A coordinate transformation method for single atoms in complex group-substituted perovskites

The coordinate conversion method replaces single atoms in perovskites with complex atom groups, which solves the problem of low modeling accuracy and efficiency, simplifies the introduction of complex groups, and improves the calculation and design accuracy of photoelectric properties.

CN115458074BActive Publication Date: 2025-07-08FUZHOU UNIV +2
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Patent Information

Application Number
CN202211125570.4
Authority / Receiving Office
CN · China
Patent Type
Patents(China)
Current Assignee / Owner
Filing Date
2022-09-15
Publication Date
2025-07-08
Estimated Expiration
2042-09-15

AI Technical Summary

Technical Problem

The prior art is difficult to introduce complex atomic groups into perovskite unit cells in a simple and efficient manner, resulting in low modeling accuracy and low efficiency, affecting the reliable calculation and design of photoelectric properties.

Method used

The coordinate conversion method is used to replace complex atomic groups with single atoms in perovskites, and the doped unit cell model is constructed by downloading, optimizing and visualizing files.

Benefits of technology

It realizes the rapid and accurate introduction of complex groups, improves modeling accuracy and efficiency, and provides reliable guarantees for the calculation and design of photoelectric properties.

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Abstract

The present invention relates to a coordinate transformation method for single atoms in complex group-substituted perovskites. This method can introduce complex atomic groups into the perovskite unit cell to replace the original atoms or atomic groups through simple coordinate transformations, effectively and quickly constructing complex unit cell models, providing accurate guarantees for subsequent optimization calculations. At the same time, when performing multi-atom or atomic group substitution doping in the system, this method can record the coordinates of each atomic group used to replace atoms or atomic groups in tools such as Excel tables and Word through coordinate transformation, and can be arbitrarily combined in subsequent optimization calculations. At the same time, this method can also perform operations such as orientation changes on the doped atomic groups through coordinate transformation, which is simple, fast and effective.
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Description

Technical Field

[0001] The present invention relates to a coordinate conversion method for single atoms in complex group-substituted perovskites. Background Art

[0002] Traditional perovskite (CaTiO3), as the name of a mineral, was first discovered by mineralogist Gustav Rose in skarn in 1839. Initially, this mineral did not arouse the interest of scientists and mineralogists when it was discovered, but now it has become one of the most widely used ores. The crystal structure of perovskite materials is generally represented by ABX3, where A and B are monovalent and divalent cations respectively, and X is a monovalent anion.

[0003] As an emerging energy material, perovskite has broad application prospects in the fields of solar cells, field-effect transistors, LEDs, photodetectors, and lasers due to its high absorption coefficient, high carrier mobility, long carrier diffusion length, and adjustable direct bandgap. In particular, perovskite solar cells have attracted extensive attention from researchers around the world because of their simple preparation process, low cost, and rich variety. Their power conversion efficiency (PCE) has rapidly increased from 3.8% to 27% in just a few years, and their power conversion performance has exceeded that of dye-sensitized solar cells and other thin-film solar cells. Methylammonium lead iodide (CH3NH3PbI3), as the core material of organic-inorganic hybrid perovskite solar cells, has advantages such as a suitable bandgap, high light absorption coefficient, and long carrier lifetime. It can absorb photons to generate electron-hole pairs and thus achieve photoelectric conversion. The CH3NH3PbI3 perovskite material has poor stability, is volatile in the presence of oxygen, and decomposes easily in water. Generally, researchers regard whether a material can exist stably and be continuously used as a criterion for evaluating its commercial application. However, due to the ionic nature of perovskite materials themselves, their stability is very poor. Introducing impurities into organic-inorganic hybrid perovskites is a relatively effective way to solve these problems. Reasonable doping of different elements at different positions can improve structural stability, adjust the bandgap to introduce new energy levels, and regulate the emission wavelength to improve luminescence efficiency, etc. CH3NH3PbI3 has a variety of derivatives, all of which can be obtained by replacing atoms or complex atomic groups. Among them, doping different ratios of A-site organic cations can effectively adjust the bandgap; partial substitution of X-site halide ions by another anion has been shown to cause a significant shift in the absorption band and enhance carrier transport; doping of B-site metal ions can significantly reduce the lead content in perovskite, reduce the toxicity of lead, and at the same time introduce additional energy transport channels in the matrix to obtain unique photovoltaic properties. Therefore, tuning the composition by doping metal halide perovskite ABX3 can significantly improve the optoelectronic properties of perovskite materials, and these properties are ideal for applications in high-efficiency solar cells, photodetectors, and light-emitting diodes (LEDs). Such tuning is achieved by doping at the A-site such as methylamine (MA), formamidine (FA), Cs, at the B-site with Pb, Sn, and at the X-site with Cl, I, Br, etc. Among the three-position doping, A-site doping introduces complex atomic groups. The complex atomic groups face problems such as bond length, bond angle, and overall orientation of the group, and it is not easy to accurately establish the model using modeling software such as MaterialsStudio.

