Enhancing the Light Harvesting Efficiency , Open Circuit Voltage and Stability of Molybdenum Doped ZnO 6 Nanocluster in Dye-sensitized Solar cells : ( A DFT study )

In this study, the electronic and structural properties of drum structured Mo-doped Zn6O6 (MoZn5O6) cluster as the π conjugated bridging in the dye-sensitized solar cells (DSSC) were compared with its pristine form by density functional theory (DFT) calculations under Gaussian 09 Program. The frontier molecular orbital study was explored to determine the charge transport characteristics of donor-acceptor moieties over the entire visible range and the electron injection from the valence band (LUMO) orbital to the conduction band (HOMO) orbital of MoZn5O6. The energy gap (Eg), binding energy (EB), global reactivity descriptors, thermodynamic parameters and the dipole moment were also calculated for MoZn5O6 and compared with Zn6O6. The density of states (DOS) of MoZn5O6 material was investigated to demonstrate the importance of d orbital of Mo atom in hybridization. To examine the charge distribution, Mulliken atomic charge distribution and molecular electrostatic potential (MEP) were analyzed. A spectroscopic study was included for the better perception of the interaction of Mo with Zn6O6 cluster. The increased value of the first-order hyperpolarizability of MoZn5O6 from its pure cluster manifests the MoZn5O6 is a better candidate with the superior nonlinear optical property. The analysis of UV-Vis spectra through the time-dependent density functional theory (TD-DFT) discovers that the MoZn5O6 has larger light harvesting efficiency (LHE) which influences the higher photon to current conversion efficiency. As a result, the valence band (LUMO) of MoZn5O6 is intense than the conduction band (HOMO) of MoZn5O6 making an increase in the open circuit voltage (VOC) and hence it confirms that the MoZn5O6 material can be a used in photovoltaic applications.


INTRODUCTION
Nanostructured materials are currently of prodigious attention due to their reduced dimensions and are majorly take part in a large number of new devices.Among the renewable energy sources, solar energy is the favorable and sustainable alternative.Several photovoltaic devices are manufactured on II-VI semiconductor nanostructures. 1,2Dye-sensitized solar cells (DSSC) are the real replacement to the well established silicon-based solar cells owing to their greater incident photon to current conversion efficiency, low cost, ease of device fabrication and durable stability.The DSSCs are hinged on the absorption of photon energy over wide ranges and dye sensitizers.The π conjugated elements are used to stimulate the photosynthesis because of their electrochemical properties. 3Recently, the evolution of ZnO nanomaterials are growing exponentially, which was proven by the ZnO related papers in the literature. 4,5The ZnO is a semiconductor metal oxide with broad energy gap has a higher probability in field effect transistors, solar cells, gas sensors, photodetectors, photocatalysts and optoelectronics due to its higher excitation binding energy. 6,7The ZnO nanomaterials have replaced the bulk materials through their nanomorphology, functionality, low toxicity, good thermal stability, oxidation resistivity, biocompatibility, larger surface to volume ratio, higher chemical reactivity, and greater electron mobility. 8,9o extend the range of uses of ZnO nanomaterial, there are novel procedures to rephrase the electronic structures of ZnO such as depositing or doping various atoms in bulk ZnO materials experimentally and theoretically. 10e introduction of Mo atom into the ZnO material is an elemental reach to refine the properties of the host material. 11Doping mechanism is the introduction of substitutional impurity by replacing single Zn atom by single Mo atom or single O atom by single Mo atom of the Zn 6 O 6 at any position causes the significant upgrade in optoelectronics successfully. 12,13The n-type Zn 6 O 6 semiconductor material doping with an element of group VI as Mo, its physical properties can be tuned finely.Mo plays an essential character in the modern semiconductor industry and it is a predominant doping material to upgrade the performance of ZnO nanostructured materials.Recently, Chang-Lin Yu et.al., 14 has prepared Mo-doped ZnO photocatalysts by a grinding calcination method.They analyzed that, the Mo doping provided higher photocatalytic activity and stability than pure ZnO nanoparticles.R. Swapna et.al., 15 and V. Gokula Krishnan et.al., 16 have studied Mo-doped ZnO thin films by using the spray pyrolysis technique.They showed that the films have shown minimum resistivity, maximum carrier concentration and high electrical conductivity upon Mo doping.
In the present work, the Mo-doped Zn 6 O 6 nano-cluster was studied and compared with its pristine form through energy, geometry, binding site, electronic properties, HOMO/LUMO energies, Mulliken charge distribution, DOS spectra, simulated IR, UV-Vis spectra and molecular electrostatic potential.A challenging way to inscribe this study is to utilize DFT and TD-DFT computational methods. 17The achievement of the solar cells was strengthened by the π conjugated system of the bridge.The structural unit of dyes is represented as D-π-A system.The Zn 0 O 6 interacts with Mo which intensifies the light harvesting efficiency, open circuit voltage, the electron injection and the stability of solar cells.The MoZn 5 O 6 material discovers extensive requirements in solar cells since an efficient photosensitizer which harvest the sunlight and retard the charge combination.

