Optical Properties of ScnYn (Y = N, P As) Nanoparticles

In this work, using Density Functional Theory (DFT) and Time Dependent DFT, the absorption spectrum, the optical gap, and the binding energy of scandium pnictogen family nanoparticles (NPs) are examined. The calculated structures are created from an initial cubic-like building block of the form Sc4Y4, where Y = N, P, As after elongation along one and two perpendicular directions. The existence of stable structures over a wide range of morphologies was one of the main findings of this research, and this led to the study of several exotic NPs. The absorption spectrum of all the studied structures is within the visible spectrum, while the optical gap varies between 1.62 and 3 eV. These NPs could be used in the field in photovoltaics (quantum dot sensitized solar cells) and display applications.


Introduction
Industrial revolution, the lifestyle of the developed world, urbanization, globalization, and technological advancements have contributed to escalated environmental pollution and the depletion of fossil fuel resources [1].Climate change is one of the most serious issues facing the worldwide community, and it directly affects fuel supply and energy production [2,3].Increasing emissions of CO 2 into the atmosphere from human activities, forest fires, global warming, greenhouse gas emissions, and deforestation negatively affect climate change [4,5].Also, more and more studies have been conducted on how to reduce CO 2 emissions over both short-and long-term time horizons [6].Renewable energy consumption is crucial for achieving sustainable environmental goals, and it discourages fossil fuel use in the energy mix, thereby aiming for a sustainable environment.The photovoltaic (PV) industry, solar cells, and other greenhouse technologies have played a significant part in achieving the goal of low carbon development and accomplishing sustainable economic growth [7][8][9].
Nanotechnology, as one of the most developing fields today, offers innovative materials that find application in energy production and conservation.More specifically, semiconductor nanoparticles (NPs), which are commonly named quantum dots (QDs), have great potential for applications in medical diagnostics, drug delivery, gene therapy, medicine, and biology, both in vivo and in vitro, in areas including pharmacokinetics, biosensors, and bio-imaging [10][11][12].Also, quantum dots are widely used in the field of photovoltaics technologies because they benefit from unique quantum confinement effects [13][14][15].
Quantum dots composed of a combination of at least one of the pnictogen family (phosphorus (P), arsenic (As), and nitrogen (N)) are widely used in applications based on their optical and structural properties.More specifically, nitrogen quantum dots have unique and distinct photoluminescence properties, with an increasing percentage of nitrogen compared to the neighboring carbon dots [16], while doping of N is a promising strategy to modulate electronic, chemical, and structural functionalities of graphene (G) and graphene quantum dots (GQDs) in energy and environmental applications, such as supercapacitors, batteries, sensors, fuel cells, solar cells, and photocatalysts [17,18].Also, there have been many scientific studies to explore synthetic methods (such as ultrasonic and electrochemical exfoliation, solvothermal treatment, blender breaking, milling crushing, and pulsed laser irradiation), properties, and modifications of black phosphorus quantum dots (BPQDs), exhibiting a broad range of applications in the fields of bioimaging, fluorescence sensing, nonlinear optical absorbers, cancer therapy, intelligent electronics, photovoltaics, optoelectronics, and flexible devices [19,20].Recent research has shown that Sc doping in Titanium Dioxide (TiO 2 ) can be used for applications in photocatalytic water-splitting technology in low-cost and eco-friendly hydrogen production [21], while the interstitial dimers of Sc formed in silicon can introduce several intermediate-bands (IBs) in the band gap, making the material a high-efficiency IB solar cell [22].Furthermore, the conduction band structure and electron mobility in rocksalt ScN were recently studied using DFT [23], while there has been progress to overcome the materials engineering challenges to grow high-quality epitaxial, nominally single crystallin metal/semiconductor superlattices based on transition metal nitrides [24,25].
In the present study, using the Density Functional Theory and Time Dependent DFT, the absorption spectrum, the optical gap, and the binding energy of scandium-pnictogen family nanoparticles are examined.The calculated structures are of the form Sc x Y x where Y = N, As, P, while additionally a wide range of stable configurations are presented.This work aims to provide non-toxic and easy to find semiconducting NPs, which can be used in the field of renewable energy source such as photovoltaic technologies [26,27].

