Aromatic-like behavior of germanium nanocrystals

Abstract

Based on density functional theory calculations, aromatic germanium nanocrystals Ge₁₉H₁₂, which are composed of three parallel, planar hexagons with one additional Ge atom close to the cluster center, have been predicted. By exploring electron deficiency and electron delocalization in the proposed nanocrystals, the definition of the electron-deficiency aromaticity concept is extended to germanium nanocrystals. The natural bond orbital analysis and nucleus independent chemical shifts have been used to investigate the electron delocalization in the nanocrystals. We show new patterns for the optical spectrum of Ge₁₉H₁₂ which may be attributed to the special electronic structure of the studied nanoparticles. This study reports relevant details for the synthesis and structuring of overcoordinated germanium nanocrystals and deserves further work for the development of germanium-based nanoparticles for energy and microengineering purposes.

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1. Introduction

Aromaticity, which was originally developed to account for the properties of planar organic molecules, has been recognized as a useful concept in structure stability of aromatic hydrocarbons. In general, aromaticity is not an observable and measurable quantity. Despite the lack of a clear and unambiguous definition of aromaticity, however, the conventional carbon aromaticity is referring to the electronic cyclic delocalization in aromatic species. This concept has nowadays extended to involve inorganic systems.^1–5 More recently, based on first principal calculations, Vach proposed a novel approach to induce electron delocalization and, hence, aromatic-like behavior in silicon nanocrystals Si NCs.^6,7 The ultrastable Si₁₉H₁₂ is composed of three parallel, planar hexagons with one additional Si atom close to the cluster center causing its hypervalent and electron-deficient character. We like to remind you here that “ultrastable” does not necessarily mean global minimum energy structure, but rather that the electron deficiency induces strong electron delocalization that leads to non-tetrahedral entities that are more stable than their tetrahedral counterparts.⁸ Consequently, the use of those non-tetrahedral nanocrystals for the fabrication of nanodevices in realistic plasma reactors has been predicted. In an extensive quantum chemical study, we considered a series of modifications on hydrogenated silicon nanocluster, with additional insertion of one silicon Si or one Ge atom close to the center of the selected Si₁₈X₁₂ nanostructures, where X = F, Cl, Br, NH₂, COOH, and OH.⁹ Our calculations shown a series of new patterns for optical, chemical, electronic, and conductive properties, which can be attributed to the special structure and modifications by various substitutional molecular groups of silicon nanoparticles.

Silicon and germanium nanocrystals have emerged as one of the most intriguing candidates to control quantum phenomena at the nanoscale. This control leads to outstanding properties and make them to a wide field of applications ranging from memory devices, solar cells, optoelectronic devices and the use as biomarkers.^10–14 Compared with Si, Ge has larger excitonic Bohr radius which implies more prominent quantum confinement effects than that of Si.¹⁵ In general, the pure Ge clusters are known to be chemically reactive and not quite stable and suitable as building blocks of self-assembly materials.¹⁶ By using an appropriate dopant, it is however possible to modify the cluster chemical properties but those metals are often expensive or toxic.

The presence of aromaticity in silicon nanocrystals raises the question whether Ge can be able to form such aromatic-like behavior nanocrystals? In other words, the proposed new concept of electron-deficiency aromaticity might be expended to germanium nanocrystals Ge NCs showing a tendency to overcoordination? In this study, we predict the existence of hydrogenated germanium nanocrystals Ge₁₉H₁₂; see Fig. 1, which has remarkably similar properties to Si₁₉H₁₂. The studied overcoordinated nanocrystals exhibits a highly aromatic character and potential applications in nanotechnological systems. By using density functional theory DFT calculations, we will explore the origin of electron delocalization and aromaticity properties of studied germanium nanocrystals. In addition, Ge₁₉H₁₂ nanocrystals exhibits enhanced stability compared to empty Ge₁₈H₁₂ that can be rationalized by the presence of aromaticity in overcoordinated Ge₁₉H₁₂. The results obtained in this paper extend the bonding capacity of germanium to planar hexacoordination in pure Ge NCs with new pattern for optical properties without the need for expensive or toxic metal atoms. Due to the technological importance of aromatic derivatives, we believe that the proposed Ge NCs with aromatic-like behavior will show an attractive future studies. Therefore, such aromatic NCs, if successfully synthesized, could have application areas ranging from photovoltaic, light-emitting and memory devices to photothermal cancer treatment.

