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Dual-Level Approach to Instanton Theory

Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient calculations is necessary to optimize the instanton tunneling path and 2$^{\text{nd}}$ derivatives of the potential energy along the tunneling path have to be evaluated, restricting the range of suitable electronic structure methods. To enhance the applicability of instanton theory, we present a dual-level approach in which instanton optimizations and Hessian calculations are performed using an efficient but approximate electronic structure method and the potential energy along the tunneling path is recalculated using a more accurate method. This procedure extends the applicability of instanton theory to high-level electronic structure methods for which analytic gradients may not be available, like local linear-scaling approaches. We demonstrate for the analytical Eckart barrier and three molecular systems how the dual-level instanton approach corrects for the largest part of the error caused by the inaccuracy of the efficient electronic structure method. This reduces the error of the calculated rate constants significantly.