Materials and Methods
In this manuscript, the optical and the structural properties of more than thirty different geometries were calculated by Density Functional Theory and Time Dependent DFT (TD-DFT).The structures studied herein were initially formed after elongation of an initial geometry in one and two perpendicular directions.From the study of structurally stable configurations, stable morphologies were formed.Using the gradient corrected functional of Perdew, Burke, and Ernzerhof (PBE) [28], with the triple-ζ quality def2-TZVP basis set [29], the geometries of the studied structures were optimized.Subsequently, with the help of the TD-DFT on the ground state geometries, the lowest singlet vertical excitation energies and the ultraviolet-visible absorption spectra were calculated.Note that the initial calculations were made only for the small nanostructures, due to the lack of experimental data on the absorption spectrum of the large structures.We were very concerned about choosing the functional for each group of the scandium-pnictogen family.It is true that if we use a consistent functional (especially PBE) for all studied absorption spectra, the calculations would be faster (and perhaps more comparable to each other).However, the results from the comparison with the EOM-CCSD [30] functional showed us that it is better and more accurate to calculate the absorption spectrum with a different functional for each group of the scandium-pnictogen family.The functionals used to calculate the absorption spectra were PBE, M06-2X [31], and CAM-B3LYP [32] for Sc x N x , Sc x P x , and Sc x As x nanoparticles, respectively.A specified script representing each excitation as a Gaussian function centered on the TD-DFT calculated excitation energy and with a standard deviation (broadening) of 0.1 eV was used to calculate the absorption spectrum.Also, in order to approximate the peak shape, which is observed experimentally, the latter value of the spectrum was chosen.Additionally, the calculation package TURBOMOLE [33] was used in all calculations, while the Particle Swarm Optimization (PSO) [34] was used to ensure that the studied nanostructures are indeed realistic.

Results
Classified as a rare-earth element, scandium has attracted much research interest in its properties.The optical, structural, and electronic properties of Sc, such as the refractory nitrides ScN, make it an excellent candidate semiconductor for optoelectronic and DMS applications [35,36].Also, Yu Gong and Mingfei Zhou showed that the cyclic Sc(µ-N)2Sc molecules dimerize on annealing to form a cubic Sc 4 N 4 cluster with tetrahedral symmetry, which is a fundamental building block for ScN NPs and crystals [37].Note that in small-size nanocrystals, the Sc 4 N 4 units prefer to arrange into the rectangular-like wire structures, and they arrange into the compact rectangular-like or cubic-like configurations in large-size nanocrystals [38].Recent research has shown that the cage unit tends to arrange into the compact configurations, and the occupied positions of N atoms shift from the surface towards the center of the coordination site with the increasing number of Sc atoms, while there is a study in which the calculated optical spectra (by using DFT) suggest that 2D tetragonal ScN and YN nanosheets have high visible light absorption efficiency [39,40].
All of the studied structures were created from an initial cubic-like building block of the form Sc 4 Y 4 , where Y = N, P, As. Figure 1 shows the elongation of this block, from which new stable structures with interesting optical properties could be created.So, the nanostructures of Sc, which are formed, fall into three categories.In the first category belong the elongated nanoparticles in one direction (1D); in the second belong the NPs in two vertical directions; and, in the third category, belong the exotic structures.Regarding the shape of the structure (Figure 1), we notice that the geometry of Sc 4 N 4 NP is almost a perfect cube, because the corresponding angles are almost 90 degrees, while the geometry of phosphorus and arsenic structures is like a distorted cube (the angles formed are acute and obtuse).Also, the third category of studied NPs is formed by creating a hole in the structures (categories one and two) after extracting atoms from them.Note that the study of examined nanostructures showed very interesting results in green technology applications.
nitrides ScN, make it an excellent candidate semiconductor for optoelectronic and DMS applications [35,36].Also, Yu Gong and Mingfei Zhou showed that the cyclic Sc(µ-N)2Sc molecules dimerize on annealing to form a cubic Sc4N4 cluster with tetrahedral symmetry, which is a fundamental building block for ScN NPs and crystals [37].Note that in smallsize nanocrystals, the Sc4N4 units prefer to arrange into the rectangular-like wire structures, and they arrange into the compact rectangular-like or cubic-like configurations in large-size nanocrystals [38].Recent research has shown that the cage unit tends to arrange into the compact configurations, and the occupied positions of N atoms shift from the surface towards the center of the coordination site with the increasing number of Sc atoms, while there is a study in which the calculated optical spectra (by using DFT) suggest that 2D tetragonal ScN and YN nanosheets have high visible light absorption efficiency [39,40].
All of the studied structures were created from an initial cubic-like building block of the form Sc4Y4, where Y = N, P, As. Figure 1 shows the elongation of this block, from which new stable structures with interesting optical properties could be created.So, the nanostructures of Sc, which are formed, fall into three categories.In the first category belong the elongated nanoparticles in one direction (1D); in the second belong the NPs in two vertical directions; and, in the third category, belong the exotic structures.Regarding the shape of the structure (Figure 1), we notice that the geometry of Sc4N4 NP is almost a perfect cube, because the corresponding angles are almost 90 degrees, while the geometry of phosphorus and arsenic structures is like a distorted cube (the angles formed are acute and obtuse).Also, the third category of studied NPs is formed by creating a hole in the structures (categories one and two) after extracting atoms from them.Note that the study of examined nanostructures showed very interesting results in green technology applications.
Figure 1.The initial cubic-like building block Sc4Y4 (Y = N, P, As).The top view refers to the top view of the cubes, while the bottom view refers to the side view (45 degree).The white color corresponds to the Sc atom, the blue one to the N atom, the orange one to the P atom, and the purple one to the As atom.

