Optical Properties of the Most Stable GaxPy (x+y=2 to 5) Nanoclusters predicted through First Principles

Optical Properties of the Most Stable GaxPy (x+y=2 to 5) Nanoclusters predicted through First Principles | 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 Optical Properties of the Most Stable Ga x P y (x+y=2 to 5) Nanoclusters predicted through First Principles Dheeraj Kumar Pandey, Anilesh This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6688960/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 A TDDFT study has been performed for the optical properties of the most stable Ga x P y (x + y = 2 to 5) nanoclusters. A B3LYP-DFT/6-31G(d) method is employed to optimize the geometries of GaP nanoclusters and a TDDFT method is used for the study of optical properties of the most stable structures of individual configurations. The zero-point energy correction is also considered in this study. The structure having minimum energy in evaluation to other structures for the same values of “x” and “y” is considered as the most stable one. Some of the nanoclusters show at least one imaginary vibrational frequency, which consequences to their instability. Almost all the nanoclusters show strong absorption in the ultraviolet region or the extreme ultraviolet region. Some nanoclusters show appreciable absorption in the visible region. These investigations reveal that in most of the nanoclusters; the absorption is obtained in the lower energy side in Ga-rich nanoclusters and on the higher energy side in P-rich nanoclusters. The development of these most stable nanoclusters may be possible in the experiments. Nanoscience Materials Theory and Modeling Nanoclusters Optical Properties Oscillator Strength EELS TDDFT study Figures Figure 1 Figure 2 Figure 3 1. Introduction The scientific community's primary emphasis is on understanding and modifying the nanostructures of group III–V semiconductor materials. The community has a curiosity in modifying group III–V semiconductors' properties in the nanoscale domain. Despite the possible applications in optoelectronics, microwave devices, and high-speed digital circuits, group III–V compound semiconductors have been the focus of numerous studies [ 1 , 2 ]. Gallium phosphide (GaP) is one among the group III–V compound semiconductors. Gallium phosphide (GaP), an indirect gap III–V semiconductor, has several significant uses, especially in high-temperature and light-emitting devices [ 3 , 4 ]. For UV applications, GaP's exceptionally high absorption coefficients at shorter wavelengths are important. GaP has been used in the blue and ultraviolet wavelength range of 250–500 nm. There have been studies on GaP nanomaterials, including quantum dots, nanorods, nanowires, and nanoparticles [ 5 – 9 ]. The fabrication of GaP quantum dots has so far been comprehensively studied using a range of approaches, including solvothermal approach [ 13 – 15 ], solid-state metathesis [ 11 , 12 ], and metalorganic chemical vapor deposition (MOCVD) [ 10 ]. High-boiling solvents and certain stabilizers can be used for producing GaP nanocrystals in a controlled manner, despite the lack of development in the required solution chemistry [ 13 , 16 ]. Moreover, crystalline GaP nanoparticles [ 15 ] and nanowires [ 17 ] have been successfully synthesized in a mild aqueous solution. Compared to quantum dots, anisotropic nanostructures including one-dimensional (1D) structures, film, superlattice, etc. have many advantages particularly in constructing nanodevices [ 18 ]. Recently, well-crystallized GaP nanowires [ 17 , 19 ], nanorods [ 16 , 20 ], and nanotubes [ 21 ] have been prepared via high-temperature pyrogenation [ 19 – 21 ] and solvothermal approaches [ 16 , 17 ], respectively. However, research on the other anisotropic GaP nanostructures is very limited, despite the technological importance of these materials. Dendritic nanostructures have recently attracted much attention because of their interesting morphology and potential applications [ 22 ]. To date, multiform dendrites have been prepared including metal [ 23 ], metal oxide [ 24 ], and chalcogenide [ 22 ], etc. It has been accepted that size and shape have a significant impact on the physicochemical characteristics of nanomaterials. In order to further develop the III–V semiconductor community and permit more possible applications, it is important to investigate the potentially significant properties of GaP nanoparticles. Theoretical techniques are crucial because they allow the realization of basic physics and the optimization of devices produced from nanostructure materials, even though the practical application of semiconducting nonmaterials necessitates substantial experimental research. The electronic transport characteristics of pure gallium phosphide nanoribbon