Computational Theories Used in the Study of Quantum Dots

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Computational Theories Used in the Study of Quantum Dots

N. Mhlanga, T.A. Ntho

Quantum dots (QDs) are intriguing semiconductors with remarkable quantum confinement, optical and electrical properties which avails for various industrial and commercial applications to revolutionize our world. However, their optimal utilization hinges on the understanding of their properties and computational theories are imperative to explore both existing and new QDs properties. This chapter gives a comprehensive analysis of molecular mechanics and quantum mechanics computational approaches used in the study of the QDs properties.

Keywords
Quantum Dots, Density Functional Theory, Effective Mass Approximation, Schrodinger, Time-Dependent Density Functional Theory

Published online 2/1/2020, 32 pages

Citation: N. Mhlanga, T.A. Ntho, Computational Theories Used in the Study of Quantum Dots, Materials Research Foundations, Vol. 96, pp 113-144, 2021

DOI: https://doi.org/10.21741/9781644901250-5

Part of the book on Quantum Dots

References
[1] C. Dykstra, G. Frenking, K. Kim, G. Scuseria, Theory and applications of computational chemistry, the first forty years. Elsevier, 2011.
[2] O. Lehtonen, D. Sundholm, T. Vänskä, Computational studies of semiconductor quantum dots, Phys. Chem. Chem. Phys. 10 (228) 4535-4550. https://doi.org/10.1039/B804212H
[3] Y. Hong, Y. Wu, S. Wu, X. Wang, J. Zhang, Overview of computational simulations in quantum dots,Isr. J. Chem. 59 (2019) 661-672. https://doi.org/10.1002/ijch.201900026
[4] D. Bera, L. Qian, T.-K. Tseng, P.H. Holloway, Quantum dots and their multimodal applications: a review, Materials 3 (2010) 2260-2345. https://doi.org/10.3390/ma3042260
[5] A.L. Kaledin, D. Kong, K. Wu, T. Lian, D.G. Musaev, Quantum confinement theory of auger-assisted biexciton recombination dynamics in type-I and quasi type-II quantum dots,‎J. Phys. Chem. C. 122 (2018) 18742-18750. https://doi.org/10.1021/acs.jpcc.8b04874
[6] N.S. Makarov, P.C. Lau, C. Olson, K.A. Velizhanin, K.M. Solntsev, K. Kieu, S. Kilina, S. Tretiak, R.A. Norwood, N. Peyghambarian, Two-photon absorption in CdSe colloidal quantum dots compared to organic molecules, ACS nano 8 (2014) 12572-12586. https://doi.org/10.1021/nn505428x
[7] N. Zeiri, A. Naifar, S.A.-B. Nasrallah, M. Said, Theoretical studies on third nonlinear optical susceptibility in CdTe–CdS–ZnS core–shell–shell quantum dots, Photonic. Nanostruct. 36 (2019) 100725. https://doi.org/10.1016/j.photonics.2019.100725
[8] S. Nasa, S. Purohit, Linear and third order nonlinear optical properties of GaAs quantum dot in terahertz region, Physica E Low Dimens. Syst. Nanostruct. 118 (2019) 113913. https://doi.org/10.1016/j.physe.2019.113913
[9] J. Vinasco, A. Radu, A. Tiutiunnyk, R. Restrepo, D. Laroze, E. Feddi, M. Mora-Ramos, A. Morales, and C. Duque, Revisiting the adiabatic approximation for bound states calculation in axisymmetric and asymmetrical quantum structures,Superlattice Microst. 138 (2019) 106384. https://doi.org/10.1016/j.spmi.2019.106384
[10] F. Aydin, H. Sari, E. Kasapoglu, S. Sakiroglu, I. Sokmen, Anisotropy dependence of the optical response in an impurity doped quantum dot under intense laser field,Physica E Low Dimens. Syst. Nanostruct. 114 (2019) 113566. https://doi.org/10.1016/j.physe.2019.113566
[11] P. Borah, D. Siboh, P. Kalita, J. Sarma, and N. Nath, Quantum confinement induced shift in energy band edges and band gap of a spherical quantum dot, Physica B Condens. 530 (2018) 208-214. https://doi.org/10.1016/j.physb.2017.11.046
