Background & Summary

Atomically thin two-dimensional (2D) materials are regarded as promising candidates for various applications, including electronics, optoelectronics, sensors and flexible devices. This is attributed to their unique characteristics, which include high carrier mobility, tunable bandgaps, large specific surface area, and thickness at the atomic level1,2,3. To date, more than sixty compounds have been synthesized or exfoliated as monolayers, including well-known semiconductors (e.g. metallic transition metal dichalcogenides (TMDCs), phosphorene)4,5, insulators (e.g. GaN, BN)6,7, semi-metals and metals (e.g. graphene, silicene, borophene)8,9. However, the already known monolayer 2D materials are only the tip of a much larger iceberg. In fact, recent data mining studies predict that more than 6,000 monolayer 2D materials could be exfoliated from known layered bulk crystals or synthesized experimentally directly by chemical vapor deposition and molecular beam epitaxy10,11,12.

To accelerate discovery and deployment of these novel advanced 2D materials and realize the increasing requirements for these functional applications, materials preparation and structures characterization are the first prerequisite. Raman spectroscopy is a versatile technique for probing the vibrational modes of molecules and crystals from inelastically scattered light and is widely used for identifying materials through their unique vibrational fingerprints13. As a high-sensitivity and nondestructive spectral analysis method, Raman spectra can quickly characterize a lot of features, such as chemical composition, layer thickness, interlayer coupling, strain, crystal symmetries, and sample quality. It has taken a long time to develop the theoretical methods and numerical algorithms to calculate Raman spectroscopy. The ab-initio computational scheme based on full quantum mechanical treatment has been successfully deployed to calculate Raman spectra of both molecules and solids14,15,16,17,18. As a quantitatively accurate description, its calculated Raman spectra show a good agreement with the experimentally measured spectra13,17,18,19,20. In comparison with the experimental measurement of Raman spectroscopy, the high-throughput computation of Raman spectra will be more cost-effective and convenient. Systematic calculations will lead to a standard data set, facilitating the identification and classification of material structures, the discovery of correlations, and the application of machine learning techniques to identify deep and complex correlations in the materials space. Therefore, the compilation of a comprehensive library of Raman spectra of 2D materials across different crystal structures and chemical compositions is a critical and timely endeavor.

In this work, we design an efficient ab initio high-throughput workflow to calculate Raman spectra of monolayer 2D materials, which allow us to calculate structures with more than thirty atoms. Our calculation method is based on all-electron density functional perturbation theory (DFPT) implementation in FHI-aims software employing a localized atomic orbital (LCAO) basis set. The initial monolayer structures for two-dimensional materials are from 2D Materials Encyclopedia (2DMatPedia) database (http://www.2dmatpedia.org/.)10. Their structural, electronic and energetic properties have been obtained by high-throughput calculations. We focus on the first-order Raman processes in which only a single phonon is involved. Typically, this is the dominant scattering process in perfect crystals. We use the Tianhe supercomputer to calculate the harmonic Raman spectra of 3504 two-dimensional materials. Our work is not only a valuable reference for experimentalists and theoreticians working in the field of 2D materials, but also represents a step in the direction of autonomous (in situ) characterization of materials.

Methods

Computational workflow

We use the DFPT implementation in the FHI-aims software package18,21 to evaluate the polarizability, as illustrated in Fig. 1(a). For more information, please refer to Supplementary information (S1). After completing the ground state DFT calculation, the ground state density of the system n(0)(r) is obtained. The DFPT cycle then begins by using an initial guess for the response of the density matrix P(1), which allows the construction of the respective density n(1)(r). The associated response of the electrostatic potential \({V}_{es,tot}^{(1)}({\bf{r}})\) is calculated by solving the Poisson equation in real space. The response Hamiltonian H(1) is then calculated using the response density and potential. With these ingredients, the Sternheimer equation can be set up. Solving the Sternheimer equation allows the update of the response expansion coefficients C(1). To accelerate convergence, a linear or more efficient Pulay-mixing scheme22 is employed. The DFPT loop is iteratively repeated until self-consistency is reached, i.e., until the changes in P(1) become smaller than a user-given threshold. Finally, physical properties such as the polarizability tensor α are evaluated using the converged response density matrix. Our Raman spectrum calculation workflow is shown in Fig. 1(b). The data is obtained from the 2DMatPedia database10 and using the DFPT method21 to calculate the Raman spectrum. The overall calculation is divided into four steps: first, we obtain the material structure data in POSCAR format from the 2DMatPedia database10, and convert the data format to the format that FHI-aims can read. In the second step, we optimized all the material structures. Since the calculation time is proportional to the number of atoms in the structure, we split the structure of the materials that contain more than 15 atoms. The split structures are divided into multiple computation nodes for parallel calculation, thus reducing the calculation time. Third, FHI-aims is used to calculate the harmonic Raman spectrum of the finite difference method. Finally, we summarize the data and upload it to the cloud database for users to access. The above calculation process is automated and can be executed in parallel on a large scale.

Fig. 1
Fig. 1
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Computational workflow of the harmonic Raman spectra based on all-electron DFPT calculation in FHI-aims.

