Stability and Reactivity of Silicon Magic Numbers Doped with

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Stability and Reactivity of Silicon Magic Numbers Doped with Aluminum and Phosphorus Atoms Gabriel F. S. Fernandes, Max Pinheiro Jr., Francisco Bolivar Correto Machado, and Luiz Fernando de Araujo Ferrão J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b10214 • Publication Date (Web): 04 Dec 2018 Downloaded from http://pubs.acs.org on December 9, 2018

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The Journal of Physical Chemistry

Stability and Reactivity of Silicon Magic Numbers Doped with Aluminum and Phosphorus Atoms Gabriel F.S. Fernandes1, Max Pinheiro Júnior1, Francisco B. C. Machado1, Luiz F. A. Ferrão1* 1Departamento

de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP

12228-900, Brasil.

__________________________________ *Corresponding author. E-mail address: [email protected]

ACS Paragon Plus Environment

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Abstract The progressive scaling down of the silicon-based electronics has allowed to develop devices at nanometer scale, requiring new engineering techniques guided by fundamental chemical and physical concepts. Particularly, the nanostructured cluster systems are promising materials since their physical-chemical properties are sensitive to its shape, size and chemical components, such that completely different materials can be produced by the simple addition or removal of a single atom. These size-tunable properties can open a new area in materials science and engineering. In the present work, quantum chemical methods were used to study the chemical substitution effects caused by subvalent (aluminum) and supervalent (phosphorus) atoms in the physical-chemical properties of some small silicon clusters which demonstrate high stability, called magic numbers. The changes in the electronic structure and chemical acceptance to the dopants were evaluated with respect to: ionization potential, electronic excitation energy, stability and reactivity parameters. Taken together, these results enable to identify the most stable silicon-doped clusters. Regarding electrophilic reactions, Si10P is the most favorable system, while for nucleophilic reactions, none of the doped clusters resulted in higher stability.


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I. Introduction The tremendous increasing rate of electronic device miniaturization over the past decade, pushing the limits of the Moore’s law1–4, has enabled the industrial production of silicon transistors with tens of nanometers using top-down techniques, such as extreme ultraviolet lithography5,6. In laboratorial scale, 1 nm transistor gate length has become a reality, been synthesized by atomic layer deposition (ALD) technique of ZrO2 in single wall carbon nanotube (SWNCT) followed by pick-and-place dry transfer of MoS2 onto the SWCNT covered with ZrO27. This capacity to synthesize nanomaterials made of few atoms with pre-defined positions allow the development of devices with specific properties and application in many technological areas8, such as chemical sensors9–11, solar cells12,13 and catalysis14–22, for example. This broad range of applications of nanomaterials in industry rise due to the ability to modulate their electronic structure by tailoring the composition, size and topology, thus resulting in a non-linear size dependent behavior of their properties not observed in the bulk material Also, they can be applied as building blocks in the development of new materials23–25. Recently, functionalized nanodevices built by silicon clusters arranged in cage-like structures were proposed because of their unique opto-electronic and magnetic properties26. Silicon nanoclusters, Si2-11, were extensively studied by previous theoretical and experimental works27–37, focusing in the global minimum, electronic structure and magic numbers (n = 4, 6, 7 and 10) characterization. However, none of these works have systematically sought to characterize cage-like silicon clusters, since their experimental formation is difficult to obtain because of their sp3 hybridization38–40. Cage-like structure was experimentally observed on small fullerene cluster (C28) by uranium addition inside the



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carbon cluster41. Motivated by this work41, Jackson and Nellermoe40 studied the chemical substitution on Si20 cage structure with carbon, oxygen, germanium, tin, selenium and zirconium atoms by means of density function theory (DFT) within local density functional approximation (LDA), and found zirconium as the best candidate atom to stabilize the silicon cage. Previous theoretical and experimental works26,42–53 have also demonstrated that the transition metal atoms are encapsulated by silicon clusters, showing a relation between the transition metal valence with the silicon cluster size. Kulshreshtha et al.47 doped Si10 cluster with lithium, sodium, beryllium, magnesium, boron, aluminum and carbon using B3LYP/631G(d) methodology, showing that the beryllium atom is the only one able to form the cagelike structure. The choice of aluminum as dopant atom in the silicon clusters is motivated by at least four observations: firstly, the self-assembled aluminum-silicon nanowires networks on glass and silicon substrates54; secondly, the electrical conductivity enhancement in silicon nanowires (SiNW) as compared to pristine SiNW55. Thirdly, the formation of superlattice on the Si (111) 7x7 surface of identical-size nanoclusters (magic clusters)56 and, lastly, by its electronic structure that has one less electron than the silicon, corresponding to the cation Si. The phosphorus atom was selected based on its application on the semiconductor industry as p-dopant type, its behavior as the anion Si and electron donor in SiNW57. Previous theoretical works51,58 characterized the global minimum of the aluminum doped silicon clusters series (Si1-13Al) through density functional theory (B3LYP/6-31(d)) and molecular dynamics. Energetics properties of these molecular systems such as binding energy, dissociation energy and fragmentation energy were determined. Tam et al.59,60 studied the stability and electronic structure of both aluminum and phosphorus doped silicon