ScxYx NPs
Figure 2 shows the absorption spectra of the initial cubic-like building blocks for the studied NPs, i.e., the structures Sc4Y4, where Y = N, P, As.In the case of Sc4N4, the first five excitation energies on the AS appear at 2.59, 3.63, 3.82, 4.07, and 4.44 eV, with corresponding absorption of 0.10, 0.13, 0.01, 0.20, and 0.02.Similarly, the first five excitation energies in the case of Sc4P4 appear at 2.79, 2.93, 3.11, 3.27, and 3.42 eV, with the corresponding absorption varying around 0.007, 0.01, 0.09, 0.24, and 0.01.When Sc4As4 is considered in the calculations, the first five excitation energies of the AS appear at 2.44, 2.56, 2.63, 2.83, and 2.99 eV, with corresponding absorbance of 0.01, 0.04, 0.05, 0.06, and 0.02.Also, as we can observe, the smallest optical gap is 2.44 eV, and it appears in the case of Sc4As4, while

Sc x Y x NPs
Figure 2 shows the absorption spectra of the initial cubic-like building blocks for the studied NPs, i.e., the structures Sc 4 Y 4 , where Y = N, P, As.In the case of Sc 4 N 4 , the first five excitation energies on the AS appear at 2.59, 3.63, 3.82, 4.07, and 4.44 eV, with corresponding absorption of 0.10, 0.13, 0.01, 0.20, and 0.02.Similarly, the first five excitation energies in the case of Sc 4 P 4 appear at 2.79, 2.93, 3.11, 3.27, and 3.42 eV, with the corresponding absorption varying around 0.007, 0.01, 0.09, 0.24, and 0.01.When Sc 4 As 4 is considered in the calculations, the first five excitation energies of the AS appear at 2.44, 2.56, 2.63, 2.83, and 2.99 eV, with corresponding absorbance of 0.01, 0.04, 0.05, 0.06, and 0.02.Also, as we can observe, the smallest optical gap is 2.44 eV, and it appears in the case of Sc 4 As 4 , while for the structures Sc 8 Y 8 where Y = N, P, As, the smallest optical gap shifts to lower energies (Figure 3).From the comparison of Figures 2 and 3, we observed that in the case of Sc 8 N 8 , the optical gap appeared at 2.41 eV, i.e., 0.18 eV lower than the initial cubic structure and the optical gap of Sc 8 P 8 appears at 2.43 eV, i.e., 0.50 eV lower than the corresponding Sc 4 P 4 , while the value of the optical gap for Sc 8 As 8 appears at 2.21 eV and it is lower by 0.23 eV than the corresponding cubic structure.Furthermore, the strength of the absorbance of the Sc 8 Y 8 structures shows an upward trend as we move into larger energies.The first five excitation energies for the Sc 8 N 8 on the AS appear at 2.41, 2.53, 2.74, 2.99, and 3.14 eV, while the corresponding absorbances are about 0.03, 0.05, 0.02, 0.06, and 0.03.For the Sc 8 P 8 NPs, the first five excitation energies appear at 2.43, 2.61, 2.80, 3.02, and 3.10 eV and the corresponding absorbances are about 0.01, 0.15, 0.01, 0.08, and 0.09.Similarly, in the case of Sc 8 As 8 , the first five peak positions appear at 2.21, 2.39, 2.52, 2.81, and 2.96 eV with absorbance of 0.05, 0.11, 0.04, and 0.09, respectively.
for the structures Sc8Y8 where Y = N, P, As, the smallest optical gap shifts to lower energies (Figure 3).From the comparison of Figures 2 and 3, we observed that in the case of Sc8N8, the optical gap appeared at 2.41 eV, i.e., 0.18 eV lower than the initial cubic structure and the optical gap of Sc8P8 appears at 2.43 eV, i.e., 0.50 eV lower than the corresponding Sc4P4, while the value of the optical gap for Sc8As8 appears at 2.21 eV and it is lower by 0.23 eV than the corresponding cubic structure.Furthermore, the strength of the absorbance of the Sc8Y8 structures shows an upward trend as we move into larger energies.The first five excitation energies for the Sc8N8 on the AS appear at 2.41, 2.53, 2.74, 2.99, and 3.14 eV, while the corresponding absorbances are about 0.03, 0.05, 0.02, 0.06, and 0.03.For the Sc8P8 NPs, the first five excitation energies appear at 2.43, 2.61, 2.80, 3.02, and 3.10 eV and the corresponding absorbances are about 0.01, 0.15, 0.01, 0.08, and 0.09.Similarly, in the case of Sc8As8, the first five peak positions appear at 2.21, 2.39, 2.52, 2.81, and 2.96 eV with absorbance of 0.05, 0.11, 0.04, and 0.09, respectively.The following is the stability of the examined NPs by the binding energies per formula unit (BE per f.u.).The BE, EB, is defined as follows: (  ) = () + () − (  ) The following is the stability of the examined NPs by the binding energies per formula unit (BE per f.u.).The BE, E B , is defined as follows: where E(Sc) is the energy of the isolated atoms of Sc, E(Y) is the energy of the isolated atoms of Y = N, P, As, and the index x indicates each examined formula of the structure (formula unit).E(Sc x Y x ) is the total energy of the examined NPs.Also, the binding energy per f.u., (E b ) is The BE per f.u. for the Sc 4 N 4 , Sc 4 P 4 , and Sc 4 As 4 is 10.45, 8.53, and 7.40 eV, respectively.

