WyFormer generated structures

WyFormer generated datasetsStructures generated by WyFormer, with various post processing. Used in the ICML 2025 paper "Wyckoff Transformer: Generation of Symmetric Crystals".The folder structure is the following: the first is the dataset which was used for training WyFormer, using only train and validation parts. Then the folder structure corresponds to transformations of the data.<i>mp_20/WyckoffTransformer</i> 10k formally valid Wyckoff representations generated by WyFormer trained on MP-20 dataset.<i>mp_20/WyckoffTransformer/DiffCSP++10k</i> 9999 structures obtained with DifCSP++; it failed for one Wyckoff representation, we consider this structure unstable. <b>Can be considered as the "official" WyFormer sample.</b><i>mp_20/WyckoffTransformer/DiffCSP++10k/CHGNet_free/DFT</i> CHGNet pre-relaxation followed by DFT relaxation; for some structures the DFT relaxation failed, we consider them unstable. The relaxation was obtained using MP-compatiable <code>MPGGADoubleRelaxStaticMaker</code>. Note that material indices unfortunately got permuted at the CHGNet pre-relaxations step. Used in Table 1. <b>Can be considered as the "official" WyFormer DFT-relaxed sample.</b><i>mp_20/WyckoffTransformer/DiffCSP++10k/CHGNet_free/DFT-GGA-relax-1</i> same as above, but relaxed with a single invocation of <code>MPRelaxSet</code>. This is less precise, not strictly compatible to Materials Project, but is the same as reported in FlowMM paper and code. Used in Table 1.<i>mp_20/WyckoffTransformer/DiffCSP++/</i> 1k structures obtained with DifCSP++<i>mp_20/WyckoffTransformer/DiffCSP++/DFT/</i> DFT relaxation of 105 <i>novel and unique</i> structures, <code>MPGGADoubleRelaxStaticMaker</code><i>mp_20/WyckoffTransformer/CrySPR/CHGNet_fix/</i> 1k structures obtained with CrySPR and CHGNet, <i>whith a constraint during the relaxation that maintained the Wyckoff positions</i><i>mp_20/WyckoffTransformer/CrySPR/CHGNet_fix/DFT/</i> DFT relaxation of 105 <i>novel and unique</i> structures, <code>MPGGADoubleRelaxStaticMaker.</code><i>mpts_52/WyckoffTransformer/CrySPR/CHGNet_fix</i> 1k structures generated with Wyformer trained on MPTS-52 dataset, then CrySPR and CHGNet, <i>with a constraint during the relaxation that maintained the Wyckoff positions</i>.Format description<code>structure</code> - <code>pymatgen.core.structure.Structure</code><code>group</code>, <code>species</code>, <code>numIons,</code> <code>sites</code> - arguments to <code>pyxtal.from_random</code>. For <code>*/WyckoffTransformer/data.csv.gz</code> they were generated with WyFormer, for the rest they were obtained from structures with <code>pyxtal.from_seed</code>. Note the the indexing within those fields is by chemical element, not by Wyckoff position.<code>site_symmetries</code>, <code>elements</code>, <code>multiplicity</code>, <code>wyckoff_letters</code>, <code>sites_enumeration</code>, <code>dof</code> - information about the Wyckoff positions, indexed by Wyckoff position. The <code>dof</code> is the number of degrees of freedom for the Wyckoff position, i.e. the number of free parameters in the Wyckoff position. <code>sites_enumeration</code> enumerates the Wyckoff position with the same site symmetry, see the paper for details. For example, for space group <code>2</code> aka <code>P-1</code>, Wyckoff position <code>a</code> has site symmetry <code>-1</code> and enumeration <code>0</code>, while <code>b</code> has site symmetry <code>-1</code> and enumeration <code>1</code>.<code>sites_enumeration_augmented</code> - possible variants of the enumeration, depend on the arbitrary choice of the space group Euclidean normalizer, e. g. unit cell center. See the preprint for details.<code>smact_validity</code> - "Compositional Validity" computed with SMACT. Not all structures in MP-20 conform to this criterion.<code>structural_validity</code> - "Structural Validity" introduced by CDVAE, whether any two atoms are closer than 0.5 Angstroms<code>cdvae_e</code> - energy predicted by the model included in CDVAE, used for EMD(E) distribution similarity metric<code>chgnet_energy_per_atom</code> - energy per atom from CHGNet relaxation<code>chgnet_e_above_hull_corrected</code> - energy above hull from CHGNet relaxation, taking into account MP energy correction<code>dft_e_uncorrected</code> - raw potential energy from DFT relaxation<code>dft_e_corrected</code> - potential energy from DFT relaxation, corrected with <code>MaterialsProject2020Compatibility</code><code>dft_e_above_hull_corrected</code> - energy above hull computed from DFT relaxation computed using <code>2023-02-07-ppd-mp.pkl.gz</code> distributed by matbench-discovery as reference.<code>entry</code> - <code>pymatgen.entries.ComputedEntry</code> containing the results of the DFT run.Citatation<pre>@article{kazeev2025wyckoff,<br> title={{Wyckoff Transformer: Generation of symmetric crystals}},<br> author={Kazeev, Nikita and Nong, Wei and Romanov, Ignat and Zhu, Ruiming and Ustyuzhanin, Andrey and Yamazaki, Shuya and Hippalgaonkar, Kedar},<br> journal={arXiv preprint arXiv:2503.02407},<br> year={2025}<br>}</pre>