[12] P. Ganesan, L. Senthilkumar, The influence of interfaces and intra-band transitions on the band gap of CdS/HgS and GaN/X (X= InN, In0. 33Ga0. 67N) core/shell/shell quantum dot quantum well–A theoretical study, Physica. E Low. Dimens. Syst. Nanostruct. 74 (2015) 204-212. https://doi.org/10.1016/j.physe.2015.07.002
[13] F. Qu, F.V. Moura, F.M. Alves, R. Gargano, Optical tunability of magnetic polaron stability in single-Mn doped bulk GaAs and GaAs/AlGaAs quantum dots, Chem. Phys. Lett. 561 (2013) 107-114. https://doi.org/10.1016/j.cplett.2013.01.042
[14] C. Pemmaraju, Valence and core excitons in solids from velocity-gauge real-time TDDFT with range-separated hybrid functionals: An LCAO approach, Comput. Condens. Matter. 18 (2019) e00348. https://doi.org/10.1016/j.cocom.2018.e00348
[15] S. Saha, P. Sarkar, Tuning the HOMO–LUMO gap of SiC quantum dots by surface functionalization, Chem. Phys. Lett. 536 (2012) 118-122. https://doi.org/10.1016/j.cplett.2012.03.107
[16] R. Bertel, M. Mora-Ramos, J. Correa, Electronic properties and optical response of triangular and hexagonal MoS2 quantum dots. A DFT approach, Physica ELow Dimens. Syst. Nanostruct. 109 (2019) 201-208. https://doi.org/10.1016/j.physe.2019.01.021
[17] V. Sharma, H.L. Kagdada, J. Wang, P.K. Jha, Hydrogen adsorption on pristine and platinum decorated graphene quantum dot: A first principle study,Int. J. Hydrogen. Energ. (2019). https://doi.org/10.1016/j.ijhydene.2019.09.021
[18] D. Lee, J.L. DuBois, Y. Kanai, Importance of Excitonic Effect in Charge Separation at Quantum-Dot/Organic Interface: First-Principles Many-Body Calculations, Nano Lett. 14 (2014) 6884-6888. https://doi.org/10.1021/nl502894b
[19] J. Feng, Q. Guo, H. Liu, D. Chen, Z. Tian, F. Xia, S. Ma, L. Yu, L. Dong, Theoretical insights into tunable optical and electronic properties of graphene quantum dots through phosphorization, Carbon 155 (2019) 491-498. https://doi.org/10.1016/j.carbon.2019.09.009
[20] R. Das, N. Dhar, A. Bandyopadhyay, D. Jana, Size dependent magnetic and optical properties in diamond shaped graphene quantum dots: A DFT study, J. Phys. Chem. Solids. 99 (2016) 34-42. https://doi.org/10.1016/j.jpcs.2016.08.004
[21] I. Bryndal, J. Lorenc, L. Macalik, J. Michalski, W. Sąsiadek, T. Lis, J. Hanuza, Crystal structure, vibrational and optic properties of 2-N-methylamino-3-methylpyridine N-oxide–Its X-ray and spectroscopic studies as well as DFT quantum chemical calculations, J. Mol. 1195 (2019) 208-219. https://doi.org/10.1016/j.molstruc.2019.05.064
[22] M. V. Mukhina, V.G. Maslov, A.V. Baranov, A.V. Fedorov, A.O. Orlova, F. Purcell-Milton, J. Govan, Y.K. Gun’ko, Intrinsic chirality of CdSe/ZnS quantum dots and quantum rods, Nano lett. 15 (2015) 2844-2851. https://doi.org/10.1021/nl504439w
[23] J. Nagakubo, T. Nishihashi, K. Mishima, K. Yamashita, First-principles approach to the first step of metal–phosphine bond formation to synthesize alloyed quantum dots using dissimilar metal precursors, Chem. Phys. 528 (2020) 110512. https://doi.org/10.1016/j.chemphys.2019.110512
[24] M. Algarra, V. Moreno, J.M. Lázaro-Martínez, E. Rodríguez-Castellón, J. Soto, J. Morales, A. Benítez, Insights into the formation of N doped 3D-graphene quantum dots. Spectroscopic and computational approach,J. Colloid. Interf. Sci. 561 (2020) 678-686. https://doi.org/10.1016/j.jcis.2019.11.044
[25] A. D. Laurent, D. Jacquemin, TDDFT benchmarks: a review, Int. J. Quantum Chem. 113 (2013) 2019-2039. https://doi.org/10.1002/qua.24438.