Elongated Sc x Y x NPs along One Direction
As mentioned above, the scandium NPs are divided into three categories.First, nanostructures were created by elongation of the initial cubic-like building block, Sc 4 Y 4 (Y = N, P, As), along one direction.The general form of the created NPs is Sc x Y x , where x = 8, 16, 24.As we can observe from Figure 4, the structure with x = 8 consists of two initial cubic-like building blocks, the structure with x = 16 consists of four corresponding cubes, and the structure with x = 24 contains six individual initial corresponding cubes.These structures are optimized as geometrically stable due to not finding imaginary frequencies.We clarify that the Sc x N x and Sc x As x nanostructures are almost the same as the Sc x P x shown.The results of calculating optical properties of the examined NPs and BE per f.u are shown in the Table 1.We observe that as the number of atoms in the structure increases, a significant decrease in the optical gap is observed in three cases of ScxYx in this category.For the ScxNx NPs, the optical gap decreases from 2.59 eV (for Sc4N4) gradually to 2.41 and 2.29 eV (for Sc8N8 and Sc16N16, respectively), while for Sc24N24, it is 2 eV.The BE per f.u. has particularly high values compared to ΜgxYx NPs [41], which indicates that the Sc monopnictogen structures are significantly more stable.Also, the binding energy is 10.45 eV for Sc4N4, while it increases to 11.57 eV for the Sc24N24.In the case of ScxPx NPs, it is noted that for x = 4, the optical gap is 2.93 eV, while as the nanostructure becomes bigger, a large reduction in the OG is observed.More specifically, the OG for Sc8P8 is 0.5 eV less than Sc4P4, while it is 2.18 eV for the Sc24P24.In the case of ScxAsx NPs in this category, the absorption spectrum and the oscillator strength have the same intensity as the corresponding ScxPx.So, the OG is 2.44 and 2.00 eV for Sc4As4 and Sc24As24, respectively, and the oscillator strength is 1.18.
Table 1.Binding energy (BE) per f.u., optical gap (OG), and oscillator strength (OS) for ScxYx NPs (x = 4, 4, 16 and Y = N, P, As), which were created after elongation of the initial cubic-like building block Sc4Y4 (Y = N, P, As) along one direction.The results of calculating optical properties of the examined NPs and BE per f.u are shown in the Table 1.We observe that as the number of atoms in the structure increases, a significant decrease in the optical gap is observed in three cases of Sc x Y x in this category.For the Sc x N x NPs, the optical gap decreases from 2.59 eV (for Sc 4 N 4 ) gradually to 2.41 and 2.29 eV (for Sc 8 N 8 and Sc 16 N 16 , respectively), while for Sc 24 N 24 , it is 2 eV.The BE per f.u. has particularly high values compared to Mg x Y x NPs [41], which indicates that the Sc monopnictogen structures are significantly more stable.Also, the binding energy is 10.45 eV for Sc 4 N 4 , while it increases to 11.57 eV for the Sc 24 N 24 .In the case of Sc x P x NPs, it is noted that for x = 4, the optical gap is 2.93 eV, while as the nanostructure becomes bigger, a large reduction in the OG is observed.More specifically, the OG for Sc 8 P 8 is 0.5 eV less than Sc 4 P 4 , while it is 2.18 eV for the Sc 24 P 24 .In the case of Sc x As x NPs in this category, the absorption spectrum and the oscillator strength have the same intensity as the corresponding Sc x P x .So, the OG is 2.44 and 2.00 eV for Sc 4 As 4 and Sc 24 As 24 , respectively, and the oscillator strength is 1.18.
Table 1.Binding energy (BE) per f.u., optical gap (OG), and oscillator strength (OS) for Sc x Y x NPs (x = 4, 4, 16 and Y = N, P, As), which were created after elongation of the initial cubic-like building block Sc 4 Y 4 (Y = N, P, As) along one direction.

