A comparative ab initio study to investigate the rich structural variety and electronic properties of Ga_mTe_n (m = 1, 2 and n = 1–4) with analogous oxides, sulfides and selenides

Abstract

A series of gallium telluride, Ga_mTe_n (m = 1, 2 and n = 1–4), clusters has been examined using density functional theory (DFT), second-order Møller–Plesset perturbation theory (MP2) and the coupled cluster approach with single and double substitutions and a perturbative treatment of triple excitations [CCSD(T)]. The study unravels the question of whether neutral GaTe₂ is isostructural with BO₂ as proposed earlier by a previous experiment (Trans. Faraday Soc. 1968, 64, 2998). The results of gallium tellurides are compared with the oxygen, sulfur and selenium analogues. In most cases, the substitution of O/S/Se by Te atoms in the gallium clusters does not drastically affect the structural characteristics. The adiabatic electron affinities (AEAs) of Ga_mTe_n (m = 1, 2 and n = 1–4) clusters range from 1.33 to 3.46 eV at the CCSD(T)//B3LYP level. The AEAs of gallium tellurides are found to be independent on the electrophilicity of the clusters. Further, the adiabatic ionization potentials (AIPs) of the clusters are in good agreement with available experimental data. This research is expected to provide insight into the structural characteristics and electronic properties of gallium chalcogenides.

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1. Introduction

Gallium chalcogenides have attracted scientific and commercial interest because they are semiconducting materials with extensive technological applications. The interaction between gallium and tellurium atoms is of prime importance due to their wide usage in optoelectronic and photovoltaic devices.^1,2 Gallium monotelluride, GaTe is a heteronuclear gallium telluride which has been intensively studied.³ Owing to its band gap of around 1.7 eV, GaTe is useful in photoelectronic devices, radiation detectors,^1,2 field-effect transistors and phototransistors.⁴ Doped gallium telluride clusters such as AgGaTe₂ is used in thin film solar cells,⁵ CuGaTe₂ as a high-performance thermoelectric material⁶ and LiGaTe₂ for optical applications.⁷ Neutral telluroether complexes containing gallium atoms are used in chemical vapor deposition^8,9 and as phase change memory materials.¹⁰

Extensive efforts have been devoted to the study of gallium chalcogenide clusters.^1–24 Experiments and high level computations have shown GaO₂ to be linear.^22,23 However, theoretical results reveal that GaS₂ and GaSe₂ adopt cyclic geometries while anionic GaX₂ (X = O–Se) prefers a linear configuration (D_∞h).^11–15 The lowest-energy structure of neutral and anionic GaX₄ (X = O–Se) possesses a kite-shape with a trichalcogenide unit.^14–16 Ga₂Se and Ga₂Te adopt bent configurations^11,16 unlike Ga₂O which is linear.¹² For neutral and anionic Ga₂X₃ (X = O–Te),^13,17,19,20 a V-shape and kite-shape are obtained, respectively. In the case of the Ga₂X₃ (X = O–Te)^13,17,19,20 series, a decrease in the adiabatic electron affinity (AEA) values is noted at the CCSD(T)//B3LYP level of theory. Ga₂X₄ and their respective anions (X = O–Se) have similar ground state geometries.^15,16,21 Structural differences are observed when Ga₃X₂ (X = O–Te) clusters are compared. Neutral Ga₃O₂ ¹⁷ and Ga₃S₂ ¹⁵ adopt kite-shape geometries while Ga₃Se₂ and Ga₃Te₂ adopt three-dimensional structures with D_2h and C_2v symmetries.^20,22 In the same vein, Ga₃S₂⁻, Ga₃Se₂⁻ and Ga₃Te₂^−16,19,24 prefer three-dimensional structures with a D_3h symmetry differing from the planar kite geometry of Ga₃O₂⁻.¹⁷

In view of the above, structural and electronic changes are highlighted by substitution of atoms. Fueled by these interesting results and an urge to see whether significant differences are noted on going down the periodic table, a systematic theoretical investigation of gallium tellurides, Ga_mTe_n (m = 1, 2 and n = 1–4) was embarked to assess the structural and electronic properties. The objectives of the research are: (i) to study the equilibrium structures; (ii) to provide a reliable theoretical prediction of the relative stabilities, harmonic vibrational frequencies and energetic features such as electron detachment energies, electron affinities and ionization potentials (iii) to compare the ground state geometries and variations in the electronic properties with analogous oxides, sulfides and selenides and (iv) to compare the electron affinities of gallium telluride clusters with chlorine atom in order to determine whether they can be classified as superhalogens.

