Fast calculation method and device for crystal infrared reflection spectrum

Abstract

The application discloses a kind of fast calculation method of crystal infrared reflectance spectrum, through the data set of less time-consuming VASP, to train matrix tensor machine learning potential (MTP), further accurately and effectively simulate high-order force constant, avoid the process of calculating high-order force constant with first principle, which consumes a lot of time and computing resources, to accelerate the extraction of phonon vibration parameters, which are then included in the infrared vibration model to calculate the dielectric function and infrared reflectivity of the material.Compared with the traditional method, the vibration characteristics can be accurately determined with the precision of first principle level without the need for empirical parameters, and the calculation cost is reduced by more than two orders of magnitude;For low-symmetry structure, the calculation cost can even be reduced by three orders of magnitude.It helps to bridge the long-term gap between the slow speed of first-principle calculation of infrared optical properties and the low accuracy of molecular dynamics calculation, and provides a powerful tool for accelerating the discovery and design of infrared optical materials.

Description

Technical Field

[0001] This invention belongs to the technical field of infrared optics, and particularly relates to a method and apparatus for rapid calculation of the infrared reflection spectrum of a crystal. Background Technology

[0002] Infrared optical materials play a crucial role in infrared detection, medical infrared imaging, astronomy, and spectroscopy. The successful and widespread application of infrared optical materials hinges on their infrared optical properties, which are considered the fingerprints of these materials. Therefore, deeply capturing these fingerprints is fundamental to the development of infrared optical materials. In recent years, although some experimental techniques have provided opportunities to identify microscopic features, rapidly and accurately characterizing the inherent infrared optical properties of materials remains challenging. Advances in theoretical modeling and computational power have reshaped materials science, making accurate calculations of infrared optical properties possible. Early theoretical studies characterizing infrared vibrational features primarily employed numerical calculations or molecular dynamics (MD) simulations. While these methods improved characterization efficiency and applicability, they also had significant limitations. They typically could only calculate the positions of infrared vibrational peaks in aperiodic systems, not wavelength-dependent infrared reflectivity. Furthermore, these techniques rely on the coupling of MD with dipole moment models or numerical schemes, which can reduce the accuracy of calculations for systems with significant quantum effects.

[0003] To overcome these limitations and achieve reliable predictions of infrared spectra for nonharmonic periodic systems, first-principles infrared spectroscopy based on the quantum scale, developed in recent years, has become a powerful framework. This approach combines density function perturbation theory (DFPT) with the phonon Boltzmann transport equation (BTE) and higher-order phonon scattering theory, enabling accurate predictions of high-frequency dielectric constants and ground-state infrared phonon mode frequencies. However, despite their high prediction accuracy, they come at the cost of significant computational resources and time, especially when using DFPT to calculate higher-order force constants. The computational cost rises rapidly with increasing atomic complexity and decreasing crystal symmetry, limiting their application in high-throughput material screening. Therefore, accelerating the calculation of infrared vibrational spectra without compromising accuracy has become a core challenge in computational infrared spectroscopy research. Summary of the Invention

[0004] The purpose of this invention is to provide a rapid calculation method for the infrared reflectance spectrum of crystals. Compared with traditional methods, the calculation cost is reduced by more than two orders of magnitude. For low-symmetry structures, the calculation cost can even be reduced by three orders of magnitude.

[0005] To solve the above problems, the technical solution of the present invention is as follows: A rapid method for calculating the infrared reflectance spectrum of a crystal, comprising: AIMD calculations were performed on crystal structures using VASP to generate a structure-interatomic force-energy dataset. Based on the generated dataset, train the MTP machine learning interatomic potential; The MTP machine learning model, trained to convergence, simulates the corresponding higher-order force constants from the interatomic potential. The generated higher-order force constants are input into ShengBTE to solve the Boltzmann equation and obtain the phonon vibration parameters. Substituting the obtained phonon vibration parameters into the Lorentz vibration model, the dielectric function of the crystal material is obtained, and the frequency-dependent reflectance is calculated according to the Fresnel formula to obtain the infrared reflectance spectrum of the crystal.