Computational methods
Geometrical optimization of pure Zn 6 O 6 , Single Mo atom and MoZn 5 O 6 were analyzed using density functional theory (DFT) method.9][20] For pure Zn 6 O 6 and MoZn 5 O 6 material, electronic states for a low spin as the singlet state (spin multiplicity = 1) were applied.To evaluate the excitation energy, UV-Vis electronic transition, light harvesting efficiency and oscillator strength of photosensitizers, TD-DFT calculations were employed at the CAM-B3LYP/6-31G level.The density of states (DOS) for pure Zn 6 O 6 and MoZn 6 O 6 nanostructures were plotted by employing Gauss Sum Program. 21The determination of dipole moment, chemical parameters and polarizability were employed by the B3LYP/6-31G in Gaussian 09 program. 22In further, natural bond orbital (NBO) analysis, molecular electrostatic potential (MEP) analysis and Mulliken charge distribution of each atom in the title compounds were also implemented in the Gaussian 09 program.The thermodynamic parameters and the vibrational frequency were computed at the same level of theory. 23The vibrational frequencies were evaluated to get all the structures are at a local minimum.Excited states analysis were performed using Time Dependent-Density Functional Theory (TD-DFT) Kohn-Sham equations in Gaussian 09 program. 24The interaction between Mo and Zn 6 O 6 cluster can be achieved by calculating binding energy as Where E Mo-Zn6O6 is the total energy of MoZn 5 O 6 cluster, E Mo is the total energy of the isolated Mo atom and EZn 6 O 6 is the total energy of the isolated Zn 6 O 6 cluster. 25The negative value of the binding energy stipulates the exothermic process. 26he energy gap Eg is defined as, Where, E HOMO and E LUMO are the energies of HOMO and LUMO, respectively.The energy shift ∆E g was calculated as the ratio of the difference of E g1 measured in pure Zn 6 O 6 (reference value) and E g2 measured in MoZn 5 O 6 with respect to the reference value. 27 g = [(E g2 -E g1 ) / (E g1 )] (3) The middle of the energy gap E g is the chemical potential (µ).The chemical potential (µ) of free gas of electron is equal to its Fermi level.The Fermi level of MoZn 5 O 6 was determined as the center of the energy gap E g . 28

Structures and stability
The optimized geometries of four isomeric structures of pure Zn 6 O 6 nanocluster were obtained by using the Gaussian 09 program in the singlet ground state are shown in Fig. 1, whereas Fig. 2 represents the optimized drum structured Zn 6 O 6 with MoZn 5 O 6 .The Zn 6 O 6 nanocluster has four structural variants.Among all the structures, the properties of three-dimensional drum structured Zn 6 O 6 have been scrutinized in this manuscript.The most known ZnO presentations are related to hexagonal forms and we expect that Zn 6 O 6 nanocluster represents a superior potential source for further more research. 29The structural data in the ground state and excited state of pure Zn 6 O 6 and MoZn 5 O 6 were listed in Table 1.The nanostructure of drum structured pure Zn 6 O 6 cluster has two hexagonal rings and six tetragons in the singlet ground state. 30The symmetry of the Zn 6 O 6 cluster is C 1 point group symmetry.Two different kinds of Zn-O bond lengths were identified within the pure Zn 6 O 6 .The bond distance of 1.93 Å was mutually shared between the two hexagons and the bond length of 1.99 Å was observed between the tetragon and a hexagon in DFT optimization.This bond length prediction is fine accordance with the Zn-O bond was calculated by Birajdar et.al., 31 and seetawan et.al., 32 11) position elongates the bond distance among the two hexagons as 1.96Å and the bond distance connecting the hexagon and the tetragon as 2.01Å in the ground state and decreases at excited state analysis.The doping of Mo at Zn (5)  and Zn(1) position produces a slight variation in the bond length than the pure cluster in both DFT and TD-DFT calculations.The huge difference in the bond length of Mo substituted structure and the pure form was observed at Zn (12) position of Mo doping in the singlet ground state.The interaction between Mo and the Zn 6 O 6 nanocluster were studied by calculating the corresponding binding energy EB as -1.76 Kcal/Mol.This calculation reveals that there were exothermic interaction with negative binding energy. 35

