Electronically excited states of molecules are at the heart of
photochemistry, photophysics, as well as photobiology and also play a role in
material science. Their theoretical description requires highly accurate
quantum chemical calculations, which are computationally expensive. In this
review, we focus on how machine learning is employed not only to speed up such
excited-state simulations but also how this branch of artificial intelligence
can be used to advance this exciting research field in all its aspects.
Discussed applications of machine learning for excited states include
excited-state dynamics simulations, static calculations of absorption spectra,
as well as many others. In order to put these studies into context, we discuss
the promises and pitfalls of the involved machine learning techniques. Since
the latter are mostly based on quantum chemistry calculations, we also provide
a short introduction into excited-state electronic structure methods,
approaches for nonadiabatic dynamics simulations and describe tricks and
problems when using them in machine learning for excited states of molecules.

本文综述了如何应用机器学习来加速电子激发态分子的计算，涵盖了电子激发态的动力学模拟、吸收光谱的计算等，并对机器学习技术所面临的问题和挑战，以及量子化学计算的基础进行了介绍和总结。

分子电子激发态的机器学习

Machine learning for electronically excited states of molecules

Machine learning advances chemistry and materials science by enabling
large-scale exploration of chemical space based on quantum chemical
calculations. While these models supply fast and accurate predictions of
atomistic chemical properties, they do not explicitly capture the electronic
degrees of freedom of a molecule, which limits their applicability for reactive
chemistry and chemical analysis. Here we present a deep learning framework for
the prediction of the quantum mechanical wavefunction in a local basis of
atomic orbitals from which all other ground-state properties can be derived.
This approach retains full access to the electronic structure via the
wavefunction at force field-like efficiency and captures quantum mechanics in
an analytically differentiable representation. On several examples, we
demonstrate that this opens promising avenues to perform inverse design of
molecular structures for target electronic property optimisation and a clear
path towards increased synergy of machine learning and quantum chemistry.

本文提出了一种基于深度学习的量子力学波函数预测框架，以实现分子结构的反向设计，用于优化目标电子性质，表明这种方法打开了机器学习和量子化学更协同的前景。

机器学习与量子化学的统一 - 分子波函数的深度神经网络

Unifying machine learning and quantum chemistry -- a deep neural network  for molecular wavefunctions

Last year, at least 30,000 scientific papers used the Kohn-Sham scheme of
density functional theory to solve electronic structure problems in a wide
variety of scientific fields, ranging from materials science to biochemistry to
astrophysics. Machine learning holds the promise of learning the kinetic energy
functional via examples, by-passing the need to solve the Kohn-Sham equations.
This should yield substantial savings in computer time, allowing either larger
systems or longer time-scales to be tackled, but attempts to machine-learn this
functional have been limited by the need to find its derivative. The present
work overcomes this difficulty by directly learning the density-potential and
energy-density maps for test systems and various molecules. Both improved
accuracy and lower computational cost with this method are demonstrated by
reproducing DFT energies for a range of molecular geometries generated during
molecular dynamics simulations. Moreover, the methodology could be applied
directly to quantum chemical calculations, allowing construction of density
functionals of quantum-chemical accuracy.

本文介绍一种基于机器学习的方法，通过学习电子结构问题的动能泛函，直接学习测试系统和各种分子的密度势和能量密度图，并演示了该方法通过复制分子动力学模拟期间生成的一系列分子几何体系，实现了改进的精度和较低的计算成本，同时还探讨了该方法可直接应用于量子化学计算，以构建量子化学精度的密度泛函。