[0006] According to an embodiment of the present invention, using VASP to perform AIMD calculations on crystal structures to generate a structure-interatomic force-energy dataset further includes: The material structure was optimized using the first-principles calculation software VASP until convergence, resulting in a CONTCAR file, which was then converted into a POSCAR file. The POSCAR structure was expanded using the VASPKT tool; First-principles molecular dynamics calculations were performed on the expanded cell structure using VASP, and NPT simulations were performed using a Langevin thermostat to generate an OUTCAR file. The MLIP-2 software was used to read the OUTCAR file and uniformly sample its structure-interatomic force-energy data to generate a sample dataset for MTP training.

[0007] According to one embodiment of the present invention, training the interatomic potential of MTP machine learning based on the generated dataset further includes: Initialize the MTP training parameters and call the train module of the MLIP-2 software to perform the first training until convergence; Using the machine learning potential trained in the first training as input, the MLIP-2 software is called to execute the select-add module, select some extreme data and add them to the training set, and perform a second training until convergence, resulting in the p.mtp file.

[0008] According to one embodiment of the present invention, simulating the corresponding higher-order force constants from the MTP machine learning interatomic potential trained to convergence further includes: The POSCAR cell was expanded using Phonopy software, and density functional perturbation calculations were performed using VASP to obtain the BORN charge and the high-frequency dielectric constant ε. ∞ Prepare the band.conf file; Place the POSCAR file, p.mtp file, and band.conf in the same folder, execute the interface program mlip_phonopy designed for Phonopy in the MLIP-2 software, obtain the second-order force constant file FORCE_CONSTANTS, and rename it to FORCE_CONSTANTS_2ND. Place the POSCAR file, p.mtp file, and the interface program fake_vasp_calcs.py designed for thirdorder in the MLIP-2 software into the same folder. Pass the cell expansion parameters and the nearest neighbor atom parameters into the interface program and execute it to obtain the higher-order force constant file FORCE_CONSTANTS_3RD.

[0009] According to one embodiment of the present invention, the generated higher-order force constants are input into ShengBTE to solve the Boltzmann equation, and the phonon vibration parameters obtained further include: Place the FORCE_CONSTANTS_2ND and FORCE_CONSTANTS_3RD files in the same folder, prepare the CONTROL file, and write the POSCAR file into it; The ShengBTE software was called to perform Boltzmann transport calculations and obtain the BTE.w_anharmonic file. From this file, the degenerate phonon vibration modes near point G and their corresponding phonon damping coefficients were extracted. The BORN charge is appended to the CONTROL file, and the ShengBTE software is called again to perform Boltzmann transport calculations to obtain the BTE.w_anharmonic file. From this file, the phonon vibration mode after splitting and its corresponding phonon damping coefficient are extracted near point G after BORN correction. Compare and extract degenerate phonon vibration modes ω TO and its corresponding phonon damping coefficient γ TO and the phonon vibration mode ω generated after splitting LO and its corresponding phonon damping coefficient γ LO Write it to the file lorentz.txt.

[0010] According to one embodiment of the present invention, the obtained phonon vibration parameters are substituted into the Lorentz vibration model to obtain the dielectric function of the crystal material, and the frequency-dependent reflectivity is calculated according to the Fresnel formula, further including: Calculate the frequency-dependent dielectric function based on the Lorentz vibration model: In the formula ε ∞ ω is the high-frequency dielectric constant. j and γ jThe j-th infrared active phonon vibration mode and the corresponding phonon damping coefficient are derived from the file lorentz.txt; After obtaining the dielectric function, the Fresnel equation is used to calculate the reflection spectrum of the infrared optical material: .