[26] D. Raeyani, S. Shojaei, S. Ahmadi-Kandjani, Optical graphene quantum dots gas sensors: Theoretical study, SuperlatticeMicrost. 114 (2018) 321-330. https://doi.org/10.1016/j.spmi.2017.12.050
[27] S.S. Yamijala, M. Mukhopadhyay, S.K. Pati, Linear and nonlinear optical properties of graphene quantum dots: A computational study, J. Phys. Chem. 119 (2015) 12079-12087. https://doi.org/10.1021/acs.jpcc.5b03531
[28] D. Mombrú, M. Romero, R. Faccio, Á.W. Mombrú, Electronic and optical properties of sulfur and nitrogen doped graphene quantum dots: A theoretical study, Physica E Low Dimens. Syst. Nanostruct. 113 (2019) 130-136. https://doi.org/10.1016/j.physe.2019.05.004
[29] S. Gopalakrishnan, P. Kolandaivel, Electronic, optical and magnetic properties of Co, Fe and Ni doped (ZnX) 6;(X= O, S & Se) quantum dots–A DFT study, Comput. Theor. Chem. 1111 (2017) 56-68. https://doi.org/10.1016/j.comptc.2017.04.005
[30] F. Gao, C.-L. Yang, M.-S. Wang, X.-G. Ma, W.-W. Liu, Theoretical studies on the feasibility of the hybrid nanocomposites of graphene quantum dot and phenoxazine-based dyes as an efficient sensitizer for dye-sensitized solar cells, Spectrochim. Acta A 206 (2019) 216-223. https://doi.org/10.1016/j.saa.2018.08.012
[31] Q.R. Dong, Y. Li, C. Jia, F.-L. Wang, Y.-T. Zhang, C.-X. Liu, Electrically-induced polarization selection rules of a graphene quantum dot, Solid State Commun. 273 (2018) 55-59. https://doi.org/10.1016/j.ssc.2018.02.009
[32] H. Ryu, D. Nam, B.-Y. Ahn, J.R. Lee, K. Cho, S. Lee, G. Klimeck, M. Shin, Optical TCAD on the Net: A tight-binding study of inter-band light transitions in self-assembled InAs/GaAs quantum dot photodetectors, Math. Comput. Model. 58 (2013) 288-299. https://doi.org/10.1016/j.mcm.2012.11.024
[33] K.A. Nguyen, P.N. Day, R. Pachter, Understanding structural and optical properties of nanoscale CdSe magic-size quantum dots: insight from computational prediction, J. Phys. Chem. 114 (2010) 16197-16209. https://doi.org/10.1021/jp103763d
[34] J. Shu, X. Zhang, P. Wang, R. Chen, H. Zhang, D. Li, P. Zhang, J. Xu, Monte-Carlo simulations of optical efficiency in luminescent solar concentrators based on all-inorganic perovskite quantum dots, Physica B Condens. 548 (2018) 53-57. https://doi.org/10.1016/j.physb.2018.08.021
[35] F. Trani, G. Scalmani, G. Zheng, I. Carnimeo, M.J. Frisch, V. Barone, Time-dependent density functional tight binding: new formulation and benchmark of excited states, J. Chem. Theory Comput. 7 (2011) 3304-3313. https://doi.org/10.1021/ct200461y
[36] F. Zaouali, A. Bouazra, M. Said, Numerical modelling of electronic and optical properties of isolated and self-assembled InAs/InP quantum dots,Optik 182 (2019) 731-738. https://doi.org/10.1016/j.ijleo.2019.01.075
[37] S.N. Mohajer, A. Ibral, J. El Khamkhami, E.M. Assaid, Quantum confined Stark effects of single dopant in polarized hemispherical quantum dot: Two-dimensional finite difference approach and Ritz-Hassé variation method, Physica B Condens. 537 (2018) 40-50. https://doi.org/10.1016/j.physb.2018.01.061
[38] S.N. Mohajer, A. Ibral, J. El Khamkhami,E.M. Assaid, Energies and wave functions of an off-centre donor in hemispherical quantum dot: Two-dimensional finite difference approach and ritzvariational principle, Physica B Condens. 497 (2016) 51-58. https://doi.org/10.1016/j.physb.2016.05.028
