[fairchem](https://github.com/facebookresearch/fairchem)は、材料科学と量子化学の分野で使用される、FacebookのAI研究チーム（Facebook AI Research, FAIR; 現在のMeta AI）が開発したソフトウェアプラットフォームである。 > FAIR Chemistry（フェア・ケミストリー）はMeta（旧Facebook）の人工知能研究所「FAIR」の化学研究部門である。 以下の記事に紹介がある通り、"UMA"（*Meta’s Universal Model for Atoms*）という汎用NNP（ニューラルネットワークポテンシャル）が公開されたので、その使用感を手元でチェックしてみる。 https://ai.meta.com/blog/meta-fair-science-new-open-source-releases/ fairchemの最新リリースはv2であり、公式にはUMAはv1向けにリリースされている。しかし、現時点で配布されているUMAのチェックポイントファイル（以下、ptファイル）はv2でも読み込めるため、ここでは現在最新の**fairchem-core-2.2.0**を導入する。 モデルポテンシャルのptファイルはHuggingFaceにユーザー登録してfairchemの開発チームに利用許諾の申請を行えばダウンロード可能。 https://github.com/facebookresearch/fairchem > fairchemは[MIT License](https://github.com/facebookresearch/fairchem/blob/main/LICENSE.md)で提供されている。著作権表記とライセンス文を保持する限り、商用/非商用を問わず無償で利用可能である。 * * * **以下では、すべてのコマンドを `/bin/bash` の環境で実行する。** * * *
【実行環境について】 ```:GNU C ライブラリ（glibc）バージョン $ ldd --version ldd (Ubuntu GLIBC 2.39-0ubuntu8.4) 2.39 ``` ```:カーネル・ホスト名・CPU アーキテクチャ $ uname -a Linux 5.15.167.4-microsoft-standard-WSL2 #1 SMP Tue Nov 5 00:21:55 UTC 2024 x86_64 x86_64 x86_64 GNU/Linux ``` ```:CPU AMD Ryzen 7 5800X3D 8-Core Processor (8コア16スレッド) ``` ```:GPU NVIDIA GeForce RTX 3070 Ti, 8 GB ``` ```:実装RAM 64.0 GB, 2667 MHz ```
# GPU関連の準備 必要であればGPU周りについて調べておく。fairchemでGPUを利用した計算を実行したい場合はGPU版のPyTorchをインストールする必要がある。 ```:cudaツールキットの導入（未導入の場合） sudo apt install nvidia-cuda-toolkit ``` ```:cudaのバージョン確認 $ nvcc -V nvcc: NVIDIA (R) Cuda compiler driver Copyright (c) 2005-2023 NVIDIA Corporation Built on Fri_Jan__6_16:45:21_PST_2023 Cuda compilation tools, release 12.0, V12.0.140 Build cuda_12.0.r12.0/compiler.32267302_0 ``` → ここでは、cuda-12.0 に対応するライブラリをインストールすることにする。 # 仮想環境の作成 fairchem-coreのPythonのバージョン依存は以下の通り。（PyTorchの依存も同様） ``` requires-python = ">=3.9, <3.13" ``` fairchemチームはパッケージマネージャーとして[uv](https://docs.astral.sh/uv/getting-started/installation/)を推奨しているが、簡単のために[Anaconda](https://www.anaconda.com/)を利用して導入する（minicondaでも特に問題ないと思われる）。ここでは仮想環境のPythonのバージョンを3.12.7とした。 > Linux用のAnacondaのインストーラは公式サイトから取得できる。 > https://www.anaconda.com/download/success > Python-3.12.7は2024年10月にリリースされたバージョンである。ライブラリさえ対応していれば任意のバージョンを導入して良い。 ```shell:仮想環境の作成 conda create -n uma312 python=3.12.7 ```
【新たにインストールされるパッケージ一覧】 ```sh: The following NEW packages will be INSTALLED: _libgcc_mutex pkgs/main/linux-64::_libgcc_mutex-0.1-main _openmp_mutex pkgs/main/linux-64::_openmp_mutex-5.1-1_gnu bzip2 pkgs/main/linux-64::bzip2-1.0.8-h5eee18b_6 ca-certificates pkgs/main/linux-64::ca-certificates-2025.2.25-h06a4308_0 expat pkgs/main/linux-64::expat-2.7.1-h6a678d5_0 ld_impl_linux-64 pkgs/main/linux-64::ld_impl_linux-64-2.40-h12ee557_0 libffi pkgs/main/linux-64::libffi-3.4.4-h6a678d5_1 libgcc-ng pkgs/main/linux-64::libgcc-ng-11.2.0-h1234567_1 libgomp pkgs/main/linux-64::libgomp-11.2.0-h1234567_1 libstdcxx-ng pkgs/main/linux-64::libstdcxx-ng-11.2.0-h1234567_1 libuuid pkgs/main/linux-64::libuuid-1.41.5-h5eee18b_0 libxcb pkgs/main/linux-64::libxcb-1.17.0-h9b100fa_0 ncurses pkgs/main/linux-64::ncurses-6.4-h6a678d5_0 openssl pkgs/main/linux-64::openssl-3.0.16-h5eee18b_0 pip pkgs/main/noarch::pip-25.1-pyhc872135_2 pthread-stubs pkgs/main/linux-64::pthread-stubs-0.3-h0ce48e5_1 python pkgs/main/linux-64::python-3.12.7-h5148396_0 readline pkgs/main/linux-64::readline-8.2-h5eee18b_0 setuptools pkgs/main/linux-64::setuptools-78.1.1-py312h06a4308_0 sqlite pkgs/main/linux-64::sqlite-3.45.3-h5eee18b_0 tk pkgs/main/linux-64::tk-8.6.14-h993c535_1 tzdata pkgs/main/noarch::tzdata-2025b-h04d1e81_0 wheel pkgs/main/linux-64::wheel-0.45.1-py312h06a4308_0 xorg-libx11 pkgs/main/linux-64::xorg-libx11-1.8.12-h9b100fa_1 xorg-libxau pkgs/main/linux-64::xorg-libxau-1.0.12-h9b100fa_0 xorg-libxdmcp pkgs/main/linux-64::xorg-libxdmcp-1.1.5-h9b100fa_0 xorg-xorgproto pkgs/main/linux-64::xorg-xorgproto-2024.1-h5eee18b_1 xz pkgs/main/linux-64::xz-5.6.4-h5eee18b_1 zlib pkgs/main/linux-64::zlib-1.2.13-h5eee18b_1 ```
```shell:仮想環境の起動 conda activate uma312 ``` > 仮想環境を作り直す場合は以下のようにして削除できる。 > ```shell:仮想環境の削除 > conda remove -n uma312 --all > ``` # PyTorchをインストールする fairchem-core-2.2.0のPyTorchのバージョン依存は以下の通り。 ```:fairchem_core-2.2.0.tar.gz/fairchem_core-2.2.0/pyproject.toml より抜粋 "torch~=2.6.0" ``` → PyTorchの2.6系としては 2.6.0 のみがリリースされているので、PyTorch-2.6.0およびこれに対応するライブラリをインストールする。 筆者の環境ではcuda-12.0なので、conda-forgeから「PyTorch-2.6.0 + CUDA-12.6」などのビルドを取得すればよい。もしくは、pytorch公式のwhlファイルを参照してインストールする。 > CUDAには下方互換性があるのでCUDA 12.6対応バイナリをインストールすれば良い。 ここで、単純な `conda install pytorch` で導入するとCPU版がビルドされることになり、fairchemライブラリがGPUを利用できなくなるので注意。 > GPUが無いマシンの場合はCPU版のみで問題ないので、 > ```shell:CPU版PyTorchのインストール（PyPI） > pip install torch==2.6.0 > ``` > などとすれば良い。conda-forgeからインストールする場合は以下の通り。 > ```shell:CPU版PyTorchのインストール（conda-forge） > conda install -c conda-forge pytorch=2.6.0 -y > ``` > -y オプションは"yes"の略で、インストール時に表示される確認プロンプト（"Proceed ([y]/n)?" など）に自動的に"yes"と答えて処理を進めることができる。 > 因みに、この後に導入する `fairchem-core-2.2.0` は新しすぎてconda-forge上に無いため、PyPIからインストールする必要がある。 GPU版をインストールする方法の例として、今回は以下のようにpytorch公式のwhlファイルを参照してインストールする。 ```shell:GPU版PyTorchのインストール（cuda-12.x対応版の公式whlで導入する場合） pip install torch==2.6.0+cu126 --index-url https://download.pytorch.org/whl/cu126 ```
【torchインストール時のログ】 ``` Looking in indexes: https://download.pytorch.org/whl/cu126 Collecting torch==2.6.0+cu126 Downloading https://download.pytorch.org/whl/cu126/torch-2.6.0%2Bcu126-cp312-cp312-manylinux_2_28_x86_64.whl.metadata (28 kB) Collecting filelock (from torch==2.6.0+cu126) Using cached https://download.pytorch.org/whl/filelock-3.13.1-py3-none-any.whl.metadata (2.8 kB) Collecting typing-extensions>=4.10.0 (from torch==2.6.0+cu126) Using cached https://download.pytorch.org/whl/typing_extensions-4.12.2-py3-none-any.whl.metadata (3.0 kB) Requirement already satisfied: setuptools in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch==2.6.0+cu126) (78.1.1) Collecting sympy==1.13.1 (from torch==2.6.0+cu126) Using cached https://download.pytorch.org/whl/sympy-1.13.1-py3-none-any.whl (6.2 MB) Collecting networkx (from torch==2.6.0+cu126) Using cached https://download.pytorch.org/whl/networkx-3.3-py3-none-any.whl.metadata (5.1 kB) Collecting jinja2 (from torch==2.6.0+cu126) Using cached https://download.pytorch.org/whl/Jinja2-3.1.4-py3-none-any.whl.metadata (2.6 kB) Collecting fsspec (from torch==2.6.0+cu126) Using cached https://download.pytorch.org/whl/fsspec-2024.6.1-py3-none-any.whl.metadata (11 kB) Collecting nvidia-cuda-nvrtc-cu12==12.6.77 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_cuda_nvrtc_cu12-12.6.77-py3-none-manylinux2014_x86_64.whl.metadata (1.5 kB) Collecting nvidia-cuda-runtime-cu12==12.6.77 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_cuda_runtime_cu12-12.6.77-py3-none-manylinux2014_x86_64.whl.metadata (1.5 kB) Collecting nvidia-cuda-cupti-cu12==12.6.80 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_cuda_cupti_cu12-12.6.80-py3-none-manylinux2014_x86_64.whl.metadata (1.6 kB) Collecting nvidia-cudnn-cu12==9.5.1.17 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_cudnn_cu12-9.5.1.17-py3-none-manylinux_2_28_x86_64.whl.metadata (1.6 kB) Collecting nvidia-cublas-cu12==12.6.4.1 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_cublas_cu12-12.6.4.1-py3-none-manylinux2014_x86_64.manylinux_2_17_x86_64.whl.metadata (1.5 kB) Collecting nvidia-cufft-cu12==11.3.0.4 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_cufft_cu12-11.3.0.4-py3-none-manylinux2014_x86_64.whl.metadata (1.5 kB) Collecting nvidia-curand-cu12==10.3.7.77 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_curand_cu12-10.3.7.77-py3-none-manylinux2014_x86_64.whl.metadata (1.5 kB) Collecting nvidia-cusolver-cu12==11.7.1.2 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_cusolver_cu12-11.7.1.2-py3-none-manylinux2014_x86_64.whl.metadata (1.6 kB) Collecting nvidia-cusparse-cu12==12.5.4.2 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_cusparse_cu12-12.5.4.2-py3-none-manylinux2014_x86_64.whl.metadata (1.6 kB) Collecting nvidia-cusparselt-cu12==0.6.3 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_cusparselt_cu12-0.6.3-py3-none-manylinux2014_x86_64.whl.metadata (6.8 kB) Collecting nvidia-nccl-cu12==2.21.5 (from torch==2.6.0+cu126) Using cached https://download.pytorch.org/whl/nvidia_nccl_cu12-2.21.5-py3-none-manylinux2014_x86_64.whl (188.7 MB) Collecting nvidia-nvtx-cu12==12.6.77 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_nvtx_cu12-12.6.77-py3-none-manylinux2014_x86_64.whl.metadata (1.6 kB) Collecting nvidia-nvjitlink-cu12==12.6.85 (from torch==2.6.0+cu126) Downloading https://download.pytorch.org/whl/cu126/nvidia_nvjitlink_cu12-12.6.85-py3-none-manylinux2010_x86_64.manylinux_2_12_x86_64.whl.metadata (1.5 kB) Collecting triton==3.2.0 (from torch==2.6.0+cu126) Using cached 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19.7/19.7 MB 80.1 MB/s eta 0:00:00 Downloading https://download.pytorch.org/whl/cu126/nvidia_nvtx_cu12-12.6.77-py3-none-manylinux2014_x86_64.whl (89 kB) Using cached https://download.pytorch.org/whl/triton-3.2.0-cp312-cp312-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl (166.7 MB) Using cached https://download.pytorch.org/whl/typing_extensions-4.12.2-py3-none-any.whl (37 kB) Using cached https://download.pytorch.org/whl/filelock-3.13.1-py3-none-any.whl (11 kB) Using cached https://download.pytorch.org/whl/fsspec-2024.6.1-py3-none-any.whl (177 kB) Using cached https://download.pytorch.org/whl/Jinja2-3.1.4-py3-none-any.whl (133 kB) Using cached https://download.pytorch.org/whl/networkx-3.3-py3-none-any.whl (1.7 MB) Installing collected packages: triton, nvidia-cusparselt-cu12, mpmath, typing-extensions, sympy, nvidia-nvtx-cu12, nvidia-nvjitlink-cu12, nvidia-nccl-cu12, nvidia-curand-cu12, nvidia-cuda-runtime-cu12, nvidia-cuda-nvrtc-cu12, nvidia-cuda-cupti-cu12, nvidia-cublas-cu12, networkx, MarkupSafe, fsspec, filelock, nvidia-cusparse-cu12, nvidia-cufft-cu12, nvidia-cudnn-cu12, jinja2, nvidia-cusolver-cu12, torch Successfully installed MarkupSafe-2.1.5 filelock-3.13.1 fsspec-2024.6.1 jinja2-3.1.4 mpmath-1.3.0 networkx-3.3 nvidia-cublas-cu12-12.6.4.1 nvidia-cuda-cupti-cu12-12.6.80 nvidia-cuda-nvrtc-cu12-12.6.77 nvidia-cuda-runtime-cu12-12.6.77 nvidia-cudnn-cu12-9.5.1.17 nvidia-cufft-cu12-11.3.0.4 nvidia-curand-cu12-10.3.7.77 nvidia-cusolver-cu12-11.7.1.2 nvidia-cusparse-cu12-12.5.4.2 nvidia-cusparselt-cu12-0.6.3 nvidia-nccl-cu12-2.21.5 nvidia-nvjitlink-cu12-12.6.85 nvidia-nvtx-cu12-12.6.77 sympy-1.13.1 torch-2.6.0+cu126 triton-3.2.0 typing-extensions-4.12.2 ```
【この段階で導入されているライブラリ】 ``` $ pip list Package Version ------------------------ ----------- filelock 3.13.1 fsspec 2024.6.1 Jinja2 3.1.4 MarkupSafe 2.1.5 mpmath 1.3.0 networkx 3.3 nvidia-cublas-cu12 12.6.4.1 nvidia-cuda-cupti-cu12 12.6.80 nvidia-cuda-nvrtc-cu12 12.6.77 nvidia-cuda-runtime-cu12 12.6.77 nvidia-cudnn-cu12 9.5.1.17 nvidia-cufft-cu12 11.3.0.4 nvidia-curand-cu12 10.3.7.77 nvidia-cusolver-cu12 11.7.1.2 nvidia-cusparse-cu12 12.5.4.2 nvidia-cusparselt-cu12 0.6.3 nvidia-nccl-cu12 2.21.5 nvidia-nvjitlink-cu12 12.6.85 nvidia-nvtx-cu12 12.6.77 pip 25.1 setuptools 78.1.1 sympy 1.13.1 torch 2.6.0+cu126 triton 3.2.0 typing_extensions 4.12.2 wheel 0.45.1 ```
> conda-forgeから取得する場合は以下のようにする。 > ```shell:GPU版PyTorchのインストール（cuda-12.x対応版をconda-forgeから取得する場合） > conda install torch pytorch-cuda=12.6 -c conda-forge > ``` > `-c pytorch -c nvidia` として公式PyTorchチャンネルを指定するよりも、`-c conda-forge` としてconda-forgeチャンネルからCUDA-12.x対応バイナリを導入するのが良い。 # fairchem-coreをインストールする 続いて、fairchem-coreについてextrasを含めた依存ライブラリをすべてインストールする。PyTorchがインストール済みなので、以下を実行するだけで良い。依存関係を含め、すべての必要なパッケージが収集される。 ```shell:fairchem-coreのインストール pip install fairchem-core==2.2.0 ```
