Theoretical investigation of the spectroscopic properties of ZnTe, ZnTe + , and ZnTe - systems

doi:10.21203/rs.3.rs-1879560/v1

Zinc telluride (ZnTe) system presents appealing optoelectronic properties used in radiology as well as in the detection of terahertz radiation (THz). In this work, we report a theoretical investigation of the ground and excited states of ZnTe and its ions ZnTe⁺ and ZnTe⁻ using different ab inito methods. The potential energy curves (PES) are computed using the CASSCF/LANL2DZ and MRCI/LANL2DZ methods. These curves allows to infer the different spectroscopic constants such as the internuclear distance (R_e), the harmonic vibration frequency (ω_e), the rotation constant (B_e) and the dissociation energy (D_e). It was found that the electronic states of ZnTe and its ions converge to several lower dissociation limits. The existence of instable and the crossings states is due to the presence of rotational and spin-orbit interactions. The results obtained are compared to the existing experimental data and have generally shown a reasonable agreement.

ab initio Methods

ZnTe

Electronic structure

Spectroscopic constant

Potential energy curves

The field of electronic spectroscopy is a main subject of research carried out in several laboratories of chemistry, physics and astrophysics. The diatomic molecules constitute a very important test of the electronic spectroscopy considering the increasing interest to know the maximum of information on the spectroscopic properties. Recently, much attention has been given to spectroscopic studies of 3d-transition metal compounds[1], [2].

Zinc telluride (ZnTe) is one of transition metal compounds, it has a great interest because of their promising applications in optoelectronic devices [3]–[6]. It is used in various fields such as electronic luminescence [7], optical rectification and laser manufacturing [8]–[11]. It is a good candidate for potential applications in biology and medicine such as fluorescent labeling of biological molecules for the exploration of living organisms [12], [13].Currently, ZnTe is employed in the detection of terahertz radiation (THZ)[14], [15]. This spectral zone is located between the radio frequencies of the microwaves and the optical frequencies of the infrared. It is very promising in many fields such as radio astronomy, imaging and spectroscopy [16].ZnTe has also various applications in the development of solar energy systems [17]–[21].

ZnTe as a nano crystal has been the subject of several experimental and theoretical studies [22]–[25]. In the molecular state, some theoretical studies [26], [27] are recorded for this compound using the DFT theory. These studies dealt with the structural and energetic properties of the ground state.

The ZnTe⁺ and ZnTe^- systems are the ZnTe ions. To our knowledge they have not been the subject of any theoretical study prior to our own.

ZnTe and its ions are an essential test for the evaluation of theoretical methodologies that can be studied at high levels. High accuracy calculations provide effective values in the absence of experimental data, especially for ionic systems.

In this paper, we have been interested in the application of electron spectroscopy to the diatomic system ZnTe and its ions ZnTe⁺ and ZnTe^-. The structural and energetic properties of these systems are presented and the electronic affinities and the ionization potentials are calculated. The various spectroscopic constants are determined for these systems in the ground state and the different excited states. The comparison between the values of the present work is generally in reasonable agreement with those available in the literature.

The structural and energetic parameters of ground state of ZnTe and its ions are computed using the following methods: HF [28], MP₂[29], CCSD (T) [30]and MRCI[31, 32] implemented in the Gaussian 09and MOLPRO softwares[33, 34]. The notion of open shell (unrestricted) is taken into account for the ions ZnTe⁺ and ZnTe⁻. In all the calculations, we have used the Relativistic effective core potential basis set of double zeta quality LANL2DZ [35].The calculations of the electronic structures are carried out by the program MOLPRO [34], which serve to identify the excited states with different spin multiplicities. The systems are presented in the symmetry group C_2V where the representations B1 and B2 are equivalently described. Our calculations are performed at the active space self-consistent field (CASSCF) method [36]. The following pseudo potential basis: ECP28MWB [37]for Zn and ECP46MWB [38] for Te are used.

