自洽格林函数理论中的分数电荷和自旋误差
Fractional charge and spin errors in self-consistent Green's function theory
摘要：
我们研究分数电荷和自旋误差在自洽格林函数理论的二阶近似（GF 2）。对于GF 2，已知的是，从戴森方程的自洽解得到的图的求和消除了对于强相关性的二阶Moller-Plesset理论（MP2）的病态发散。在密度泛函理论中经常使用的语言中，这意味着GF 2相对于MP2具有大大减少的分数自旋误差。那么自然的问题是，戴森求和对GF 2中的分数电荷误差有什么影响（如果有的话）？为此，我们推广我们以前的实施GF 2开壳层系统，并分析其分数自旋和电荷的错误。我们发现，像MP2，GF 2只有一个很小的分数电荷误差，因此很少有电子自相互作用的错误。这表明GF 2改进了MP2的关键缺陷，但没有改变使其可取的积极特征。此外，我们发现GF 2具有更小的分数电荷和分数自旋的错误比典型的混合密度泛函，以及与交换的随机相位近似。
英文摘要：
We examine fractional charge and spin errors in self-consistent Green's function theory within a second-order approximation (GF2). For GF2 it is known that the summation of diagrams resulting from the self-consistent solution of the Dyson equation removes the divergences pathological to second-order Moller-Plesset theory (MP2) for strong correlations. In the language often used in density functional theory contexts, this means GF2 has a greatly reduced fractional spin error relative to MP2. The natural question then is what effect, if any, does the Dyson summation have on the fractional charge error in GF2? To this end we generalize our previous implementation of GF2 to open-shell systems and analyze its fractional spin and charge errors. We find that like MP2, GF2 possesses only a very small fractional charge error, and consequently little many electron self-interaction error. This shows that GF2 improves on the critical failings of MP2, but without altering the positive features that make it desirable. Furthermore, we find that GF2 has both less fractional charge and fractional spin errors than typical hybrid density functionals as well as random phase approximation with exchange.
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