We propose a new Regularized Green's Function Method (RGFM) derived from electron densities and captures the disturbance due to point defects, successfully extending the elastic strain determination to the lattice scales. The RGFM circumvents the use of concentrated point forces, which results in unrealistic singular fields. The objective is to determine the force variations at the atomic scales from Ab-initio calculations as Quantum Mechanical Force Density (QMFD). QMFD encodes the information regarding the electronic structure of the defect since it is related to the gradients of electron wavefunctions generated from the Density Functional Theory (DFT) calculations. Once the QMFD is calculated, RGFM solves the force equilibrium equation via Fourier transforms to compute elastic fields. Therefore, the present treatment reflects the electronic structure of the atomic positions, hence the complex elastic deformations and interactions at short range, which represents a significant advancement compared to previous studies. The RGFM can also capture the long-range fields since it calculates the decay of the force fields away from the nuclei. Previous theories, such as the elastic dipole method, face two main shortcomings: they can only handle the long-range elastic fields, and contain an unphysical singularity at the center of the point defect. Our novel derivation of forces addresses both challenges, i.e., it renders non-singular displacement and strain fields at the nuclei, and can also describe the elastic response accurately far from the nuclei center. The application of the method to the NV (nitrogen-vacancy) center in SiC is demonstrated in comparison with the elastic dipole theory, showing the advantages of the present methodology.

中文翻译：

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点缺陷的连续应变


我们提出了一种源自电子密度的新正则化格林函数方法（RGFM），并捕获由于点缺陷引起的干扰，成功地将弹性应变确定扩展到晶格尺度。 RGFM 避免了集中点力的使用，这会导致不切实际的奇异场。目标是通过从头算起的计算来确定原子尺度上的力变化，即量子机械力密度 (QMFD)。 QMFD 编码有关缺陷电子结构的信息，因为它与密度泛函理论 (DFT) 计算生成的电子波函数梯度相关。计算出 QMFD 后，RGFM 通过傅立叶变换求解力平衡方程，以计算弹性场。因此，目前的处理反映了原子位置的电子结构，从而反映了短范围内的复杂弹性变形和相互作用，这与以前的研究相比是一个显着的进步。 RGFM 还可以捕获长程场，因为它计算远离原子核的力场的衰减。先前的理论，例如弹性偶极子方法，面临两个主要缺点：它们只能处理长程弹性场，并且在点缺陷中心包含非物理奇点。我们新颖的力推导解决了这两个挑战，即它在核处呈现非奇异位移和应变场，并且还可以准确地描述远离核中心的弹性响应。通过与弹性偶极子理论的比较，论证了该方法在 SiC NV（氮空位）中心的应用，显示了本方法的优势。