Tao Yunwen, Pei Zheng, Bellonzi Nicole, Mao Yuezhi, Zou Zhu, Liang Wanzhen, Yang Zhibo, Shao Yihan
Department of Chemistry and Biochemistry, University of Oklahoma, Norman, OK 73019.
State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, P. R. China.
Int J Quantum Chem. 2020 Mar 15;120(6). doi: 10.1002/qua.26123. Epub 2019 Nov 24.
In the modeling of spin-crossing reactions, it has become popular to directly explore the spin-adiabatic surfaces. Specifically, through constructing spin-adiabatic states from a two-state Hamiltonian (with spin-orbit coupling matrix elements) at each geometry, one can readily employ advanced geometry optimization algorithms to acquire a "transition state" structure, where the spin crossing occurs. In this work, we report the implementation of a fully-variational spin-adiabatic approach based on Kohn-Sham density functional theory spin states (sharing the same set of molecular orbitals) and the Breit-Pauli one-electron spin-orbit operator. For three model spin-crossing reactions [predissociation of NO, singlet-triplet conversion in CH, and CO addition to Fe(CO)], the spin-crossing points were obtained. Our results also indicated the Breit-Pauli one-electron spin-orbit coupling can vary significantly along the reaction pathway on the spin-adiabatic energy surface. On the other hand, due to the restriction that low-spin and high-spin states share the same set of molecular orbitals, the acquired spin-adiabatic energy surface shows a cusp (i.e. a first-order discontinuity) at the crossing point, which prevents the use of standard geometry optimization algorithms to pinpoint the crossing point. An extension with this restriction removed is being developed to achieve the smoothness of spin-adiabatic surfaces.
在自旋交叉反应的建模中，直接探索自旋绝热表面已变得很流行。具体而言，通过在每个几何构型下从一个双态哈密顿量（带有自旋轨道耦合矩阵元）构建自旋绝热态，人们可以很容易地采用先进的几何优化算法来获取自旋交叉发生处的“过渡态”结构。在这项工作中，我们报告了一种基于Kohn-Sham密度泛函理论自旋态（共享同一组分子轨道）和Breit-Pauli单电子自旋轨道算符的全变分自旋绝热方法的实现。对于三个模型自旋交叉反应[NO的预解离、CH中的单重态-三重态转换以及CO加到Fe(CO)上]，我们获得了自旋交叉点。我们的结果还表明，Breit-Pauli单电子自旋轨道耦合在自旋绝热能量表面上沿反应路径可能会有显著变化。另一方面，由于低自旋态和高自旋态共享同一组分子轨道的限制，所获得的自旋绝热能量表面在交叉点处显示出一个尖点（即一阶不连续性），这使得无法使用标准的几何优化算法来精确确定交叉点。正在开发一种去除此限制的扩展方法，以实现自旋绝热表面的平滑性。