[39] M. Choubani, H. Maaref, F. Saidi, Nonlinear optical properties of lens-shaped core/shell quantum dots coupled with a wetting layer: effects of transverse electric field, pressure, and temperature, J. Phys. Chem. Solids. 139 (2020) 109226. https://doi.org/10.1016/j.jpcs.2019.109226
[40] J.S. Ahn, Finite difference method for the arbitrary potential in two dimensions: Application to double/triple quantum dots, Superlattice. Microst. 65 (2014) 113-123. https://doi.org/10.1016/j.spmi.2013.10.044
[41] M. Garagiola, O. Osenda, Excitonic states in spherical layered quantum dots. Physica E Low Dimens. Syst. Nanostruct. 116 (2020) 113755. https://doi.org/10.1016/j.physe.2019.113755
[42] Y. Liu, S. Bose, W. Fan, Effect of size and shape on electronic and optical properties of CdSe quantum dots,Optik. 155(2018) 242-250. https://doi.org/10.1016/j.ijleo.2017.10.165
[43] S. Kilina, K.A. Velizhanin, S. Ivanov, O.V. Prezhdo, S. Tretiak, Surface ligands increase photoexcitation relaxation rates in CdSe quantum dots, ACS nano. 6 (2012) 6515-6524. https://doi.org/10.1021/nn302371q
[44] K. Hyeon-Deuk, O.V. Prezhdo, Multiple exciton generation and recombination dynamics in small si and cdse quantum dots: An ab initio time-domain study, ACS nano. 6 (2012) 1239-1250. https://doi.org/10.1021/nn2038884
[45] C. Dong, X. Li, P. Jin, W. Zhao, J. Chu, J. Qi, Intersubunit electron transfer (IET) in quantum dots/graphene complex: what features does IET endow the complex with? J. Phys. Chem. C, 116 (2012) 15833-15838. https://doi.org/10.1021/jp304624y
[46] Y. Li, H. Shu, X. Niu,J. Wang, Electronic and optical properties of edge-functionalized graphene quantum dots and the underlying mechanism. J. Phys. Chem. C, 119 (2015) 24950-24957. https://doi.org/10.1021/acs.jpcc.5b05935
[47] S. Zhai, P. Guo, J. Zheng, P. Zhao, B. Suo, Y. Wan, Density functional theory study on the stability, electronic structure and absorption spectrum of small size g-C3N4 quantum dots, Comput. Mater. Sci. 148 (2018) 149-156. https://doi.org/10.1016/j.commatsci.2018.02.023
[48] H-P. Li, Z.-T. Bi, R.-F. Xu, K. Han, M.-X. Li, X.-P. Shen, Y.-X. Wu, Theoretical study on electronic polarizability and second hyperpolarizability of hexagonal graphene quantum dots: Effects of size, substituent, and frequency, Carbon, 122 (2017) 756-760. https://doi.org/10.1016/j.carbon.2017.07.033
[49] C. Wang, Y. Ding, X. Bi, J. Luo, G. Wang, Y. Lin, Carbon quantum dots-Ag nanoparticle complex as a highly sensitive “turn-on” fluorescent probe for hydrogen sulfide: a DFT/TD-DFT study of electronic transitions and mechanism of sensing, Sensor. Actuat. B-Chem. 264 (2018) 404-409. https://doi.org/10.1016/j.snb.2018.02.186
[50] A.L. Kaledin, T. Lian, C.L. Hill, D.G. Musaev, A hybrid quantum mechanical approach: Intimate details of electron transfer between type-I CdSe/ZnS quantum dots and an anthraquinone molecule, J. Phys. Chem. B, 119 (2015) 7651-7658. https://doi.org/10.1021/jp511935z
[51] A. El Aouami, E. Feddi, M. El-Yadri, N. Aghoutane, F. Dujardin, C. Duque, H.V. Phuc, Electronic states and optical properties of single donor in GaN conical quantum dot with spherical edge. Superlattice Microst. 114 (2018) 214-224. https://doi.org/10.1016/j.spmi.2017.12.043