Elongated NPs along Two Perpendicular Directions
The second group of Sc nanostructures examined in this work contains the initial building block, which was elongated along two perpendicular directions.The general form of the proposed nanoparticles is Sc x N x , where x = 16, 24, 32, 36, and 48.The resulting nanostructures are shown in Figure 5 and the calculated optical properties are collected in Table 2.Note that the nanostructures depicted in the first row of Figure 5 were derived from Sc 8 Y 8 and they have a square shape, while the corresponding structures in the second row were derived from Sc 16 Y 16 and they have a rectangular shape.The optical gap for the examined Sc x N x in this category ranges between 2.33 eV and 2.07 eV, while the Sc 36 N 36 and Sc 48 N 48 nanostructures for which we do not give a value for the optical gap are unstable.The BE per f.u. for the examined NPs is approximately the same as those of NPs elongated along one direction and range between 11.68 eV and 12.13 eV for Sc 16 N 16 and Sc 48 N 48 , respectively.
When the second part of the NP is phosphorus, the optical gap is 2.16 eV and 1.73 eV for Sc 16 P 16 and Sc 48 P 48 NPs, respectively, while the OS for Sc 36 P 36 is much higher than other examined nanostructures in this category.Regarding the BE per f.u. for the studied NPs, the calculated values range between 9.91 eV and 10.41 eV.Also, the Sc 36 P 36 NPs seem to be more stable than Sc 32 P 32 NPs (with a hole in the center of their geometry) because they have a higher BE by 0.35 eV.
The calculations continued by considering arsenic as the second part of the examined NPs.The BE per f.u. of the smallest nanostructure (Sc 16 As 16 ) elongated along two directions is 2.02 eV, while the oscillator strength ranges between 0.02 and 0.10.
A very interesting case from the nanostructures that are examined and created by elongation of the initial building block along one and two perpendicular directions is the one where x = 16.In Figure 6, the absorption spectra of these cases of Sc 16 Y 16 NPs are shown.A notable general observation is that the most excitation energies are within the visible spectrum.More specifically, for the elongated along one direction Sc 16 N 16 NP, the first six excitation energies appear at 2.03, 2.29, 2.49, 2.58, 2.73, and 2.87 eV, while for the elongated along two perpendicular directions Sc 16 N 16 NP, the relative excitation energies are 2.33, 2.41, 2.53, 2.70, 2.93, and 3.09 eV.Also, in the case of Sc 16 P 16 NP elongated along one direction, the absorption spectrum showed the first six excitation energies at 2.26, 2.36, 2.67, 2.80, 3.01, and 3.09 eV, while for the corresponding NPs elongated along two directions, the AS showed the corresponding energies at 2.16, 2.23, 2.51, 2.84, 3.09, and 3.24 eV.For Sc 16 As 16 NPs, the calculations showed the first six resonances at 2.07, 2.24, When the second part of the NP is phosphorus, the optical gap is 2.16 eV and 1.73 eV for Sc16P16 and Sc48P48 NPs, respectively, while the ΟS for Sc36P36 is much higher than other examined nanostructures in this category.Regarding the BE per f.u. for the studied NPs, the calculated values range between 9.91 eV and 10.41 eV.Also, the Sc36P36 NPs seem to be more stable than Sc32P32 NPs (with a hole in the center of their geometry) because they have a higher BE by 0.35 eV.
The calculations continued by considering arsenic as the second part of the examined NPs.The BE per f.u. of the smallest nanostructure (Sc16As16) elongated along two directions is 2.02 eV, while the oscillator strength ranges between 0.02 and 0.10.