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clusters, SinAlm// and SinPm// with n = 1 – 10 and m = 1 – 2, by DFT methodology (B3LYP/6-31+G(d)). The stability analysis was also carried out by dissociation and clustering energies, while the electronic structure was described employing the jellium model61, in which density of states (DOS) was performed for the closed shell clusters. The present work focuses in study the chemical doping effects caused by subvalent (aluminum) and supervalent (phosphorus) atoms in the physical-chemical properties on silicon clusters Sin, n = 6, 7, 10 and 11. These systems were chosen by their remarkable high/low (Si6, Si7, Si10) or low/high (Si11) stability/reactivity, when compared to neighbor clusters (in size). In particular, Si11 was chosen as a counterexample of the most stable clusters (Si6, Si7, Si10) in the silicon series (Si2-11). Therefore, from a quantum chemical perspective, it is an interesting system to be investigated in terms of electronic structure changes induced by the doping species that could eventually lead to improved stabilization properties. To analyze the physical-chemical properties of the doped silicon clusters, simple stability and reactivity descriptors derived from wavefunction methodologies were considered, namely, the Hartree-Fock method and the multiconfigurational approach CASPT2. As a starting point to investigate the electronic properties, the Hartree-Fock orbitals diagram was employed, in special, the highest occupied molecular orbital (HOMO). The multiconfigurational CASPT2 method was applied to compute the vertical excitation energy (Te) and the electronic density variation due to the doping. The chemical stability was probed by means of our previously developed 3 function37, which encompasses both thermodynamical and kinetic aspects of the systems based on the HOMO energy, vertical excitation energy and the atomization free energy. Also, the reactivity was studied using Fukui’s functions62–66 calculated by electronic density of the neutral and ionic species.



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II. Computational Methods The initial structures can be built by using sophisticated techniques such as the particle swarm optimization method67–78 or global optimization methods, e.g. basin hopping (BH)79, simulated annealing80, minima hopping (MH)81,82, genetic algorithm (GA)82,83, funneling hopping (FH)84 and random sampling search85. Alternatively, an initial space of isomers can also be obtained by simpler techniques, as it was employed in the present work, by performing substitution23,44,47,50,86 and addition (exohedral) routes 23,42,47,52,87, as shown in Fig.1. Also, point group symmetry was considered to construct structures27–36 which were not taken into account by the substitution or addition routes when incorporating aluminum and phosphorus atoms on the pure silicon clusters37. For each starting structure, the allowed spin multiplicities were also considered. Single doped clusters exhibit an odd number of electrons, then only doublet and quartet spin multiplicity were considered. For the double doped structures, singlet and triplet states were computed. The initial structures were optimized using density functional theory within a hybrid meta-GGA approximation, M0688, combined with 6-311++G(3df,3pd) basis set89. Frequencies analysis was carried out to identify any possible saddle point and the global minimum was determined employing zeropoint energy correction on the total electronic energy. The ground state total energy was further corrected with single-point calculations by perturbation theory to the second order (MS-CASPT2)90–95, which uses as the zero order wave function the complete active self-consistent field (CASSCF)96,97 at the same atomic basis set, 6-311++G(3df,3pd)89. The CASSCF wave function was built in a state-average fashion, including the ground state and the first excited electronic state. For each doped silicon cluster, an analysis of the natural orbitals occupations of a preliminary averaged quadradic coupled cluster (AQCC) calculation was performed to select the most adequate ACS Paragon Plus Environment

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active space orbitals for the CASSCF and CASPT2 wavefunctions. Orbitals with occupations in the range of 0.1 to 1.9 were included in the CASSCF wavefunction and correlated in the perturbation step, the resulting active spaces for all systems are displayed on Table S1. In the CASPT2 calculation, a level shift (0.1 hartree) was included to remove possible intruder states in the excited states calculations98.

