电子激发谱与神经网络波函数激发态的恢复
Electronic excitation spectra and recovery of excited states with neural network wave functions
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中文总结 AI 辅助
本文提出将神经网络波函数与洛伦兹积分变换结合，直接在连续坐标中计算电子激发谱，无需预设激发态，可恢复束缚激发和电离连续谱，并在氦原子上验证了激发能量与振子强度的提取。
中文摘要 AI 辅助
精确的电子谱需要同时具备对电子关联的灵活描述以及对构成响应的众多态的可处理性。我们将神经网络波函数与洛伦兹积分变换相结合，直接在连续坐标中计算电子谱，避免了固定单电子基组的截断误差，并且每一步优化的计算成本呈多项式增长。该方法不是构造一组预设的激发态，而是在选定的复能量下求解非齐次薛定谔方程。这一表述原则上能够访问与微扰耦合的整个谱，包括束缚激发和电离连续谱，而无需显式确定所有低 lying 本征态。一个有限的虚能量控制分辨率并保持响应平方可积。在孤立的束缚激发附近，当宽度趋于零时，归一化响应也能恢复相应的本征态。氦原子的应用展示了激发能量和振子强度的提取。该表述为从神经描述的电子关联到超越少数低 lying 态流形的谱提供了一条途径。
英文摘要
Accurate electronic spectra require both a flexible description of electron correlation and a tractable treatment of the many states contributing to the response. We combine neural network wave functions with the Lorentz integral transform to calculate electronic spectra directly in continuous coordinates, without truncation error from a fixed one-electron basis and with polynomial computational cost per optimization step. Instead of constructing a prescribed set of excited states, the method solves an inhomogeneous Schrödinger equation at a chosen complex energy. This formulation gives access, in principle, to the entire spectrum coupled to a perturbation, including bound excitations and the ionization continuum, without explicitly determining all lower-lying eigenstates. A finite imaginary energy controls the resolution and keeps the response square integrable. Near an isolated bound excitation, the normalized response also recovers the corresponding eigenstate as the width tends to zero. A helium application illustrates the extraction of an excitation energy and oscillator strength. The formulation provides a route from neural descriptions of electronic correlation to spectra beyond a small manifold of low-lying states.
发表机构
- ByteDance Seed（字节跳动种子）
- Department of Chemistry, The University of Hong Kong（香港大学化学系）
- College of Chemistry and Molecular Engineering, Peking University（北京大学化学与分子工程学院）
- School of Physics, Peking University（北京大学物理学院）
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