We’ve investigated various electronic properties in this study which were done by Mulliken charge distribution

We’ve investigated various electronic properties in this study which were done by Mulliken charge distribution. Mulliken charge distribution analysis or simply charge analysis is an ideal method to analyze the net charge transferred in a molecular system. It helps to understand the molecular interactions of a multimolecular system and also the atomic interactions inside the molecules. By observing the difference of charge distribution in various nanocluster system, the stability and other structural properties of the nanoclusters can be predicted 35,42–44. Bond lengths of the different atoms within the molecular systems are directly affected by charge distribution of the system 32.
From the Mulliken charge distribution analysis of the planer B_6 ring, we’ve found that the terminal two red coloured atoms (1B and 4B) are partially negative and the rest green coloured (2B-3B, 5B-6B) are partially positively charged. The nature of charge can also be apprehended from the colour scales, where red ones are electron acceptors and green ones are donors. From the optimized pristine B_6 nanocluster in Figure 1(a) it is also visible, which also contains numerical values of charges, according to Pauling Scale 33. The partial charges occur because shared electrons oscillate between the bonded atoms 34. This phenomena occurs due to the difference of electronegativity between boron (2.04) and manganese (1.55) atoms 35. After doping Mn atom pyramidically, the B6 motif structure bended slightly in boat shaped due to the contribution of Mn.
From Figure 1(c), we have observed that even though the terminal B atoms (1B and 4B) bended slightly towards the direction of Mn with negligible change is partial charges, the Mn atom remains almost charge neutral. This occurred due to the combined effect of charge distribution of atoms. On the other hand, in bi-pyramidically Mn doped nanocluster, the Mn atoms donated electrons to the B_6 motif. We’ve found the previously partially positive charged B atoms (2B-3B, 5B-6B) received electrons, this time without bending the 1B ; 4B atoms, as shown in Figure 1(d). After doping manganese (Mn) into B_6 motif, the bond lengths have been observed to change significantly as given in Table 1 and Figure 1, which we’ve found to be in accordance with our analyses described previously 36.

Figure 1. Mulliken charge distribution of B_6 and Mn doped B_6 nanoclusters.

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Table 1. Representation of bond-length among different atoms of B_6, MnB_6 and ?Mn_2 B?_(6 ).
Bond
Element 1B-2B 2B-3B 3B-4B 4B-5B 5B-6B 6B-1B
B_6 1.537 1.632 1.537 1.537 1.632 1.537
MnB_6 1.577 1.631 1.581 1.577 1.631 1.581
?Mn_2 B?_(6 ) 1.599 2.864 3.256 2.864 1.599 1.599

3.2. Adsorption Energy
The interaction energy between adsorbate and adsorbent at a particular temperature (here room temperature) brings up adsorption energy (E_Ads) of the system. From the value of the adsorption energy of different clusters, more stable structures can be identified. In case of the cluster system, the stronger adsorbed structure have more negative value of adsorption energy 37. Using the equation (1) we have calculated the E_Ads of Mn doped structures and these values are tabulated in Table 2.
The value of adsorption energy of MnB6 and Mn2B6 are -4.32eV and -5.67eV respectively, for SDD basis set and it follows the same trend for LanL2DZ. By observing the calculated values of adsorption energies, bi-pyramidal structure shows more negative value than pyramidal structure, which established that Mn2B6 is more stable than MnB6. The negative values of EAds also represent that the exothermic reaction has occurred for the both cases, upon adsorption of Mn on B6 plane structure, furthermore it can be predicted that the energy transfers from B6 ring to Mn atom(s) due to negative value of EAds 23.
Enthalpy is the total heat energy that is equivalent to the internal energy of a system. The capability of a system is estimated from the value of Gibbs free energy and the value of entropy informs us about the disorderness of a system. The changes of enthalpy (?H), Gibbs free energy (?G), entropy (?S) have been also calculated by using SDD and LanL2DZ basis sets, these values are listed in Table 3. From the calculated data, the values of enthalpy are negative for the both cases (-5.69 for MnB6 and -7.75 for ?Mn_2 B?_(6 )) which refers that chemisorption occurred for TM doping in B6. The negative values of Gibbs free energy increases for the bi-pyramidal structures that is also same for the value of entropy which exhibits that all the adsorption processes are ordered and spontaneous respectively in this investigation 38. The Figure 2(a) represent the adsorption energy versus number of adsorbed atoms, here we see that adsorption energy increased linearly with increased of the number of add atoms i.e. the stability is increased in bipyramidal structure and it is true for both the basis sets that we are used in our work and Figure 2(b) shows the Mulliken charge distribution.
Table 2. Adsorption energy ( E_Ads) in electron volt, dipole moment (µ_D) in Debye unit and Mulliken charge ( Q_Mulliken) for pristine and doped B6 nanoclusters.
System E_Ads µ_D Q_Mulliken
SDD LanL2DZ SDD LanL2DZ SDD LanL2DZ
B_6 0 0 0 0 0.29 0.284
MnB_6 -4.32 -4.15 2.91 1.96 0.213 0.208
?Mn_2 B?_(6 ) -5.67 -5.60 0.0005 0.0002 0.042 0.119