The programs NUMEROV [39]and MOLPRO make possible to calculate the spectroscopic constants from the energy of the vibrational levels. We can thus determine the values of ω_e, and ω_ex_e, as well as α_e and β_e. All these parameters are given by the position of the minimum of the potential well.

Dissociation energies are estimated from curves of potential energy surfaces. As for the wavelengths, the oscillator forces and excitation energies of the studied systems are obtained using the TDDFT-B3LYP method [40]included in the Gaussian 09 program.

Optimization of geometry

The interatomic distances (R_e), the dipole moments (μ) and the vibration frequencies (ω_e) of ZnTe system and its ions ZnTe⁺ and ZnTe^- are given in (Table 1). The analysis for this table shows that all calculation models used underestimate the internuclear distance (R_e) from ZnTe. The MRCI method gives the smallest value of the internuclear distance Re = 2.414 Å of ZnTe. The CCSD(T) method provides a distance that approximates the experimental value (the difference is of 4.13%)[41].The internuclear distance of the ZnTe⁺cation decreases in this order: R_e (UHF)> R_e (UCCSD (T))> R_e (UMP2)>R_e (MRCI).The order for the ZnTe^-anion is: R_e (UCCSD (T))> R_e (UHF)> R_e(UMP2)>R_e (MRCI).For ZnTe, MRCI and CCSD (T) methods give a vibration frequency in good agreement with the experimental value (the difference is about 3%)[42].The values of the dipole moment increase by passing from the anion (ZnTe^-) to the neutral (ZnTe) towards the cation (ZnTe⁺).For ZnTe, ZnTe⁺, and ZnTe^-the large value of the dipole moment is obtained at the level of the MRCI method.

Ionization energy and electronic affinity of ZnTe and its ions

The ionization potential (IP) and the electronic affinity (EA) are calculated with Koopmans' theorem: IP (X system) = - E_HOMO of X, EA (X system) = - E_LUMO of X where X = ZnTe, ZnTe⁺, or ZnTe^-.

The values of the HOMO and the LUMO energies and the energy gap, the ionization potential and the electronic affinity of the ZnTe system and its ions are represented in (Table 2). For ZnTe, the table indicates similar values of IP for the different methods with a small difference of 0.01 eV. For the anion, the largest energy gap is obtained at the CCSD level. The negative electronic affinity values of ZnTe^- mean that it would be necessary to supply energy to this molecule to attach an electron to it. Regarding the ionization potentials and the electronic affinities of the studied systems, the order of evolution is as follows: IP_cation˃ IP_neutral˃I P_anion

Dissociation energies of ZnTe and its ions

Experimentally, the values of the dissociation energy are based essentially on thermochemical data in the case for the ZnTe neutral system [43].In theory, only a few studies have been done to determine the dissociation energy (D_e) of ZnTe. RenginPekoz, SakirErkoç[26] and Mustafa Kurban[27] calculated D_e and showed that ZnTe dissociates according to the relation below:

ZnTe (X ¹Σ⁺) → Zn (¹S) + Te (¹D)

For ZnTe⁺, we give the dissociation following this relation:

ZnTe⁺ (X²Π) → Zn ⁺ (²S) + Te (³P)

For ZnTe^-, the dissociation is:

ZnTe^- (X ²Σ⁺) → Zn (¹S) + Te^- (²P)

The dissociation energies of the studied systems are obtained from the potential energy curves plotted with the different models used. These curves are shown respectively for ZnTe, ZnTe ⁺ and ZnTe^- in Fig.1, Fig.2, Fig.3, Fig.4 and Fig.5.