Fig. 1 Optimized structures of (A) Ge₁₈H₁₂; (B) Ge₁₉H₁₂, peripheral germanium atoms (Ge_P), middle-layer germanium atoms (Ge_M) and the central germanium atom (Ge_C).

2. Computational details

The Ge₁₈H₁₂ and Ge₁₉H₁₂ nanocrystals were optimized in Gaussian 03 (ref. 17) and using the B3LYP functional¹⁸ with the 6-31G* basis set.¹⁹ Frequency calculations of the optimized structures were carried out to find the true minima on the potential energy surface and did not show any imaginary frequency for optimized nanocrystals. Single point energy calculations were carried on the optimized geometry at MP2/6-311++G** level.^20,21 The same package was used to calculate optical absorption spectra using time-dependent density-functional theory (TDDFT) at B3LYP/6-31G* level. For each structure, 150 singlet excited states were computed for the absorption spectra. Natural population analysis (NPA) was conducted using the NBO3.1 module embedded in the Gaussian package. For each donor–acceptor NBO interactions, the stabilization energy E⁽²⁾ associated with electron delocalization between donor and acceptor is estimated as:where q_i is the orbital occupancy, ε_j, ε_i are diagonal elements and F_i,j is the off-diagonal NBO Fock matrix element.

Mayer bond order calculations were performed using Multiwfn 3.3.8.²² Density of states diagram analysis were done via GaussSum 3.0 program.²³

The optimized structures of molecules were used as input to calculation of magnetic susceptibility Λ and nuclear independent chemical shift NICS parameters using gauge included atomic orbital, GIOA, method²⁴ by DFT/B3LYP level and 6-311++G** basis set. Negative NICS values indicate aromaticity and positive NICS values denote antiaromaticity of the system.

3. Results and discussion

To obtain all necessary information regarding the properties of proposed Ge NCs, it is desirable to perform a complete characterization that includes structural, geometry, electronic and optical specifications. In the following subsections we will do as is desired.

3.1. Geometry, stability, DOS

The empty Ge₁₈H₁₂ and the endohedrally filled Ge₁₉H₁₂ were optimized without any symmetry constrained at B3LYP/6-31G(d) level of theory, see Fig. 1. The calculated first frequencies 94.42 cm⁻¹, 73.38 cm⁻¹ for Ge₁₈H₁₂ and Ge₁₉H₁₂, respectively, indicate that the clusters to be stable. In order to better understand the properties of the studied Ge NCs, we first compare their geometry and stability. As shown in Fig. 1, both Ge NCs are composed of three parallel and planer hexagons with one additional Ge atom close to the cluster center in the case of Ge₁₉H₁₂. Also, three types of Ge atoms can be classified; Ge_P and Ge_M are related to the peripheral and middle-layer germanium atoms, respectively, and Ge_C which is the central germanium atom in Ge₁₉H₁₂ cluster. The optimized geometrical parameters including bond distances and bond angles are summarized in Table 1. By introducing 19^th Ge atom inside the cage, it is found that the Ge_M–Ge_P and Ge_M–Ge_M are slightly elongated. In contrast, Ge_P–Ge_P is decreased about 0.1 Å. Furthermore, the Ge_C is positioned in the center of the Ge₁₉H₁₂ nanotube with bond lengths of 2.512 Å connected to six neighbors Ge_M atoms.