[0011] A rapid calculation device for crystal infrared reflectance spectra, comprising: The dataset acquisition module is configured to use VASP to perform AIMD calculations on crystal structures and generate a structure-interatomic force-energy dataset. The atomic potential training module is configured to train the MTP machine learning atomic potential based on the generated dataset; The higher-order force constant calculation module is configured to simulate the corresponding higher-order force constants from the MTP machine learning interatomic potential trained to convergence; The phonon vibration parameter calculation module is configured to input the generated higher-order force constants into ShengBTE, solve the Boltzmann equation, and obtain the phonon vibration parameters. The infrared reflectance spectroscopy calculation module is configured to substitute the obtained phonon vibration parameters into the Lorentz vibration model to obtain the dielectric function of the crystal material, and calculate the frequency-dependent reflectance according to the Fresnel formula to obtain the infrared reflectance spectrum of the crystal.

[0012] According to an embodiment of the present invention, the higher-order force constant calculation module is further configured as follows: The POSCAR cell was expanded using Phonopy software, and density functional perturbation calculations were performed using VASP to obtain the BORN charge and the high-frequency dielectric constant ε. ∞ Prepare the band.conf file; Place the POSCAR file, p.mtp file, and band.conf in the same folder, execute the interface program mlip_phonopy designed for Phonopy in the MLIP-2 software, obtain the second-order force constant file FORCE_CONSTANTS, and rename it to FORCE_CONSTANTS_2ND. Place the POSCAR file, p.mtp file, and the interface program fake_vasp_calcs.py designed for thirdorder in the MLIP-2 software into the same folder. Pass the cell expansion parameters and the nearest neighbor atom parameters into the interface program and execute it to obtain the higher-order force constant file FORCE_CONSTANTS_3RD.

[0013] Because the present invention adopts the above technical solution, it has the following advantages and positive effects compared with the prior art: One embodiment of this invention provides a rapid calculation method for the infrared reflectance spectrum of crystals. This method generates a dataset using a less time-consuming first-principles molecular dynamics approach, which is then used to train the moment tensor machine learning potential (MTP). This allows for accurate and efficient simulation of higher-order force constants, avoiding the time-consuming and computationally resource-intensive process of calculating these constants using first-principles calculations. This accelerates the extraction of phonon vibrational parameters, which are subsequently incorporated into an infrared vibrational model to calculate the material's dielectric function and infrared reflectivity. Therefore, compared to traditional methods, our method can accurately determine vibrational properties with first-principles-level precision without requiring empirical parameters. Under conservative estimates, the computational cost is reduced by more than two orders of magnitude; for low-symmetry crystal structures, the cost can be reduced by even three orders of magnitude. This helps bridge the long-standing gap between the slow speed of first-principles calculations and the low accuracy of molecular dynamics calculations for infrared optical properties, providing a powerful tool for accelerating the discovery and design of infrared optical materials. Attached Figure Description

[0014] Figure 1 This is a flowchart of a rapid calculation method for the infrared reflectance spectrum of a crystal according to an embodiment of the present invention; Figure 2 This is a schematic diagram comparing the traditional first-principles calculation method and the crystal infrared reflectance spectroscopy calculation method based on machine learning interatomic interaction potential in one embodiment of the present invention. Figure 3 This is a schematic diagram of the crystal structure in one embodiment of the present invention; Figure 4 This is a schematic diagram comparing the infrared reflectance spectra of a crystal calculated using conventional first-principles calculations (DFT) and machine learning-based interatomic interaction potentials (MTP) in one embodiment of the present invention. Figure 5 This is a schematic diagram comparing the time consumption of traditional first-principles calculation (DFT) and machine learning-based interatomic interaction potential (MTP) calculation methods in one embodiment of the present invention. Detailed Implementation

[0015] The following detailed description, in conjunction with the accompanying drawings and specific embodiments, provides a rapid calculation method for the infrared reflectance spectrum of a crystal according to the present invention. The advantages and features of the present invention will become clearer from the following description and claims.

[0016] Please refer to Figure 1 This embodiment provides a rapid method for calculating the infrared reflectance spectrum of a crystal, including: AIMD calculations were performed on crystal structures using VASP to generate a structure-interatomic force-energy dataset. Based on the generated dataset, train the MTP machine learning interatomic potential; The MTP machine learning model, trained to convergence, simulates the corresponding higher-order force constants from the interatomic potential. The generated higher-order force constants are input into ShengBTE to solve the Boltzmann equation and obtain the phonon vibration parameters. Substituting the obtained phonon vibration parameters into the Lorentz vibration model, the dielectric function of the crystal material is obtained, and the frequency-dependent reflectance is calculated according to the Fresnel formula to obtain the infrared reflectance spectrum of the crystal.