[52] Q. Dong, Electrical spin switch in a two-electron triangular graphene quantum dot. Physica E Low Dimens, Syst. Nanostruct. 116 (2020) 113779. https://doi.org/10.1016/j.physe.2019.113779
[53] A. Tiutiunnyk, C. Duque, F. Caro-Lopera, M. Mora-Ramos, J. Correa, Opto-electronic properties of twisted bilayer graphene quantum dots. Physica E Low Dimens, Syst. Nanostruct. 112 (2019) 36-48. https://doi.org/10.1016/j.physe.2019.03.028
[54] H. Abdelsalam, H. Elhaes, M.A. Ibrahim, First principles study of edge carboxylated graphene quantum dots, Physica B Condens. 537 (2018) 77-86. https://doi.org/10.1016/j.physb.2018.02.001
[55] H. Abdelsalam, V.A. Saroka, W.O. Younis, Phosphorene quantum dot electronic properties and gas sensing, Physica E Low Dimens. Syst. Nanostruct. 107 (2019) 105-109. https://doi.org/10.1016/j.physe.2018.11.012
[56] D. Gabay, X. Wang, V. Lomakin, A. Boag, M. Jain, A. Natan, Size dependent electronic properties of silicon quantum dots—An analysis with hybrid, screened hybrid and local density functional theory,Comput. Phys. Commun. 221 (2017) 95-101. https://doi.org/10.1016/j.cpc.2017.08.005
[57] N. Thongsai, P. Jaiyong, S. Kladsomboon, I. In, P. Paoprasert, Utilization of carbon dots from jackfruit for real-time sensing of acetone vapor and understanding the electronic and interfacial interactions using density functional theory, Appl. Surf. 487 (2019) 1233-1244. https://doi.org/10.1016/j.apsusc.2019.04.269
[58] N. Pattarapongdilok, V. Parasuk, Theoretical study on electronic properties of curved graphene quantum dots, Comput. Theor. Chem. 1140 (2018)86-97. https://doi.org/10.1039/C8CP01403E
[59] T.D. Rodríguez, J. Reyes-Nava, M. Pacio, H. Juárez, and J. Muñiz, Theoretical study on the electronic structure properties of a PbS quantum dot adsorbed on TiO2 substrates and their role on solid-state devices, Comput. Theor. Chem. 1100 (2017) 83-90. https://doi.org/10.1021/jp952869n
[60] A. Samia, E. Feddi, C. Duque, M. Mora-Ramos, V. Akimov, J. Correa, Optoelectronic properties of phosphorene quantum dots functionalized with free base porphyrins, Comput. Mater. Sci. 171 (2020) 109278. https://doi.org/10.1016/j.commatsci.2019.109278
[61] Y. Liu, L. Du, K. Gu, M. Zhang, Effect of Tm dopant on luminescence, photoelectric properties and electronic structure of In2S3 quantum dots,J. Lumin. 217 (2020) 116775. https://doi.org/10.1016/j.jlumin.2019.116775
[62] H. Abdelsalam, V.A. Saroka, M. Ali, N.H. Teleb, H. Elhaes, M.A. Ibrahim, Stability and electronic properties of edge functionalized silicene quantum dots: A first principles study,Physica E Low Dimens. Syst. Nanostruct. 108 (2019) 339-346. https://doi.org/10.1016/j.physe.2018.07.022
[63] S. Bondwal, P. Debnath, P.P. Thankachan, Structural, electronic and optical properties of model silicon quantum dots: A computational study, Physica E Low Dimens. Syst. Nanostruct. 103 (2018) 194-200. https://doi.org/10.1016/j.physe.2018.05.037
[64] N. Li, Z. Liu, S. Hu, Q. Chang, C. Xue, H. Wang, Electronic and photocatalytic properties of modified MoS2/graphene quantum dots heterostructures: A computational study,Appl. Surf. 473 (2019) 70-76. https://doi.org/10.1016/j.apsusc.2018.12.122