Figure 2. (a) Illustration of the increasing of the adsorption energy with the increasing of the add atoms and (b) the variation of the Milliken charge distribution with respect to the number of add atoms.
Table 3. Changes of enthalpy (?H), Gibbs free energy (?G) in electron volt unit, Entropy (?S) in electron volt/mol.Kelvin unit for pristine and doped B6 nanoclusters.
System ?H ?G ?S
SDD LanL2DZ SDD LanL2DZ SDD LanL2DZ
B_6 0 0 0 0 0 0
MnB_6 -5.69 -5.25 -5.35 -4.89 -0.0011 -0.0012
?Mn_2 B?_(6 ) -7.75 -7.93 -6.94 -7.12 -0.0027 -0.0027

3.3. Optical Properties
Optical properties indicate the interactions of the sample with electromagnetic radiation (EMR). By investigating the UV-Vis spectra and CD spectra optical behaviors of the doped and undoped B6 nanoclusters have been observed.
From theoretical studies of interactions with various types of EMR, the probable applicable properties of our specimens can be predicted. In the UV-Vis spectra absorbance of light photon for a specific material is plotted against wavelength of light. It was observed that B6 nanocluster absorbs light photon in the range of about 450-600 nm, single Mn atom doped pyramidal structure absorbs about 400-600 nm EMR, and broad spectra of wavelength absorption (about 400-650 nm) takes place when two Mn atoms are doped bi-pyramidically on B6 nanocluster as shown in Figure 3. The wider absorbance capability of Mn2B6 cluster shows that it might have possible application as the absorber layer of solar cell. The peaks of the absorbance ranges keep shifting to the left with increasing number of doped atom(s) which indicates that they are capable of absorbing more energetic light since their optical band gap is increased. The UV-Vis spectroscopy also follow similar trend with the HOMO-LUMO energy gap (Eg) obtained in Table 5. This UV-Vis study shows that Mn doped B6 nanoclusters can be used as energy and heat receiving devise.
CD appears from the difference in the absorption of left?handed and right?handed circularly polarized light and occurs only when a molecule contains one or more chiral chromophores or region in the molecule where the energy difference between two separate molecular orbitals falls within the range of the visible spectrum 35. Since we haven’t observed any peak in the graph for B6, CD spectrum indicates that B6 nanocluster is optically inactive but pyramidal (MnB6) and bi-pyramidal (Mn2B6) nanoclusters become optically active for doping which have been drawn by using ‘Gauss Sum’ package as attached in Figure 4. Because of the optical activity these might be used as analyzer, polarizer and might also have potential use in medical sector and other different optical applications.