[0017] This method generates a dataset using first-principles molecular dynamics, which is less time-consuming, to train the moment tensor machine learning potential (MTP), thereby accurately and efficiently simulating higher-order force constants. For comparisons with traditional methods, please refer to... Figure 2 Traditional methods employ first-principles calculations of higher-order force constants, a time-consuming and computationally resource-intensive process. The computational cost rises rapidly with increasing atomic complexity and decreasing crystal symmetry. The method of this embodiment accelerates the extraction of phonon vibrational parameters, which are then incorporated into an infrared vibrational model to calculate the material's dielectric function and infrared reflectivity. Therefore, compared to traditional methods, this embodiment can accurately determine vibrational properties with first-principles-level precision without requiring empirical parameters. Under conservative estimates, the computational cost is reduced by more than two orders of magnitude, and for low-symmetry structures, the cost can be reduced by up to three orders of magnitude. Furthermore, this method has a degree of versatility across a wide range of binary and ternary compounds. Therefore, this invention helps bridge the long-standing gap between the slow speed of first-principles calculations for infrared optical properties and the low accuracy of molecular dynamics calculations, providing a powerful tool for accelerating the discovery and design of infrared optical materials.

[0018] The following section describes this method for rapidly calculating the infrared reflectance spectra of crystals using specific crystal structures: Example 1: Step 1: Perform AIMD calculations on the 3C-SiC crystal structure using VASP to generate a structure-interatomic force-energy dataset; specifically: Step 1.1: Use the first-principles calculation software VASP to perform structural optimization calculations on the material structure until convergence, obtain the CONTCAR file, and copy it as a POSCAR file; Step 1.2: Expand the POSCAR structure after convergence in Step 1.1 to approximately 100 atoms using the VASPKT tool; Step 1.3: First-principles molecular dynamics calculations were performed on the expanded cell structure using VASP, a first-principles calculation software developed by the University of Vienna. NPT simulations were performed using a Langevin thermostat at 300 K for 1000 steps to generate the OUTCAR file. The pseudopotential was sampled using the projected plane wave method with Gamma sampling. The cutoff energy was set to 450 eV. The convergence criteria for force and energy were -2 × 10⁻⁶ eV and -10⁻⁶ eV, respectively. -2 eV / Å and 1×10 -5 eV. The MLIP-2 software developed by the Skolkovo Institute of Technology was used to read the OUTCAR file and uniformly sample 1000 steps of structure-atom force-energy data to generate a subsample dataset for MTP training; Step 2: Train the MTP machine learning interatomic potential using the dataset generated in Step 1; specifically: Step 2.1: Prepare an untrained machine learning potential file (included with the MLIP-2 software), and modify the element types, cutoff radius, and other parameters accordingly based on the computational system. Place the subsample dataset generated in Step 1 in the same folder as the aforementioned machine learning potential, set the energy weight to 1, the force weight to 0.1, and the stress weight to 0.001, and call the train module of the MLIP-2 software for the first training until convergence; Step 2.2: Using the trained machine learning potential as input, call the MLIP-2 software to execute the select-add module, select some extreme data and add them to the training set, and execute Step 2.1 again to perform a second training until convergence, and obtain the p.mtp file; Step 3: Use the MTP machine learning interatomic potential trained to convergence in Step 2 to simulate the corresponding higher-order force constants; specifically: Step 3.1: Prepare the POSCAR described in Step 1.1, and expand its cell using the Phonepy software. The cell expansion parameters need to be dynamically determined based on the number of atoms in the material system, ensuring that the number of atoms after expansion is between 100 and 1000. Then, call VASP to perform density functional perturbation calculations. During the calculation, LEPSILON = .TRUE. must be enabled to obtain the BORN charge after the calculation. Prepare the band.conf file required for Phonepy software post-processing, write the necessary parameters such as the high symmetry point