2. Computational methods

The computations of mono and digallium telluride, Ga_mTe_n (m = 1, 2 and n = 1–4), clusters were performed with the Gaussian 09²⁵ program. To obtain the ground state structures, various initial geometries were taken from isoelectronic gallium oxides, sulfides and selenides^14–21 [Fig. 1–5]. Based on previous investigations,^{12,14,15–17,19–21} the 6-311+G(2df) one-particle basis set was employed for Ga atom while the LANL2DZdp ECP²⁶ and def2-TZVP triple split valence basis sets²⁷ were used for Te atom. The density functional theory (DFT) with the B3P86, B3PW91 and B3LYP functionals^28–33 and the MP2^34,35 level of theory were employed. The single point CCSD(T)³⁶ computations were performed using optimized geometries from the B3LYP functional.

Fig. 1 Geometrical features of diatomic GaTe with the electronic states [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp]. ^aB3P86, ^bB3PW91, ^cB3LYP and ^dMP2.

The adiabatic electron affinity (AEA), adiabatic detachment energy (ADE), vertical detachment energy (VDE), adiabatic ionization potential (AIP), vertical ionization potential (VIP) and chemical hardness (η) were calculated as follows:

AEA = E (optimized neutral at ground state) − E (optimized anion at ground state);

ADE = E (optimized corresponding neutral) − E (optimized anion);

VDE = E (neutral at optimized anion geometry) − E (optimized anion);

AIP = E (optimized cation at ground state) − E (optimized neutral at ground state);

VIP = E (cation at optimized neutral geometry) − E (optimized cation);

η ≈ (VIP − VDE)/2

The harmonic vibrational frequencies of the optimized geometries were analyzed to ensure that all the ground state structures belong to the minima on the potential energy surface. The Natural Bond orbital (NBO) analysis^37,38 was performed with the B3LYP functional to provide insight into the nature of bonding in the clusters. The HOMO–LUMO gaps and chemical hardness (η) of the neutral gallium tellurides were also calculated with the B3LYP functional. In addition, the dissociation energies (D_e) of the studied clusters were carried out.

3. Results and discussion

Optimized geometrical configurations of the lowest-energy states of gallium telluride clusters, Ga_mTe_n (m = 1, 2 and n = 1–4) are shown from Fig. 1–5. The energetic data (ΔE) is listed in Table 1. The internal coordinates and harmonic vibrational frequencies of the ground state geometries are available in Tables S1-S8 (ESI).† The AEA and AIP values are presented in Tables 2 and 3. The dissociation energies (D_e) of the gallium tellurides are shown in Table 4. The natural bond orbital (NBO)^34,35 on the gallium atoms are summarized in Table S9† while the VDE and chemical hardness (η) are given in Table S10.†

Table 1 Energy shifts (eV) of the first low-lying states with respect to ground states of the mono and digallium tellurides [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp]

Methods	B3P86	B3PW91	B3LYP	MP2
GaTe	0.08	0.08	0.01	0.20
GaTe^−	2.19	2.14	2.20	2.21
GaTe^+	0.94	0.97	0.99	0.79
GaTe2	0.18	0.18	0.18	0.01
GaTe2^−	0.93	0.92	0.92	1.33
GaTe2^+	0.35	0.35	0.34	0.35
GaTe3	0.12	0.12	0.19	0.60
GaTe3^−	0.80	0.81	0.71	1.45
GaTe3^+	0.14	0.15	0.05	0.83
GaTe4	0.09	0.07	0.17	−0.23
GaTe4^−	0.21	0.19	0.28	−0.02
GaTe4^+	0.20	0.21	0.11	0.63
Ga2Te	0.14	0.14	0.13	0.19
Ga2Te^−	0.49	0.48	0.42	0.45
Ga2Te^+	0.12	0.13	0.12	0.28
Ga2Te2	0.57	0.57	0.49	0.33
Ga2Te2^−	0.62	0.61	0.54	0.65
Ga2Te2^+	0.39	0.39	0.38	0.43
Ga2Te3^+	0.19	0.20	0.17	0.67
Ga2Te4	0.17	0.18	0.28	0.44
Ga2Te4^−	0.23	0.23	0.22	0.60
Ga2Te4^+	0.19	0.20	0.12	0.77

