Chu Shibing, Bovi Daniele, Cappelluti Francesco, Orellana Alberto Giacomo, Martin Henry, Guidoni Leonardo
Dipartimento di Scienze Fisiche e Chimiche, Università degli studi dell'Aquila , Via Vetoio (Coppito), 67100 L'Aquila, Italy.
J Chem Theory Comput. 2017 Oct 10;13(10):4675-4683. doi: 10.1021/acs.jctc.7b00316. Epub 2017 Sep 8.
Multicenter transition metal complexes are the key moieties of many processes in chemistry, biochemistry, and materials science such as in the active sites of enzymes, molecular catalysts, and biological electron carriers. Their electronic structure, often characterized by high-spin-polarized metal sites, is a challenge for theoretical chemists because of their high degree of dynamical and static correlation. Static correlation is necessary both for the appropriate description of the metal-ligand bonding and for a correct description of the multideterminant character arising from the magnetic interactions between spin centers. Density functional theory (DFT) is usually applied using a single-determinant broken-symmetry state that is lacking the correct spin symmetry when the ground state has total low-spin character. To alleviate this drawback, we use the extended broken-symmetry (EBS) approach to derive approximate ground-state energies and, for the first time, forces for the correctly symmetric ground state of an arbitrary number of spin centers within the framework of the Heisenberg-Dirac-van Vleck Hamiltonian. Remarkably, the proposed procedure supplies relaxed geometries that are fully consistent with the calculated J-coupling constants. We apply the method to investigate the relaxed geometrical structure of the low-spin ground state of iron-sulfur clusters with two, three, and four iron centers. We observed significant differences in both geometrical parameters and coupling constant J between the symmetrized ground state, the high-spin, and the broken-symmetry optimized structures. These changes are often comparable with the differences observed by using different functionals, and the use of EBS always improves the description of the studied systems. It will be therefore important to include it in any DFT attempt to quantitatively describe multicenter transition metal complexes in the future.
多中心过渡金属配合物是化学、生物化学和材料科学中许多过程的关键部分，例如酶的活性位点、分子催化剂和生物电子载体。它们的电子结构通常以高自旋极化金属位点为特征，由于其高度的动态和静态相关性，对理论化学家来说是一个挑战。静态相关性对于适当描述金属-配体键合以及正确描述自旋中心之间磁相互作用产生的多行列式特征都是必要的。密度泛函理论（DFT）通常使用单行列式破缺对称态来应用，当基态具有总低自旋特征时，该态缺乏正确的自旋对称性。为了缓解这一缺点，我们使用扩展破缺对称（EBS）方法来推导近似基态能量，并首次在海森堡-狄拉克-范弗莱克哈密顿量框架内，为任意数量自旋中心的正确对称基态推导力。值得注意的是，所提出的程序提供了与计算出的J耦合常数完全一致的松弛几何结构。我们应用该方法研究了具有两个、三个和四个铁中心的铁硫簇低自旋基态的松弛几何结构。我们观察到对称基态、高自旋态和破缺对称优化结构在几何参数和耦合常数J方面都存在显著差异。这些变化通常与使用不同泛函观察到的差异相当，并且使用EBS总是能改善对所研究体系的描述。因此，在未来任何试图定量描述多中心过渡金属配合物的DFT尝试中纳入它都将很重要。