【fairchem-coreインストール時のログ】 ``` Collecting fairchem-core==2.2.0 (from fairchem-core[all]==2.2.0) Using cached fairchem_core-2.2.0-py3-none-any.whl.metadata (9.3 kB) Collecting ase-db-backends>=0.10.0 (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached ase_db_backends-0.10.0-py3-none-any.whl.metadata (600 bytes) Collecting ase>=3.25.0 (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached ase-3.25.0-py3-none-any.whl.metadata (4.2 kB) Collecting e3nn>=0.5 (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached e3nn-0.5.6-py3-none-any.whl.metadata (5.4 kB) Collecting huggingface-hub>=0.27.1 (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached huggingface_hub-0.32.4-py3-none-any.whl.metadata (14 kB) Collecting hydra-core (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached hydra_core-1.3.2-py3-none-any.whl.metadata (5.5 kB) Collecting lmdb (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached lmdb-1.6.2-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (1.1 kB) Collecting numba>=0.61.2 (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached numba-0.61.2-cp312-cp312-manylinux2014_x86_64.manylinux_2_17_x86_64.whl.metadata (2.8 kB) Collecting numpy<2.3,>=2.0 (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached numpy-2.2.6-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (62 kB) Collecting orjson (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached orjson-3.10.18-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (41 kB) Collecting pymatgen>=2023.10.3 (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached pymatgen-2025.5.28-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (13 kB) Collecting pyyaml (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached PyYAML-6.0.2-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (2.1 kB) Collecting requests (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached requests-2.32.3-py3-none-any.whl.metadata (4.6 kB) Collecting submitit (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached submitit-1.5.3-py3-none-any.whl.metadata (7.9 kB) Collecting tensorboard (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached tensorboard-2.19.0-py3-none-any.whl.metadata (1.8 kB) Collecting torchtnt (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached torchtnt-0.2.4-py3-none-any.whl.metadata (3.1 kB) Requirement already satisfied: torch~=2.6.0 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (2.6.0+cu126) Collecting tqdm (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached tqdm-4.67.1-py3-none-any.whl.metadata (57 kB) Collecting wandb (from fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached wandb-0.20.1-py3-none-manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (10 kB) Requirement already satisfied: filelock in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (3.13.1) Requirement already satisfied: typing-extensions>=4.10.0 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (4.12.2) Requirement already satisfied: setuptools in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (78.1.1) Requirement already satisfied: sympy==1.13.1 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (1.13.1) Requirement already satisfied: networkx in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (3.3) Requirement already satisfied: jinja2 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (3.1.4) Requirement already satisfied: fsspec in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (2024.6.1) Requirement already satisfied: nvidia-cuda-nvrtc-cu12==12.6.77 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (12.6.77) Requirement already satisfied: nvidia-cuda-runtime-cu12==12.6.77 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (12.6.77) Requirement already satisfied: nvidia-cuda-cupti-cu12==12.6.80 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (12.6.80) Requirement already satisfied: nvidia-cudnn-cu12==9.5.1.17 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (9.5.1.17) Requirement already satisfied: nvidia-cublas-cu12==12.6.4.1 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (12.6.4.1) Requirement already satisfied: nvidia-cufft-cu12==11.3.0.4 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (11.3.0.4) Requirement already satisfied: nvidia-curand-cu12==10.3.7.77 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (10.3.7.77) Requirement already satisfied: nvidia-cusolver-cu12==11.7.1.2 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (11.7.1.2) Requirement already satisfied: nvidia-cusparse-cu12==12.5.4.2 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (12.5.4.2) Requirement already satisfied: nvidia-cusparselt-cu12==0.6.3 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (0.6.3) Requirement already satisfied: nvidia-nccl-cu12==2.21.5 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (2.21.5) Requirement already satisfied: nvidia-nvtx-cu12==12.6.77 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (12.6.77) Requirement already satisfied: nvidia-nvjitlink-cu12==12.6.85 in ./anaconda3/envs/uma312/lib/python3.12/site-packages (from torch~=2.6.0->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) (12.6.85) Requirement already satisfied: triton==3.2.0 in 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Collecting tensorboard-data-server<0.8.0,>=0.7.0 (from tensorboard->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached tensorboard_data_server-0.7.2-py3-none-manylinux_2_31_x86_64.whl.metadata (1.1 kB) Collecting werkzeug>=1.0.1 (from tensorboard->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached werkzeug-3.1.3-py3-none-any.whl.metadata (3.7 kB) Collecting psutil (from torchtnt->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached psutil-7.0.0-cp36-abi3-manylinux_2_12_x86_64.manylinux2010_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl.metadata (22 kB) Collecting pyre-extensions (from torchtnt->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached pyre_extensions-0.0.32-py3-none-any.whl.metadata (4.0 kB) Collecting typing-inspect (from pyre-extensions->torchtnt->fairchem-core==2.2.0->fairchem-core[all]==2.2.0) Using cached typing_inspect-0.9.0-py3-none-any.whl.metadata (1.5 kB) Collecting mypy-extensions>=0.3.0 (from 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pandas-2.3.0-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (12.0 MB) Using cached plotly-6.1.2-py3-none-any.whl (16.3 MB) Using cached narwhals-1.41.1-py3-none-any.whl (358 kB) Using cached pyparsing-3.2.3-py3-none-any.whl (111 kB) Using cached python_dateutil-2.9.0.post0-py2.py3-none-any.whl (229 kB) Using cached pytz-2025.2-py2.py3-none-any.whl (509 kB) Using cached PyYAML-6.0.2-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (767 kB) Using cached requests-2.32.3-py3-none-any.whl (64 kB) Using cached charset_normalizer-3.4.2-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (148 kB) Using cached idna-3.10-py3-none-any.whl (70 kB) Using cached urllib3-2.4.0-py3-none-any.whl (128 kB) Using cached certifi-2025.4.26-py3-none-any.whl (159 kB) Using cached ruamel.yaml-0.18.13-py3-none-any.whl (118 kB) Using cached ruamel.yaml.clib-0.2.12-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (754 kB) Using cached scipy-1.15.3-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (37.3 MB) Using cached six-1.17.0-py2.py3-none-any.whl (11 kB) Using cached spglib-2.6.0-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (809 kB) Using cached tabulate-0.9.0-py3-none-any.whl (35 kB) Using cached tqdm-4.67.1-py3-none-any.whl (78 kB) Using cached tzdata-2025.2-py2.py3-none-any.whl (347 kB) Using cached uncertainties-3.2.3-py3-none-any.whl (60 kB) Using cached cryptography-45.0.3-cp311-abi3-manylinux_2_34_x86_64.whl (4.5 MB) Using cached cffi-1.17.1-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (479 kB) Using cached hydra_core-1.3.2-py3-none-any.whl (154 kB) Using cached omegaconf-2.3.0-py3-none-any.whl (79 kB) Using cached lmdb-1.6.2-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (300 kB) Using cached opt_einsum-3.4.0-py3-none-any.whl (71 kB) Using cached psycopg2_binary-2.9.10-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (3.0 MB) Using cached pycparser-2.22-py3-none-any.whl (117 kB) Using cached PyMySQL-1.1.1-py3-none-any.whl (44 kB) Using cached submitit-1.5.3-py3-none-any.whl (75 kB) Using cached cloudpickle-3.1.1-py3-none-any.whl (20 kB) Using cached tensorboard-2.19.0-py3-none-any.whl (5.5 MB) Using cached tensorboard_data_server-0.7.2-py3-none-manylinux_2_31_x86_64.whl (6.6 MB) Using cached absl_py-2.3.0-py3-none-any.whl (135 kB) Using cached grpcio-1.72.1-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (5.8 MB) Using cached markdown-3.8-py3-none-any.whl (106 kB) Using cached protobuf-6.31.1-cp39-abi3-manylinux2014_x86_64.whl (321 kB) Using cached werkzeug-3.1.3-py3-none-any.whl (224 kB) Using cached torchtnt-0.2.4-py3-none-any.whl (163 kB) Using cached psutil-7.0.0-cp36-abi3-manylinux_2_12_x86_64.manylinux2010_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl (277 kB) Using cached pyre_extensions-0.0.32-py3-none-any.whl (12 kB) Using cached typing_inspect-0.9.0-py3-none-any.whl (8.8 kB) Using cached mypy_extensions-1.1.0-py3-none-any.whl (5.0 kB) Using cached wandb-0.20.1-py3-none-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (23.2 MB) Using cached pydantic-2.11.5-py3-none-any.whl (444 kB) Using cached pydantic_core-2.33.2-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl (2.0 MB) Using cached annotated_types-0.7.0-py3-none-any.whl (13 kB) Using cached click-8.2.1-py3-none-any.whl (102 kB) Using cached GitPython-3.1.44-py3-none-any.whl (207 kB) Using cached gitdb-4.0.12-py3-none-any.whl (62 kB) Using cached smmap-5.0.2-py3-none-any.whl (24 kB) Using cached sentry_sdk-2.29.1-py2.py3-none-any.whl (341 kB) Using cached typing_inspection-0.4.1-py3-none-any.whl (14 kB) Using cached platformdirs-4.3.8-py3-none-any.whl (18 kB) Using cached setproctitle-1.3.6-cp312-cp312-manylinux_2_5_x86_64.manylinux1_x86_64.manylinux_2_17_x86_64.manylinux2014_x86_64.whl (31 kB) Installing collected packages: pytz, lmdb, antlr4-python3-runtime, werkzeug, urllib3, uncertainties, tzdata, typing-inspection, tqdm, tensorboard-data-server, tabulate, smmap, six, setproctitle, ruamel.yaml.clib, pyyaml, pyparsing, pymysql, pydantic-core, pycparser, psycopg2-binary, psutil, protobuf, platformdirs, pillow, palettable, packaging, orjson, opt-einsum, numpy, narwhals, mypy-extensions, markdown, llvmlite, kiwisolver, joblib, idna, hf-xet, grpcio, fonttools, cycler, cloudpickle, click, charset-normalizer, certifi, annotated-types, absl-py, typing-inspect, tensorboard, submitit, spglib, sentry-sdk, scipy, ruamel.yaml, requests, python-dateutil, pydantic, plotly, omegaconf, numba, gitdb, contourpy, cffi, bibtexparser, pyre-extensions, pandas, monty, matplotlib, hydra-core, huggingface-hub, gitpython, cryptography, wandb, torchtnt, pymatgen, opt_einsum_fx, ase, e3nn, ase-db-backends, fairchem-core Successfully installed absl-py-2.3.0 annotated-types-0.7.0 antlr4-python3-runtime-4.9.3 ase-3.25.0 ase-db-backends-0.10.0 bibtexparser-1.4.3 certifi-2025.4.26 cffi-1.17.1 charset-normalizer-3.4.2 click-8.2.1 cloudpickle-3.1.1 contourpy-1.3.2 cryptography-45.0.3 cycler-0.12.1 e3nn-0.5.6 fairchem-core-2.2.0 fonttools-4.58.2 gitdb-4.0.12 gitpython-3.1.44 grpcio-1.72.1 hf-xet-1.1.3 huggingface-hub-0.32.4 hydra-core-1.3.2 idna-3.10 joblib-1.5.1 kiwisolver-1.4.8 llvmlite-0.44.0 lmdb-1.6.2 markdown-3.8 matplotlib-3.10.3 monty-2025.3.3 mypy-extensions-1.1.0 narwhals-1.41.1 numba-0.61.2 numpy-2.2.6 omegaconf-2.3.0 opt-einsum-3.4.0 opt_einsum_fx-0.1.4 orjson-3.10.18 packaging-25.0 palettable-3.3.3 pandas-2.3.0 pillow-11.2.1 platformdirs-4.3.8 plotly-6.1.2 protobuf-6.31.1 psutil-7.0.0 psycopg2-binary-2.9.10 pycparser-2.22 pydantic-2.11.5 pydantic-core-2.33.2 pymatgen-2025.5.28 pymysql-1.1.1 pyparsing-3.2.3 pyre-extensions-0.0.32 python-dateutil-2.9.0.post0 pytz-2025.2 pyyaml-6.0.2 requests-2.32.3 ruamel.yaml-0.18.13 ruamel.yaml.clib-0.2.12 scipy-1.15.3 sentry-sdk-2.29.1 setproctitle-1.3.6 six-1.17.0 smmap-5.0.2 spglib-2.6.0 submitit-1.5.3 tabulate-0.9.0 tensorboard-2.19.0 tensorboard-data-server-0.7.2 torchtnt-0.2.4 tqdm-4.67.1 typing-inspect-0.9.0 typing-inspection-0.4.1 tzdata-2025.2 uncertainties-3.2.3 urllib3-2.4.0 wandb-0.20.1 werkzeug-3.1.3 ```
【この段階で導入されているライブラリ】 ``` $ pip list Package Version ------------------------ ----------- absl-py 2.3.0 annotated-types 0.7.0 antlr4-python3-runtime 4.9.3 ase 3.25.0 ase_db_backends 0.10.0 bibtexparser 1.4.3 certifi 2025.4.26 cffi 1.17.1 charset-normalizer 3.4.2 click 8.2.1 cloudpickle 3.1.1 contourpy 1.3.2 cryptography 45.0.3 cycler 0.12.1 e3nn 0.5.6 fairchem-core 2.2.0 filelock 3.13.1 fonttools 4.58.2 fsspec 2024.6.1 gitdb 4.0.12 GitPython 3.1.44 grpcio 1.72.1 hf-xet 1.1.3 huggingface-hub 0.32.4 hydra-core 1.3.2 idna 3.10 Jinja2 3.1.4 joblib 1.5.1 kiwisolver 1.4.8 llvmlite 0.44.0 lmdb 1.6.2 Markdown 3.8 MarkupSafe 2.1.5 matplotlib 3.10.3 monty 2025.3.3 mpmath 1.3.0 mypy_extensions 1.1.0 narwhals 1.41.1 networkx 3.3 numba 0.61.2 numpy 2.2.6 nvidia-cublas-cu12 12.6.4.1 nvidia-cuda-cupti-cu12 12.6.80 nvidia-cuda-nvrtc-cu12 12.6.77 nvidia-cuda-runtime-cu12 12.6.77 nvidia-cudnn-cu12 9.5.1.17 nvidia-cufft-cu12 11.3.0.4 nvidia-curand-cu12 10.3.7.77 nvidia-cusolver-cu12 11.7.1.2 nvidia-cusparse-cu12 12.5.4.2 nvidia-cusparselt-cu12 0.6.3 nvidia-nccl-cu12 2.21.5 nvidia-nvjitlink-cu12 12.6.85 nvidia-nvtx-cu12 12.6.77 omegaconf 2.3.0 opt_einsum 3.4.0 opt-einsum-fx 0.1.4 orjson 3.10.18 packaging 25.0 palettable 3.3.3 pandas 2.3.0 pillow 11.2.1 pip 25.1 platformdirs 4.3.8 plotly 6.1.2 protobuf 6.31.1 psutil 7.0.0 psycopg2-binary 2.9.10 pycparser 2.22 pydantic 2.11.5 pydantic_core 2.33.2 pymatgen 2025.5.28 PyMySQL 1.1.1 pyparsing 3.2.3 pyre-extensions 0.0.32 python-dateutil 2.9.0.post0 pytz 2025.2 PyYAML 6.0.2 requests 2.32.3 ruamel.yaml 0.18.13 ruamel.yaml.clib 0.2.12 scipy 1.15.3 sentry-sdk 2.29.1 setproctitle 1.3.6 setuptools 78.1.1 six 1.17.0 smmap 5.0.2 spglib 2.6.0 submitit 1.5.3 sympy 1.13.1 tabulate 0.9.0 tensorboard 2.19.0 tensorboard-data-server 0.7.2 torch 2.6.0+cu126 torchtnt 0.2.4 tqdm 4.67.1 triton 3.2.0 typing_extensions 4.12.2 typing-inspect 0.9.0 typing-inspection 0.4.1 tzdata 2025.2 uncertainties 3.2.3 urllib3 2.4.0 wandb 0.20.1 Werkzeug 3.1.3 wheel 0.45.1 ```