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Table 2 Adiabatic electron affinities (AEAs) of the gallium telluride clusters using different levels of theory [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp]

Cluster	B3P86	B3PW91	B3LYP	MP2	CCSD(T)//B3LYP
a AEA values in parenthesis were obtained using single point CCSD(T) with def2-TZVP basis set.b AEA value in bold was obtained at the CCSD(T) level of theory.
GaTe	3.20	2.65	2.67	2.48	2.46 (2.57)^a, 2.46^b
GaTe2	3.83	3.29	3.23	3.55	3.46 (3.38)
GaTe3	3.94	3.40	3.31	3.20	3.23 (3.50)
GaTe4	3.81	3.27	3.24	3.23	3.10 (3.30)
Ga2Te	1.92	1.39	1.25	1.32	1.33 (1.37)
Ga2Te2	2.95	2.40	2.35	2.49	2.46 (2.34)
Ga2Te3	3.71	3.18	3.02	2.77	2.77 (3.10)
Ga2Te4	4.07	3.51	3.50	3.14	3.01 (3.41)

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Table 3 Adiabatic ionization potentials (AIPs) of the gallium telluride clusters using different levels of theory [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp]

Cluster	B3P86	B3PW91	B3LYP	MP2	CCSD(T)//B3LYP
a AIP values in parenthesis were obtained using single point CCSD(T) with def2-TZVP basis set.b AIP value in bold was obtained at the CCSD(T) level of theory.
GaTe	8.82	8.25	8.17	8.08	7.85 (8.20)^a, 8.01^b
GaTe2	8.36	7.80	7.65	7.73	7.84 (7.75)
GaTe3	7.84	7.29	7.36	7.08	6.85 (7.13)
GaTe4	7.64	7.08	7.14	6.45	6.52 (6.92)
Ga2Te	8.21	7.65	7.62	7.54	7.55 (7.63)
Ga2Te2	8.22	7.65	7.51	7.27	7.13 (7.64)
Ga2Te3	7.66	7.10	7.22	6.92	6.86 (7.03)
Ga2Te4	7.54	7.00	7.10	6.80	6.93 (6.95)

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Table 4 Dissociation energies (D_e, kJ mol⁻¹) of gallium tellurides through different channels [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp]

Channels	B3P86	B3PW91	B3LYP	MP2	CCSD(T)//B3LYP
GaTe → Ga + Te	282.3	272.6	259.6	266.2	260.5
GaTe2 → Ga + Te2	266.5	258.4	243.8	275.7	265.9
GaTe2 → GaTe + Te	274.7	266.2	252.9	234.9	224.1
GaTe2 → Ga + 2Te	557.0	538.8	512.5	501.0	484.7
GaTe3 → GaTe + Te2	169.5	163.4	144.2	217.3	192.1
GaTe3 → GaTe2 + Te	185.4	177.6	159.9	207.7	186.7
GaTe3 → GaTe + 2Te	460.1	443.8	412.8	442.6	410.8
GaTe4 → GaTe2 + Te2	139.2	131.9	105.9	196.9	171.4
GaTe4 → GaTe + Te3	232.4	225.8	207.7	294.2	264.8
GaTe4 → GaTe3 + Te	244.3	234.6	214.6	214.2	203.4
GaTe4 → Ga + 2Te2	405.7	390.3	349.7	472.6	437.3
Ga2Te → GaTe + Ga	293.1	285.4	282.6	284.7	276.3
Ga2Te → 2Ga + Te	575.4	558.0	542.2	550.9	536.8
Ga2Te2 →2GaTe	265.1	258.8	242.2	236.6	235.9
Ga2Te2 → Ga2Te + Te	254.4	246.0	219.1	238.1	220.2
Ga2Te2 → GaTe2 + Ga	272.8	262.2	248.9	288.0	272.3
Ga2Te3 → Ga2Te + Te2	172.6	166.3	136.0	278.6	253.6
Ga2Te3 → GaTe + GaTe2	199.1	193.3	174.8	287.6	263.9
Ga2Te3 → Ga2Te2 + Te	208.7	200.7	185.5	265.8	252.2
Ga2Te3 → Ga2Te + 2Te	463.1	446.7	404.6	503.9	472.3
Ga2Te4 → Ga2Te2 + Te2	165.5	161.2	131.1	279.1	272.4
Ga2Te4 → 2GaTe2	171.2	168.1	136.1	291.3	278.8
Ga2Te4 → GaTe3 + GaTe	261.1	256.6	229.1	318.4	316.2
Ga2Te4 → Ga2Te3 + Te	247.3	241.0	214.3	238.6	239.0
Ga2Te4 → Ga2Te2 + 2Te	456.0	441.6	399.7	504.3	491.1