and defect gallium phosphide nanoribbon have been investigated theoretically and through first-principles studies, respectively [ 25 ]. Material properties can be effectively predicted using the Density Functional Theory (DFT) approach without the use of experimental data. Consequently, a better way to investigate the transport properties of GaP nanostructures is to use the DFT method. For GaP nanoparticles, not much research has been reported thus far using the DFT approach. We previously carried out a comprehensive ab-initio investigation of the structural, electronic, vibrational and optical properties of ZnO, ZnS, ZnSe, and ZnTe up to nanoclusters of five atoms [ 26 – 32 ]. To the best of the authors' knowledge, the optical characteristics of the most stable small GaxPy nanoclusters up to five atoms (x + y = 2 to 5) have not yet been published. The intermediate state of matter between molecules and bulk is called a nanocluster. Our first principle investigation into the optical properties of the most stable small GaxPy nanoclusters has been explored in this research paper. With the goal to learn more regarding these nanoclusters' possible applications in the fabrication of nanodevices, the current study also invites experimental researchers to produce them. The technique (TDDFT) utilized in the excitation energy investigations is presented in Section 2 . We provide the explanations regarding the computation and findings in Section 3 . The last Section 4 contains the conclusions. 2. Method We employed the B3LYP-DFT/6-31G(d) version of the Gaussian code [ 32 ], which uses the hierarchy of procedures corresponding with different approximation approaches, for the structural optimization of the GaP nanoclusters. Analytical differentiation of the gradient yields the harmonic vibrational frequencies. In the DFT, the exchange-correlation functional—a more generic statement that includes terms for both the exchange energy and the electron correlation—replaces the exact exchange in the Hartree-Fock theory for a single determinant. We examine the correlation function of Lee, Yang, and Parr (LYP) [ 34 , 35 ], which takes into account both the local and nonlocal contributions, as well as the Becke [ 33 ] exchange functional. We also use Becke's three-parameter hybrid functional [ 33 ]. It should be mentioned that the Becke functional takes into account the two aspects of Slater exchange and the modifications related to the density gradient (Becke) [ 33 ]. For the most precise calculation, a large basis set has been selected associated with each atom. The 6-31G basis set, which uses the contracted functions per orbital, is what we use. The Gaussian function combinations have the name contracted functions. The benefit of using the split valance basis set is that it permits orbitals to vary in size without influencing their shape. Furthermore, orbitals with angular momentum greater than what is required to describe each atom's ground state are added using a polarizable basis set 6-31G(d). We incorporate the d function for the Ga and P atoms. The triple zeta basis set and several polarization functions have been taken into consideration for developing very accurate structural parameters. However, the DFT's fundamental inadequacy for computing excited-state characteristics is one of its main drawbacks. For this reason, the excitation energies of the most stable GaxPy nanoclusters have been calculated using the standard Time Dependent Density Functional Theory (TDDFT) in the present research. 3. Calculation and results Different types of all possible structures, including linear chains, rings, planar, and three-dimensional ones for each configuration, have been considered in the optimization of GaP nanoclusters [31]. Each structure is optimized 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 a 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 Ga x P 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 We present the calculated optical absorption spectra, which will be similar to the electron energy loss spectra (EELS) in Figs. 2 and 3. In most of the nanoclusters, the absorption spectrum is strong in the ultraviolet region but in a few one observed weak absorption in the visible region. The excitation energies with the largest oscillator strengths for the most stable Ga x P y nanoclusters are given in Table 1. Now the absorption spectra of each nanocluster is discussed below. GaP For the simplest diatomic GaP nanocluster (Fig. 1(a)), the calculated absorption is obtained strongly in the visible energy region 1.85–3.67 eV as well as the extreme ultraviolet region 7.13–9.02 eV as shown in Fig. 2(a). A strong peak appears at 2.10 eV, which is close to the experimentally observed value of 2.19 eV [36]. Ga x P y (x + y = 3) For the Triangular