SPAᴴM(a,b): encoding the density information from guess Hamiltonian in quantum machine learning representations

Recently, we introduced a class of molecular representations for kernel-based regression methods — the spectrum of approximated Hamiltonian matrices (SPAᴴM) — that takes advantage of lightweight one-electron Hamiltonians traditionally used as an SCF initial guess. The original SPAᴴM variant is built from occupied-orbital energies (\ie, eigenvalues) and naturally contains all the information about nuclear charges, atomic positions, and symmetry requirements. Its advantages were demonstrated on datasets featuring a wide variation of charge and spin, for which traditional structure-based representations commonly fail. SPAᴴM(a,b), as introduced here, expands eigenvalue SPAᴴM into local and transferable representations. It relies upon one-electron density matrices to build fingerprints from atomic or bond density overlap contributions inspired from preceding state-of-the-art representations. The performance and efficiency of SPAᴴM(a,b) is assessed on the predictions for datasets of prototypical organic molecules (QM7) of different charges and azoheteroarene dyes in an excited state. Overall, both SPAᴴM(a) and SPAᴴM(b) outperform state-of-the-art representations on difficult prediction tasks such as the atomic properties of charged open-shell species and of π-conjugated systems.

近期，我们提出了一种适用于核回归方法的分子表示法类别——近似哈密顿矩阵谱（SPAᴴM），该表示法充分利用了轻量级单电子哈密顿量，这些哈密顿量传统上被用作自洽场计算（SCF）的初始猜测。原始的SPAᴴM版本由占据轨道能量（即，特征值）构成，并自然地包含了关于核电荷、原子位置和对称性要求的全部信息。其优势已在具有广泛电荷和自旋变化的数据库中得到验证，对于这些数据库，传统的基于结构的表示法通常失效。在本研究中引入的SPAᴴM(a,b)将特征值SPAᴴM扩展为局部和可转移的表示法。它依赖于单电子密度矩阵，通过从原子或键密度重叠贡献中构建指纹，这些贡献灵感来源于先前最先进的表示法。SPAᴴM(a,b)的性能和效率在预测典型有机分子（QM7）的数据库中得到了评估，这些分子具有不同的电荷和处于激发态的叠氮杂环染料。总体而言，SPAᴴM(a)和SPAᴴM(b)在如带电开壳物种的原子属性和π共轭系统的预测等困难的预测任务上，均优于最先进的表示法。