Figure 1. Doped silicon clusters addition and substitution scheme, showing some doping possibilities. All the non-equivalent doping positions were considered as starting geometries of a given system. Red and blue colors refers to the dopant. The chemical substitution effects on the electronic structure of the silicon clusters were evaluated through the molecular orbitals energy diagrams, vertical excitation energy and the electronic density variation under the addition (phosphorus) or removal (aluminum) of an electron. Hartree-Fock orbitals energy diagrams were selected to analyze the electronic structure of the silicon doped clusters since the HOMO energy have physical significance, as the ionization energy by Koopman's theorem. From the characterization of the first excited



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electronic states, the vertical excitation energy and electronic density difference between the excited state and ground state were obtained using the single-point CASPT2//M06/6311++G(3df,3pd) methodology. Applying the single-point methodology, the electron addition or removal effects caused by the subvalent and supervalent substitution on the electronic density of the silicon clusters was evaluated performing an electronic density difference between the doped silicon cluster and pure silicon cluster. An estimate of the chemical affinity between the silicon clusters and the doping atoms was performed through the 3 function, recently proposed in our previous work.37 The 3 function37 is a stability ranking function composed by a thermodynamical descriptor, the atomization free energy (∆G°atom, 298K), and two indirect kinetics descriptors, the HOMO energy (homo) and vertical excitation energy (Te). ε3 = |∆𝐺°𝑎𝑡𝑜𝑚, 298𝐾| ∗ | εℎ𝑜𝑚𝑜| ∗ |𝑇𝑒|

(1)

The reactivity of the doped silicon clusters was studied using the Fukui’s functions62– 66, f(r)

and f(r). It has been showed that the Fukui’s functions are useful tools to identify

nucleophilic, electrophilic and radicalar chemical reactions sites62–66, since these functions are based on the variation of the number of electrons in the molecule. Anionic and cationic structures were optimized using the same methodology applied on the neutral clusters (M06/6-311++G(3df,3pd)). From the optimized geometries, the Fukui’s functions were calculated using the electronic density and Mulliken charge difference between the neutral and ionic structures, in both cases. The electronic densities of the neutral and ionics species were calculated separately using the single-point CASPT2//M06/6-311++G(3df,3pd) methodology, as given by the equations 1 - 4 below.


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𝑓 + (𝑟) = 𝜌𝑆𝑖𝑛―― 1𝐴𝑙/𝑃 ― 𝜌𝑆𝑖𝑛 ― 1𝐴𝑙/𝑃

(2)

𝑓 + (𝑟) = 𝜌𝑆𝑖𝑛―― 2𝐴𝑙𝑃 ― 𝜌𝑆𝑖𝑛 ― 2𝐴𝑙𝑃

(3)

𝑓 ― (𝑟) = 𝜌𝑆𝑖𝑛 ― 1𝐴𝑙/𝑃 ― 𝜌𝑆𝑖𝑛+― 1𝐴𝑙/𝑃

(4)

𝑓 ― (𝑟) = 𝜌𝑆𝑖𝑛 ― 2𝐴𝑙𝑃 ― 𝜌𝑆𝑖𝑛+― 2𝐴𝑙𝑃

(5)

The electronic density differences were plotted using an isosurface value of 0.003. The difference between the doped and pure silicon clusters was plotted on the doped cluster geometry, and the Fukui’s functions difference was plotted on the neutral cluster geometry. Performing the electronic density calculation in separated geometries did not show any significant changes from the electronic densities calculated in the same geometry. The electronic density colors red and blue shows the electronic redistribution on the molecule. The red color refers to electron poor regions in the molecule and the blue color is related to electron rich regions when compared to the reference density, i.e., the anion compared to the neutral system for f(r) and the neutral compared to the cation system for f(r). The geometry optimization was performed using the Gaussian 09 package99 and the CASSCF and CASPT2 calculations by Molpro 2015100.