[0004] Meanwhile, as three-dimensional perovskite materials are vulnerable to damage under high temperature, high humidity, and light, their poor long-term stability and lead toxicity are hindering their practical applications. To overcome these problems, researchers have attempted to develop new types of low-dimensional perovskite materials. Compared with traditional three-dimensional perovskites, the structures of these low-dimensional perovskites are more complex to quantitatively describe. After doping with complex groups, it becomes even more difficult to describe the atomic positions in these complex groups, which not only affects the modeling accuracy but also results in very low modeling efficiency. A large number of attempts are required to obtain a relatively reasonable and effective doping structure for reliable calculation and design of their optoelectronic properties.

[0005] Therefore, we need to use a more simple and effective general modeling method to introduce complex atomic groups into the perovskite unit cell to replace the original atoms.

[0006] A method for doping atomic groups by coordinate transformation is proposed. This method can introduce complex atomic groups into the perovskite unit cell to replace the original atoms through simple coordinate transformation, effectively and quickly constructing a complex unit cell model, providing accurate guarantee for subsequent optimization calculations. Summary of the Invention

[0007] The purpose of the present invention is to provide a coordinate transformation method for replacing single atoms in perovskite with complex groups, which can introduce complex atomic groups into the perovskite unit cell to replace the original atoms through simple coordinate transformation, effectively and quickly constructing a complex unit cell model for reliable calculation and design of its optoelectronic properties.

[0008] To achieve the above objective, the technical solution of the present invention is: a coordinate transformation method for replacing single atoms in perovskite with complex groups, comprising the following steps:

[0009] Step S1: Identify the atomic group to be used for replacement and the atoms in the original compound to be replaced;

[0010] Step S2: Download the *.cif format structure file of a simple compound containing the atomic group to be used for replacement from websites such as Materials Project, where * is the compound name, convert it to a POSCAR file using VESTA software, and optimize it using VASP;

[0011] Step S3: After the optimization in Step S2, download the CONTCAR file, extract the coordinates of a group of atomic groups therein, and visualize them using VESTA software;

[0012] Step S4: In the POSCAR file of the original compound, find and record the coordinates of the atoms to be replaced;

[0013] Step S5: Determine the central position of the atomic group to be substituted in the CONTCAR file (the "center" here does not refer to the definition of the physical or structural center point, but a point with special position information), and confirm the relative position with the atom to be substituted; subtract the coordinates of the central position of the atomic group to be substituted from the coordinates of the atom to be substituted, and then add the difference to the coordinates of each atom of the atomic group.

[0014] Step S6: Put the coordinates of the atomic group into the POSCAR file, and delete the coordinates of the original atoms to obtain the new doped POSCAR file; visualize the crystal structure of the doped system with VESTA software, and after checking and confirming, perform the optimization calculation.

[0015] In an embodiment of the present invention, in step S3, when optimizing the CONTCAR file with VASP, the fractional coordinates should be converted into Cartesian coordinates.

[0016] In an embodiment of the present invention, in step S3, when it is found through inspection that the coordinates of each atom in one set of atomic groups extracted do not lie within one atomic group, a coordinate transformation is performed, that is: when the atomic groups are arranged periodically and the atomic coordinates do not lie within one unit cell, by adding or subtracting the corresponding multiples of the lattice constants in the coordinates, the atomic coordinates of the atomic group are transformed to lie within one unit cell.

[0017] In an embodiment of the present invention, in step S4, for the POSCAR file of the original simple compound, Cartesian coordinates should be selected.

