electrostatic difference potential (c,d) of armchair structures IV. Conclusions To summarize, we have carried out theoretical investigations by performing PM3 semi-empirical molecular orbital calculations, in the context of RHF type quantum chemical treatment. The purpose has been to explore the variation in structural, electronic and thermodynamical properties; when these systems undergo shape and size transformation. We have observed that the energy band gap and heat of formation follow definite trends; as size is varied; both in zigzag and armchair configurations. The band gap in case of armchair carbon nanocapsules is greater than that in zigzag form; establishing that zigzag form of fullerenes or capsules are more reactive. References [1] Kroto, H. W.; Heath, J. R.; O’Brien, S. C.; Curl, R. F.; Smalley, R. E. C60: Buckminsterfullerene. Nature 1985, 318, 162-163. [2] Iijima, S. Helical microtubes of graphitic carbon. Nature 1991, 354, 56-58. [3] Ge, M.; Sattler, K. Observation of fullerene cones. Chem. Phys. Lett. 1994, 220 (issue3-5), 192-196. [4] Krishnan, A.; Dujardin, E.; Treacy, M. M. J.; Hugdhal, J.; Lynum, S.; Ebbesem, T. W. Graphite cones and the nucleation of curved carbon surfaces. Nature 1997, 388, 451-454. [5] Saito, Y.; Yoshikawa, T.; Okuda, M.; Ohkohchi, M.; Ando, Y.; Kasuya, A.; Nishina, Y. Synthesis and electron-beam incision of carbon nanocapsules encaging YC2. Chem. Phys. Lett. 1993, 209(issue 1-2) 72-76. [6] Hihara, T.; Onodera, H.; Sumiyama, K.; Suzuki, K.; Kasuya, A.; Nishina, Y.; Satio, Y.; Yoshikawa, T.; Okuda, M. Magnetic properties of iron in nanocapsules. Jpn. J. Appl. Phys. 1994, 33, L24-L25. [7] Satio, Y.; Okuda, M.; Yoshikawa, T.; Bandow, S.; Yamamuro, S.; Wakob, K.; Sumiyama, K.; Suzuki, K. Synthesis of Sc15C19 crystallites encapsulated in carbon nanocapsules by arc evaporation of Sc-C composite. Jpn. J. Appl. Phys. 1994, 33, L186-L189. [8] Satio, Y.; Yoshikawa, T.; Okuda, M.; Fujimoto, N.; Sumiyama, K.; Suzuki, K.; Kasuya, A.; Nishina, Y. Carbon nanocapsules encaging metals and carbides. J. Phys. & Chem. Solids 1993, 54(12) 1849- 1860
  • 12. Transition from Carbon Nanoballs to Nanocapsules With Reference To Structural and Molecular www.ijres.org 47 | Page [9] Satio, Y.; Yoshikawa, T.; Okuda, M.; Kasuya, A.; Nishina. Y. Correlation between volatility of rare earth metals and encapsulation of their carbides in carbon nanocapsules. J. Phys. Chem. 1994, 98(27) 6696-6698. [10] Gleiter, H. Nanocrystalline materials. Progress in Material Science 1989, 33, 223-315. [11] Pekoz, R.; Erkoc, S. Structural and electronic properties of Lithium endohedral doped defected carbon nanocapsules. Physica E 2007, 36, 211-216. [12] Pekoz, R.; Erkoc, S. Quantum chemical treatment of Li/Li+ doped defected carbon nanocapsules. Physica E 2008, 40(8), 2752-2760. [13] Stoyanov, S. R.; Kral, P. Multifunctional metal doped carbon nanocapsules. J. Chem. Phys. 2008,129, 234702-1 – 234702-10. [14] Suyetin, M. V.; Vakhrushev, A. V. Guided carbon naoncapsules for hydrogen storage. J. Phys. Chem. C, 2011, 115, 5485-5491. [15] Suyetin, M. V.; Vakhrushev, A. V. Nanocapsule with pump for methane storage. Phys. Chem. Chem. Phys. 2011, 13, 9863-9870. [16] Ganji, M. D. Ab initio investigation of the possibility of formation of endohedral complexes between H2 molecules and B-, N- and Si doped C60. Physica E 2009, 41, 1406-1409. [17] Ganji, M. D.; Valizadeh, G.; Jahan-tigh, M. Hydrogen storage capacity of C120 nanocapsules: Density functional theory based treatments. Commun. Theor. Phys. 2011, 55, 519-526. [18] Stewart, J. J. P. Optimazation of parameters for semiempirical methods I. Method. J. Comput. Chem. 1989, 10, 209-220. [19] Carvalho, A. C. M.; dos Santos, M. C. Nitrogen-substituted nanotubes and nanojunctions: Conformation and electronic properties. J. Appl. Phys. 2006, 100, 84305-84310. [20] Viani, L.; dos Santos, M. C. Comparative study of lower fullerenes doped with boron and nitrogen. Solid State Commun. 2006, 138, 498-501. [21] Burkert, U.; Allinger, N. L. Molecular Mechanics, ACS Washington D. C. Monogr. 1982, 177 . 339pp. [22] Allinger, N. L. Conformational analysis.130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms. J. Am. Chem. Soc. 1977, 99, 8127-8134. [23] Roothaan, C. C. New developments in Molecular Orbital Theory. J. Rev. Mod. Phys. 1951, 23, 69-89. [24] Hypercube, Inc., Gainesville FL. (USA) [25] Atomistix ToolKit version 12.2.2.X, QuantumWise A/S (www.quantumwise.com).