A very interesting case from the nanostructures that are examined and created by elongation of the initial building block along one and two perpendicular directions is the one where x = 16.In Figure 6, the absorption spectra of these cases of Sc16Y16 NPs are shown.A notable general observation is that the most excitation energies are within the visible spectrum.More specifically, for the elongated along one direction Sc16N16 NP, the first six excitation energies appear at 2.03, 2.29, 2.49, 2.58, 2.73, and 2.87 eV, while for the elongated along two perpendicular directions Sc16N16 NP, the relative excitation energies are 2.33, 2.41, 2.53, 2.70, 2.93, and 3.09 eV.Also, in the case of Sc16P16 NP elongated along one direction, the absorption spectrum showed the first six excitation energies at 2.26, 2.36, 2.67, 2.80, 3.01, and 3.09 eV, while for the corresponding NPs elongated along two directions, the AS showed the corresponding energies at 2.16, 2.23, 2.51, 2.84, 3.09, and 3.24 eV.For Sc16As16 NPs, the calculations showed the first six resonances at 2.07, 2.24, 2.52, 2.80, 2.96, and 3.23 eV for those created from elongation along one direction and 2.02, 2.19, 2.30, Table 2. Binding energy (BE) per f.u., optical gap (OG), and oscillator strength (OS) for Sc x Y x NPs (x = 16, 24, 32, 36, 18 and Y = N, P, As), which were created after elongation of the initial cubic-like building block Sc 4 Y 4 (Y = N, P, As) along two directions.Style T refers to square-shaped structures in the first raw in Figure 8, and style-O refers to rectangular-shaped structures in the second raw in Figure 8.The calculated binding energy per f.u.versus the number of the formula (x) of each examined NP is shown in Figure 7.It is observed that the nanostructures that present higher BE per f.u. are those that have a lighter atom in the second part of the NP.It takes higher values for the case of nitrogen and a further decrease for the cases of phosphorus and arsenic.So, when the second part of the studied NP is N, P, and As, the BE per f.u.ranges between 10.48 and 12.16 eV, 8.5 and 10.38 eV, and 7.25 and 8.78 eV, respectively.Furthermore, for all cases of Sc x Y x (where Y = N, P, As), the corresponding curves have the same trend, i.e., when the formula number is less than 16, the BE per f.u.raises slightly, while when the x is greater than 36, the BE per f.u. is almost unchanged.Also, the flattening of the curve (in the case that x > 36) strongly indicates that the calculated values for the BE per f.u.would not differentiate significantly with the values of the bulk.The calculated binding energy per f.u.versus the number of the formula (x) of each examined NP is shown in Figure 7.It is observed that the nanostructures that present higher BE per f.u. are those that have a lighter atom in the second part of the NP.It takes higher values for the case of nitrogen and a further decrease for the cases of phosphorus and arsenic.So, when the second part of the studied NP is N, P, and As, the BE per f.u.ranges between 10.48 and 12.16 eV, 8.5 and 10.38 eV, and 7.25 and 8.78 eV, respectively.Furthermore, for all cases of ScxYx (where Y = N, P, As), the corresponding curves have the same trend, i.e., when the formula number is less than 16, the BE per f.u.raises slightly, while when the x is greater than 36, the BE per f.u. is almost unchanged.Also, the flattening of the curve (in the case that x > 36) strongly indicates that the calculated values for the BE per f.u.would not differentiate significantly with the values of the bulk.The calculated binding energy per f.u.versus the number of the formula (x) of each examined NP is shown in Figure 7.It is observed that the nanostructures that present higher BE per f.u. are those that have a lighter atom in the second part of the NP.It takes higher values for the case of nitrogen and a further decrease for the cases of phosphorus and arsenic.So, when the second part of the studied NP is N, P, and As, the BE per f.u.ranges between 10.48 and 12.16 eV, 8.5 and 10.38 eV, and 7.25 and 8.78 eV, respectively.Furthermore, for all cases of ScxYx (where Y = N, P, As), the corresponding curves have the same trend, i.e., when the formula number is less than 16, the BE per f.u.raises slightly, while when the x is greater than 36, the BE per f.u. is almost unchanged.Also, the flattening of the curve (in the case that x > 36) strongly indicates that the calculated values for the BE per f.u.would not differentiate significantly with the values of the bulk.