> もし `fairchem_core-1.10.0` などv1系をインストールする場合は `torch_extras` として以下のものが要求されるので、別途インストールする必要がある。 > ``` > torch_extras = ["torch_scatter", "torch_sparse", "torch_cluster"] > ``` > >
【torch_extrasのインストール（fairchem-core v1系の場合のみ）】 > > ``` > conda install -c conda-forge torch_scatter > conda install -c conda-forge torch_sparse > conda install -c conda-forge torch_cluster > ``` > >
> > fairchem-coreのv1系は今後サポートされなくなると考えられるので、できるだけv2系を導入するのが望ましい。 * * * 以上の手順により、fairchem-core-2.2.0が導入できる。 # 汎用NNP "UMA" の動作テスト 汎用NNP "UMA" は[HuggingFace](https://huggingface.co/)上の[FacebookのUMAに関するページ](https://huggingface.co/facebook/UMA)からダウンロードできる。ただし、HuggingFaceへのユーザー登録および開発チームへの使用許諾の申請が必要である。 記事執筆時点（2025/06/10）では、UMAのスモールモデルである `uma-s-1.pt` のみがダウンロード可能なので、これを利用する。 以上で、当初の目的であった汎用NNP "UMA" の動作テストの準備が整った。 * * * 今回のリリースの目玉である小分子系のトレーニングセット`Omol25`を用いた`omol`タスクについて、テスト計算を実施する。`Omol25`には「小分子、バイオ分子、金属錯体、電解質を含む約8,300万のユニークな分子系」が収録されているため、有機分子に限らず金属錯体などにも適用できる。 公式ドキュメントでは以下のように注意点が記載されている。（和訳は筆者によるもの） | Task | `omol` | |:-----------|:-----------| | **Dataset** | `Omol25` | | **計算レベル** | ORCA6に実装されている `wB97M-V/def2-TZVPD`（非局所分散を含む）。溶媒和はすべて明示的に扱うこと。| | **関連する応用先** | 生物学、有機化学、タンパク質のフォールディング（折りたたみ）、小分子医薬品、有機物質の溶液物性、均一系触媒。| | **使用上の注意** | 全電荷およびスピン多重度が分からない場合、電荷系や開殻系をモデリングするときは特段の注意を要する。本手法はラジカル化学の研究や、磁気状態が分子構造に与える影響を理解するために利用可能である。すべてのトレーニングデータは非周期的（aperiodic）であるため、周期的系を扱う場合は慎重に取り扱うこと。無機材料にはおそらく適用が難しいであろう。 | 学習データにはimplicitな溶媒モデル（連続誘電体モデルなど）を用いていないため、溶媒効果を考慮する場合は、溶媒分子を露わに配置するなどして系に含める必要がある、ということである。したがって、`omol`タスクを利用する際は溶媒の取り扱いに注意が必要である。（特に、溶液中の系を対象とするDFT計算の結果と比較する場合など） https://github.com/facebookresearch/fairchem/blob/8f31b4f17e572ee559e232b1faaa5c10efe3709f/docs/core/uma.md ## C4 炭化水素 `omol`タスクで用いられるモデルは、[ORCA](https://www.faccts.de/orca/)-6.x系のSCF計算で得られる "Total Energy" の値を学習データとしている。 そこでまずは、C4アルカンおよびアルケンの異性体のエネルギー差について、UMAとORCAのωB97M-V/def2-TZVPDの計算結果を比較してみる。 > 初期構造および最適化後の構造は末尾に示した。 計算には以下のようなスクリプトが利用できる。fairchem-coreのv1系では `OCPCalculator` という関数でモデルを呼び出していたがv2系では廃止されており、`FAIRChemCalculator` という関数を用いる。 ```py:butane_cis.py from ase.io import read from ase.optimize import LBFGS from fairchem.core import FAIRChemCalculator from fairchem.core.units.mlip_unit import load_predict_unit uma_predictor = load_predict_unit( path="./uma-s-1.pt", device="cpu", ) calc = FAIRChemCalculator( uma_predictor, task_name="omol", # options: "omol", "omat", "odac", "oc20", "omc" ) mol = read('./butane_cis.xyz') mol.info = {"charge": 0, "spin": 1} mol.calc = calc energy_init = mol.get_potential_energy() print("Initial energy [eV]:", energy_init) opt = LBFGS(mol) opt.run(0.01, 100) energy_final = mol.get_potential_energy() print("Final energy [eV]: ", energy_final) ``` エネルギーの単位はORCAおよびfairchem.coreの出力に倣い [eV] としている。 > ORCAはソフトウェア名、UMAはモデル名であり、カテゴリ違いでちぐはぐに見えるという指摘が有り得るが、ここでは便宜上下記のように並べて表記する。 | Species | ORCA-6.0.1 | UMA-s-1 | |:-----------|:-----------|:-----------| | butane_cis | -4310.28322 | -4310.28269 | | butane_trans | -4310.30855 | -4310.30803 | | 2-butene_cis | -4277.13356 | -4277.13306 | | 2-butene_trans | -4277.18144 | -4277.18109 | これを見ると、eV単位で小数点以下第2位～3位の精度で一致していることが分かる。 計算速度に関しては、CPU利用で秒間7点程度、GPUを利用した場合は秒間8点程度であった。十数原子程度の大きさの分子では、GPUを利用するメリットはあまり感じられないだろう。 * * * また、歪んだcis体のブテンについてLBFGS法で構造最適化したところ、ステップ数はCPU利用時で66、GPU利用時で90であった。 一般に、CPU計算が通常64ビット倍精度浮動小数点（float64）を使用するのに対して、GPU計算ではメモリ効率とパフォーマンス最適化のために32ビット単精度浮動小数点（float32）を使用するため、勾配計算の精度が異なる。この事情により、GPU計算ではLBFGS法のヘッセ(逆)行列の近似精度が低下し、収束判定の閾値に到達するまでにより多くのステップ数を要する傾向がある。 > ただ単に、ASEのLBFGS法の実装の問題である可能性も考えられる。 ## クライゼン転位反応 アリルビニルエーテルの異性化反応であり、通常は不可逆的に進行する。この反応の最も基本的な系の遷移状態について、エネルギーおよび振動数を比較してみる。 ![image.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/697094/f6399e20-cd82-4fa3-9018-de9a76b78558.png) > 各構造の座標は末尾に示した。 以下の表にエネルギーの計算値を示す。 | Species | ORCA-6.0.1 | UMA-s-1 | |:-----------|:-----------|:-----------| | 反応物 | -7360.36385 | -7360.36482 | | 遷移状態 | -7359.01857 | -7359.02055 | | 生成物 | -7361.15792 | -7361.15754 | 最も誤差の大きな遷移状態でも、0.19 kJ/molという僅かな誤差でORCAの計算を再現できていることが確かめられた。 次に振動数について見てみる。横軸をORCAのωB97M-V/def2-TZVPDの計算値、縦軸をUMAの計算値として振動数解析の結果をプロットしたところ、$y=x$の直線から大きく外れる振動モードはなかった。 ![image.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/697094/6c158d5f-63f6-47d3-84c9-3ed28ebea09f.png)
【反応物と生成物の振動数】 ```py:反応物の振動数（UMA + ASEの結果） Potential energy [eV]: -7360.364823535767 --------------------- # meV cm^-1 --------------------- 0 1.1i 9.1i 1 0.0i 0.3i 2 0.1 0.4 3 0.1 0.5 4 0.5 3.7 5 0.6 4.8 6 6.0 48.3 7 11.0 88.4 8 14.8 119.4 9 35.9 289.4 10 43.6 351.7 11 52.8 425.6 12 65.3 526.4 13 83.7 675.2 14 88.1 710.7 15 108.2 872.7 16 110.9 894.3 17 115.6 932.4 18 121.2 977.2 19 122.3 986.1 20 123.4 995.2 21 129.0 1040.6 22 138.8 1119.4 23 143.2 1155.3 24 149.5 1206.1 25 161.3 1301.3 26 163.0 1315.1 27 166.7 1344.4 28 171.2 1380.7 29 176.8 1426.1 30 180.4 1455.3 31 184.5 1488.3 32 214.6 1731.2 33 215.4 1737.0 34 376.0 3032.9 35 386.0 3112.9 36 390.5 3149.3 37 391.5 3158.0 38 393.0 3170.1 39 394.9 3185.1 40 401.5 3238.1 41 406.4 3277.5 --------------------- Zero-point energy: 3.219 eV ``` ```py:生成物の振動数（UMA + ASEの結果） Potential energy [eV]: -7361.157535667282 --------------------- # meV cm^-1 --------------------- 0 0.7i 5.3i 1 0.0i 0.3i 2 0.0 0.2 3 0.0 0.4 4 0.5 4.3 5 0.6 5.1 6 7.3 58.8 7 10.8 87.0 8 14.0 113.3 9 32.8 264.7 10 43.7 352.8 11 53.3 430.0 12 63.0 508.2 13 82.4 664.8 14 92.9 749.2 15 107.8 869.3 16 112.0 903.7 17 119.8 965.9 18 123.8 998.6 19 127.9 1031.9 20 129.6 1045.5 21 132.3 1067.5 22 144.0 1161.4 23 152.0 1226.1 24 153.1 1234.9 25 163.8 1321.0 26 166.6 1343.8 27 167.6 1351.8 28 175.2 1413.5 29 179.4 1447.3 30 180.2 1453.2 31 183.3 1478.2 32 215.3 1736.6 33 227.8 1837.5 34 358.7 2893.5 35 377.3 3043.3 36 378.4 3051.9 37 382.6 3085.5 38 386.3 3116.0 39 390.1 3146.0 40 391.1 3154.7 41 401.5 3238.4 --------------------- Zero-point energy: 3.215 eV ``` ```py:反応物の振動数（ORCAの結果） $vibrational_frequencies 42 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 74.9883640232371533 7 90.9301552745855446 8 126.9492623772070345 9 288.6576236534389182 10 351.3395805381115338 11 420.5388238978900404 12 528.0657919757780974 13 676.1817871811510940 14 714.3730084966985032 15 873.8901922621080303 16 894.2015240264963722 17 931.9257599355349839 18 974.7524847344734553 19 986.1812708133778642 20 993.1857338801559081 21 1037.1314482220561786 22 1118.6547018759874845 23 1156.6106922429110000 24 1205.9464794334699036 25 1300.9001437593590254 26 1314.7649579605879353 27 1344.3934779571775380 28 1380.5580997054748877 29 1424.4799552026001948 30 1453.5063449186527578 31 1488.2694148237728768 32 1732.5478331280367001 33 1738.1374718841664162 34 3034.0978780899558842 35 3111.8839562736939115 36 3148.4952061105059329 37 3158.5635418603278595 38 3172.4368790901530701 39 3184.6449390092352587 40 3240.6310051875661884 41 3280.0000973548912953 ``` ```py:生成物の振動数（ORCAの結果） $vibrational_frequencies 42 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 63.8666040650782705 7 94.6924280001958323 8 127.1116946286074381 9 266.6589725737520666 10 355.9600066862305994 11 427.8016956984284320 12 511.5546381531314637 13 665.2947701497770367 14 754.9545461546490515 15 868.0471372940571655 16 906.0536641732217049 17 965.1480167526805189 18 998.9911970423327148 19 1031.9295658842493140 20 1048.0183822480998970 21 1067.4274992719333568 22 1160.7497965753473181 23 1225.2829439409115366 24 1234.9074891336838391 25 1320.4221507172428574 26 1341.6368034552936024 27 1352.2228194052393064 28 1413.7055063539523871 29 1445.8538731220644422 30 1451.9637550082582038 31 1476.8141781916156106 32 1737.2104663986349351 33 1839.4806413016253828 34 2895.4371877476528425 35 3042.6929917353390920 36 3048.8517202949246894 37 3088.3049155616149619 38 3120.0597786384605570 39 3146.1716051507814882 40 3155.2944554488271933 41 3241.2987520404449242 ```
遷移状態の振動数については以下で議論する。 * * * ### 遷移状態の振動数解析（CPU） 以下の通り、同じ構造での振動数は、虚の振動数だけでなく高次の振動数も含めて良好な精度で再現できているようである。 ```py:UMA + ASEでの振動数解析（CPU） from ase.io import read, write from ase.vibrations import Vibrations from fairchem.core import FAIRChemCalculator from fairchem.core.units.mlip_unit import load_predict_unit uma_predictor = load_predict_unit( path="./uma-s-1.pt", device="cpu", ) calc = FAIRChemCalculator( uma_predictor, task_name="omol", ) ts = read("claisen_ts.xyz") ts.info = {"charge": 0, "spin": 1} ts.calc = calc energy = ts.get_potential_energy() print("Potential energy [eV]:", energy) vib = Vibrations(atoms=ts, name="claisen_tsvib_cpu", delta=0.005) vib.run() vib.summary() vib.clean() vib.write_mode(0) ```
【UMA + ASEでの振動数解析の結果（CPU）】 ```py:UMA + ASEでの振動数解析の結果（CPU） Potential energy [eV]: -7359.020552889195 --------------------- # meV cm^-1 --------------------- 0 75.2i 606.7i 1 0.2i 1.3i 2 0.0i 0.3i 3 0.1 0.6 4 0.8 6.1 5 1.3 10.3 6 2.6 20.8 7 21.8 175.6 8 39.3 317.2 9 40.5 326.7 10 48.8 393.6 11 54.8 441.7 12 58.6 472.9 13 65.7 529.6 14 92.7 747.5 15 99.9 805.9 16 108.1 871.6 17 112.5 907.4 18 118.9 959.1 19 123.9 999.0 20 124.4 1003.1 21 126.9 1023.5 22 128.4 1035.5 23 130.7 1054.1 24 136.4 1099.8 25 155.3 1252.5 26 157.2 1267.8 27 160.2 1291.8 28 167.1 1347.8 29 175.7 1416.9 30 180.4 1455.0 31 187.5 1512.4 32 190.2 1533.8 33 201.9 1628.7 34 373.5 3012.6 35 389.5 3141.9 36 390.4 3148.5 37 390.6 3150.6 38 392.8 3167.9 39 399.1 3219.0 40 401.1 3235.2 41 401.4 3237.3 --------------------- Zero-point energy: 3.175 eV ```
【（参考）ORCA-6.0.1での振動数解析の結果】 ```py:（参考）ORCA-6.0.1での振動数解析の結果 Total Energy : -270.43897268117342 Eh -7359.01857 eV Zero point energy ... 0.11723512 Eh 73.57 kcal/mol # eV単位に換算すると ≈ 3.1901301 eV $vibrational_frequencies 42 0 0.0000000000000000 1 0.0000000000000000 2 0.0000000000000000 3 0.0000000000000000 4 0.0000000000000000 5 0.0000000000000000 6 -587.5092404601411999 7 174.6142659987480954 8 307.9396725630247715 9 329.9802237915248497 10 390.4832906912052408 11 444.7988409444523086 12 482.1953484382101465 13 536.5167981489061049 14 756.5862975828496246 15 812.7315626068763095 16 878.2632549611893182 17 911.5092571834773025 18 964.5602919811398124 19 1001.8709172469359601 20 1006.9144226047300208 21 1030.2540944757570287 22 1039.8711469585466602 23 1060.5775876974137191 24 1110.4976681997598007 25 1254.3532428553878617 26 1273.4106927198245103 27 1295.3448387371813624 28 1343.2870435155007272 29 1425.6003894521231814 30 1463.8993560426436034 31 1524.5284705172921349 32 1545.3336452250980528 33 1640.5617869806330873 34 3020.5466961088195603 35 3154.8209701278092325 36 3163.2824572046988578 37 3168.5316722740922160 38 3184.2315224409621806 39 3246.9805428992667657 40 3256.4408280407742495 41 3258.9490835835576945 ```
> ASEの`Vibrations`モジュールでは数値微分による固有値解析が行われるため並進・回転のモードは必ずしも完全にゼロにならない。 * * * ### 遷移状態の振動数解析（GPU） 一方で、全く同じ構造に対してGPUを用いた振動数解析を実施したところ、ORCAの結果と比べて誤差がやや大きくなった。先ほど言及した数値計算の精度が影響しているものと考えられる。UMAポテンシャルで自由エネルギーなどの議論をする際は、GPUではなくCPUを利用するのが良さそうである。
【UMA + ASEでの振動数解析の結果（GPU版）】 ```py:UMA + ASEでの振動数解析の結果（GPU版） Potential energy [eV]: -7359.020588651982 --------------------- # meV cm^-1 --------------------- 0 74.9i 604.4i 1 4.6i 37.2i 2 1.8i 14.3i 3 0.8i 6.7i 4 2.3 18.3 5 3.1 24.8 6 5.5 44.6 7 21.7 175.1 8 39.3 316.9 9 40.7 328.3 10 48.7 393.1 11 54.6 440.2 12 58.4 471.1 13 65.8 530.3 14 93.0 749.9 15 99.7 804.3 16 107.8 869.4 17 112.6 908.1 18 118.4 954.8 19 123.0 992.4 20 124.4 1003.4 21 126.6 1021.5 22 128.0 1032.5 23 131.1 1057.2 24 137.4 1108.1 25 155.1 1250.7 26 157.1 1267.4 27 160.4 1293.6 28 167.3 1349.6 29 175.7 1417.1 30 180.5 1455.7 31 187.4 1511.2 32 190.2 1534.4 33 202.0 1628.9 34 373.7 3014.5 35 389.4 3140.6 36 390.2 3147.2 37 390.7 3151.3 38 392.3 3164.5 39 399.0 3218.5 40 401.1 3234.7 41 401.4 3237.3 --------------------- Zero-point energy: 3.178 eV ```
> float64で計算すれば精度は改善すると考えられるが、GPUを用いた計算ではfloat64の演算を行うと計算効率が下がることが知られている。誤差が大きくなりそうな巨大分子では、GPU版とCPU版はそもそも「異なる計算レベル」であると見なし、GPUは大域的な構造探索、CPU版は構造とエネルギーの改善、という別々の用途で利用するのが賢い選択かもしれない。 > とはいえ、エネルギーで言えば数kJ/mol程度しか変わらず、振動数もそこまで大きな誤差がある訳ではないため、UMAポテンシャルを利用して構造や反応経路のinitial guessを得たいというだけであれば、速度重視でGPU版のみ使う、という選択も当然あり得る。 ## L-システイン [L-システイン](https://en.wikipedia.org/wiki/Cysteine)のコンフォメーションのエネルギー差を比較してみる。 ![image.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/697094/f9324185-5ef5-408a-bd53-a2534c7d5061.png) | | ORCA-6.0.1 | UMA-s-1 | |:-----------|:-----------|:-----------| | 分子内水素結合なし | -19645.16772 | -19645.16844 | | 分子内水素結合あり | -19645.33379 | -19645.33663 | 先ほどと同様に、ORCAとUMAでエネルギーが小数点以下2桁目まで一致した。最適化後の構造はUMAとORCAで同じ（同一の平衡構造）であった。 > 初期構造および最適化後の構造は末尾に示した。 > なお「分子内水素結合なし」とラベリングしているが、この構造ではチオール基とアミノ基が弱く相互作用しているという解釈も成り立つ。 > 今回の結果には含めておらずUMAポテンシャルとも直接関係ないが、より大きなポリペプチドの双性イオンに対してORCAで構造最適化を実施したところ、SCF計算が収束しないことがあった。 ## SN2反応 クロロメタンのSN2反応の計算結果を以下に示す。 > 系全体の電荷を -1 として計算を実施した。 ![image.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/697094/8e27028f-ae66-4ac7-869a-9e27de48ce7e.png) 2列目と3列目に `Total Energy` の計算値(eV)、4列目と5列目にクロロメタンをエネルギーの基準とした相対エネルギー(kJ/mol)を示した。 | | ORCA (eV)| UMA (eV) | ΔE @ ORCA (kJ/mol) | ΔE @ UMA (kJ/mol) | |:-----------|:-----------|:-----------|:-----------|:-----------| | **CH₃Cl + Cl⁻** | -26132.79889 | -26132.79253 | 0.00 | 0.00 | | **Cl...CH₃...Cl⁻ (TS)** | -26132.21494 | -26132.21066 | 56.34 | 56.14 | | | ORCA-6.0.1 | UMA-s-1 | ΔE @ ORCA (kJ/mol) | ΔE @ UMA (kJ/mol) | |:-----------|:-----------|:-----------|:-----------|:-----------| | **CH₃Cl + Br⁻** | -83653.13344 | -83653.12779 | 0.00 | 0.00 | | **Cl...CH₃...Br⁻ (TS)** | -83652.43687 | -83652.44185 | 67.21 | 66.18 | | **Cl⁻ + CH₃Br** | -83652.83920 | -83652.83727 | 28.39 | 28.03 | UMAポテンシャルの計算値によると、クロロメタンが臭化物イオンに求核攻撃されるときの活性化エネルギーは 66.18 kJ/mol、逆反応の活性化エネルギーは 38.15 kJ/molと求められた。これはORCAの計算値と比較して誤差2%未満であり、電荷を有する系でも活性化エネルギーを精度よく与えている。 遷移状態の構造には僅かな差異があるが、エネルギーは実用的なレベルの精度で求められている。 > Br⁻はCl⁻よりも大きいため分極しやすく、相対的に良い脱離基として働くことが知られている。上記の計算では溶媒分子の存在を考慮していないが、定性的に妥当な結果を与えている。