GaP 2 nanocluster (Fig. 1(b)), the strong absorption is obtained in the 6.70–9.50 eV energy region as shown in Fig. 2(b). A very strong sharp peak appears at 8.33 eV with a weak peak at 7.23 eV in the extreme ultraviolet region. For the linear Triangular Ga 2 P nanocluster (Fig. 1(c)), the absorption spectrum is spread in the wide energy range of ultraviolet region 4.46–8.54 eV as shown in Fig. 2(c). Strong absorption peak appears at 7.77 eV with three weak peaks at 4.77, 6.12 and 6.57 eV in the upper side of the visible region. Ga x P y (x + y = 4) For the rhombus GaP 3 (Fig. 1(d)) nanocluster, one found strong absorption in the near visible energy region. Comparatively strong absorption is seen in the energy range 2.40–8.47 eV with a strong peak at 3.60 eV in the upper side of the visible region. For the rhombus Ga 2 P 2 (Fig. 1(e)) nanocluster, absorption appears in the ultraviolet region. The absorption occurs in the range 4.97–8.69 eV as shown in Fig. 2(e). A strong absorption peak appears at 5.17 eV. For the linear Ga 3 P (Fig. 1(f)) nanocluster, strong absorption in the upper side of visible range of 4.50–5.30 eV is observed. Two close strong absorption peaks appear at 4.65 & 5.17 eV in the extreme ultraviolet region as shown in Fig. 2(f). Ga x P y (x + y = 5) For the Bent-1 GaP 4 (Fig. 1(g)) nanocluster, strong absorption in the extreme ultraviolet range of 7.24–9.60 eV is observed. A strong absorption peak appears at 8.66 eV as shown in Fig. 3(a). Strong absorption for pentagonal Ga 2 P 3 structure (Fig. 1(h)) in the ultraviolet region 6.40–9.30 eV is found. A strong absorption peak appears at 9.26 eV with two weak peaks at 6.52 and 7.44 eV in the extreme ultraviolet region as shown in Fig. 3(b). For Bent-2 Ga 3 P 2 structure (Fig. 1(i)) strong absorption is found in the ultraviolet region 4.00–8.70 eV. A strong peak appears at 4.66 with two weak peaks at 5.67 and 6.10 eV as depicted in Fig. 3(c). Strong absorption for pentagonal-2 Ga 4 P structure (Fig. 1(j)) in the extreme ultraviolet region 5.50–7.80 eV is found. Two close strong peaks appear at 6.37 & 7.12 eV as depicted in Fig. 3(d). Most of the nanoclusters show strong absorption in the ultraviolet region except few. These investigations reveal that in most of the nanoclusters, the absorption is obtained in lower energy side in Ga-rich nanoclusters and higher energy side in P-rich nanocluster. 4. Conclusion This study presents the optical properties of the most stable structures up to five-atom GaP nanoclusters. Almost all the nanoclusters show strong absorption in the ultraviolet region or the extreme ultraviolet region. Some nanoclusters show appreciable absorption in the visible region. These investigations reveal that in most of the nanoclusters, the absorption is obtained in lower energy side in Ga-rich nanoclusters and on higher energy side in P-rich nanoclusters. The development of these most stable nanoclusters may be possible in the experiments. 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, Methodology, Resources, Software, Supervision; Mr. Anilesh: Writing & Editing. Conflict of Interest The authors of this work declare that they have no conflicts of interest. 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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-6688960","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":458096373,"identity":"5ad6c045-02b2-4e58-8bd4-33b71e3453ed","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":458096374,"identity":"78a0e966-5124-4b6f-83ed-b0135efbe38a","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":""}],"badges":[],"createdAt":"2025-05-17 21:17:11","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-6688960/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6688960/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":83107860,"identity":"06e3a639-8bf9-4372-9fbf-257e668da0fa","added_by":"auto","created_at":"2025-05-20 06:43:22","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1102209,"visible":true,"origin":"","legend":"\u003cp\u003eMost stable structures of GaP, GaP\u003csub\u003e2, \u0026nbsp;\u003c/sub\u003eGa\u003csub\u003e2\u003c/sub\u003eP, GaP\u003csub\u003e3,\u0026nbsp; \u003c/sub\u003eGa\u003csub\u003e2\u003c/sub\u003eP\u003csub\u003e2,\u003c/sub\u003e Ga\u003csub\u003e3\u003c/sub\u003eP, GaP\u003csub\u003e4,\u003c/sub\u003e Ga\u003csub\u003e2\u003c/sub\u003eP\u003csub\u003e3, \u003c/sub\u003eGa\u003csub\u003e3\u003c/sub\u003eP\u003csub\u003e2\u003c/sub\u003e and \u0026nbsp;Ga\u003csub\u003e4\u003c/sub\u003eP 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-6688960/v1/17709d60ab4d4ffaca3b75e7.png"},{"id":83107855,"identity":"baed7bad-05a6-49de-842b-9456e577d94e","added_by":"auto","created_at":"2025-05-20 06:43:22","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":716788,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption spectra for the most stable structures of \u003cstrong\u003e(a)\u003c/strong\u003e Linear GaP \u003cstrong\u003e(b)\u003c/strong\u003e Triangular \u0026nbsp;GaP\u003csub\u003e2\u003c/sub\u003e \u003cstrong\u003e(c)\u003c/strong\u003e Triangular Ga\u003csub\u003e2\u003c/sub\u003eP \u003cstrong\u003e(d)\u003c/strong\u003e Rhombus GaP\u003csub\u003e3\u0026nbsp;\u0026nbsp; \u003c/sub\u003e\u003cstrong\u003e(e)\u003c/strong\u003e Rhombus Ga\u003csub\u003e2\u003c/sub\u003eP\u003csub\u003e2\u0026nbsp; \u003c/sub\u003e\u0026nbsp;and \u003cstrong\u003e(f)\u003c/strong\u003e Linear Ga\u003csub\u003e3\u003c/sub\u003eP.