path, cell expansion parameters, and enable the output force constant command, and call Phonepy to obtain the BORN charge and high-frequency dielectric constant ε. ∞ ; Step 3.2: Place the POSCAR file mentioned in Step 1.1, the p.mtp file mentioned in Step 2.2, and the same band.conf file mentioned in Step 3.1 into the same folder, execute the interface program mlip_phonopy designed for Phonopy in the MLIP-2 software, obtain the second-order force constant file FORCE_CONSTANTS, and rename it to FORCE_CONSTANTS_2ND. Step 3.3: Place the POSCAR file mentioned in Step 1.1, the p.mtp file mentioned in Step 2.2, and the interface program fake_vasp_calcs.py designed for thirdorder in MLIP-2 software into the same folder. Pass in the cell expansion parameters and nearest neighbor atom parameters that are consistent with those in Step 3.1 and execute the interface program to obtain FORCE_CONSTANTS_3RD. Step 4: Input the higher-order force constants generated in Step 3 into ShengBTE, solve the Boltzmann equation, and obtain the phonon vibration parameters. Specifically: Step 4.1: Place the FORCE_CONSTANTS_2ND files from Step 3.2 and the FORCE_CONSTANTS_3RD files from Step 3.3 into the same folder to prepare the CONTROL file. Write the POSCAR file from Step 1.1 into this file, and set the remaining parameters to default. Use the ShengBTE software to perform Boltzmann transport calculations to obtain the BTE.w_anharmonic file. Extract the degenerate phonon vibration modes near point G and their corresponding phonon damping coefficients from this file. Step 4.2: Similar to Step 4.1, except that the BORN file described in Step 3.1 is appended to the CONTROL file. The ShengBTE software is called to perform Boltzmann transport calculations, obtaining the BTE.w_anharmonic file. From this file, the phonon vibration modes near point G after BORN correction and their corresponding phonon damping coefficients after splitting are extracted. Step 4.3: Compare and extract the transverse phonon vibration modes (ω) in the degenerate state from Step 4.1. TO ) and its corresponding phonon damping coefficient (γ) TO ) and the longitudinal phonon vibration mode (ω) that splits accordingly in step 4.2 LO ) and its corresponding phonon damping coefficient (γ) LO Write it to lorentz.txt; Step 5: Substitute the obtained phonon vibration parameters into the Lorentz vibration model to obtain the dielectric function of the material, and calculate the frequency-dependent reflectivity according to Fresnel's formula. Specifically: Step 5.1: The frequency-dependent dielectric function can be obtained from the Lorentz vibration model: the calculation formula is as follows: In the formula ε ∞ The high-frequency dielectric constant is extracted from step 3.1, ω. j and γ j The j-th infrared active phonon vibration mode and the corresponding phonon damping coefficient are derived from lorentz.txt described in step 4.3; After obtaining the dielectric function, the reflection spectrum of the material can be obtained using the Fresnel equation, and the calculation formula is as follows: .

[0019] Examples 2 and 3 follow the same procedures as Example 1, except that their crystal structures differ from Example 1 (3C-SiC), being SiO2 and Mg2SiO4, respectively. Please refer to... Figures 3 to 5 As atomic complexity increases and crystal symmetry decreases, the method (MTP) used in this embodiment has more and more obvious advantages compared to the traditional method (DFT).

[0020] Based on the same concept, this embodiment also provides a fast calculation device for crystal infrared reflectance spectra, including: The dataset acquisition module is configured to use VASP to perform AIMD calculations on crystal structures and generate a structure-interatomic force-energy dataset. The atomic potential training module is configured to train the MTP machine learning atomic potential based on the generated dataset; The higher-order force constant calculation module is configured to simulate the corresponding higher-order force constants from the MTP machine learning interatomic potential trained to convergence; The phonon vibration parameter calculation module is configured to input the generated higher-order force constants into ShengBTE, solve the Boltzmann equation, and obtain the phonon vibration parameters. The infrared reflectance spectroscopy calculation module is configured to substitute the obtained phonon vibration parameters into the Lorentz vibration model to obtain the dielectric function of the crystal material, and calculate the frequency-dependent reflectance according to the Fresnel formula to obtain the infrared reflectance spectrum of the crystal.

