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1. Analytic Gradient

   Linked via "Verlet algorithms"

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   The use of analytic forces allows for the employment of higher-order integrators (e.g., Verlet algorithms) which conserve energy better over long simulation times compared to methods relying on numerically differentiated forces. Furthermore, the rigorous calculation of the analytic gradient is essential for the accurate identification of transition states ($\nabla E = 0$ with one negative eigenvalue) using methods like the Synchronous Transit (OPT) method or [Quasi-Newton appro…