Density Functional Theory Study on B30N20 ...

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Density Functional Theory Study on B30N20 Nanocage in Structural Properties and Thermochemical Outlook a

b

M. Monajjemi , M. Jafari Azan & F. Mollaamin

c

a

Department of Chemistry, Science and Research Branch, Islamic Azad University, Tehran, Iran b

M.Sc Student, Science and Research Branch, Islamic Azad University, Tehran, Iran c

Department of Chemistry, Qom Branch, Islamic Azad University, Qom, Iran Published online: 07 Dec 2012.

To cite this article: M. Monajjemi , M. Jafari Azan & F. Mollaamin (2013): Density Functional Theory Study on B30N20 Nanocage in Structural Properties and Thermochemical Outlook, Fullerenes, Nanotubes and Carbon Nanostructures, 21:6, 503-515 To link to this article: http://dx.doi.org/10.1080/1536383X.2011.629762

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Fullerenes, Nanotubes, and Carbon Nanostructures, 21: 503–515, 2013 Copyright © Taylor & Francis Group, LLC ISSN: 1536-383X print / 1536-4046 online DOI: 10.1080/1536383X.2011.629762

Density Functional Theory Study on B30 N20 Nanocage in Structural Properties and Thermochemical Outlook M. MONAJJEMI1 , M. JAFARI AZAN2 AND F. MOLLAAMIN3

Downloaded by [Monash University Library] at 23:28 24 May 2013

1

Department of Chemistry, Science and Research Branch, Islamic Azad University, Tehran, Iran 2 M.Sc Student, Science and Research Branch, Islamic Azad University, Tehran, Iran 3 Department of Chemistry, Qom Branch, Islamic Azad University, Qom, Iran In this research, by the using group theory with the state of projection operators, a systematic method for investigating Boron nitride nanocage (B30 N20 ) molecules was studied. The combination and the normalization coefficients of B30 N20 nanocage in C2V point group was calculated, and the effect of dielectric constants on the thermodynamic properties was studied. Also, the solvent effect on the relative energies, dipole moment and zero point energy values in gas, water, methanol and carbon tetrachloride surrounding nanocage by density functional theory at the B3LYP/6-31G∗ and 6-31G∗∗ levels. We have found that B30 N20 nanocage plays an important role in imparting extra stability. The aim of this work is to discuss the aspects of the electronic structure of this system for theoretical results to increase their usefulness in practical applications. Keywords B30 N20 nanocage, DFT, symmetry, primitive, thermodynamic properties

Introduction Besides carbon nanotubes, which are a promising material due to both their mechanical strength and their interesting electronic properties, boron nitride (BN) tubes have recently attracted increased attention. Considerable interest has been aroused recently by boron nutride nanotubes (BNNTs) for application in nanoscale devices. Modification of the electronic properties of nanotubes by doping is an important issue for designing nanodevices based on nanotubes. The doped nanotubes can exhibit dramatic changes with respect to the undoped material. There has been a significant interest in experimental studies of Bn Nm clusters that can be found in the literature, and several research groups have described the production of boron nitride-based nanostructures (1–6). Recently, various cages and (BN)n cubes have been synthesized (7–12), and BN polyhedral have also been successfully synthesized by reaction of BCl3 with NH3 in a laser beam (13,14). BNNT is formed by rolling a single layer of sp2 boron into a seamless hollow cylindrical tube with nanoscale dimensions. Besides their unique physical properties (i.e., elasticity, tensile strength, stiffness and deformation), nanotubes exhibit varying electrical properties, depending on the direction that the structure spirals around the tube (quantified by the “chiral vector” and other factors, such as doping), and can be superconductor, conductor (metallic), semiconductor or insulator. The geometrical and electronic structure of BNNTs 503