[65] H. Abdelsalam, H. Elhaes, M.A. Ibrahim, Tuning electronic properties in graphene quantum dots by chemical functionalization: Density functional theory calculations,Chem. Phys. Lett. 695 (2018) 138-148. https://doi.org/10.1016/j.cplett.2018.02.015
[66] F. Dujardin, E. Assaid, E. Feddi, New way for determining electron energy levels in quantum dots arrays using finite difference method, Superlattice. Microst. 118 (2018) 256-265. https://doi.org/10.1016/j.spmi.2018.04.027
[67] D. Kennes, D. Schuricht, V. Meden, Efficiency and power of a thermoelectric quantum dot device, EPL. 102 (2013) 57003. https://doi.org/10.1209/0295-5075/102/57003
[68] J.D. Castaño-Yepes, D. Amor-Quiroz, Super-statistical description of thermo-magnetic properties of a system of 2D GaAs quantum dots with gaussian confinement and Rashba spin–orbit interaction, Physica. A, (2019) 123871. https://doi.org/10.1016/j.physa.2019.123871
[69] A. Armaşelu, Quantum Dots and Fluorescent and Magnetic Nanocomposites: Recent Investigations and Applications in Biology and Medicine. Nonmagnetic and Magnetic Quantum Dots, Stavrou, Vasilios N., ed. BoD–Books on Demand, 2017. https://doi: 10.5772/intechopen.70614
[70] R. Masrour, A. Jabar, Size and diluted magnetic properties of diamond shaped graphene quantum dots: Monte Carlo study,Physica A. 497 (2018) 211-217. https://doi:10.1016/j.physa.2017.12.141
[71] T. Pisanic Ii, Y. Zhang, T. Wang, Quantum dots in diagnostics and detection: principles and paradigms,Analyst. 139(2014) 2968-2981. https://doi.org/10.1039/C4AN00294F
[72] S. Hug, Classical molecular dynamics in a nutshell, in biomolecular simulations, (2012) 127–152. https://doi:10.1007/978-1-62703-017-5_6
[73] J.M. Elward, F.J. Irudayanathan, S. Nangia, A. Chakraborty, Optical signature of formation of protein corona in the firefly luciferase-CdSe quantum dot complex, J. Chem. Theory Comput. 10 (2014) 5224-5228. https://doi.org/10.1021/ct500681m
[74] E. Kaxiras, Atomic and electronic structure of solids. Cambridge University Press. 2003. https://doi.org/10.1017/CBO9780511755545
[75] T.J. Zielinski, E. Harvey, R. Sweeney, D.M. Hanson, Quantum states of atoms and molecules, J. Chem. Educ. 82 (2005) 1880. https://doi.org/10.1021/ed082p1880.2.
[76] J. Neugebauer, C.G. Van de Walle, Theory of hydrogen in GaN, in N.H Nickel (ed) R.K Wallardson, E.R. Weber. Hydrogen in Semicondictros IISemiconduct. Semimet. 61 (1999) 479-502.Academic Press, boston.
[77] N Vukmirovic´, L.-W.W., Quantum Dots: Theory.Elsevier B.V, 2011.
[78] Z. Bodroski, N. Vukmirović, S. Skrbic, Gaussian basis implementation of the charge patching method, J. Comput. Phys., 368 (2018) 196-209. https://doi.org/10.1016/j.jcp.2018.04.032
[78] I.-H. Chu, M. Radulaski, N. Vukmirovic, H.-P. Cheng, L.-W. Wang, Charge transport in a quantum dot supercrystal, J. Phys. Chem. C, 115 (2011) 21409-21415. https://doi.org/10.1021/jp206526s
[80] D. Stroud, The effective medium approximations: Some recent developments, Superlattice. Microst., 23 (1998) 567-573. https://doi.org/10.1006/spmi.1997.0524
[81] M.A.F. Richard A. Dudley, Engineered Materials and Metamaterials: Design and Fabrication, SPIE, 2017.