3.4. Infrared (IR) spectroscopy
The frequency of the periodic motion of atoms in a molecule is referred to as the vibrational frequency. When a molecular system has constant translational and rotational motion, the atoms in the molecule are in periodic motion that occur the molecular vibrations. The typical vibrational frequency of molecular vibrations is ranged as 300 cm-1 to 3000 cm-1. The technique to understand the vibrational modes of different bonds in a molecular system is known as infrared spectroscopy (IR) which deals with the interaction between constituents of a molecule and electromagnetic (EM) radiation in IR range.
Using the IR spectroscopy technique, we have studied the nature of bond, bond strength and the number of imaginary frequency of the pristine and TM doped B6 nanoclusters by using the same level of theory which is shown in Table 4. The structures have less probability to exist in nature as a stable form if it contains imaginary frequency 39,40. The bonds which have low vibrational frequencies also form less stable structure in nature. From the calculated value, we have been seen that pristine and bi-pyramidal structures have one imaginary frequency which has lower possibility to exist naturally. We have been also observed that the same result from the IR activity verses frequency graph which is shown in Figure 5. Due to the different values of vibrational frequencies and relative strengths different molecular vibrations of atoms in the clusters are observed. Pristine B6 has only bending type vibrations where both doped structures have stretching and bending type vibrations. Smaller and larger vibrational frequencies are occurred due to bending and stretching vibrations respectively in B6 cluster. Using the bending and stretching vibrations behavior the structures can be differenced from one to others nanoclusters. From the calculated values of vibrational frequencies it can be predict that a little blue shifting and broadening can be occurred in the chosen nanoclusters 41.
Since Mn2B6 has one imaginary vibration with a negative frequency (-481.01cm-1) that indicates that the geometry of the cluster (Mn2B6) at which the frequencies were calculated is not ground state energy but a transition state. Investigating of the atomic movements associated with this imaginary vibration indicate that the Mn atom is fared out of the plane of the B6 ring and on the outer parts of the pristine B6 ring have a small doming effect 42.
Table 4. Data for infrared absorption (cm-1) for different complexes and their relative variations.
System Vibrational Frequency Relative Strength Observation No. of Imaginary frequency

B6 354.30 58.47 Bending (2B,3B,5B and 6B)

1
538.42 1193.13 Bending(1B and 4B))
1212.96 47.75 Bending (6B-1B-2B and 5B-4B-3B)

MnB6 425.44 10.41 Bending (1B,2B,3B,4B,5B andB6)

0
766.71 11.72 Stretching (2B-3B and 5B-6B)
1069.50 7.41 Stretching (2B-1B-6B and 3B-4B-5B)

Mn2B6 207.50 104.72 7Mn and 8Mn bending with motif B6

1
520.93 65.82 Motif B6 bending with 7Mn and 8Mn
912.39 32.60 Stretching (2B-1B-6B and 3B-4B-5B)

3.5. Dipole Moment
Dipole moment is an important parameter to investigate the proper charge distribution, symmetricity or asymmetricity, polarity and other special properties of molecule which considers the data of geometry 30,43. The dipole moment of pristine B6 cluster is zero that means the structure is nonpolar and zero Debye relates to their intrinsic symmetrical shape 30. But Mn doped B6 nanocluster has µD = 2.91 and µD = 1.96 for basis sets SDD and LanL2DZ respectively for pyramidal fashion as shown in Table 2 which indicates that the asymmetricity of Mn doped B6 clusters. The asymmetricity has meant the chemical reactivity about the nanoclusters. On the other hand, the bi-pyramidal nanoclusters are almost zero polarity that has been occurred due to their different charge distributions.
3.6. Chemical Potential and Physical Properties
The total amount of energy that is added or released in chemical reaction or phase transition is referred to as chemical potential (µ). In any complex system, the reactivity decreases and stability increases due to decrease the value of chemical potential 44,45. In this study, the chemical potential is calculated by using the equation (5) with the help of the value of EHOMO and ELUMO and listed in Table 5. Investigating the calculated value of µ, it has been seen that for the both cases of doped clusters that values are smaller than pristine B6. It has been occurred because of the transition of electrons from the higher orbitals of doped TM to the lower orbitals of B6 motif. Since the negative values of the chemical potential have decreased thus the doped structures have lost their reactivity which informs us that these are more stable than pristine B6 in the natural environment. So we can predict that they cannot make any reaction with natural elements, that’s why these can be used in large scale in open place.
The physical parameters hardness (?), softness (S) and electrophilicity (?) are correlated with the value of chemical potential (µ) and HOMO-LUMO energy gap which explain the stability of the structures. The stability increases when the values of softness and electrophilicity decrease with increasing the value of hardness. The physical parameters are calculated with the help of equations (6), (7) and (8) respectively as shown in Table 5. The value of hardness of pristine B6 for different two basis sets are same (0.39 eV), this value is decreased for TM doped both clusters which means that the doped clusters are more stable than pristine B6 structures that is the same agreement of adsorption energy and chemical potential calculations.

Figure 6. HOMO-LUMO orbitals of pristine and doped B6 nanoclusters.