III. Results and Discussions The atomization Free Gibbs energy, atomization enthalpy, electronic excitation energy, transition moment, electronic configuration, the cartesian coordinates of the characterized isomers are displayed in the supplementary material on Fig.S1, Table S2, S3, S4, respectively. Reactive parameters such as Fukui’s functions (f f f), global hardness



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(), local softness (sk, sk, sk) (calculated by Mulliken charge) are gathered on Table S5 and the Mulliken charge are collected on Table S6.

A. Structural properties The optimized ground state geometries of Sin-a-bAlaPb characterized by M06/6311++G(3df,3pd) are shown in Fig.2, while the cartesian coordinates are presented in Table S4 in the supplementary material.

Figure 2. Ground state geometries optimized of Sin-a-bAlaPb (n= 6, 7, 10 and 11; a, b =0, 1) with 6-311++G(3df,3pd). Orange refers to the phosphorus atom and beige to the aluminum atom. The chemical substitution behavior of the aluminum and phosphorus atoms on the silicon clusters differs from the one observed in semiconductors of type p and n. In solidstate physics, the chemical doping behavior substitutional (substituting matrix atom for


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dopant atom) or interstitial (dopant atom added in structural sites) is predicted by HumeRothery101 rules, but these rules might not be applicable to nanometric systems. If the HumeRothery rules were valid, the aluminum doping would have a substitutional character while the phosphorus doping would present an interstitial behavior in the case of silicon crystal. However, in the nanoclusters systems, the aluminum and phosphorus doping character are correlated with the cluster size, as illustrated in Fig.2. In the case of six atoms clusters, n = 6, aluminum atom substitutes one silicon atom on Si6, exhibiting a substitutional behavior and the phosphorus chemical substitution presents a hollow addition on Si5, characterizing an interstitial doping, which, in this case, agrees with Hume-Rothery rules101. But in the Si4AlP cluster the doping behavior is inverted, the phosphorous doping presents a substitutional character and the aluminum chemical substitution has a bridge addition site. For the remaining doped clusters, n = 7, 10 and 11, the aluminum and phosphorus chemical doping behavior are the same for clusters with the same size. For n = 7, the chemical substitution presents a substitutional character, while on the n = 10 and 11 possess a hollow addition nature. Based on the Mulliken charge and the electronic density distribution on the doped silicon clusters, Table S6 and Fig.4, respectively, the chemical substitution sites on the pure silicon clusters can be associated to the charge transferred between the dopants and the silicon cluster. The aluminum sites tend to be the ones that provide less electrons to the silicon cluster, while the phosphorus sites are the ones that acquire electrons from the silicon atoms. The charge transferred is also related to the dopant coordination number and the cluster size. The coordination number (number of neighboring atoms) can be also associated to the dopant electronegativity. In the subvalent chemical substitution, the aluminum coordination number



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tend to be as minimal as possible, since presents lower values of electronegativity. The opposite occurs in the case of the supervalent chemical substitution, where the phosphorus coordination number tend to be as maximal as possible. It is found that there is an enhancement of the charge transfer effect as the cluster size increases, (probably) due to the large pool of valence electrons provided by the neighboring silicon atoms. Therefore, as bigger is the cluster, more electrons are available and consequently, more negative charge is transferred to the dopant. However, there are some exceptions to the cluster size effect on the charge transfer, such as Si10Al and Si10P. On the Si10Al cluster, the aluminum atom coordinates only three atoms (as in Si9Al) rather than four, as seen in Si5Al and Si6Al. In this way, it acquires more negative charge from the silicon cluster. On the other hand, the phosphorus atom on the Si10P has its lower coordination number and also the lowest negative charge. In contrast to the donor character of the phosphorus atom seen in crystalline silicon or silicon nanoparticles, the phosphorus atoms present an acceptor behavior when doping small silicon clusters such as those studied in this work. Therefore, there is a balance between the cluster size and the doping atom coordination number on the charge transferred to the dopant. B. Electronic structure In general, molecular systems near and in the equilibrium region can be adequately described by a monoconfigurational wavefunction. In this sense, the Hartree-Fock method can be considered as a good starting-point to qualitatively describe the electronic groundstate, providing molecular orbital energies with physical interpretation.