[82] F. Flory, Y.-J. Chen, C.-C. Lee, L. Escoubas, J.-J. Simon, P. Torchio, J. Le Rouzo, S. Vedraine, H. Derbal-Habak, I. Shupyk, Optical properties of dielectric thin films including quantum dots, Appl. opt., 50 (2011) C129-C134. https://doi.org/10.1364/AO.50.00C129
[83] E.O. Chukwuocha, M.C. Onyeaju, T.S. Harry, Theoretical studies on the effect of confinement on quantum dots using the brus equation, 2012. https;//doi.org: 10.4236/wjcmp.2012.22017
[84] S.V. Kilina, P.K. Tamukong, D.S. Kilin, Surface chemistry of semiconducting quantum dots: theoretical perspectives, Acc. Chem. Res. 49 (2016) 2127-2135. https://doi.org: 10.1021/acs.accounts.6b00196
[85] J. Pipek, P.G. Mezey, A fast intrinsic localization procedure applicable for abinitio and semiempirical linear combination of atomic orbital wave functions, J. Chem. Phys., 90 (1989) 4916-4926. https://doi.org/10.1063/1.456588
[86] Y.S. Sarun Arunragsa, W. Pon-On, C. Wongchoosuk,Hydroxyl edge-functionalized graphene quantum dots for gas-sensing applications, Diam. Relat. Mater., (2020) 107790. https://doi.org/10.1016/j.diamond.2020.107790
[87] S. Niaz, A.D. Zdetsis, Comprehensive ab initio study of electronic, optical, and cohesive properties of silicon quantum dots of various morphologies and sizes up to infinity, J. Phys. Chem. C., 120 (2016) 11288-11298. https://doi.org/10.1021/acs.jpcc.6b02955
[88] P.J. Hasnip, K. Refson, M.I. Probert, J.R. Yates, S.J. Clark, C.J. Pickard, Density functional theory in the solid state, Philos. T. R. Soc. A. 372 (2014) 20130270. https://doi.org/10.1098/rsta.2013.0270
[89] S.J Clark, J. Robertson, Screened exchange density functional applied to solids, Phys. Rev. B. 82 (2010) 085208. https://doi.org/10.1103/PhysRevB.82.085208
[90] K. Zhuravlev, PbSe vs. CdSe: Thermodynamic properties and pressure dependence of the band gap. Phys. B: Condens. Matter, 394 (2007) 1-7. https://doi.org/10.1016/j.physb.2007.01.030
[91] F. Thierry, J. Le Rouzo, F. Flory, G. Berginc, L. Escoubas. Optimization of the optical properties of nanostructures through fast numerical approaches. in Nanophotonic Materials XI. International Society for Optics and Photonics. 2014. https://doi.org/ 10.1117/12.2061042
[92] A. Laref, N. Alshammari, S. Laref, S. Luo, Surface passivation effects on the electronic and optical properties of silicon quantum dots, Sol. Energy Mater. Sol. Cells, 120 (2014) 622-630. https://doi.org/10.1016/j.solmat.2013.10.005
[93] X. Wang, R. Zhang, T.A. Niehaus, T. Frauenheim, Excited state properties of allylamine-capped silicon quantum dots, J. Phys. Chem. C., 111 (2007) 2394-2400. https://doi.org/10.1021/jp065704v
[94] M. Anas, A. Othman, G. Gopir. First-principle study of quantum confinement effect on small sized silicon quantum dots using density-functional theory. in AIP Conference Proceedings, American Institute of Physics, 2014. https://doi.org/10.1063/1.4895180
[95]. M.G. Mavros, D.A. Micha, D.S. Kilin, Optical properties of doped silicon quantum dots with crystalline and amorphous structures, J. Phys. Chem. C. 115 (2011) 19529-19537. https://doi.org/10.1021/jp2055798
[96] M.M.-A Anas,. G. Gopir, Electronic and optical properties of small hydrogenated silicon quantum dots using time-dependent density functional theory,J. Nanomat., 2015 (2015).https://doi.org/10.1155/2015/481087
[97] G. Zerveas, E. Caruso, G. Baccarani, L. Czornomaz, N. Daix, D. Esseni, E. Gnani, A. Gnudi, R. Grassi, M. Luisier, Comprehensive comparison and experimental validation of band-structure calculation methods in III–V semiconductor quantum wells, Solid State Electron. 115 (2016) 92-102.https://doi.org/10.1016/j.sse.2015.09.005
[98] X. Wang, Y. Feng, P. Dong, J. Huang, A mini review on carbon quantum dots: preparation, properties and electrocatalytic application, Front. Chem. 7 (2019) 671.https://doi.org/10.3389/fchem.2019.00671