The k-point density was determined by dividing 50 Å by the lattice constant, and a vacuum spacing of approximately 20 Å was introduced to minimize interactions between periodic images. We employed the Tkatchenko-Scheffler method with iterative Hirshfeld partitioning to calculate the vdW corrections23. The vdW correction is mainly used for interlayer interactions. For monolayers, increasing the vdW correction usually does not affect the calculations, but in some complex 2D systems, dispersion forces cannot be ignored. Increasing the vdW correction can ensure that these systems are calculated correctly. A scalar relativistic treatment with the atomic zeroth order regular approximation(ZORA) was included in calculations24. All of our calculations were performed with ‘light’ numerical settings and basis-set configurations within the FHI-aims code. In the structure optimization, the convergence tolerance of energy, charge density, and sum of eigenvalues were set to 1 × 10−6 eV, 1 × 10−6e/Å3 and 1 × 10−4 eV. The structures were relaxed with PBE functional plus vdw correction using a Broyden-Fletcher-Goldfarb-Shanno (BFGS) optimization algorithm until the maximum force on each atom was less than 0.01 eV/ Å3. To ensure the accuracy of our calculations, we optimized all the 2D structures by introducing a vacuum layer, following the approach used in the Materials Encyclopedia (2DMatPedia) database.

We calculated harmonic Raman simulation through the finite differences method and obtain the polarizability tensor from the DFPT theory18. We calculate the polarizability tensors with the local density approximation (LDA) functional given that we have previously shown in this article18 that it is much cheaper and this method will not cause obvious accuracy loss of the Raman spectrum. The convergence tolerance of energy, charge density, sum of eigenvalues were set to 1 × 10−8 eV, 1 × 10−8e/Å3, 1 × 10−6 eV.

Data Records

Computational data record

The final database contains geometry data, Raman frequencies, and intensities. These are stored in separate files and can be downloaded directly from the Materials Cloud Archive25. The data can also be browsed online in Computational Raman Database website (http://mathtc.nscc-tj.cn/raman).

Technical Validation

We validated our computational results by comparing them with experimental Raman spectra of 12 different structures13. The 12 materials are BN19, Graphene26, MoS227, MoTe228, MoTe2T29, Pd2Se430, Phosporene31, PtS232, PtSe233, WS234, WSe227, WTe235. The comparison results are shown in Fig. 2. The discrepancies between our calculated results and experimental measurements can be attributed to limitations in our calculation method. In our current approach, we only considered harmonic vibrations and did not account for non-harmonic effects, substrate influences, or excitonic effects. To address these shortcomings, we plan to incorporate non-harmonic effects and perform high-precision calculations in future iterations of the database. Furthermore, we recognize that experimental measurement conditions also contribute to the discrepancies between our theoretical predictions and experimental observations. Experimental measurements often employ angle-resolved Raman spectroscopy, which differs from the theoretical principles used in our calculations. The constraints imposed by experimental conditions, such as specific scattering angles and excitation frequencies, may result in certain Raman peaks being undetected. We have made a general analysis for the whole database, which is added into Supplementary Information (S2), and we derived the physical descriptor of the Raman shift for the binary materials. Our Raman spectrum simulation provides the orientation-averaged “powder" Raman spectrum. Our program can also calculate the angle-resolved polarized Raman spectra by exporting the Raman tensor, although this aspect has not been the primary focus of our current work. We have added the discussion about the angle-resolved polarized Raman spectra in the Supplementary Information (S3). We have also compared our results with those presented in Ref. 13. The primary methodological difference lies in the calculation approach: we use Density Functional Perturbation Theory (DFPT), where Raman tensors are computed via mixed second derivatives of the total energy with respect to atomic displacement and electric field. In contrast, Ref. 13 employs time-dependent perturbation theory, deriving Raman intensities from transition matrix elements that involve electron-phonon coupling terms, summed over intermediate states. These two approaches use different finite difference steps, which may result in variations in the calculated vibrational frequencies. Furthermore, our work utilizes all-electron full-potential calculations for both geometry optimization and Raman calculations, while Ref. 13 employs the PAW (Projector Augmented Wave) method, which can lead to slight structural differences affecting the computed frequencies. For direct comparison, we have included the results from Ref. 13 (represented by gray lines) in Fig. 2.

Fig. 2
Fig. 2
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The comparison of experimental and computational Raman spectra of 12 different materials. The blue solid line shows our computational results, while the gray solid line shows the theoretical calculations from Taghizadeh et al.13, and the red dashed line represents the experimental data.

Usage Notes

Two dimensional materials have many unique properties compared with other materials. We can quickly determine the material composition by comparing the experimental Raman spectrum data with our calculated Raman spectrum data set. At the same time, our data set also provides basic data for reducing the cost of Raman spectroscopy calculation through machine learning. At the same time, we will open source the automated computing workflow program used in the computing process. These programs are not limited to the calculation of two-dimensional material Raman spectra, and can help other researchers with high-throughput computing needs to reduce their workload. All calculated Raman spectra are open access and sharing in the our built website (http://mathtc.nscc-tj.cn/raman/) and also in our Materials Cloud Archive database25.