【遷移状態における振動数計算のログ】 ```:SN2_Cl_Cl_orca --------------------- 0 0.00000000 1 0.00000000 2 0.00000000 3 0.00000000 4 0.00000000 5 0.00000000 6 -463.66274365 7 205.07827648 8 206.58973884 9 223.77241991 10 449.97262517 11 956.11482332 12 1056.92811736 13 1386.05642326 14 1387.91275310 15 3198.67522543 16 3394.19777670 17 3409.01356773 --------------------- ``` ```:SN2_Cl_Cl_uma --------------------- # meV cm^-1 --------------------- 0 52.6i 424.6i 1 1.7i 13.7i 2 0.6i 4.9i 3 0.2i 1.3i 4 0.9 6.9 5 1.2 9.3 6 3.2 25.9 7 26.0 209.6 8 26.2 211.0 9 27.2 219.4 10 119.4 963.1 11 119.6 964.8 12 137.6 1109.5 13 171.9 1386.6 14 172.0 1387.4 15 401.2 3235.7 16 423.9 3419.0 17 424.0 3419.8 --------------------- Zero-point energy: 1.027 eV ``` ```:SN2_Cl_Br_orca --------------------- 0 0.00000000 1 0.00000000 2 0.00000000 3 0.00000000 4 0.00000000 5 0.00000000 6 -433.07631469 7 112.25939319 8 183.93004281 9 188.60164133 10 886.50576738 11 934.04319109 12 1032.78281187 13 1132.52238576 14 1388.44322501 15 2935.41459085 16 3315.24569769 17 3429.81147964 --------------------- ``` ```:SN2_Cl_Br_uma --------------------- # meV cm^-1 --------------------- 0 49.4i 398.1i 1 2.3i 18.6i 2 0.6i 4.5i 3 0.1i 0.7i 4 0.4 3.2 5 0.4 3.5 6 4.1 33.4 7 22.2 178.8 8 23.6 190.5 9 23.7 191.3 10 115.2 929.3 11 115.6 932.3 12 131.5 1060.9 13 172.2 1389.0 14 172.6 1391.9 15 400.9 3233.5 16 423.3 3414.0 17 423.3 3414.4 --------------------- Zero-point energy: 1.015 eV ```
## All-Benzene Multi-Macrocyclic Nanocarbon より大きな分子の計算例として、2024年6月に合成が報告された下図に示す計534原子（$\mathrm{C_{324}H_{210}}$、ベンゼン環54個）からなるAll-Benzene Multi-Macrocyclic Nanocarbonについて、CPUとGPUを用いた構造最適化をそれぞれ実行してみる。 ![image.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/697094/7cf69a0d-187d-4ec2-9f10-ea0d9a381699.png) > [ref.] J.-N. Gao, A. Bu, Y. Chen, M. Huang, Z. Chen, X. Li, C.-H. Tung, L.-Z. Wu, H. Cong, *Angew. Chem. Int. Ed.* 2024, **63**, e202408016. https://doi.org/10.1002/anie.202408016 例えば以下のようなスクリプトで構造最適化を実施できる。GPUを利用したい場合は `device="cuda"` とすれば良い。 ```py:CPUを利用する場合 from ase.io import read from ase.optimize import LBFGS from fairchem.core import FAIRChemCalculator from fairchem.core.units.mlip_unit import load_predict_unit uma_predictor = load_predict_unit( path="./uma-s-1.pt", device="cpu", ) calc = FAIRChemCalculator( uma_predictor, task_name="omol", # options: "omol", "omat", "odac", "oc20", "omc" ) mol = read('cpp_3_init.xyz') mol.info = {"charge": 0, "spin": 1} mol.calc = calc energy = mol.get_potential_energy() print("Potential energy [eV]:", energy) opt = LBFGS(mol, trajectory='cpp_3_cpu.traj', logfile='cpp_3_cpu.log') opt.run(0.01, 10000) energy = mol.get_potential_energy() print("Potential energy [eV]:", energy) ``` これを実行したところ、CPUを利用した場合は14分31秒を要したのに対し、GPUを利用した場合では33秒と圧倒的に速い計算速度で収束に至った。**単純計算で26.4倍の加速率**である。型落ちのGPUでこれなので、最新のGPUではさらに数段高速な推論が可能だと思われる。 最適化のステップ数は、CPU利用で114、GPU利用で116とほぼ同等であった。これは論文のSIから取得した初期構造が既にある程度最適化された構造だった（初期構造が極小点のごく近傍だった）ため、CPU/GPUで最適化のステップ数に違いがほとんど見られなかったものと考えられる。 > 上記のスクリプトでは収束判定条件となる `fmax`（勾配の最大値）の値を 0.01 とやや厳しめに設定している。 > (2025/06/14追記) CPUを Intel Core i7 14700KF として同様の計算を実行したところ、9分55秒/104ステップで終了した。メモリは64GB（5600MHz）を使用。
【構造最適化のログ】 ```:UMA + ASEによる構造最適化（CPU利用） Initial energy [eV]: -339406.515888828 Step Time Energy fmax LBFGS: 0 21:58:59 -339406.515889 0.688373 LBFGS: 1 21:59:11 -339406.693885 0.307700 LBFGS: 2 21:59:22 -339406.788087 0.171372 LBFGS: 3 21:59:33 -339406.880219 0.153865 LBFGS: 4 21:59:45 -339406.991288 0.198507 LBFGS: 5 21:59:54 -339407.049048 0.124665 LBFGS: 6 22:00:03 -339407.082652 0.091563 LBFGS: 7 22:00:12 -339407.111647 0.089651 LBFGS: 8 22:00:20 -339407.134780 0.103748 LBFGS: 9 22:00:28 -339407.146605 0.053413 LBFGS: 10 22:00:35 -339407.152026 0.041127 LBFGS: 11 22:00:44 -339407.157134 0.047082 LBFGS: 12 22:00:52 -339407.165000 0.061017 LBFGS: 13 22:01:00 -339407.173030 0.058819 LBFGS: 14 22:01:08 -339407.178702 0.048412 LBFGS: 15 22:01:16 -339407.182974 0.044544 LBFGS: 16 22:01:24 -339407.187279 0.042113 LBFGS: 17 22:01:31 -339407.192034 0.050348 LBFGS: 18 22:01:39 -339407.196564 0.054562 LBFGS: 19 22:01:47 -339407.200400 0.037360 LBFGS: 20 22:01:55 -339407.203890 0.043116 LBFGS: 21 22:02:03 -339407.207259 0.040634 LBFGS: 22 22:02:10 -339407.210532 0.055370 LBFGS: 23 22:02:18 -339407.214076 0.052662 LBFGS: 24 22:02:25 -339407.218072 0.043593 LBFGS: 25 22:02:33 -339407.222323 0.042393 LBFGS: 26 22:02:41 -339407.226065 0.042956 LBFGS: 27 22:02:48 -339407.228942 0.046996 LBFGS: 28 22:02:56 -339407.231419 0.033611 LBFGS: 29 22:03:03 -339407.233977 0.035387 LBFGS: 30 22:03:11 -339407.236369 0.035177 LBFGS: 31 22:03:18 -339407.238213 0.035607 LBFGS: 32 22:03:26 -339407.239392 0.025449 LBFGS: 33 22:03:33 -339407.240170 0.018326 LBFGS: 34 22:03:41 -339407.240779 0.017195 LBFGS: 35 22:03:48 -339407.241530 0.023315 LBFGS: 36 22:03:56 -339407.242600 0.028218 LBFGS: 37 22:04:04 -339407.244033 0.033985 LBFGS: 38 22:04:12 -339407.245545 0.032207 LBFGS: 39 22:04:19 -339407.246716 0.027472 LBFGS: 40 22:04:26 -339407.247599 0.019719 LBFGS: 41 22:04:34 -339407.248339 0.019175 LBFGS: 42 22:04:42 -339407.249093 0.023232 LBFGS: 43 22:04:49 -339407.249827 0.021624 LBFGS: 44 22:04:57 -339407.250537 0.019153 LBFGS: 45 22:05:05 -339407.251307 0.019740 LBFGS: 46 22:05:12 -339407.252135 0.019317 LBFGS: 47 22:05:20 -339407.252989 0.023660 LBFGS: 48 22:05:27 -339407.253901 0.022299 LBFGS: 49 22:05:34 -339407.254910 0.021126 LBFGS: 50 22:05:42 -339407.255856 0.019253 LBFGS: 51 22:05:49 -339407.256703 0.021767 LBFGS: 52 22:05:56 -339407.257470 0.024547 LBFGS: 53 22:06:04 -339407.258189 0.022156 LBFGS: 54 22:06:12 -339407.259001 0.019600 LBFGS: 55 22:06:19 -339407.259831 0.021138 LBFGS: 56 22:06:27 -339407.260707 0.021346 LBFGS: 57 22:06:34 -339407.261511 0.021489 LBFGS: 58 22:06:41 -339407.262276 0.018410 LBFGS: 59 22:06:49 -339407.262911 0.016828 LBFGS: 60 22:06:56 -339407.263524 0.018699 LBFGS: 61 22:07:04 -339407.264063 0.018004 LBFGS: 62 22:07:11 -339407.264603 0.017004 LBFGS: 63 22:07:18 -339407.265076 0.013012 LBFGS: 64 22:07:25 -339407.265496 0.015004 LBFGS: 65 22:07:33 -339407.265956 0.015633 LBFGS: 66 22:07:40 -339407.266490 0.017525 LBFGS: 67 22:07:48 -339407.267079 0.015675 LBFGS: 68 22:07:55 -339407.267548 0.014815 LBFGS: 69 22:08:02 -339407.267909 0.011945 LBFGS: 70 22:08:10 -339407.268218 0.012558 LBFGS: 71 22:08:17 -339407.268542 0.013277 LBFGS: 72 22:08:25 -339407.268830 0.013706 LBFGS: 73 22:08:32 -339407.269107 0.010976 LBFGS: 74 22:08:39 -339407.269421 0.011852 LBFGS: 75 22:08:47 -339407.269736 0.011884 LBFGS: 76 22:08:55 -339407.270108 0.013779 LBFGS: 77 22:09:02 -339407.270476 0.014715 LBFGS: 78 22:09:10 -339407.270867 0.013091 LBFGS: 79 22:09:17 -339407.271252 0.012240 LBFGS: 80 22:09:24 -339407.271605 0.011768 LBFGS: 81 22:09:32 -339407.271958 0.015107 LBFGS: 82 22:09:39 -339407.272347 0.017287 LBFGS: 83 22:09:46 -339407.272790 0.013543 LBFGS: 84 22:09:54 -339407.273167 0.014202 LBFGS: 85 22:10:02 -339407.273520 0.013338 LBFGS: 86 22:10:09 -339407.273881 0.016005 LBFGS: 87 22:10:17 -339407.274253 0.012334 LBFGS: 88 22:10:24 -339407.274586 0.012588 LBFGS: 89 22:10:31 -339407.274907 0.012385 LBFGS: 90 22:10:39 -339407.275229 0.012112 LBFGS: 91 22:10:46 -339407.275517 0.011343 LBFGS: 92 22:10:54 -339407.275777 0.012980 LBFGS: 93 22:11:01 -339407.276038 0.013634 LBFGS: 94 22:11:09 -339407.276229 0.012319 LBFGS: 95 22:11:16 -339407.276498 0.013063 LBFGS: 96 22:11:23 -339407.276749 0.010231 LBFGS: 97 22:11:30 -339407.276969 0.012101 LBFGS: 98 22:11:39 -339407.277249 0.013397 LBFGS: 99 22:11:46 -339407.277512 0.016035 LBFGS: 100 22:11:54 -339407.277804 0.016431 LBFGS: 101 22:12:01 -339407.278071 0.011722 LBFGS: 102 22:12:08 -339407.278346 0.011278 LBFGS: 103 22:12:16 -339407.278617 0.010127 LBFGS: 104 22:12:23 -339407.278899 0.010872 LBFGS: 105 22:12:30 -339407.279181 0.012030 LBFGS: 106 22:12:38 -339407.279513 0.012405 LBFGS: 107 22:12:45 -339407.279860 0.012407 LBFGS: 108 22:12:52 -339407.280188 0.012253 LBFGS: 109 22:13:00 -339407.280514 0.011763 LBFGS: 110 22:13:07 -339407.280766 0.012042 LBFGS: 111 22:13:15 -339407.280989 0.011958 LBFGS: 112 22:13:22 -339407.281224 0.010293 LBFGS: 113 22:13:30 -339407.281445 0.009090 Final energy [eV]: -339407.2814451635 ``` ```:UMA + ASEによる構造最適化（GPU利用） Potential energy [eV]: -339406.5104452553 Step Time Energy fmax LBFGS: 0 22:23:58 -339406.510445 0.688165 LBFGS: 1 22:23:58 -339406.687804 0.306347 LBFGS: 2 22:23:58 -339406.782515 0.171488 LBFGS: 3 22:23:59 -339406.873963 0.154230 LBFGS: 4 22:23:59 -339406.986006 0.205795 LBFGS: 5 22:23:59 -339407.043885 0.126727 LBFGS: 6 22:24:00 -339407.077698 0.091715 LBFGS: 7 22:24:00 -339407.106888 0.086739 LBFGS: 8 22:24:00 -339407.129029 0.103512 LBFGS: 9 22:24:01 -339407.141133 0.057198 LBFGS: 10 22:24:01 -339407.146111 0.041968 LBFGS: 11 22:24:01 -339407.151719 0.048488 LBFGS: 12 22:24:01 -339407.158019 0.064346 LBFGS: 13 22:24:02 -339407.167479 0.059431 LBFGS: 14 22:24:02 -339407.174273 0.048195 LBFGS: 15 22:24:02 -339407.175967 0.044841 LBFGS: 16 22:24:03 -339407.181502 0.042088 LBFGS: 17 22:24:03 -339407.186452 0.051250 LBFGS: 18 22:24:03 -339407.190528 0.056719 LBFGS: 19 22:24:03 -339407.194367 0.043337 LBFGS: 20 22:24:04 -339407.197211 0.045731 LBFGS: 21 22:24:04 -339407.201306 0.040726 LBFGS: 22 22:24:04 -339407.204819 0.057235 LBFGS: 23 22:24:05 -339407.209677 0.055408 LBFGS: 24 22:24:05 -339407.212104 0.043405 LBFGS: 25 22:24:05 -339407.217166 0.043245 LBFGS: 26 22:24:05 -339407.219100 0.045840 LBFGS: 27 22:24:06 -339407.222968 0.050065 LBFGS: 28 22:24:06 -339407.225541 0.035695 LBFGS: 29 22:24:06 -339407.228076 0.036800 LBFGS: 30 22:24:07 -339407.230391 0.034591 LBFGS: 31 22:24:07 -339407.232737 0.039775 LBFGS: 32 22:24:07 -339407.234326 0.028915 LBFGS: 33 22:24:08 -339407.234723 0.019379 LBFGS: 34 22:24:08 -339407.236058 0.016893 LBFGS: 35 22:24:08 -339407.235596 0.022424 LBFGS: 36 22:24:08 -339407.236556 0.029385 LBFGS: 37 22:24:09 -339407.236319 0.031724 LBFGS: 38 22:24:09 -339407.238604 0.036267 LBFGS: 39 22:24:09 -339407.241492 0.030933 LBFGS: 40 22:24:10 -339407.243088 0.024990 LBFGS: 41 22:24:10 -339407.241673 0.021239 LBFGS: 42 22:24:10 -339407.243508 0.024044 LBFGS: 43 22:24:10 -339407.244801 0.023782 LBFGS: 44 22:24:11 -339407.244115 0.019349 LBFGS: 45 22:24:11 -339407.245272 0.019654 LBFGS: 46 22:24:11 -339407.246760 0.020273 LBFGS: 47 22:24:12 -339407.248179 0.022038 LBFGS: 48 22:24:12 -339407.249184 0.022475 LBFGS: 49 22:24:12 -339407.250020 0.024658 LBFGS: 50 22:24:12 -339407.249776 0.021438 LBFGS: 51 22:24:13 -339407.251208 0.020396 LBFGS: 52 22:24:13 -339407.250525 0.020762 LBFGS: 53 22:24:13 -339407.252427 0.024058 LBFGS: 54 22:24:13 -339407.254323 0.021192 LBFGS: 55 22:24:14 -339407.254910 0.023464 LBFGS: 56 22:24:14 -339407.255217 0.022326 LBFGS: 57 22:24:14 -339407.255915 0.024062 LBFGS: 58 22:24:15 -339407.257775 0.018146 LBFGS: 59 22:24:15 -339407.258443 0.022077 LBFGS: 60 22:24:15 -339407.257647 0.019816 LBFGS: 61 22:24:16 -339407.259061 0.017725 LBFGS: 62 22:24:16 -339407.259020 0.018317 LBFGS: 63 22:24:16 -339407.260123 0.013440 LBFGS: 64 22:24:16 -339407.260138 0.014982 LBFGS: 65 22:24:17 -339407.261515 0.015489 LBFGS: 66 22:24:17 -339407.260171 0.016693 LBFGS: 67 22:24:17 -339407.262683 0.019473 LBFGS: 68 22:24:18 -339407.261075 0.016896 LBFGS: 69 22:24:18 -339407.262692 0.016815 LBFGS: 70 22:24:18 -339407.262461 0.012457 LBFGS: 71 22:24:18 -339407.262646 0.013922 LBFGS: 72 22:24:19 -339407.263404 0.014055 LBFGS: 73 22:24:19 -339407.264483 0.013205 LBFGS: 74 22:24:19 -339407.263768 0.013211 LBFGS: 75 22:24:19 -339407.264012 0.013624 LBFGS: 76 22:24:20 -339407.263705 0.013554 LBFGS: 77 22:24:20 -339407.264598 0.016125 LBFGS: 78 22:24:20 -339407.265214 0.016489 LBFGS: 79 22:24:21 -339407.266028 0.013640 LBFGS: 80 22:24:21 -339407.265532 0.015061 LBFGS: 81 22:24:21 -339407.266503 0.012710 LBFGS: 82 22:24:22 -339407.266219 0.013592 LBFGS: 83 22:24:22 -339407.268246 0.014463 LBFGS: 84 22:24:22 -339407.267573 0.015033 LBFGS: 85 22:24:22 -339407.267987 0.015421 LBFGS: 86 22:24:23 -339407.267733 0.014389 LBFGS: 87 22:24:23 -339407.268376 0.015151 LBFGS: 88 22:24:23 -339407.268389 0.017257 LBFGS: 89 22:24:24 -339407.269608 0.015159 LBFGS: 90 22:24:24 -339407.269423 0.013760 LBFGS: 91 22:24:24 -339407.270871 0.012214 LBFGS: 92 22:24:24 -339407.269667 0.012451 LBFGS: 93 22:24:25 -339407.270392 0.012865 LBFGS: 94 22:24:25 -339407.271500 0.013253 LBFGS: 95 22:24:25 -339407.270545 0.011503 LBFGS: 96 22:24:26 -339407.271372 0.012333 LBFGS: 97 22:24:26 -339407.271975 0.012782 LBFGS: 98 22:24:26 -339407.271441 0.014463 LBFGS: 99 22:24:26 -339407.272587 0.010633 LBFGS: 100 22:24:27 -339407.272103 0.013269 LBFGS: 101 22:24:27 -339407.271304 0.012146 LBFGS: 102 22:24:27 -339407.273137 0.015132 LBFGS: 103 22:24:28 -339407.272751 0.011818 LBFGS: 104 22:24:28 -339407.272235 0.011239 LBFGS: 105 22:24:28 -339407.272803 0.011866 LBFGS: 106 22:24:28 -339407.273204 0.013803 LBFGS: 107 22:24:29 -339407.273921 0.012429 LBFGS: 108 22:24:29 -339407.273215 0.014053 LBFGS: 109 22:24:29 -339407.274150 0.014119 LBFGS: 110 22:24:30 -339407.275843 0.015322 LBFGS: 111 22:24:30 -339407.275099 0.011096 LBFGS: 112 22:24:30 -339407.275010 0.013901 LBFGS: 113 22:24:30 -339407.275593 0.012098 LBFGS: 114 22:24:31 -339407.275387 0.012459 LBFGS: 115 22:24:31 -339407.275551 0.009838 Potential energy [eV]: -339407.27555145643 ```