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A. Structural properties

The electronic ground state of neutral GaTe is ²Σ⁺, which is in agreement with GaO³⁹ and GaSe.¹⁶ The quartet and sextet states of GaTe are well separated from the doublet ground state by 2.68 and 5.23 eV, respectively at the CCSD(T)//B3LYP level. The most stable electronic states of GaTe⁻ and GaTe⁺ are ¹Σ⁺ and ³Σ⁺ (Fig. 1), respectively. This result is consistent with anionic and cationic GaO³⁹ and GaSe.¹⁶ A cyclic structure is found as the lowest-energy structure for GaTe₂ with the DFT and MP2 methods. However, single point CCSD(T) using DFT and MP2 geometries, reveals a linear structure (Fig. 2) by analogy with BO₂.¹¹ This ambiguity was solved with def2-TZVP,²⁷ being a large basis set. Single point CCSD(T) computations with def2-TZVP basis set reveals a cyclic structure for GaTe₂. Furthermore, the linear structure is a saddle point with the MP2 method. In this vein, the linear structure of GaTe₂ is the first low-lying isomer. For the tri-atomic series, GaTe₂ is cyclic as GaS₂ ¹⁵ and GaSe₂ ¹⁶ while GaO₂ is linear.^22,23

Fig. 2 Geometrical features of GaTe₂ and Ga₂Te with the electronic states [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp]. ^aB3P86, ^bB3PW91, ^cB3LYP and ^dMP2.

Akin to GaO₂⁻,¹² GaS₂^− 15 and GaSe₂⁻,¹⁶ anionic GaTe₂ prefers a linear centrosymmetric (D_∞h) configuration. The first low-lying geometry of GaTe₂⁻ is bent (¹A₁). As its selenide congener,¹⁶ cationic GaTe₂ adopts a bent configuration with a C_s symmetry. The lowest-energy configuration of neutral, negatively and positively charged GaTe₃ consists of a diatomic GaTe molecule bound perpendicularly to a Te₂ moiety (Fig. 3). Similar neutral and anionic ground state geometries were reported for gallium selenide clusters.¹⁶ Neutral, negatively and positively charged GaTe₃ adopt a rhombic structure as the first low lying isomer. GaTe₄ and its anion adopt kite geometries with a tritelluride unit (²B₁) analogous to gallium oxide,¹⁴ sulfide¹⁵ and selenide.¹⁶ This result is further confirmed by the CCSD(T)//B3LYP and CCSD(T)//MP2 computations. The low-lying structure of neutral and anionic GaTe₄ is of D_2d symmetry, which is the lowest-energy structure for GaTe₄⁺. On the other hand, the low-lying structure of GaTe₄⁺ adopts the kite geometry which is 0.63 eV above the ground state geometry with the MP2 level.

Fig. 3 Geometrical features of GaTe₃ and Ga₂Te₂ with the electronic states [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp]. ^aB3P86, ^bB3PW91, ^cB3LYP and ^dMP2.

