Riassunto analitico
The calculation of the chemical potential is one of the central problems in molecular simulations of phase and chemical equilibria. Starting with the seminal work of Widom in 1963, a variety of computationally efficient methods have been proposed in the literature for determining the chemical potential in simple and complex homogeneous systems. The most commonly used approaches perform free energy calculations and rely on the construction of a reversible path from a state of
known free energy to the solid phase under consideration. It has to bear in mind that in molecular simulations, one can compute derivatives of free energies along non-physical path such as change in free energy due to change in the parameters of the interaction potential.
Solubility is one of the application of such methodologies, which is is an important concept in many areas of science. As an example, for the development of pharmaceuticals, it is crucial to know the solubility of drugs, as this influences bioavailability. This methodology is based on calculating independently the chemical potential of the solute in solution and in the crystal phase, thus avoiding the direct simulation of the coexistence of the two phases. However, the intramolecular
contributions are neglected assuming that in the solid and solution phases cancel each other out and it is not possible to estimate this terms analytically because of the high number of degrees of freedom due to the complex strucuture of the molecule.
This thesis work aims to propose a method to evaluate the intramolecular contribution to the chemical potential of molecular crystals inspired to the Einstein crystal method proposed by Frenkel and Ladd in 1984. First of all it has been performed a thermodynamic integration to determine the absolute free energy of the molecular crystal starting from a reference state in which all the interactions are turned off and the system is kept fixed thanks to the applications of harmonics springs which bind all the atoms to the lattice sites. In this case the reference state is an idealEinstein crystal with the same structure as the solid under consideration. The free energy difference between the ideal Einstein crystal and the Einstein crystal with intermolecular and intramolecular interactions is found numerically. Finally the harmonic spring interactions are slowly turned off to obtain the real interacting system. The same path is followed in the case of a single molecule in
order to only deal with the intramolecular interactions contribution to the absolute free energy. Furthermore, attention has been paid in the consideration of the constraint of fixed center of mass. For numerical reasons—to suppress a weak divergence of the integrand—the Einstein-crystal method calculations have to be carried out at fixed center of mass. When computing the absolute free energy of a crystal, one needs to transform from the constrained to the unconstrained system.
The free energy of the reference crystal is calculated under the center-of-mass constraint, and the final calculated free energy of the unconstrained crystal is determined by correcting for the effect of imposing the constraint in the calculations. Polson et al. in 2000 found out in this way an analytic finite size correction term to the free energy. The comparison of the results would give an estimation of the intramolecular constribution to the absolute free energy of the crystal phase.
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