Theoretical Description of Electromagnetic Nonbonded Interactions of Radical, Cationic,and Anionic NH2BHNBHNH2 Inside of the B18N18 Nanoring

M. Monajjemi,*,†,# V. S. Lee,‡ M. Khaleghian,§ B. Honarparvar,† and F. Mollaamin⊥

Department of Chemistry, Science and Research Branch, Islamic Azad UniVersity, Tehran, Iran,Computational Simulation and Modeling Laboratory (CSML), Department of Chemistry and Center forInnoVation in Chemistry, Thailand Center of Excellence in Physics (ThEP), Faculty of Science, Chiang MaiUniVersity, Chiang Mai, Thailand, Department of Chemistry, Islamshahr Branch, Islamic Azad UniVersity,Islamshahr, Iran, and Department of Chemistry, Qom Branch, Islamic Azad UniVersity, Qom, Iran

ReceiVed: May 11, 2010; ReVised Manuscript ReceiVed: June 27, 2010

The electromagnetic nonbounded interactions of the NH2BHNBHNH2 molecule inside of the B18N18 ringhave been investigated with hybrid density functional theory (B3LYP) using the EPR-III and EPR-II basissets for a physicochemical explanation of electromagnetic nonbounded interactions within these nanosystems.Optimized structures and hyperfine spectroscopic parameters such as total atomic charges, spin densities,electrical potential, and isotropic Fermi coupling constants of radical, cationic, and anionic forms of theNH2BHNBHNH2 molecule in different loops and bonds of the B18N18-NH2BHNBHNH2 systems have beencalculated. The correlations between structural, electronic, and spectral properties have been contributed toidentify the characteristics of hyperfine electronic structure. Besides structural characteristics, the lowestunoccupied molecular orbital and the highest occupied molecular orbital for the lowest energy have beenderived to examine the structural stability of the B18N18-NH2BHNBHNH2 systems. We have also carried outthe calculation for the alanine-glycine amino acids coupled with the NH2BHNBHNH2 molecule inside ofthe B18N18 ring (ALA-NH2BHNBHNH2-GLY) and obtained quantized transitional frequencies among theforms of radical, anionic, and cationic. In a similar way, in B18N18-NH2BHNBHNH2, the three frequencieshave been yielded as νr-c ) 486948.498 GHz, νa-c ) 1792900.812 GHz, and νr-a ) 2507076.816 GHz. Itcan be seen that all observed frequencies appeared in the IR and macrowave regions. It seems that theB18N18-NH2BHNBHNH2 nonbonded system can be used for the measurement of rotational spectra relatedto electrical voltage differences existing in a part of biomacromolecules. The radial coordinate of the dipolemoment vector (r) as well as the voltage differences (∆V) and relative energies (∆E) of the radical, anionicand cationic forms of the NH2BHNBHNH2 in the B18N18-NH2BHNBHNH2 system exhibited Gaussiandistribution. The expectations of the ∆E and ∆V and r have been calculated from the Gaussian curves, whichhave been fitted by various eigenvalues. In addition, the natural bond orbital (NBO) analysis has been performed,which was informative to reveal some important atomic and structural features. Also, analysis of the NQRhyperfine structure of the B18N18-NH2BHNBHNH2 system has been performed in terms of the electric fieldgradient at each nitrogen nucleus, and the changes in the extent of electric charge distribution that accompaniescomplex formation have been explored.

1. Introduction

Heterofullerenes became a subject of research interest soonafter the establishment of fullerene research itself.1-3 Thefullerenes containing boron and/or nitrogen atoms [refs 4-13of ref 6] represent one distinguished class, though other elementshave been combined with the fullerenes too.4-6

Boron nitride (BN) is a synthetic III-V compound withextraordinary mechanical, thermal, electrical, optical, andchemical properties widely applied for technological purposes.1

Since BN units are isoelectronic with hexagonal BN possessinga graphene-like layered structure, BN becomes the natural

candidate to form heterofullerenes, which results in a certainisomorphism. BN crystalline samples were synthesized at roomtemperature and atmospheric pressure as structures containinghexagonal sp2-bonded sheets isomorphic with graphene.7 BNnanomaterials are expected in extentive application due to thegood stability at high temperatures with high electronic insula-tion in air.8 Despite the carbon nanotubes, BN nanotubes areconstant band gap materials and thus provide an attractiveopportunity for practical applications.9 The wide range of theirelectronic properties from metallic to wide-gap semiconductors,depending on their chemical composition, makes them suitablecandidates for nanosize electronic devices.10,11

Due to the similarity between B-N and C-C units, a lot ofeffort has been devoted to BN fullerene-like materials in recentyears, which have excellent properties such as heat resistance,insulation, and structural stability.12,13 Several studies have beenmade on BN nanomaterials such as BN nanotubes, BN nano-capsules, and BN clusters since they have excellent propertiessuch as heat resistance in air and insulation, and these nano-

* To whom correspondence should be addressed. E-mail: m_monajjemi@cm.utexas.edu.

† Science and Research Branch, Islamic Azad University.‡ Chiang Mai University.§ Islamshahr Branch, Islamic Azad University.⊥ Qom Branch, Islamic Azad University.# Visiting Researcher: Department of Chemistry and Biochemistry,

Institute for Theoretical Chemistry, The University of Texas at Austin,Austin, TX.

J. Phys. Chem. C 2010, 114, 15315–15330 15315

10.1021/jp104274z 2010 American Chemical SocietyPublished on Web 08/23/2010

particles are expected to be useful as electronic devices, highheat resistance semiconductors, and insulator lubricants.14-17

From the experimental standard formation enthalpy, the energiesof hybridized sp2 and sp3 B-N bonds are known to be strongerin comparison with those of B-B and N-N bonds, namely,4.00, 2.32, and 2.11 eV, respectively.18 Along with theexperimental efforts, extensive theoretical studies have also beencarried out on BN fullerenes to understand their relative stabilityand size dependence of the properties.19-21 Several investigationshave dealt with the possibility of inorganic analogues of thefullerene cages that would be constructed entirely of BNpairs.22-25

Since the thermodynamic conditions for growth of BNnanotubes from nuclei are still not well-defined, comprehensivetheoretical simulations on these nanotubes continue to attractenhanced attention, and the lack of theoretical thermodynamicdata precludes a more detailed analysis.26

These nanotubes are found to be chiral or nonchiral; however,a preference toward the armchair and zigzag configurations issuggested. Electron energy loss spectroscopy yields a B/N ratioof approximately 1 and a perfect chemical homogeneity.27 Thispaper focuses on the tubes generated with the single-wall boronnanotube (SWBNNT) from a MWNT ) 1 as an armchairnanotube (n,m) with chirality n ) 6, m ) 6 and with a tube

Figure 1. (a) The geometrical structure of the generation of our considered armchair nanotube (n ) m ) 6) through folding of a section of agraphene sheet. (b) The optimized structure of the B18N18 ring at the B3LYP/EPR-III level of theory. (c) The optimized structure of alanine-NH2BHNBHNH2-glysine at the B3LYP/EPR-III level of theory.

15316 J. Phys. Chem. C, Vol. 114, No. 36, 2010 Monajjemi et al.

length of 3 Å. The schematics of the generation of theconsidered nanotube through folding of a section of a graphenesheet and the optimized structure of the alanine-B18N18-glysineare displayed in Figure 1, where C ) na1 + ma2 ) (n,m); a1

and a2 are the primitive lattice vectors of the graphene, and nand m are integers.28,29

2. Computational Details

The geometry of the B18N18-NH2BHNBHNH2 system hasbeen optimized by Becke’s hybrid three-parameter exchangefunctional and the nonlocal correlation functional of the Lee,Yang,and Parr (B3LYP) method30,31 with the EPR-III and EPR-II basis sets of Barone.32 The Gaussian quantum chemistrypackage was used for all calculations.33 The optimization wasdone along with a frequency calculation to verify that thegeometry was a real minimum without any imaginary frequency.

EPR-II is a double-� basis set with a single set of polarizationfunctions and an enhanced s part, (6,1)12,21 for H and (10,5,1)12,13,23

for B-F. EPR-III is a triple-� basis set including diffusefunctions, double d-polarizations, and a single set of f-polarization functions. Also in this case, the s-part is improvedto better describe the nuclear region, (6,2)10,13 for H and12,13,24,27

for B-F. Vibrational frequencies have been calculated at theB3LYP/EPR-II level of theory to verify that the geometry wasa real minimum without any imaginary frequency and analyzethe thermochemical functions including enthalpies and Gibbsfree energies.34

In the current study, we have performed systematic first-principle calculations on the atomic and electronic nanostruc-tures of the B18N18-NH2BHNBHNH2. Structure, stability, andspectroscopic properties of this system have been explored. Anattempt is made to explain the anomalous nonbounded interac-tions of the NH2BHNBHNH2 molecule inside of the B18N18 ringwith a quantized nanospectrophotometer detection of variousquantized parameters of a given alanine-glysine amino acid.In other words, a supposed picture of the electronic structureof these magnetically unusual nanoparticles encouraged us toimagine such a nanosystem as a quantized transition systemwhich would induce an electromagnetic field through electro-static interaction of the NH2BHNBHNH2 molecule inside ofthe B18N18 ring and also has the capability of detecting thequantized parameters of the system considered as well as otherbimolecular amino acids which can be coupled with this system.In other words, there is mutual electrostatic interaction betweenthe NH2BHNBHNH2 molecule and the B18N18 ring, which yieldsthe quantization of the radial component of the dipole momentvector (r) as well as the voltage differences (∆V) and relativeenergies (∆E) of the NH2BHNBHNH2 radical, cation, and anion.The NH2BHNBHNH2 molecule moves among quantized coor-dinates of the radial component (r) of the dipole moment aswell as energy levels, and then, a specific spectrum wouldappear. Therefore, when the NH2BHNBHNH2 is coupled withtwo points of the amino acids inside of the B18N18 ring, differentradical, cationic, and anionic forms of the NH2BHNBHNH2 areexpected to appear due to the potential energy difference orvoltage caused by the NH2BHNBHNH2. Therefore, investigationof the electrostatic interaction of the NH2BHNBHNH2 with itssurrounding ring along with exploring the variations of differentphysicochemical properties such as dipole and quadropolemoments as well as NBO and NQR parameters of the B18N18-NH2BHNBHNH2 system would be of great importance.

It has been demonstrated how this mechanistic question maybe addressed in the framework of modern electronic structuremethods, specifically with the B3LYP hybrid density functional

method and EPR-III basis set. Natural bond orbital (NBO)analysis has been employed to analyze the calculated electrondensity in terms of localized Lewis structure and resonancetheoretical concepts.35 As a check on the quality of the calculatedgeometrical parameters and their stability with respect to thelevel of theory, the HOMO and the LUMO differences havebeen explored.

In the course of determining hyperfine parameters and relatingthem to the underlying electronic structure of the consideredsystem, anisotropic magnetic effects have been explained andprovided useful information on the interaction characteristics.26

The HOMO corresponds to a combination of lone pair orbitalson the N atoms as well as the LUMO, which is characterizedby large contributions from vacant p orbitals on B atoms withsome admixture of N-based orbitals having been calculated.36

The NBO analysis has been performed by using NBO asimplemented in the Gaussian quantum chemistry package.35 Theasymmetry parameters as well as the quadrupole couplingconstant of nitrogen atoms involved in the B18N18-NH2BHNBHNH2 system, which have been correlated withatomic charges, have been computed.

