First Principles Calculation of Magnetic Resonance Properties of Cu 2− δ X (X = Se, S, Te)

In order to have a better understanding of the electronic structures and physical properties of Cu 2−δ X (X = Se, S, Te) copper chalcogenides. First principles were performed to calculate the chemical shift, band structure, and electron density of states of Cu 2−δ X (X = Se, S, Te). By comparing our calculation results with previous experimental works, we found that the predicted electronic structures of Cu 2 Se, Cu 2 Te and Cu 2 S transform from semimetal to semiconductor after adding on-site Coulomb U, which reflects the real properties of the materials. By using (Density Functional Theory) DFT + U method, the calculation result is close to the real electronic structure. The calculation result of chemical shift of adding U does not reach the ideal expecta-tion, and the reason is not clear at present. In this paper, the theoretical electronic structures of Cu 2 Se, Cu 2 Te and Cu 2 S are better calculated by DFT + U method and compared with the actual properties. The effect of Cu-s electron on the chemical shift is understood, and a theoretical result of the chemical shift is calculated, which provides a powerful reference for the subsequent research and understanding of the electronic structure and physical properties of the compounds with S groups of Cu.


Journal of Applied Mathematics and Physics
of Cu ions in the Se atomic crystalline sublattice results in low thermal conductivity and high ZT (thermoelectric figure of merit) [3] [4] [5] [6], which is beneficial for the performance of such thermoelectric materials [7] [8]. The development of thermoelectric technology provides an efficient and emission-free method for the recycling of industrial waste heat [9] [10] [11]. Moreover, Cu 2 Se is a typical P-type semiconductor with an indirect band gap of 1.23 eV, which is close to the ideal value for solar cell applications. Therefore, Cu 2 Se is considered as a possible energy conversion material in photovoltaic as well [12]. These excellent performances of Cu 2 Se provide a good way to solve the global energy shortage and improve the efficiency of energy conversion and utilization.
The crystal structure of Cu 2 Se is complex. There are two different phase structures for Cu 2 Se, which are distinguished by low temperature α-phase and high temperature β-phase, respectively [13] [14]. Below 400 K, the low temperature α-phase Cu 2 Se has several possible crystal structures. The Cu sublattice changes from ordered to disordered as the temperature increases, but the details of the process are still not very clear [15] [16]. The high temperature and low temperature phases of Cu 2 Se have been studied. But crystal structure of the low temperature monoclinic phase is relatively complex and is still not fully understood [17] [18]. The high-temperature phase has been identified as the cubic phase (space group Fm-3m) [19]. The superior performance of Cu 2 Se (ZT) is influenced by its electrical transport property, which in turn strongly correlated with the electronic structure of it. Therefore, the properties of Cu 2 Se, Cu 2 S and Cu 2 Te are closely related to their electronic structures, better understanding of their electronic structures can help optimizing the performance of such materials. Nuclear magnetic resonance (NMR) is considered as an important technique for investigating the local chemical environment of certain isotropic. It is also a local probe for observing the ionic diffusion [20] [21]. Moreover, NMR chemical shift can well reflect the related characteristics of electronic structure. The study of this paper is based on first principles, using VASP, CASTEP and other software; some parameters of NMR were calculated theoretically. The theoretical calculation results of chemical shift in NMR are compared with those of energy band structure and electron density of states, The theoretical results of NMR chemical shift and electronic structure are calculated by different methods, and the electronic structure characteristics of S group compounds of Cu are analyzed and compared theoretically from different angles, It is helpful to deepen the understanding of structural properties of S group metal materials such as Cu 2 Se [22].
There have been studies on NMR based on sulfur-based metal compounds, on this basis, Cu 2 Se's high temperature phase is selected as the research system (space group is Fm-3m), There are two Cu crystallographic sites in the average structure of Cu 2 Se, namely 8(c) and 32(f) sites [23] [24]. The structure of Cu 2 Se calculated in this paper only considers the 8(c) bits of Cu atom. Asadov et al.
summarized the previous experiments of Cu 2 Te phase. There are many different phases at different temperatures, and phase transitions occur with temperature, Cu 2 Te has a cubic antifluorite structure at 835 K [25] [26]. Cu 2 Se and Cu 2 S also Journal of Applied Mathematics and Physics have complex phase transitions with different temperatures [27] [28]. Cu 2 S is a face-centered cubic phase structure at 700 K, so the space group of Cu 2 S is also selected as Fm-3m to do relevant calculations [29]. The high temperature opposite fluorite structure of Cu 2 Se is shown in Figure 1. The NMR chemical shift characteristics of Cu 2 Se are studied by VASP and CASTEP, and compared with the theoretical calculation of electronic structure.
Previous NMR experiments can measure Chemical Shifts, which can reflect some electronic properties and characteristics, but have no way of associating Knight shift with specific atoms. In recent years, the method of matching chemical shifts with specific atoms has been developed, and the chemical shifts calculated by NMR simulation have been compared with the theoretical calculations of electronic structures, which provide a new perspective and reference for the understanding of the properties of electronic structures, making the calculation results more reliable and meaningful.
Therefore, the purpose of this paper is to explore how to obtain the electronic structures of Cu 2 Se, Cu 2 Te and Cu 2 S that are more consistent with the actual conditions through first-principles calculation. The chemical shifts of the three materials are also calculated to obtain the information of electronic structure.
The main contribution of this paper is that the calculation using (Density Functional Theory) DFT + U can better reflect the real electronic structures of the three materials. Through the analysis of the electron density of states of the materials, it is known that Cu-s electrons should have the greatest influence on the chemical shift, but the results calculated by VASP and CASTEP do not meet the expectation.

