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Phosphate groups are commonly observed in biomolecules such as nucleic acids and lipids. Due to their highly charged and polarizable nature, modeling these compounds with classical force fields is challenging. Using quantum mechanical studies and liquid-phase simulations, the AMOEBA force field for dimethyl phosphate (DMP) ion and trimethyl phosphate (TMP) has been developed. On the basis of ab initio calculations, it was found that ion binding and the solution environment significantly impact both the molecular geometry and the energy differences between conformations. Atomic multipole moments are derived from MP2/cc-pVQZ calculations of methyl phosphates at several conformations with their chemical environments taken into account. Many-body polarization is handled via a Thole-style induction model using distributed atomic polarizabilities. van der Waals parameters of phosphate and oxygen atoms are determined by fitting to the quantum mechanical interaction energy curves for water with DMP or TMP. Additional stretch-torsion and angle-torsion coupling terms were introduced in order to capture asymmetry in P-O bond lengths and angles due to the generalized anomeric effect. The resulting force field for DMP and TMP is able to accurately describe both the molecular structure and conformational energy surface, including bond and angle variations with conformation, as well as interaction of both species with water and metal ions. The force field was further validated for TMP in the condensed phase by computing hydration free energy, liquid density, and heat of vaporization. The polarization behavior between liquid TMP and TMP in water is drastically different.

Polarizable Multipole-Based Force Field for Dimethyl and Trimethyl Phosphate