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Figure 3. Orbital energy diagram obtained with the RHF//M06/6-311++G(3df,3pd) method for the studied clusters. The red and blue colors refer to the contribution of the aluminum and phosphorous atomic orbitals to each molecular orbital. The physical interpretation of the Hartree-Fock orbital is focused in the frontier orbitals, HOMO and LUMO. As it is well known, the HOMO energy can represent the ionization potential (Koopman’s theorem) being associated to the strength of the weakest electron bonded in the molecular system and indicate, in some extent, the stability of the cluster. Although more inaccurately due to the lack of electron correlation, the LUMO energy can still be correlated to the electron affinity, providing information about the electronacceptor character of the system. Based on this interpretation, the chemical substitution (Al,



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P, or AlP) on all studied silicon clusters (Si6, Si7 and Si10), except for Si11, result in less bonded doped clusters, as suggested by the increase of the HOMO energy of these systems, shown in Fig.3. As expected, the silicon clusters with high stability (Si6, Si7 and Si10) do not accept substitutions, even the isoelectronic substitution (a subvalent and a supervalent substitution). On the other hand, the highly unstable Si11, benefits from any substitution, but mostly from the subvalent and supervalent chemical doping. In addition to providing information on the physical-chemical properties, ionization potential and electron-acceptor behavior, the Hartree-Fock orbitals diagram indicates how occurs the chemical bond among the atoms. Variations in the molecular orbital energy of the pure clusters indicates how the atomic orbitals of the dopants interacts with the silicon clusters molecular orbitals. Comparing the subvalent and supervalent substitution changes on the pure silicon cluster molecular orbitals (Fig.3), the aluminum atomic orbitals participate more of the frontier orbitals formation than the phosphorus orbitals, causing lower variations on the HOMO energy than the phosphorus substitution, suggesting the possibility of the Sin1Al

clusters be more bonded than the Sin-1P. However, the subvalent substitution also lowers

the energy of molecular orbitals that are mostly formed by silicon atoms, indicating an increment on the cohesion energy, and suggests that the phosphorus orbitals contribute more on the internal molecular orbitals.


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Figure 4. Electronic density difference between the doped and pure silicon clusters obtained through CASPT2//M06/6-311++G(3df,3pd) with isosurface value of 0.003 𝑒.𝑏𝑜ℎ𝑟 ―3. Yellow and white circles refers to aluminum and phosphorus atoms, respectively. In order to qualitatively evaluate the charge transfer, discussed in the geometry section, the electronic density between the doped and pure silicon clusters was employed to analyze the addition (phosphorus) or removal (aluminum) of one electron in the electronic density, displayed in Fig.4. In the smallest aluminum doped clusters, n = 6 and 7, the dopant atom is under poor regions of electronic density (red color), thus suggesting a charge transfer from the aluminum to the neighboring silicon atoms. However, this charge transfer direction is inverted on the larger clusters (n = 10 and 11), where the aluminum atom is under the rich region of electronic density (blue color), acting as an electron acceptor center on the silicon cluster. On the other hand, the supervalent substitution redistributes a significant part of the electronic density to the dopant surroundings, and therefore, the phosphorus atom behaves as



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electron acceptor site, due its higher electronegativity. When both doping atoms are present on the doped cluster, the electrons are basically transferred from the aluminum atom to the phosphorus atom direction, especially on the Si4AlP and Si5AlP. These results are consistent with the analysis of atomic charge distribution based on Mulliken population. (Table S6 in the supplementary material).

Figure 5. Electronic difference between the ground state and the first excited state of the doped silicon clusters obtained using CASPT2//M06/6-311++G(3df,3pd) with isosurface value of 0.003 𝑒.𝑏𝑜ℎ𝑟 ―3. A quantitative analysis of the electronic structure (Tables S2 and S3) was carried out by vertical excitations on the electronic ground state through the single-point CASPT2 methodology. For the phosphorus doped nanoclusters, Sin-1P and Sin-2AlP, the first excited state corresponds to one electron promotion characterized as the HOMO–LUMO transition, observed previously for the Si2-11 series27–37, except for Si5P cluster, in which the transition


