密度泛函理论转化为单电子约化密度矩阵泛函理论捕获静态关联
Density Functional Theory Transformed into a One-electron Reduced Density Matrix Functional Theory for the Capture of Static Correlation
摘要：
密度泛函理论（DFT）是现代计算化学中应用最广泛的方法，但它不能准确描述强关联体系的电子结构。在这里，我们表明，DFT可以正式和实际转化为一个电子约化密度矩阵（1-RDM）泛函理论，它可以解决DFT的局限性，同时保持良好的计算缩放相比，基于波函数的方法。除了放松动能项中对1-RDM的幂等性限制外，我们还在DFT的基于密度的交换相关泛函中增加了一个基于二次1-RDM的项。我们的方法，我们实现了二次半定规划在DFT的计算缩放$O(r^{3})$，产生了实质性的改进，比传统的DFT在静态相关的化学结构和过程，如单线双自由基和键离解的描述。
英文摘要：
Density functional theory (DFT), the most widely adopted method in modern computational chemistry, fails to describe accurately the electronic structure of strongly correlated systems. Here we show that DFT can be formally and practically transformed into a one-electron reduced-density-matrix (1-RDM) functional theory, which can address the limitations of DFT while retaining favorable computational scaling compared to wavefunction-based approaches. In addition to relaxing the idempotency restriction on the 1-RDM in the kinetic energy term, we add a quadratic 1-RDM-based term to DFT's density-based exchange-correlation functional. Our approach, which we implement by quadratic semidefinite programming at DFT's computational scaling of $O(r^{3})$, yields substantial improvements over traditional DFT in the description of static correlation in chemical structures and processes such as singlet biradicals and bond dissociations.
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