[0018] In an embodiment of the present invention, when performing multi-atom or atomic group substitution doping, this method can record the coordinates of each atomic group used to replace the atom or atomic group through coordinate transformation in tools including Excel tables and Word, so as to be arbitrarily combined in the optimization calculation; at the same time, this method can also perform operations including orientation changes on the doped atomic groups through coordinate transformation.

[0019] Compared with the prior art, the present invention has the following beneficial effects: Compared with the modeling methods of software such as Materials Studio, the present invention can easily and accurately complete the doping of complex atomic groups through coordinate transformation, and can study complex problems such as orientation and subsequent arbitrary combinations of doped groups, which is simple, fast and effective. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is the unit cell structure of CsPbI3 in Case 1 of the present invention;

[0021] Figure 2 It is MA in Case 1 of the present invention +(CH3NH3 + ) Group structure diagram;

[0022] Figure 3 This is the POSCAR file of CsPbI3 in Example 1 of the present invention;

[0023] Figure 4 This is the POSCAR file of MAPbI3 in Example 1 of the present invention;

[0024] Figure 5 This is the unit cell structure of MAPbI3 in Example 1 of the present invention;

[0025] Figure 6 This is for changing MA + The POSCAR file of MAPbI3 with the orientation changed in Example 1 of the present invention;

[0026] Figure 7 This is for changing MA + The unit cell structure of MAPbI3 with the orientation changed in Example 1 of the present invention;

[0027] Figure 8 This is the unit cell structure of Cs3Cu2I5 in Example 2 of the present invention;

[0028] Figure 9 This is for a group of NH4 + Visualization of group atoms;

[0029] Figure 10 This is for the visualization of NH4 + Group atoms after coordinate transformation in Example 2 of the present invention;

[0030] Figure 11 This is the POSCAR file of Cs3Cu2I5 in Example 2 of the present invention;

[0031] Figure 12 This is the POSCAR file of Cs3Cu2I5 with Cs1 replaced in Example 2 of the present invention;

[0032] Figure 13 This is the crystal structure of Cs3Cu2I5 with Cs1 replaced in Example 2 of the present invention. Detailed implementation mode

[0033] Next, in conjunction with the attached drawings, the technical solutions of the present invention will be specifically described.

[0034] The "coordinate transformation method for single atoms in complex group substituted perovskites" of the present invention includes the following steps:

[0035] Step S1, confirm the atomic group used for substitution and the atoms in the original compound to be substituted;

[0036] Step S2: Download the structure file in *.cif format of a simple compound containing the atomic group to be substituted on websites such as Materials Project, where * is the compound name, convert it into a POSCAR file using VESTA software, and optimize it using VASP;

[0037] Step S3: After the optimization in Step S2, download the CONTCAR file, extract the coordinates of a group of atomic groups therein, and visualize them using VESTA software;

[0038] Step S4: In the POSCAR file of the original compound, find and record the coordinates of the atom to be substituted;

[0039] Step S5: Determine the central position of the atomic group to be substituted in the CONTCAR file (the so-called center here does not refer to the definition of the physical or structural center point, but a point with special position information), and confirm the relative position with the atom to be substituted; Subtract the coordinates of the central position of the atomic group to be substituted from the coordinates of the atom to be substituted, and then add the difference to the coordinates of each atom of the atomic group;

[0040] Step S6: Put the coordinates of the atomic group into the POSCAR file, and delete the coordinates of the original atoms to obtain a new POSCAR file after doping; Visualize the crystal structure of the doping system using VESTA software, and after checking that it is correct, perform optimization calculations.

[0041] The present invention will be further described below in conjunction with two implementation cases.

[0042] Case 1: Doping MA + (CH3NH3 + ) group in the three-dimensional perovskite CsPbI3 unit cell.

[0043] In this embodiment, taking the perovskite CsPbI3 as an example, using MA + (CH3NH3 + ) this functional group to replace Cs + therein, a coordinate conversion method for replacing a single atom in a perovskite with a complex group is provided, including the following steps:

[0044] Step S1: Confirm using MA + (CH3NH3 + ) to replace Cs + in CsPbI3, and the unit cell structure of CsPbI3 is as Figure 1 shown;

[0045] Step S2: Download the one containing MA + (CH3NH3+ ) The structure file of the simple compound MAPbI3 (CH3NH3PbI3) of the group in cif format was converted into a POSCAR file using VESTA software and optimized using VASP;

[0046] Step S3: After optimization, download the CONTCAR file and extract a set of MA + (CH3NH3 + ) The coordinates of the group are shown in Table 1. The extracted MA + group was visualized using VESTA software, as Figure 2 shown.

