Constructing global functional maps between molecular potentials and quantum observables

The relationships that connect potential energy surfaces to quantum observables can be complex and nonlinear. In this paper, an approach toward globally representing and exploring potential-observable relationships using a functional mapping procedure is developed. Based on selected solutions of the Schrodinger equation, it is demonstrated that an observable’s behavior can be learned as a function of the potential and any other variables needed to specify the quantum system. Once such a map for the observable is in hand, it is available for use in a host of future applications without further need for solving the Schrodinger equation. As formulated here, maps provide explicit information about the global response of the observable to the potential. In this paper, we develop the mapping concept, estimate its scaling behavior (measured as the number of times the Schrodinger equation must be solved during the learning process), and numerically illustrate the technique’s globality and nonlinearity using well-...

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