The lowest-energy state of neutral Ga₂Te is ²A₂ with a bent configuration (C_2v) (Fig. 2). This result is consistent with Uy et al.¹¹ This geometry is isostructural with Ga₂Se¹⁶ but differs from Ga₂O, which is linear.¹² The next low-lying geometry of Ga₂Te is linear. Anionic and cationic Ga₂Te maintain the bent configuration of the neutral species but with C_2v and C_s symmetries, respectively. Same behavior was pointed out with gallium selenide.¹⁶ A distinct difference is noticed within the Ga₂X₂ (X = O–Te) family as Ga₂O₂ is linear,¹² Ga₂S₂ is rhombic,¹⁵ Ga₂Se₂ is L-shape¹⁶ and Ga₂Te₂ has a butterfly structure with a C_2v symmetry (Fig. 3). The structure of Ga₂Te₂⁻ is rhombic, which is analogous to Ga₂O₂⁻,¹² Ga₂S₂^{− 15} and Ga₂Se₂⁻.¹⁶ For Ga₂Te₂⁺, a L-shape structure is obtained as Ga₂Se₂⁺.¹⁶ The low-lying isomers of neutral, anionic and cationic Ga₂Te₂ adopt linear, cyclic and L-shape configurations, respectively. The lowest-energy structure of neutral and anionic Ga₂Te₄ can be viewed as rhombic with one terminal tellurium atom attached to each gallium atom (D_2h) (Fig. 5). Similar ground state geometry was found with gallium oxide,²¹ sulfide¹⁵ and selenide.¹⁶ Ga₂Te₄⁺ adopts a similar ‘fish-like’ structure as Ga₂Se₄⁺.¹⁶ The next energetically low-lying isomer of Ga₂Te₄ is a ‘fish-like’ structure which is 0.44 eV above the ground state geometry (MP2). The low-lying isomer of anionic Ga₂Te₄ is a twisted hexagon configuration and cationic Ga₂Te₄ prefers a planar configuration with D_2h symmetry. Gallium telluride clusters prefer planar structures with the exception of mono and digallium tetratelluride cations. A structural evolution is revealed upon addition of a tellurium atom to the GaTe_n and Ga₂Te_n series (Fig. S1 and S2†). The NBO charges on gallium atoms are positive with the exception of GaTe⁻ and Ga₂Te₄⁺ (Table S9†). No significant pattern is observed in the natural charge of gallium atom upon sequential addition of tellurium atoms with the exception of GaTe_n⁺ and Ga₂Te_n⁻.

Fig. 4 Geometrical features of GaTe₄ and Ga₂Te₃ with the electronic states [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp]. ^aB3P86, ^bB3PW91, ^cB3LYP and ^dMP2.

Fig. 5 Geometrical features of Ga₂Te₄ with the electronic states [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp]. ^aB3P86, ^bB3PW91, ^cB3LYP and ^dMP2.

B. Geometrical properties

Akin to GaO³⁹ and GaSe,¹⁶ a slight elongation of 0.072 Å (B3LYP) and 0.095 Å (MP2) is observed in the monotelluride Ga–Te bond length from GaTe to GaTe⁻. As expected, an increase in the bond angle at the apex is observed with the cyclic structure of GaO₂ (38.0°),¹² GaS₂ (47.5°),¹⁵ GaSe₂ (51.0°)¹⁶ and GaTe₂ (55.4°) [B3LYP]. Unlike the GaX₃/GaX₃⁻ (X = O and Se)^16,18 system, addition of an electron to GaTe₃ shortens the terminal Ga–Te bond length (DFT and MP2). On the other hand, there is an increase in the terminal Ga–Te bond from GaTe₃ to GaTe₃⁺. Like gallium selenide,¹⁶ the bridge Ga–Te bond is elongated whereas the terminal Ga–Te bond is shortened from GaTe₄ to GaTe₄⁻ (DFT and MP2). However, the reverse pattern was observed with the gallium oxide¹⁴ and sulfide¹⁵ congener. For the GaX₄ (X = O–Te)^14–16 series, a compression in the bond angle of the trichalcogenide unit is noted in all cases. Turning to the Ga₂Te_n series, the Ga–Te–Ga bond angle compresses (DFT and MP2) from Ga₂Te to Ga₂Te⁻. Similar finding was found with gallium oxide¹² and selenide.¹⁶ Upon addition of an electron to Ga₂Te₂, the three-dimensional structure turns into a planar configuration unlike Ga₂Se₂ ¹⁶ where both neutral and cation maintain the planar L-shaped geometry. The bridge Ga–Te bonds of Ga₂Te₄ are slightly shorter than the anion whereas the terminal Ga–Te bonds are longer. The bond angle between the terminal Ga–Te and neighboring tellurium atom of Ga₂Te₄ is smaller than that of Ga₂O₄,²¹ Ga₂S₄ ¹⁵ and Ga₂Se₄.¹⁶

The Ga–Te bond lengths of the neutral gallium tellurides are within the range 2.357–2.845 Å (B3P86), 2.331–2.851 Å (B3PW91), 2.342–2.884 Å (B3LYP) and 2.316–2.791 Å (MP2). The Ga–Te bond lengths of the gallium tellurides are in agreement with mixed chalcogenide cubanes,⁴⁰ KGa₂Te₆,⁴¹ monoclinic GaTe,^42,43 hexagonal GaTe,⁴⁴ Ga₂Te₅ ⁴⁵ and telluroether gallium complexes.⁹ The Te–Te bond lengths of the neutral gallium tellurides are within the range 2.662–2.776 Å (B3P86), 2.663–2.777 Å (B3PW91), 2.680–2.827 Å (B3LYP) and 2.681–2.905 Å (MP2). The Te–Te bond lengths of the gallium tellurides are smaller than that of contact ion pair of tellurium system.⁴⁵