[0047] Table 1 Coordinates of a set of MA + (CH3NH3 + ) group

[0048] x y z C 4.8382 5.2389 9.5556 <![CDATA[H1]]> 4.0746 6.0225 9.5556 <![CDATA[H2]]> 5.4551 5.3113 10.4569 <![CDATA[H3]]> 5.4551 5.3113 8.6543 N 4.1487 3.9121 9.5556 <![CDATA[H4]]> 3.5450 3.8054 10.3849 <![CDATA[H5]]> 4.8152 3.1211 9.5556 <![CDATA[H6]]> 3.5450 3.8054 8.7262

[0049] Among them, for the POSCAR file optimized using VASP, the fractional coordinates should be converted into Cartesian coordinates;

[0050] Step S4: For the POSCAR file of CsPbI3, also select Cartesian coordinates, as Figure 3 shown, find and record the coordinates (3.2071, 3.2071, 3.2071) of the Cs atom to be replaced;

[0051] Step S5: Determine the central position X of the MA + (CH3NH3 + ) group (i.e., the position coordinates of the midpoint of the C-N bond), and confirm the relative position between X and the replaced Cs atom. Subtract the original coordinates of the central position X of the MA + (CH3NH3 + ) group from the coordinates of the Cs atom, and then add the difference to the original coordinates of the C, N, and H atoms of the MA + (CH3NH3 + ) group;

[0052] From C(4.8382, 5.2389, 9.5556) and N(4.1487, 3.9121, 9.5556), the original coordinates of the central position X can be obtained as [(4.8382 + 4.1487) / 2, (5.2389 + 3.9121) / 2, (9.5556 + 9.5556) / 2], that is, the original coordinates of X are (4.4934, 4.3752, 7.1969). The coordinates of the Cs atom are (3.2071, 3.2071, 3.2071). Using MA + (CH3NH3 +) The Cs atom is replaced by a group, that is, the central position X of the group replaces the Cs atom coordinates. At this time, the coordinates of the central position X are (3.2071, 3.2071, 3.2071). Using the above method, the coordinates of C are obtained as (3.2071 - 4.4934 + 4.8382, 3.2071 - 4.3752 + 5.2389, 3.2071 - 7.1969 + 9.5556), that is, the coordinates of C are (3.5518, 4.0708, 5.5657). Similarly, the coordinates of H1, H2, H3, N, H4, H5, and H6 can be obtained, as shown in Table 2.

[0053] Table 2 Atomic coordinates of MA + (CH3NH3 + ) after coordinate transformation

[0054] x y z C 3.5518 3.8704 3.2071 <![CDATA[H1]]> 2.7882 4.6540 3.2071 <![CDATA[H2]]> 4.1687 3.9429 4.1084 <![CDATA[H3]]> 4.1687 3.9429 2.3058 N 2.8623 2.5437 3.2071 <![CDATA[H4]]> 2.2586 2.4369 4.0364 <![CDATA[H5]]> 3.5288 1.7527 3.2071 <![CDATA[H6]]> 2.2586 2.4369 2.3777

[0055] Step S6: Delete the Cs atom and its coordinates from the POSCAR file of CsPbI3, and put the coordinates of the substituted MA + (CH3NH3 + ) group into the POSCAR file, and then the doped POSCAR file is obtained, as Figure 4 shown. The obtained POSCAR file of the doped system is visualized with VESTA software, as Figure 5 shown.

[0056] If the influence of the orientation problem of the group needs to be studied, this coordinate transformation can also be easily used to achieve the effect. In Example 1, if it is necessary to change the orientation of the MA + (CH3NH3 + ) group, the atoms of the MA + (CH3NH3 + ) group after coordinate transformation can be mirrored with respect to the plane where x = 4.4934 with the center point X as the center, and then the MA + (CH3NH3 + ) group with the changed orientation can be obtained. Taking the C atom as an example. The coordinates of C are (3.5518, 4.0708, 5.5657), and the coordinates of X after coordinate transformation are (3.2071, 3.2071, 3.2071) at this time. The coordinates of the symmetric C are (2×3.2071 - 3.5518, 3.8704, 3.2071), that is, the coordinates of C after changing the orientation are (2.8623, 3.8704, 3.2071). Similarly, the coordinates of other atoms can be obtained, as shown in Table 3.