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can be described by a chiral vector, the angle between the axis of its hexagonal pattern and the axis of the tube which is presented by the (n1 ; n2 ) chirality’s indices. When the indices are (n1 , 0) called zigzag, (n1 , n1 ) called armchair, and (n1 , n2 ) where n1 = 0 and n2 = 0 known as chiral BNNTs. There are mainly two structural classes for (BN)n cages (15,16). One is constructed from alternate BN units and governed by an isolated square rule (17,18), which is the counterpart of the isolated pentagon rule (19) of carbon fullerenes. Another class is of fullerene-like structures based on a combination of 5- and 6-membered rings, with the existence of N-N and B-B bonds. In addition to the theoretical predictions for the structures, physical properties of such molecules of B24 C12 N24 molecule (16) and the B12 N12 , B16 N16 and B28 N28 molecules, the experimental synthesis and various spectrometer are needed for the final confirmation of their stability for structures (17,20). However, there is basically no experimental information on the Bn Nm cluster thermo chemistry, though some information for small aggregates can be derived from ab initio calculations (21–24). Nanotubes of BN have a structure similar to that of carbon nanotubes, that is, graphene (or BN) sheets rolled on themselves, whereas carbon nanotubes can be metallic or semiconducting depending on the rolling direction and radius. A BN nanotube is an electrical insulator with a wide band gap of 5.5 ev which is almost independent of tube chirality and morphology. It has a layered structure similar to graphite. In each layer, boron and nitrogen atoms are bound by strong covalent bonds, and layers are held together by weak van der Waals forces (25–27). We have employed single-walled borane nanotube (SWBNNT) from kind MWNT = 1 as armchair nanotubes (n, m) with chirality n = 5, m = 5, and the tube length was 3Å. The schematics of the generation of our considered nanotube through folding a section of a graphene sheet and the optimized structure of adenine-B15 N15 -thymine are displayed in the scheme whereby C = n a1 + m a2 = (n,m), and a1 and a2 are the primitive lattice vectors of the graphene and n,m are integers (28,29). Recently, an increasing number of studies on atomic charges have been performed (30–33). Moreover, nuclear quadrupole resonance (NQR) parameters have been known as the proper tool for the description of the electrostatic interaction and charge transfer properties of B15 N15 -BNB system (34–36). In this study, to accomplish the evaluation of partial atomic charges we have used chelp G quantum chemical ECP method for various anion, cation and radical types of BNB molecule inside the B15 N15 ring. To establish this target, it is important to examine the structural stability of the BNBB15 N15 system. It is expected that BNB will be located strictly inside the B15 N15 ring. So, the BNB-B15 N15 system has been optimized using hybrid DFT calculations at the B3LYP level of theory as an efficient tool for theoretical studies on (BN)n rings and cages (37,38) with the EPR- II and EPR-III proposed by Barone (39,40) as suitable basis sets for identification of the electromagnetic properties of nanosystems. The purpose of this paper is to present an accurate ab initio by some basis sets density functional theory (DFT) calculation study of BN and B30 N20 including anharmonic force fields for their respective ground states.

Theoretical Background and Computational Method The uniform electronic properties suggest that BN nanotubes may have significant advantages for applications in electronic and mechanical devices. Furthermore, the bottom of the conduction band is a nearly free electron-like state. This state remains the bottom of the conduction band even in the multi-walled case and, in the case of n-type doping, will play an important role for potential applications in field emission devices and molecular transport.


Density Functional Theory Study

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Figure 1. Boron nitride nanocage (B30 N20 ) molecule with symmetry of C2V have been shown (color figure available online).

The main objective of this study was to gain further insight into the electrostatic as well as electromagnetic nature of these non-bonded interactions in accounting for the capability of quantized rotation of BNB molecule inside the B15 N15 ring. The character of interactions has been compared along with translation and rotation of radical, cationic and anionic forms of BNB in B15 N15 -BNB system through calculations of the following different physicochemical parameters. The main goal was to make a systematic exploration of the structure pattern of these boron nitrogen cage structures; that is, presuming the B15 N15 ring as a quantum mechanical rotating system holding a specific rotation axis as BNB, we planned to simulate BNB inside the B15 N15 ring in accordance with an quantized nanospectophotometer detection of various quantized parameters of a given biomolecule. The electronic structure of condensed matter is usually described in terms of oneelectron basis sets. Basis functions used for computation are often simple, for example, Gaussians or plane waves, but their number is large, 1–2 orders of magnitude larger than the number of electrons to be described. This is so because the potential in the effective one-electron Schrödinger equation, arising, for example, in DFT, is rather deep inside the atoms. The results of this kind of computation require interpretation and simplification in terms of a small set of intelligible orbitals. The results of band-structure calculations for crystals, for instance, are often parameterized in terms of tight-binding models. The Boron nitride nanocage (B30 N20 ) molecule structure were built using the tool in HyperChem7.0 (41) (Figure 1). The symmetry of the nanocage is C2V. The indicated system have studied in gas phase and solvent media by various dielectric constants (ε) including 1,78.39, 32.63 and 2.228. Energy minimum of system was carried out by DFT method at 6-31 G∗ and 6-31G∗∗ basis sets to optimize the structure of the nanocage using by Gaussian 98 program package (42).