The spin-spin magnetic hyperfine Hamiltonian as a part ofthe molecular Hamiltonian can be presented as eq 1

where gS and µB are the free electron g-factor and the Bohrmagneton, respectively, gS and µB are the nuclear g-factor and

the nuclear magneton, SIfSi and IR

f are “the spins of the electron

i and the nucleus R, and rIRf represents the distance between an

electron i and nucleus R; i and R are referred to as electronsand magnetic nuclei, respectively. This operator acts both inthe state space of the electrons and in the state space of thenuclei. The anisotropic dipole-dipole interaction between theelectronic and nuclear spin magnetic moments is representedby the first and the second parts of the considered equation.The last term, the isotropic Fermi contact term, arises from themagnetic field inside of the nucleus, created by its magneticmoment. The terms in the effective Hamiltonian are obtainedafter integration over electronic spatial coordinates; each termcontains angular momentum operators and molecular param-eters.37

Th isotropic Fermi contact constant bF (in MHz) is definedby

where bF ) b + c/3. Thus, the basic quantities that determinethe HF interaction at the Nth nucleus are those in brackets and|Ψ(0)|N2 . The ab initio calculated isotropic constant, bF ) (2µ0/3h)gSgNµBµNPS(N), directly depends on the Fermi contact spindensity function per unpaired electron at a nucleus.36

3. Results and Discussion

The aim of this section is to first discuss the different aspectsof the electronic structure of the B18N18-NH2BHNBHNH2

HhfSS )

µ0

4πgSµBµN ∑

i,RgR{3

(Sif · riRf)(IR

f · riRf)

riR5

-(Sif · IRf)

riR3

+

8π3

× (Sif · IRf) ·δ(3)(riR

f)} (1)

bF )2µ0

3hgSgNµBµN|Ψ(0)|2

NH2BHNBHNH2 Inside of the B18N18 Nanoring J. Phys. Chem. C, Vol. 114, No. 36, 2010 15317

system for further validation of theoretical results to increasetheir usefulness in practical applications or for pre-experimentalmodeling. Second, we have explored the electromagnetic natureof the B18N18-NH2BHNBHNH2 system by calculating thefollowing parameters, which provide valuable information onthe interaction characteristics.

3.1. Relative Energies. To verify the structural stability ofour considered B18N18-NH2BHNBHNH2 system, we haveoptimized the B18N18-NH2BHNBHNH2 system using DFTmethod (B3LYP) with both EPR-II and EPR-III basis sets.Undoubtedly, since we have focused on electromagnetic induc-tion of NH2BHNBHNH2 inside of the B18N18 ring, employingthese employed basis sets seemed useful and helped us findlogical relationships between obtained data. The calculatedenergy (Hartree), relative energy (kcal/mol), and BSSE (kcal/mol) corrected interaction energy (kcal/mol) for cationic, radical,and anionic forms of NH2BHNBHNH2 in the B18N18-NH2BHNBHNH2 system within transition are compared inTable 1.

Strikingly, despite the intrinsic linearity of NH2BHNBHNH2 indifferent radical, cationic, and anionic forms, in this step, theobtained optimization results confirmed the stability of theB18N18-NH2BHNBHNH2 system, and the NH2BHNBHNH2 mol-ecule was located strictly in the center of the B18N18 ring vertically.According to the frequency calculation at the B3LYP/EPR-II levelof theory, observing no negative frequency as well as obtainingthermochemical functions such as ∆G ) -67.7929888325 kcal/mol and ∆H ) -124.401248337 kcal/mol confirmed thestructural stability of the B18N18 ring. This effect is probablydue to the large dipole moments of the B-N bonds, whichpreferentially enhance the ring stability. Regarding the system’sstability within transitions and rotations of radical, cationicmand anionic forms of NH2BHNBHNH2, it is notable that theobtained barrier energies for the radical, cationic and anionicforms were 3.876, 2.655, and 5.224 kcal/mol, respectively. Thegraphs of rotational and transition energy barriers of radical,anionic, and cationic forms of NH2BHNBHNH2 in theB18N18-NH2BHNBHNH2 system are displayed in Figure 2. Toaccount for these observations, two observed points are not-able. First, for radical, anionic, and cationic forms ofNH2BHNBHNH2, the most stable condition has been observedin the case that NH2BHNBHNH2 is located exactly in the centerof the B18N18 ring, that is, the coordination of nitrogen atomswas (0,0,0). Second, the reported BSSE data revealed thatdespite insignificant changes of barrier energies based on theplotted graphs, the entire trend has not changed essentially fromthat of the first energy calculations. These obtained results

motivated us to investigate the rotation of NH2BHNBHNH2.Therefore, we have rotated the center of NH2BHNBHNH2

around one of its axes. In this case, the barrier energy for theradical form was significant (48.5091 kcal/mol). On the basisof such a considerably high barrier energy, we have observedthat the radical form of NH2BHNBHNH2 strongly resists underthis rotation and exhibits no tendency for rotation in thehorizontal state.

It has been understood that the only possible movement whichprobably caused the system’s structural distortion was internalrotation of the radical form of NH2BHNBHNH2 inside of thering. It is evident that with such a high barrier energy, we couldnot expect any rotation.

According to the plotted rotational graph (Figure 1), it hasbeen found out that the energy barrier of the NH2BHNBHNH2

radical stands as the highest value, and the following trend couldbe observed

3.2. HOMO-LUMO Gap of the System. The LUMO-HOMO band gap is a gap between the LUMO (the lowestunoccupied molecular orbital) and HOMO (the highest occupiedmolecular orbital).38 BN nanotubes have a wide band gap (E)of ∼6 eV and nonmagnetism independent of the tube diameters.The large LUMO-HOMO gap is often regarded as a moleculestability condition.39 More sophisticated treatment of large gapsis seen to occur for systems with high relative stability.40 Theband gap of the B18N18-NH2BHNBHNH2 system as the relativedifferences in the energy of the HOMO and the LUMO is reportedin Table 2. According to the results in Table 2, in anionic andradical forms of the NH2BHNBHNH2 molecule, the system showedthe highest structural stability compared with the cationic state. Inother words, the obtained values for the anionic and radical forms

TABLE 1: Calculated Relative Corrected Interaction BSSEEnergy (kcal/mol) for Cationic, Radical, and Anionic Formsof NH2BHNBHNH2 in the B18-N18-NH2BHNBHNH2 Systemwithin Transition

B18N18-NH2

BHNBHNH2 transition (Å)

∆E (kcal/mol)

anion cation radical

0.0 0 0 00.4 0.4029 0.3367 0.13520.8 1.7404 1.4300 1.25441.2 3.2098 2.4105 2.48201.6 4.2482 2.6559 3.65122.0 4.6999 2.2783 3.87602.4 5.0443 1.4876 3.72062.8 5.2242 0.7574 3.34873.2 5.0070 0.2040 2.55723.6 4.2051 0.1613 1.51744.0 2.9775 0.0923 0.6075

Figure 2. The graphs of the rotational and transitional BSSE energybarriers of NH2BHNBHNH2 in the B18N18-NH2BHNBHNH2 system.

NH2BHNBHNH2 (radical) > NH2BHNBHNH2 (anion) >NH2BHNBHNH2 (cation)

15318 J. Phys. Chem. C, Vol. 114, No. 36, 2010 Monajjemi et al.

were 26-27 Hartree, which were significantly different from thoseof the cationic form (0.0161-0.18339 Hartree). In these anionicand radical cases, especially in the anionic form at the 0,0,30coordinate, the highest HOMO-LUMO was at 27.0925 Hartree.After inspecting the highest HOMO-LUMO band gaps in allthree radical, anionic, and cationic forms, it seems that in allthree considered cases, the highest ∆(HOMO-LUMO) valuesand the highest stability occurred in the center coordinates andwith the B18N18 ring. Therefore, in the cation, anion, and radicalat the 0,0,50, 0,0,30, and 0,0,90 coordinates, the highestHOMO-LUMO band gaps were 0.18398, 27.0925, and 26.87556Hartree, respectively.

It is understood that in the case of the anionic form at the0,0,70 and 0,0,90 coordinates, for the cationic form at 0,0,130and 0,0,150, and for the radical form at 0,0,30 and 0,0,170, thesame HOMO-LUMO band gaps could be observed.

3.3. Natural Bond Orbital (NBO) Analysis. The conceptsof natural atomic orbital (NAO) and NBO analyses are usefulfor distributing electrons into atomic and molecular orbitals usedfor the one-electron density matrix to define the shape of theatomic orbitals in the molecular environment and then derivemolecular bonds from electron density between atoms.

The NAOs will normally resemble the pure atomic orbitalsand may be divided into a natural minimal basis, correspond-ing to the occupied atomic orbitals for the isolated atom,and a remaining set of natural Rydberg orbitals based on themagnitude of the occupation numbers. The minimal setof NAOs will normally be strongly occupied, while theRydberg NAO usually will be weakly occupied. There areas many NAOs as the size of the atomic basis set, and thenumber of Rydberg NAOs thus increases as the basis set isenlarged .The results of NBO analysis at the B3LYP/EPR-III level of theory are listed in Table 3.

At each considered coordination, the bonding and antibondingcoefficients of s and p orbitals of B-N bonds were 0.5 and0.8. However, for both the B37-N38 and B39-N40 bonds,the constant coefficients of 0.3 and 0.9 have been yielded. Onthe basis of the constant values of the coefficients of a linearcombination of s and p orbitals of different bonds (0.5 and 0.8),a specific voltage difference could be expected.

It is observed that the percent of s and p orbitals for differentbonds of the NH2BHNBHNH2 anion in the B18N18-NH2BHNBHNH2 system at all coordinations refers to sp2

hybridization for B as well as sp3 hybridization for the N atom,which is in agreement with the intrinsic sp2 hybridization of Band N atoms. The obtained relationship between NBO and ∆Vvalues of different bonds of the B18N18-NH2BHNBHNH2

system revealed that in the case of the NH2BHNBHNH2 radical,the closeness of the obtained ∆V values (55.245 au) derived by

EPR calculations was the lowest value of ∆V compared withthose of the NH2BHNBHNH2 cation and anion. In other words,the average value of ∆V in the case of the NH2BHNBHNH2

radical low average (∆V ) 55.245 au) revealed the sharpGaussian distribution and could be related with the constantbonding molecular orbital coefficients. Meanwhile, the oppositebehavior has been seen especially for the NH2BHNBHNH2

cation. It is notable that these values were in accordance withthe estimation of the sp2 hybridization of the B atom derivedby NBO analysis, while such a direct relationship has not beenobserved for the NH2BHNBHNH2 cation and anion.

3.4. Nuclear Quadrupole Resonance Parameters. Theresults obtained in the hitherto studies confirmed the usefulnessof NQR spectroscopy for determination of physical and chemicalproperties of compounds and prediction of their chemicalactivity. Moreover, the spectroscopic EPR and NQR parameterscharacterizing the electronic effects are correlated with theactivity of the B18N18-NH2BHNBHNH2 system studied. Theinformation inferred from the NQR study on the local electrondensity distribution together with analysis of the charge distribu-tion by the density functional methods provided suitablemeans for determination of reactive sites of the B18N18-NH2BHNBHNH2 system and hence indicated possible promisingdirections to be followed in nanodevices.41,42

The asymmetry parameters and quadrupole coupling constantsof nitrogen atoms of the B18N18-NH2BHNBHNH2 system atdifferent coordinates are listed in Table 4. It can be seen thatthe coupling constants of nitrogen atoms of all differentcoordinates increased from 0,0,0 up to a maximum point andthen decreased to the lowest value. As a whole, it is understoodthat the maximum amount of charge density on the nitrogennuclei was concentrated at the edges and in the center of theB18N18 ring, and at these regions, the lowest asymmetryparameters could be observed. Another point is that amongnitrogen atoms, the N38 of the anionic form with � ) 3.773MHz and the N40 with � ) 3.578 MHz yielded the highestcoupling constant values. It is notable that such a high value of� and, consequently, a high charge density corresponded tonitrogen atoms of the NH2BHNBHNH2 molecule inside of thering and at the 0,0,50 and 0,0,30 coordinates for the radicaland cationic forms, respectively.