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-6688960/v1/c0ea9594162a6819f5abea95.png"},{"id":83107854,"identity":"25cc0e04-b110-48e9-9729-18fa51c530a1","added_by":"auto","created_at":"2025-05-20 06:43:22","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":567086,"visible":true,"origin":"","legend":"\u003cp\u003eAbsorption spectra for the most stable structures of \u003cstrong\u003e(a)\u003c/strong\u003e Bent-1 GaP\u003csub\u003e4\u003c/sub\u003e \u003cstrong\u003e(b)\u003c/strong\u003e Seesaw GaP\u003csub\u003e2\u003c/sub\u003e \u003cstrong\u003e(c)\u003c/strong\u003e Bent-2 Ga\u003csub\u003e3\u003c/sub\u003eP\u003csub\u003e2\u003c/sub\u003e and \u003cstrong\u003e(d)\u003c/strong\u003e Pentagonal-2 Ga\u003csub\u003e4\u003c/sub\u003eP.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-6688960/v1/7396b2e38c286ca9e5424a14.png"},{"id":83110565,"identity":"5cfa8225-b786-4cb1-82df-ffa05e8992a0","added_by":"auto","created_at":"2025-05-20 07:15:24","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3423325,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6688960/v1/e67439d3-15d8-465c-855f-15de11997834.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eOptical Properties of the Most Stable Ga\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ex\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eP\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003ey\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e (x+y=2 to 5) Nanoclusters predicted through First Principles\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe scientific community's primary emphasis is on understanding and modifying the nanostructures of group III\u0026ndash;V semiconductor materials. The community has a curiosity in modifying group III\u0026ndash;V semiconductors' properties in the nanoscale domain. Despite the possible applications in optoelectronics, microwave devices, and high-speed digital circuits, group III\u0026ndash;V compound semiconductors have been the focus of numerous studies [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. Gallium phosphide (GaP) is one among the group III\u0026ndash;V compound semiconductors. Gallium phosphide (GaP), an indirect gap III\u0026ndash;V semiconductor, has several significant uses, especially in high-temperature and light-emitting devices [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. For UV applications, GaP's exceptionally high absorption coefficients at shorter wavelengths are important. GaP has been used in the blue and ultraviolet wavelength range of 250\u0026ndash;500 nm. There have been studies on GaP nanomaterials, including quantum dots, nanorods, nanowires, and nanoparticles [\u003cspan additionalcitationids=\"CR6 CR7 CR8\" citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. The fabrication of GaP quantum dots has so far been comprehensively studied using a range of approaches, including solvothermal approach [\u003cspan additionalcitationids=\"CR14\" citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e], solid-state metathesis [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e], and metalorganic chemical vapor deposition (MOCVD) [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]. High-boiling solvents and certain stabilizers can be used for producing GaP nanocrystals in a controlled manner, despite the lack of development in the required solution chemistry [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Moreover, crystalline GaP nanoparticles [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] and nanowires [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] have been successfully synthesized in a mild aqueous solution. Compared to quantum dots, anisotropic nanostructures including one-dimensional (1D) structures, film, superlattice, etc. have many advantages particularly in constructing nanodevices [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Recently, well-crystallized GaP nanowires [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e, \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e], nanorods [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e], and