Results and Discussion Structural Evaluation In view of the structural similarity of graphite and bulk boron nitride, it is usual to discuss these new materials in terms of modifications of the carbon fullerene and nanotube models.


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A boron nitride nanotube can be imagined as a graphite-like sheet rolled on itself, where carbon atoms are alternately substituted by nitrogen and boron atoms. Structurally, it is a close analog of the carbon nanotube, namely a long cylinder with diameter of several to hundred nanometers and length of many microns. We anticipate that examining such an imagined prediction would be a promising way to improve the physical and chemical properties of fullerenes and may serve as a starting point for designing electromagnetic nanosystems to be considered in experiments. The major focus of the present study was the investigation of the electrostatic interactions within the BNB-B15 N15 system. For further investigation about electrostatic interactions, the quantum mechanical atomic charges caused by the asymmetric distribution of electrons in chemical bonds play an important role in simulations of intermolecular forces and condensed phase properties and they are also often used for a qualitative understanding of the structural aspects. In this work, the covalent solid boron nitride has generated much interest. The precursors of these materials in surface coating are the Bn Nm , clusters. A comprehensive picture of the electronic structure of these magnetically unusual nanoparticles motivated us to imagine such a nanosystem as a quantized mechanic rotating system which would induced an electromagnetic field through electrostatic interaction of BNB to the B15 N15 ring and also has a capability of detecting the quantized parameters of the system considered as well as other bimolecular systems which can be coupled with this system. In other words, there is mutual electrostatic interaction between B and N atoms ring which causes the quantization of dipole moment and zero point energy (ZPE) (Table 1 and Figure 2). The graph of dipole moment of B30 N20 nanocage in different media has been displayed in Figure 2. According to Figure 3, we can clearly observe that for B30 N20 nanocage the variation of dipole moment was more evident in different solvent media and exhibited a significant sensitivity to the solvents polarity. Surprisingly, all considered B30 N20 nanocage exhibited the similar physico-chemical behavior in water (Figure 3). That is, in the B30 N20 nanocage with the increase in dielectric constant of different solvents from the gas phase up to water, the dipole moment values of B30 N20 nanocage has been increased and the maximum value obtained in water, which confirmed the higher stability of B30 N20 nanocage in water. The possibility of intra- and inter-hydrogen binding network is increased with water as a protic solvent. The solvent effect of water, methanol and carbon tetrachloride solvents on the dipole moment values was insignificant. This fact can be related to the methyl groups, which increase the hydrophobic characteristics of B30 N20 nanocage and showed insignificant changes to the variation of dielectric constants of these solvents.

Symmetric and properties Assuming that the closing caps at the cage are constructed such that they do not further reduce the symmetry of the system, the point group is Cnv coinciding with the point group of the unit cell. Finite-length chiral tubes have either no point group symmetry or a very low n-fold rotation axis, depending on the rotation symmetry of the unit cell. In this paper, the boron nitride nanorcage (B30 N20 ) molecule with symmetry of C2V has been given in Figure 1. By analyzing of indicated structure to different parts, a complete set of the linear combinations and their normalization coefficients are achieved (Table 2). On the other hand, its point group symmetry of different parts is C2V and it has three normal vibrations (from 3N-6 normal modes).