[0021] The steps of this device for implementing the above-mentioned rapid calculation method for the infrared reflectance spectrum of crystals are similar in implementation and will not be described again here.

[0022] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the above embodiments. Even if various changes are made to the present invention, if these changes fall within the scope of the claims of the present invention and their equivalents, they shall still fall within the protection scope of the present invention.

Claims

1. A rapid calculation method for the infrared reflectance spectrum of a crystal, characterized in that, include: AIMD calculations were performed on crystal structures using VASP to generate a structure-interatomic force-energy dataset. Based on the generated dataset, train the MTP machine learning interatomic potential; The MTP machine learning model, trained to convergence, simulates the corresponding higher-order force constants from the interatomic potential. The generated higher-order force constants are input into ShengBTE to solve the Boltzmann equation and obtain the phonon vibration parameters. Substituting the obtained phonon vibration parameters into the Lorentz vibration model, the dielectric function of the crystal material is obtained, and the frequency-dependent reflectance is calculated according to the Fresnel formula to obtain the crystal infrared reflectance spectrum. The AIMD calculation of crystal structures using VASP to generate a structure-interatomic force-energy dataset further includes: The material structure was optimized using the first-principles calculation software VASP until convergence, resulting in a CONTCAR file, which was then converted into a POSCAR file. The POSCAR structure was expanded using the VASPKT tool; First-principles molecular dynamics calculations were performed on the expanded cell structure using VASP, and NPT simulations were performed using a Langevin thermostat to generate an OUTCAR file. The MLIP-2 software was used to read the OUTCAR file and uniformly sample its structure-interatomic force-energy data to generate a sample dataset for MTP training. The MTP machine learning model, trained to convergence, simulates the corresponding higher-order force constants of the interatomic potential, further including: The BORN charge and high-frequency dielectric constant ε are obtained by using Phonopy software to expand the cell of POSCAR and calling VASP for density functional perturbation calculation ∞ , and preparing a band.conf file; Place the POSCAR file, p.mtp file, and band.conf in the same folder, execute the interface program mlip_phonopy designed for Phonopy in the MLIP-2 software, obtain the second-order force constant file FORCE_CONSTANTS, and rename it to FORCE_CONSTANTS_2ND. Place the POSCAR file, p.mtp file, and the interface program fake_vasp_calcs.py designed for thirdorder in the MLIP-2 software into the same folder. Pass the cell expansion parameters and the nearest neighbor atom parameters into the interface program and execute it to obtain the higher-order force constant file FORCE_CONSTANTS_3RD. The generated higher-order force constants are input into ShengBTE to solve the Boltzmann equation, yielding phonon vibration parameters that further include: Place the FORCE_CONSTANTS_2ND and FORCE_CONSTANTS_3RD files in the same folder, prepare the CONTROL file, and write the POSCAR file into it; The ShengBTE software was called to perform Boltzmann transport calculations and obtain the BTE.w_anharmonic file. From this file, the degenerate phonon vibration modes near point G and their corresponding phonon damping coefficients were extracted. The BORN charge is appended to the CONTROL file, and the ShengBTE software is called again to perform Boltzmann transport calculations to obtain the BTE.w_anharmonic file. From this file, the phonon vibration mode after splitting and its corresponding phonon damping coefficient are extracted near point G after BORN correction. Compare and extract degenerate phonon vibration modes ω TO and its corresponding phonon damping coefficient γ TO and the phonon vibration mode ω generated after splitting LO and its corresponding phonon damping coefficient γ LO Write it to the file lorentz.txt.

