Supplementary information files for Energy component analysis for electronically excited states of molecules: why the lowest excited state is not always the HOMO/LUMO transition

Supplementary files for article Energy component analysis for electronically excited states of molecules: why the lowest excited state is not always the HOMO/LUMO transitionThe ability to tune excited-state energies is crucial to many areas of molecular design. In many cases, this is done based on the energies of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). However, this viewpoint is incomplete neglecting the many-body nature of the underlying excited-state wave functions. Within this work, we highlight the importance of two crucial terms, other than orbital energies, that contribute to the excitation energies and show how to quantify them from quantum chemistry computations: a Coulomb attraction and a repulsive exchange interaction. Using this framework, we explain under which circumstances the lowest excited state of a molecule, of either singlet or triplet multiplicity, is not accessed via the HOMO/LUMO transition and show two paradigmatic examples. In the case of the push-pull molecule ACRFLCN, we highlight how the lowest triplet excited state is a locally excited state lying below the HOMO/LUMO charge transfer state due to enhanced Coulomb binding. In the case of the naphthalene molecule, we highlight how the HOMO/LUMO transition (the ¹L_a state) becomes the second excited singlet state due to its enhanced exchange repulsion term. More generally, we explain why excitation energies do not always behave like orbital energy gaps, providing insight into photophysical processes as well as methodogical challenges in describing them.

论文《分子电子激发态的能量组分分析：为何最低激发态并非总是HOMO/LUMO跃迁》的补充材料。调控激发态能级的能力是分子设计诸多领域的核心诉求。此类调控通常基于最高占据分子轨道（Highest Occupied Molecular Orbital, HOMO）与最低未占据分子轨道（Lowest Unoccupied Molecular Orbital, LUMO）的能级差开展。然而，该视角因忽略了激发态波函数的多体本质而存在局限性。本研究着重阐明了除轨道能级外，影响激发能的两项关键组分，并展示了如何通过量子化学计算对其进行量化：库仑吸引作用与排斥性交换相互作用。基于该分析框架，我们阐释了在何种条件下，分子的最低激发态（无论单重态或三重态多重度）无法通过HOMO/LUMO跃迁获得，并展示了两个典型案例：对于推拉型分子ACRFLCN，我们阐明了由于库仑结合作用增强，其最低三重激发态为局域激发态，能级低于HOMO/LUMO电荷转移态；对于萘分子，我们展示了由于交换排斥项的增强，HOMO/LUMO跃迁对应的¹L_a态成为第二激发单重态。总体而言，本研究解释了激发能为何并不总是遵循轨道能隙的变化规律，为光物理过程的理解以及相关描述方法面临的挑战提供了新的视角。