<b>Hessian QM9 Dataset</b>

<pre><br></pre><b>Overview</b>Hessian QM9 is the first database of equilibrium configurations and numerical Hessian matrices, consisting of 41,645 molecules from the QM9 dataset at the $\omega$B97x/6-31G* level. Molecular Hessians were calculated in vacuum, as well as in water, tetrahydrofuran, and toluene using an implicit solvation model.A pre-print article associated with this dataset is available at here.<b>Data records</b>The dataset is stored in Hugging Face's dataset format. For each of the four implicit solvent environments (vacuum, THF, toluene, and water), the data is divided into separate datasets containing vibrational analysis of 41,645 optimized geometries. Labels are associated with the QM9 molecule labelling system given by Ramakrishnan <i>et al</i>.Please note that only molecules containing H, C, N, O were considered. This exclusion was due to the limited number of molecules containing fluorine in the QM9 dataset, which was not sufficient to build a good description of the chemical environment for fluorine atoms. Including these molecules may have reduced the overall precision of any models trained on our data.**Important:** To avoid issues caused by Figshare's DOI numbering system, where 8-digit numbers are prepended to the file names upon downloading, it is recommended to use the provided Python script for downloading and unzipping the dataset. This script ensures that the files are extracted without unnecessary prefixes, preserving the correct file names for easier access and use.<br><b>To download and load the dataset:</b>Use the following Python script to download, extract, and rename the files:```pythonimport requestsimport zipfileimport osfrom datasets import load_from_disk<br># Download the dataseturl = 'https://figshare.com/ndownloader/articles/26363959/versions/1?folder_path=hessian_qm9_DatasetDict'response = requests.get(url)zip_filename = 'data.zip'<br># Save and extract the fileswith open(zip_filename, 'wb') as f: f.write(response.content)<br>with zipfile.ZipFile(zip_filename, 'r') as zip_ref: zip_ref.extractall('./')<br># Remove the DOI prefixes from filenamesroot_directory = 'hessian_qm9_DatasetDict'for subdir in os.listdir(root_directory): subdir_path = os.path.join(root_directory, subdir) if os.path.isdir(subdir_path): for filename in os.listdir(subdir_path): if filename[:8].isdigit() and filename[8] == '_': new_filename = filename[9:] os.rename(os.path.join(subdir_path, filename), os.path.join(subdir_path, new_filename))<br># Load the datasetdataset = load_from_disk(root_directory)print(dataset)```<br>Expected output:<br>```pythonDatasetDict({ vacuum: Dataset({ features: ['energy', 'positions', 'atomic_numbers', 'forces', 'frequencies', 'normal_modes', 'hessian', 'label'], num_rows: 41645 }), thf: Dataset({ features: ['energy', 'positions', 'atomic_numbers', 'forces', 'frequencies', 'normal_modes', 'hessian', 'label'], num_rows: 41645 }), toluene: Dataset({ features: ['energy', 'positions', 'atomic_numbers', 'forces', 'frequencies', 'normal_modes', 'hessian', 'label'], num_rows: 41645 }), water: Dataset({ features: ['energy', 'positions', 'atomic_numbers', 'forces', 'frequencies', 'normal_modes', 'hessian', 'label'], num_rows: 41645 })})```<br><b>DFT Methods</b>All DFT calculations were carried out using the NWChem software package. The density functional used was $\omega$B97x with a 6-31G* basis set to create data compatible with the ANI-1/ANI-1x/ANI-2x datasets. The self-consistent field (SCF) cycle was converged when changes in total energy and density were less than 1e-6 eV. All molecules in the set are neutral with a multiplicity of 1. The Mura-Knowles radial quadrature and Lebedev angular quadrature were used in the integration. Structures were optimized in vacuum and three solvents (tetrahydrofuran, toluene, and water) using an implicit solvation model.The Hessian matrices, vibrational frequencies, and normal modes were computed for a subset of 41,645 molecular geometries using the finite differences method.<b>Example model weights</b>An example model trained on Hessian data is included in this dataset. Full details of the model will be provided in an upcoming publication. The model is an E(3)-equivariant graph neural network using the `e3x` package with specific architecture details. To load the model weights, use:<br>```pythonparams = jnp.load('params_train_f128_i5_b16.npz', allow_pickle=True)['params'].item()```