Computational Details
The calculation of this work is based on density functional theory (DFT) [30] and implemented in the Vienna Ab initio Simulation Package (VASP) [31] [32].
We use the Perdew-Burke-Ernzerhof (PBE) type of generalized gradient approximation (GGA) as the exchange-correlation functional [33] [34] [35]. The Se (4s 2 , 4p 4 ), Te (5s 2 , 5p 4 ) and S (3s 2 , 3p 4 ). The interaction between the core electrons and the valence electrons is included by the standard frozen-core projector augmented-wave (PAW) potentials provided within the VASP package [36]. In this paper, we use the PBE + U method to calculate the band structure, density of states, and chemical shifts. During Cu 2 Se Structure optimization, we adopt the Monkhorst-Pack scheme k-point mesh from gamma to the 21 × 21 × 21 point and use finer k-points to further calculate the electronic structures; the convergence precision of ions and electrons is 1 × 10 −6 eV, and the cut-off energy is set to 500 eV. VASP and CASTEP were used to calculate the NMR chemical shifts, the cut-off energy is set to 1000 eV, and the Automatic mesh k-points grid was 21 × 21 × 21.

Results and Discussion
It is found that the 63 Cu NMR chemical shifts of existing literature of Cu 2 Se samples remain almost unchanged above 400 K [20]. As we know, the addition of Cu atoms in Cu 2 Se will provide more free electrons.

NMR Chemical Shift Calculation Results
In order to further understand its electronic structure, energy band structure and other characteristics, we used different software to calculate the theoretical results of NMR chemical shift, and analyzed the changes of solid NMR chemical shift after adding U. The calculated NMR isotropic chemical shifts are listed in Table 1. Various on sites Coulomb U values are added to search the effect of U on the calculated chemical shifts. Generally, the calculated chemical shifts of Cu 2 S, Cu 2 Se, and Cu 2 Te using VASP program are close. With increasing U values, the calculated shifts became smaller and smaller. Thus, according to the results of VASP, the effect of on-sites Coulomb U cannot be neglected. The results of CASTEP are different. The calculated chemical shifts are much more different from each other. Moreover, the varied U values had nearly no effect on the calculated chemical shifts. The differences between these VASP and CASTEP are not very clear. Figure 2 shows the calculated density of states of Cu 2 S, Cu 2 Se and Cu 2 Te. Since we will discuss the chemical shifts of Cu, only the contribution made by Cu atoms are shown. According to the calculation results of PBE method, it can be seen from −4 eV to Fermi level, the density of states is mainly contributed by Cu-3d electrons. It can be seen that among the three kinds of materials, the

Band Structure
In the calculation of energy band structure and electronic density of states, VASP is used to calculate Cu 2 Se, Cu 2 S, Cu 2 Se with various on-site Coulomb U. The method of PBE + U (U = 10 eV) has been used to explore the electronic structure of Cu 2 Se, and reliable results have been obtained by Rasander M, Bergqvist L, Delin A. [39]. According to the works of Rasander M. 4 eV, 7.5 eV and 10 eV are applied in this work. The cut-off energy was set to 1000 eV. Figure 4 shows the band structure diagram of the high-temperature phase of Cu 2 Se, Cu 2 S, Cu 2 Te. It can be seen that when U is not added, there is no band gap in the band structure of Cu 2 Se, so it is predicted as a semimetal. When U is added to 10 eV, the band gap appears obviously. That is to say, its band structure is considered as a semiconductor. Therefore, the band gap generated when U is added more accurately reflects the real band structure, indicating that adding U can make the theoretical results closer to the real band structure. It can be seen Figures 4(c)-(f), the same situation occurs when Cu 2 S and Cu 2 Te U were added in the calculation of energy band. Therefore, when calculating the band structure of such materials and calculating the electronic density of states, it is necessary to add U appropriately to ensure the accuracy of calculation. With the consideration above, DFT + U method were performed to the calculation of chemical shifts of these copper chalcogenides.

Conclusion
In this paper, the density of states, band structures and NMR chemical shifts of Cu 2 Se, Cu 2 S and Cu 2 Te have been systematically studied by first principles calculation. By performing a DFT + U calculation, the band gap of Cu 2 X opened and showed semiconductor structures. Our calculation of DOS shows that the density of states of Cu 2 Se, Cu 2 S and Cu 2 Te is mainly contributed by the d electrons. However, due to the influence of Van Vleck paramagnetization, the d electron has little effect on the chemical shift. However, the contribution of p-electron