C. Vibrational properties

All the ground state geometries of the gallium telluride clusters have real frequencies. The frequencies of GaTe with DFT functionals (257 cm⁻¹ and 242 cm⁻¹) agree very well with Uy et al. (250 cm⁻¹).¹¹ Like GaSe,¹⁶ the stretching frequency of GaTe and GaTe⁻ are close to each other. From Uy et al.¹¹ investigation, GaTe₂ has three vibrational frequencies 152, 104 and 92 cm⁻¹, respectively. With linear GaTe₂, four wavenumbers were achieved and this feature negates its possibility as ground state geometry. The theoretical vibrational frequencies are higher than the experimental values with the DFT and MP2 methods. The highest frequency mode of GaTe₃ is attributed to the symmetrical stretching of terminal Ga–Te bond. Same observations were noted with GaO₃ ¹⁸ and GaSe₃.¹⁶ The highest frequency mode of GaX₄ (X = O–Te)^12,14–16 corresponds to the stretching of X–X bond. Turning to digallium chalcogenides, the most active mode of Ga₂X (X = O, Se, Te)^12,16 is the asymmetrical stretching of Ga–X bond. However, the harmonic vibrational frequencies of Ga₂Te are not in good correlation with the values reported by Uy et al.¹¹ Smaller wavenumbers are obtained with the DFT and MP2 levels of theory (Tables S2, S4, S6 and S8†). The highest frequency vibrations of Ga₂X₂ and Ga₂X₄ (X = O–Te)^12,15,16,21 correspond to the stretching of X–X and terminal Ga–X bond, respectively. No significant pattern is observed in the frequencies upon sequential addition of tellurium atom to the GaTe_n and Ga₂Te_n (n = 1–4) series.

D. Electronic properties

I. Adiabatic electron affinities (AEAs). The AEA of GaTe ranges from 2.46 eV [CCSD(T)//B3LYP] to 3.20 (B3P86). The AEA of GaTe at the CCSD(T) level is the same as reported at the single point CCSD(T)//B3LYP with LANL2DZdp basis set. The ground state electronic configuration of GaTe₂⁻ is (6σ_g)²(6π_u)²(4π_g)²(4σ_u)²(2δ_g)². The AEA of GaTe₂ varies from 3.23 eV (B3LYP) to 3.83 eV (B3P86). The excess electron of GaTe₂⁻ is distributed over the tellurium atoms (Fig. S3†). Similar HOMO plots were observed for GaX₂⁻ (X = S and Se).^15,16 The electronic configuration of GaTe₃⁻ is (12a₁)²(6b₂)²(5b₁)²(2a₂)² and that of GaTe₄⁻ is (13a₁)²(7b₂)²(6b₁)²(2a₂)². Their AEA values range from 3.20 to 3.94 and 3.10 to 3.81 eV, respectively. Akin to gallium selenide,¹⁶ the excess electron of GaTe₃⁻ and GaTe₄⁻ is localized on the terminal tellurium atom (Fig. S3†).

The electronic configuration of Ga₂Te⁻ is (14a₁)¹(12b₂)²(5b₁)²(4a₂)² and the electron detachment process of ¹A₁ (C_2v) + e⁻ ← ²A₁ (C_2v) involves the removal of an electron from the 14a₁ molecular orbital (MO) to yield the ¹A₁ (C_2v) ground state of Ga₂Te. The AEAs of Ga₂Te vary from 1.25 eV (B3LYP) to 1.92 eV (B3P86). The lowest-lying doublet state of Ga₂Te₂⁻ has an electronic configuration of (10a_g)²(9b_2u)¹(5b_1u)²(4b_3u)²(4b_3g)²(3b_1g)²(2b_2g)²(1a_u)² and the AEAs vary from 2.34 [CCSD(T)//B3LYP] to 2.95 eV (B3P86). Like the sulfur¹⁵ and selenium¹⁶ analogies, the extra electron of Ga₂Te₂⁻ is distributed over the bridge tellurium atoms (Fig. S4†). The electronic configuration of anionic Ga₂Te₄ is (11a_g)²(10b_1u)²(6b_2u)²(5b_3g)¹(4b_2g)²(2b_3u)²(2b_1g)²(1a_u)² and transition ³B_1u (D_2h) + e⁻ ← ²B_2g (D_2h) involves the removal of a b_3g electron from the anion to produce the ³B_1u (D_2h) ground state of Ga₂Te₄. The AEAs range from 3.01 eV to 4.07 eV. For the Ga₂X₄ (X = O–Te)^15,16,21 series, the extra electron of the anion is localized around the terminal chalcogen atoms (Fig. S4†). The ADEs and AEAs are the same for the studied gallium telluride clusters, with the exception of Ga₂Te₂ and Ga₂Te₃, because of the similar ground state geometries of the neutral and anion.