3.5. Nonbonded Interaction of NH2BHNBHNH2 with theB18N18 Ring. In this section, the major point is embeddedin the investigation of the electrostatic interaction ofNH2BHNBHNH2 with its surrounding B18N18 ring, which formsthe basis for more detailed studies of other systems withnonbounded interactions. To investigate the electrostatic interac-tion on NH2BHNBHNH2 with six different segments includingsix loops and six connecting bonds of the B18N18 ring withinthe vertical transition, first, the five hexagon loops have beenfreezed, and the electrostatic interaction of NH2BHNBHNH2

with the one remaining active loop has been considered. Otherloops have been examined one by one in the same way, andthe changes of all of the following calculated quantities havebeen explored. Next, we were focused on each bond of B18N18

individually and evaluated the interaction of NH2BHNBHNH2

with each of the six connecting bonds of the B18N18 ring andrepeated the calculations along each bond.

3.5.1. Analysis of Dipole Moments. The only known mech-anisms for the creation of dipole moments are by current loopsor quantum mechanical spin since the existence of monopoleshas never been experimentally demonstrated.43-45 On the otherhand, dipole expansions are used in the study of electromagneticfields of charge and current distributions. The efficiency of such

TABLE 2: Band Gap of the B18N18-NH2BHNBHNH2

System As the Relative Differences in the Energy of theHOMO and LUMO in Atomic Units

band gap (HOMO-LUMO) (Hartree)

coordinates anion cation radical

0.0,0.0,0.0 27.07986 0.02235 26.862930.0,0.0,10.0 27.08589 0.02186 26.870040.0,0.0,30.0 27.0925 0.0161 26.862820.0,0.0,50.0 27.08153 0.18398 26.863110.0,0.0,70.0 27.08313 0.02201 26.868180.0,0.0,90.0 27.08313 0.02128 26.875560.0,0.0,110.0 27.08092 0.0231 26.862870.0,0.0,130.0 27.08205 0.02202 26.866270.0,0.0,150.0 27.08533 0.02202 26.868490.0,0.0,170.0 27.08011 0.02355 26.86282

NH2BHNBHNH2 Inside of the B18N18 Nanoring J. Phys. Chem. C, Vol. 114, No. 36, 2010 15319

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*(sp

2.13

)B+

0.86

49*(

sp1.

00)N

BD

(2)

B37

-N

380.

3276

*(sp

99.9

9 d8.71

)B+

0.94

48*(

sp1.

00)N

-0.

3278

*(sp

99.9

9 d7.24

)B+

0.94

48*(

sp1.

00)N

BD

(1)

B37

-N

410.

5009

*(sp

1.97

)B+

0.86

55*(

sp1.

22d0.

01)N

0.52

64*(

sp1.

74)B

+0.

8502

*(sp

1.39

d0.01

)N0.

5014

*(sp

1.97

)B+

0.86

52*(

sp1.

23d0.

01)N

BD

(1)

N38

-B

390.

8648

*(sp

1.00

)N+

0.50

21*(

sp2.

12)B

0.86

47*(

sp1.

00)N

+0.

5022

*(sp

2.23

d0.01

)B0.

8649

*(sp

1.00

)N+

0.50

20*(

sp2.

13)B

BD

(1)

B39

-N

400.

5008

*(sp

1.99

)B+

0.86

56*(

sp1.

22d0.

01)N

0.52

65*(

sp1.

74)B

+0.

8502

*(sp

1.39

d0.01

)N0.

5013

*(sp

1.99

)B+

0.86

53*(

sp1.

23d0.

01)N

BD

(2)

B39

-N

400.

3542

*(sp

99.9

9 d0.88

)B+

0.93

52*(

sp99

.99 d0.

03f0.

08)N

-0.

3561

*(sp

99.9

9 d0.76

)B+

0.93

44*(

sp99

.99 d0.

02f0.

07)N

0.0,

0.0,

30.0

BD

(1)

B37

-N

380.

5195

*(sp

2.10

)B+

0.85

44*(

sp1.

00)N

0.50

17*(

sp2.

24d0.

01)B

+0.

8650

*(sp

1.00

)N0.

5019

*(sp

2.13

)B+

0.86

49*(

sp1.

00)N

BD

(2)

B37

-N

380.

3527

*(sp

1.00

)B+

0.93

57*(

sp1.

00)N

-0.

3280

*(sp

99.9

9 d25.6

6 )B+

0.94

47*(

sp1.

00)N

BD

(1)

B37

-N

410.

5181

*(sp

1.88

)B+

0.85

53*(

sp1.

31)N

0.52

75*(

sp1.

73)B

+0.

8496

*(sp

1.41

d0.01

)N0.

5019

*(sp

1.97

)B+

0.86

50*(

sp1.

23d0.

01)N

BD

(1)

N38

-B

390.

8544

*(sp

1.00

)N+

0.51

95*(

sp2.

10)B

0.86

50*(

sp1.

00)N

+0.

5018

*(sp

2.24

d0.01

)B0.

8649

*(sp

1.00

)N+

0.50

19*(

sp2.

13)B

BD

(1)

B39

-N

400.

3552

*(sp

99.9

9 d4.50

)B+

0.93

48*(

sp99

.99 d0.

11f0.

49)N

0.52

75*(

sp1.

73)B

+0.

8495

*(sp

1.41

d0.01

)N0.

5019

*(sp

1.98

)B+

0.86

49*(

sp1.

23d0.

01)N

BD

(2)

B39

-N

400.

5180

*(sp

1.89

)B+

0.85

54*(

sp1.

31)N

-0.

3554

*(sp

99.9

9 d1.56

)B+

0.93

47*(

sp99

.99 d0.

05f0.

16)N

0.0,

0.0,

50.0

BD

(1)

B37

-N

380.

5021

*(sp

2.12

)B+

0.86

48*(

sp1.

00)N

0.50

33*(

sp2.

23)B

+0.

8641

*(sp

1.00

)N0.

5020

*(sp

2.13

)B+

0.86

49*(

sp1.

00)N

BD

(2)

B37

-N

380.

3275

*(sp

1.00

)B+

0.94

49*(

sp1.

00)N

-0.

3277

*(sp

1.00

)B+

0.94

48*(

sp1.

00)N

BD

(1)

B37

-N

410.

5015

*(sp

1.97

)B+

0.86

52*(

sp1.

21)N

0.37

92*(

sp1.

00)B

+0.

9253

*(sp

99.9

9 d1.34

f1.99

)N0.

5018

*(sp

1.97

)B+

0.86

50*(

sp1.

21)N

BD

(2)

B37

-N

41-

0.52

55*(

sp1.

75)B

+0.

8508

*(sp

1.38

d0.01

)N-

BD

(1)

N38

-B

390.

8648

*(sp

1.00

)N+

0.50

21*(

sp2.

12)B

0.86

41*(

sp1.

00)N

+0.

5033

*(sp

2.22

)B0.

8648

*(sp

1.00

)N+

0.50

20*(

sp2.

13)B

BD

(1)

B39

-N

400.

5016

*(sp

1.98

)B+

0.86

51*(

sp1.

21)N

0.37

90*(

sp1.

00)B

+0.

9254

*(sp

1.00

)N0.

5019

*(sp

1.98

)B+

0.86

49*(

sp1.

21)N

BD

(2)

B39

-N

400.

3544

*(sp

99.9

9 d2.76

)B+

0.93

51*(

sp99

.99 d0.

11f0.

28)N

-0.

3558

*(sp

99.9

9 d2.18

)B+

0.93

46*(

sp99

.99 d0.

08f0.

22)N

0.0,

0.0,

70.0

BD

(1)

B37

-N

380.

5021

*(sp

2.12

)B+

0.86

48*(

sp1.

00)N

0.50

22*(

sp2.

23d0.

01)B

+0.

8648

*(sp

1.00

)N0.

5020

*(sp

2.13

)B+

0.86

49*(

sp1.

00)N

BD

(2)

B37

-N

380.

3276

*(sp

99.9

9 d6.55

)B+

0.94

48*(

sp1.

00)N

-0.

3277

*(sp

99.9

9 d5.09

)B+

0.94

48*(

sp1.

00)N

BD

(1)

B37

-N

410.

5005

*(sp

1.97

)B+

0.86

57*(

sp1.

23d0.

01)N

0.52

65*(

sp1.

74)B

+0.

8502

*(sp

1.39

d0.01

)N0.

5009

*(sp

1.97

)B+

0.86

55*(

sp1.

24d0.

01)N

BD

(1)

N38

-B

390.

8648

*(sp

1.00

)N+

0.50

21*(

sp2.

12)B

0.86

47*(

sp1.

00)N

+0.

5022

*(sp

2.23

d0.01

)B0.

8649

*(sp

1.00

)N+

0.50

20*(

sp2.

13)B

BD

(1)

B39

-N

400.

5004

*(sp

2.00

)B+

0.86

58*(

sp1.

23d0.

01)N

0.52

65*(

sp1.

74)B

+0.

8501

*(sp

1.39

d0.01

)N0.

5007

*(sp

2.01

)B+

0.86

56*(

sp1.

24d0.

01)N

BD

(2)

B39

-N

400.

3548

*(sp

99.9

9 d0.63

)B+

0.93

49*(

sp99

.99 d0.

02)N

-0.

3568

*(sp

99.9

9 d0.51

)B+

0.93

42*(

sp99

.99 d0.

02f0.

05)N

0.0,

0.0,

90.0

BD

(1)

B37

-N

380.

5193

*(sp

2.10

)B+

0.85

46*(

sp1.

00)N

0.50

18*(

sp2.

24d0.

01)B

+0.

8650

*(sp

1.00

)N0.

5019

*(sp

2.13

)B+

0.86

50*(

sp1.

00)N

BD

(2)

B37

-N

380.

3522

*(sp

1.00

)B+

0.93

59*(

sp1.

00)N

-0.

3280

*(sp

1.00

)B+

0.94

47*(

sp1.

00)N

BD

(1)

B37

-N

410.

5181

*(sp

1.88

)B+

0.85

53*(

sp1.

30)N

0.52

71*(

sp1.

74)B

+0.

8498

*(sp

1.41

)N0.

5021

*(sp

1.97

)B+

0.86

48*(

sp1.

22d0.

01)N

BD

(1)

N38

-B

390.

8546

*(sp

1.00

)N+

0.51

93*(

sp2.

10)B

0.86

50*(

sp1.

00)N

+0.

5018

*(sp

2.24

d0.01

)B0.

8650

*(sp

1.00

)N+

0.50

19*(

sp2.

13)B

BD

(1)

B39

-N

400.

3547

*(sp

99.9

9 d11.7

3 )B+

0.93

50*(

sp99

.99 d0.

27f1.

27)N

0.52

71*(

sp1.

74)B

+0.

8498

*(sp

1.41

d0.01

)N0.

5022

*(sp

1.97

)B+

0.86

48*(

sp1.

22d0.

01)N

BD

(2)

B39

-N

400.

5181

*(sp

1.88

)B+

0.85

53*(

sp1.

31)N

-0.

3550

*(sp

99.9

9 d3.43

)B+

0.93

49*(

sp99

.99 d0.

09f0.

36)N

0.0,

0.0,

110.

0B

D(1

)B

37-

N38

0.50

21*(

sp2.

12)B

+0.

8648

*(sp

1.00

)N0.

5033

*(sp

2.23

)B+

0.86

41*(

sp1.

00)N

0.50

20*(

sp2.

13)B

+0.

8649

*(sp

1.00

)NB

D(2

)B

37-

N38

0.32

75*(

sp99

.99 d27

.22 )B

+0.

9448

*(sp

1.00

)N-

0.32

78*(

sp99

.99 d19

.81 )B

+0.

9448

*(sp

1.00

)NB

D(1

)B

37-

N41

0.50

13*(

sp1.

97)B

+0.

8652

*(sp

1.21

)N0.

3792

*(sp

99.9

9 d4.91

)B+

0.92

53*(

sp99

.99 d0.

28f0.

43)N

0.50

16*(

sp1.

97)B

+0.

8651

*(sp

1.21

)NB

D(2

)B

37-

N41

-0.

5254

*(sp

1.76

)B+

0.85

09*(

sp1.

38d0.

01)N

-B

D(1

)N

38-

B39

0.86

48*(

sp1.