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corresponds to one electron excitation from the HOMO-1 to singly occupied molecular orbital (SOMO), as seen for the aluminum doped clusters (Sin-1Al). This HOMO-1–SOMO transition has lower excitation energy than the HOMO–LUMO transition. Concerning to the electronic ground state, the wave function of almost all doped (Al or P and AlP) structures preservers the monoconfigurational character observed on the pure silicon clusters37, except for Si5P and Si9Al clusters. As one goes to the excited states, there is a significant wave function multiconfigurational character for the Si5P, Si5AlP, Si9Al, Si8AlP, Si10Al and Si9AlP clusters, as seen in Table S3. To evaluate the consistency of the Hartree-Fock method to describe the electronic structure, we can compare the electron displacement on the cluster provided by the electronic density difference between the ground state and excited state calculated by our single-point CASPT2 methodology, with the atomic orbitals contribution on the molecular orbital construction obtained by the RHF methodology. The electronic transitions occurs among the HOMO-1, HOMO (isoelectronic) or SOMO (subvalent and supervalent) and LUMO, these molecular orbitals are considered in the analysis of Fig.3. Taken together, the results of Fig.3 and Fig.5, one can see that the atoms largely contributing for the electronic density variations upon excitation are the same which have strong participation in the construction of the Hartree-Fock molecular orbitals. The Hartree-Fock electronic structure differs from the CASPT2 for the Si10Al and Si10P clusters. Therefore, the Hartree-Fock wave function is in qualitatively good agreement with the CASPT2 methodology.



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C. Stability and reactivity The stability and reactivity of a molecular system can be used to estimate which chemical substitution and silicon cluster combination produce favorable doped clusters. Variations in the molecular system stability can be used as a parameter to evaluate the chemical affinity of a given molecular system with respect to the introduction of a dopant atom. Which is investigated here by means of the 3 function (Fig.6). The ability of a molecule to react is related to the electronic density of the frontier orbitals, since these regions represent the reactive regions to an electrophilic and nucleophilic reaction. To determine these reactive sites, Fukui’s functions (f(r) and f(r))62–66 (Fig.7) use the variation of the spatial electronic distribution (density) in respect to the number of electrons, as given in equations 1 - 4.

Figure 6. Stability ranking function (3), applied on doped silicon clusters. Color black, red, blue and green refers to n =6, 7, 10 and 11, respectively.


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As discussed in detail in our previous study37, small values of 3 indicates low stability, while large values represents high stability. In this way, in Fig.6, the 3 function37 demonstrates that the Si11 has a higher acceptance degree to the chemical substitutions (Al, P or AlP) than the Si6, Si7 and Si10 clusters, since the doped silicon clusters (Si10Al, Si10P and Si9AlP) possess higher values of 3 than the Si11, indicating a higher stability. The Si6, Si7 and Si10 clusters have lower acceptance degree because they are more stable than their respective doped structure. These results could be expected, based on the fact that, the Si11 is one of the less stable on the Si2-11 series and the Si6, Si7 and Si10 are the most stable ones37. In general, the double substitution (AlP) produces more stable clusters than the monodoping (Al or P), once they combine both aluminum and phosphorus stability properties; the increase on the strength of the weakest chemical bond and the increase on the cohesion energy, respectively.



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Figure 7. Fukui's functions calculated using electronic density difference between the neutral and ionics species obtained using CASPT2//M06/6-311++G(3df,3pd) with isosurface value of 0.003 𝑒.𝑏𝑜ℎ𝑟 ―3. Yellow and white circles refers to aluminum and phosphorus atoms, respectively. From the Fukui's functions, Fig.7, in general, one can infer that the chemical substitution tends to increase the Si6, Si7 and Si10 reactivity due to the significant increment of the electronic density volume. However, no significant variation on the electronic density volume were observed for the Si6Al and Si9P (electrophilic reactions, f(r)), and Si4AlP, Si9Al and Si9P (nucleophilic reactions, f(r)). The chemical substitutions effects on the Si11 reactivity, suggest to produce high reactive species (Si10Al, Si10P), since their electronic density volume are equal or higher than the Si11. This extremely reactive character occurs by the presence of the electronic density covering the whole doped structure, except for Si10P,


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whose reactivity drastically decreases, indicating a kinetic stability for electrophilic reactions. Combining the stability and reactivity analysis, one can conclude that the clusters with higher stability and lower reactivity are prompter to be formed. Magic numbers (n= 6, 7 and 10) still are the stable ones among the studied clusters, considering clusters with same size. And, the Si11 possess, exclusively, a chemical substitution acceptor character, if stability analysis is considered individually. However, if the reactivity is also considered, the results indicate that the synthesis of the Si10P can be achieved. The others studied doped silicon clusters are more unstable and reactive than their pure silicon counterparts.