Frontier molecular orbital theory
The π type molecular orbital characteristics were exhibited by the HOMO/LUMO contours.The bonding behavior was specified by the HOMO orbital and the anti-bonding features were enumerated by the LUMO orbital.The HOMO/LUMO transition is identified as π -π* intramolecular interaction 36 .Fig. 3 shows the distribution of HOMO and LUMO of pure Zn 6 O 6 and MoZn 5 O 6 .The Zn atoms in the cluster have a positive charge which is an acceptor and O atoms have a negative charge which is the donor.The positive region appeared in green color and the negative region appeared in red color.The energies of HOMO and LUMO for pure Zn 6 O 6 were -6.16eV and -2.89eV with energy gap E g of 3.27eV was inadequate concurrence with the study done by Anitha et.al., 37 The high energy gap of pure cluster indicates the thermal stability and inertness towards reactivity.It specifies that the electron in the valence band requires more energy to go to the conduction band.The larger energy gap makes the ZnO nanocluster applied in electronic devices.
The HOMO and LUMO describe the charge transfer between Mo and Zn 6 O 6 cluster.The energies of HOMO and LUMO are changed to -4.64eV, -0.475eV and the energy gap is 4.16eV.38 The HOMO of the MoZn 5 O 6 significantly shifted to the higher energies by -1.52eV.The photovoltaic properties of the above compound in solar cell applications were analyzed because of the extraordinary property of ZnO nanocluster as a shallow donor or acceptor. 39he LUMO energy of the MoZn 5 O 6 was higher than the conduction band (HOMO) of MoZn 5 O 6 , which predicts that this compound may be an effective candidate in a photovoltaic cell uses.The open circuit voltage of the organic solar cells is linearly related with the HOMO of the donor and LUMO of the acceptor. 40The open circuit voltage VOC was calculated by, The dye MoZn 5 O 6 takes up the photon of energy which drives electrons to LUMO of the dye and then to the conduction band of MoZn 5 O 6 .The V OC of pure Zn 5 O 6 and MoZn 5 O 6 were calculated to be 3.57eV and 4.46eV.The MoZn 5 O 6 has high V OC and the MoZn 5 O 6 was used as efficient photosensitizers due to the good light absorption characteristics.All the methods of calculation used here are affirming that the energy gap of MoZn 5 O 6 material is sensitive towards Mo doping.The energy gap values of Zn 6 O 6 and MoZn 5 O 6 were calculated at B3LYP/6-31G, B3LYP/6-311G, B3LYP/LANL2DZ has been listed in Table 2.     3.For a pure Zn 6 O 6 cluster, Zn1, Zn3, Zn5, Zn10, Zn11, and Zn12 atoms possess positive charges which are acceptor atoms and the atoms O2, O4, O6, O7, O8, and O9 own negative charges which are donor atoms.The oxygen atom (O7) in Zn 6 O 6 has a more negative charge which is a donor.The Zinc atom (Zn10) has a more positive charge which is an acceptor.For MoZn5O6, Zn1, Zn3, Zn5, Zn10, Zn11, and Mo12 atoms possess positive charges which are acceptor atoms and the atoms O2, O4, O6, O7, O8, and O9 hold negative charges which are donor atoms. 41The Zn1 atom manifests more positive charge with a value 0.973e and O7 atom manifests more negative charge with a value 0.972e.The Mulliken atomic charge distributions of pure Zn 6 O 6 and MoZn 5 O 6 have been presented in Fig. 5.The NBO charges of pure Zn 6 O 6 and MoZn 5 O 6 in the singlet ground state are also shown in Table 3.In MoZn 5 O 6 , the charge transfers from the dopant Mo to the remaining part of the material as compared with the atomic charge of Zn atom of undoped Zn 6 O 6 .The metal dopant atom Mo acts as an electron acceptor.