00)N

+0.

5021

*(sp

2.12

)B0.

8641

*(sp

1.00

)N+

0.50

33*(

sp2.

23)B

0.86

49*(

sp1.

00)N

+0.

5020

*(sp

2.13

)BB

D(1

)B

39-

N40

0.50

14*(

sp1.

98)B

+0.

8652

*(sp

1.21

)N0.

3790

*(sp

99.9

9 d8.03

)B+

0.92

54*(

sp99

.99 d0.

55f0.

84)N

0.50

17*(

sp1.

98)B

+0.

8650

*(sp

1.21

)NB

D(2

)B

39-

N40

0.35

43*(

sp99

.99 d1.

80)B

+0.

9351

*(sp

99.9

9 d0.07

f0.18

)N0.

5254

*(sp

1.75

)B+

0.85

09*(

sp1.

38d0.

01)N

0.35

60*(

sp99

.99 d1.

41)B

+0.

9345

*(sp

99.9

9 d0.05

f0.14

)N0.

0,0.

0,13

0.0

BD

(1)

B37

-N

380.

5021

*(sp

2.13

)B+

0.86

48*(

sp1.

00)N

0.50

21*(

sp2.

24d0.

01)B

+0.

8648

*(sp

1.00

)N0.

5020

*(sp

2.13

)B+

0.86

49*(

sp1.

00)N

BD

(2)

B37

-N

380.

3278

*(sp

99.9

9 d7.98

)B+

0.94

47*(

sp1.

00)N

-0.

3279

*(sp

99.9

9 d5.89

)B+

0.94

47*(

sp1.

00)N

BD

(1)

B37

-N

410.

5007

*(sp

1.98

)B+

0.86

56*(

sp1.

22)N

0.52

64*(

sp1.

74)B

+0.

8502

*(sp

1.39

d0.01

)N0.

5011

*(sp

1.97

)B+

0.86

54*(

sp1.

23d0.

01)N

BD

(1)

N38

-B

390.

8648

*(sp

1.00

)N+

0.50

21*(

sp2.

12)B

0.86

48*(

sp1.

00)N

+0.

5021

*(sp

2.24

d0.01

)B0.

8649

*(sp

1.00

)N+

0.50

20*(

sp2.

13)B

BD

(1)

B39

-N

400.

5006

*(sp

2.00

)B+

0.86

57*(

sp1.

22)N

0.52

65*(

sp1.

74)B

+0.

8502

*(sp

1.39

d0.01

)N0.

5009

*(sp

2.00

)B+

0.86

55*(

sp1.

23d0.

01)N

BD

(2)

B39

-N

400.

3543

*(sp

99.9

9 d0.78

)B+

0.93

51*(

sp99

.99 d0.

02f0.

07)N

-0.

3566

*(sp

99.9

9 d0.59

)B+

0.93

42*(

sp99

.99 d0.

02f0.

06)N

15320 J. Phys. Chem. C, Vol. 114, No. 36, 2010 Monajjemi et al.

a fast method is superior if the system is clustered and has largedensity fluctuation.44 Therefore, the lack of experimentaldemonstration and its importance in theoretical simulations wasa motivation for us to investigate dipole moments from atheoretical point of view.

The coefficients of angular coordinates of multipole momentare defined as a sum of following spherical harmonics

Therefore, the electromagnetic potential can be obtained as

The tailor expansion of V(r - R) around the r ) 0 is

where

Therefore, the above equation can be considered as thedifferential of V in terms of r.

3.5.2. Interaction of Two NonoWerlapping Parts ofNH2BHNBHNH2 and B18N18. The total electrostatic interactionenergy of the considered system (UNH2BHNBHNH2-B18N18

) betweenthe two charge distributions of two B18N18 and NH2BHNBHNH2

molecules is

As a consequence of the electrostatic B18N18-NH2BHNBHNH2

interaction, the charge distribution of the NH2BHNBHNH2

molecule inside of the B18N18 ring polarizes the B18N18 chargedistribution and induces the electromagnetic field in theB18N18-NH2BHNBHNH2 system.

Considering rXY ) rY - rX, it can be defined as

Since the two distributions do not overlapTA

BL

E3:

Con

tinu

ed

NB

Oan

alys

is

orie

ntat

ions

bond

anio

nca

tion

radi

cal

0.0,

0.0,

150.

0B

D(1

)B

37-

N38

0.50

20*(

sp2.

13)B

+0.

8649

*(sp

1.00

)N0.

5019

*(sp

2.24

d0.01

)B+

0.86

49*(

sp1.

00)N

0.50

19*(

sp2.

13)B

+0.

8650

*(sp

1.00

)NB

D(2

)B

37-

N38

0.32

80*(

sp1.

00)B

+0.

9447

*(sp

1.00

)N-

0.32

82*(

sp1.

00)B

+0.

9446

*(sp

1.00

)NB

D(1

)B

37-

N41

0.50

16*(

sp1.

97)B

+0.

8651

*(sp

1.21

)N0.

5268

*(sp

1.74

)B+

0.85

00*(

sp1.

39d0.

01)N

0.50

22*(

sp1.

97)B

+0.

8647

*(sp

1.21

)NB

D(1

)N

38-

B39

0.86

49*(

sp1.

00)N

+0.

5020

*(sp

2.13

)B0.

8649

*(sp

1.00

)N+

0.50

19*(

sp2.

24d0.

01)B

0.86

49*(

sp1.

00)N

+0.

5019

*(sp

2.13

)BB

D(1

)B

39-

N40

0.50

16*(

sp1.

98)B

+0.

8651

*(sp

1.21

)N0.

5269

*(sp

1.74

)B+

0.85

00*(

sp1.

39d0.

01)N

0.50

23*(

sp1.

97)B

+0.

8647

*(sp

1.21

)NB

D(2

)B

39-

N40

0.35

30*(

sp99

.99 d4.

59)B

+0.

9356

*(sp

99.9

9 d0.13

f0.50

)N-

0.35

50*(

sp99

.99 d6.

18)B

+0.

9349

*(sp

99.9

9 d0.16

f0.66

)N0.

0,0.

0,17

0.0

BD

(1)

B37

-N

380.

5020

*(sp

2.13

)B+

0.86

49*(

sp1.

00)N

0.50

33*(

sp2.2

3 d0.01

)B+

0.86

41*(

sp1.

00)N

0.50

19*(

sp2.

13)B

+0.

8649

*(sp

1.00

)NB

D(2

)B

37-

N38

0.32

77*(

sp1.

00)B

+0.

9448

*(sp

1.00

)N-

0.32

80*(

sp1.

00)B

+0.

9447

*(sp

1.00

)NB

D(1

)B

37-

N41

0.50

16*(

sp1.

97)B

+0.

8651

*(sp

1.20

)N0.

3790

*(sp

99.9

9 d5.73

)B+

0.92

54*(

sp99

.99 d0.

33f0.

52)N

0.50

21*(

sp1.

97)B

+0.

8648

*(sp

1.20

)NB

D(2

)B

37-

N41

-0.

5253

*(sp

1.76

)B+

0.85

09*(

sp1.

37d0.

01)N

-B

D(1

)N

38-

B39

0.86

49*(

sp1.

00)N

+0.

5020

*(sp

2.13

)B0.

8641

*(sp

1.00

)N+

0.50

33*(

sp2.

23d0.

01)B

0.86

49*(

sp1.

00)N

+0.

5019

*(sp

2.13

)BB

D(1

)B

39-

N40

0.50

16*(

sp1.

98)B

+0.

8651

*(sp

1.19

)N0.

3788

*(sp

99.9

9 d15.1

0 )B+

0.92

55*(

sp99

.99 d1.

09f1.

71)N

0.50

22*(

sp1.

97)B

+0.

8648

*(sp

1.20

)NB

D(2

)B

39-

N40

0.35

33*(

sp99

.99 d6.

04)B

+0.

9355

*(sp

99.9

9 d0.20

f0.64

)N0.

5253

*(sp

1.75

)B+

0.85

09*(

sp1.

37d0.

01)N

0.35

53*(

sp99

.99 d6.

06)B

+0.

9347

*(sp

99.9

9 d0.19

f0.64

)N

f(θ, �) ) ∑l)0

∞

∑m)-l

l

ClmYl

m(θ, �) (2)

V ) (r, θ, �) ∑i)0

∞

∑m)-l

l

Clm(r)Yl

m(θ, �) )

∑j)1

∞

∑l)0

∞

∑m)-l

l Dl,jm

rjYl

m(θ, �) (3)

V(r - R) ) V(R) - ∑R)x,y,z

raVR(R) +

12 ∑

R)x,y,z∑

�)x,y,z

rRr�Va�(R) - ... + ... (4)

VR(R) ) (∂V(r - R)∂rR ) and VR�(R) ) (∂2V(r - R)

∂rR∂r�)

r)0

(5)

UB18N18-NH2BHNBHNH2) ∑

µ∈B18N18

∑V∈NH2BHNBHNH2

qµqV

4πε0rµV

(6)

RB18N18-NH2BHNBHNH2+ rNH2BHNBHNH2,V + rVµ - rµ,B18N18

) 0

(7)

NH2BHNBHNH2 Inside of the B18N18 Nanoring J. Phys. Chem. C, Vol. 114, No. 36, 2010 15321

TA

BL

E4:

NQ

RP

aram

eter

sof

Nit

roge

nA

tom

sof

B18

N18-

NH

2BH

NB

HN

H2

inth

eA

nion

ic,

Cat

ioni

c,an

dR

adic

alF

orm

sat

the

B3L

YP

/EP

R-I

IIL

evel

ofT

heor

y

η

�(M

Hz)

anio

nic

catio

nic

atom

s0,

0,0

0,0,

100,

0,30

0,0,

500,

0,70

0,0,

900,

0,11

00,

0,13

00,

0,15

00,

0,17

00,

0,0

0,0,

100,

0,30

0,0,

500,

0,70

0,0,

900,

0,11

00,

0,13

00,

0,15

00,

0,17

0

N4

0.50

70.

502

0.49

90.

503

0.49

30.

493

0.49

10.

496

0.50

00.

504

0.50

30.

476

0.43

20.

443

0.44

30.

490

0.50

10.

524

0.52

40.

512

1.85

81.

873

1.89

91.

904

1.91

51.

915

1.91

31.

890

1.86

51.

858

1.93

91.

949

1.94

91.

961

1.96

11.

945

1.95

01.

943

1.94

31.

942

N5

0.20

70.

202

0.18

30.

178

0.19

10.

191

0.21

30.

212

0.21

30.

205

0.26

10.

269

0.28

50.

234

0.23

40.

216

0.23

10.

234

0.23

40.

220

2.31

22.

303

2.29

62.

302

2.31

32.

313

2.32

12.

318

2.31

02.

286

2.37

02.

391

2.42

92.

428

2.42

82.

394

2.36

32.

344

2.34

42.

379

N7

0.22

00.

217

0.19

50.

197

0.20

20.

202

0.21

40.

209

0.21

20.

216

0.21

80.

234

0.32

90.

325

0.32

50.

233

0.22

40.

222

0.22

20.

251

2.24

32.

233

2.31

92.

375

2.32

92.

329

2.30

92.

319

2.32

32.

315

2.35

42.

374

2.50

72.

542

2.54

22.

367

2.35

92.

369

2.36

92.

395

N8

0.49

30.

495

0.50

20.

509

0.50

50.

505

0.50

30.

498

0.49

10.

490

0.51

10.

522

0.54

50.

524

0.52

40.

434

0.44

40.

464

0.46

40.

502

1.90

21.

885

1.85

91.

848

1.87

51.

875

1.90

41.

910

1.91

61.

912

1.94

51.

943

1.93

61.

934

1.93

41.

958

1.96

21.

954

1.95

41.

951

N10

0.21

60.

213

0.22

20.

218

0.21

50.

215

0.20

20.

205

0.21

50.

212

0.23

60.

238

0.20

70.

219

0.21

90.

304

0.32

20.