IV. Conclusions The doping effects in the physical-chemistry properties caused by subvalent and supervalent atoms, aluminum and phosphorus, on the Si6, Si7, Si10 and Si11 silicon clusters were studied using molecular quantum chemistry methods. The applicability of the HumeRothery rules, were tested in nanometric systems, comparing the aluminum and phosphorus substitution character observed on the doped clusters with the Hume-Rothery predictions. It was observed that the chemical doping character changes according to the cluster size, i.e., a size-dependent property, differing from the Hume-Rothery predictions. The most probable substitution sites were determined combining the Mulliken charge and the electronic density difference between the doped and pure silicon cluster. We noticed that aluminum and phosphorus preferable sites are related to the negative charge transferred between the dopant and the silicon cluster, where the aluminum position are the ones that transfer less electrons



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and the phosphorus sites the ones that acquires electrons. Using the energy diagram of the Hartree-Fock orbitals, we could, in a qualitative approach, evaluate changes on the weakest bond and electron acceptor behavior of the systems, showing that the chemical substitution, except for Si11, produced less bonded clusters. With respect to the wave function character, the chemical substitutions maintain the ground state monoconfigurational behavior observed on the silicon clusters. Regarding the vertical excitation energies, the subvalent substitution lowered the excitation energy by changing the molecular orbitals involved on the electronic transition. Combining the stability and reactivity analysis, the most favorable chemical substitution on the studied silicon clusters can be pointed out. Considering an electrophilic environment, the Si10P is the most probable cluster to be found, while for nucleophilic reactions, none of the doped clusters resulted in higher stability. Supporting Information The atomization Free Gibbs energy, atomization enthalpy, electronic excitation energy, transition moment, electronic configuration, the cartesian coordinates of the characterized isomers are displayed in the supplementary material on Fig.S1, Table S2, S3, S4, respectively. Reactive parameters such as Fukui’s functions (f f f), global hardness (), local softness (sk, sk, sk) (calculated by Mulliken charge) are gathered on Table S5 and the Mulliken charge are collected on Table S6.

Acknowledgements This work has been supported by Brazilian agencies Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) under grants 2017/07707-3 and 2017/01359-3, Conselho


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Nacional de Desenvolvimento Científico e Tecnológico (CNPq) under grants 307052/20168,

404337/2016-3,

309051/2016-9

and

406107/2016-5

and

Coordenação

de

Aperfeiçoamento de Pessoal de Nível Superior (CAPES) under Project CAPES/ITA Project No. 88882.161993/2017-01.

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TOC Graphic


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Doped silicon clusters addition and substitution scheme, showing some doping possibilities. All the nonequivalent doping positions were considered as starting geometries of a given system. Red and blue colors refers to the dopant. 338x190mm (96 x 96 DPI)



Ground state geometries optimized of Sin-a-bAlaPb (n= 6, 7, 10 and 11; a, b =0, 1) with 6311++G(3df,3pd). Orange refers to the phosphorus atom and beige to the aluminum atom. 338x190mm (96 x 96 DPI)


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Orbital energy diagram obtained with the RHF//M06/6-311++G(3df,3pd) method for the studied clusters. The red and blue colors refer to the contribution of the aluminum and phosphorous atomic orbitals to each molecular orbital. 169x131mm (300 x 300 DPI)



Electronic density difference between the doped and pure silicon clusters obtained through CASPT2//M06/6311++G(3df,3pd) with isosurface value of 0.003 e.bohr-3. Yellow and white circles refers to aluminum and phosphorus atoms, respectively. 338x190mm (96 x 96 DPI)


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Electronic difference between the ground state and the first excited state of the doped silicon clusters obtained using CASPT2//M06/6-311++G(3df,3pd) with isosurface value of 0.003 e.bohr-3. 338x190mm (96 x 96 DPI)



Stability ranking function (ε3), applied on doped silicon clusters. Color black, red, blue and green refers to n =6, 7, 10 and 11, respectively. 169x130mm (300 x 300 DPI)


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Fukui's functions calculated using electronic density difference between the neutral and ionics species obtained using CASPT2//M06/6-311++G(3df,3pd) with isosurface value of 0.003 e.bohr-3. Yellow and white circles refers to aluminum and phosphorus atoms, respectively. 338x190mm (96 x 96 DPI)


Stability and Reactivity of Silicon Magic Numbers Doped with

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