507

298 301 304 307 310

298 301 304 307 310

298 301 304 307 310

298 301 304 307 310

Water

Methanol

Carbon Tetrachloride

Temps

Gas

Solvents

0.218329 0.217549 0.216762 0.215970 0.215172

0.218000 0.217220 0.216434 0.215643 0.214846

0.217976 0.217196 0.216411 0.215619 0.214823

0.218476 0.217733 0.216946 0.216153 0.215355

G

0.295595 0.296166 0.296743 0.297326 0.297914

0.295177 0.295748 0.296325 0.296908 0.297496

0.295149 0.295720 0.296297 0.296880 0.297468

0.295888 0.296430 0.297007 0.297590 0.298177

H

1829.570793 1829.570793 1829.570793 1829.570793 1829.570793

1829.5726322 1829.5726322 1829.5726322 1829.5726322 1829.5726322

1829.5727408 1829.5727408 1829.5727408 1829.5727408 1829.5727408

1829.5694698 1829.5694698 1829.5694698 1829.5694698 1829.5694698

−E

6-31G∗

8.1576 8.1576 8.1576 8.1576 8.1576

9.1917 9.1917 9.1917 9.1917 9.1917

9.2527 9.2527 9.2527 9.2527 9.2527

7.4121 7.4121 7.4121 7.4121 7.4121

162.702 163.899 165.095 166.292 167.488

162.515 163.712 164.909 166.106 167.303

162.506 163.703 164.900 166.097 167.294

162.927 164.064 165.260 166.456 167.652

Dipole S CAL/ Moment MOL(Debye) KELVIN

168.51909 168.51909 168.51909 168.51909 168.51909

168.26896 168.26896 168.26896 168.26896 168.26896

168.25192 168.25192 168.25192 168.25192 168.25192

168.67142 168.67142 168.67142 168.67142 168.67142

ZPVE Kcal/ Mol

0.191247 0.190418 0.189583 0.188742 0.187895

0.192115 0.191295 0.190469 0.189636 0.188798

0.192142 0.191323 0.190497 0.189664 0.188826

0.194424 0.193687 0.192904 0.192116 0.191321

G

0.273243 0.273864 0.274490 0.275122 0.275760

0.273268 0.273888 0.274514 0.275146 0.275783

0.273266 0.273886 0.274512 0.275144 0.275781

0.271321 0.271892 0.272500 0.273113 0.273733

H

1840.9348614 1840.9348614 1840.9348614 1840.9348614 1840.9348614

1840.9356854 1840.9356854 1840.9356854 1840.9356854 1840.9356854

1840.9357369 1840.9357369 1840.9357369 1840.9357369 1840.9357369

1840.9343217 1840.9343217 1840.9343217 1840.9343217 1840.9343217

−E

6-31G∗∗

5.3135 5.3135 5.3135 5.3135 5.3135

6.3162 6.3162 6.3162 6.3162 6.3162

6.3778 6.3778 6.3778 6.3778 6.3778

4.6401 4.6401 4.6401 4.6401 4.6401

Dipole Total

Table 1 Structural properties, Energy and thermodynamic parameters of B30 N20 Nanocage at B3LYP/6-31G∗ /6-31G∗∗ . Levels at different temperatures and media


172.664 173.964 175.263 176.561 177.859

170.886 172.186 173.484 174.782 176.079

170.825 172.124 173.423 174.721 176.017

161.842 163.039 164.300 165.560 166.819

S

152.93755 152.93755 152.93755 152.93755 152.93755

153.03478 153.03478 153.03478 153.03478 153.03478

153.03688 153.03688 153.03688 153.03688 153.03688

152.75848 152.75848 152.75848 152.75848 152.75848

ZPVE


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Figure 2. Plotting of Zero point energy (ZPE) via different dielectric constants of B30 N20 Nanocage at B3LYP/6-31G∗ /6-31G∗∗ . Levels at temperatures: 298, 301, 304, 307 and 310 K.

Figure 3. Plotting of dipole moment (Debye) via different dielectric constants of B30 N20 Nanocage at B3LYP/6-31G∗ /6-31G∗∗ . Levels at temperatures: 298, 301, 304, 307 and 310 K.

Also, there is a close relationship between symmetry and irreducible presentation of the particular point group to which the molecule belongs (Table 3). With group theoretical arguments, it is easy to deduce to which symmetries the different vibrations of a molecule will belong.