Table 1 Calculated bond distances (R/Å) and angles (∠/deg) for Ge₁₈H₁₂ and Ge₁₉H₁₂ nanocrystals

Geometry	Ge18H12	Ge19H12
R(GeM–GeP)	2.438	2.532
R(GeM–GeM)	2.383	2.512
R(GeP–GeP)	2.461	2.399
R(GeP–H)	1.552	1.558
R(GeC–GeM)	—	2.512
∠GeP–GeM–GeM	90.9	88.7
∠H–GeP–GeP	112.6	113.4
∠H–GeP–GeM	131.6	124.9
∠GeP–GeP–GeP	120.0	120.0
∠GeM–GeM–GeM	120.0	120.0

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By introducing 19^th Ge atom in the Ge₁₈H₁₂ nanostructure, we found the optimized Ge₁₉H₁₂ structure that gains 4.5 eV in stability. This value is comparable with the reported 5.1 eV value by Vach for similarly silicon nanostructure.⁷ As we will see in below this unusual stability is related to the aromaticity of the nanocrystals as indicated by some aromaticity criterion.

To confirm the effect of the inserted 19^th Ge atom on the electronic structure, density of state DOS calculations and highest occupied molecular orbitals (HOMO) and the lowest-lying unoccupied molecular orbitals (LUMO) analysis carried out for studied nanotubes, Fig. 2 and 3. The energy change between the highest occupied molecular orbital E_HOMO and the lowest unoccupied molecular orbital E_LUMO decreased from 2.24 eV value for Ge₁₈H₁₂ to 1.72 eV for Ge₁₉H₁₂ nanocrystals. The inserted 19^th Ge atom produces a new state into the forbidden region of Ge₁₈H₁₂, and hence narrows the HOMO–LUMO gap. The HOMO and LUMO distributions of Ge₁₈H₁₂ and Ge₁₉H₁₂ nanotubes are illustrated in Fig. 3. In general, the HOMO represents the electron donating ability, whereas LUMO indicates electron accepting ability of the molecule, which are important in chemical reactions and optical properties of nanocrystals. The LUMO for both Ge₁₈H₁₂ and Ge₁₉H₁₂ is distributed over the molecule. On the other hand, the HOMO of Ge₁₉H₁₂ is mainly focused on the Ge_C atom and the HOMO of Ge₁₈H₁₂ is predominantly focused around the middle-layer germanium atoms. This HOMO feature may be related to the ability of Ge₁₈H₁₂ to host additional Ge atom as over-coordinated in the center.

Fig. 2 Density of states maps for (a) Ge₁₈H₁₂ and (b) Ge₁₉H₁₂.

Fig. 3 Molecular orbitals of Ge₁₈H₁₂ and Ge₁₉H₁₂ at B3LYP/6-31G* level.

3.2. NBO analysis, Mayer bond order and electron-deficiency aromaticity

In order to make the effect of inserted atom on the charges of the atoms, we calculated Natural Population Analysis (NPA) charges of the atoms in the Ge₁₈H₁₂ and Ge₁₉H₁₂, the results are listed in Table 2. For both nanostructures Ge_M atoms have more electron than Ge_P atoms, and hydrogen atoms are partially negatively charged. This phenomenon is somewhat expected, because hydrogen has a higher electronegativity than germanium. By insertion of a Ge atom into the center of the Ge₁₈H₁₂ cluster, while each peripheral germanium atoms become only 0.018ē more negative; conversely, each middle-layer germanium atoms become 0.167ē more positive. Natural charge calculations also indicate that Ge_C atom in Ge₁₉H₁₂ serves as the negative charge center by −0.778ē, to keep the overall charge balance.

Table 2 NPA charges of the q_H, peripheral silicon atoms q_Ge-peri, middle-layer silicon atoms q_Ge-mid and the inserted atom q_Ge-ins of Ge₁₈H₁₂ and Ge₁₉H₁₂, the Mayer bond orders of Ge–H and G–Ge bonds

	qH	qGe-peri	qGe-mid	qGe-ins	GeP–H	GeP–GeP	GeP–GeM	GeM–GeM	GeM–GeC
Ge18H12	−0.091	0.163	−0.143	—	0.889	0.861	0.789	0.862	—
Ge19H12	−0.092	0.145	0.024	−0.778	0.886	0.897	0.660	0.602	0.492