259

0.25

90.

222

2.31

92.

319

2.30

72.

276

2.23

02.

230

2.37

42.

325

2.30

72.

310

2.35

92.

350

2.38

82.

357

2.35

72.

491

2.53

62.

431

2.43

12.

366

N13

0.21

10.

207

0.21

60.

213

0.20

30.

203

0.18

20.

193

0.20

40.

210

0.21

10.

209

0.23

20.

257

0.25

70.

267

0.23

40.

224

0.22

40.

230

2.31

42.

320

2.32

42.

320

2.29

82.

298

2.30

02.

307

2.31

82.

321

2.37

72.

381

2.36

82.

365

2.36

52.

408

2.43

12.

406

2.40

62.

365

N16

0.50

30.

497

0.49

40.

490

0.49

60.

496

0.50

80.

503

0.49

90.

501

0.45

40.

464

0.49

10.

501

0.50

10.

530

0.52

00.

474

0.47

40.

444

1.90

51.

911

1.91

41.

914

1.88

61.

886

1.85

01.

871

1.89

61.

906

1.95

31.

948

1.92

71.

948

1.94

81.

945

1.93

61.

948

1.94

81.

961

N17

0.19

30.

197

0.21

10.

210

0.21

20.

212

0.21

40.

207

0.19

10.

183

0.28

10.

251

0.21

40.

219

0.21

90.

250

0.25

50.

277

0.27

70.

236

2.35

02.

328

2.30

82.

312

2.32

02.

320

2.32

02.

299

2.29

32.

298

2.48

92.

435

2.41

32.

368

2.36

82.

357

2.38

42.

430

2.43

02.

454

N19

0.18

80.

192

0.20

60.

209

0.21

60.

216

0.21

00.

205

0.19

80.

198

0.22

80.

222

0.19

60.

228

0.22

80.

211

0.21

80.

237

0.23

70.

309

2.30

22.

308

2.31

72.

324

2.32

02.

320

2.28

62.

248

2.32

02.

371

2.43

22.

416

2.43

52.

372

2.37

22.

396

2.37

12.

383

2.38

32.

528

N20

0.50

50.

502

0.50

30.

502

0.50

10.

501

0.49

00.

496

0.50

00.

505

0.50

20.

475

0.43

10.

442

0.44

20.

490

0.50

10.

524

0.52

40.

512

1.85

71.

876

1.89

41.

906

1.91

01.

910

1.91

31.

890

1.86

41.

859

1.94

01.

949

1.94

71.

960

1.96

01.

937

1.94

91.

944

1.94

41.

941

N22

0.20

80.

201

0.18

20.

175

0.19

40.

194

0.21

00.

215

0.21

30.

206

0.26

20.

269

0.28

80.

234

0.23

40.

221

0.23

00.

234

0.23

40.

221

2.31

32.

302

2.29

42.

302

2.30

92.

309

2.32

32.

317

2.31

02.

283

2.36

92.

392

2.43

12.

429

2.42

92.

386

2.36

42.

344

2.34

42.

376

N25

0.22

00.

217

0.19

40.

194

0.20

70.

207

0.21

00.

211

0.21

30.

216

0.21

80.

236

0.33

40.

324

0.32

40.

225

0.22

50.

220

0.22

00.

251

2.24

52.

232

2.31

82.

373

2.32

42.

324

2.31

02.

318

2.32

32.

313

2.35

62.

375

2.50

52.

545

2.54

52.

372

2.35

92.

372

2.37

22.

398

N28

0.49

30.

497

0.49

70.

510

0.51

10.

511

0.50

20.

499

0.49

20.

491

0.51

00.

522

0.54

70.

523

0.52

30.

438

0.44

40.

464

0.46

40.

503

1.90

21.

885

1.85

31.

849

1.86

61.

866

1.90

61.

907

1.91

51.

911

1.94

71.

944

1.93

51.

936

1.93

61.

947

1.96

21.

953

1.95

31.

950

N29

0.21

40.

216

0.21

90.

219

0.21

20.

212

0.19

90.

206

0.21

40.

214

0.24

00.

240

0.20

70.

217

0.21

70.

308

0.32

20.

260

0.26

00.

223

2.32

12.

317

2.31

12.

274

2.22

82.

228

2.37

22.

325

2.30

62.

308

2.35

32.

345

2.38

72.

360

2.36

02.

469

2.53

72.

427

2.42

72.

364

N31

0.20

90.

210

0.21

30.

213

0.20

10.

201

0.17

80.

193

0.20

30.

212

0.21

40.

211

0.22

80.

260

0.26

00.

261

0.23

50.

221

0.22

10.

229

2.31

52.

318

2.32

82.

319

2.29

62.

296

2.30

02.

307

2.31

82.

320

2.37

22.

377

2.37

32.

362

2.36

22.

431

2.43

12.

411

2.41

12.

365

N32

0.50

20.

498

0.48

90.

491

0.49

00.

490

0.50

90.

501

0.49

80.

502

0.45

50.

465

0.48

90.

500

0.50

00.

534

0.52

00.

474

0.47

40.

445

1.90

81.

910

1.92

01.

914

1.88

01.

880

1.85

11.

871

1.89

71.

904

1.95

51.

949

1.92

91.

950

1.95

01.

940

1.93

61.

946

1.94

61.

961

N34

0.19

10.

200

0.21

00.

213

0.20

70.

207

0.21

40.

208

0.19

10.

186

0.28

20.

252

0.21

60.

221

0.22

10.

240

0.25

50.

276

0.27

60.

237

2.35

02.

328

2.31

22.

311

2.32

52.

325

2.31

82.

300

2.29

42.

299

2.48

92.

435

2.41

22.

363

2.36

32.

370

2.38

02.

433

2.43

32.

452

N36

0.18

50.

196

0.20

50.

213

0.21

10.

211

0.21

00.

205

0.19

80.

200

0.22

90.

223

0.19

80.

232

0.23

20.

224

0.21

70.

239

0.23

90.

308

2.30

22.

308

2.32

02.

322

2.32

42.

324

2.28

52.

249

2.32

12.

371

2.42

82.

412

2.43

32.

365

2.36

52.

378

2.37

32.

380

2.38

02.

527

N38

0.47

10.

469

10.

472

0.46

80.

468

0.47

00.

469

0.46

50.

471

0.35

80.

355

0.35

30.

358

0.35

80.

357

0.35

60.

355

0.35

50.

356

3.77

13.

769

3.76

33.

773

3.76

83.

768

3.76

83.

765

3.75

73.

764

8.99

29.

091

9.46

39.

013

9.01

39.

137

8.99

59.

089

9.08

98.

959

N40

0.40

50.

413

0.42

60.

404

0.41

20.

412

0.40

40.

407

0.41

40.

402

0.06

10.

024

0.03

00.

065

0.06

50.

013

0.06

20.

041

0.04

10.

068

3.56

43.

483

3.38

43.

578

3.48

93.

489

3.56

73.

520

3.44

43.

572

3.53

83.

471

3.42

43.

564

3.56

43.

373

3.55

03.

502

3.50

23.

541

N41

0.40

50.

413

0.42

60.

404

0.41

20.

412

0.40

40.

408

0.41

50.

402

0.06

20.

025

0.02

90.

065

0.06

50.

010

0.06

30.

042

0.04

20.

068

3.56

63.

479

3.39

13.

572

3.50

03.

500

3.56

23.

521

3.44

13.

575

3.53

73.

471

3.42

13.

561

3.56

13.

382

3.54

73.

499

3.49

93.

539

15322 J. Phys. Chem. C, Vol. 114, No. 36, 2010 Monajjemi et al.

TA

BL

E4:

Con

tinu

ed

η

�(M

Hz)

radi

cal

atom

s0,

0,0

0,0,

100,

0,30

0,0,

500,

0,70

0,0,

900,

0,11

00,

0,13

00,

0,15

00,

0,17

0

N4

0.49

80.

476

0.43

20.

462

0.47

40.

481

0.48

50.

495

0.50

50.

504

1.96

51.

973

1.96

81.

989

1.98

81.

984

1.97

81.

973

1.97

01.

968

N5

0.25

80.

269

0.28

50.

237

0.24

40.

244

0.24

90.

254

0.25

50.

254

2.35

02.

350

2.31

82.

364

2.36

02.

362

2.36

12.

353

2.34

02.

318

N7

0.27

60.

234

0.32

90.

265

0.26

30.

257

0.25

30.

252

0.25

50.

263

2.28

32.

284

2.34

82.

446

2.38

02.

351

2.35

12.

356

2.35

62.

348

N8

0.49

00.

522

0.54

50.

510

0.48

50.

460

0.46

20.

474

0.48

00.

485

1.97

51.

976

1.97

91.

960

1.96

81.

986

1.99

01.

986

1.98

61.

979

N10

0.25

40.

238

0.20

70.

267

0.27

60.

268

0.27

00.

263

0.25

90.

254

2.35

82.

353

2.35

02.

306

2.28

42.

380

2.44

52.

383

2.35

12.

350

N13

0.25

10.

209

0.23

20.

258

0.25

80.

250

0.24

10.

244

0.24

60.

249

2.35

42.

356

2.36

02.

352

2.34

82.

354

2.36

12.

360

2.36

12.

360

N16

0.47

10.

464

0.49

10.

485

0.49

50.

508

0.51

00.

484

0.46

30.

464

1.98

81.

988

1.99

01.

979

1.97

61.

968

1.96

21.

973

1.98

71.

990

N17

0.25

80.

251

0.21

40.

252

0.25

00.

253

0.26

00.

263

0.25

40.

244

2.41

52.

382

2.35

82.

352

2.35

72.

357

2.35

12.

343

2.35

12.

358

N19

0.24

30.

222

0.19

60.

248

0.25

30.

257

0.25

80.

268

0.26

50.

266

2.36

02.

358

2.44

12.

362

2.35

42.

340

2.31

62.

296

2.38

62.

441

N20

0.49

80.

475

0.43

10.

463

0.47

40.

481

0.48

50.

495

0.50

50.

504

1.96

51.

973

1.96

81.

989

1.98

71.

984

1.97

81.

973

1.97

01.

968

N22

0.25

80.

269

0.28

80.

237

0.24

40.

244

0.24

80.

254

0.25

50.

254

2.35

02.

350

2.31

72.

364

2.36

02.

362

2.36

12.

353

2.34

02.

317

N25

0.27

60.

236

0.33

40.

266

0.26

30.

257

0.25

30.

252

0.25

50.

264

2.28

32.

284

2.34

82.

445

2.37

92.

350

2.35

12.

357

2.35

62.

348

N28

0.49

00.

522

0.54

70.

510

0.48

50.

460

0.46

30.

475

0.48

00.

485

1.97

51.

975

1.97

91.

960

1.96

81.

986

1.98

91.

986

1.98

51.

979

N29

0.25

40.

240

0.20

70.

267

0.27

60.

268

0.27

00.

264

0.25

90.

254

2.35

82.

352

2.35

02.

306

2.28

42.

380

2.44

52.

382

2.35

12.

350

N31

0.25

20.

211

0.22

80.

258

0.25

80.

250

0.24

10.

244

0.24

60.

249

2.35

42.

356

2.36

02.

352

2.34

82.

354

2.36

12.

360

2.36

12.

360

N32

0.47

10.

465

0.48

90.

485

0.49

60.

508

0.51

00.

484

0.46

30.

464

1.98

81.

988

1.99

01.

979

1.97

61.

968

1.96

21.

973

1.98

71.

990

N34

0.25

80.

252

0.21

60.

252

0.25

10.

253

0.26

00.

263

0.25

30.

244

2.41

62.

383

2.35

82.

352

2.35

72.

357

2.35

12.

343

2.35

12.

358

N36

0.24

30.

223

0.19

80.

248

0.25

30.

257

0.25

80.

267

0.26

50.

266

2.36

02.

358

2.44

02.

361

2.35

42.

340

2.31

62.

296

2.38

62.

440

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0.46

30.

355

0.35

30.

