Department of Chemistry, School of Natural Sciences, Ulsan National Institute of Science and Technology (UNIST), Ulsan 689-798, South Korea.
Department of Chemistry and the PULSE Institute, Stanford University, Stanford, California 94305, USA and SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA.
J Chem Phys. 2017 Jul 21;147(3):034113. doi: 10.1063/1.4994542.
The state-averaged (SA) spin restricted ensemble referenced Kohn-Sham (REKS) method and its state interaction (SI) extension, SI-SA-REKS, enable one to describe correctly the shape of the ground and excited potential energy surfaces of molecules undergoing bond breaking/bond formation reactions including features such as conical intersections crucial for theoretical modeling of non-adiabatic reactions. Until recently, application of the SA-REKS and SI-SA-REKS methods to modeling the dynamics of such reactions was obstructed due to the lack of the analytical energy derivatives. In this work, the analytical derivatives of the individual SA-REKS and SI-SA-REKS energies are derived. The final analytic gradient expressions are formulated entirely in terms of traces of matrix products and are presented in the form convenient for implementation in the traditional quantum chemical codes employing basis set expansions of the molecular orbitals. The implementation and benchmarking of the derived formalism will be described in a subsequent article of this series.
状态平均（SA）自旋限制的参考 Kohn-Sham（REKS）方法及其状态相互作用（SI）扩展 SI-SA-REKS，使得人们能够正确描述经历键断裂/形成反应的分子的基态和激发势能面的形状，包括对于非绝热反应的理论建模至关重要的锥形交叉等特征。直到最近，由于缺乏分析能量导数，SA-REKS 和 SI-SA-REKS 方法在模拟此类反应动力学方面的应用受到阻碍。在这项工作中，推导出了各个 SA-REKS 和 SI-SA-REKS 能量的分析导数。最终的分析梯度表达式完全由矩阵乘积的迹表示，并以方便在传统量子化学代码中使用分子轨道基组展开的形式呈现。在本系列的后续文章中，将描述所推导形式的实现和基准测试。
