First Principles Study for the Optical Properties of the Most Stable small ZnTe Nanoclusters

First Principles Study for the Optical Properties of the Most Stable small ZnTe Nanoclusters | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article First Principles Study for the Optical Properties of the Most Stable small ZnTe Nanoclusters Dheeraj Kumar Pandey, Anilesh, P. S. Yadav This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6711847/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The optical properties of the most stable Zn x Te y (x + y = 2 to 5) nanoclusters have been investigated based on a first-principles study. The geometries of ZnTe nanoclusters are optimized using the B3LYP-DFT/LANL2DZ approach. At the same time, the optical properties of the most stable structures of individual configurations are studied using the Time-Dependent Density Functional Theory (TDDFT). This study also takes the zero-point energy modification into account. The most stable nanocluster has been defined as the structure with the lowest energy when compared to other structures for the same values of "x" and "y." The instability of certain of the nanoclusters is caused by the existence of at least one imaginary vibrational frequency. With a few exceptions, most nanoclusters exhibit significant optical absorption in the ultraviolet range but slight optical absorption in the visible region. By these investigations, absorption occurs on the higher energy side of Te-rich nanoclusters and the lower energy side of Zn-rich nanoclusters in the majority of nanoclusters. In the experiments, it may be possible to grow the most stable nanoclusters. Nanoscience Nanoclusters Optical Properties Oscillator Strength EELS TDDFT study Figures Figure 1 Figure 2 Figure 3 1. Introduction Semiconductor nanoclusters are nanomaterials that exhibit peculiar size-dependent electronic and optical properties due to the Quantum Confinement Effect of the charge carriers [ 1 – 4 ]. Because of these substantial properties, nanoclusters are promising replacements for photoactive molecular species and are being extensively explored for different type of applications that include chemical and biosensing, biological imaging, medical field, opto-electronic devices and solar cells technology [ 5 – 7 ]. Generally, a nanocluster is an intermediate state of matter between molecule and bulk of the same components. Nanoclusters are generally prepared by reacting inorganic precursors in the occurrence of organic ligands, which eventually form a molecular coating around the Quantum Dots core and stabilize the nanoparticles against aggregation [ 8 ]. The selection of II–VI semiconductors that do not cover harmful elements and possess an energy gap suitable for visible absorption and emission seems to be limited to ZnTe compound material [ 9 – 12 ]. The size-controlled synthesis of colloidal ZnTe nanoparticles [ 13 – 16 ] is particularly challenging and has received much less attention compared to that of other II–VI compounds. ZnTe is a semiconducting material with a direct energy gap of 2.26 eV equivalent to a wavelength of around 550 nm [ 17 ]. Presently, the ZnTe nanomaterial is mainly produced by evaporating ZnTe powder at very high temperatures (about 900 ℃) with always using gold as catalyst [ 18 – 19 ]. Other type of nanomaterials like ZnTe nanowires and ZnTe nanorods are also obtained by wet chemical method largely implicated the burst nucleation and further aggregation of the monomers produced by precursors [ 20 – 22 ]. There is different type of experimental techniques, which have been also employed by several researchers to synthesize the Zinc Telluride nanomaterials [ 23 – 26 ]. RojasChávez et al. [ 23 ] have synthesized ZnTe nanoparticle by a mechanochemical synthesis procedure, while Lincheneau et al. [ 27 ] reported the size-controlled preparation and characterization of ZnTe and ZnTe/ZnS core/shell Quantum Dots. Although this real-world application of semiconducting nonmaterial involves extensive experimental research, theoretical approaches are of fundamental importance as they allow both to understand the elementary physics and to optimize devices made from nanostructure materials. There have been several theoretical research of the structural stabilities, HOMO–LUMO gaps and optical absorption of some nanoclusters of (ZnTe) n type [ 28 , 29 ]. Earlier, we have performed comprehensive an ab-initio study of structural and electronic properties of ZnO, ZnS, ZnSe and ZnTe upto five atoms’ nanoclusters [ 30 – 34 ] but the other physical properties like optical properties for the most stable small Zn x Te y nanoclusters upto five atoms (x + y = 2 to 5) have not been reported so far up to the knowledge of the authors. In this research paper, we have extended our first principle study for the optical properties of the most stable small Zn x Te y nanoclusters. The current study also encourages experimental investigators to produce these nanoclusters to further investigate their potential uses in the fabrication of nanodevices. Section 2 contains the method (TDDFT) used in the investigations for the excitation energies. In Section 3 , we present the discussions about the calculation and results. The conclusions are contained in the last Section 4 . 