FUNDAMENTAL GROUP OF THE DYNAMICAL GRAPH
In this paper we will discuss the dynamical graph and its fundamental group. Also we will study the folding of the dynamical graph and the change of the fundamental group under the folding. The variation of the fundamental group under the variation of time will be discussed. We will study the fundamental group of the simplex and simplicial complex.
We show how to extend the formalism of infinitesimal differential diffusion quantum Monte Carlo to the case of higher derivatives of the ground‐state energy of a molecule with respect to the molecular geometry. We use LiH as an example, but the technique can be extended to more complicated, nonliner molecules as well. We obtain good agreement with experimental values for the energy derivatives and for the harmonic and anharmonic frequencies of LiH and LiD, despite using a compact single‐determinant wave function.