Analysis of Chemical parameters
The ionization potential (I), electron affinity (A), chemical hardness (η), chemical softness (S), chemical potential (µ), and electrophilicity index (w) of MoZn 5 O 6 were determined and compared with the pure Zn 6 O 6 cluster and their values are tabulated in Table 4.The global reactivity descriptors were estimated from the energies of HOMO and LUMO to study the chemical stability and reactivity of MoZn 5 O 6 .(5) The chemical potential (µ) increases for MoZn 5 O 6 than its pure cluster.The calculated value of chemical potential (µ) for pure Zn 6 O 6 was -4.52eV and -2.55eV for MoZn 5 O 6 .The Fermi level (EF) of the MoZn 5 O 6 is sited at the nucleus of the energy gap E g .The chemical potential (µ) is also the middle point of the energy gap E g therefore Fermi level is similar to the chemical potential (µ).The electronegativity (Ψ) is the negative of the chemical potential (µ).The chemical hardness (η) was calculated by, The chemical hardness (η) of Zn 6 O 6 cluster was calculated as 1.635eV.The higher value of chemical hardness (η) in Zn 6 O 6 predicts its rigid chemical stability.The chemical hardness (η) increases to 2.08eV after Mo substitution over the cluster.The chemical hardness (η) depends on the ionization potential (I) and electron affinity (A).The chemical softness (S) and the electrophilicity index (w) are explained as The chemical softness (S) is a perceptual of the chemical hardness (η).The chemical softness (S) of Zn 6 O 6 was calculated as 0.30eV.The chemical softness (S) decreases to 0.24eV when a Mo atom was substituted on the pure Zn 6 O 6 cluster.The electrophilicity index (w) of Zn 6 O 6 was calculated as 6.26 eV and 1.56eV for MoZn 5 O 6 .The electrophilicity index (w) computes the tendency of the material to accept electrons.

Analysis of NLO parameters
The dipole moment is a salient electronic property which explains the charge distribution of the system.The calculated dipole moment for the pure cluster was found as 0.189 Debye and 1.867 Debye for MoZn 5 O 6 .The high value of dipole moment predicts the strong interaction among Mo and Zn 6 O 6 cluster and it favors the greater NLO property.The polarizability and the first order hyperpolarizability were determined using DFT calculations. 44e hyperpolarizability was expressed as The total hyperpolarizability, The mean polarizability, <α> = 1/3(α xx +α yy +α zz ) ( The calculated mean polar izability of pure Zn 6 O 6 was -92.0865Debye.The total hyperpolarizability of Zn

Thermodynamic parameters
The thermodynamic parameters of pure Zn 6 O 6 and MoZn 5 O 6 are displayed in Table 5 Where, HMoZn 5 O 6 , HZn 6 O 6 , and HMo are the sum of electronic and thermal enthalpies of  45 The values of ∆H, ∆S and ∆G were calculated as 65.4454, 38.078 and

Molecular electrostatic potential
Molecular electrostatic potential (MEP) predicts the three-dimensional charge distribution of Zn 6 O 6 and MoZn 5 O 6 .All isosurfaces are depicted with isovalue of 0.0004e/au3 in Gauss view software. 46EP plot offers the positive and the negative region of Zn 6 O 6 cluster and MoZn 5 O 6 are shown in Fig. 6.In Fig. 6a, the Zn atoms were positively charged which are present in blue color.The O atoms were negatively charged which are appeared in red color.This reveals that there is the charge transfer from Zn atoms to O atoms which results in ionic bonds in the Zn 6 O 6 nanocluster.In Fig. 6b, based on the MEP calculation upon MoZn 5 O 6 cluster, the Zn atoms were specified by red color shows negative in charge.This confirms that there is a charge transfer from Mo doping material to the nanocluster because of the strong interaction.The total charge of MoZn 5 O 6 material was -1.0.MEP surface prompted by the charge distribution of Zn 6 O 6 and MoZn 5 O 6 at an atomic site is described as (15)   Where ZA is the charge on nucleus A located at R A . 47