2. Method Geometrical optimization for small Zn x Te y nanoclusters has been established previously by our group [33, 34]. All the geometrical structures were fully optimized employing the hybrid gradient-corrected functional (B3LYP) within the Density Functional Theory (DFT) framework [35] in the Gaussian-03 code [36]. In this study, we consider the Becke exchange functional and the correlation function of Lee, Yang and Parr (LYP) that includes contributions for both the local and nonlocal. Also, we employ the three-parameter hybrid functional of Becke. Here, Becke functional considers the Slater exchange along with the corrections involving the gradient of the density (Becke). We also use a basis set LANL2DZ which is necessary for the description of the ground state of each atom. The core electrons are replaced by effective core potential in LanL2DZ basis sets. The pseudo potential approximation is to replace the combined effects of motion of bound electrons of an atom and the effective potential of the nucleus is denoted as pseudo potential in which the Schrödinger equation contains a modified potential term. Since, Zinc and Tellurium have the atomic number of 30 and 52 correspondingly, LANL2DZ basis set will yield a improved outcome with pseudo potential approximation. This is why B3LYP/LANL2DZ basis set is selected to fully optimize the Zn x Te y nanoclusters. For each optimized structures the harmonic vibrational frequencies were also calculated by analytical differentiation of gradients. The polarizable triple split valance basis set 6-311G(3df) was used as the basic basis set in this study for the most precise calculation after selecting a large number of basis set for each atom. The three d electrons and one f electrons of Zn and Se atoms were taken with the valence electrons as a polarized function due to their importance for the description of the ground state of each atom in three dimensions. But, a major limitation of the DFT is that it is inherently unsuitable for the computation of excited state properties. This is why in the present work, the usual Time Dependent Density Functional Theory (TDDFT) calculations have been performed for the excitation energies of the most stable Zn x Te y nanoclusters. 3. Calculation and results Different types of all possible structures including the linear chains, rings, planar and three-dimensional ones for each configuration have been considered in the optimization of ZnTe nanoclusters [33, 34]. Each structure is achieved to its minimum energy by relaxing the atomic positions. The convergence in the system energy up to 10 -7 meV and the forces of 10 -3 eV/Å on each atom were obtained. The structure for each configuration having minimum energy in comparison to other structures possessing same value of “x” and “y” is considered as stable structure. Thus, the stability of nanocluster depends upon the binding energy of the nanocluster. The total energy of a nanocluster is subtracted from the sum of the energies of all the isolated atoms present in the nanocluster and then we divide the resultant quantity by the number of atoms. We have named this as the binding energy (BE) per atom. For a more precise calculation, we have calculated the harmonic vibrational frequencies and the corresponding zero-point energy (ZPE) which is further subtracted from the calculated binding energy (BE) per atom and it gives the final binding energy (FBE). For a particular chemical formula Zn x Te y , the configuration possessing the maximum value of FBE is named as the most stable structure as shown in Fig 1. In the stability of these structures the vibrational frequencies are also studied. The imaginary frequency for a structure point to its instability. The imaginary frequency having maximum final binding energy of a structure causes its in stability and gives an opportunity for next structure having maximum final binding energy of the same configuration to be considered as most stable. 