Sc x Y x Exotic NPs
The third category of scandium nanostructures studied in this work includes the exotic NPs, which are so named because of their morphology characteristics.The stability of these structures was checked by calculating their vibrational spectrum.No negative frequencies were found for the 24 different NPs shown.The general form of those structures is Sc x Y x , where Y = N, P, As and x ranges between 12 and 40.The studied exotic NPs are divided into two groups.The first group of exotic NPs includes structures whose morphology does not change (or only slightly changes) with their geometry optimization (Figure 8), while the second group includes nanostructures that change their shape (Figure 9).As we can observe from Figure 8, NPs have several familiar shapes.So, there are N with L-type (a, b c cases), with C-type (d case), with Z-type (e), with Cross-type (h,I with W-type (g), with O-type (n), and with D-type (o) shapes.Also, the (j) nanostruct consists of three crosses joined together (without a cube in the center for each cross), (l) nanostructure forms a 2D-cross, and the (m) one consists of two joined crosses.The three structures that did not change their morphology with geometry optimization are (p), (q), and (r) cases.The first one consists of two individual squares of 2 × 2 initial cub like building blocks, the second is formed by three identical squares, and the last comes from the previous structure, but by removing two cubes from the perimeter As we can observe from Figure 8, NPs have several familiar shapes.So, there are NPs with L-type (a, b c cases), with C-type (d case), with Z-type (e), with Cross-type (h, I, k), with W-type (g), with O-type (n), and with D-type (o) shapes.Also, the (j) nanostructure consists of three crosses joined together (without a cube in the center for each cross), the (l) nanostructure forms a 2D-cross, and the (m) one consists of two joined crosses.The last three structures that did not change their morphology with geometry optimization are the (p), (q), and (r) cases.The first one consists of two individual squares of 2 × 2 initial cubic-like building blocks, the second is formed by three identical squares, and the last one comes from the previous structure, but by removing two cubes from the perimeter (it looks like two letters ''Γs" are formed anti-diametrically).The initial configurations of the structures shown in Figure 8h,l are similar, except that the outer-left and out-right atoms (four on each side) have been removed in Figure 8h's case.After geometry optimization, the final configuration shown in Figure 8l has been almost the same as its initial configuration.However, the final configuration shown in Figure 8h has been significantly changed from its original configuration.This is a clear indication that the stable configurations consist of cubic-like building blocks Sc 4 Y 4 (Y = N, P, As).
The optical gap (OG), the oscillator strength (OS), and the BE per f.u. of the proposed optimized structures were numerically examined.The results of this set of calculations are shown in Table 3.Note that the structures, in which the OG has not been calculated, are not stable.When the second part of the studied NPs in this category is nitrogen, the optical gap takes various values between 1.65 and 2.34 eV, while the BE per f.u.varies from 11.30 eV to 11.86 eV.As we can observe, the structure of this category that has the minimum optical gap (1.65 eV) with the best resonance (0.09) and BE per atom (11.86 eV) is the Sc 40 N 40 NP (case q).When the second part of the exotic NPs is the phosphorus, the calculated OG is 1.95, 1.89, 1.88, 1.84, 1.82, 1.76, 1.74, and 1.72 eV, while the resonance is 0.05, 0.06, 0.12, 0.01, 0.10, 0.09, 0.05, and 0.14 for the cases (e), (l), (g), (f), (p), (o), (m), and (r), respectively.Also, the BE per f.u range is between 9.40 eV and 10.12 eV.In the case of arsenic, the optical gap is 1.98, 1.90, 1.89, 1.89, 1.84, 1.82, 1.81, 1.80, 1.75, and 1.73 eV for the cases (h), (i), (a), (c), (d), (b), (f), (n), (l), (p), (e), (g), and (r), respectively.Similarly to the aforementioned group of nanostructures, Sc 40 N 40 NP has the largest BE per atom (8.68 eV) and the strongest resonance (0.24), while its OG is 1.65 eV.Notable cases of this category are also (m) and (q) cases, in which the OG is 1.63 and 1.68 eV, respectively.
The second group of studied exotic NPs includes nanostructures that change their morphology after geometry optimization.Figure 9 shows all of the examined structures created again from the initial cubic-like building block and presents the initial and final nanostructures.It is noteworthy that the final morphology changes significantly when the second element is N, while the structures that have in the second element P or As the morphology remain almost unchanged.The final shape that each optimized NP is strongly related to is the initial shape before optimization.Also, for the T-type shapes, and for the C-type with the extensions (cases (a), (b), (c), and (d) of the relevant Figures), the final shape of the central building block of the optimized NP takes a hexagonal form.In Figure 9e,f, NPs with A-type and cross-H-type shapes are presented, respectively.It is observed that all optimized A-type NPs are similar to each other, while the cross-H-type Sc x As x NP is not stable and it is not presented.
The optical gap (OG), the oscillator strength, and the binding energy per f.u. of the proposed structures were also numerically examined.The results of this set of calculations are collected in Table 4.When the second part of the studied NPs in this category is nitrogen, the optical gap varies from 2.13 eV to 2.47 eV and the oscillator strength is weak, while the values for the BE per atom vary from 11.37 to 11.71 eV.Also, when the second part of the exotic NPs is the phosphorus, the calculated OG is 1.88, 1.85, and 1.76 eV, while the BE per f.u. is 9.75, 9.70, and 9.96 eV for the cases (d), (c), and (e), respectively.In the case of arsenic, the calculated OG is 2.09, 2.00, 1.94, 1.94, and 1.73 eV for the cases (a), (e), (b), (d), and (c), respectively.The smallest calculated value for the BE per f.u. is 5.14 eV and the larger is the 8.57 eV.
Therefore, among the most characteristic NPs studied is Sc 16 Y 16 (where Y = N, P, As), and the corresponding absorption spectra are shown in the following graphs.In Figure 10, an L-type Sc 12 Y 12 and Sc 16 Y 16 composed after elongation of the initial building block along one and two perpendicular directions are additionally shown.A notable general observation is that the exotic examined NPs have much weaker oscillator strengths than the elongated corresponding NPs.However, in the case of nitrogen, the absorption spectrum has an increasing trend, and it was calculated at 2.12, 2.22, 2.23, 2.29, and 2.42 eV for Z-type, Middle-type, L-type, Cross-type, and T-type NPs.The same behavior is observed regarding the case of phosphorus and arsenic.The optical gap takes values of 1.95 eV for Z-type, 2.06 for L-type, 2.08 for Middle-type, 2.11 for T-type, and 2.52 eV for Cross-type Sc 16 P 16 NPs, while the OG was calculated at 1.80, 1.89, 2.11, 2.20, and 2.27 eV for Z-type, Middle-L-type, T-type, L-type, and Cross-type of Sc 16 As 16 NPs, respectively.Table 3. Binding energy (BE) per f.u., optical gap (OG), and oscillator strength (OS) for exotic optimized Sc x Y x NPs (x ranges between 12 and 40 and Y = N, As, P), whose morphologies do not change (or only slightly change) with their geometry optimization.Cases and shapes are shown in Figure 8.