> 初期構造および最適化後の構造は末尾に示した。 ### 鎖を4つに増やした場合 鎖を4つに増やした712原子からなる分子の構造を作成し、UMAで計算を実施してみた。 `fmax=0.03` の条件で最適化し、ともにステップ数は277であった。計算時間はCPU計算では46分31秒、GPU計算では1分41秒であり、やはり**GPU計算の方がCPU計算に比べて27.6倍も速い**という結果となった。 このように、GPUを用いた推論は非常に効率的に実行できることが確かめられた。
【構造最適化のログ】 ```:CPU Step Time Energy fmax LBFGS: 0 00:16:36 -452517.670587 19.832589 LBFGS: 1 00:16:45 -452526.823473 6.148534 LBFGS: 2 00:16:56 -452531.527803 3.344507 LBFGS: 3 00:17:06 -452534.515541 2.806852 LBFGS: 4 00:17:16 -452535.524068 1.919322 LBFGS: 5 00:17:26 -452536.280475 1.448389 LBFGS: 6 00:17:36 -452537.048811 1.584875 LBFGS: 7 00:17:46 -452537.576137 0.977498 LBFGS: 8 00:17:56 -452538.005020 0.830794 LBFGS: 9 00:18:05 -452538.315837 0.881901 LBFGS: 10 00:18:16 -452538.544124 0.725888 LBFGS: 11 00:18:26 -452538.777790 0.592174 LBFGS: 12 00:18:35 -452539.057182 0.666215 LBFGS: 13 00:18:45 -452539.317073 0.725424 LBFGS: 14 00:18:56 -452539.533218 0.584175 LBFGS: 15 00:19:06 -452539.698310 0.427466 LBFGS: 16 00:19:16 -452539.843101 0.441206 LBFGS: 17 00:19:26 -452539.991622 0.484938 LBFGS: 18 00:19:35 -452540.124977 0.457695 LBFGS: 19 00:19:45 -452540.228435 0.440532 LBFGS: 20 00:19:55 -452540.322917 0.385982 LBFGS: 21 00:20:05 -452540.424762 0.369278 LBFGS: 22 00:20:15 -452540.519592 0.354950 LBFGS: 23 00:20:24 -452540.599777 0.363211 LBFGS: 24 00:20:34 -452540.675647 0.392975 LBFGS: 25 00:20:44 -452540.750694 0.316479 LBFGS: 26 00:20:54 -452540.818317 0.277217 LBFGS: 27 00:21:04 -452540.873436 0.270808 LBFGS: 28 00:21:14 -452540.919735 0.309145 LBFGS: 29 00:21:24 -452540.963905 0.261848 LBFGS: 30 00:21:34 -452541.007381 0.237177 LBFGS: 31 00:21:44 -452541.046463 0.240482 LBFGS: 32 00:21:54 -452541.081203 0.300639 LBFGS: 33 00:22:03 -452541.116405 0.329135 LBFGS: 34 00:22:13 -452541.153038 0.238708 LBFGS: 35 00:22:23 -452541.186546 0.189677 LBFGS: 36 00:22:33 -452541.213970 0.205752 LBFGS: 37 00:22:43 -452541.237628 0.245055 LBFGS: 38 00:22:52 -452541.260616 0.221470 LBFGS: 39 00:23:02 -452541.284271 0.205127 LBFGS: 40 00:23:12 -452541.308746 0.238424 LBFGS: 41 00:23:22 -452541.333309 0.241223 LBFGS: 42 00:23:31 -452541.355842 0.196037 LBFGS: 43 00:23:41 -452541.375576 0.189685 LBFGS: 44 00:23:51 -452541.393936 0.182980 LBFGS: 45 00:24:01 -452541.412723 0.164168 LBFGS: 46 00:24:10 -452541.431461 0.187248 LBFGS: 47 00:24:20 -452541.448093 0.147530 LBFGS: 48 00:24:30 -452541.462635 0.149575 LBFGS: 49 00:24:40 -452541.477561 0.184443 LBFGS: 50 00:24:49 -452541.494602 0.194989 LBFGS: 51 00:25:00 -452541.513050 0.163941 LBFGS: 52 00:25:10 -452541.530635 0.143923 LBFGS: 53 00:25:19 -452541.546871 0.135242 LBFGS: 54 00:25:30 -452541.562885 0.132078 LBFGS: 55 00:25:39 -452541.579059 0.130837 LBFGS: 56 00:25:49 -452541.594604 0.154202 LBFGS: 57 00:25:59 -452541.609142 0.157427 LBFGS: 58 00:26:09 -452541.622722 0.114197 LBFGS: 59 00:26:19 -452541.635234 0.119652 LBFGS: 60 00:26:29 -452541.646995 0.135608 LBFGS: 61 00:26:39 -452541.659282 0.138939 LBFGS: 62 00:26:48 -452541.673282 0.119931 LBFGS: 63 00:26:58 -452541.688682 0.140983 LBFGS: 64 00:27:08 -452541.704036 0.155425 LBFGS: 65 00:27:18 -452541.718200 0.132592 LBFGS: 66 00:27:28 -452541.731254 0.123756 LBFGS: 67 00:27:38 -452541.743206 0.114921 LBFGS: 68 00:27:48 -452541.754135 0.105099 LBFGS: 69 00:27:58 -452541.764270 0.115186 LBFGS: 70 00:28:08 -452541.774578 0.113940 LBFGS: 71 00:28:18 -452541.785411 0.100799 LBFGS: 72 00:28:28 -452541.796459 0.106843 LBFGS: 73 00:28:38 -452541.807544 0.143837 LBFGS: 74 00:28:47 -452541.819339 0.150170 LBFGS: 75 00:28:58 -452541.831890 0.137828 LBFGS: 76 00:29:08 -452541.843582 0.136239 LBFGS: 77 00:29:18 -452541.853313 0.116795 LBFGS: 78 00:29:28 -452541.861465 0.108734 LBFGS: 79 00:29:38 -452541.869220 0.127895 LBFGS: 80 00:29:48 -452541.877162 0.108470 LBFGS: 81 00:29:58 -452541.885021 0.102556 LBFGS: 82 00:30:08 -452541.893096 0.119137 LBFGS: 83 00:30:18 -452541.902118 0.120276 LBFGS: 84 00:30:28 -452541.911987 0.141155 LBFGS: 85 00:30:38 -452541.922035 0.122146 LBFGS: 86 00:30:48 -452541.931610 0.107093 LBFGS: 87 00:30:58 -452541.940502 0.089158 LBFGS: 88 00:31:08 -452541.948211 0.080127 LBFGS: 89 00:31:19 -452541.954521 0.101410 LBFGS: 90 00:31:28 -452541.960136 0.107408 LBFGS: 91 00:31:38 -452541.966259 0.086044 LBFGS: 92 00:31:48 -452541.973587 0.082826 LBFGS: 93 00:31:58 -452541.981208 0.075650 LBFGS: 94 00:32:08 -452541.988243 0.085716 LBFGS: 95 00:32:18 -452541.995483 0.100712 LBFGS: 96 00:32:28 -452542.003578 0.076941 LBFGS: 97 00:32:38 -452542.012115 0.085065 LBFGS: 98 00:32:48 -452542.019847 0.081656 LBFGS: 99 00:32:58 -452542.026725 0.077103 LBFGS: 100 00:33:08 -452542.033355 0.076268 LBFGS: 101 00:33:18 -452542.040180 0.082869 LBFGS: 102 00:33:28 -452542.047439 0.090820 LBFGS: 103 00:33:38 -452542.054874 0.095669 LBFGS: 104 00:33:47 -452542.062461 0.080130 LBFGS: 105 00:33:58 -452542.069530 0.078232 LBFGS: 106 00:34:08 -452542.075981 0.072745 LBFGS: 107 00:34:18 -452542.082195 0.077412 LBFGS: 108 00:34:28 -452542.088531 0.079724 LBFGS: 109 00:34:38 -452542.094741 0.080679 LBFGS: 110 00:34:48 -452542.100479 0.075229 LBFGS: 111 00:34:58 -452542.105987 0.078268 LBFGS: 112 00:35:09 -452542.112083 0.085668 LBFGS: 113 00:35:18 -452542.118980 0.074021 LBFGS: 114 00:35:29 -452542.126049 0.087731 LBFGS: 115 00:35:39 -452542.132667 0.080974 LBFGS: 116 00:35:48 -452542.138801 0.090207 LBFGS: 117 00:35:58 -452542.144947 0.090894 LBFGS: 118 00:36:09 -452542.151340 0.076310 LBFGS: 119 00:36:19 -452542.157894 0.079114 LBFGS: 120 00:36:29 -452542.164596 0.076202 LBFGS: 121 00:36:39 -452542.171737 0.080358 LBFGS: 122 00:36:49 -452542.179222 0.085716 LBFGS: 123 00:36:59 -452542.186882 0.086452 LBFGS: 124 00:37:10 -452542.194946 0.086216 LBFGS: 125 00:37:20 -452542.203357 0.076786 LBFGS: 126 00:37:30 -452542.211578 0.074003 LBFGS: 127 00:37:40 -452542.218921 0.078908 LBFGS: 128 00:37:50 -452542.225437 0.079414 LBFGS: 129 00:38:01 -452542.231670 0.069495 LBFGS: 130 00:38:11 -452542.237823 0.073274 LBFGS: 131 00:38:21 -452542.243724 0.087928 LBFGS: 132 00:38:31 -452542.249240 0.076851 LBFGS: 133 00:38:41 -452542.254428 0.062756 LBFGS: 134 00:38:51 -452542.259380 0.068527 LBFGS: 135 00:39:01 -452542.264308 0.064910 LBFGS: 136 00:39:11 -452542.269626 0.068294 LBFGS: 137 00:39:21 -452542.275447 0.067964 LBFGS: 138 00:39:31 -452542.281116 0.054962 LBFGS: 139 00:39:42 -452542.285968 0.050035 LBFGS: 140 00:39:51 -452542.290164 0.061064 LBFGS: 141 00:40:02 -452542.294311 0.061779 LBFGS: 142 00:40:13 -452542.299037 0.063933 LBFGS: 143 00:40:22 -452542.303962 0.061200 LBFGS: 144 00:40:33 -452542.308780 0.066109 LBFGS: 145 00:40:43 -452542.313484 0.059287 LBFGS: 146 00:40:53 -452542.318367 0.067145 LBFGS: 147 00:41:03 -452542.323398 0.057254 LBFGS: 148 00:41:14 -452542.328624 0.067425 LBFGS: 149 00:41:24 -452542.333747 0.067630 LBFGS: 150 00:41:34 -452542.338638 0.061637 LBFGS: 151 00:41:44 -452542.343009 0.051881 LBFGS: 152 00:41:54 -452542.347129 0.057182 LBFGS: 153 00:42:04 -452542.351577 0.064403 LBFGS: 154 00:42:15 -452542.356777 0.081655 LBFGS: 155 00:42:25 -452542.362274 0.072731 LBFGS: 156 00:42:35 -452542.367588 0.061674 LBFGS: 157 00:42:46 -452542.372432 0.057488 LBFGS: 158 00:42:55 -452542.376953 0.053599 LBFGS: 159 00:43:06 -452542.381019 0.051161 LBFGS: 160 00:43:16 -452542.384613 0.051331 LBFGS: 161 00:43:26 -452542.387943 0.056862 LBFGS: 162 00:43:36 -452542.391307 0.048766 LBFGS: 163 00:43:46 -452542.394981 0.051487 LBFGS: 164 00:43:56 -452542.398922 0.060137 LBFGS: 165 00:44:06 -452542.403205 0.053016 LBFGS: 166 00:44:16 -452542.407714 0.058799 LBFGS: 167 00:44:26 -452542.412063 0.058962 LBFGS: 168 00:44:36 -452542.415996 0.056967 LBFGS: 169 00:44:46 -452542.419578 0.058940 LBFGS: 170 00:44:57 -452542.423206 0.049743 LBFGS: 171 00:45:07 -452542.426963 0.051581 LBFGS: 172 00:45:17 -452542.430671 0.050457 LBFGS: 173 00:45:28 -452542.434242 0.053041 LBFGS: 174 00:45:38 -452542.438114 0.057695 LBFGS: 175 00:45:47 -452542.442321 0.064423 LBFGS: 176 00:45:58 -452542.446880 0.063607 LBFGS: 177 00:46:08 -452542.451450 0.062460 LBFGS: 178 00:46:18 -452542.455898 0.058714 LBFGS: 179 00:46:28 -452542.460163 0.056804 LBFGS: 180 00:46:39 -452542.464351 0.058888 LBFGS: 181 00:46:49 -452542.468601 0.065096 LBFGS: 182 00:46:59 -452542.472934 0.061331 LBFGS: 183 00:47:09 -452542.477321 0.057476 LBFGS: 184 00:47:19 -452542.481479 0.058062 LBFGS: 185 00:47:29 -452542.485363 0.053525 LBFGS: 186 00:47:40 -452542.489231 0.046643 LBFGS: 187 00:47:49 -452542.493145 0.059527 LBFGS: 188 00:48:00 -452542.497051 0.050324 LBFGS: 189 00:48:10 -452542.500698 0.056705 LBFGS: 190 00:48:20 -452542.504123 0.048418 LBFGS: 191 00:48:30 -452542.507400 0.049203 LBFGS: 192 00:48:40 -452542.510711 0.046467 LBFGS: 193 00:48:50 -452542.513992 0.054165 LBFGS: 194 00:49:00 -452542.517440 0.049246 LBFGS: 195 00:49:10 -452542.520996 0.043511 LBFGS: 196 00:49:20 -452542.524620 0.049509 LBFGS: 197 00:49:30 -452542.528194 0.051106 LBFGS: 198 00:49:41 -452542.531776 0.049614 LBFGS: 199 00:49:51 -452542.535377 0.050571 LBFGS: 200 00:50:01 -452542.539009 0.046040 LBFGS: 201 00:50:11 -452542.542442 0.047877 LBFGS: 202 00:50:21 -452542.545707 0.049266 LBFGS: 203 00:50:31 -452542.548866 0.045325 LBFGS: 204 00:50:42 -452542.552150 0.041950 LBFGS: 205 00:50:52 -452542.555713 0.052490 LBFGS: 206 00:51:02 -452542.559700 0.052144 LBFGS: 207 00:51:12 -452542.563816 0.051337 LBFGS: 208 00:51:22 -452542.567832 0.051633 LBFGS: 209 00:51:32 -452542.571514 0.051149 LBFGS: 210 00:51:42 -452542.575004 0.055183 LBFGS: 211 00:51:52 -452542.578395 0.046988 LBFGS: 212 00:52:02 -452542.581626 0.040664 LBFGS: 213 00:52:12 -452542.584495 0.045443 LBFGS: 214 00:52:22 -452542.587196 0.048652 LBFGS: 215 00:52:32 -452542.590076 0.043731 LBFGS: 216 00:52:41 -452542.593265 0.053321 LBFGS: 217 00:52:52 -452542.596462 0.051458 LBFGS: 218 00:53:02 -452542.599559 0.049813 LBFGS: 219 00:53:12 -452542.602371 0.045871 LBFGS: 220 00:53:22 -452542.605022 0.060317 LBFGS: 221 00:53:32 -452542.607406 0.044203 LBFGS: 222 00:53:42 -452542.609733 0.040335 LBFGS: 223 00:53:53 -452542.612110 0.043523 LBFGS: 224 00:54:03 -452542.614730 0.047276 LBFGS: 225 00:54:13 -452542.617488 0.052288 LBFGS: 226 00:54:24 -452542.620361 0.041030 LBFGS: 227 00:54:35 -452542.623394 0.045093 LBFGS: 228 00:54:46 -452542.626609 0.053383 LBFGS: 229 00:54:56 -452542.629875 0.050479 LBFGS: 230 00:55:08 -452542.632995 0.050971 LBFGS: 231 00:55:18 -452542.635913 0.038776 LBFGS: 232 00:55:28 -452542.638759 0.043435 LBFGS: 233 00:55:43 -452542.641571 0.043188 LBFGS: 234 00:55:54 -452542.644466 0.042447 LBFGS: 235 00:56:05 -452542.647583 0.047922 LBFGS: 236 00:56:15 -452542.651008 0.049854 LBFGS: 237 00:56:25 -452542.654514 0.050008 LBFGS: 238 00:56:36 -452542.658042 0.050431 LBFGS: 239 00:56:46 -452542.661472 0.048964 LBFGS: 240 00:56:56 -452542.664886 0.043079 LBFGS: 241 00:57:06 -452542.668094 0.043775 LBFGS: 242 00:57:17 -452542.670990 0.042485 LBFGS: 243 00:57:27 -452542.673542 0.042249 LBFGS: 244 00:57:37 -452542.675914 0.044330 LBFGS: 245 00:57:47 -452542.678298 0.036493 LBFGS: 246 00:57:57 -452542.680725 0.037617 LBFGS: 247 00:58:08 -452542.683090 0.040991 LBFGS: 248 00:58:18 -452542.685569 0.041755 LBFGS: 249 00:58:28 -452542.687915 0.050267 LBFGS: 250 00:58:38 -452542.690033 0.049097 LBFGS: 251 00:58:49 -452542.692001 0.034767 LBFGS: 252 00:58:59 -452542.694114 0.035331 LBFGS: 253 00:59:09 -452542.696426 0.036922 LBFGS: 254 00:59:20 -452542.698810 0.040763 LBFGS: 255 00:59:30 -452542.701107 0.043580 LBFGS: 256 00:59:40 -452542.703357 0.036122 LBFGS: 257 00:59:50 -452542.705791 0.037493 LBFGS: 258 01:00:01 -452542.708404 0.039870 LBFGS: 259 01:00:11 -452542.710983 0.040661 LBFGS: 260 01:00:21 -452542.713527 0.038191 LBFGS: 261 01:00:31 -452542.716064 0.039209 LBFGS: 262 01:00:42 -452542.718540 0.042267 LBFGS: 263 01:00:52 -452542.720775 0.038162 LBFGS: 264 01:01:02 -452542.722820 0.031929 LBFGS: 265 01:01:13 -452542.724803 0.032662 LBFGS: 266 01:01:23 -452542.726875 0.031645 LBFGS: 267 01:01:33 -452542.729026 0.036289 LBFGS: 268 01:01:44 -452542.731201 0.033823 LBFGS: 269 01:01:54 -452542.733364 0.037905 LBFGS: 270 01:02:04 -452542.735492 0.035952 LBFGS: 