A significant increase in the AEA values is seen when progressing from Ga₂Te to Ga₂Te₄ (Fig. 6). This trend was observed with gallium oxides,²¹ sulfides¹⁵ and selenides.¹⁶ Similar increase in the AEAs is expected for the GaTe_n series but instead, a drop in the electron affinity values is obtained for GaTe₃ and GaTe₄ (Fig. 6). Among the gallium tellurides, GaTe₂ has the highest electron affinity at the CCSD(T)//B3LYP level of theory. However, the electron affinity of GaTe₂ is less than chlorine atom (3.62 eV)⁴⁶ with different levels of theory and it has a VDE of 3.42 eV with the B3LYP functional. This is obvious due to electronegativity values. In this vein, unlike analogous gallium oxide,¹² sulfide¹⁵ and selenide,¹⁶ GaTe₂ cannot exhibit superhalogen properties. The AEA of the Ga₂X₂ (X = O–Te) system is the lowest among the series studied (Fig. S5†). No significant trend is observed in the AEA values, with of exception Ga₂X₃, when changing the O/S/Se substituents to Te.^{12–17,19–22} This clearly demonstrates that the electron affinities of gallium chalcogenide clusters are independent of electronegative atoms in the system but are related to the electronic structures.

Fig. 6 Electron affinities of the gallium telluride clusters at the CCSD(T)//B3LYP level [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp].

II. Adiabatic ionization potentials (AIPs). The calculated AIPs of GaTe and GaTe₂ are in accordance with the available experimental data¹¹. In the case of GaTe, the B3PW91 functional provides a reliable theoretical value while for GaTe₂, the B3P86 yields a value closer to the experimental one. The AIP values of GaTe₃ range from 6.85 [CCSD(T)//B3LYP] to 7.84 (B3P86) eV and GaTe₄ from 6.45 (MP2) to 7.64 (B3P86) eV. Turning to digallium telluride series, the AIP of Ga₂Te ranges from 7.54 (MP2) to 8.21 eV (B3P86), Ga₂Te₂ from 7.13 (CCSD(T)//B3LYP) to 8.22 (B3P86) eV, Ga₂Te₃ from 6.86 [CCSD(T)/B3LYP] to 7.66 (B3P86) eV and Ga₂Te₄ from 6.80 (MP2) to 7.54 (B3P86) eV. As expected, the AIP results of Ga₂Te and Ga₂Te₂ are consistent with Uy et al.¹¹ experimental data. The AIPs of the gallium tellurides are lower than the gallium selenides.¹⁶ As shown in Fig. 7, the AIPs decrease upon sequential addition of tellurium atom to the GaTe_n series. This shows that AIP is not only related to the total number of tellurium atoms but also on electronic structures. Similar observation was highlighted with AEA.

Fig. 7 Ionization potentials of the gallium telluride clusters at the CCSD(T)//B3LYP level [basis sets Ga: 6-311+G(2df) and Te: LANL2DZdp].

III. Mean unsigned error (MUE). The accuracies of the different methods used in the research were examined by calculating the mean unsigned error (MUE).⁴⁷ The single point CCSD(T)//B3LYP values with the def2-TZVP basis set were taken as reference data. With the AEA values, the MUE was 0.56 eV (B3P86), 0.07 eV (B3PW91), 0.10 eV (B3LYP), 0.18 eV (MP2) and 0.19 eV CCSD(T)//B3LYP with the LANL2DZdp basis set. Similarly, the MUE of the studied gallium tellurides was calculated by using the AIPs values. The calculated MUE is 0.85 eV (B3P86), 0.07 eV (B3PW91), 0.13 eV (B3LYP), 0.17 eV (MP2) and 0.23 eV CCSD(T)//B3LYP with the LANL2DZdp basis set. In both cases, the B3PW91 functional gives meaningful values.