Vibrational analysis
The vibration frequencies were the unique parameter to explore the local minimum in structures.The theoretical FTIR spectra of Zn 6 O 6 and MoZn 5 O 6 were presented in Fig. 7. Transmittance is the principal features of Zn-O vibration. 48There are 30 possible modes of vibrations in pure Zn 6 O 6 .The simulated IR spectrum of pure Zn 6 O 6 shows the absorption peaks at 430 cm -1 , 451 cm -1 and 547 cm -1 have corresponded to the Zn-O stretching vibrations. 49,50owbagya et.al., 51 have synthesized Mo-doped ZnO nanoparticles and studied the FTIR spectrum.They showed that the Zn-O stretching vibration was observed at 443 cm -1 .The existence of Mo-O 3 depicted with the peak around 556 cm -1 , 859 cm -1 and 617cm -1 .The stretching vibration of Mo=O was observed at 925 cm -1 .In this present theoretical investigation, the Mo-doped Zn 6 O 6 exhibits 30 modes of vibrations.The peak at 438 cm -1 was assigned to the stretching vibration of the Zn-O bond.The peaks at 533 cm -1 , 606 cm -1 and 842 cm -1 were assigned to the various bonds of Mo(12)-O(2), Mo(12)-O (6)  and Mo(12)-O( 7) respectively.The absorption band at 952 cm -1 indicating the Mo=O stretching vibration.The presence of additional absorption bands from 438 cm -1 to 1001 cm -1 indicates the existence of Mo and its oxides.

Absorption Spectra and Photovoltaic properties
The UV-Vis spectra of pure Zn 6 O 6 and MoZn 5 O 6 were analyzed and the wavelength (λmax), excitation energies (∆E) and oscillator strength (f) were computed using the singlet excited state at the B3LYP/6-31G by the time-dependent density functional theory calculations (TD-DFT) and the results were listed in Table 6.
The high absorption of the Zn 6 O 6 and MoZn 5 O 6 were studied from the energy gap (E g ).The lowest singlet to singlet excited state transitions were investigated to study the electronic absorption mechanism in whole visible/near-IR regions.On the basis of Frank Condon principle, the maximum peak correlates with vertical excitation.The electronic excitation observed as ππ* transitions.The energy gap of Zn 6 O 6 cluster was 3.27 eV so that the λ max was fall in the visible region.There are three peaks with excitation energies 2.14eV, 2.19eV, and 2.33eV for the pure Zn 6 O 6 .The excitation wavelengths (λ max ) of the absorption spectrum of Zn 6 O 6 were determined as 578 nm, 565 nm, and 531 nm.The higher value of oscillator strength (f) was calculated as 0.60 with the excitation energy (∆E) of 2.14eV.After the Mo doping in Zn 6 O 6 cluster, the excitation energies (∆E) were calculated as 2.43eV, 2.97eV, and 3eV.The higher value of oscillator strength (f) was calculated as 0.90 with the excitation energy 3eV.The MoZn 5 O 6 material is beneficent in increasing the light harvesting efficiency which leads to the higher short circuit current density (Jsc). 52The short-circuit current density (Jsc) is closely related to the charge conversion efficiency (η) of the solar cell can be calculated by the following equation Jsc = ∫LHE (λ) φ Inject .ηcollect dλ (16)   Where LHE (λ) is the light harvesting efficiency, φ Inject is the electron injection efficiency to the conduction band of MoZn 5 O 6 and η collect is the electron collection efficiency.The φ Inject is associated with the driving force ∆G inject for the electron injection.The light harvesting efficiency LHE (λ) can be expressed as 53

LHE
Where f is the oscillating strength of the maximum absorption spectra of Zn 6 O 6 and MoZn 5 O 6 .
The large φ Inject leads to the higher Jsc.The φ Inject is directly proportional to the free energy of electron injection as φ Inject α f (-∆ GInject ) ∆G Inject = E dye * -ECB (18)   Where E dye * represent the oxidation potential energy in the excited state and ECB represent the reduction potential of the conduction band.E dye * can be estimated by Where Edye represents the energy of oxidation potential in the ground state and ∆E is the energy of the electronic vertical transition corresponding to λ max .The oxidation potential of the dye is directly related to the HOMO level and the driving force for the reduction of oxidized dye increase at the larger oxidation potential.The values of an electron injection (∆G Inject ), oxidation potential (E dye * and E dye ) and open circuit voltage (VOC) of pure Zn 6 O 6 and MoZn 5 O 6 are summarized in Table 7 .