271 01:02:15 -452542.737426 0.040271 LBFGS: 272 01:02:25 -452542.739196 0.036634 LBFGS: 273 01:02:36 -452542.741001 0.032404 LBFGS: 274 01:02:46 -452542.742855 0.031843 LBFGS: 275 01:02:56 -452542.744617 0.031439 LBFGS: 276 01:03:07 -452542.746219 0.029525 ``` ```:GPU Step Time Energy fmax LBFGS: 0 01:03:26 -452517.666173 19.835621 LBFGS: 1 01:03:26 -452526.821718 6.149104 LBFGS: 2 01:03:27 -452531.525165 3.344012 LBFGS: 3 01:03:27 -452534.512863 2.808691 LBFGS: 4 01:03:27 -452535.521921 1.925726 LBFGS: 5 01:03:28 -452536.277635 1.448719 LBFGS: 6 01:03:28 -452537.046926 1.585292 LBFGS: 7 01:03:29 -452537.574291 0.980445 LBFGS: 8 01:03:29 -452538.003543 0.831254 LBFGS: 9 01:03:29 -452538.313598 0.878633 LBFGS: 10 01:03:30 -452538.543060 0.724931 LBFGS: 11 01:03:30 -452538.776767 0.592139 LBFGS: 12 01:03:30 -452539.057621 0.666980 LBFGS: 13 01:03:31 -452539.314308 0.726378 LBFGS: 14 01:03:31 -452539.532093 0.583313 LBFGS: 15 01:03:32 -452539.697155 0.427009 LBFGS: 16 01:03:32 -452539.841636 0.443812 LBFGS: 17 01:03:32 -452539.989864 0.485564 LBFGS: 18 01:03:33 -452540.124149 0.456904 LBFGS: 19 01:03:33 -452540.226924 0.439189 LBFGS: 20 01:03:33 -452540.321247 0.383025 LBFGS: 21 01:03:34 -452540.423061 0.369686 LBFGS: 22 01:03:34 -452540.517257 0.355262 LBFGS: 23 01:03:34 -452540.597934 0.361123 LBFGS: 24 01:03:35 -452540.674514 0.389857 LBFGS: 25 01:03:35 -452540.749626 0.315862 LBFGS: 26 01:03:35 -452540.816333 0.279586 LBFGS: 27 01:03:36 -452540.870513 0.273134 LBFGS: 28 01:03:36 -452540.918388 0.315816 LBFGS: 29 01:03:37 -452540.962146 0.260959 LBFGS: 30 01:03:37 -452541.006450 0.238206 LBFGS: 31 01:03:37 -452541.045028 0.238482 LBFGS: 32 01:03:38 -452541.079971 0.304746 LBFGS: 33 01:03:38 -452541.115352 0.329883 LBFGS: 34 01:03:38 -452541.150775 0.236581 LBFGS: 35 01:03:39 -452541.185646 0.192435 LBFGS: 36 01:03:39 -452541.212890 0.205813 LBFGS: 37 01:03:39 -452541.236431 0.240569 LBFGS: 38 01:03:40 -452541.260032 0.223195 LBFGS: 39 01:03:40 -452541.281776 0.201173 LBFGS: 40 01:03:40 -452541.305496 0.244016 LBFGS: 41 01:03:41 -452541.331375 0.238450 LBFGS: 42 01:03:41 -452541.354667 0.198776 LBFGS: 43 01:03:42 -452541.373947 0.192019 LBFGS: 44 01:03:42 -452541.392288 0.184455 LBFGS: 45 01:03:42 -452541.410419 0.166643 LBFGS: 46 01:03:43 -452541.428737 0.184071 LBFGS: 47 01:03:43 -452541.445999 0.146576 LBFGS: 48 01:03:43 -452541.461231 0.154644 LBFGS: 49 01:03:44 -452541.474960 0.180307 LBFGS: 50 01:03:44 -452541.493244 0.192279 LBFGS: 51 01:03:44 -452541.509853 0.160246 LBFGS: 52 01:03:45 -452541.528934 0.147486 LBFGS: 53 01:03:45 -452541.544055 0.133550 LBFGS: 54 01:03:45 -452541.562076 0.129435 LBFGS: 55 01:03:46 -452541.577190 0.135741 LBFGS: 56 01:03:46 -452541.591495 0.159299 LBFGS: 57 01:03:47 -452541.606514 0.154724 LBFGS: 58 01:03:47 -452541.620224 0.112743 LBFGS: 59 01:03:47 -452541.632278 0.124542 LBFGS: 60 01:03:48 -452541.643772 0.131535 LBFGS: 61 01:03:48 -452541.656402 0.130401 LBFGS: 62 01:03:48 -452541.671398 0.123749 LBFGS: 63 01:03:49 -452541.687000 0.146043 LBFGS: 64 01:03:49 -452541.701637 0.160180 LBFGS: 65 01:03:49 -452541.714458 0.131757 LBFGS: 66 01:03:50 -452541.729034 0.122690 LBFGS: 67 01:03:50 -452541.740642 0.118548 LBFGS: 68 01:03:50 -452541.751464 0.109612 LBFGS: 69 01:03:51 -452541.761322 0.115347 LBFGS: 70 01:03:51 -452541.771923 0.109713 LBFGS: 71 01:03:52 -452541.782314 0.096790 LBFGS: 72 01:03:52 -452541.793479 0.109098 LBFGS: 73 01:03:52 -452541.804805 0.145719 LBFGS: 74 01:03:53 -452541.817298 0.145109 LBFGS: 75 01:03:53 -452541.827159 0.132379 LBFGS: 76 01:03:53 -452541.839988 0.143841 LBFGS: 77 01:03:54 -452541.850662 0.115541 LBFGS: 78 01:03:54 -452541.857921 0.105119 LBFGS: 79 01:03:54 -452541.866725 0.127623 LBFGS: 80 01:03:55 -452541.873699 0.101685 LBFGS: 81 01:03:55 -452541.882141 0.100558 LBFGS: 82 01:03:56 -452541.891193 0.112535 LBFGS: 83 01:03:56 -452541.900180 0.119455 LBFGS: 84 01:03:56 -452541.908985 0.130289 LBFGS: 85 01:03:57 -452541.919513 0.114481 LBFGS: 86 01:03:57 -452541.927604 0.110026 LBFGS: 87 01:03:57 -452541.938167 0.090709 LBFGS: 88 01:03:58 -452541.945980 0.079520 LBFGS: 89 01:03:58 -452541.952590 0.099031 LBFGS: 90 01:03:58 -452541.958320 0.105763 LBFGS: 91 01:03:59 -452541.963073 0.076213 LBFGS: 92 01:03:59 -452541.971000 0.087027 LBFGS: 93 01:04:00 -452541.977935 0.070992 LBFGS: 94 01:04:00 -452541.984848 0.087419 LBFGS: 95 01:04:00 -452541.992469 0.093474 LBFGS: 96 01:04:01 -452541.999469 0.079980 LBFGS: 97 01:04:01 -452542.008884 0.083603 LBFGS: 98 01:04:01 -452542.016151 0.089075 LBFGS: 99 01:04:02 -452542.024108 0.072694 LBFGS: 100 01:04:02 -452542.030376 0.070931 LBFGS: 101 01:04:02 -452542.037307 0.084624 LBFGS: 102 01:04:03 -452542.044036 0.089374 LBFGS: 103 01:04:03 -452542.051116 0.089589 LBFGS: 104 01:04:04 -452542.060478 0.085496 LBFGS: 105 01:04:04 -452542.065147 0.076243 LBFGS: 106 01:04:04 -452542.072502 0.073002 LBFGS: 107 01:04:05 -452542.078556 0.074895 LBFGS: 108 01:04:05 -452542.085166 0.071647 LBFGS: 109 01:04:05 -452542.091060 0.084871 LBFGS: 110 01:04:06 -452542.097801 0.071438 LBFGS: 111 01:04:06 -452542.101516 0.072048 LBFGS: 112 01:04:06 -452542.109115 0.080040 LBFGS: 113 01:04:07 -452542.113807 0.079595 LBFGS: 114 01:04:07 -452542.121856 0.081713 LBFGS: 115 01:04:08 -452542.130531 0.083539 LBFGS: 116 01:04:08 -452542.135864 0.081665 LBFGS: 117 01:04:08 -452542.142307 0.071479 LBFGS: 118 01:04:09 -452542.148555 0.089443 LBFGS: 119 01:04:09 -452542.154941 0.080469 LBFGS: 120 01:04:09 -452542.161281 0.077507 LBFGS: 121 01:04:10 -452542.166305 0.089881 LBFGS: 122 01:04:10 -452542.176113 0.080403 LBFGS: 123 01:04:10 -452542.182136 0.082550 LBFGS: 124 01:04:11 -452542.190681 0.082713 LBFGS: 125 01:04:11 -452542.198524 0.071505 LBFGS: 126 01:04:12 -452542.207511 0.072910 LBFGS: 127 01:04:12 -452542.212810 0.090127 LBFGS: 128 01:04:12 -452542.222118 0.085164 LBFGS: 129 01:04:13 -452542.227333 0.063173 LBFGS: 130 01:04:13 -452542.234245 0.075361 LBFGS: 131 01:04:13 -452542.239654 0.074412 LBFGS: 132 01:04:14 -452542.246467 0.076754 LBFGS: 133 01:04:14 -452542.252586 0.066457 LBFGS: 134 01:04:14 -452542.255024 0.072518 LBFGS: 135 01:04:15 -452542.259605 0.063907 LBFGS: 136 01:04:15 -452542.265651 0.064034 LBFGS: 137 01:04:16 -452542.271881 0.057594 LBFGS: 138 01:04:16 -452542.278911 0.057086 LBFGS: 139 01:04:16 -452542.282428 0.052452 LBFGS: 140 01:04:17 -452542.287052 0.066540 LBFGS: 141 01:04:17 -452542.291153 0.064761 LBFGS: 142 01:04:17 -452542.295532 0.061795 LBFGS: 143 01:04:18 -452542.300190 0.060040 LBFGS: 144 01:04:18 -452542.306198 0.061956 LBFGS: 145 01:04:18 -452542.309101 0.057298 LBFGS: 146 01:04:19 -452542.315853 0.054651 LBFGS: 147 01:04:19 -452542.318187 0.066330 LBFGS: 148 01:04:20 -452542.324417 0.072125 LBFGS: 149 01:04:20 -452542.330677 0.067807 LBFGS: 150 01:04:20 -452542.335399 0.058222 LBFGS: 151 01:04:21 -452542.338764 0.048763 LBFGS: 152 01:04:21 -452542.343696 0.056170 LBFGS: 153 01:04:21 -452542.348903 0.056935 LBFGS: 154 01:04:22 -452542.353675 0.056905 LBFGS: 155 01:04:22 -452542.357196 0.066935 LBFGS: 156 01:04:23 -452542.363597 0.058076 LBFGS: 157 01:04:23 -452542.368858 0.067571 LBFGS: 158 01:04:23 -452542.372608 0.062652 LBFGS: 159 01:04:24 -452542.375305 0.062627 LBFGS: 160 01:04:24 -452542.380241 0.057626 LBFGS: 161 01:04:24 -452542.384433 0.051937 LBFGS: 162 01:04:25 -452542.389308 0.045226 LBFGS: 163 01:04:25 -452542.391861 0.056010 LBFGS: 164 01:04:25 -452542.394832 0.052111 LBFGS: 165 01:04:26 -452542.399574 0.062861 LBFGS: 166 01:04:26 -452542.404495 0.055981 LBFGS: 167 01:04:27 -452542.407520 0.056647 LBFGS: 168 01:04:27 -452542.411296 0.059152 LBFGS: 169 01:04:27 -452542.415363 0.057686 LBFGS: 170 01:04:28 -452542.420471 0.060669 LBFGS: 171 01:04:28 -452542.423080 0.067587 LBFGS: 172 01:04:28 -452542.427124 0.051422 LBFGS: 173 01:04:29 -452542.429832 0.057615 LBFGS: 174 01:04:29 -452542.433437 0.053546 LBFGS: 175 01:04:29 -452542.437995 0.067298 LBFGS: 176 01:04:30 -452542.443340 0.076403 LBFGS: 177 01:04:30 -452542.445743 0.070372 LBFGS: 178 01:04:31 -452542.450378 0.051934 LBFGS: 179 01:04:31 -452542.454639 0.056162 LBFGS: 180 01:04:31 -452542.459831 0.060028 LBFGS: 181 01:04:32 -452542.462387 0.054753 LBFGS: 182 01:04:32 -452542.467182 0.052622 LBFGS: 183 01:04:32 -452542.471206 0.058425 LBFGS: 184 01:04:33 -452542.476524 0.053126 LBFGS: 185 01:04:33 -452542.480251 0.050070 LBFGS: 186 01:04:33 -452542.484489 0.049137 LBFGS: 187 01:04:34 -452542.487567 0.055258 LBFGS: 188 01:04:34 -452542.494358 0.055857 LBFGS: 189 01:04:35 -452542.496650 0.049583 LBFGS: 190 01:04:35 -452542.501583 0.043539 LBFGS: 191 01:04:35 -452542.502376 0.050299 LBFGS: 192 01:04:36 -452542.507335 0.045368 LBFGS: 193 01:04:36 -452542.510219 0.044985 LBFGS: 194 01:04:36 -452542.513019 0.051113 LBFGS: 195 01:04:37 -452542.515445 0.053974 LBFGS: 196 01:04:37 -452542.521156 0.054239 LBFGS: 197 01:04:38 -452542.522735 0.049646 LBFGS: 198 01:04:38 -452542.526889 0.046866 LBFGS: 199 01:04:38 -452542.530361 0.047899 LBFGS: 200 01:04:39 -452542.534961 0.048942 LBFGS: 201 01:04:39 -452542.537803 0.046023 LBFGS: 202 01:04:39 -452542.542053 0.046956 LBFGS: 203 01:04:40 -452542.544067 0.040363 LBFGS: 204 01:04:40 -452542.547676 0.049377 LBFGS: 205 01:04:40 -452542.550563 0.045506 LBFGS: 206 01:04:41 -452542.554466 0.042843 LBFGS: 207 01:04:41 -452542.558357 0.049164 LBFGS: 208 01:04:42 -452542.561626 0.052845 LBFGS: 209 01:04:42 -452542.566555 0.049954 LBFGS: 210 01:04:42 -452542.570068 0.045590 LBFGS: 211 01:04:43 -452542.572769 0.042973 LBFGS: 212 01:04:43 -452542.576355 0.047200 LBFGS: 213 01:04:43 -452542.579246 0.049534 LBFGS: 214 01:04:44 -452542.581729 0.040574 LBFGS: 215 01:04:44 -452542.584892 0.041293 LBFGS: 216 01:04:45 -452542.588031 0.048310 LBFGS: 217 01:04:45 -452542.591720 0.049372 LBFGS: 218 01:04:45 -452542.594112 0.037771 LBFGS: 219 01:04:46 -452542.597129 0.047435 LBFGS: 220 01:04:46 -452542.600734 0.042661 LBFGS: 221 01:04:46 -452542.602375 0.036399 LBFGS: 222 01:04:47 -452542.606765 0.041447 LBFGS: 223 01:04:47 -452542.608009 0.035973 LBFGS: 224 01:04:47 -452542.610569 0.040590 LBFGS: 225 01:04:48 -452542.612503 0.046445 LBFGS: 226 01:04:48 -452542.615200 0.039841 LBFGS: 227 01:04:49 -452542.618316 0.041343 LBFGS: 228 01:04:49 -452542.620903 0.041987 LBFGS: 229 01:04:49 -452542.624919 0.056738 LBFGS: 230 01:04:50 -452542.627571 0.047685 LBFGS: 231 01:04:50 -452542.630363 0.042569 LBFGS: 232 01:04:50 -452542.634471 0.045577 LBFGS: 233 01:04:51 -452542.636577 0.036840 LBFGS: 234 01:04:51 -452542.640251 0.038714 LBFGS: 235 01:04:52 -452542.642742 0.047969 LBFGS: 236 01:04:52 -452542.646137 0.047584 LBFGS: 237 01:04:52 -452542.648258 0.053639 LBFGS: 238 01:04:53 -452542.651653 0.050272 LBFGS: 239 01:04:53 -452542.653846 0.044469 LBFGS: 240 01:04:53 -452542.658798 0.053356 LBFGS: 241 01:04:54 -452542.662090 0.047043 LBFGS: 242 01:04:54 -452542.664749 0.040917 LBFGS: 243 01:04:54 -452542.667694 0.042314 LBFGS: 244 01:04:55 -452542.670787 0.039968 LBFGS: 245 01:04:55 -452542.672458 0.038937 LBFGS: 246 01:04:56 -452542.677135 0.043878 LBFGS: 247 01:04:56 -452542.677185 0.047536 LBFGS: 248 01:04:56 -452542.681743 0.039857 LBFGS: 249 01:04:57 -452542.683162 0.038993 LBFGS: 250 01:04:57 -452542.686199 0.036076 LBFGS: 251 01:04:57 -452542.687290 0.034429 LBFGS: 252 01:04:58 -452542.689075 0.036826 LBFGS: 253 01:04:58 -452542.691501 0.039804 LBFGS: 254 01:04:59 -452542.693557 0.038328 LBFGS: 255 01:04:59 -452542.694980 0.041195 LBFGS: 256 01:04:59 -452542.698478 0.045980 LBFGS: 257 01:05:00 -452542.701133 0.038297 LBFGS: 258 01:05:00 -452542.702869 0.038867 LBFGS: 259 01:05:00 -452542.705162 0.040391 LBFGS: 260 01:05:01 -452542.707759 0.043106 LBFGS: 261 01:05:01 -452542.709968 0.043874 LBFGS: 262 01:05:02 -452542.713504 0.036210 LBFGS: 263 01:05:02 -452542.714847 0.040469 LBFGS: 264 01:05:02 -452542.717552 0.039176 LBFGS: 265 01:05:03 -452542.720840 0.046139 LBFGS: 266 01:05:03 -452542.722332 0.038285 LBFGS: 267 01:05:03 -452542.724475 0.034612 LBFGS: 268 01:05:04 -452542.726127 0.039285 LBFGS: 269 01:05:04 -452542.727348 0.037254 LBFGS: 270 01:05:04 -452542.731967 0.034547 LBFGS: 271 01:05:05 -452542.733402 0.034891 LBFGS: 272 01:05:05 -452542.735897 0.035649 LBFGS: 273 01:05:06 -452542.737098 0.035092 LBFGS: 274 01:05:06 -452542.737712 0.038817 LBFGS: 275 01:05:06 -452542.740348 0.030400 LBFGS: 276 01:05:07 -452542.742874 0.029249 ```
