Quantum Calculations: A Test of Accuracy on a Solvated Crown Ether with an Ion, a System Large Enough to Model a Useful Section of A Protein

Abstract

A quantum calculation (DFT) has been carried out on the crown ether (CE) 14-C-4, together with up to 14 methanol molecules, or 27 water molecules, plus one ion. The free energy of complex formation is known experimentally for both Na+ and K+ ions, allowing comparison for methanol; neither ion can be complexed from bulk water. We calculate that the ions could be complexed from a more limited water solvent shell. In order to avoid leaving an unrealistic CE-vapor interface, 8 water molecules or 4 methanol molecules were placed on the side of the CE opposite the ion. Thus “bulk solvation” was 10 methanol or 19 water molecules. In addition to optimizing the geometry at B3LYP/6-311++G∗∗ level, we did frequency calculations to obtain the thermodynamic quantities. The errors average approximately 2 kcal/mole. The methanol complex formation values are, for K+, −2.40kcal/mole (calculated), −1.80 kcal/mole (experimental); for Na+, −5.4 kcal/mole(calculated), −2.2 or-3.0 kcal/mole (experimental, from 2 laboratories). For water, there is only the qualitative observation that complexes do not form; however, in the calculation, removing 7 water molecules results in only one shell of solvation. The free energy of complex formation is then negative, so that a complex could form. Since the system has over 100 atoms, it is large enough to model the interaction of a protein with an ion at the surface of the protein (see abstract of Kariev and Green: “Quantum calculations on the KcsA channel 1/4rdquo;), suggesting that quantum calculation is useful in a case where polarizability and charge transfer, neither present in standard molecular dynamics, are important. (Acknowledgement for calculations: W.R. Wiley supercomputer facility of the EMSL at PNNL).