本数据集为WyFormer生成数据集，由WyFormer生成并经过各类后处理流程，用于ICML 2025收录的论文《Wyckoff Transformer：对称晶体生成》（Wyckoff Transformer: Generation of Symmetric Crystals）。

数据集的文件夹结构如下：首个数据集为用于训练WyFormer的基础数据集，仅包含训练集与验证集；其余文件夹对应数据的各类变换形式。
1. *mp_20/WyckoffTransformer*：基于MP-20（Materials Project 20）数据集训练得到的WyFormer生成的10000份形式合法的Wyckoff表示。
2. *mp_20/WyckoffTransformer/DiffCSP++10k*：通过DiffCSP++生成的9999个晶体结构（因1个Wyckoff表示生成失败，视为不稳定结构），可视为**官方标准的WyFormer采样结果**。
3. *mp_20/WyckoffTransformer/DiffCSP++10k/CHGNet_free/DFT*：先通过CHGNet进行预弛豫，再进行DFT（密度泛函理论）弛豫的数据集；部分结构的DFT弛豫失败，视为不稳定结构。本次弛豫采用与Materials Project兼容的`MPGGADoubleRelaxStaticMaker`工具完成。需注意，在CHGNet预弛豫步骤中，材料的索引不幸发生了置换。该数据集用于表1，可视为**官方标准的经DFT弛豫的WyFormer采样结果**。
4. *mp_20/WyckoffTransformer/DiffCSP++10k/CHGNet_free/DFT-GGA-relax-1*：与上述数据集一致，但仅通过单次调用`MPRelaxSet`完成弛豫。该流程精度较低，且未严格兼容Materials Project标准，但与FlowMM论文及代码中采用的流程一致，用于表1。
5. *mp_20/WyckoffTransformer/DiffCSP++/*：通过DiffCSP++生成的1000个晶体结构。
6. *mp_20/WyckoffTransformer/DiffCSP++/DFT/*：对105个**新颖且唯一**的晶体结构进行DFT弛豫，采用`MPGGADoubleRelaxStaticMaker`工具。
7. *mp_20/WyckoffTransformer/CrySPR/CHGNet_fix/*：通过CrySPR与CHGNet生成的1000个晶体结构，弛豫过程中施加了约束以维持Wyckoff位置不变。
8. *mp_20/WyckoffTransformer/CrySPR/CHGNet_fix/DFT/*：对105个**新颖且唯一**的晶体结构进行DFT弛豫，采用`MPGGADoubleRelaxStaticMaker`工具。
9. *mpts_52/WyckoffTransformer/CrySPR/CHGNet_fix*：基于MPTS-52数据集训练得到的WyFormer生成的1000个晶体结构，后续通过CrySPR与CHGNet处理，弛豫过程中施加了约束以维持Wyckoff位置不变。

### 数据格式规范
- `structure`：对应`pymatgen.core.structure.Structure`对象。
- `group`、`species`、`numIons`、`sites`：为`pyxtal.from_random`函数的输入参数。对于路径匹配`*/WyckoffTransformer/data.csv.gz`的数据集，由WyFormer生成；其余路径下的数据则通过`pyxtal.from_seed`从已有结构生成。需注意，上述字段的索引基于化学元素，而非Wyckoff位置。
- `site_symmetries`、`elements`、`multiplicity`、`wyckoff_letters`、`sites_enumeration`、`dof`：为Wyckoff位置的相关信息，以Wyckoff位置为索引。其中`dof`表示该Wyckoff位置的自由度，即该位置的自由参数数量。`sites_enumeration`用于枚举具有相同位点对称性的Wyckoff位置，详细说明参见论文。例如，对于空间群编号2（即`P-1`），Wyckoff位置`a`的位点对称性为`-1`，枚举编号为0；而Wyckoff位置`b`的位点对称性为`-1`，枚举编号为1。
- `sites_enumeration_augmented`：枚举的可选变体，取决于空间群欧式归一化子的任意选择（例如单胞中心），详细说明参见论文预印本。
- `smact_validity`：通过SMACT计算得到的**组分合法性**。MP-20数据集中并非所有结构均满足该准则。
- `structural_validity`：由CDVAE提出的**结构合法性**，即任意两个原子之间的距离均不小于0.5埃（Angstrom）。
- `cdvae_e`：CDVAE内置模型预测的能量，用于EMD(E)分布相似度度量。
- `chgnet_energy_per_atom`：CHGNet弛豫得到的单原子能量。
- `chgnet_e_above_hull_corrected`：经Materials Project能量校正后的CHGNet弛豫结果的凸包能量高于凸包值。
- `dft_e_uncorrected`：DFT弛豫得到的原始势能能量。
- `dft_e_corrected`：经`MaterialsProject2020Compatibility`校正后的DFT弛豫势能能量。
- `dft_e_above_hull_corrected`：基于matbench-discovery发布的参考文件`2023-02-07-ppd-mp.pkl.gz`计算得到的、经DFT弛豫后的凸包能量高于凸包值。
- `entry`：包含DFT运行结果的`pymatgen.entries.ComputedEntry`对象。

### 引用格式
bibtex
@article{kazeev2025wyckoff,
title={{Wyckoff Transformer: Generation of symmetric crystals}},
author={Kazeev, Nikita and Nong, Wei and Romanov, Ignat and Zhu, Ruiming and Ustyuzhanin, Andrey and Yamazaki, Shuya and Hippalgaonkar, Kedar},
journal={arXiv preprint arXiv:2503.02407},
year={2025}
}