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Table 2 Linear combination of primitives and their normalization coefficients based on their symmetric A1 A2 B1 B2 for boron nitride nanocage (B30 N20 ) molecule A1 1 – 15

B1 26 – 38

A2 16 – 25

B2 39 – 50


Linear Combination of Primitives Based on their Symmetric A1 A2 B1 B2 1 = 1/sqrt (2) (ϕ1 + ϕ34) 2 = 1/sqrt(2) (ϕ2 + ϕ43) 3 = 1/2 (ϕ3 + ϕ4 + ϕ24 + ϕ25) 4 = 1/2 (ϕ5 + ϕ42 + ϕ9 + ϕ41) 5 = 1/2 (ϕ6 + ϕ36 + ϕ10 + ϕ33) 6 = 1/2 (ϕ7 + ϕ15 + ϕ8 + ϕ14) 7 = 1/2 (ϕ11 + ϕ48 + ϕ18 + ϕ46) 8 = 1/2 (ϕ12 + ϕ35 + ϕ16 + ϕ32) 9 = 1/2 (ϕ13 + ϕ27 + ϕ17 + ϕ23) 10 = 1/sqrt(2) (ϕ19 + ϕ50) 11 = 1/2(ϕ20 + ϕ44 + ϕ28 + ϕ39) 12 = 1/2(ϕ21 + ϕ49 + ϕ29 + ϕ47) 13 = 1/sqrt(2) (ϕ22 + ϕ26) 14 = 1/sqrt(2) (ϕ30 + ϕ37) 15 = 1/2(ϕ31 + ϕ45 + ϕ38 + ϕ40) 16 = 1/2 (ϕ3 + ϕ 36 − ϕ4 − ϕ24) 17 = 1/2 (ϕ5 + ϕ42 − ϕ9 − ϕ41) 18 = 1/2 (ϕ6 + ϕ36 − ϕ10 − ϕ33) 19 = 1/2 (ϕ7 + ϕ15 − ϕ8 − ϕ14) 20 = 1/2 (ϕ11 + ϕ48 − ϕ18 − ϕ46) 21 = 1/2 (ϕ12 + ϕ35 − ϕ16 − ϕ32) 22 = 1/2 (ϕ13 + ϕ27 − ϕ17 − ϕ23) 23 = 1/2 (ϕ20 + ϕ44 − ϕ28 − ϕ39) 24 = 1/2 (ϕ21 + ϕ49 − ϕ29 − ϕ47) 25 = 1/2 (ϕ31 + ϕ45 − ϕ38 − ϕ40)

26 = 1/sqrt(2) (ϕ1 − ϕ34) 27 = 1/sqrt(2) (ϕ2 − ϕ43) 28 = 1/2 (ϕ3 − ϕ25 + ϕ4 − ϕ24) 29 = 1/2 (ϕ5 − ϕ42 + ϕ9 − ϕ41) 30 = 1/2 (ϕ6 − ϕ36 + ϕ10 − ϕ33) 31 = 1/2(ϕ7 − ϕ15 + ϕ8 − ϕ14) 32 = 1/2 (ϕ11 − ϕ48 + ϕ18 − ϕ14) 33 = 1/2 (ϕ12 − ϕ35 + ϕ16 − ϕ32) 34 = 1/2 (ϕ13 − ϕ27 + ϕ17 − ϕ23) 35 = 1/sqrt(2) (ϕ19 − ϕ50) 36 = 1/2 (ϕ20 − ϕ44 + ϕ28 − ϕ39) 37 = 1/2 (ϕ21 − ϕ49 + ϕ29 − ϕ47) 38 = 1/2 (ϕ31 − ϕ45 + ϕ38 − ϕ40) 39 = 1/2 (ϕ3 − ϕ25 − ϕ4 + ϕ24) 40 = 1/2 (ϕ5 − ϕ42 − ϕ9 + ϕ41) 41 = 1/2 (ϕ6 − ϕ36 − ϕ10 + ϕ33) 42 = 1/2 (ϕ7 − ϕ15 − ϕ8 + ϕ14) 43 = 1/2 (ϕ11 − ϕ48 − ϕ18 + ϕ46) 44 = 1/2 (ϕ12 − ϕ35 − ϕ16 + ϕ32) 45 = 1/2 (ϕ13 − ϕ27 − ϕ17 + ϕ23) 46 = 1/2 (ϕ20 − ϕ44 − ϕ28 + ϕ39) 47 = 1/2 (ϕ21 − ϕ49 − ϕ29 + ϕ47) 48 = 1/sqrt(2) (ϕ22 − ϕ26) 49 = 1/sqrt(2) (ϕ30 − ϕ37) 50 = 1/2 (ϕ31 − ϕ45 − ϕ38 + ϕ40)

