Datta Sambhu N, Pal Arun K
Department of Chemistry, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India.
School of Chemical Science, Indian Association for the Cultivation of Science, Jadavpur, Kolkata 700032, India.
J Phys Chem A. 2022 Apr 21;126(15):2309-2318. doi: 10.1021/acs.jpca.1c10251. Epub 2022 Apr 8.
This work takes a new look at the spin alternation rule in unrestricted self-consistent-field (USCF) calculations in terms of structural characteristics such as periodicity, impurity location, and Coulomb exchange. For clarity, the systems considered are biradicals produced from linear conjugated hydrocarbons. Both site-parametrized Hamiltonian models for theoretical analysis and spin unrestricted density functional theory (DFT) calculations are used. Theoretical analysis leads to the following conclusions: (1) The diradical state is an excited state of a linear chain of conjugated carbon atoms (when is about ≤ 10). Spin alternation is a consequence of the (truncated) periodic symmetry combined with filling each closed-shell pi orbital with two electrons and each singly occupied molecular orbital (SOMO) with one electron. Spin polarization is evident in triplet () and broken symmetry () solutions for an odd and only in the solution for an even . Spin alternation is visible in the for an odd and always remains muted in the calculated . (2) For a doped chain with two radical centers, spin alternation is generally visible in the for an odd . The sign of spin population on the radical centers in the indicates the stable spin. For radical centers separated by an odd (even) number of p electrons, spin alternation favors () state with FM (AFM) interaction. Spin oscillation remains less transparent for an even without exchange. (3) In an unrestricted treatment with exchange, spin alternation becomes observable. Without SCF iterations, the more stable state can be identified from a clear spin oscillation in the . An irregular oscillation indicates a possible singlet ground state. These observations are supported by density functional calculations using the B3LYP functional and the 6-311+g(d,p) basis set on linear decapentaene diradicals with nitronyl nitroxide moieties substituted on two sets of conjugated atoms, (3,9) and (3,10). Because of the SCF procedure, one finds spin alternation in the () solution and erratic oscillation in the () solution of the 3,9 (3,10) diradical in respective equilibrium geometries. The ground state is (). DFT adiabatic coupling constants, SOMO energies, spin population plots, and SOMO lobe diagrams compare well with molecular electronic characteristics from theoretical analysis using Hamiltonian parameters.
这项工作从诸如周期性、杂质位置和库仑交换等结构特征的角度，对无限制自洽场（USCF）计算中的自旋交替规则进行了新的审视。为清晰起见，所考虑的体系是由线性共轭烃产生的双自由基。使用了用于理论分析的位点参数化哈密顿模型和自旋无限制密度泛函理论（DFT）计算。理论分析得出以下结论：（1）双自由基态是共轭碳原子线性链的激发态（当 ≤ 10 左右时）。自旋交替是（截断的）周期性对称性与每个闭壳层π轨道填充两个电子以及每个单占据分子轨道（SOMO）填充一个电子相结合的结果。对于奇数 ，在三重态（）和破缺对称性（）解中自旋极化明显，而对于偶数 ，仅在 解中明显。对于奇数 ，在 中可见自旋交替，并且在计算的 中始终不明显。（2）对于具有两个自由基中心的掺杂链，对于奇数 ，自旋交替通常在 中可见。 中自由基中心上自旋布居的符号表明稳定的自旋。对于被奇数（偶数）个p电子隔开的自由基中心，自旋交替有利于具有铁磁（反铁磁）相互作用的 （）态。对于偶数 且无交换时，自旋振荡仍然不太明显。（3）在有交换的无限制处理中，自旋交替变得可观察到。在没有自洽场迭代的情况下，可以从 中清晰的自旋振荡识别出更稳定的状态。不规则振荡表明可能是单重基态。使用B3LYP泛函和6 - 311 + g(d,p)基组对在两组共轭原子（3,9）和（3,10）上取代有硝酰基氮氧化物部分的线性癸五烯双自由基进行密度泛函计算，支持了这些观察结果。由于自洽场过程，在各自平衡几何结构的3,9（3,10）双自由基的 （）解中发现自旋交替，在 （）解中发现不规则振荡。基态是 （）。DFT绝热耦合常数、SOMO能量、自旋布居图和SOMO瓣图与使用哈密顿参数的理论分析得到的分子电子特征吻合良好。
