Hermann Jan, Schätzle Zeno, Noé Frank
Department of Mathematics and Computer Science, FU Berlin, Berlin, Germany.
Machine Learning Group, TU Berlin, Berlin, Germany.
Nat Chem. 2020 Oct;12(10):891-897. doi: 10.1038/s41557-020-0544-y. Epub 2020 Sep 23.
The electronic Schrödinger equation can only be solved analytically for the hydrogen atom, and the numerically exact full configuration-interaction method is exponentially expensive in the number of electrons. Quantum Monte Carlo methods are a possible way out: they scale well for large molecules, they can be parallelized and their accuracy has, as yet, been only limited by the flexibility of the wavefunction ansatz used. Here we propose PauliNet, a deep-learning wavefunction ansatz that achieves nearly exact solutions of the electronic Schrödinger equation for molecules with up to 30 electrons. PauliNet has a multireference Hartree-Fock solution built in as a baseline, incorporates the physics of valid wavefunctions and is trained using variational quantum Monte Carlo. PauliNet outperforms previous state-of-the-art variational ansatzes for atoms, diatomic molecules and a strongly correlated linear H, and matches the accuracy of highly specialized quantum chemistry methods on the transition-state energy of cyclobutadiene, while being computationally efficient.
电子薛定谔方程只能对氢原子进行解析求解，而数值精确的全组态相互作用方法在电子数量上呈指数级计算成本。量子蒙特卡罗方法是一种可能的解决方案：它们对于大分子具有良好的扩展性，可以进行并行计算，并且其精度目前仅受所用波函数假设灵活性的限制。在此，我们提出了泡利网络（PauliNet），这是一种深度学习波函数假设，对于含多达30个电子的分子能实现电子薛定谔方程的近乎精确解。泡利网络内置多参考哈特里 - 福克解作为基线，纳入了有效波函数的物理原理，并使用变分量子蒙特卡罗进行训练。泡利网络在原子、双原子分子和强关联线性氢体系上优于先前的最优变分假设，在环丁二烯过渡态能量方面与高度专业化的量子化学方法精度相当，同时计算效率高。