2. The rapid calculation method for the infrared reflectance spectrum of a crystal as described in claim 1, characterized in that, Based on the generated dataset, training the MTP machine learning interatomic potential further includes: Initialize the MTP training parameters and call the train module of the MLIP-2 software to perform the first training until convergence; Using the machine learning potential trained in the first training as input, the MLIP-2 software is called to execute the select-add module, select some extreme data and add them to the training set, and perform a second training until convergence, resulting in the p.mtp file.

3. The rapid calculation method for the infrared reflectance spectrum of a crystal as described in claim 1, characterized in that, Substituting the obtained phonon vibration parameters into the Lorentz vibration model, the dielectric function of the crystal material is obtained, and the frequency-dependent reflectivity is calculated according to the Fresnel formula, further including: Calculate the frequency-dependent dielectric function based on the Lorentz vibration model: In the formula ε ∞ ω is the high-frequency dielectric constant. j and γ j The j-th infrared active phonon vibration mode and the corresponding phonon damping coefficient are derived from the file lorentz.txt; After obtaining the dielectric function, the Fresnel equation is used to calculate the reflection spectrum of the infrared optical material: 。 4. A rapid calculation device for crystal infrared reflectance spectra, characterized in that, include: The dataset acquisition module is configured to use VASP to perform AIMD calculations on crystal structures and generate a structure-interatomic force-energy dataset. The atomic potential training module is configured to train the MTP machine learning atomic potential based on the generated dataset; The higher-order force constant calculation module is configured to simulate the corresponding higher-order force constants from the MTP machine learning interatomic potential trained to convergence; The phonon vibration parameter calculation module is configured to input the generated higher-order force constants into ShengBTE, solve the Boltzmann equation, and obtain the phonon vibration parameters. The infrared reflectance spectrum calculation module is configured to substitute the obtained phonon vibration parameters into the Lorentz vibration model to obtain the dielectric function of the crystal material, and calculate the frequency-dependent reflectance according to the Fresnel formula to obtain the infrared reflectance spectrum of the crystal. The dataset acquisition module is further configured as follows: The material structure was optimized using the first-principles calculation software VASP until convergence, resulting in a CONTCAR file, which was then converted into a POSCAR file. The POSCAR structure was expanded using the VASPKT tool; First-principles molecular dynamics calculations were performed on the expanded cell structure using VASP, and NPT simulations were performed using a Langevin thermostat to generate an OUTCAR file. The MLIP-2 software was used to read the OUTCAR file and uniformly sample its structure-interatomic force-energy data to generate a sample dataset for MTP training. The higher-order force constant calculation module is further configured as follows: The POSCAR cell was expanded using Phonopy software, and density functional perturbation calculations were performed using VASP to obtain the BORN charge and the high-frequency dielectric constant ε. ∞ Prepare the band.conf file; Place the POSCAR file, p.mtp file, and band.conf in the same folder, execute the interface program mlip_phonopy designed for Phonopy in the MLIP-2 software, obtain the second-order force constant file FORCE_CONSTANTS, and rename it to FORCE_CONSTANTS_2ND. Place the POSCAR file, p.mtp file, and the interface program fake_vasp_calcs.py designed for thirdorder in the MLIP-2 software into the same folder. Pass the cell expansion parameters and the nearest neighbor atom parameters into the interface program and execute it to obtain the higher-order force constant file FORCE_CONSTANTS_3RD. Place the FORCE_CONSTANTS_2ND and FORCE_CONSTANTS_3RD files in the same folder, prepare the CONTROL file, and write the POSCAR file into it; The ShengBTE software was called to perform Boltzmann transport calculations and obtain the BTE.w_anharmonic file. From this file, the degenerate phonon vibration modes near point G and their corresponding phonon damping coefficients were extracted. The BORN charge is appended to the CONTROL file, and the ShengBTE software is called again to perform Boltzmann transport calculations to obtain the BTE.w_anharmonic file. From this file, the phonon vibration mode after splitting and its corresponding phonon damping coefficient are extracted near point G after BORN correction. Compare and extract degenerate phonon vibration modes ω TO and its corresponding phonon damping coefficient γ TO and the phonon vibration mode ω generated after splitting LO and its corresponding phonon damping coefficient γ LO Write it to the file lorentz.txt.

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