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Mayer bond order²⁵ is a quantity frequently used to study multiplicity of bonds and compare strength of the same kind of bonds. To study the characteristics of the Ge–Ge and Ge–H bonds and to reveal the influence of atomic insertion, we computed Mayer bond order for all Ge–Ge bonds and listed them in Table 2. Calculated bond orders are smaller than 1.0 and in the range of 0.492–0.897, which suggest that, less than one pair of electrons is involved in each of these bonds. This observation is in line with ref. 9, which showed that most Si–Si and Si–Ge bonds in Si₁₉H₁₂ and Si₁₈GeH₁₂ are electron-deficient. Based on the calculated bond order, the strengths of Ge–Ge bonds in Ge₁₈H₁₂ follow the trends of Ge_M–Ge_M ≅ Ge_P–Ge_P > Ge_M–Ge_P. After inserting a Ge atom in the cluster center, the bond order of Ge_P–Ge_P are not considerably changed, and bond orders of Ge_P–Ge_M and Ge_M–Ge_M are decreased by about 0.129 and 0.260 values, respectively. The bonding between inserted Ge atom and six middle-layer Ge atoms has the bond order 0.492. This value suggest Ge_C atom is able to bonded to Ge_M atoms as covalent “half-bonds” which strengthen idea of an electron deficient nanostructure.

In order to more investigate the electron deficient and detailed information regarding the electronic conjugation between the Ge–Ge bonds, the occupancies and stabilization energies E₂ values of the most important donor–acceptor interactions were analyzed for Ge₁₉H₁₂ structure. For similar silicon nanocrystals structure, Vach demonstrated the aromatic-like properties of Si₁₉H₁₂ due to the strong electron delocalization.⁶ Owing to this phenomenon, Si₁₉H₁₂ shows more stability than any other known silicon nanocrystals and proposed their experimental synthesis is very likely. In the NBO method, electron delocalization between Lewis-type (donor) and non-Lewis (acceptor) corresponds to stabilizing donor–acceptor interactions. The stabilization energy E⁽²⁾ associated with these interactions can be estimated by eqn (1). These NBOs results are illustrated in Fig. 4 and 5 and Table 3. The interaction between σ_GeP–GeP orbital as donor and , and orbitals as an acceptor are depicted in Fig. 4. While natural bond orbitals σ_GeP–GeP (1.920ē) and σ_GeP–H (1.972ē) in up and down rings are almost fully electron occupied, the σ_GeM–GeM and σ_GeM–GeP bonds are founded to have considerable depletion in electron with 1.6326ē and 1.779ē, respectively. Furthermore, the two lone-pairs, LP1 (Ge_G) with 1.588ē and LP2 (Ge_G) with 1.201ē, of the center germanium atom Ge_G, see Fig. 5, show strong depletion and lone-pair orbitals LP3*(Ge_G) with 0.990ē and LP4*(Ge_G) with 0.9879ē are highly occupied. Large electron deficiency of σ_GeM–GeM bonds in the middle layer are related to their strong interactions with LP*(3) and LP*(4) of the central Ge_C atom, see Table 3. Two binding orbitals σ_GeA–GeB and σ_GeD–GeE in the middle layer have been interacted with LP*(4) Ge_G by E⁽²⁾ values about 193 kcal mol⁻¹. On the other hand, four other bonds in the middle layer have also strong interactions with both LP*(3) Ge_G and LP*(3) Ge_G, where the total resulted E⁽²⁾ values are yet again about 193 kcal mol⁻¹. The donor–acceptor interactions in the middle layer of Ge₁₉H₁₂ nanocrystals are shown in Fig. 5. These strong interactions indicate that electron-deficiency of Ge–Ge bonds in Ge₁₉H₁₂ nanocrystals are resolved by delocalizing participating electrons. This electron delocalization phenomenon is similar to what is known for aromatic compounds and Vach termed it as “electron-deficiency aromaticity”. Therefore, the results from NBO calculations suggest the strong electron delocalization caused by electron deficiency in Ge₁₉H₁₂ can be related to calculated stabilization energy shown in Fig. 1 by creation of aromaticity.

Fig. 4 Stabilization energies E⁽²⁾ resulting from delocalization between donor σ_GeP–GeP and acceptor sites (a) (b) and (c) . Energies are given in kcal mol⁻¹.