Molecular motions can be assigned by the potential energy distribution (PED) analysis among internal coordinates by the method of the projection operator. There are good agreement among most cases. Thermodynamic investigation The application of high-level quantum chemical calculations to more realistic systems is clearly desirable but exceeds the present computer capacity of most research groups. Considering the size of most nanoparticles systems, the DFT method still seems to be the tool of choice in the description of relevant systems. Thermo chemical parameters have a spread influence on the mechanism of electron transfer in complexes, and their studies could provide a deeper improvement in quantitative treatment of charge transfer reactions in nanotubes. Also, these parameters provide a mentioned mechanism for many chemical reactions.

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M. Monajjemi et al. Table 3 Irreducible presentation of the particular point group (C2V ) for Boron nitride nanocage (B30 N20 ) molecule


Irreducible Presentation ϕ1 ϕ2 ϕ3 ϕ4 ϕ5 ϕ6 ϕ7 ϕ8 ϕ9 ϕ10 ϕ11 ϕ12 ϕ13 ϕ14 ϕ15 ϕ16 ϕ17 ϕ18 ϕ19 ϕ20 ϕ21 ϕ22 ϕ23 ϕ24 ϕ25 ϕ26 ϕ27 ϕ28 ϕ29 ϕ30 ϕ31 ϕ32 ϕ33 ϕ34 ϕ35 ϕ36 ϕ37 ϕ38 ϕ39 ϕ40

E

C2

σ xz

σ yz

ϕ1 ϕ2 ϕ3 ϕ4 ϕ5 ϕ6 ϕ7 ϕ8 ϕ9 ϕ10 ϕ11 ϕ12 ϕ13 ϕ14 ϕ15 ϕ16 ϕ17 ϕ18 ϕ19 ϕ20 ϕ21 ϕ22 ϕ23 ϕ24 ϕ25 ϕ26 ϕ27 ϕ28 ϕ29 ϕ30 ϕ31 ϕ32 ϕ33 ϕ34 ϕ35 ϕ36 ϕ37 ϕ38 ϕ39 ϕ40




(Continued)


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Table 3 (Continued)


Irreducible Presentation ϕ41 ϕ42 ϕ43 ϕ44 ϕ45 ϕ46 ϕ47 ϕ48 ϕ49 ϕ50

E

C2

σ xz

σ yz

ϕ41 ϕ42 ϕ43 ϕ44 ϕ45 ϕ46 ϕ47 ϕ48 ϕ49 ϕ50

ϕ9 ϕ5 ϕ2 ϕ20 ϕ31 ϕ18 ϕ29 ϕ11 ϕ21 ϕ19

ϕ42 ϕ41 ϕ43 ϕ39 ϕ40 ϕ48 ϕ49 ϕ46 ϕ47 ϕ50

ϕ5 ϕ9 ϕ2 ϕ28 ϕ38 ϕ11 ϕ21 ϕ18 ϕ29 ϕ19

The structural flexibility studied through equilibrium fluctuations contributes to the conformational entropy and to the entropy change during unfolding (S) and have a profound influence on the free energy of stabilization (43). In the present article we have focused mainly on the thermo stability, which is only one of the properties characterizing B30 N20 nanocage. To study the structural stability of our considered B30 N20 nanocage system, we have optimized this system using DFT (B3LYP) method by 6-31G∗ and 6-31G∗∗ basis sets. Employing these basis sets seemed useful and helped us acquire logical relationships between obtained data. In this study, the thermo chemical analysis were calculated, and the values of the enthalpy, Gibbs free energy and entropy are shown in Table 1, in which temperatures are 298, 301, 304, 307 and 310 K. These variations at two levels of theory and six temperatures obtained are plotted in Figures 4a and b. As can be inferred from the Figures 4a and b that there is good agreement between the 6-31G∗ and 6-31G∗∗ basis sets. We found that there was some difference between these functions obtained by the HF and B3LYP methods. The Gibbs free energy of stabilization (G) according to equation (1) depends on the balance of enthalpy and entropy contributions (44). G = H − TS

(1)

The lower S would increase G and explain the temperature dependence of the free energy of stabilization (44). In the present study, the influence of the nanotube on the relative stability of active site was studied, and it seems that in all three considered basis sets compared with experimental studies the highest stability occurred. The G values decreased and S values increased with increasing temperature, so that at 310 K this can be perceived that the greatest S value and the least amount of G happened, so the highest stability occurred at 310K. We found that the Gibbs free energies (G) of B30 N20 nanocage in 310 K are smaller than other temperature; that is, interactions in 310 K are stronger than at other temperatures. The result obtained at the B3LYP/6-31G∗ level is more negative than those of the others calculations because these methods take correlation energy into account differently (Figures 4a, b, and Table 1).