IV. HOMO–LUMO gaps. The HOMO–LUMO gaps of neutral gallium telluride clusters are shown in Table S10.† A large value of the HOMO–LUMO energy gap enhances chemical stability of the cluster.⁴⁸ The HOMO–LUMO gaps for the lowest-energy configurations are large, varying from 2.61 (GaTe₄) to 3.99 eV (GaTe) with the B3LYP functional. For the GaTe_n series, a general decrease in the HOMO–LUMO gaps is noted with an increase in the tellurium-to-metal ratio. However, no correlation is observed for the Ga₂Te_n series. Even though the substitution of O/S/Se by Te does not lead to a significant trend for the HOMO–LUMO energy gap, a decrease in the HOMO–LUMO energy gap values is noted for the Ga₂X₃ and Ga₂X₄ ^15,16,18,21 series.

V. Chemical hardness (η). Pearson states: ‘Clusters arrange their electronic structures so as to have the maximum possible hardness’.⁴⁹ The chemical hardness of the gallium tellurides varies from 1.58 to 3.19 eV with the B3LYP functional (Table S10†). An increase in the tellurium-to-metal ratio decreases the chemical hardness of the Ga₂Te_n clusters. The HOMO–LUMO gaps can be related to hardness (η). Clusters with small HOMO–LUMO gaps are said to be ‘soft’.⁵⁰ As mentioned earlier, the HOMO–LUMO gaps of some studied gallium tellurides are relatively large and thereby they can be considered as ‘hard’ clusters.

E. Thermodynamic stability

The dissociation energy (D_e) is obtained as the difference in total energies of the initial state and the sum of total energies of the decay fragments. The dissociation energies are positive indicating that the clusters are stable (Table 4). The D_e values of GaTe are in agreement with the experimental data (222–272 kJ mol⁻¹).¹¹ To compare the chalcogen effect for GaX (X = O–Te) series, the D_e of GaO and GaS were calculated. The D_e of GaX¹⁶ decreases with increasing atomic number of the chalcogen element. This implies that it is easier to cleave a Ga–Te than a Ga–O bond. The monogallium tellurides, with the exception of GaTe, favour a cascade release of tellurium molecule. The dissociation of Ga₂Te₄ results into Ga₂Te₂ and a Te molecule. This is because the terminal tellurium atoms are cleaved easier compared to bridge tellurium ones. Similar feature was observed for gallium sulfide and selenide.^15,16,21 The D_e of the preferred channel decreases upon sequential addition of tellurium atom to GaTe_n and Ga₂Te_n series. Similar observation was seen with the selenium analogue.¹⁶

4. Conclusions

Using a number of computational methods, the structural and electronic properties of gallium telluride Ga_mTe_n (m = 1, 2 and n = 1–4) clusters were investigated. One prime focus was to explore the substitution of O/S/Se by Te in the gallium clusters. The substitution of O/S/Se by Te in the studied gallium tellurides does not induce much structural changes. A structural divide is observed for the Ga₂X₂ (X = O–Te) series where Ga₂O₂ is linear, Ga₂S₂ is rhombic, Ga₂Se₂ is L-shape and Ga₂Te₂ has a butterfly structure. The reported Ga–Te bond lengths, AIPs and D_e are found to be in agreement with experimental data. The B3PW91 functional was found to provide more reliable data as it gives a smaller mean unsigned error. This is further confirmed from AIP values. Akin to gallium selenide clusters, the AEAs and AIPs of gallium tellurides are not solely related to the total number of tellurium atoms but also dependant on electronic structures. In contrast to analogous GaO₂, GaS₂ and GaSe₂, GaTe₂ is not classified as a superhalogen because it has lower AEA and VDE values than chlorine atom. The results of this research show that the substitution of an atom by another can open the door to novel structural and electronic properties.

Acknowledgements

N. S. acknowledges support from the Mauritius Tertiary Education Commission (TEC). The authors also acknowledge facilities from the University of Mauritius and the University of Namibia. The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for the research group Project No. RGP VPP-207. The authors would like to thank the anonymous reviewers for useful comments to improve the manuscript.

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Footnote

† Electronic supplementary information (ESI) available: Tables containing harmonic vibrational frequencies, ADEs, VDEs, VIPs (eV) and chemical hardness (η) of gallium telluride clusters. Figures presenting the structural evolution of mono and digallium tellurides. See DOI: 10.1039/c5ra07594g

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