The dissociation energy values (D_e) are collated in (Table 3).We note that the dissociation energy of the neutral system is greater than those of the ions for MP2, CCSD(T), and MRCI methods. For these methods, the increasing order of energies is as follows: Anion<Cation<Neutral. For ZnTe and ZnTe⁺, the dissociation energy is the same at MRCI level. The largest dissociation energy is obtained by MRCI method for both ZnTe and ZnTe⁺ systems. Concerning ZnTe^-, the higher dissociation energy is obtained at CCSD (T) level. The De value of ZnTe estimated by the previous method is more or less in agreement with the experiment with a difference of19-44%.

Fig 2 represents the potential energy curves of ZnTe, ZnTe⁺, and ZnTe^-molecules in their ground states obtained by the MRCI and CASSCF methods. The calculation was made over a distance of 1.4-11.38 Å for a step of 0.02 Å. It is noted that the MRCI methods minimizes the potential energy of the molecule better than the CASSCF.

Curves of potential energy and spectroscopic constants

The potential energy curves of the ground state and the different excited states for the ZnTe and its ions are studied using the program Molpro. Theses curves are represented respectively for ZnTe, ZnTe⁺ and ZnTe^- in Figures 2, 3, 4 and 5.Table 4 summarizes the spectroscopic constants of the ground state and the excited states of the studied systems.

The potential energy curves (see Fig 3) are shown for ground state X¹Σ⁺ and the three singlet excited states: B¹Σ⁺, A¹Π and C¹Π, as well as the four triplet states: d³Σ⁺, b³Σ⁺, a³Π and d³Π.The electron states correlate adiabatically to these dissociation limits: Zn (¹S) + Te (³P), Zn (¹S) + Te (¹D), Zn (¹S) + Te (¹S).We note from Fig 3 that several avoided crossings are remarkable between the ground state X¹Σ⁺of ZnTe and the excited states a³Π and A¹Π.

These electronic states intersect in the energy range (8.8-8.6 a.u), which implies the presence of rotational and spin-orbit interactions.

The potential energy curves show that the energy of the state a³Πis less than that of the singlet state, this can be interpreted with the notion of the hole Fermi. This suggests that two electrons of opposite spins are more likely to repel each other if they have parallel spins. By analyzing the results of the spectroscopic constants reported in Table 4, we observe that the internuclear distance R_e of the ground state is less than the experimental values [38], the deviation is of 19%.

The same value of R_e is recorded for the ground state X¹Σ⁺ and the excited state B¹Σ⁺ (R^"_e= R_e^') which means that R_estay invariant during the transition and ZnTe molecule describes a vertical path without variation of the value of R_e: this is the first case of Franck Condon principle.

The distance R_e of the excited state A¹Π differs from that of the ground state X¹Σ⁺, so that R_e^'>R_e^": this is the second case of Franck Condon principle. For the state C¹Π, R_e^'> ˃R_e^", this is the third case of Franck Condon principle.

The vibration frequency ω_e of the ground state is in agreement with the experimental value [42], the deviations are of the order of 4.39 %. We record that most of the vibration frequencies of the excited states are greater than that of the ground state. The majority of the energies of dissociation of the excited states are lower than that of the ground state apart from the states b³Σ⁺ and c³Π.

The calculated value of the dissociation energy of the ground state is in good agreement with the experimental result [43] compared to the calculations performed with the Gaussian program. The difference is of 17%. The electronic state X¹Σ⁺ has the small value of the rotational constant B_e. Our results are compared to the work of Fancher et al [44] done on zinc oxide and its anion.

For ZnTe⁺cation, the potential energy curves (Fig 4) are presented for the ground state X²Πand the three doublet electronic states: A²Σ⁺, C²Π, and B²Σ⁺ as well as the four quartet states: b⁴Π, c⁴Π, a⁴Σ⁺ and d⁴Σ⁺.

These electron states converge to the following lowest dissociation limits: Zn ⁺ (²S) + Te (³P), Zn ⁺(²S) + Te (¹D), Zn ⁺ (²S) + Te (¹S). Our results are compared to the work of Maatouk et al [45] carried out on the MgO⁺cation. We note the absence of potential wells for the states c⁴Π, d⁴Σ⁺ and a⁴Σ⁺ (table 4), this complicates the calculation of the spectroscopic constants.