[0057] Table 3 Atomic coordinates of MA + (CH3NH3 + ) after changing the orientation

[0058]

[0059]

[0060] The POSCAR file of the MAPbI3 with the changed orientation is as Figure 6 shown and visualized with the VESTA software as Figure 7 shown.

[0061] In Case 2, NH4 + atomic groups are doped into the 0D perovskite Cs3Cu2I5.

[0062] In this embodiment, taking the perovskite Cs3Cu2I5 as an example, using the NH4 + functional group to replace Cs + in it, a coordinate conversion method for replacing atoms with complex groups of perovskite is provided, including the following steps:

[0063] Step S1: Confirm that NH4 + is used to replace Cs in Cs3Cu2I5, and the unit cell structure of Cs3Cu2I5 is as + shown; Figure 8 shown.

[0064] Step S2: Download the structure file in cif format of the simple compound NH4PbI3 containing the NH4 + group from websites such as Materials Project, convert it into a POSCAR file with the VESTA software, and optimize it with VASP;

[0065] Step S3: After optimization, download the CONTCAR file, convert the fractional coordinates into Cartesian coordinates, and extract the coordinates of a group of NH4 + atomic groups, as shown in Table 4;

[0066] Table 4 Extracted coordinates of a group of NH4 + atomic groups

[0067] x y z N 0.0000 0.0000 0.0000 <![CDATA[H1]]> 0.3781 5.6307 0.7216 <![CDATA[H2]]> 0.7065 0.1632 5.5145 <![CDATA[H3]]> 5.4118 5.8637 5.8752 <![CDATA[H4]]> 6.0456 0.8951 0.4536

[0068] Upon inspection of the coordinates, it is found that these four atoms are not located within an NH4 + group. Visualized with the VESTA software as Figure 9 shown. Next, we need to perform an important coordinate transformation. According to theoretical experience, when the functional groups are arranged periodically, the atomic coordinates are not located within a single unit cell. We can convert the atomic coordinates of the functional groups to be within a single unit cell by adding or subtracting appropriate multiples of the lattice constants in the coordinates.

[0069] NH4 at this time + The NH4 group can subtract the corresponding lattice constants at coordinates greater than 1 through this method. The lattice constants in the unit cell are a = 6.2759, b = 6.2779, and c = 6.2645 respectively. Thus, we obtain the atomic coordinates of the converted NH4 + group as shown in Table 5;

[0070] Table 5 Coordinates of the NH4 + atomic group after subtracting the corresponding multiple of the lattice constant

[0071]

[0072]

[0073] The calculated bond lengths of the converted N-H bonds are 1.0404, 1.0432, 1.0343, and 1.0296 respectively, and the bond angles are 110.4750°, 108.3969°, 108.4492°, 110.9687°, and 109.0920° respectively. After consulting the literature, the N-H bond of NH4 + is about 1.03 - 1.04, and the bond angle is 109°28'. By comparison, it is found that the conversion is correct. Visualization with VESTA software is as shown Figure 10 below.

[0074] Step S4: For the POSCAR file of Cs3Cu2I5, select Cartesian coordinates, as shown Figure 11 below, find and record the coordinates of the Cs atom to be substituted;

[0075] Step S5: Determine the central position of the NH4 + group (i.e., the position coordinates of the N atom), and confirm the relative position with the substituted Cs atom. Subtract the coordinates of the N atom from the coordinates of the Cs atom, and then add the difference to the coordinates of the H atoms of the NH4 + group;

[0076] Taking the 1st Cs atom (abbreviated as Cs1) as an example, the coordinates of Cs1 are (9.7526, 0.5335, 11.5584). The original NH4 +The coordinates of the N atom in the group are (0, 0, 0), and the coordinates of the 4 H atoms are H1(0.3781, -0.6471, 0.7216), H2(0.7065, 0.1632, -0.7500), H3(-0.8641, -0.4142, -0.3893), and H4(-0.2303, 0.8951, 0.4536) respectively. Substitute the N atom for the Cs1 atom, and the coordinates of N are (9.7526, 0.5335, 11.5584). Using the above method, the coordinates of the H1 atom are (9.7526 - 0 + 0.3781, 0.5335 - 0 + 0.6471, 11.5584 - 0 + 0.7216), that is, H1(10.1307, -0.1136, 12.2800). Similarly, the coordinates of H2, H3, and H4 can be obtained. Thus, after conversion, the NH4 that replaces the Cs1 atom + The coordinates of the group are shown in Table 6;

