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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: [email protected].
† 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
N38
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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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.