nanotubes [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] have been prepared via high-temperature pyrogenation [\u003cspan additionalcitationids=\"CR20\" citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] and solvothermal approaches [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e], respectively. However, research on the other anisotropic GaP nanostructures is very limited, despite the technological importance of these materials. Dendritic nanostructures have recently attracted much attention because of their interesting morphology and potential applications [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. To date, multiform dendrites have been prepared including metal [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e], metal oxide [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e], and chalcogenide [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e], etc. It has been accepted that size and shape have a significant impact on the physicochemical characteristics of nanomaterials. In order to further develop the III\u0026ndash;V semiconductor community and permit more possible applications, it is important to investigate the potentially significant properties of GaP nanoparticles. Theoretical techniques are crucial because they allow the realization of basic physics and the optimization of devices produced from nanostructure materials, even though the practical application of semiconducting nonmaterials necessitates substantial experimental research. The electronic transport characteristics of pure gallium phosphide nanoribbon and defect gallium phosphide nanoribbon have been investigated theoretically and through first-principles studies, respectively [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e]. Material properties can be effectively predicted using the Density Functional Theory (DFT) approach without the use of experimental data. Consequently, a better way to investigate the transport properties of GaP nanostructures is to use the DFT method. For GaP nanoparticles, not much research has been reported thus far using the DFT approach. We previously carried out a comprehensive ab-initio investigation of the structural, electronic, vibrational and optical properties of ZnO, ZnS, ZnSe, and ZnTe up to nanoclusters of five atoms [\u003cspan additionalcitationids=\"CR27 CR28 CR29 CR30 CR31\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e]. To the best of the authors' knowledge, the optical characteristics of the most stable small GaxPy nanoclusters up to five atoms (x\u0026thinsp;+\u0026thinsp;y\u0026thinsp;=\u0026thinsp;2 to 5) have not yet been published. The intermediate state of matter between molecules and bulk is called a nanocluster. Our first principle investigation into the optical properties of the most stable small GaxPy nanoclusters has been explored in this research paper. With the goal to learn more regarding these nanoclusters' possible applications in the fabrication of nanodevices, the current study also invites experimental researchers to produce them. The technique (TDDFT) utilized in the excitation energy investigations is presented in Section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. We provide the explanations regarding the computation and findings in Section \u003cspan refid=\"Sec3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The last Section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e4\u003c/span\u003e contains the conclusions.\u003c/p\u003e"},{"header":"2. Method","content":"\u003cp\u003eWe employed the B3LYP-DFT/6-31G(d) version of the Gaussian code [\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e], which uses the hierarchy of procedures corresponding with different approximation approaches, for the structural optimization of the GaP nanoclusters. Analytical differentiation of the gradient yields the harmonic vibrational frequencies. In the DFT, the exchange-correlation functional\u0026mdash;a more generic statement that includes terms for both the exchange energy and the electron correlation\u0026mdash;replaces the exact exchange in the Hartree-Fock theory for a single determinant. We examine the correlation function of Lee, Yang, and Parr (LYP) [\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e, \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e], which takes into account both the local and nonlocal contributions, as well as the Becke [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e] exchange functional. We also use Becke's three-parameter hybrid functional [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. It should be mentioned that the Becke functional takes into account the two aspects of Slater exchange and the modifications related to the density gradient (Becke) [\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e]. For the most precise calculation, a large basis set has been selected associated with each atom. The 6-31G basis set, which uses the contracted functions per orbital, is what we use. The Gaussian function combinations have the name contracted functions. The benefit of using the split valance basis set is that it permits orbitals to vary in size without influencing their shape. Furthermore, orbitals with angular momentum greater than what is required to describe each atom's ground state are added using a polarizable basis set 6-31G(d). We incorporate the d function for the Ga and P atoms. The triple zeta basis set and several polarization functions have been taken into consideration for developing very accurate structural parameters. However, the DFT's fundamental inadequacy for computing excited-state characteristics is one of its main drawbacks. For this reason, the excitation energies of the most stable GaxPy nanoclusters have been calculated using the standard Time Dependent Density Functional Theory (TDDFT) in the present research.\u003c/p\u003e"},{"header":"3. Calculation and results","content":"\u003cdiv\u003e\n \u003cp\u003eDifferent types of all possible structures, including linear chains, rings, planar, and three-dimensional ones for each configuration, have been considered in the optimization of GaP nanoclusters [31]. Each structure is optimized 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/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 a 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 Ga\u003csub\u003ex\u003c/sub\u003eP\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\u003c/div\u003e\n\u003cdiv id=\"Sec4\"\u003e\n \u003ch2\u003e3.1. Optical properties\u003c/h2\u003e\n \u003cp\u003eWe present the calculated optical absorption spectra, which will be similar to the electron energy loss spectra (EELS) in Figs. 2 and 3. In most of the nanoclusters, the absorption spectrum is strong in the ultraviolet region but in a few one observed weak absorption in the visible region. The excitation energies with the largest oscillator strengths for the most stable Ga\u003csub\u003ex\u003c/sub\u003eP\u003csub\u003ey\u003c/sub\u003e nanoclusters are given in Table 1. Now the absorption spectra of each nanocluster is discussed below.\u003c/p\u003e\n \u003cdiv\u003e\n \u003ctable id=\"Tab1\" border=\"1\"\u003e\u003c/table\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cstrong\u003eGaP\u003c/strong\u003e\u003c/p\u003e\n \u003cdiv\u003e\n \u003cp\u003eFor the simplest diatomic GaP nanocluster (Fig. 1(a)), the calculated absorption is obtained strongly in the visible energy region 1.85–3.67 eV as well as the extreme ultraviolet region 7.13–9.02 eV as shown in Fig. 2(a). A strong peak appears at 2.10 eV, which is close to the experimentally observed value of 2.19 eV [36].\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cstrong\u003eGa\u003c/strong\u003e \u003csub\u003e\u0026nbsp;\u003cstrong\u003ex\u003c/strong\u003e\u0026nbsp;\u003c/sub\u003e \u003cstrong\u003eP\u003c/strong\u003e \u003csub\u003e\u0026nbsp;\u003cstrong\u003ey\u003c/strong\u003e\u0026nbsp;\u003c/sub\u003e \u003cstrong\u003e(x + y = 3)\u003c/strong\u003e\u003c/p\u003e\n \u003cdiv\u003e\n \u003cp\u003eFor the Triangular GaP\u003csub\u003e2\u003c/sub\u003e nanocluster (Fig. 1(b)), the strong absorption is obtained in the 6.70–9.50 eV energy region as shown in Fig. 2(b). A very strong sharp peak appears at 8.33 eV with a weak peak at 7.23 eV in the extreme ultraviolet region.\u003c/p\u003e\n \u003cp\u003eFor the linear Triangular Ga\u003csub\u003e2\u003c/sub\u003eP nanocluster (Fig. 1(c)), the absorption spectrum is spread in the wide energy range of ultraviolet region 4.46–8.54 eV as shown in Fig. 2(c). Strong absorption peak appears at 7.77 eV with three weak peaks at 4.77, 6.12 and 6.57 eV in the upper side of the visible region.\u003c/p\u003e\n \u003c/div\u003e\n \u003cp\u003e\u003cstrong\u003eGa\u003c/strong\u003e \u003csub\u003e\u0026nbsp;\u003cstrong\u003ex\u003c/strong\u003e\u0026nbsp;\u003c/sub\u003e \u003cstrong\u003eP\u003c/strong\u003e \u003csub\u003e\u0026nbsp;\u003cstrong\u003ey\u003c/strong\u003e\u0026nbsp;\u003c/sub\u003e \u003cstrong\u003e(x + y = 4)\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eFor the rhombus GaP\u003csub\u003e3\u003c/sub\u003e (Fig. 1(d)) nanocluster, one found strong absorption in the near visible energy region. Comparatively strong absorption is seen in the energy range 2.40–8.47 eV with a strong peak at 3.60 eV in the upper side of the visible region.\u003c/p\u003e\n \u003cp\u003eFor the rhombus Ga\u003csub\u003e2\u003c/sub\u003eP\u003csub\u003e2\u003c/sub\u003e (Fig. 1(e)) nanocluster, absorption appears in the ultraviolet region. The absorption occurs in the range 4.97–8.69 eV as shown in Fig. 2(e). A strong absorption peak appears at 5.17 eV.