Fig. 5 Some of stabilization energies E⁽²⁾ resulting from delocalization between donor and acceptor sites in the middle layer of Ge₁₉H₁₂ nanocrystals. Energies are given in kcal mol⁻¹.

Table 3 Calculated occupancy and the second-order perturbation energy E⁽²⁾ at B3LYP/6-31G* level for Ge₁₉H₁₂

Lewis-type NBOs (donor)			Non-Lewis NBOs (acceptor)			E^(2) (kcal mol^−1)
Type	Occupancy		Type	Occupancy
	Ge18H12	Ge19H12		Ge18H12	Ge19H12
σGeA–GeB	1.897	1.633	LP*(4) GeG	—	0.989	193.12
σGeA–GeF	1.897	1.633	LP*(3) GeG	—	0.990	129.37
σGeA–GeF	1.897	1.633	LP*(4) GeG	—	0.989	65.37
σGeB–GeC	1.897	1.633	LP*(3) GeG	—	0.990	160.98
σGeB–GeC	1.897	1.633	LP*(4) GeG	—	0.989	33.91
σGeC–GeD	1.897	1.633	LP*(3) GeG	—	0.990	129.3
σGeC–GeD	1.897	1.633	LP*(4) GeG	—	0.989	65.17
σGeD–GeE	1.897	1.633	LP*(4) GeG	—	0.989	192.64
σGeE–GeF	1.897	1.633	LP*(3) GeG	—	0.990	160.72
σGeE–GeF	1.897	1.633	LP*(4) GeG	—	0.989	33.67

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3.3. NICS and aromaticity

As we discussed in previous section, introducing one Ge atom in the center of Ge₁₈H₁₂ leading to stable overcoordinated Ge₁₉H₁₂ with strong electron delocalization and aromatic like properties. Due to the presence of delocalized electrons in the germanium cluster studied here, aromaticity criterion is an interesting theoretical property and highly worthy to be investigated. Nucleus independent chemical shifts NICS, proposed by Schleyer and co-workers have become the most popular index for measuring aromaticity due to its simplicity and efficiency.^26,27 The negative isotropic chemical shielding −σ_iso at some selected point is defined as NICS. Negative NICS values indicate aromaticity and positive NICS values denote antiaromaticity of the system. In some literature, it was shown that NICS_ZZ is a better index than the original NICS.²⁸ Actually, NICS is an average of its components NICS_XX, NICS_YY and NICS_ZZ. However, in this study NICS_ZZ component and NICS were considered to evaluate the aromaticity of the studied nanocrystals. For cylindrical clusters such as Ge₁₈H₁₂ and Ge₁₉H₁₂, a more thorough way to characterize aromaticity may be plotting the NICS curve along the symmetry axis of the cluster. The NICS results, calculated at the B3LYP/6-311++G** level of theory, along the longitudinal direction in the center of the Ge₁₈H₁₂ and Ge₁₉H₁₂ nanoparticle are shown in Fig. 6. For comparison, the NICS curves, obtained at the same level, of benzene (the reference of aromatic species) and Si₁₉H₁₂ are also given in Fig. 6. Notice that the occurrence of very negative values in the middle region of the NICS curve of Si₁₉H₁₂ and Ge₁₉H₁₂ is because the sample points exactly cross the inserted atom, whose inner-core electrons shield external magnetic fields significantly. However, this does not hamper fair comparison of aromaticity, as long as the middle region of the NICS curves is ignored. As it can be seen from this Fig. 6, Ge₁₈H₁₂ with negative NICS_ZZ index values show aromaticity character and antiaromaticity property from positive NICS index values around the cage center. The positive NICS values are caused by the positive NICS_XX and NICS_YY components and thus one may conclude that this cluster possesses a weak antiaromaticity character. However, after inserting one Ge atom into the Ge₁₈H₁₂ cluster center, the aromaticity becomes significant and even stronger than benzene and slightly more than Si₁₉H₁₂.

Fig. 6 (a) NICS (b) NICS_ZZ values along the longitudinal distance from the center.

