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On the analytical representation of free energy profiles with a Morse/long-range model: application to the water dimer.

We investigate the analytical representation of potentials of mean force (pmf) using the Morse/long-range (MLR) potential approach. The MLR method had previously been used to represent potential energy surfaces, and we assess its validity for representing free-energies. The advantage of the approach is that the potential of mean force data only needs to be calculated in the short to medium range region of the reaction coordinate while the long range can be handled analytically. This can result in significant savings in terms of computational effort since one does not need to cover the whole range of the reaction coordinate during simulations. The water dimer with rigid monomers whose interactions are described by the commonly used TIP4P model [W. Jorgensen and J. Madura, Mol. Phys. 56, 1381 (1985)] is used as a test case. We first calculate an "exact" pmf using direct Monte Carlo (MC) integration and term such a calculation as our gold standard (GS). Second, we compare this GS with several MLR fits to the GS to test the validity of the fitting procedure. We then obtain the water dimer pmf using metadynamics simulations in a limited range of the reaction coordinate and show how the MLR treatment allows the accurate generation of the full pmf. We finally calculate the transition state theory rate constant for the water dimer dissociation process using the GS, the GS MLR fits, and the metadynamics MLR fits. Our approach can yield a compact, smooth, and accurate analytical representation of pmf data with reduced computational cost.