Table 5. HOMO energies (EHOMO¬), LUMO energies (ELUMO), Chemical potential (µ), Hardness (?), Softness (S) in eV-1, Electrophilicity (?) in electron volt (eV) and HOMO-LUMO energy gap (Eg) in eV-1 unit in case of pristine and Mn doped B6 nanoclusters.

System EHOMO ELUMO µ ? S ?
SDD LANL2DZ SDD LANL
2DZ SDD LANL2DZ SDD LANL
2DZ SDD LANL2DZ SDD LAN
L2DZ
B6 -5.61 -5.61 -4.84 -4.84 5.22 5.23 0.39 0.39 1.29 1.29 35.26 35.25
MnB6 -6.18 -6.26 -2.83 -2.87 4.50 4.54 2.95 1.39 0.30 0.30 6.10 6.18
Mn2B6 -5.53 -5.43 -3.90 -3.90 4.71 4.70 0.81 0.99 0.61 0.62 13.63 13.77

3.6. Electronic Property Investigations
To study the electronic property, we’ve investigated energy gap (Eg) between HOMO and LUMO of the above mentioned structures. If Eg increases, the energy required for an electron to jump from HOMO to LUMO will increase as well and the complex system will absorb more energetic EMR. The HOMO energy, LUMO energy and Eg have been analyzed from the density of states (DOS) plots which have been generated by ‘Gauss Sum’ package and drawn in Figure 6 and HOMO-LUMO orbitals are shown in Figure 6. The DOS plot gives the information about Eg and the distribution of unpaired electron in a complex system 40,46. The HOMO-LUMO gap for pristine B6 complex is 0.77 eV which is shown in Table 5. When Mn atom is doped in B6 both pyramidal and bi-pyramidal fashion, the values of Eg increase and similar phenomena is observed in the DOS plot. If we compare the Eg from Table 6, between pyramidal and bi-pyramidal structures, bi-pyramidal complex shows less Eg value and DOS also reaffirm this comparison. The calculated results using two basis sets show the same trend, which indicate the study can be validated by experiment.
Table 6. HOMO energies (EHOMO¬), LUMO energies (ELUMO) and HOMO-LUMO energy gap (Eg) in eV unit in case of pristine and Mn doped B6 nanoclusters.

System EHOMO ELUMO Eg
SDD LANL2DZ SDD LANL2DZ SDD LANL2DZ
B6 -5.61 -5.61 -4.84 -4.84 0.77 0.77
MnB6 -6.18 -6.26 -2.83 -2.87 3.34 3.33
Mn2B6 -5.53 -5.43 -3.90 -3.90 1.63 1.60

According to Luo, Jia et al., if a complex structure shows alpha and beta molecular orbital in their DOS spectrum, it possesses spin density and magnetic property 47. Among the structures, Mn2B6 shows separate alpha and beta molecular orbitals as shown in Figure 9 which might have application in spintronic technology and magnetic devices fabrication industry.

Figure 7. Representation of the changing of the HOMO-LUMO gap (band gap) with the number of adsorbed transition metal (Mn) for mentioned two basis sets.

Figure 8. DOS spectra of pristine and manganese (Mn) doped (pyramidal and bi-pyramidal) B6 nanoclusters.
5. Conclusions
In this study, we have investigated different properties of pristine B6 and manganese (Mn) doped (pyramidal and bi-pyramidal) B6 clusters. The total Mulliken charge of the clusters is distributed among of the constituents of clusters and the net charge is zero. The stability of the structures has been investigated by the adsorption energy and thermodynamic parameters analysis. Adsorption energies have been increased in case of doping atoms where bi-pyramidal structure shows more increment compared with pyramidal structures. From thermodynamic parameter studies, it has also been observed that bi-pyramidal structure is more stable than pyramidal structure. The dipole moment studies also back up the same phenomena. From the UV-Vis spectra analysis, it has been found that the doped bi-pyramidal structures absorb broad EMR than pristine B6 and doped pyramidal structures, similarly the values of HOMO-LUMO energy gap increases for doped structures than pristine B6 cluster. The CD properties indicate that doped clusters show more chirality and more optically active behavior than pristine B6. The values of chemical potential are also increase for doping which is same for all other physical parameters the hardness (?), softness (S), electrophilicity (?) and these inform that the doped structures are more stable than pristine B6 cluster.

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