464

0.46

00.

456

0.46

30.

460

0.45

70.

463

3.76

23.

760

3.76

13.

766

3.76

03.

754

3.76

23.

756

3.75

43.

761

N40

0.39

40.

024

0.03

00.

392

0.39

60.

404

0.39

30.

394

0.39

70.

392

3.53

23.

429

3.54

03.

558

3.44

73.

341

3.54

33.

473

3.39

03.

540

N41

0.39

40.

025

0.02

90.

393

0.39

70.

404

0.39

30.

394

0.39

70.

392

3.53

13.

429

3.53

93.

556

3.44

73.

342

3.54

23.

472

3.38

83.

539

NH2BHNBHNH2 Inside of the B18N18 Nanoring J. Phys. Chem. C, Vol. 114, No. 36, 2010 15323

The Laplace expansion could be considered as

whereILM and RL

M are irregular and regular solid harmonics,respectively. The dipole moment can be measured by a varietyof experimental methods or computed with an atomic chargedistribution directly derived from molecular orbital calculations,as well as the interaction energy of two B18N18 andNH2BHNBHNH2 charge distributions at a distance ofRB18N18-NH2BHNBHNH2

apart. Since

A dipole moment which appears to be due to an electric chargedistribution usually involves powers (or inverse powers) of thedistance to the origin (r) as well as some angular dependence(Θ and Φ), where Θ is the angle with the x and y axes and Φis the angle with the vertical axis inside of the ring.44,45 Thedipole moment converges under two conditions, (1) if thecharges are localized close to the origin and the point at whichthe potential is observed is far from the origin where thecoefficients of the series expansion are called exterior dipolemoments or simply dipole moments and (2) if the chargesare located far from the origin and the potential is observedclose to the origin, namely, interior dipole moments. Theimportance of this quantity is embedded in the fact that thepotential at a position within a charge distribution can often becomputed by combining interior and exterior dipoles.43-45 Whena single NH2BHNBHNH2 molecule is just supposed, the Θ )Φ ) 0, that is, the dipole vector, is expected to be coincidenton the NH2BHNBHNH2 axis. According to obtained dipolemoments, it can be distinguished that the r component of thedipole moment vector of each the radical, cationic, and anionicforms of NH2BHNBHNH2 involved in the ring had the tendencyto rotate in three different cone surfaces. Therefore, it could berealized that our observed dipole moment has been directedlinearly, and this observation supported the intrinsic linear formof the NH2BHNBHNH2 molecule.

In this regard, it seems that if a biomolecule is being set inthe B18N18-NH2BHNBHNH2 system due to generation ofradical, anion, and cation forms of NH2BHNBHNH2, theelectrical current will cross along the ring that changes allcalculated atomic physicochemical properties. Here, it is notable

that the three emerged radical, cationic, and anionic forms ofNH2BHNBHNH2 generate frequently to each other, and if thesethree species are imagined in the three quantized cone surfaces,it can be deduced that the variation of the radial vector ofsystem’s dipole moment (r) would be quantized within crossingof these three cone levels.

An induced dipole of any polarizable charge distribution Fof the NH2BHNBHNH2 molecule has been caused by an electricfield external to F that originated from an ion or polar moleculein the vicinity of F .The strength of the induced dipole is equalto the product of the strength of the external field and the dipolepolarizibility of F. Therefore, along with the variation of theradial component (r), the two other remaining components ofthe dipole moment, namely, Θ and Φ, will be changed and causethe quantized rotation of the NH2BHNBHNH2 molecule dueto the electrical charge of NH2BHNBHNH2. Its inducedelectrostatic interaction on the ring will be affected, and therotation of the B18N18 ring will also be expected to be quantized.On the other hand, for a dipole moment (m), the energy of thedipole interaction (U) is defined as43-45

Supposing eq 11, the logical variation of the dipole momentat different rotational angles of the NH2BHNBHNH2 radicalwas satisfactory. The average value of the dipole moment vector(r) for anion, cation, and radical forms of NH2BHNBHNH2 hasbeen obtained as 10.842, 5.258, and 3.302 D, respectively. Alongwith the high values of Θ and Φ, the r of the dipole momentholds a Gaussian distribution; this fact can be observed in theplotted Gaussian graphs of the dipole moment (r) versus the Θand Φ angles (Figure 3). Here, it is interesting that for eachradical, cation, and anion of NH2BHNBHNH2, three individualexpectation values of ⟨∆E⟩, ⟨∆V⟩, and ⟨∆r⟩ have been obtained,and as a whole, it seems that the r component of the system’sdipole moment, voltage differences, and relative energies isquantized, and the system undergoes quantization throughrotation.

3.6. Electromagnetic Hyperfine Parameters. In this section,the major point is embedded in the investigation of theelectrostatic interaction of NH2BHNBHNH2 with its surroundingB18N18 ring, which forms the basis for more detailed studies ofother systems with nonbounded interactions. Total atomiccharges, spin densities, electric potential, and isotropic Fermicoupling constants of cationic and anionic forms ofNH2BHNBHNH2 in different loops and bonds of the B18N18

system are reported in Table 5.The expectation values of the quantized radical coordinate

of the dipole moment, voltage differences (au), and relativeenergies of B18N18-NH2BHNBHNH2 systems are displayed inFigure 3. Also, the relative energies (∆E), radial coordinate ofthe dipole moment (r), as well as the voltage differences (∆V)and transition of the B18N18-NH2BHNBHNH2 and B18N18-Ala-NH2BHNBHNH2-Gly systems are given in Tables 6 and 7,respectively.

The voltage differences of the anionic form of theNH2BHNBHNH2 molecule for each bond were scatteredcompared with those of the NH2BHNBHNH2 cationic andradical forms and yielded the highest values (78.62-183.41 au).In the case of the cationic form of NH2BHNBHNH2, the bonding∆V values were close together and were between those ofanionic and radical forms (70.90-82.91 au).

|RB18N18-NH2BHNBHNH2| > |rB18BHNBHNH2,V - rB18N18,µ|

(8)

1|rV - rµ|

)

1|RB18N18-NH2BHNBHNH2

- (rB18N18,µ - rNH2BHNBHNH2,V)|)

∑L)0

∞

∑M)-L

L

(-1)MIL-M(RB18N18-NH2BHNBHNH2

) ×

RLM(rB18N18,µ - rNH2BHNBHNH2,V)

(9)

IlB18N18+lNH2BHNBHNH2

-(mB18N18+mNH2BHNBHNH2)(RB18N18-NH2BHNBHNH2) )

[ 4π2lB18N18

+ 2lNH2BHNBHNH2+ 1]1/2

×

YlB18N18+lNH2BHNBHNH2

-(mB18N18+mNH2BHNBHNH2)(RB18N18-NH2BHNBHNH2)

RB18N18-NH2BHNBHNH2

lB18N18+lNH2BHNBHNH2+1(10)

U ) -m ·B (11)

15324 J. Phys. Chem. C, Vol. 114, No. 36, 2010 Monajjemi et al.

The bonding ∆V of the NH2BHNBHNH2 radical was lowerthan those of the anionic and cationic forms, and the negativevalues have been found for bond 6 and bond 3 (-8.77 and-72.24 au).

The graphs of ∆V values of the anion, cation, and radicalversus θ are exhibited in Figure 4. In each case, linearrelationships have been found between ∆V and θ values. Anapproximate coincidence has been observed between the cationicand radical forms, and it is notable that at θ ) 88.32 and 95.15,which correspond to the negative bonding voltages (∆V )-8.77and 12.24 au, respectively), the two figures crossed each other.However, in the case of the NH2BHNBHNH2 anion, thevariation of θ had no effect on the bonding ∆V for the cation’s

two broadened picks (at θ ) 90.79 and ∆V ) 76.79 au) andfor the radical’s single broad Gaussian curve (at θ ) 0.99 and∆V ) 148.05). A similar trend with a minimum pick could beobserved for the NH2BHNBHNH2 radical and cationic forms,and conversely, the maximum belonged to the NH2BHNBHNH2

anion.

The graphs of the isotropic Fermi constants versus the spindensities in each loop of the B18N18-NH2BHNBHNH2 systemare exhibited in Figure 5a and b. The two distinct trends amongthe various loops of the B18N18-NH2BHNBHNH2 anion couldbe observed. In more detail, dished and bulged points could bedistinguished for even and odd loops, respectively.

Figure 3. The Gaussian distributions and expectation values of the quantized radical coordinate of the dipole moment, voltage differences (au) andrelative energies of B18N18-NH2BHNBHNH2 systems at the B3LYP/EPR-III level of theory.

NH2BHNBHNH2 Inside of the B18N18 Nanoring J. Phys. Chem. C, Vol. 114, No. 36, 2010 15325

TA

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1-

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0.55

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5.05

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77.7

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0.74

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666

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3N

(28)

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2-

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166

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34-

0.71

286

--

18.2

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--

0.72

597

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5-

18.3

896

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7)0.

1047

650.

7560

39-

11.6

176

174.

5651

0.99

131.

680.

5624

99-

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4-

90.1

870

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0.51

7304

0.15

3492

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515

6.99

6888

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57.3

2N

(28)

-0.

8936

10.

4520

83-

18.5

850

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0131

095

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-0.

3555

6-

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6-

48.6

7-

0.51

677

-0.

1524

1-

18.3

362

-10

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026

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loop

6B

(27)

0.69

4157

0.52

0844

-11

.603

427

4.28

110.

8616

36-

-11

.166

2-

0.83

5479

-0.

0008

3-

11.3

171

-0.

1462

0N

(29)

-1.

0469

60.

1817

03-

18.6

242

49.3

9048

-0.

7234

0-

-18

.244

9-

-0.

7721

80.

0001

49-

18.4

094

0.00

258

B(3

0)0.

6884

940.

0755

60-

11.6

212

78.4

6328

0.99

0.76

1249

--

11.2

442

-89

.43

0.74

5799

-0.

0009

6-

11.3

957

-0.

0181

989

.72

N(3

1)-

1.06

391

0.18

0575

-18

.623

949

.172

3812

5.27

-0.

7293

8-

-18

.247

3-

62.1

0-

0.78

116

0.00

0235

-18

.409

6-

0.04

513

157.

65N

(32)

-0.

9032

6-

0.03

906

-18

.601

914

.453

20-

0.64

668

--

18.2

201

--

0.75

136

0.00

0977

-18

.394

2-

0.01

150

B(3

3)0.

6754

680.

0773

23-

11.6

216

78.5

5123

0.75

6490

--

11.2

445

-0.

7407

00-

0.00

088

-11

.395

80.

0074

1bo

nd6

N(3

2)-

0.88

202

0.47

0138

-18

.588

5-

6.91

405

0.99

145.

79-

0.28

129

--

88.7

282

.91

-1.

4474

8-

0.01

138

-19

.386

8-

1.11

873

88.3

2-

8.77

B(3

5)0.

0931

330.

7340

27-

11.6

160

166.

3131

156.

180.

5995

37-

-2.

79-

0.54

586

0.00

4108

-12

.101

78.

7620

216

0.46

15326 J. Phys. Chem. C, Vol. 114, No. 36, 2010 Monajjemi et al.

TA

BL

E6:

Par

tof

the

Qua

ntit

ativ

eE

xpec

tati

onV

alue

sof

Dat

aIn

clud

ing

Rel

ativ

eE

nerg

ies

(∆E

),th

eR

adia

lC

oord

inat

eof

the

Dip

ole

Mom

ent

(r),

As

Wel

lA

sth

eV

olta

geD

iffe

renc

es(∆

V)

and

Tra

nsit

ion

ofth

eB

18N

18-

NH

2BH

NB

HN

H2

Syst

em

0.0,

0.0,

0.0

0.0,

0.0,

10.0

0.0,

0.0,

30.0

0.0,

0.0,

50.0

0.0,

0.0,

70.0

B18

N18-

NH

2BH

NB

HN

H2

r∆

E∆

Vr

∆E

∆V

r∆

E∆

Vr

∆E

∆V

r∆

E∆

V

Ani

on3,

4-N

H2B

HN

BH

NH

216

.593

9-

297.

