Melander Marko, Jónsson Elvar Ö, Mortensen Jens J, Vegge Tejs, García Lastra Juan Maria
Department of Energy Conversion and Storage, Technical University of Denmark , DK-4000 Roskilde, Denmark.
COMP, Applied Physics Department, Aalto University FI-00076 Aalto, Espoo, Finland.
J Chem Theory Comput. 2016 Nov 8;12(11):5367-5378. doi: 10.1021/acs.jctc.6b00815. Epub 2016 Oct 27.
Combining constrained density function theory (cDFT) with Marcus theory is an efficient and promising way to address charge transfer reactions. Here, we present a general and robust implementation of cDFT within the projector augmented wave (PAW) framework. PAW pseudopotentials offer a reliable frozen-core electron description across the whole periodic table, with good transferability, as well as facilitate the extraction of all-electron quantities. The present implementation is applicable to two different wave function representations, atomic-centered basis sets (LCAO) and the finite-difference (FD) approximation utilizing real-space grids. LCAO can be used for large systems, molecular dynamics, or quick initialization, while more accurate calculations are achieved with the FD basis. Furthermore, the calculations can be performed with flexible boundary conditions, ranging from isolated molecules to periodic systems in one-, two-, or three-dimensions. As such, this implementation is relevant for a wide variety of applications. We also present how to extract the electronic coupling element and reorganization energy from the resulting diabatic cDFT-PAW wave functions for the parametrization of Marcus theory. Here, the combined method is applied to important test cases where practical implementations of DFT fail due to the self-interaction error, such as the dissociation of the helium dimer cation, and it is compared to other established cDFT codes. Moreover, for charge localization in a diamine cation, where it was recently shown that the commonly used generalized gradient and hybrid functionals of DFT failed to produce the localized state, cDFT produces qualitatively and quantitatively accurate results when benchmarked against self-interaction corrected DFT and high-level CCSD(T) calculations at a fraction of the computational cost.
将约束密度泛函理论（cDFT）与马库斯理论相结合是解决电荷转移反应的一种有效且有前景的方法。在此，我们在投影增强波（PAW）框架内给出了一种通用且稳健的cDFT实现方式。PAW赝势能够在整个周期表范围内提供可靠的冻结核心电子描述，具有良好的可转移性，并且便于提取全电子量。当前的实现方式适用于两种不同的波函数表示形式，即以原子为中心的基组（LCAO）和利用实空间网格的有限差分（FD）近似。LCAO可用于大型系统、分子动力学或快速初始化，而使用FD基组可实现更精确的计算。此外，计算可以在灵活的边界条件下进行，范围从孤立分子到一维、二维或三维的周期性系统。因此，这种实现方式适用于广泛的应用。我们还展示了如何从所得的非绝热cDFT - PAW波函数中提取电子耦合元素和重组能，用于马库斯理论的参数化。在此，该组合方法被应用于重要的测试案例，在这些案例中，由于自相互作用误差，DFT的实际实现会失败，例如氦二聚体阳离子的解离，并将其与其他已有的cDFT代码进行比较。此外，对于二胺阳离子中的电荷局域化，最近研究表明，常用的DFT广义梯度和杂化泛函无法产生局域态，而与自相互作用校正的DFT和高水平的CCSD(T)计算相比，cDFT在计算成本仅为其一小部分的情况下，能产生定性和定量准确的结果。