These states have very large internuclear distances and tend towards ionization. The distances R_e of the excited states are greater than that of the ground state. The excited states give frequencies of vibration lower than that of the ground state. Concerning the electronic state C²Π, it has a very low dissociation energy, which confirms its instability. The internuclear distance of this state is so greater than that of the ground state (R_e'> ˃R_e''), thus we note the presence of the third case of Franck Condon principle. About ZnTe^- anion (Fig.5), the potential energy curves are presented for the ground state X²Σ⁺ and the two doublet electronic states: B²Σ⁺ and A²Π. The calculation did not give results for quartet excited states. All electron states converge adiabatically towards the lowest dissociation limit Zn (¹S) + Te^- (²P).A crossing between the X²Σ⁺ and A²Π states is recorded, this results reveals the presence of rotational and spin-orbit interactions. The comparison between internuclear distances indicates that the first transition X²Σ⁺ B²Σ⁺is placed within the framework of the second case of Franck Condon principle (R_e '> R "_e).The highest vibration frequency is given to the ground state X²Σ⁺.

The electronic state B²Σ⁺ gives the highest dissociation energy, although the state A²Π indicates the lowest dissociation energy. Our results are compared to the work of Fancher et al [44] about zinc oxide and its anion.

Evolution of transition moments

The evolution of the transition moments for ZnTe and its ions ZnTe⁺ and ZnTe^- are reported respectively in Figs.6(a), 6(b) and 6(c).We only considered the allowed transitions. These curves show changes at different internuclear distances.

Sudden jumps are noted for these moments, this can be explained by the existence of avoided crosses between potential energy curves at these particular distances. On the other hand, these changes are often related to the strong interactions (responsible for the transfer of electrons) and the change of sign of electronic wave functions. For the dipole-allowed transition between the lowest states for the same spin. Our theoretical results will be useful in the design of future experiments (fluorescence, luminescence, etc.) for the molecule ZnTe and its ions. We bring to mind that zinc was detected in the interstellar medium [46] the same thing for tellurium [47]. Advanced research in this field will soon be used to detect our diatomic systems.

Properties of excited states of ZnTe and its ions

The excitation energies, the oscillator forces, the wavelengths of the system ZnTe and its ions are calculated using the TDDFT method with B3LYP functional and shown in (Table 5).The examination of this table indicate that the oscillator force increases in this order ZnTe→ZnTe^-→ZnTe⁺. ZnTe system has wavelengths greater than those of ZnTe^-and ZnTe⁺(Fig.7). The excitation energies of ZnTe⁺ are very higher compared to the other studied systems. The majoritar transitions for the intense band absorption are: HOMO-2→LUMO (48.02%) for ZnTe, HOMO-1→LUMO + 1 (98%) for ZnTe + and HOMO-1→LUMO + 1 (50%) for ZnTe^-.

In this paper, we investigated the spectroscopy of ZnTe molecule and its ions ZnTe⁺ and ZnTe. We calculate their structural and energetic parameters as well as the potential energy curves (PEC).The theoretical spectroscopic constants (R_e, ω_e, B_e,D_e) have been also considered for the three systems. Concerning the results we note generally a good agreement with the available experimental data. The electronic states of ZnTe and its ions converge to several lower dissociation limits. We record the presence of instable states and the existence of crossings between a few states which is due to the presence of rotational and spin-orbit interactions. We note also the presence of the three cases of Franck Condon principle. All these theoretical results could help to any future experiments (fluorescence, luminescence ... etc) or interstellar detection.

Acknowledgment.

The authors thank the Instituto de Estructura de la Materia, IEM-C.S.I.C., Serrano, Madrid (Spain) for making the preliminary calculations available. We would particularly thank Dr. Vicente Timon, Department of physics, CSIC Madrid Spain and professor Maria Luisa Sent Diaz.