3.1. Optical properties In Figures 2 and 3, we demonstrate the calculated optical absorption spectra, which resemble the electron energy loss spectra (EELS). A few nanoclusters have weak absorption in the visible spectrum, while the majority of them have high absorption in the ultraviolet. Table 1 provides the excitation energies for the most stable ZnxTey nanoclusters that exhibit the strongest oscillators. Following is a discussion of each nanocluster's absorption spectra. ZnTe As depicted in Fig. 2(a), the calculated absorption for the most basic diatomic nanocluster (Fig. 1(a)) falls within the energy range of 2.98 to 10.00 eV. Approaching the experimentally recorded value of 4.95 eV, a prominent peak may be seen at 6.81 eV [27]. At 8.95 eV, a very weak peak additionally shows up. Zn x Te y (x+y = 3) As shown in Fig. 2(b), the linear TeZnTe nanocluster (Fig. 1(b)) demonstrates a high absorption in the energy spectrum ranging from 4.83 to 6.36 eV. At 6.30 eV, a very strong, sharp peak appears. As apparent in Fig. 2(c), the absorption spectrum for the linear ZnTeZn nanocluster (Fig. 1(c)) is dispersed spanning the broad energy range of 0.51 – 7.94 eV. At 4.67 eV, a strong absorption peak appears to be seen in the visible region's upper side. Zn x Te y (x+y = 4) The visible energy range showed poor absorption for the rhombus ZnTe3 (Fig. 1(d)) nanocluster. The energy range of 5.71 to 7.41 eV reveals comparatively substantial absorption, with a strong peak at 7.22 eV. The rhombus Zn2Te2 (Fig. 1(e)) nanocluster exhibits significant absorption in the ultraviolet range and poor absorption in the infrared. As demonstrated in Fig. 3(a), the absorption takes place between 6.04 and 7.01 eV. At 6.97 eV, a prominent absorption peak is visible. Strong absorption has been observed for the linear Zn3Te (Fig. 1(f)) nanocluster in the visible range of 0.93 to 3.89 eV. At 3.28 eV, a prominent absorption peak is visible. Zn x Te y (x+y = 5) Although all of the ZnTe4 configuration structures under investigation have imaginary frequencies, they are certainly all unstable. The pentagonal Zn2Te3 structure (Fig. 1(g)) demonstrates strong absorption in the UV range of 6.79–7.42 eV. In Fig. 3(c), two prominent peaks can be observed at 7.04 and 7.38 eV. The pentagonal Zn3Te2 structure (Fig. 1(h)) exhibits strong absorption in the UV range of 5.43 to 8.03 eV. Figure 3(d) shows three weak peaks at 6.15, 8.01, and 5.54 eV and an exceptionally large peak at 6.70. The planer Zn4Te structure (Fig. 1(i)) exhibits strong absorption in the UV range of 4.03 to 6.76 eV. As shown in Fig. 3(e), a prominent peak can be seen at 6.11 eV. The vast majority of the nanoclusters exhibit significant UV absorption. In accordance to these studies, absorption is observed on the lower energy side of Zn-rich nanoclusters and on the higher energy side of Te-rich nanoclusters in the majority of nanoclusters. 4. Conclusion The optical characteristics of the most stable ZnTe nanocluster formations up to five atoms are presented in this work. Since every structure of the ZnTe4 configuration that has been studied contains at least one imaginary vibrational frequency, we conclude that only this configuration has no stable structure for x + y = 5. In contrast, the Zn2Te3, Zn3Te2, and Zn4Te configurations all have stable structures. The experimental data and our estimated result for the linear ZnTe nanocluster's excitation energies show good agreement. Nearly all of the nanoclusters demonstrate significant UV absorption. In the visible spectrum, certain nanoclusters exhibit considerable absorption. In accordance to these studies, absorption occurs in the lower energy side of Zn-rich nanoclusters and on the higher energy side of Te-rich nanoclusters in the majority of nanoclusters. In the experiments, it might be possible to produce these most stable nanoclusters. Declarations Acknowledgement The authors thank Lalit Narayan Mithila University, Darbhanga, Bihar, India, for the support. Funding This work was supported by ongoing institutional funding. No additional grants were obtained to carry out or direct this particular research. Author Information Dheeraj Kumar Pandey, ORCID: https://orcid.org/0000-0002- 4011-952X Credit Authorship Contribution Statement Dr. Dheeraj Kumar Pandey: Conceptualization, Formal analysis, Investigation, Visualization; Mr. Anilesh: Writing & Editing; Prof. P. S. Yadav: Methodology, Resources, Software, Supervision. Conflict of Interest The authors of this work declare that they have no conflicts of interest. References Murray C B, Kagan C R & Bawendi M G, Annu Rev Mater Sci 30 (2000) 545. Dekker, Semiconductor and Metal Nanocrystals, ed. V. I. Klimov, New York, (2012). Rogach A L, Semiconductor Nanocrystal Quantum Dots, Springer-Verlag, Wien, (2008). Efros A L & Rosen M, Annu Rev Mater Sci 30 (2000) 475. 