> 最適化後の構造は以下のようになった。 > > ![image.png](https://qiita-image-store.s3.ap-northeast-1.amazonaws.com/0/697094/875ba9d9-19e0-4904-9656-523174e6f25a.png) # まとめ ここまで、fairchem-coreを導入し、UMAポテンシャルを用いた計算環境を整備した。実際にUMAモデルを用いていくつかの有機分子のエネルギー計算を行い、リファレンスとしてORCAによる計算値とも比較した。また、CPU版とGPU版の推論速度を比較し、GPU版では大幅な高速化が可能であることを確認した。 本稿では簡単なテスト計算のみであったが、検証した範囲ではエネルギー精度は概ね良好であった。今後、金属元素を含む系や電荷を有する分子についても更なる検証が必要である。近くリリース予定のmiddleモデルやlargeモデルについても、より高い汎用性や精度が期待される。 今後、他のニューラルネットワークポテンシャル（NNP）との性能比較ベンチマークも報告されると考えられるため、それらの結果も参考にしつつ、大規模な反応経路探索や分子動力学（MD）シミュレーションへの応用を推奨したい。 # 【参考】whlファイルの一括ダウンロードについて `fairchem-core-2.2.0` 用の仮想環境を `activate` した後に ``` pip freeze > requirements.txt ``` を実行して得られる`requirements.txt`に各種パッケージのバージョンが書き出される。 例えば `Python3.12` 対応かつ `glibc_2_17` 対応の `linux_x86_64` 版パッケージを一括ダウンロードしたい場合、以下のコマンドを実行する。 ```:CPU版パッケージのダウンロード pip download \ --requirement requirements.txt \ --dest ./wheels \ --platform linux_x86_64 \ --platform manylinux1_x86_64 \ --platform manylinux2010_x86_64 \ --platform manylinux2014_x86_64 \ --platform manylinux_2_17_x86_64 \ --python-version 3.12 \ --abi cp312 \ --implementation cp \ --only-binary=:all: \ --index-url https://pypi.org/simple/ \ --extra-index-url https://pypi.python.org/simple/ \ --extra-index-url https://download.pytorch.org/whl/cpu ```
【requirements.txt の例】 ```:requirements.txt の例 absl-py==2.3.0 annotated-types==0.7.0 antlr4-python3-runtime==4.9.3 ase==3.25.0 ase_db_backends==0.10.0 bibtexparser==1.4.3 certifi==2025.4.26 cffi==1.17.1 charset-normalizer==3.4.2 click==8.2.1 cloudpickle==3.1.1 contourpy==1.3.2 cryptography==45.0.3 cycler==0.12.1 e3nn==0.5.6 fairchem-core==2.2.0 filelock==3.13.1 fonttools==4.58.2 fsspec==2024.6.1 gitdb==4.0.12 GitPython==3.1.44 grpcio==1.72.1 hf-xet==1.1.3 huggingface-hub==0.32.4 hydra-core==1.3.2 idna==3.10 Jinja2==3.1.4 joblib==1.5.1 kiwisolver==1.4.8 llvmlite==0.44.0 lmdb==1.6.2 Markdown==3.8 MarkupSafe==2.1.5 matplotlib==3.10.3 monty==2025.3.3 mpmath==1.3.0 mypy_extensions==1.1.0 narwhals==1.41.1 networkx==3.3 numba==0.61.2 numpy==2.2.6 nvidia-cublas-cu12==12.6.4.1 nvidia-cuda-cupti-cu12==12.6.80 nvidia-cuda-nvrtc-cu12==12.6.77 nvidia-cuda-runtime-cu12==12.6.77 nvidia-cudnn-cu12==9.5.0.50 nvidia-cufft-cu12==11.3.0.4 nvidia-curand-cu12==10.3.7.77 nvidia-cusolver-cu12==11.7.1.2 nvidia-cusparse-cu12==12.5.4.2 nvidia-cusparselt-cu12==0.6.3 nvidia-nccl-cu12==2.21.5 nvidia-nvjitlink-cu12==12.6.85 nvidia-nvtx-cu12==12.6.77 omegaconf==2.3.0 opt-einsum-fx==0.1.4 opt_einsum==3.4.0 orjson==3.10.18 packaging==25.0 palettable==3.3.3 pandas==2.3.0 pillow==11.2.1 platformdirs==4.3.8 plotly==6.1.2 protobuf==6.31.1 psutil==7.0.0 psycopg2-binary==2.9.10 pycparser==2.22 pydantic==2.11.5 pydantic_core==2.33.2 pymatgen==2025.5.28 PyMySQL==1.1.1 pyparsing==3.2.3 pyre-extensions==0.0.32 python-dateutil==2.9.0.post0 pytz==2025.2 PyYAML==6.0.2 requests==2.32.3 ruamel.yaml==0.18.13 ruamel.yaml.clib==0.2.12 scipy==1.15.3 sentry-sdk==2.29.1 setproctitle==1.3.6 setuptools==78.1.1 six==1.17.0 smmap==5.0.2 spglib==2.6.0 submitit==1.5.3 sympy==1.13.1 tabulate==0.9.0 tensorboard==2.19.0 tensorboard-data-server==0.7.2 torch==2.6.0 torchtnt==0.2.4 tqdm==4.67.1 triton==3.2.0 typing-inspect==0.9.0 typing-inspection==0.4.1 typing_extensions==4.12.2 tzdata==2025.2 uncertainties==3.2.3 urllib3==2.4.0 wandb==0.20.1 Werkzeug==3.1.3 wheel==0.45.1 ```
> ただし上記の場合はCPU版のPyTorchがインストールされる。GPU対応版をインストールする場合はrequirements.txtのtorchの行を `torch==2.6.0+cu126` に変更し、`pip download` のオプションを以下のように変更する。 > ```:GPU版パッケージのダウンロード > pip download \ > --requirement requirements.txt \ > --dest ./wheels \ > --platform manylinux2014_x86_64 \ > --platform manylinux_2_17_x86_64 \ > --python-version 3.12 \ > --abi cp312 \ > --implementation cp \ > --only-binary=:all: \ > --index-url https://download.pytorch.org/whl/cu126 \ > --extra-index-url https://pypi.org/simple/ \ > --extra-index-url https://pypi.python.org/simple/ > ``` > `index-url`をPyPIのままにしてしまうとCPU対応版のPyTorchが先に見つかってしまい、GPU対応版PyTorchがダウンロードできなくなってしまう。そのため、`index-url`にはPyTorchのURLを指定する必要がある。 > また、一部のライブラリについてはソースコード（tar.gz）を別途入手する必要がある。 ダウンロードされたパッケージは `./wheels` に置かれるので、これをtarで圧縮するなどして所望の環境に移動すればよい。このときrequirements.txtも一緒に移動すること。 展開後、仮想環境を立ち上げて以下のコマンドを実行する。 ``` pip install --find-links ./wheels --no-index -r requirements.txt ``` # 補足資料
【C4化合物の座標】 ```:butane_cis.xyz 14 Coordinates for butane_cis C -0.45626403761155 -0.21828760445967 -1.45108540706761 H -1.50096201028764 -0.45707155522402 -1.23822997955834 H 0.14705413039995 -1.07995265739171 -1.16326266612702 H -0.16836197699003 0.61260873234773 -0.80610132729148 C -0.26763646428860 0.11978677067875 -2.92585839474876 H 0.77920529088884 0.38188745993094 -3.11020481755513 H -0.47086806358281 -0.77022622874538 -3.52689137216225 C -1.15965356913750 1.26075328510539 -3.41180054618367 H -1.04039747151852 1.36926233454463 -4.49285024092344 H -2.20737358835563 0.99092613880135 -3.24437273802820 C -0.86436601226933 2.59700621428798 -2.73928242662960 H -1.47511866260798 3.39537567493964 -3.16229164344915 H -1.06604580466478 2.56351092924304 -1.66809624049792 H 0.18403578942857 2.87473326504332 -2.87148780142440 ``` ```:butane_trans.xyz 14 Coordinates for butane_trans C -0.45368627158607 -0.21206658938994 -1.46185868071740 H -1.48501846433364 -0.50449598387288 -1.25368791581930 H 0.19464144017124 -1.03011550419494 -1.14622643300330 H -0.22512838406441 0.65466967770936 -0.83820496855113 C -0.26858323784226 0.11667979844520 -2.93752836763169 H 0.77631107958275 0.38019489949569 -3.12929372936480 H -0.47430567760128 -0.77147541123958 -3.54310198233371 C -1.16421598579625 1.25757037405228 -3.40510203046878 H -2.20926773600897 0.99335821112384 -3.21543133188157 H -0.95984475454321 2.14499326858749 -2.79791363465787 C -0.97682353086737 1.58863393512854 -4.87996112392855 H -1.62649122384689 2.40558842120560 -5.19574362364901 H 0.05430707518215 1.88372123790995 -5.08510514670058 H -1.20225036262080 0.72261652795739 -5.50580196444730 ``` ```:butene_cis.xyz 12 Coordinates for butene_cis C 0.08424233599090 -0.11259801494431 -1.57653590835079 H -0.11970892018818 0.71795925199968 -0.90406227194062 H -0.43530748734101 -0.99261239441347 -1.19079697217522 H 1.15329378371080 -0.33094703962964 -1.52587359142069 C -0.32941984183713 0.16607138030855 -2.98940823131744 H -0.13949976705610 -0.63822986330852 -3.69411494178991 C -0.89338112972921 1.27115604259994 -3.46437285158492 H -1.12578119540920 1.29482945488792 -4.52500887664052 C -1.25457178858738 2.51020071568037 -2.70339800494228 H -2.32420365407744 2.71462251026826 -2.78846140608475 H -1.01008943060889 2.44293617584891 -1.64546738859095 H -0.73468049100515 3.37862339773030 -3.11412559194486 ``` ```:butene_trans.xyz 12 Coordinates for butene_trans C -0.07390236803001 -0.05999279423152 -1.57706528261144 H -0.30382497102009 0.85337987194408 -1.02808061857366 H -0.56784133497235 -0.89387412101111 -1.07328916622820 H 1.00128222302749 -0.23893064748105 -1.50609846065028 C -0.51082571793853 0.04295953077080 -3.00540570037970 H -0.32069622413641 -0.82302826084910 -3.63598147215858 C -1.10277856599522 1.10026833150590 -3.54280930822588 H -1.29249444754356 1.96634439711240 -2.91222864025164 C -1.53956817004947 1.20345765468552 -4.97117060271770 H -1.30851460045663 0.29075632596927 -5.52078254604749 H -2.61495108850415 1.38118989415075 -5.04223690575454 H -1.04647012866206 2.03828466304005 -5.47420214902689 ``` ``` 12 A distorted coordinates for butene_cis (input structure) C -0.705046643753 -0.725942808188 -1.845644084552 H -1.128368971093 -0.180600594979 -1.004785976484 H -1.436323955330 -1.472010062375 -2.164656622989 H 0.167608947308 -1.274888424020 -1.484749508450 C -0.329419841837 0.166071380309 -2.989408231317 H -0.157360970226 -0.523707990719 -3.810493998505 C -0.949323702954 1.318909071686 -3.216433110769 H -1.733487772475 1.322638180646 -3.967826352980 C -0.931794636213 3.016524533083 -2.460845653561 H -1.912284650043 3.262459260679 -2.046971490885 H -0.197777911763 3.117148429011 -1.664223026158 H -0.711596357321 3.772019931410 -3.218395313851 ```
【クライゼン転位の各構造の座標】 クライゼン転位の反応物： ```:claisen_rct.xyz 14 The RCT for claisen rearrangement of allyl vinyl ether C -0.95828687606299 0.34720368883157 -5.00897014694143 O -0.59664926419534 1.47063257779500 -4.33367651320257 C 0.79420726608380 1.78211839554579 -4.38622768963203 C 1.61830581558901 0.82299935116836 -3.58443312879385 C 2.66190069082371 0.16857571507165 -4.06877390622584 C -2.19272430907355 -0.12886017538449 -4.97965103489850 H -0.16627982868148 -0.12762706099480 -5.58111965164397 H -2.43541496171351 -1.01200850377880 -5.54997957387751 H -2.96723928054255 0.35075211652599 -4.39737378049682 H 1.13790644276250 1.80737175808989 -5.42572752783714 H 0.87012732770476 2.78984147883659 -3.97797809121587 H 1.31083816524697 0.68540799411307 -2.55249609105285 H 2.97175185676174 0.29054800942258 -5.10082480578105 H 3.24672235026993 -0.50336287898539 -3.45483681066156 ``` クライゼン転位の遷移状態： ```:claisen_ts.xyz 14 The TS for claisen rearrangement of allyl vinyl ether C -0.90543502927919 0.64442365169854 -5.14048055452429 O -0.77749357068573 1.74927919727154 -4.50447803160282 C 1.04783568251424 2.03729843169715 -4.22271601984667 C 1.42472872692340 0.85608508611517 -3.58688742407350 C 1.41158219438336 -0.31555341526835 -4.31086042949386 C -0.77803344408384 -0.58021161251713 -4.52938683241473 H -0.90956226236003 0.67938051513908 -6.23822491829570 H -0.91037071543998 -1.48309074007011 -5.11335790585425 H -0.90827797691070 -0.65913241224689 -3.45996355564752 H 1.28661717997436 2.17235789316551 -5.26964871771412 H 0.95776257991063 2.95422668580626 -3.65868759638935 H 1.36368100718599 0.80809537385713 -2.50618412767186 H 1.60559651058365 -0.29610940171860 -5.37491243869715 H 1.58655321915385 -1.26957408090830 -3.83052633150214 ``` クライゼン転位の生成物： ```:claisen_prd.xyz 14 The PRD for claisen rearrangement of allyl vinyl ether C -1.00190271613351 0.80245252216766 -5.16863498749949 O -1.99597608990912 1.38267408803826 -4.82483594612584 C 2.28376907265457 1.94393042897168 -3.98237988340149 C 1.55215105327906 0.93736787635736 -3.52969244252763 C 1.13172441180940 -0.24782817987801 -4.34709357706182 C -0.39335360351058 -0.36532422596838 -4.43817586753785 H -0.46590829119434 1.10778760547454 -6.09238803859260 H -0.65921761353629 -1.26639386427655 -5.00140227521387 H -0.85671832156865 -0.43951387816410 -3.45366482320147 H 2.64659669413719 1.96159052050692 -5.00411191921150 H 2.54740159347276 2.78162816190157 -3.35071024931197 H 1.19942163146488 0.95664274694501 -2.50155372711832 H 1.56012213518141 -0.17175184640090 -5.35018536742566 H 1.52684022747121 -1.16455710962703 -3.90285343162147 ```
【L-システインの各構造の座標】 ```:分子内水素結合なしの初期構造（UMAとORCAで共通） C 1.483978416475 -0.277455946439 -1.370709416152 C 1.372733772524 -0.297739230705 0.165895257001 C 2.263207442341 -1.420986589089 0.730265574089 N 1.814835753730 0.996593424340 0.706968648973 O 3.475522477090 -1.284581682810 0.753892623133 O 1.672122806884 -2.641450500092 1.185482786321 S 0.437470333371 1.042239143657 -2.034073875832 H 1.158913684711 -1.228406340829 -1.768011239108 H 2.511189519767 -0.099539963277 -1.655297654661 H 0.345597941179 -0.475304245392 0.450247645808 H 1.743292590594 0.983106961328 1.715286560714 H 1.231758457842 1.734519967524 0.336222608612 H 0.725446240710 -2.795087827528 1.138198165908 H 0.456231973375 1.217516021374 -3.362439398096 ``` ```:分子内水素結合ありの初期構造（UMAとORCAで共通） C 1.483978416475 -0.277455946439 -1.370709416152 C 1.372733772524 -0.297739230705 0.165895257001 C 2.263207442341 -1.420986589089 0.730265574089 N 1.814835753730 0.996593424340 0.706968648973 O 3.475522477090 -1.284581682810 0.753892623133 O 1.672122806884 -2.641450500092 1.185482786321 S 0.437470333371 1.042239143657 -2.034073875832 H 1.158913684711 -1.228406340829 -1.768011239108 H 2.511189519767 -0.099539963277 -1.655297654661 H 0.345597941179 -0.475304245392 0.450247645808 H 1.743292590594 0.983106961328 1.715286560714 H 1.231758457842 1.734519967524 0.336222608612 H 2.826683573958 1.325271126320 0.477691987405 H 0.456231973375 1.217516021374 -3.362439398096 ``` ```:分子内水素結合なし（UMA） 14 Properties=species:S:1:pos:R:3:forces:R:3 charge=0 spin=1 energy=-19645.16843530807 stress="-0.015272552147507668 -0.002861426677554846 0.000481288181617856 -0.002861426677554846 -0.013819992542266846 -0.00515572028234601 0.000481288181617856 -0.00515572028234601 -0.0011064920108765364" free_energy=-19645.16843530807 pbc="F F F" C 1.43812817 -0.55309955 -1.42055605 C 1.27357039 -0.22805762 0.06973231 C 2.10437237 -1.23713653 0.86686272 N 1.66851132 1.14245182 0.31892053 O 3.19144995 -0.99870450 1.30424945 O 1.55886055 -2.46492335 1.01882522 S 0.28341766 0.36765206 -2.46516346 H 1.24544157 -1.60845006 -1.61761437 H 2.46749981 -0.34775326 -1.71709178 H 0.21778455 -0.34138624 0.33198193 H 2.68091369 1.18592639 0.38307373 H 1.31013429 1.46304743 1.20910776 H 0.66990136 -2.48811536 0.64392866 H 0.58231537 1.56197067 -1.93432727 ``` ```:分子内水素結合なし（ORCA） 14 Coordinates from ORCA-job peptide1 E -721.946673319190 C 1.45489591067881 -0.52091115051120 -1.42670180347240 C 1.26876768504770 -0.23741111601701 0.06928495502783 C 2.09601676759815 -1.26116764437985 0.85213246578316 N 1.65007242651661 1.12845143347454 0.36173302023359 O 3.17118935640740 -1.02369400096258 1.31873286095141 O 1.56208656458764 -2.49882023892493 0.95773597610942 S 0.31019908579448 0.42250147113577 -2.46184519629235 H 1.26942664652047 -1.57129707904918 -1.65510898779856 H 2.48706745014258 -0.30314262539267 -1.70379737227661 H 0.21058402891102 -0.36617667904640 0.31463083329952 H 2.66049294717432 1.17468234540019 0.45342881021672 H 1.26709134403021 1.42589924700586 1.24984950083067 H 0.68094902198139 -2.52089734881379 0.56483307473524 H 0.60346217520218 1.60540657814326 -1.90297985063762 ``` ```:分子内水素結合あり（UMA） 14 Properties=species:S:1:pos:R:3:forces:R:3 charge=0 spin=1 energy=-19645.33663389358 stress="-0.01067496370524168 -0.015448457561433315 -0.009271287359297276 -0.015448457561433315 0.016899939626455307 -0.004302574787288904 -0.009271287359297276 -0.004302574787288904 -0.010466237552464008" free_energy=-19645.33663389358 pbc="F F F" C 1.28941693 -0.28259118 -1.35454565 C 1.30556362 -0.21261912 0.17262001 C 2.26215907 -1.31248942 0.65121289 N 1.77136418 1.09465408 0.62415607 O 3.44977061 -0.86318381 1.06304657 O 1.97587270 -2.47585450 0.61805359 S 0.05739007 0.87412395 -2.03923204 H 1.05417062 -1.29930083 -1.65769230 H 2.27297866 -0.01627243 -1.74065407 H 0.31341444 -0.47878237 0.54931095 H 1.40227837 1.32206976 1.53903701 H 1.45564137 1.81582176 -0.01538625 H 3.39744088 0.11411538 1.00043829 H 0.78607704 1.29409156 -3.07894317 ``` ```:分子内水素結合あり（ORCA） 14 Coordinates from ORCA-job peptide2 E -721.952776235772 C 1.31254524644612 -0.17877605375334 -1.39931581832065 C 1.42864134092761 -0.16886774479885 0.11928811078994 C 2.36578338716074 -1.30231086643839 0.56773900432388 N 1.86113100080863 1.10112768104590 0.70272163866465 O 3.14405555408561 -0.98715730309465 1.60299785153887 O 2.37282088529037 -2.38279204275962 0.04750988250251 S 0.08983585470727 1.07210560998428 -1.89924350339737 H 1.00115215035136 -1.16697195197186 -1.72475728734745 H 2.28327612211156 0.04456895868360 -1.84517112935419 H 0.45293604418326 -0.41812087375521 0.54606480009722 H 1.07727967666536 1.69506181510113 0.93528557936037 H 2.45304451587480 1.61710260910202 0.06141196039305 H 2.95523430088726 -0.04434081449240 1.79608148035073 H -0.00419733565901 0.69315312305738 -3.17919046139456 ```