\u003c/p\u003e\n \u003cp\u003eFor the linear Ga\u003csub\u003e3\u003c/sub\u003eP (Fig. 1(f)) nanocluster, strong absorption in the upper side of visible range of 4.50–5.30 eV is observed. Two close strong absorption peaks appear at 4.65 \u0026amp; 5.17 eV in the extreme ultraviolet region as shown in Fig. 2(f).\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003eGa\u003c/strong\u003e \u003csub\u003e\u0026nbsp;\u003cstrong\u003ex\u003c/strong\u003e\u0026nbsp;\u003c/sub\u003e \u003cstrong\u003eP\u003c/strong\u003e \u003csub\u003e\u0026nbsp;\u003cstrong\u003ey\u003c/strong\u003e\u0026nbsp;\u003c/sub\u003e \u003cstrong\u003e(x + y = 5)\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003eFor the Bent-1 GaP\u003csub\u003e4\u003c/sub\u003e (Fig. 1(g)) nanocluster, strong absorption in the extreme ultraviolet range of 7.24–9.60 eV is observed. A strong absorption peak appears at 8.66 eV as shown in Fig. 3(a).\u003c/p\u003e\n \u003cp\u003eStrong absorption for pentagonal Ga\u003csub\u003e2\u003c/sub\u003eP\u003csub\u003e3\u003c/sub\u003e structure (Fig. 1(h)) in the ultraviolet region 6.40–9.30 eV is found. A strong absorption peak appears at 9.26 eV with two weak peaks at 6.52 and 7.44 eV in the extreme ultraviolet region as shown in Fig. 3(b).\u003c/p\u003e\n \u003cp\u003eFor Bent-2 Ga\u003csub\u003e3\u003c/sub\u003eP\u003csub\u003e2\u003c/sub\u003e structure (Fig. 1(i)) strong absorption is found in the ultraviolet region 4.00–8.70 eV. A strong peak appears at 4.66 with two weak peaks at 5.67 and 6.10 eV as depicted in Fig. 3(c).\u003c/p\u003e\n \u003cp\u003eStrong absorption for pentagonal-2 Ga\u003csub\u003e4\u003c/sub\u003eP structure (Fig. 1(j)) in the extreme ultraviolet region 5.50–7.80 eV is found. Two close strong peaks appear at 6.37 \u0026amp; 7.12 eV as depicted in Fig. 3(d).\u003c/p\u003e\n \u003cp\u003eMost of the nanoclusters show strong absorption in the ultraviolet region except few. These investigations reveal that in most of the nanoclusters, the absorption is obtained in lower energy side in Ga-rich nanoclusters and higher energy side in P-rich nanocluster.\u003c/p\u003e\n\u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eThis study presents the optical properties of the most stable structures up to five-atom GaP nanoclusters. Almost all the nanoclusters show strong absorption in the ultraviolet region or the extreme ultraviolet region. Some nanoclusters show appreciable absorption in the visible region. These investigations reveal that in most of the nanoclusters, the absorption is obtained in lower energy side in Ga-rich nanoclusters and on higher energy side in P-rich nanoclusters. The development of these most stable nanoclusters may be possible in the experiments.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAcknowledgement\u003c/strong\u003e\u003c/p\u003e\n\n\u003cp\u003eThe authors thank Lalit Narayan Mithila University, Darbhanga, Bihar, India, for the support.\u0026nbsp;\u003c/p\u003e\n\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\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\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, Methodology, Resources, Software, Supervision; \u003cstrong\u003eMr. Anilesh:\u003c/strong\u003e Writing \u0026amp; Editing. \u0026nbsp;\u003c/p\u003e\n\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\n"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eMorko\u0026ccedil; H and Mohammad S N 1995 High-Luminosity Blue and Blue-Green Gallium Nitride Light-Emitting Diodes. \u003cem\u003eScience\u003c/em\u003e 267 51\u0026ndash;5.\u003c/li\u003e\n\u003cli\u003eTrentler T J, Hickman K M, Goel S C, Viano A M, Gibbons P C and Buhro W E 1995 Solution- iquid-Solid Growth of Crystalline III-V Semiconductors: An Analogy to Vapor-Liquid-Solid Growth. \u003cem\u003eScience\u003c/em\u003e 270 1791\u0026ndash;4.\u003c/li\u003e\n\u003cli\u003eFlores-Perez R, Zemlyanov D Y and Ivanisevic A 2008 Quantitative Evaluation of Covalently Bound Molecules on GaP (100) Surfaces. \u003cem\u003eThe Journal of Physical Chemistry C\u003c/em\u003e 112 2147\u0026ndash;55.\u003c/li\u003e\n\u003cli\u003eLin G, Zhang Q, Lin X, Zhao D, Jia R, Gao N, Zuo Z, Xu X and Liu D 2015 Enhanced photolumines- cence of gallium phosphide by surface plasmon resonances of metallic nanoparticles. \u003cem\u003eRSC Advances\u003c/em\u003e 5 48275\u0026ndash;80.\u003c/li\u003e\n\u003cli\u003eBermeo M, Franzen S M, Hetherington C, Johansson J and Messing M E 2023 Branched-gallium phosphide nanowires seeded by palladium nanoparticles. \u003cem\u003eNanotechnology\u003c/em\u003e 34 395603.\u003c/li\u003e\n\u003cli\u003eSantos C B E and Schmidt T M 2010 Direct band gap GaP nanowires predicted through first principles. \u003cem\u003eJournal of Applied Physics\u003c/em\u003e 108.