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Lincheneau C, Matteo A, Oszajca M, Boccia A, D'Orazi C F, Madrigale M, Zanoni R, Mazzaro R, Ortolani R, Morandi V, Silvi S, Szaciłowski K & Credi A, J Mater Chem C, 2 (2014) 2877. Sriram S, Chandiramouli R, Balamurugan D & Thayumanvan A, E Phy J App Phys 62 (2013) 30101. Xu S, Wang C & Cui Y, J Mol Struct 938 (2009) 133. Yadav P S, Pandey D K, Agrawal S & Agrawal B K, Eur Phys J Plus 130 (2015) 60. Yadav P S, Pandey D K, Agrawal S & Agrawal B K, J Nanopart Res 12 (2010) 737. Yadav P S & Pandey DK, Adv Sci Eng Med 3 (2011) 230. Yadav P S & Pandey D K, Adv Sci Eng Med 12 (2020) 930. Pandey D K, Anilesh & Yadav P S, Ind J Pure and App Phy 62 (2024) 189. Miehlich B, Savin A, Stoll H & Preuss H, Chem Phys Lett 157, 200 (1989). C.03 (Pittsburgh, PA: Gaussian). Gaussian, Inc. (2003) GAUSSIAN 03 , Revision. Table Table 1 Excitation energies ( ∆ E, in eV) having largest oscillator strengths (f) for the most stable configurations of Zn x Te y (x+y = 2 to 5) nanoclusters. Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6711847","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":459607818,"identity":"2faadceb-b8cb-485d-b820-64903fbafa25","order_by":0,"name":"Dheeraj Kumar Pandey","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAElEQVRIiWNgGAWjYDCCG2CSjUGCgfn4hw8gJjvxWtjSGGeAmMzEaWEAauExY+YBsQhp4bvdfPBxRQ2f3czZbWmPbX5tk+djZmD88DEHtxbJO8eSDc8cY0ueLXP4uHFu323DNmYGZsmZ23BrMbiRYybZwMaWLCeRliCd23ObEaiFjZkXr5b87z8b/oG05BhIW/bctidCSw4bY2Mbm520RI6ZNMOP24kEtUjeSDOWbOxjS5CcA/RUb8Pt5DZmxma8fuG7kfzwY8O3Y/YSwKB78OPPbdv57c0HP3zEowUKjiU2SAApxjYQh7GBoHogqLFnAGlh+EOM4lEwCkbBKBhpAADcglREEAWWtwAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-4011-952X","institution":"Department of Physics, Ramashray Baleshwar College (A Constituent Unit of Lalit Narayan Mithila University, Darbhanga), Dalsingsarai, Samastipur, Bihar - 848114, India","correspondingAuthor":true,"prefix":"","firstName":"Dheeraj","middleName":"Kumar","lastName":"Pandey","suffix":""},{"id":459607819,"identity":"660da4db-50df-4a85-81be-ae345573e839","order_by":1,"name":"Anilesh","email":"","orcid":"","institution":"Department of Physics, R. N. A. R. College (A Constituent Unit of Lalit Narayan Mithila University, Darbhanga), Samastipur, Bihar - 848101, India","correspondingAuthor":false,"prefix":"","firstName":"","middleName":"","lastName":"Anilesh","suffix":""},{"id":459607820,"identity":"f278ce43-8af3-4452-a25f-27cb60af4759","order_by":2,"name":"P. S. Yadav","email":"","orcid":"","institution":"Department of Physics, University of Allahabad, Prayagraj, Uttar Pradesh – 211002, India","correspondingAuthor":false,"prefix":"","firstName":"P.","middleName":"S.","lastName":"Yadav","suffix":""}],"badges":[],"createdAt":"2025-05-21 02:50:08","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":true,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":true},"doi":"10.21203/rs.3.rs-6711847/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6711847/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83338991,"identity":"f8c13246-35e0-4ea6-80f3-4db3cea43af4","added_by":"auto","created_at":"2025-05-23 10:04:10","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":239491,"visible":true,"origin":"","legend":"\u003cp\u003eMost stable structures of ZnTe, ZnTe\u003csub\u003e2, \u0026nbsp;\u003c/sub\u003eZn\u003csub\u003e2\u003c/sub\u003eTe, ZnTe\u003csub\u003e3,\u0026nbsp; \u003c/sub\u003eZn\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e2,\u003c/sub\u003e Zn\u003csub\u003e3\u003c/sub\u003eTe,\u0026nbsp; Zn\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e3, \u003c/sub\u003eZn\u003csub\u003e3\u003c/sub\u003eTe\u003csub\u003e2,\u003c/sub\u003e and \u0026nbsp;Zn\u003csub\u003e4\u003c/sub\u003eTe nanocluster.\u0026nbsp; (All the bond lengths are in A\u003csup\u003e0\u003c/sup\u003e)\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-6711847/v1/223516bc217cea77d1e9b7e2.png"},{"id":83339936,"identity":"e2f67bc4-b76c-4a78-a470-713c3aaf8851","added_by":"auto","created_at":"2025-05-23 10:20:10","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":125274,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption spectra for the most stable structures of (a) Linear ZnTe (b) Linear ZnTe\u003csub\u003e2\u003c/sub\u003e (c) Linear Zn\u003csub\u003e2\u003c/sub\u003eTe and (d) Rhombus ZnTe\u003csub\u003e3\u003c/sub\u003e.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6711847/v1/f7346d4124c5f37bd7ed2e34.png"},{"id":83340574,"identity":"2b3caab2-c173-4804-8736-0f5ae758ba48","added_by":"auto","created_at":"2025-05-23 10:28:10","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":179953,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption spectra for the most stable structures of (a) Rhombus Zn\u003csub\u003e2\u003c/sub\u003eTe\u003csub\u003e2 \u003c/sub\u003e(b) Linear Zn\u003csub\u003e3\u003c/sub\u003eTe\u003csub\u003e \u0026nbsp;\u003c/sub\u003eand (c) \u0026nbsp;Pentagonal Zn\u003csub\u003e3\u003c/sub\u003eTe\u003csub\u003e2\u003c/sub\u003e (d) \u0026nbsp;Pentagonal Zn\u003csub\u003e3\u003c/sub\u003eTe\u003csub\u003e2\u0026nbsp; \u003c/sub\u003e(e) \u0026nbsp;Planer Zn\u003csub\u003e4\u003c/sub\u003eTe .