**概述**
Hessian QM9是首个收录平衡构型与数值海森矩阵（numerical Hessian matrices）的数据库，其数据源自QM9数据集中的41645个分子，所有计算均采用ωB97x/6-31G*级别完成。分子海森矩阵在真空环境下计算，同时通过隐式溶剂化模型分别在水、四氢呋喃与甲苯三种溶剂环境中完成计算。本数据集关联的预印本文章可在此获取。

**数据记录**
本数据集采用Hugging Face数据集格式存储。针对四种隐式溶剂环境（真空、四氢呋喃、甲苯与水），数据被划分为独立的数据集，每个数据集均包含41645个优化后几何构型的振动分析结果。数据集标签采用Ramakrishnan等人提出的QM9分子命名系统。
请注意，本数据集仅包含含氢、碳、氮、氧的分子。排除含氟分子的原因在于QM9数据集中含氟分子数量极少，无法为氟原子的化学环境提供充分的描述依据，若纳入此类分子可能会降低基于本数据集训练的模型的整体精度。

**重要提示**
为避免Figshare的DOI编号系统引发的问题——该系统会在下载时向文件名前添加8位数字前缀，建议使用本数据集附带的Python脚本完成下载与解压操作。该脚本可确保文件解压时不会附带多余前缀，保留正确的文件名，便于后续访问与使用。

**下载与加载数据集**
使用以下Python脚本下载、解压并重命名文件：
python
import requests
import zipfile
import os
from datasets import load_from_disk

# Download the dataset
url = 'https://figshare.com/ndownloader/articles/26363959/versions/1?folder_path=hessian_qm9_DatasetDict'
response = requests.get(url)
zip_filename = 'data.zip'

# Save and extract the files
with open(zip_filename, 'wb') as f: f.write(response.content)

with zipfile.ZipFile(zip_filename, 'r') as zip_ref: zip_ref.extractall('./')

# Remove the DOI prefixes from filenames
root_directory = 'hessian_qm9_DatasetDict'
for subdir in os.listdir(root_directory):
subdir_path = os.path.join(root_directory, subdir)
if os.path.isdir(subdir_path):
for filename in os.listdir(subdir_path):
if filename[:8].isdigit() and filename[8] == '_':
new_filename = filename[9:]
os.rename(os.path.join(subdir_path, filename), os.path.join(subdir_path, new_filename))

# Load the dataset
dataset = load_from_disk(root_directory)
print(dataset)

预期输出：
python
DatasetDict({
真空: Dataset({
features: ['能量', '坐标', '原子序数', '作用力', '振动频率', '简正模', '海森矩阵', '标签'],
num_rows: 41645
}),
四氢呋喃(THF): Dataset({
features: ['能量', '坐标', '原子序数', '作用力', '振动频率', '简正模', '海森矩阵', '标签'],
num_rows: 41645
}),
甲苯: Dataset({
features: ['能量', '坐标', '原子序数', '作用力', '振动频率', '简正模', '海森矩阵', '标签'],
num_rows: 41645
}),
水: Dataset({
features: ['能量', '坐标', '原子序数', '作用力', '振动频率', '简正模', '海森矩阵', '标签'],
num_rows: 41645
})
})

**DFT计算方法**
所有密度泛函理论（DFT, density functional theory）计算均通过NWChem软件包完成。本次计算采用ωB97x泛函与6-31G*基组，以确保生成的数据与ANI-1、ANI-1x、ANI-2x数据集兼容。当总能量与密度的变化量小于1e-6 eV时，自洽场（SCF, self-consistent field）迭代收敛。本数据集内所有分子均为多重度1的中性分子。积分过程采用Mura-Knowles径向积分格点与Lebedev角向积分格点。通过隐式溶剂化模型，在真空与三种溶剂（四氢呋喃、甲苯、水）中完成结构优化。本数据集的41645个分子几何构型的海森矩阵、振动频率与简正模均通过有限差分法计算得到。

**示例模型权重**
本数据集附带一个基于海森矩阵数据训练的示例模型，模型的完整细节将在后续发表的论文中公布。该模型为采用`e3x`包构建的E(3)等变图神经网络，具备特定的架构细节。加载模型权重的代码如下：
python
params = jnp.load('params_train_f128_i5_b16.npz', allow_pickle=True)['params'].item()