The magnetic susceptibility Λ resulting from the presence of cyclic delocalization of electrons is another important aromaticity criterion which is used here. Unlike NICS parameters which are local properties, the magnetic susceptibility is a global property of the molecule. The more negative values of magnetic susceptibility Λ exhibit more aromaticity character of the molecule. Magnetic susceptibility Λ of Ge₁₈H₁₂ and Ge₁₉H₁₂ nanocrystals are calculated to be −321.2 cgs ppm and −428.4 cgs ppm, increasing the aromaticity property of about 100 cgs ppm from empty to overcoordinated Ge NCs. The corresponding magnetic susceptibility value for benzene was also obtained Λ (C₆H₆) = −56.4 cgs ppm, which indicate that the global aromaticity properties of studied nanocrystals is significantly larger than benzene.

3.4. Absorption spectra

In our previous work, it has been shown that due to the insertion of the center silicon atom to the silicon nanocrystals Si₁₈X₁₂ (X = H, F, Cl, Br, NH₂, COOH, OH) the absorption spectrum are extended from UV-VIS region to infrared IR region.⁹ Likewise, we obtained the adsorption spectrum of studied Ge₁₈H₁₂ and Ge₁₉H₁₂ nanocrystals and are plotted in Fig. 7. While optical absorption spectrum of Ge₁₈H₁₂ is only limited in UV region by wavelengths lower than 400 nm, the overcoordinated germanium nanocrystals Ge₁₉H₁₂ can absorb light in the three spectral UV-VIS and IR regions. Two nanocrystals exhibit similar spectrum for excitation energies with wavelengths < 400 nm, but Ge₁₉H₁₂ show additional features in the spectrum with strong peaks in the range of 800–850 nm. Thus, this finding is similar to the previous results of silicon nanocrystals. In general, standard tetrahedral clusters of this size show absorption only in the UV and may absorb light in the VIS and IR only when toxic or expensive metal are incorporated.^29–32 Such an extension of spectral response by overcoordinated germanium nanocrystals might it be used to the environmentally safe replacement of other expensive or toxic elements in nanocrystals with application in solar cell and electronic devices. In particular the strong adsorption at interval 800–850 nm may open potential applications in cancer treatment where the use of gold and silver nanoparticles has been proposed where the resulting laser light absorption at about 800 nm yields optimal efficiency.^33,34 If successfully synthesized, the experimental electronic properties derived for Ge₁₉H₁₂ structure are expected to be coherent with the data derived in this text.

Fig. 7 Absorption spectra of (a) Ge₁₈H₁₂ and (b) Ge₁₉H₁₂.

4. Conclusions

In the present work, DFT calculations have been indicated that Ge₁₈H₁₂ nanocrystals can by more stabilized by insertion of one Ge atom in the center and makes overcoordinated Ge₁₉H₁₂ nanocrystals. We extend the definition of the electron-deficiency aromaticity concept to Ge nanocrystals by exploiting the electron-deficiency of a system to induce electron delocalization and, thus, enhanced stability. The NICS and magnetic susceptibility aromaticity indexes show that Ge₁₉H₁₂ nanocrystals exhibit greater aromaticity than conjugated organic molecules such as benzene. The NBO analysis have demonstrated that Ge–Ge bonds in Ge₁₉H₁₂ have strongly delocalized nature and are strongly interacted with the lone pair of central Ge atom. It has shown that pure hydrogenated germanium nanocrystals Ge₁₉H₁₂ with overcoordinated ring structures can absorb light not only in the ultraviolet, but also in the visible and infrared spectral region without the need for expensive or toxic metal atoms. This new pattern for optical spectrum of Ge₁₉H₁₂ can be attributed to the special electronic structure of studied nanoparticles. Finally, given the technological importance of aromatic derivatives, we believe that the proposed Ge NCs with aromatic-like behavior will have a significant technological impact and deserves further extensive study in various emerging nanotechnological domains.

Acknowledgements

We gratefully acknowledge discussions with Holger Vach. Allotment of computer time provided by David Vander Spoel from the Biomedical Center in Uppsala University is gratefully acknowledged. The authors also thank Kharazmi University for financial support.

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