[0077] Table 6 Coordinates of NH4 after coordinate conversion + Coordinates of the atomic group

[0078] x y z N 9.7526 0.5335 11.5584 <![CDATA[H1]]> 10.1307 -0.1136 12.2800 <![CDATA[H2]]> 10.4591 0.6967 10.8084 <![CDATA[H3]]> 8.8884 0.1193 11.1691 <![CDATA[H4]]> 9.5223 1.4286 12.0120

[0079] Step S6: Put the coordinates of the NH4 + group that replaces the Cs1 atom into the POSCAR file of Cs3Cu2I5, delete the coordinates of the Cs1 atom, and the obtained POSCAR file is as Figure 12 shown. The crystal structure of the doping system is visualized by VESTA software as Figure 13 shown.

[0080] Similarly, using the above conversion method, replace all Cs atoms to be replaced with the NH4 + atomic group, and obtain all the coordinates of the NH4 + atomic group corresponding to each replaced Cs atom, as shown in Table 7, and record them in an Excel table for convenient arbitrary combination of substitution doping and calculation optimization later.

[0081] Table 7 Coordinates of the NH4 + atomic group after conversion of all Cs atom coordinates

[0082]

[0083]

[0084]

[0085] The above are the preferred embodiments of the present invention. Any changes made according to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention in terms of the functions and effects produced shall fall within the protection scope of the present invention.

Claims

1. A coordinate conversion method for single atoms in complex group-substituted perovskites, characterized in that It includes the following steps: Step S1: Identify the atomic group to be substituted and the atoms in the original compound to be substituted; Step S2: Download the *.cif format structure file of the simple compound containing the atomic group to be substituted, where * is the compound name, convert it to a POSCAR file using VESTA software, and optimize it using VASP; Step S3: After the optimization in Step S2, download the CONTCAR file, extract the coordinates of a group of atomic groups therein, and visualize them using VESTA software; Step S4: In the POSCAR file of the original compound, find and record the coordinates of the atoms to be substituted; Step S5: Determine the central position of the atomic group to be substituted in the CONTCAR file, and confirm its relative position to the atom to be substituted; subtract the coordinates of the central position of the atomic group to be substituted from the coordinates of the atom to be substituted, and then add the difference to the coordinates of each atom of the atomic group; in Step S5, the central position of the atomic group is not defined as the physical or structural center point, but a point with special position information in the atomic group; Step S6: Put the coordinates of the atomic group into the POSCAR file, and delete the coordinates of the original atoms to obtain a new POSCAR file after doping; Visualize the crystal structure of the doped system using VESTA software. After checking and ensuring it is correct, perform optimization calculations.

2. A coordinate transformation method for single atoms in a complex group-substituted perovskite according to claim 1, characterized in that, In Step S3, when optimizing the CONTCAR file using VASP, the fractional coordinates should be converted to Cartesian coordinates.

3. A coordinate conversion method for single atoms in a complex group-substituted perovskite according to claim 1, characterized in that In Step S3, when it is found through inspection that the atoms in the extracted group of atomic groups do not lie within one atomic group, perform a coordinate transformation, that is: when the atomic group is arranged periodically and the atomic coordinates do not lie within one unit cell, convert the atomic coordinates of the atomic group to lie within one unit cell by adding or subtracting the corresponding multiples of the lattice constants in the coordinates.

4. A coordinate conversion method for single atoms in a complex group-substituted perovskite according to claim 1, characterized in that, In Step S4, for the POSCAR file of the original simple compound, Cartesian coordinates are selected.

5. The coordinate conversion method of single atoms in a complex group-substituted perovskite according to claim 1, characterized in that, When performing multi-atom or atomic group substitution doping, record the coordinates of the new atomic groups to be substituted through coordinate transformation in tools including Excel spreadsheets and Word documents for arbitrary combination in the optimization calculations; at the same time, through coordinate transformation, operations including orientation changes can also be performed on the doped atomic groups.

Citation Information

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