CONCLUSION
The theoretical investigation on geometrical structures, binding nature, UV-Vis spectra, vibrational frequencies and the electronic properties of Zn 6 O 6 and MoZn 5 O 6 have been analyzed to predict the photovoltaic properties using DFT and TD-DFT theory.The doping of Mo makes the substantial modification in the HOMO and LUMO energies which ensures the open circuit voltage (VOC) of the MoZn 5 O 6 was higher than the pristine Zn 6 O 6 cluster.The high open circuit voltage making MoZn 5 O 6 as a potential compound in the photovoltaic applications and is also been an efficient sensitizer.The density of state analysis brings the light absorption characteristics of MoZn 5 O 6 system expands consequently by the doping material.The calculations from the various basis sets predict that there was a significant charge transfer from the dopant to the pure cluster, which enhances the energy gap E g .The nonlinear optical characteristic of MoZn 5 O 6 material was studied by hyperpolarizability.The dipole moment of MoZn 5 O 6 was higher than its pure form.The increase in light harvesting efficiency of MoZn 5 O 6 was calculated from the electronic transition in UV-Vis spectra.The replacement of Mo assists the hexagonal MoZn 5 O 6 nanomaterial has more photoresponse than Zn 6 O 6 which would be a better potential originator in solar cell applications.

Fig. 1 .Fig. 2 .
Fig. 1.The optimized isomeric structures of pure Zn 6 O 6 calculated at B3LYP/6-31G level of theory depending on the structures of nanocluster.Results of TD-DFT the Zn-O bond length for pure Zn 6 O 6 cluster between 1.91Å-1.93Å is fine agreement with the theoretical studies by wang et.al., 33 The charge transfer from the Zn atom to the O atom in pure Zn 6 O 6 results the ionic bond of Zn-O.The bond angles of tetragons and the hexagons in the pure Zn 6 O 6 cluster varied from 89 o to 91 0 and 116 o to 124 0 .The calculated values of vibrational frequencies are positive from 70cm -1 to 716 cm -1 .Analyzing the optimized structure of MoZn 5 O 6 , the bond distances of Zn-O bonds are increased in size when Mo replaced oxygen atoms at any position.The replacement of Zn by Mo at Zn (12) position favors the stabilization of the material by reducing bond distances in the singlet ground state is comparable to the work by Woodley et.al., 34 They showed Mg and Cd doping with pure ZnO nanoclusters to study their stability.The larger bond length difference occurs among the two hexagons at Zn(1)-O(7), Zn(10)-O(2), Zn(10)-O(4), Zn(5)-O(8) bonds to 1.88Å and the bond distance between the tetragon and hexagon of Zn(11)-O(8) reduced to 1.94Å.The bond distance of Mo(12)-O(7), Mo(12)-O(2), Mo(12)-O(7) was calculated as 1.74Å.Results of TD-DFT for Mo doping at Zn(12) position makes the changes in bond length at Mo(12)-O(2) increases to 1.77Å and Zn(5)-O(8), Zn(10)-O(2) to 1.96Å.The replacement of Zinc by Mo at Zn(10) brings the changes in bond distance among the hexagons as 1.91Å at Zn(1)-O(2), Zn(5)-O(6), Zn(10)-O(9) and the bond distance between the tetragon and a hexagon to 1.96Å at O(2)-Zn(10), Zn(5)-O(8) in the singlet DFT calculation.TD-DFT calculation brings the changes in Zn(10)-O(9) to 1.90Å and Zn(10)-O(2) to 1.95Å while Mo doping at Zn(10) position.The replacement of Zinc by Mo at Zn(3) and Zn(

Fig. 3 .
Fig. 3.The HOMO and LUMO profiles of pure Zn 6 O 6 cluster and Mo doped Zn 6 O 6 calculated at B3LYP/6-31G level of theoryAfter substitution with Mo, the HOMO levels are mostly scattered along the Mo doping region.

Fig. 4 .
Fig. 4. The density of states plot of pure Zn6O6 cluster and Mo doped Zn6O6 nano material Charge population analysis Mulliken atomic charge distribution affords the information about the electron population of atoms in Zn 6 O 6 and MoZn 5 O 6 cluster.The Mulliken charge values were calculated from B3LYP/6-31G basis set.The Mulliken atomic charges of individual atoms present in Zn 6 O 6 and MoZn 5 O 6 are given in Table3.For a pure Zn 6 O 6 cluster, Zn1, Zn3, Zn5, Zn10, Zn11, and Zn12 atoms possess positive charges which are acceptor atoms and the atoms O2, O4, O6, O7, O8, and O9 own negative charges which are donor atoms.The oxygen atom (O7) in Zn 6 O 6 has a more negative charge which is a donor.The Zinc atom (Zn10) has a more positive charge which is an acceptor.For MoZn5O6, Zn1, Zn3, Zn5, Zn10, Zn11, and Mo12 atoms possess positive charges