【最適化計算に用いたAll-Benzene Multi-Macrocyclic Nanocarbonの初期構造】 https://onlinelibrary.wiley.com/doi/abs/10.1002/anie.202408016 Supporting Informationより引用した下記のxyz座標を初期構造として用いた。 ```:cpp_3_init.xyz 534 cpp_3 C 0.29582128 2.46388366 -16.01472807 C 1.01982765 3.64798201 -16.19542631 C -4.15914137 -0.37936531 0.69558360 C -4.03723689 0.63563602 -1.91669410 C -3.06620757 0.37493999 0.27691936 C -3.00271741 0.86948725 -1.01403157 C -5.04402318 -0.25431578 -1.54308045 C -5.10119939 -0.75764168 -0.26303385 C -4.53528565 -0.56738694 2.10278527 C -12.28510819 0.94696626 6.35838113 C -12.09794975 3.60000155 5.64568614 C -1.22688719 3.07676515 -12.64224207 C -2.00297389 3.99849113 -11.94422806 C -2.19408153 3.87188377 -10.58005060 C -0.89126554 1.86463241 -10.58591271 C -0.73572828 1.96892900 -11.95129955 C -1.58521233 2.83950992 -9.87517481 C 8.88292800 4.06106499 -15.81252482 C 8.16637026 2.86311713 -15.76838902 C 6.98354915 2.71936040 -16.45459476 C 6.46469967 3.75795450 -17.23453706 C 2.95919964 2.52037959 -17.25861956 C 4.30682648 2.53803024 -17.53840066 C 5.02818585 3.73589672 -17.53072443 C 4.27924530 4.91554253 -17.51178304 C 2.92445638 4.89707837 -17.25571329 C 2.25634588 3.69921988 -16.98452499 C -0.53879807 2.29638193 -14.92904099 C 10.63190180 4.41191080 -12.02050440 C 9.35100358 3.03260725 -8.84954054 C 9.96286992 3.08480074 -10.08154621 C 10.49820316 4.28049298 -10.56567081 C 10.58089992 5.35607384 -9.68365025 C 10.00745703 5.28904794 -8.43056947 C 9.28354225 4.16326142 -8.03175232 C 6.23968590 5.37121204 -6.29980798 C 7.50544854 5.38990790 -6.84135813 C 8.23245648 4.20829611 -7.01087122 C 7.72723616 3.05541241 -6.40699709 C 6.45407919 3.03494477 -5.87708217 C 5.64097135 4.16792544 -5.91851712 C 4.18188020 4.05576325 -5.81564389 C 3.41522551 4.83450165 -6.68642549 C 2.06893379 4.60275802 -6.84921548 C -0.16732946 4.56464022 -14.29743333 C -0.71357734 3.31810871 -13.99685810 C 0.68482042 4.72474234 -15.36840334 C 7.28700949 4.86998716 -17.43646681 C 8.46627116 5.02461995 -16.72977556 C -4.18567033 1.40158737 -3.16473547 C -5.44748315 1.92082513 -3.44137384 C -3.14532286 1.67308120 -4.04438333 C -3.36111204 2.44622053 -5.18341105 C -10.96999582 2.90825750 6.02419503 C -11.02530056 1.53898743 6.28443417 C -8.54449867 -0.78489022 4.82141690 C -9.74221947 -0.29122978 5.28946561 C -9.77279911 0.77977643 6.18169649 C -8.56178059 1.22943905 6.70718167 C -7.36199890 0.72993055 6.24092699 C -5.19035113 -1.71276275 2.55766916 C -4.62905843 2.96660392 -5.43152491 C -5.68278514 2.70086182 -4.56792221 C -9.68099725 4.19170637 -4.70408872 C -8.60964351 5.04279915 -4.96864916 C -7.31311569 4.56015819 -5.01237156 C -7.04721537 3.21554523 -4.76935219 C -8.12644584 2.34815614 -4.60784665 C -9.41832774 2.82509177 -4.58707855 C -15.77159379 3.18199811 2.73580195 C -15.22796725 2.75267703 3.92645291 C -14.35632964 3.56399678 4.66092403 C -14.29613681 4.91001796 4.28242049 C -14.81632075 5.33169014 3.07924331 C -15.45005936 4.43709125 2.20953684 C -14.80886963 3.79224202 -1.37373256 C -15.32336319 3.62249836 -0.10916486 C -15.45368093 4.70356824 0.76834034 C -15.26581424 5.98097782 0.22852115 C -14.73650936 6.14915226 -1.03462884 C -14.39056956 5.04740273 -1.81963830 C -12.16692449 3.91945199 -4.60304154 C -13.33503686 4.13641312 -3.90366658 C -13.39643524 5.10076682 -2.89538891 C -12.31006735 5.96749778 -2.76485630 C -11.14347678 5.75408378 -3.46764932 C -11.01889934 4.66349201 -4.32738109 C 2.16437534 2.86811393 -5.20770382 C 3.51881363 3.10273399 -5.04344726 C 0.05649688 3.22609259 -6.55123210 C 1.42926707 3.57670455 -6.15377771 C -0.98157873 2.98227806 -5.66187244 C -0.20132455 3.14294373 -7.91545075 C -1.47182569 2.86540018 -8.40158474 C -2.50565683 2.65844869 -7.50317721 C -2.26281680 2.70020871 -6.12975069 C 10.99965514 3.34002216 -12.83679172 C 10.59416471 3.28607926 -14.15400355 C 9.80812637 4.30417689 -14.69821069 C 9.65529433 5.47417871 -13.95256009 C 10.06278951 5.52814680 -12.63646444 C -13.42105999 1.65114972 6.00817884 C -13.33912986 2.96413217 5.53130230 C -4.52081199 0.55065681 2.93663737 C -5.31801505 0.59379182 4.06137315 C -5.97757259 -1.67242800 3.68925057 C -7.32975259 -0.22983393 5.22739987 C -6.14827117 -0.47864177 4.39406206 C 8.94575166 -6.49476017 3.93679505 C 9.74479668 -7.36065213 4.68856559 C 6.49343586 -0.57342532 -7.51398775 C 9.04314304 -0.40130831 -6.32681703 C 6.64140888 -0.56393420 -6.12655167 C 7.89227451 -0.47452691 -5.54374179 C 8.90283856 -0.56162570 -7.70551780 C 7.65741202 -0.63588572 -8.28542147 C 5.22758945 -0.30529101 -8.20291410 C 4.29671675 4.91199283 -14.20048558 C 3.57479820 7.54539339 -13.80298027 C 11.23239572 -5.44927088 1.19811854 C 12.53289948 -4.97075832 1.36115565 C 12.99750493 -3.91647333 0.60353682 C 10.93989900 -3.88455479 -0.61396144 C 10.46863089 -4.93085640 0.15372446 C 12.18377300 -3.31258275 -0.35317557 C 9.31564907 -3.31857706 11.26844813 C 8.24316634 -3.48998555 10.38720424 C 8.05068516 -4.67287042 9.71434116 C 8.93163785 -5.74534610 9.87158079 C 8.14936188 -7.39365291 6.62744760 C 7.94063655 -6.99481215 7.93127499 C 9.01889925 -6.71234804 8.77476597 C 10.28328468 -7.11957379 8.34188313 C 10.49527911 -7.49921617 7.03543371 C 9.44432008 -7.51569786 6.11534072 C 9.38986887 -5.97651367 2.74028753 C 10.97947803 0.56956597 11.25254603 C 11.49859021 3.52683943 9.02297263 C 11.00139819 2.79875833 10.08418521 C 11.66382626 1.65818059 10.54903733 C 12.95468327 1.43495944 10.05899806 C 13.45265763 2.16119161 9.00131486 C 12.68403975 3.15187167 8.38762783 C 14.55585750 3.45144723 5.15718905 C 14.31210973 3.54366098 6.51273275 C 13.00685256 3.52718670 7.00746496 C 11.96189492 3.60248087 6.08445182 C 12.20545687 3.51623076 4.73124589 C 13.50343725 3.34719143 4.24763329 C 13.67596649 2.82829097 2.88525236 C 14.53721924 1.74685137 2.69224985 C 14.46154358 0.97979226 1.54956286 C 11.38128150 -7.28445014 2.91258369 C 10.65372492 -6.29920192 2.24580071 C 10.93269232 -7.80952407 4.10803413 C 9.87041598 -5.64698280 10.90064461 C 10.05107803 -4.46544857 11.58931834 C 10.35215113 -0.01830925 -5.77870586 C 11.12249000 0.87591021 -6.51480308 C 10.82032748 -0.42921885 -4.53793661 C 12.03337215 0.04445708 -4.04393001 C 2.78211565 6.52909634 -13.30761101 C 3.16835776 5.19505836 -13.43149261 C 2.57089713 1.75713830 -12.09032045 C 2.55465513 2.79487779 -12.99890444 C 2.66978335 4.11623793 -12.57130816 C 2.62202879 4.36288282 -11.19952263 C 2.68926498 3.32541665 -10.29628430 C 5.03915473 -0.67690571 -9.53677237 C 12.79268501 0.93091902 -4.80362258 C 12.34424979 1.35247555 -6.05053364 C 13.81505988 4.46873951 -8.57422943 C 14.01823275 4.52544774 -7.19381862 C 13.62835558 3.48758751 -6.36880368 C 13.02989942 2.34407405 -6.89174189 C 12.96787782 2.22478946 -8.28020988 C 13.34464686 3.26265675 -9.10042522 C 8.21488212 8.59085055 -15.06617269 C 6.98207764 8.04814163 -15.35865235 C 5.89496149 8.23922129 -14.50201311 C 6.02853080 9.23147771 -13.52694241 C 7.25692519 9.78787220 -13.24715926 C 8.41037585 9.35668610 -13.91191460 C 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-14.65974738 C 4.80451227 7.26488016 -14.40388014 C 4.27148824 0.54340283 -7.64168542 C 3.32729384 1.17049938 -8.42643338 C 4.11306750 -0.03302865 -10.32573221 C 2.75765045 1.99745191 -10.72555475 C 3.31509949 0.99453703 -9.81294997 C -9.25664012 -4.70830848 4.53209635 C -10.27452884 -3.88474658 5.02286086 C 7.68866127 -2.63494287 6.52533620 C 4.90444364 -2.81316622 6.82012466 C 6.89323145 -1.48899654 6.51489195 C 5.52029883 -1.57673316 6.65241289 C 5.67926396 -3.96127134 6.67084261 C 7.04529568 -3.87376364 6.50990624 C 9.13202749 -2.60234639 6.78940406 C 14.79322268 -5.38328969 13.08337223 C 13.83703061 -3.48771988 14.83861020 C -6.39743852 -3.71490267 6.69964021 C -6.13660344 -2.43578392 7.19741434 C -4.85345441 -1.94051053 7.23760097 C -4.01466232 -4.03165750 6.44287460 C -5.30507892 -4.52391229 6.38458604 C -3.77579835 -2.70938286 6.80439849 C -12.55509774 2.15090236 0.45272281 C -12.87819397 0.98752321 -0.24876102 C -13.10134662 -0.20068077 0.41633063 C -13.01177657 -0.26362802 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11.86547625 -4.59158579 6.63347374 ```
【鎖を4つにしたCPPの初期構造】 ```:cpp_4_init.xyz 712 energy=-452517.6661734827 C -1.18551710 0.78107244 -17.81046777 C -0.33260629 1.79465097 -18.26227269 C -4.28290513 0.21556173 -0.96352382 C -4.16100065 1.23056306 -3.57580152 C -3.18997133 0.96986703 -1.38218806 C -3.12648117 1.46441429 -2.67313899 C -5.16778694 0.34061126 -3.20218787 C -5.22496315 -0.16271464 -1.92214127 C -4.65904941 0.02754010 0.44367785 C -12.40887195 1.54189330 4.69927371 C -12.22171351 4.19492859 3.98657872 C -2.19411017 2.14752881 -14.46629916 C -2.74683199 3.27716112 -13.86835072 C -2.78856747 3.39861030 -12.49101999 C -1.78412693 1.23768539 -12.27210300 C -1.78057614 1.09982092 -13.64335484 C -2.24725696 2.40838133 -11.67874117 C 7.50130371 1.03498919 -18.70765593 C 6.63743966 -0.01479500 -18.38800912 C 5.37242410 -0.07927032 -18.92297515 C 4.91147796 0.89118311 -19.81848688 C 1.29181729 0.22573631 -19.29318763 C 2.58572421 -0.01077029 -19.69884343 C 3.46051045 1.04636078 -19.96814863 C 2.88850051 2.31616435 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【鎖を4つにしたCPPの最適化構造】 ```:cpp_4_opt.xyz 712 energy=-452542.74287369323 C -1.21183817 0.87863031 -17.92043463 C -0.41965070 1.98812973 -18.22771928 C -4.72007212 0.16128873 -0.58736258 C -4.46710461 0.88197996 -3.29550381 C -3.71817389 1.03686945 -1.00379982 C -3.58969095 1.38971535 -2.34093989 C -5.39048297 -0.08146316 -2.89601564 C -5.51136514 -0.43987800 -1.56559733 C -5.12609987 0.02494082 0.83410988 C -12.59704443 1.40630994 5.23342562 C -12.27951915 4.11740401 4.90113701 C -2.48123636 1.86045633 -14.51895107 C -3.11249026 2.88826376 -13.81972734 C -3.14594541 2.88494893 -12.43089255 C -1.99793270 0.78592687 -12.40712430 C -1.98573945 0.78037406 -13.79021651 C -2.53300283 1.86364376 -11.70681191 C 7.61451718 1.89782085 -18.44969210 C 6.91493748 0.69306912 -18.47000458 C 5.65590478 0.60561966 -19.03153761 C 5.03092426 1.71555844 -19.60329506 C 1.45976220 0.65317234 -19.16181167 C 2.79425520 0.57784239 -19.51264677 C 3.54697975 1.72851912 -19.75982326 C 2.83075791 2.92284422 -19.87526836 C 1.48496450 2.99501090 -19.54907918 C 0.79873440 1.87851593 -19.07146063 C -2.01088293 0.86481795 -16.78953143 C 9.80007270 2.09194677 -14.84231473 C 8.77574509 0.82807310 -11.51479634 C 9.28408005 0.81040377 -12.80332881 C 9.84219208 1.95632328 -13.36512037 C 10.08311656 3.04175463 -12.52277700 C 9.59802586 3.04919293 -11.22646037 C 8.82733248 1.98675397 -10.74304527 C 5.96178477 3.55650014 -8.94878723 C 7.20180583 3.41865189 -9.54357396 C 7.80721298 2.16750538 -9.67699160 C 7.20299683 1.09036883 -9.02670701 C 5.95015035 1.22746867 -8.44885988 C 5.26615081 2.44159195 -8.48332965 C 3.79607882 2.49705307 -8.28353825 C 3.05432248 3.33214927 -9.12108463 C 1.67538296 3.27416993 -9.15053721 C -1.43713087 3.13947891 -16.35938802 C -2.06424512 1.97034031 -15.93974969 C -0.62087604 3.14538859 -17.47728175 C 5.81389471 2.86457440 -19.75033151 C 7.07776055 2.95443050 -19.18492413 C -4.60297797 1.49394755 -4.64492936 C -5.83114947 2.08460160 -4.91727791 C -3.60849712 1.54485182 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