\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6711847/v1/dfdc57b8fcb274d1400491cb.png"},{"id":83340575,"identity":"a02f67ae-f6fe-4461-b31d-72b51bd0fff9","added_by":"auto","created_at":"2025-05-23 10:28:14","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":923959,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6711847/v1/7f9acad0-d50d-48ad-b66b-837f465807d6.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eFirst Principles Study for the Optical Properties of the Most Stable small ZnTe Nanoclusters\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eSemiconductor nanoclusters are nanomaterials that exhibit peculiar size-dependent electronic and optical properties due to the Quantum Confinement Effect of the charge carriers [\u003cspan additionalcitationids=\"CR2 CR3\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Because of these substantial properties, nanoclusters are promising replacements for photoactive molecular species and are being extensively explored for different type of applications that include chemical and biosensing, biological imaging, medical field, opto-electronic devices and solar cells technology [\u003cspan additionalcitationids=\"CR6\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]. Generally, a nanocluster is an intermediate state of matter between molecule and bulk of the same components. Nanoclusters are generally prepared by reacting inorganic precursors in the occurrence of organic ligands, which eventually form a molecular coating around the Quantum Dots core and stabilize the nanoparticles against aggregation [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. The selection of II\u0026ndash;VI semiconductors that do not cover harmful elements and possess an energy gap suitable for visible absorption and emission seems to be limited to ZnTe compound material [\u003cspan additionalcitationids=\"CR10 CR11\" citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. The size-controlled synthesis of colloidal ZnTe nanoparticles [\u003cspan additionalcitationids=\"CR14 CR15\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] is particularly challenging and has received much less attention compared to that of other II\u0026ndash;VI compounds. ZnTe is a semiconducting material with a direct energy gap of 2.26 eV equivalent to a wavelength of around 550 nm [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Presently, the ZnTe nanomaterial is mainly produced by evaporating ZnTe powder at very high temperatures (about 900 ℃) with always using gold as catalyst [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]. Other type of nanomaterials like ZnTe nanowires and ZnTe nanorods are also obtained by wet chemical method largely implicated the burst nucleation and further aggregation of the monomers produced by precursors [\u003cspan additionalcitationids=\"CR21\" citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. There is different type of experimental techniques, which have been also employed by several researchers to synthesize the Zinc Telluride nanomaterials [\u003cspan additionalcitationids=\"CR24 CR25\" citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e]. RojasCh\u0026aacute;vez et al. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] have synthesized ZnTe nanoparticle by a mechanochemical synthesis procedure, while Lincheneau et al. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e] reported the size-controlled preparation and characterization of ZnTe and ZnTe/ZnS core/shell Quantum Dots.\u003c/p\u003e \u003cp\u003eAlthough this real-world application of semiconducting nonmaterial involves extensive experimental research, theoretical approaches are of fundamental importance as they allow both to understand the elementary physics and to optimize devices made from nanostructure materials. There have been several theoretical research of the structural stabilities, HOMO\u0026ndash;LUMO gaps and optical absorption of some nanoclusters of (ZnTe)\u003csub\u003en\u003c/sub\u003e type [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]. Earlier, we have performed comprehensive an ab-initio study of structural and electronic properties of ZnO, ZnS, ZnSe and ZnTe upto five atoms\u0026rsquo; nanoclusters [\u003cspan additionalcitationids=\"CR31 CR32 CR33\" citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e] but the other physical properties like optical properties for the most stable small Zn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey\u003c/sub\u003e nanoclusters upto five atoms (x\u0026thinsp;+\u0026thinsp;y\u0026thinsp;=\u0026thinsp;2 to 5) have not been reported so far up to the knowledge of the authors. In this research paper, we have extended our first principle study for the optical properties of the most stable small Zn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey\u003c/sub\u003e nanoclusters. The current study also encourages experimental investigators to produce these nanoclusters to further investigate their potential uses in the fabrication of nanodevices. Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e contains the method (TDDFT) used in the investigations for the excitation energies. In Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, we present the discussions about the calculation and results. The conclusions are contained in the last Section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e"},{"header":"2. Method","content":"\u003cp\u003eGeometrical optimization for small\u0026nbsp;Zn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey\u003c/sub\u003e nanoclusters has been established previously by our group [33, 34]. All the geometrical structures were fully optimized employing the hybrid gradient-corrected functional (B3LYP) within the Density Functional Theory (DFT) framework [35] in the Gaussian-03 code [36]. In this study, we consider the Becke exchange functional and the correlation function of Lee, Yang and Parr (LYP) that includes contributions for both the local and nonlocal. Also, we employ the three-parameter hybrid functional of Becke. Here, Becke functional considers the Slater exchange along with the corrections involving the gradient of the density (Becke). \u0026nbsp;We also use a basis set LANL2DZ which is necessary for the description of the ground state of each atom.\u0026nbsp;The core electrons are replaced by effective core potential in LanL2DZ basis sets. The pseudo potential approximation is to replace the combined effects of motion of bound electrons of an atom and the effective potential of the nucleus is denoted as pseudo potential in which the Schrödinger equation contains a modified potential term. Since, Zinc and Tellurium have the atomic number of 30 and 52 correspondingly, LANL2DZ basis set will yield a improved outcome with pseudo potential approximation. This is why B3LYP/LANL2DZ basis set is selected to fully optimize the Zn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey\u003c/sub\u003e nanoclusters.\u0026nbsp;For each optimized structures the harmonic vibrational frequencies were also calculated by analytical differentiation of gradients. The polarizable triple split valance basis set 6-311G(3df) was used as the basic basis set in this study for the most precise calculation after selecting a large number of basis set for each atom. The three d electrons and one f electrons of Zn and Se atoms were taken with the valence electrons as a polarized function due to their importance for the description of the ground state of each atom in three dimensions. But, a major limitation of the DFT is that it is inherently unsuitable for the computation of excited state properties. This is why in the present work, the usual Time Dependent Density Functional Theory (TDDFT) calculations have been performed for the excitation energies of the most stable\u0026nbsp;Zn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey\u003c/sub\u003e nanoclusters.\u003c/p\u003e"},{"header":"3. Calculation and results","content":"\u003cp\u003eDifferent types of all possible structures including the linear chains, rings, planar and three-dimensional ones for each configuration have been considered in the optimization of ZnTe nanoclusters [33, 34]. Each structure is achieved to its minimum energy by relaxing the atomic positions. The convergence in the system energy up to 10\u003csup\u003e-7\u003c/sup\u003e meV and the forces of 10\u003csup\u003e-3\u003c/sup\u003e eV/\u0026Aring; on each atom were obtained. The structure for each configuration having minimum energy in comparison to other structures possessing same value of \u0026ldquo;x\u0026rdquo; and \u0026ldquo;y\u0026rdquo; is considered as stable structure. Thus, the stability of nanocluster depends upon the binding energy of the nanocluster. The total energy of a nanocluster is subtracted from the sum of the energies of all the isolated atoms present in the nanocluster and then we divide the resultant quantity by the number of atoms. We have named this as the binding energy (BE) per atom. For a more precise calculation, we have calculated the harmonic vibrational frequencies and the corresponding zero-point energy (ZPE) which is further subtracted from the calculated binding energy (BE) per atom and it gives the final binding energy (FBE). For a particular chemical formula Zn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey\u003c/sub\u003e, the configuration possessing the maximum value of FBE is named as the most stable structure as shown in Fig 1. In the stability of these structures the vibrational frequencies are also studied. The imaginary frequency for a structure point to its instability. The imaginary frequency having maximum final binding energy of a structure causes its in stability and gives an opportunity for next structure having maximum final binding energy of the same configuration to be considered as most stable. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e3.1. Optical properties\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eIn Figures 2 and 3, we demonstrate the calculated optical absorption spectra, which resemble the electron energy loss spectra (EELS). A few nanoclusters have weak absorption in the visible spectrum, while the majority of them have high absorption in the ultraviolet. Table 1 provides the excitation energies for the most stable ZnxTey nanoclusters that exhibit the strongest oscillators. Following is a discussion of each nanocluster\u0026apos;s absorption spectra. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e ZnTe\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAs depicted in Fig. 2(a), the calculated absorption for the most basic diatomic nanocluster (Fig. 1(a)) falls within the energy range of 2.98 to 10.00 eV. Approaching the experimentally recorded value of 4.95 eV, a prominent peak may be seen at 6.81 eV [27]. At 8.95 eV, a very weak peak additionally shows up.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eZn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey \u003c/sub\u003e(x+y = 3)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAs shown in Fig. 2(b), the linear TeZnTe nanocluster (Fig. 1(b)) demonstrates a high absorption in the energy spectrum ranging from 4.83 to 6.36 eV. At 6.30 eV, a very strong, sharp peak appears. As apparent in Fig. 2(c), the absorption spectrum for the linear ZnTeZn nanocluster (Fig. 1(c)) is dispersed spanning the broad energy range of 0.51 \u0026ndash; 7.94 eV. At 4.67 eV, a strong absorption peak appears to be seen in the visible region\u0026apos;s upper side.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eZn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey\u003c/sub\u003e (x+y = 4)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe visible energy range showed poor absorption for the rhombus ZnTe3 (Fig. 1(d)) nanocluster. The energy range of 5.71 to 7.41 eV reveals comparatively substantial absorption, with a strong peak at 7.22 eV.\u003c/p\u003e\n\u003cp\u003eThe rhombus Zn2Te2 (Fig. 1(e)) nanocluster exhibits significant absorption in the ultraviolet range and poor absorption in the infrared. As demonstrated in Fig. 3(a), the absorption takes place between 6.04 and 7.01 eV. At 6.97 eV, a prominent absorption peak is visible. \u003c/p\u003e\n\u003cp\u003eStrong absorption has been observed for the linear Zn3Te (Fig. 1(f)) nanocluster in the visible range of 0.93 to 3.89 eV. At 3.28 eV, a prominent absorption peak is visible. \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eZn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey\u003c/sub\u003e (x+y = 5)\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAlthough all of the ZnTe4 configuration structures under investigation have imaginary frequencies, they are certainly all unstable.\u003c/p\u003e\n\u003cp\u003eThe pentagonal Zn2Te3 structure (Fig. 1(g)) demonstrates strong absorption in the UV range of 6.79\u0026ndash;7.42 eV. In Fig. 3(c), two prominent peaks can be observed at 7.04 and 7.38 eV.\u003c/p\u003e\n\u003cp\u003eThe pentagonal Zn3Te2 structure (Fig. 1(h)) exhibits strong absorption in the UV range of 5.43 to 8.03 eV. Figure 3(d) shows three weak peaks at 6.15, 8.01, and 5.54 eV and an exceptionally large peak at 6.70.\u003c/p\u003e\n\u003cp\u003eThe planer Zn4Te structure (Fig. 1(i)) exhibits strong absorption in the UV range of 4.03 to 6.76 eV. As shown in Fig. 3(e), a prominent peak can be seen at 6.11 eV.\u003c/p\u003e\n\u003cp\u003eThe vast majority of the nanoclusters exhibit significant UV absorption. In accordance to these studies, absorption is observed on the lower energy side of Zn-rich nanoclusters and on the higher energy side of Te-rich nanoclusters in the majority of nanoclusters.\u003c/p\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003eThe optical characteristics of the most stable ZnTe nanocluster formations up to five atoms are presented in this work. Since every structure of the ZnTe4 configuration that has been studied contains at least one imaginary vibrational frequency, we conclude that only this configuration has no stable structure for x\u0026thinsp;+\u0026thinsp;y\u0026thinsp;=\u0026thinsp;5. In contrast, the Zn2Te3, Zn3Te2, and Zn4Te configurations all have stable structures. The experimental data and our estimated result for the linear ZnTe nanocluster's excitation energies show good agreement. Nearly all of the nanoclusters demonstrate significant UV absorption. In the visible spectrum, certain nanoclusters exhibit considerable absorption. In accordance to these studies, absorption occurs in the lower energy side of Zn-rich nanoclusters and on the higher energy side of Te-rich nanoclusters in the majority of nanoclusters. In the experiments, it might be possible to produce these most stable nanoclusters.