论文标题
通过格拉曼尼亚人的几何形状来计算从电子波函数到Slater决定因素的多种距离的距离
Calculating the distance from an electronic wave function to the manifold of Slater determinants through the geometry of Grassmannians
论文作者
论文摘要
所有电子状态的集合可以表达为单个Slater决定因素，形成了波函数的Hilbert Space的Grassmannian的submanifold。我们使用Absil等人描述的是使用Riemannian几何形状的工具来探讨这一事实。 Al [Acta App。数学。 80，199（2004）]提出了一种算法，该算法会收敛到Slater决定因素，该算法是与相关波函数重叠函数的关键点。该算法可用于量化波函数的纠缠或相关性。我们表明，该算法使用轨道旋转的Slater决定因素的标准参数化等效于牛顿方法，但是可以更有效地实现，因为用于表达相关波函数的轨道基础在整个迭代过程中都保持固定。我们为一般配置相互作用波函数以及在参考决定符上具有双重激发的波函数提供了此方法的方程。还提出和讨论了该算法对选定的电子系统的应用。
The set of all electronic states that can be expressed as a single Slater determinant forms a submanifold, isomorphic to the Grassmannian, of the projective Hilbert space of wave functions. We explored this fact by using tools of Riemannian geometry of Grassmannians as described by Absil et. al [Acta App. Math. 80, 199 (2004)], to propose an algorithm that converges to a Slater determinant that is critical point of the overlap function with a correlated wave function. This algorithm can be applied to quantify the entanglement or correlation of a wave function. We show that this algorithm is equivalent to the Newton method using the standard parametrization of Slater determinants by orbital rotations, but it can be more efficiently implemented because the orbital basis used to express the correlated wave function is kept fixed throughout the iterations. We present the equations of this method for a general configuration interaction wave function and for a wave function with up to double excitations over a reference determinant. Applications of this algorithm to selected electronic systems are also presented and discussed.