Fig. 5 .
Fig. 5. Mulliken atomic charge plot of pure Zn 6 O 6 and Mo doped Zn 6 O 6 nano cluster On the basis of Koopman's theorem 42 the energies of HOMO (EHOMO) and LUMO (ELUMO) are associated with the ionization potential (I) and the electron affinity (A) as I = -E HOMO and A = -E LUMO .The ionization potential reduces when a Mo atom was substituted on Zn 6 O 6 nanocluster.The ionization potential of the pure Zn 6 O 6 was 6.16eV which declined to 4.64eV for MoZn 5 O 6 .The electron affinity decreases from 2.89eV to 0.475eV after Mo doping.This calculation correlated with Phool Singh Yadav et.al., 43 as the ionization potential (I) was greater than the electron affinity (A).The chemical potential (µ) is defined based on the equation, 6 O 6 was found to be 3.1712 Debye.The calculated mean polarizability of MoZn 5 O 6 was -108.6326Debye.The calculated total hyperpolarizability of MoZn 5 O 6 was 62.74 Debye.The highest contribution of the α zz component indicates, the pure and Mo-doped Zn 6 O 6 cluster elongated towards the Z direction and contracted to the X direction.The β xzz component contributes with a larger part of hyperpolarizability in the pure form with the value 9.6624.The β xxy component contributes more towards the hyperpolarizability of MoZn 5 O 6 with the value 20.0258.The MoZn 5 O 6 material is a captivating gadget for further research of nonlinear optical properties due to the doping of the Mo atom.
. The thermal capacity (CV) of MoZn 5 O 6 was increased to 45.07 Cal/Mol-Kelvin from 43.86 Cal/Mol-Kelvin as compared to Zn 6 O 6 cluster.The CV shows that, the thermal capacity of the Zn 6 O 6 and MoZn 5 O 6 at room temperature and constant volume.The value of zeropoint vibrational energy of Zn 6 O 6 and MoZn 5 O 6 were found to be 16.77 and 15.94 Kcal/Mol.The change in enthalpy (∆H), the change in entropy (∆S) and the change in Gibbs free energy (∆G) of pure Zn 6 O 6 and MoZn 5 O 6 were computed from the frequency calculations using the consequent equations Zn 6 O 6 , MoZn 5 O 6 , and Mo atom.GMoZn 5 O 6 , G Zn 6 O 6 , and GMo are the sum of electronic and thermal free energies of Zn 6 O 6 , MoZn 5 O 6 , and Mo atom.S MoZn 5 O 6 , SZn 6 O 6 , and SMo are the entropies of Zn 6 O 6 , MoZn 5 O 6 , and Mo atom.

Table 2 : The values of HOMO and LUMO energies (E HOMO and E LUMO ), an energy gap (E g ) and the energy shift (∆E g ) of Zn 6 O 6 and MoZn 5 O 6 calculated at B3LYP/6-311G, 6-31G and the LANL2DZ level of theory
The density of states plot of pure Zn 6 O 6 and MoZn 5 O 6 are shown in Fig. 4. The energy gap of pure Zn 6 O 6 was determined as 3.27eV.The energy gap MoZn 5 O 6 was calculated as 4.16eV.By comparing the HOMO and LUMO levels of the pure Zn 6 O 6 and MoZn 5 O 6 , the doping process causes the significant shift of HOMO of pure Zn 6 O 6 to higher energy levels and the new HOMO of MoZn 5 O 6 lies between the HOMO and LUMO of the pure Zn 6 O 6 .The DOS plot of MoZn 5 O 6 indicates that Mo atom significantly participates in having a higher value of E g and VOC compared to the pure cluster.The Fermi energy (EF) was increased after Mo doping and hence EF shifts

Table 3 : Mulliken atomic charges (Mul) and NBO charges of Zn 6 O 6 and MoZn 5 O 6 calculated at B3LYP/6-31G Atom
the conduction band.The EF was increased from -4.52eV to -2.79eV after Mo doping.This increase in Fermi level assists the decrease in work function causes the MoZn 5 O 6 material is an essential candidate in field emission.After the Mo substitution over the Zn 6 O 6 nanocluster, Mo enhances the VOC of MoZn 5 O 6 by increasing the energy gap compared to the pure Zn 6 O 6 cluster.Therefore, the MoZn 5 O 6 material was found remarkable applications in solar cell devices.