3017

142

183.

4181

297

16.6

847-

297.

3011

035

243.

1076

945

1.92

42-

297.

1875

912

72.3

2344

707

2.13

83-

297.

1474

922

64.6

0133

812

16.1

405-

297.

0409

236-

58.1

7047

422

8,11

-NH

2BH

NB

HN

H2

15.1

347-

297.

2893

226

78.6

2189

996

16.2

562-

297.

2936

626

118.

8282

092

2.13

76-

297.

1979

642

65.1

3896

048

2.77

7-

297.

1489

281

60.9

3193

854

2.67

57-

297.

1570

842

63.6

2028

381

15,1

6-N

H2B

HN

BH

NH

215

.792

8-

297.

2908

2214

8.05

1523

16.6

709-

297.

2909

0110

2.57

9910

27.

1652

-29

7.12

7735

347

.343

5324

62.

2536

-29

7.14

9556

861

.865

3864

42.

9831

-29

7.15

4413

55.0

4464

220

,23-

NH

2BH

NB

HN

H2

16.8

942-

297.

3011

118

165.

9353

767

17.4

159-

297.

3004

458

164.

3267

807

1.90

75-

297.

1870

679

71.8

3137

729

1.89

09-

297.

1879

735

71.9

3795

616

15.8

837-

297.

0459

962-

67.0

0710

058

27,2

8-N

H2B

HN

BH

NH

215

.452

3-

297.

2918

1313

1.68

9849

15.7

38-

297.

2918

986

80.7

8881

521

4.57

38-

297.

1517

731

49.4

5362

824

2.28

35-

297.

1503

905

69.5

6791

474

3.84

13-

297.

1490

317

65.8

3730

602

32,3

5-N

H2B

HN

BH

NH

215

.351

5-

297.

2923

238

145.

7998

385

14.7

36-

297.

2802

135

73.4

3455

808

7.44

77-

297.

1277

108

48.8

5264

5715

.868

-29

6.99

0738

237

.696

7353

71.

7474

-29

7.17

8325

368

.640

1426

8

Cat

ion

3,4-

NH

2BH

NB

HN

H2

5.05

4-

296.

8056

319

73.9

7205

049

4.74

05-

296.

8050

257

76.1

0088

034

5.02

26-

296.

8008

4479

.823

0313

54.

3851

-29

6.80

3828

975

.885

7160

77.

0468

-29

6.79

5840

486

.794

1162

48,

11-N

H2B

HN

BH

NH

26.

9205

-29

6.80

1661

478

.013

6012

16.

2301

-29

6.79

5907

372

.220

4997

5.96

68-

296.

7990

902

72.9

5049

491

4.69

53-

296.

8073

8771

.526

3121

75.

187

-29

6.80

3694

974

.771

3184

615

,16-

NH

2BH

NB

HN

H2

5.33

3-

296.

8001

619

76.7

9666

404

7.40

82-

296.

7975

2989

.409

8307

911

.260

3-

296.

7763

455

172.

1375

715

4.68

08-

296.

8037

056

67.9

0773

977

8.24

56-

296.

7813

171

88.7

2476

631

20,2

3-N

H2B

HN

BH

NH

24.

9366

-29

6.80

5634

375

.111

4202

25.

3907

-29

6.80

3424

375

.776

2347

13.

9444

-29

6.80

3765

274

.125

0537

64.

3045

-29

6.76

1012

247

.145

0853

24.

6699

-29

6.80

3596

673

.330

8300

227

,28-

NH

2BH

NB

HN

H2

5.47

75-

296.

8031

029

70.9

0336

144

7.57

71-

296.

7950

223

82.1

1742

053

5.38

94-

296.

8045

112

68.9

6993

479

3.89

49-

296.

7823

038

50.3

8895

636

5.00

65-

296.

8043

561

76.2

3866

152

32,3

5-N

H2B

HN

BH

NH

27.

2961

-29

6.79

1948

882

.918

4318

6.92

03-

296.

7947

496

77.9

7468

385

6.96

77-

296.

7963

587

85.9

2898

481

4.44

62-

296.

8035

5466

.467

8763

6.17

72-

296.

7957

145

72.2

4042

018

Rad

ical

3,4-

NH

2BH

NB

HN

H2

3.58

06-

297.

1511

251

.985

1541

92.

3914

-29

7.15

3087

663

.493

2574

71.

9242

-29

7.18

7591

272

.323

4470

72.

2429

-29

7.14

5082

663

.624

2011

320

.970

4-

296.

9371

613

75.6

5692

711

8,11

-NH

2BH

NB

HN

H2

2.95

37-

297.

1524

553

57.2

8597

702

2.42

35-

297.

1475

956

59.8

2793

766

2.11

17-

297.

1977

986

65.5

4155

464

3.08

91-

297.

1462

957

57.5

9232

279

7.15

32-

297.

1176

102

40.2

8868

267

15,1

6-N

H2B

HN

BH

NH

240

.081

7-

296.

3332

429-

12.2

4219

803

40.0

044-

296.

2839

468

-7.

8643

2555

720

.348

6-

296.

9256

791

58.0

8217

054

2.39

07-

297.

1478

8960

.879

7449

2.64

92-

297.

1665

714

59.3

7449

087

20,2

3-N

H2B

HN

BH

NH

23.

8248

-29

7.15

0685

751

.465

2548

114

.724

-29

7.06

7713

713

8.41

8725

34.

7775

-29

7.12

6952

242

.387

377

5.18

67-

297.

1244

024

39.7

1320

7120

.722

1-

296.

9512

951

74.9

6052

491

27,2

8-N

H2B

HN

BH

NH

22.

9454

-29

7.15

2600

457

.327

3115

22.

9955

-29

7.15

3470

556

.253

7018

43.

3971

-29

7.14

4491

652

.226

2857

32.

9732

-29

7.14

8233

758

.248

1087

94.

8733

-29

7.13

2442

341

.179

4260

932

,35-

NH

2BH

NB

HN

H2

39.9

291-

296.

2671

761

-8.

7764

8647

440

.022

7-

296.

2840

582

-8.

1787

0577

420

.369

5-

296.

9240

049

58.5

9084

503

2.55

48-

297.

1619

6361

.069

9951

22.

6715

-29

7.16

6202

58.8

9083

873

0.0,

0.0,

90.0

0.0,

0.0,

110.

00.

0,0.

0130

.00.

0,0.

0150

.00.

0,0.

0170

.0

r∆

E∆

Vr

∆E

∆V

r∆

E∆

Vr

∆E

∆V

r∆

E∆

V

Ani

on3,

4-N

H2B

HN

BH

NH

212

.976

9-

297.

0627

642

44.6

1822

651

13.9

565

-29

7.00

2555

232

.395

5117

99.

4995

-29

7.11

0477

48.0

7805

648

2.31

58-

297.

1506

274

60.3

5677

766

2.45

93-

297.

1549

528

60.7

5148

438,

11-N

H2B

HN

BH

NH

22.

0029

-29

7.18

8938

371

.505

7943

426

.241

4-

296.

8153

581

-27

6.48

2990

92.

0027

-29

7.19

5938

867

.987

8153

76.

6596

-29

7.13

0894

247

.125

3776

714

.005

9-

297.

0180

6135

.429

805

15,1

6-N

H2B

HN

BH

NH

220

.771

1-

296.

9585

247

249.

2417

773

5.03

26-

297.

1482

892

64.2

6236

827

12.9

243

-29

7.09

9243

413

5.60

7185

52.

8734

-29

7.15

5136

358

.944

5146

420

.895

8-

296.

9441

091

77.4

3602

829

20,2

3-N

H2B

HN

BH

NH

22.

2257

-29

7.14

9463

262

.450

1990

812

.813

6-

297.

0096

335

30.8

9087

891

10.0

484

-29

7.10

4234

248

.363

4239

85.

1745

-29

7.12

9555

339

.237

3029

52.

2822

-29

7.14

8756

770

.667

4762

327

,28-

NH

2BH

NB

HN

H2

2.07

05-

297.

1881

211

69.4

8339

394

40.5

363

-29

6.26

5473

4-

9.95

3363

119

1.98

27-

297.

1957

241

67.9

9681

967

13.2

866

-29

7.07

2313

256

.657

7387

215

.244

2-

296.

9961

9135

.572

0946

832

,35-

NH

2BH

NB

HN

H2

22.0

12-

296.

9228

108

618.

7871

587

2.47

29-

297.

1552

991

60.3

7678

398

2.37

03-

297.

1534

902

62.8

0676

482

3.01

28-

297.

1536

9857

.076

2871

20.9

007

-29

6.93

9944

776

.993

2640

3

Cat

ion

3,4-

NH

2BH

NB

HN

H2

9.42

18-

296.

7798

467

114.

1707

175

5.51

34-

296.

8036

4271

.973

3689

76.

456

-29

6.80

1720

575

.632

1980

35.

1701

-29

6.80

6019

867

.563

5883

75.

2756

-29

6.80

4047

473

.740

2790

48,

11-N

H2B

HN

BH

NH

23.

8956

-29

6.80

3652

773

.835

1833

54.

0205

-29

6.76

7667

848

.928

9052

64.

6703

-29

6.80

3271

173

.277

1933

925

.885

3-

296.

3983

032

-30

.775

9246

36.

3592

-29

6.80

0182

477

.612

8259

315

,16-

NH

2BH

NB

HN

H2

6.31

26-

296.

7959

193

74.8

3415

426

5.03

344.

796

-29

6.80

5208

676

.201

1233

95.

1912

-29

6.80

1313

879

.949

8708

6.15

44-

296.

7966

976

84.5

6040

114

20,2

3-N

H2B

HN

BH

NH

25.

7933

-29

6.80

1438

276

.445

4079

85.

7488

-29

6.80

2514

73.5

1607

556

8.05

26-

296.

7956

764

87.3

5570

152

6.93

89-

296.

7939

101

76.3

0993

085.

7624

-29

6.80

1584

374

.967

9768

727

,28-

NH

2BH

NB

HN

H2

5.07

41-

296.

8004

7679

.864

7091

65.

9348

-29

6.79

6227

584

.042

5043

64.

3875

-29

6.80

3145

969

.903

2729

64.

5586

-29

6.80

3802

368

.667

0705

15.

8356

-29

6.80

2401

873

.751

0575

232

,35-

NH

2BH

NB

HN

H2

5.33

48-

296.

8049

135

68.7

9834

815.

2324

-29

6.80

4691

473

.014

3141

34.

9813

-29

6.80

3846

877

.531

2906

84.

9186

-29

6.80

0599

378

.726

3901

36.

6779

-29

6.78

9412

589

.304

3591

6

Rad

ical

3,4-

NH

2BH

NB

HN

H2

2.26

31-

297.

1913

582

66.8

3628

761.

8915

-29

7.17

2601

468

.356

7902

62.

3374

-29

7.17

0286

162

.833

7329

82.

4598

-29

7.14

9254

159

.136

2037

22.

4707

-29

7.15

6344

660

.750

8496

18,

11-N

H2B

HN

BH

NH

25.

6415

-29

7.11

5316

137

.306

0846

72.

7614

-29

7.15

4143

357

.826

3628

1.70

27-

297.

1784

423

70.1

4386

203

5.61

4-

297.

1142

335

37.3

4912

396

2.89

01-

297.

1562

986

58.0

0286

999

15,1

6-N

H2B

HN

BH

NH

219

.442

5-

296.

9611

761

80.3

5437

573

3.64

52-

297.

1415

442

52.0

9335

543

2.03

41-

297.

1911

411

72.3

7388

193

42.0

227

-29

6.21

9721

4-

22.3

8555

944

42.1

078

-29

6.17

6560

1-

27.9

2069

574

20,2

3-N

H2B

HN

BH

NH

22.

3362

-29

7.14

7017

261

.429

5521

21.

7376

-29

7.17

6021

570

.138

4924

42.