Conclusions
The structural, electronic, and optical properties of ScxYx NPs (where x = 4 up to 48 and Y = N, P As) were examined in this work.Using Particle Swarm Optimization (PSO), it was confirmed that for the case where x = 4, the structure with the lowest energy is the cubic-like building block.Α total of 34 different nanostructures were studied and created by elongation of the initial cubic-like building block, Sc4Y4 (Y = N, P, As), along one, two, and three perpendicular directions.Also, geometry optimizations and structural stability

Figure 1 .
Figure 1.The initial cubic-like building block Sc 4 Y 4 (Y = N, P, As).The top view refers to the top view of the cubes, while the bottom view refers to the side view (45 degree).The white color corresponds to the Sc atom, the blue one to the N atom, the orange one to the P atom, and the purple one to the As atom.

Figure 2 .
Figure 2. The UV/Vis absorbance spectra of the initial cubic-like building blocks of Sc4Y4 (Y = N, P, As) NPs.

Figure 2 . 20 Figure 3 .
Figure 2. The UV/Vis absorbance spectra of the initial cubic-like building blocks of Sc 4 Y 4 (Y = N, P, As) NPs.Nanomaterials 2023, 13, x FOR PEER REVIEW 5 of 20

Figure 3 .
Figure 3.The UV/Vis absorbance spectra of the initial cubic-like building blocks of Sc 8 Y 8 (Y = N, P, As) NPs.

Figure 4 .
Figure 4.The examined NPs (Sc x Y x , where x = 8, 16, 24), which were created after elongation of the initial cubic-like building block Sc 4 Y 4 (Y = P, N, As) along one direction.

Figure 5 .
Figure 5.The examined NPs (Sc x Y x , where x = 16, 24, 32, 36, and 48), which were created after elongation of the initial cubic-like building block Sc 4 Y 4 (Y = P, N, As) along two perpendicular directions.

Nanomaterials 2023 ,
13,  x FOR PEER REVIEW 9 of 20 2.60, 2.84, and 3.04 eV for the NPs that were created by elongation of the initial building block along two perpendicular directions..

Figure 6 .
Figure 6.The UV-visible spectra of Sc16Y16 (Y = N (a), P (b), As (c)) when considered after elongation along one direction (blue line) and two perpendicular directions (red line).

Figure 6 .
Figure 6.The UV-visible spectra of Sc 16 Y 16 (Y = N (a), P (b), As (c)) when considered after elongation along one direction (blue line) and two perpendicular directions (red line).

Figure 6 .
Figure 6.The UV-visible spectra of Sc16Y16 (Y = N (a), P (b), As (c)) when considered after elongation along one direction (blue line) and two perpendicular directions (red line).

Figure 7 .
Figure 7.The binding energy per f.u.(Eb) of the Sc x Y x NPs for all of the examined cases.

Figure 8 .
Figure 8. Exotic nanostructures with familiar shapes and their morphologies do not change slightly change) with their geometry optimization (ScxYx, where Y = N, P, As, and x varies to 40).Each morphology is the same for all the combinations of elements (N, P, As) studied

Figure 8 .
Figure 8. Exotic nanostructures with familiar shapes and their morphologies do not change (or only slightly change) with their geometry optimization (Sc x Y x , where Y = N, P, As, and x varies from 12 to 40).Each morphology is the same for all the combinations of elements (N, P, As) studied.

Figure 9 .
Figure 9. Exotic nanostructures with familiar shapes and their morphologies change with their ometry optimization (ScxYx, where Y = N, P, As, and x varies from 16 to 40).The structures wi green color are before geometry optimization, while the rest of the structures are optimized.blue, brown, and purple atoms refer to N, P, and As, respectively.

Figure 9 .
Figure 9. Exotic nanostructures with familiar shapes and their morphologies change with their geometry optimization (Sc x Y x , where Y = N, P, As, and x varies from 16 to 40).The structures with a green color are before geometry optimization, while the rest of the structures are optimized.The blue, brown, and purple atoms refer to N, P, and As, respectively.

Figure 10 .
Figure 10.The UV-visible spectra of exotic NPs ScxYx with familiar shapes (where (a) Y = N, (b) Y = P, (c) Y = As and x = 12 and 16) and examined Sc16Y16 (where (a) Y = N, (b) Y = P, (c) Y = As) created after elongation of the initial cubic-like building block.

Figure 10 .
Figure 10.The UV-visible spectra of exotic NPs ScxYx with familiar shapes (where (a) Y = N, (b) Y = P, (c) Y = As and x = 12 and 16) and examined Sc 16 Y 16 (where (a) Y = N, (b) Y = P, (c) Y = As) created after elongation of the initial cubic-like building block.

Table 4 .
Binding energy (BE) per f.u., optical gap (OG), and oscillator strength (OS) for exotic optimized Sc x Y x NPs (x ranges between 12 and 40 and Y = N, As, P), whose morphologies change with their geometry optimization.Cases and shapes refer to Figure9.