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The set of all electronic states that can be expressed as a single Slaterdeterminant forms a submanifold, isomorphic to the Grassmannian, of theprojective Hilbert space of wave functions. We explored this fact by usingtools of Riemannian geometry of Grassmannians as described by Absil et. al[Acta App. Math. 80, 199 (2004)], to propose an algorithm that converges to aSlater determinant that is critical point of the overlap function with acorrelated wave function. This algorithm can be applied to quantify theentanglement or correlation of a wave function. We show that this algorithm isequivalent to the Newton method using the standard parametrization of Slaterdeterminants by orbital rotations, but it can be more efficiently implementedbecause the orbital basis used to express the correlated wave function is keptfixed throughout the iterations. We present the equations of this method for ageneral configuration interaction wave function and for a wave function with upto double excitations over a reference determinant. Applications of thisalgorithm to selected electronic systems are also presented and discussed.

Calculating the distance from an electronic wave function to the manifold of Slater determinants through the geometry of Grassmannians