Funding

No funding was received for conducting this study.

Conflict of interest.

The authors declare they have no conflict of interest. The authors have no relevant financial or non-financial interests to disclose.

Availability of data and material

The authors declare that they have data and material corresponding of the study.

Code availability

All final calculations (of the study) are carried out in our laboratory: Laboratoire de chimie théorique ,computationnelle et photonique (USTHB Algeria) using the Gaussian and Molpro laboratory codes.

Authors' contributions

All authors have seen and approved the manuscript and have contributed considerably for its realization:

Dr Nour El Houda BENSIRADJ realizes the Gaussian calculation and a part of Molpro calculations. She wrote the main manuscript text, and performs the interpretations of the different results.

Dr. Houssyen YOUSFI :has provided a lot of help in the calculations using the Molpro program and prepared the tables and references .

Dr. Taha BENSIRADJ: has provided invaluable help through his expertise in computational methods as well as configuring and using scientific software and high performance computing machines, and prepared the figures

Prof. Ourida OUAMERALI as the director of the laboratory which I'm a part of, has guided me all along my way to achieve the present paper and has provided invaluable help through his expertise in electronic spectroscopy.

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Table 1: Property values R_e, μ, and ω_eof ZnTe and its ions ZnTe⁺, and ZnTe^-
System	Methods’	R_e(Å)	μ(Debye)	ω_e(cm^-1)
ZnTe	HF-LANL2DZ	2.488	6.22	208.2
	MP₂- LANL2DZ	2.438	6.25	246.6
	CCSD-LANL2DZ	2.482	6.23	220.7
	MRCI-LANL2DZ	2.414	6.57	236.1
	Experimental	2.636[1]	-	228 [2]
ZnTe⁺	UHF-LANL2DZ	2.710	6.50	130.5
	UMP₂- LANL2DZ	2.536	6.86	236.9
	UCCSD-LANL2DZ LANL2DZ	2.626	6.66	188.7
	MRCI-LANL2DZ	2.522	7.51	-
ZnTe^-	UHF-LANL2DZ	2.583	1.92	177.8
	UMP₂- LANL2DZ	2.540	1.90	215.7
	UCCSD-LANL2DZ	2.593	1.92	181.1
	MRCI-LANL2DZ	2.520	2.77	193.4

Table 2: Orbital energies HOMO, LUMO, energy gap (ΔE=E_LUMO-E_HOMO), ionization potential (IP), and electronic affinity (EA) of ZnTe and its ions in eV
System	Method		HOMO	LUMO	ΔE	IP	EA
ZnTe	HF-LANL2DZ		-7.75	-1.52	6.22	7.75	1.52
	MP₂- LANL2DZ		-7.77	-1.49	6.27	7.77	1.49
	CCSD-LANL2DZ		-7.75	-1.52	6.23	7.75	1.52
	MRCI-LANL2DZ		-7.76	-1.54	6.21	7.76	1.54
ZnTe⁺	UHF-LANL2DZ		-14.45	-3.43	11.07	14.45	3.43
	UMP₂- LANL2DZ		-13.49	-6.81	6.68	13.49	6.81
	UCCSD-LANL2DZ		-14.45	-6.69	7.76	14.45	6.69
	MRCI-LANL2DZ		-13.90	-6.98	6.91	13.90	6.98
ZnTe^-	UHF-LANL2DZ		-2.20	4.72	6.92	2.20	-4.72
	UMP₂- LANL2DZ	-2.24		4.76	7.0	2.24	-4.76
	UCCSD-LANL2DZ	-2.43		5.18	7.62	2.43	-5.18
	MRCI-LANL2DZ	-2.59		4.14	6.73	2.59	-4.14