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors thank Lalit Narayan Mithila University, Darbhanga, Bihar, India, for the support.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was supported by ongoing institutional funding. No additional grants were obtained to carry out or direct this particular research.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor Information\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eDheeraj Kumar Pandey, ORCID: https://orcid.org/0000-0002- 4011-952X\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCredit Authorship Contribution Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDr. Dheeraj Kumar Pandey:\u003c/strong\u003e Conceptualization, Formal analysis, Investigation, Visualization; \u003cstrong\u003eMr. Anilesh:\u003c/strong\u003e Writing \u0026amp; Editing; \u003cstrong\u003eProf. P. S. Yadav:\u003c/strong\u003e Methodology, Resources, Software, Supervision.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflict of Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors of this work declare that they have no conflicts of interest.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMurray C B, Kagan C R \u0026amp; Bawendi M G, Annu Rev Mater Sci 30 (2000) 545.\u003c/li\u003e\n\u003cli\u003eDekker, Semiconductor and Metal Nanocrystals, ed. V. I. 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C.03 (Pittsburgh, PA: Gaussian).\u003c/li\u003e\n\u003cli\u003eGaussian, Inc. (2003) \u003cem\u003eGAUSSIAN 03\u003c/em\u003e, Revision.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Table","content":"\u003cp\u003e\u003cstrong\u003eTable 1\u003c/strong\u003e Excitation energies (\u003cstrong\u003e∆\u003c/strong\u003eE, in eV) having largest oscillator strengths (f) for the\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003emost stable configurations of Zn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey\u0026nbsp;\u003c/sub\u003e(x+y = 2 to 5) nanoclusters.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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Narayan Mithila University","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Nanoclusters, Optical Properties, Oscillator Strength, EELS, TDDFT study","lastPublishedDoi":"10.21203/rs.3.rs-6711847/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6711847/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u0026nbsp;The optical properties of the most stable Zn\u003csub\u003ex\u003c/sub\u003eTe\u003csub\u003ey\u003c/sub\u003e (x + y = 2 to 5) nanoclusters have been investigated based on a first-principles study. The geometries of ZnTe nanoclusters are optimized using the B3LYP-DFT/LANL2DZ approach. At the same time, the optical properties of the most stable structures of individual configurations are studied using the Time-Dependent Density Functional Theory (TDDFT). This study also takes the zero-point energy modification into account. The most stable nanocluster has been defined as the structure with the lowest energy when compared to other structures for the same values of \"x\" and \"y.\" The instability of certain of the nanoclusters is caused by the existence of at least one imaginary vibrational frequency. \u0026nbsp;With a few exceptions, most nanoclusters exhibit significant optical absorption in the ultraviolet range but slight optical absorption in the visible region. By these investigations, absorption occurs on the higher energy side of Te-rich nanoclusters and the lower energy side of Zn-rich nanoclusters in the majority of nanoclusters. In the experiments, it may be possible to grow the most stable nanoclusters.\u003c/p\u003e","manuscriptTitle":"First Principles Study for the Optical Properties of the Most Stable small ZnTe Nanoclusters","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-23 10:04:05","doi":"10.21203/rs.3.rs-6711847/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"a37e2ba2-cd56-43d6-9e3c-6670d858e2ae","owner":[],"postedDate":"May 23rd, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":48824658,"name":"Nanoscience"}],"tags":[],"updatedAt":"2025-05-23T10:04:05+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-23 10:04:05","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6711847","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6711847","identity":"rs-6711847","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}