Vargas-Hernández Rodrigo A, Jorner Kjell, Pollice Robert, Aspuru-Guzik Alán
Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada.
J Chem Phys. 2023 Mar 14;158(10):104801. doi: 10.1063/5.0137103.
Semiempirical quantum chemistry has recently seen a renaissance with applications in high-throughput virtual screening and machine learning. The simplest semiempirical model still in widespread use in chemistry is Hückel's π-electron molecular orbital theory. In this work, we implemented a Hückel program using differentiable programming with the JAX framework based on limited modifications of a pre-existing NumPy version. The auto-differentiable Hückel code enabled efficient gradient-based optimization of model parameters tuned for excitation energies and molecular polarizabilities, respectively, based on as few as 100 data points from density functional theory simulations. In particular, the facile computation of the polarizability, a second-order derivative, via auto-differentiation shows the potential of differentiable programming to bypass the need for numeric differentiation or derivation of analytical expressions. Finally, we employ gradient-based optimization of atom identity for inverse design of organic electronic materials with targeted orbital energy gaps and polarizabilities. Optimized structures are obtained after as little as 15 iterations using standard gradient-based optimization algorithms.
半经验量子化学最近在高通量虚拟筛选和机器学习中的应用迎来了复兴。化学领域仍在广泛使用的最简单的半经验模型是休克尔π电子分子轨道理论。在这项工作中，我们基于对现有NumPy版本的有限修改，使用JAX框架的可微编程实现了一个休克尔程序。这个可自动求导的休克尔代码能够分别基于密度泛函理论模拟中少至100个数据点，对针对激发能和分子极化率进行调整的模型参数进行基于梯度的高效优化。特别是，通过自动求导轻松计算作为二阶导数的极化率，显示了可微编程在绕过数值微分或解析表达式推导需求方面的潜力。最后，我们采用基于梯度的原子身份优化来进行具有目标轨道能隙和极化率的有机电子材料的逆设计。使用标准的基于梯度的优化算法，只需15次迭代就能获得优化结构。