Table3 : Dissociation energies (D_e) ofZnTeand its ions.
System	Method	D_e (eV)
ZnTe	HF-LANL2DZ	1.19
	MP₂- LANL2DZ	1.58
	CCSD(T)-LANL2DZ	1.14
	MRCI-LANL2DZ	1.71
	Experimental	0.95^a[43]
ZnTe⁺	UHF-LANL2DZ	0.52
	UMP₂- LANL2DZ	1.15
	UCCSD(T)-LANL2DZ	1.08
	MRCI-LANL2DZ	1.71
ZnTe^-	UHF-LANL2DZ	0.69
	UMP₂- LANL2DZ	0.9
	UCCSD(T)-LANL2DZ	1.01
	MRCI-LANL2DZ	0.87

Table 4: Spectroscopic constants of different states of ZnTe and its ions.
System	state	R_e/ (A°)	ω_e/Cm^-1	ω_eXe/Cm^-1	B_e/Cm^-1	α_e/Cm^-1	D_e (eV)
ZnTe	*X¹Σ ⁺*	2.44	218.119	1.794	0.37010	0.00399	1.12
	*B¹Σ ⁺*	2.44	333.988	0.66701	0.09518	0.00015	1.02
	*A¹Π*	2.6	455.647	3.54125	0.32115	0.00334	1.09
	*C¹Π*	4	207.221	0.32168	0.14948	0.00049	0.95
	*b³Σ ⁺*	2.6	418.432	0.20234	0.31714	0.00276	1.69
	*d³Σ ⁺*	2.8	115.223	0.77831	0.09092	0.00057	0.59
	*a³Π*	2.7	362.412	5.70112	0.30227	0.00486	0.29
	*c³Π*	3	264.104	0.99824	0.18681	0.00105	1.34
ZnTe⁺	*X²Π*	2.6	408.342	4.25648	0.31873	0.00405	0.99
	*C²Π*	4	66.515	1.56184	0.12366	1.56184	0.032
	*A²Σ ⁺*	3	254.928	1.22017	0.24323	0.00331	0.79
	*B²Σ ⁺*	3	234.313	5.78600	0.23549	0.00435	0.21
	*b⁴Π*	3	232.312	2.12933	0.20411	0.00247	0.62
	*c⁴Π*	6	-	-	-	-	-
	*d⁴ Σ ⁺*	8	-	-	-	-	-
	*a⁴ Σ ⁺*	8	-	-	-	-	-
ZnTe^-	*X²Σ ⁺*	2.5	468.397	5.70567	0.34096	0.00431	2.3
	*B²Σ ⁺*	2.8	367.672	1.07869	0.26990	0.00088	3.24
	*C²Π*	4	76.794	2.83300	0.16950	0.00590	0.18

Table 5: Excitation energie (E_exc), in eV, oscillator strength (f), transition wavelength (λ) in nm for excited states of ZnTe and its ions.
System	E_exc	λ	f	Transition
ZnTe	6.07	204.03	1.48	H-2-L (48.02%) H-1-L+1 (25.92%)
	5.37	230.83	0.06	H-L+3 (79.38%)
	3.65	339.55	0.03	H-2-L (50%)
ZnTe⁺	6.25	198.26	0.92	H-1-L+1 (98%)
	7.79	159.14	0.57	H-2-L+2 (98%)
	7.63	162.44	0.46	H-2-L+1 (98 %)
ZnTe^-	4.78	259.35	0.99	H-1-L+1(50%)
	4.31	287.68	0.06	H-1-L+2 (67.28%)
	5.07	244.31	0.04	H-3-L (85%)

No competing interests reported.

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Theoretical investigation of the spectroscopic properties of ZnTe, ZnTe + , and ZnTe - systems

Status:

Version 1

Abstract

Figures

Introduction

Computational Details

Results And Discussion

Conclusion

Declarations

References

Tables

Additional Declarations

Supplementary Files

Status:

Version 1