M. Monajjemi et al.


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Figure 4. Plotting of Gibbs Free Energy (Hartree-fock) via different temperatures of 298, 301, 304, 307 and 310 K at gas, water, methanol and carbon tetrachloride for B30 N20 Nanocage at (a) B3LYP/ 6-31G∗ and (b) 6-31G∗∗ basis sets.

The results obtained at the B3LYP/6-31G∗ can be summarized by the following communication in different media of (a) gas, (b) water, (c) methanol and (d) carbon tetrachloride (equation (2)): (a) G = −0.0003 T − 0.2967

R2 = 0.9998

(b) G = −0.0003 T + 0.2963

R2 = 1


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(c) G = −0.0003 T + 0.2963

R2 = 1

(d) G = −0.0003 T + 0.2963

R2 = 1

(2)


The calculations of the B3LYP/6-31G∗∗ method were explained by the following equation (3) in different media of (e) gas, (f) water, (g) methanol and (h) carbon tetrachloride: (e) G = −0.0003 T − 0.2717

R2 = 0.9998

(f) G = −0.0003 T − 0.2745

R2 = 1

(g) G = −0.0003 T − 0.2745

R2 = 1

(f) G = −0.0003 T − 0.2745

R2 = 1

(3)

In this study, the obtained values for H, S and G of 6-31G∗ and 6-31G∗∗ basis sets were consisted to be from (a) to (h) at B3LYP level, respectively. We found that the relation coefficient (R2 ) of 6-31G∗ and 6-31G∗∗ basis sets at B3LYP level are near each other. Also, we have shown that the graph of gas in two basis sets has a distance from other media. In this investigating works, the effect of temperature on the stability of B30 N20 nanocage form was studied at different temperatures and various media. The results have been obtained in different dielectric constants (1,78.39, 32.63 and 2.228). The lowest values of parameters in gaseous phase were where the highest value in water. Generally, increasing the dipole moments has been observed due to increase in dielectric constant. The results of solvent effects on free Gibbs energies of B30 N20 nanocage at various temperatures were given in Table 1. Also, the temperature effect on the stability of peptide nanorings in various solvents can be seen in Figures 4a and b. Considering that proper nanocage activity requires sufficient conformational fluctuations, the comparison of thermodynamic features with thermo stability and consequently nanocage activity is also relevant to understanding thermal adaptation and ultimately sufficient conformational fluctuations.

Conclusion Due to the chemical importance of electrostatic interaction intra various B30 N20 nanocage, the application of DFT methods with 6-31G∗ and 6-31G∗∗ basis sets provides a deeper insight into their molecular and hyperfine spectroscopic properties. The application of the ab initio method at the B3LYP level with the 6-31G∗ and 6-31G∗∗ allowed the unambiguous discrimination among different conformational forms of peptide B30 N20 nanocage and a conclusion as to which of the forms occurs more in the gas and solution phases. On this basis, we conclude the following points: 1. There is a difference in the charge density between B and N atoms in the ring. Highdensity around N atoms protruding toward the B-N bonds indicates charge transfer from B to N atoms. 2. For B30 N20 nanocage, the variation of dipole moment was more evident in different solvent media and exhibited a significant sensitivity to the solvents polarity.

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3. Hydroxylated B30 N20 nanocage reflected the polar behavior in water compared with other systems. 4. The more increase in temperature, the more ring stability obtained in this system. The most negative value of Gibbs free energy has been observed to water solution at 310K. 5. In comparison, the ring stability in the same medium and temperature increased with increasing the dielectric constant of solvents. 6. The B30 N20 nanocage is stable in a water environment in both room temperature and body fever temperature, which is more important to design such stable drug nanovehicles. Also, water medium is more compatible to cells and body fluid.


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