3013

-29

7.17

0890

463

.539

7367

83.

0308

-29

7.14

6125

855

.300

2278

93.

519

-29

7.14

2682

153

.306

9514

327

,28-

NH

2BH

NB

HN

H2

6.23

78-

297.

1146

633

39.4

3972

611

2.67

68-

297.

1550

241

58.5

4643

388

1.69

31-

297.

1786

703

70.0

7053

118

5.61

66-

297.

1143

962

37.2

5622

377

2.88

7-

297.

1561

308

57.9

6220

763

32,3

5-N

H2B

HN

BH

NH

220

.949

5-

296.

9150

134

169.

9426

868

2.48

45-

297.

1567

218

60.4

1087

509

2.38

72-

297.

1532

399

62.8

5021

458

42.5

942

-29

6.21

0479

8-

15.7

1696

066

38.4

851

-29

6.28

7060

1-

43.3

1491

394

Exp

ecta

tion

Val

ues

anio

n⟨r

⟩)

10.8

4223

413

(Deb

ye),

⟨∆E

⟩)

-29

7.06

3741

1(H

artr

ee),

⟨∆V

⟩)

61.5

1723

858

(au)

catio

n⟨r

⟩)

5.25

8401

161

(Deb

ye),

⟨∆E

⟩)

-29

6.79

1597

1(H

artr

ee),

⟨∆V

⟩)

70.9

7727

363

(au)

radc

al⟨r

⟩)

3.30

2491

855

(Deb

ye),

⟨∆E

⟩)

-29

6.71

7683

3(H

artr

ee),

⟨∆V

⟩)

55.2

4589

482

(au)

ν r-

c)

4869

48.4

98G

Hz,

ν a-

c)

1792

900.

812

GH

z,ν r

-a)

2507

076.

816

GH

z

NH2BHNBHNH2 Inside of the B18N18 Nanoring J. Phys. Chem. C, Vol. 114, No. 36, 2010 15327

In other words, the two maximum picks have been observedfor the loops with odd numbers (loops 1, 3, 5), and the twominimum picks are seen for loops with even numbers. Thenegative spin densities in the ∆V range of 13.49334-16.069au correspond to loops 5 and 1, respectively.

In the case of the NH2BHNBHNH2 radical (Figure 5c), similartrends were obvious for loops of the B18N18-NH2BHNBHNH2

system. The graphs of total atomic charges versus isotropicFermi coupling in different loops of (a) the NH2BHNBHNH2

anion even loops and (b) the NH2BHNBHNH2 anion odd loopsin Figure 5, and (c) the NH2BHNBHNH2 radical are exhibitedin Figure 6. The same results have been obtained in these graphsfor both the NH2BHNBHNH2 anion and the NH2BHNBHNH2

radical forms.

4. Conclusion

The procedures discussed in this study place much emphasison the importance of electronic structure properties of boronnitride rings (BN)n and their electromagnetic nonbonded interac-tion with the NH2BHNBHNH2 molecule and other biologicalamino acids to examine the capability of a quantized transitionof the NH2BHNBHNH2 molecule inside of the B18N18 ring.Indeed, the NH2BHNBHNH2 inside of the B18N18 ring issupposed as a quantized nanospectrophotometer detector ofvarious quantized parameters of a given biomolecule coupledwith this system.

Optimized structures, relative stability, HOMO-LUMO bandgaps, nuclear quadrupole resonance (NQR), and hyperfinespectroscopic parameters of radical, cationic, and anionic formsof B18N18-NH2BHNBHNH2 systems including total atomiccharges, spin densities, electric potential, and isotropic Fermicoupling constants of radical, cationic, and anionic forms ofNH2BHNBHNH2 in different loops and bonds of consideredsystem have been compared. The information inferred fromNQR study on the local electron density distribution togetherwith analysis of the charge distribution provided logical meansfor determination of reactive sites and indicated possiblepromising directions to be followed in the design of (BN)n

nanodevices.It has been observed that the radial coordinate of the dipole

moment vector (r) as well as the voltage differences (∆V) andrelative energies (∆E) exhibited Gaussian distributions. We haveobtained a relationship between dipole moments and the voltagedifferences and the system’s energy.

Moreover, the calculation has been repeated for the alanine-glycine (Ala-NH2BHNBHNH2-Gly) amino acid coupled withT

AB

LE

7:R

elat

ive

Ene

rgie

s(∆

E),

Rad

ial

Coo

rdin

ate

ofth

eD

ipol

eM

omen

t(r

),A

sW

ell

As

the

Vol

tage

Dif

fere

nces

(∆V

)an

dQ

uant

ized

Tra

nsit

iona

lF

requ

enci

es(∆

ν)of

the

B18

N18

-Ala

-NH

2BH

NB

HN

H2-

Gly

Syst

ema

anio

nca

tion

radi

cal

B18

N18

-Ala

-NH

2BH

NB

HN

H2-

Gly

r(D

ebye

)∆

E(H

artr

ee)

∆V

(au)

r(D

ebye

)∆

E(H

artr

ee)

∆V

(au)

r(D

ebye

)∆

E(H

artr

ee)

∆V

(au)

3,4-

A-N

H2B

HN

BH

NH

2-G

11.7

354

-90

3.34

0563

1-

205.

9800

94.

9936

-90

2.85

8574

9-

64.5

3652

2.92

21-

903.

2296

04-

71.6

7513

456

ν r-

c)

2444

361.

716

GH

z,ν r

-a)

7310

05.1

317

GH

z,ν a

-c)

3175

366.

848

GH

z8,

11-A

-NH

2BH

NB

HN

H2-

G14

.287

4-

903.

3425

49-

138.

1479

295.

7416

-90

2.82

4828

3-

64.6

2006

1.31

08-

903.

2308

26-

67.9

0846

566

ν r-

c)

2674

736.

927

GH

z,ν r

-a)

7360

37.7

502

GH

z,ν a

-c)

3410

774.

677

GH

z15

,16-

A-N

H2B

HN

BH

NH

2-G

15.6

987

-90

2.12

5349

4.89

7124

36.8

571

-90

1.84

1091

34.

6483

481.

8499

-90

3.18

9705

2-

68.5

2583

119

ν r-

c)

8884

748.

358

GH

z,ν r

-a)

7012

041.

771

GH

z,ν a

-c)

1872

706.

587

GH

z20

,23-

A-N

H2B

HN

BH

NH

2-G

16.7

144

-90

3.33

5254

-14

0.82

2952

2.50

53-

902.

8423

343

-73

.555

014.

5518

-90

3.18

3920

2-

61.8

0784

132

ν r-

c)

2250

388.

168

GH

z,ν r

-a)

9969

96.0

498

GH

z,ν a

-c)

3247

384.

218

GH

z27

,28-

A-N

H2B

HN

BH

NH

2-G

16.0

366

-90

3.33

6087

7-

121.

7420

2028

.702

7-

902.

4849

156

296.

5360

84.

4671

-90

3.18

6344

9-

70.9

7328

31ν r

-c)

4621

057.

829

GH

z,ν r

-a)

9865

14.4

475

GH

z,ν a

-c)

5607

572.

277

GH

z32

,35-

A-N

H2B

HN

BH

NH

2-G

13.6

583

-90

3.33

0093

4-

130.

3839

2967

.040

7-

901.

6791

866

7.20

1567

216

.728

9-

903.

0327

035

25.2

6434

969

ν r-

c)

8917

049.

613

GH

z,ν r

-a)

1959

222.

299

GH

z,ν a

-c)

1087

6271

.91

GH

z1,

2,4,

34,3

5,36

-A-N

H2B

HN

BH

NH

2-G

14.9

210

-10

62.7

8290

98-

3.17

64-

1062

.372

0006

-2.

3371

-10

62.6

9225

1-

ν r-

c)

2109

828.

629

GH

z,ν r

-a)

5972

65.5

513

GH

z,ν a

-c)

2707

094.

18G

Hz

3,5,

6,7,

8,9-

A-N

H2B

HN

BH

NH

2-G

14.6

633

-10

62.7

8338

84-

4.01

42-

1062

.368

4315

-4.

0649

-10

62.6

8597

7-

ν r-

c)

2092

008.

587

GH

z,ν r

-a)

6417

52.0

806

GH

z,ν a

-c)

2733

760.

668

GH

z10

,11,

12,1

3,14

,16-

A-N

H2B

HN

BH

NH

2-G

17.6

144

-10

62.7

8162

06-

3.87

31-

1062

.369

7555

-4.

1171

-10

62.6

9118

5-

ν r-

c)

2117

596.

61G

Hz,

ν r-

a)

5957

95.0

964

GH

z,ν a

-c)

2713

391.

706

GH

z15

,17,

18,1

9,20

,21-

A-N

H2B

HN

BH

NH

2-G

19.7

195

-10

62.7

8091

04-

3.75

38-

1062

.372

1402

-3.

8230

-10

62.6

9181

4-

ν r-

c)

2106

029.

954

GH

z,ν r

-a)

5869

72.3

674

GH

z,ν a

-c)

2693

002.

321

GH

z22

,23,

24,2

5,26

,28-

A-N

H2B

HN

BH

NH

2-G

18.9

285

-10

62.7

6808

81-

3.89

88-

1062

.357

1579

-2.

1848

-10

62.6

7444

5-

ν r-

c)

2090

306.

233

GH

z,ν r

-a)

6169

26.2

967

GH

z,ν a

-c)

2707

232.

529

GH

z27

,29,

30,3

1,32

,33-

A-N

H2B

HN

BH

NH

2-G

17.4

394

-10

62.7

7654

92-

2.03

35-

1062

.364

7987

-1.

2576

-10

62.6

8625

4-

ν r-

c)

2117

766.

582

GH

z,ν r

-a)

5948

70.1

329

GH

z,ν a

-c)

2712

636.

714

GH

z

aN

ote:

The

freq

uenc

ies

calc

ulat

edar

ede

fined

as:

ν(G

Hz)

)[(

⟨∆E

⟩×

627.

5095

×4.

184

×10

00)/

(6.0

23×

1023

×6.

62×

10-

34)]

×10

-9 .

Figure 4. Graph of the bonding voltage at different dipole coordinates.

15328 J. Phys. Chem. C, Vol. 114, No. 36, 2010 Monajjemi et al.

the NH2BHNBHNH2 molecule inside of the B18N18 ring, andthe quantized frequencies in different cationic, radical, andanionic forms of NH2BHNBHNH2 have been obtained. There-fore, it seems that these B18N18-NH2BHNBHNH2 systems canbe used for the measurement of rotational spectra aroused byelectrical voltage differences existing in these amino acids. Forfurther structural information, the LUMO and the HOMOdifferences, namely, band gaps, have been reported to explorethe capability of the suitable NH2BHNBHNH2 candidate whichmakes a stable B18N18-NH2BHNBHNH2 system.

The obtained results confirmed the structural stability of theB18N18 ring and quantized characteristics of radial coordinate,

voltage differences (∆V), and relative energies (∆E) whichshowed Gaussian distribution. Our current analysis is a prereq-uisite to better clarify their role and to calculate a wide spectrumof ring properties. Indeed, such a considered nanodevice canserve as a nanospectrophotometer detector and supplies asufficient impetus for further experimental research on the B/Ncluster system.

References and Notes

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Figure 5. Graphs of the total atomic spin densities versus isotropic Fermi coupling in different loops of the (a) NH2BHNBHNH2 anion even loops,(b) NH2BHNBHNH2 anion odd loops, and (c) NH2BHNBHNH2 radical.

Figure 6. Graphs of the total atomic charges versus the isotropic Fermi coupling in different loops of the (a) NH2BHNBHNH2 anion even loopsand (b) NH2BHNBHNH2 anion odd loops.

NH2BHNBHNH2 Inside of the B18N18 Nanoring J. Phys. Chem. C, Vol. 114, No. 36, 2010 15329

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15330 J. Phys. Chem. C, Vol. 114, No. 36, 2010 Monajjemi et al.