Density Functional Theory and QM / MM Illustration of the Behavior of B 23 N 23 nano-cone : EPR & NMR Investigation

In this work, the B23N23 nano-cone has been investigated using the DFT exchange-correlation functional of theory by electron paramagnetic resonance of EPR2 and EPR3 basis sets. The results of ab initio and QM/MM calculations of NMR chemical shift values of iso, aniso, ,  and · parameters of with GIAO and CSGT approximations of B23N23 have been obtained. The relative energies have been compared between EPR2 and EPR3methods. Also, Atoms charge transfers have considered to full alternation B and N atoms in B23N23 nano-cone. The stability of B23N23 was confirmed in a theoretical work based on a combination of density functional theory and the temperature effect on stability have been studied. The results, obtained of EPR2 andEPR3 levels with both of approximation were excellent in agreement.

Its structure, which is in the form of a hexagonal mesh, resembles a graphite sheet and it carries a carbon atom located on the vertex of each mesh.The sheet has rolled and its two edges have connected seamlessly [9][10][11][12][13][14][15] .
CNT can be classified into single-wall CNT, double-wall CNT and multi-wall CNT according to the number of layers of the rolled graphite.The type attracting most attention is the single-wall CNT, which has a diameter deserving the name of "nanotube" of 0.4 to 2 nanometers [20][21][22][23][24][25][26] .
The length is usually in the order of microns, but single-wall CNT with a length about centimeters have recently released.The extremities of the CNT have usually closed with lids of the graphite sheet 21- 30 .
Theoretical studies have been performed for fullerene-like B12N12 clusters  , in which it has been found that a structure built from squares and hexagons is more stable than those built from pentagons and hexagons. This s because in the second case less stable B-B and N-N bonds are formed.
The most stable B12N12 structure is built from six squares and eight hexagons  .
In this work, we focused on B23N23 nanocon.Our aim was to obtain the global minimum energy structure.For this structure, we use the hybrid B3LYP exchange-correlation functional within density functional theory.Primary, structure optimization calculated and then Nuclear Magnetic Resonance (NMR) parameters by density Functional Theory (DFT) method calculated on the optimized structure.Isotropic chemical shielding, anisotropic chemical shielding parameters at all of the atoms nuclei are presented in Table 1.And also, Thermodynamic Properties have been considered in Table 2 DFT calculations of B23N23 B23N23 clusters have been studied using the hybrid B3LYP density functional and (EPR and EPR2) methods.All Density Functional Theory (DFT) quantum calculations were performed using Gaussian 98 program package on structure of boron-nitride nano-cone.
The structure first optimized with Becke3, Lee-Yang-Parr (B3LYP) method and EPRandEPR2 basis sets including QM/MM calculations.
Nuclear Magnetic Resonance (NMR) parameters at all of the nuclei optimized structure calculated by B3LYP method and EPR2andEPR3 basis sets.The results are listed in table1-4 and Figures1-5.The energy differences have been compared with those obtained within EPR2 and EPR3.The NMR of paramagnetic compounds (compounds possessing unpaired electron) play an important role in different application of chemistry and biochemistry.The stability ofB23N23 was confirmed in a theoretical work based on a density functional calculation.Geometry optimizations and energy calculations on the boron nitrides B23N23 was carried out using the B3LYP method.The major result is that boron nitride cages are more stable than rings if at least two of the six four-member rings are isolated by hexagons.

NMR
The NMR chemical shift d is a parameter that use for recognizing magnetically in equivalent nuclei in a molecule.The use of density functional theory (DFT) to nuclear magnetic resonance (NMR) and electron spin resonance (ESR) spectroscopes is a new and notable subject.Today NMR methods are powerful tools in chemistry and biochemistry because of the NMR chemical shifts.In liquid, or gas, the molecules are freely tumbling so one does comprehend an average chemical shift (isotropic chemical shift).The quantity in quantum mechanics is depended to the NMR chemical shift.The shielding is determined as the mixed second derivative of the energy with consideration to magnetic moment of the nucleus and the strength of the used magnetic field.It is solved through the second-order perturbation theory with the Zee man Hamiltonian.
The first order contribution is called diamagnetic while the second order (which requires knowledge of excited electronic states) is termed paramagnetic.The calculation methods employed are the ab-initio (from first principles) Hartee-Fock or density functional calculations.The first method solves the electronic Schrödinger equation in the absence of any magnetic field.The density functional method was allowed to change with the applied of a magnetic moment and a static external magnetic field.The zero order and first order density matrices are used to obtain the diamagnetic and paramagnetic terms, respectively.The integrity of these calculations depends on the level of theory used, the basis set employed and the structure of molecule.Gaussian basis sets are employed as the basis functions to match the electronic orbital in a molecule.
For use, the ab-initio packages it is necessary that the molecular geometry be defined.This work presented the results of B and N NMR investigations on the B23N23nanocone obtained via Density functional theory.

RESULTS
On the basis of the WU Haishun et al studies into (BN)n cages, it is found that among several isomers of these structures the isomers without direct B -B and N -N bonding are more stable.Then, in this work, we have investigated on B23N23 nano-cone.The B-N bond length at the peak of nanocone is short to compare to another bonds too in this optimized structure, atomic charges are notable.The charge distribution values of are in agreement with structure coordinate.

Table 1: NMR Parameters of B23N23 for 5 atoms of Nitrogen and 5 atoms of Boron with two level of theory
Atom charge transfers have considered to full alternation B and N atoms in B23N23 nanocone.At direct interactions between indicated atoms in EPR3 level have shown that the charges of atoms at ring had the most charge distribution with GIAO and CSGT approximates.
In addition, Atom charge transfers in nitrogen atoms had the same behavior as it performed in tables.This is notable that the atom charge transfer values in top at nano-cone had the close behavior in EPR2 and EPR3 levels.
The agreement between the calculated values Atom charge transfers for EPR2 and EPR3 levels with GIAO and CSGT approximations were remarkably good.

NMR results
The GIAO and CSGT approximations of NMR calculations for Structural study of the B23N23 cluster to obtain nuclei Magnetic Resonance Parameters via Density Functional Theory method were performed at the EPR2 and EPR3 levels and reported in Table1.theCSGT results have confirm the GIAO results.The agreement between the observed and calculated values of the shielding anisotropies and asymmetries for both EPR2 and EPR3 were remarkably good.
The results of ab initio calculations of NMR chemical shift values of  iso ,  aniso , ,  and • parameters of with GIAO and CSGT approximations of B23N23 have been obtained and results have given by table1.
Calculated isotropic chemical shielding parameters of nitrogen Nuclei have almost similar behaviors and these atoms have maximum values to compare to another atom.In table 1, we have reported the NMR parameters of in EPR2 level and in EPR3 level and also these parameters with CSGT and GIAO approximation are calculated.The same process has been seen in CSGT approximation too.Calculated anisotropic shielding in nitrogen has the same behavior as it performed in table1 It has been shown that the behavior of chemical shift tensor components (isotropic and anisotropic) have depended on the Geometry coordinates of BN nanotube.By given data, we will

Thermodynamic Properties
According to the thermochemical calculations at the B3LYP/EPR2 and B3LYP/EPR3 levels of theory, obtaining thermochemical functions such as H, S and G.

CONCLUSIONS
The hybrid B3LYP density functional and (EPR2 and EPR3) methods has been used to characterize the geometry of a B23N23nanocone.Optimized structures, relative stability, nuclear dipole moment and NMR parameters of system including total atomic charges, shielding isotropies, shielding anisotropies chemical shift and asymmetry of considered system have been compared and results have been in good agreement with the experimental data.