\u003c/li\u003e\n\u003cli\u003eWang B-P, Zhang Z-C and Zhang N 2010 Fabrication and optical properties of gallium phosphide nanoparticulate thin film. \u003cem\u003eSolid State Sciences\u003c/em\u003e 12 1188\u0026ndash;91.\u003c/li\u003e\n\u003cli\u003eAssali S, Zardo I, Plissard S, Kriegner D, Verheijen M A, Bauer G, Meijerink A, Belabbes A, Bechstedt F, Haverkort J E M and Bakkers E P A M 2013 Direct Band Gap Wurtzite Gallium Phosphide Nanowires. \u003cem\u003eNano Letters\u003c/em\u003e 13 1559\u0026ndash;63.\u003c/li\u003e\n\u003cli\u003eHasen\u0026ouml;hrl S, Eli\u0026aacute;\u0026scaron; P, \u0026Scaron;olt\u0026yacute;s J, Stoklas R, Dujavov\u0026aacute;-Laurenč\u0026iacute;kov\u0026aacute; A and Nov\u0026aacute;k J 2013 Zinc-doped gallium phosphide nanowires for photovoltaic structures. \u003cem\u003eApplied Surface Science\u003c/em\u003e 269 72\u0026ndash;6.\u003c/li\u003e\n\u003cli\u003eMac Dougall J E, Eckert H, Stucky G D, Herron N, Wang Y, Moller K, Bein T and Cox D 1989 Synthesis and characterization of group III-V semiconductor clusters: gallium phosphide GaP in zeolite. \u003cem\u003eJournal of the American Chemical Society\u003c/em\u003e 111 8006\u0026ndash;7.\u003c/li\u003e\n\u003cli\u003eTreece R E, Macala G S and Kaner R B 1992 Rapid synthesis of gallium phosphide and gallium arsenide from solid-state precursors. \u003cem\u003eChemistry of Materials\u003c/em\u003e 4 9\u0026ndash;11.\u003c/li\u003e\n\u003cli\u003eChen L, Luo T, Huang M, Gu Y, Shi L and Qian Y 2004 A mild reduction\u0026ndash;phosphidation approach to nanocrystalline GaP. \u003cem\u003eSolid State Communications\u003c/em\u003e 132 667\u0026ndash;71.\u003c/li\u003e\n\u003cli\u003eMicic O I, Sprague J R, Curtis C J, Jones K M, Machol J L, Nozik A J, Giessen H, Fluegel B, Mohs G and Peyghambarian N 1995 Synthesis and Characterization of InP, GaP, and GaInP2 Quantum Dots. \u003cem\u003eThe Journal of Physical Chemistry\u003c/em\u003e 99 7754\u0026ndash;9.\u003c/li\u003e\n\u003cli\u003eKher S S and Wells R L 1994 A Straightforward, New Method for the Synthesis of Nanocrystalline GaAs and GaP. \u003cem\u003eChemistry of Materials\u003c/em\u003e 6 2056\u0026ndash;62.\u003c/li\u003e\n\u003cli\u003eGao S, Lu J, Chen N, Zhao Y and Xie Y 2002 Aqueous synthesis of III\u0026ndash;V semiconductor GaP and InP exhibiting pronounced quantum confinement. \u003cem\u003eChem. 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Phys. 53 (2020) 29510. \u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Table 1","content":"\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-6688960/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6688960/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eA TDDFT study has been performed for the optical properties of the most stable Ga\u003csub\u003ex\u003c/sub\u003eP\u003csub\u003ey\u003c/sub\u003e (x\u0026thinsp;+\u0026thinsp;y\u0026thinsp;=\u0026thinsp;2 to 5) nanoclusters. A B3LYP-DFT/6-31G(d) method is employed to optimize the geometries of GaP nanoclusters and a TDDFT method is used for the study of optical properties of the most stable structures of individual configurations. The zero-point energy correction is also considered in this study. The structure having minimum energy in evaluation to other structures for the same values of \u0026ldquo;x\u0026rdquo; and \u0026ldquo;y\u0026rdquo; is considered as the most stable one. Some of the nanoclusters show at least one imaginary vibrational frequency, which consequences to their instability. Almost all the nanoclusters show strong absorption in the ultraviolet region or the extreme ultraviolet region. Some nanoclusters show appreciable absorption in the visible region. These investigations reveal that in most of the nanoclusters; the absorption is obtained in the lower energy side in Ga-rich nanoclusters and on the higher energy side in P-rich nanoclusters. The development of these most stable nanoclusters may be possible in the experiments.\u003c/p\u003e","manuscriptTitle":"Optical Properties of the Most Stable GaxPy (x+y=2 to 5) Nanoclusters predicted through First Principles","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-05-20 06:43:17","doi":"10.21203/rs.3.rs-6688960/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 20th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":48771013,"name":"Nanoscience"},{"id":48771014,"name":"Materials Theory and Modeling"}],"tags":[],"updatedAt":"2025-05-20T06:43:17+00:00","versionOfRecord":[],"versionCreatedAt":"2025-05-20 06:43:17","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6688960","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6688960","identity":"rs-6688960","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}