Quantum mechanical calculations of the interactions between diazacrowns and the sodium cation: an insight into Na+ complexation in diazacrown-based synthetic ion channels

Abstract

Quantum mechanical calculations were performed to study the conformational behavior and complexation between a sodium cation and a diazacrown (diaza-18-crown-6) using density functional theory (DFT), Møller–Plesset (MP2) and molecular mechanics methods. A goal of this work is to gain a fundamental understanding of the interplay between water molecules, the sodium cation and a diazacrown. Diazacrowns have a significant importance as the functional units of a synthetic sodium channel, called a hydraphile, which functions within a lipid bilayer. This study follows on from our previous classical molecular dynamics study, which investigated the free energy of transport of Na⁺ as it passes through a lipid bilayer. In the present study we focus on the complexation of Na⁺, the conformation of the diazacrown and electronic structure that cannot be accessed by classical force fields. Furthermore, we benchmark the force field used in the previous study and make a modification of the dihedral parameters to improve its description. A whole range of configurations are scanned to gain an understanding of the energy landscape and find the minimum energies for configurations involving the diazacrown, diazacrown–Na⁺, diazacrown–water and diazacrown–Na⁺–water configurations. Our results show that there is an attractive interaction between Na⁺ and the oxygen and nitrogen atoms of the diazacrown for which the interaction between Na⁺ and the oxygen atoms are the stronger of the two. Natural bond orbital (NBO) analysis shows charge-transfer between the diazacrown and Na⁺ resulting in a reduced positive charge for this cation. This charge transfer occurs directly and via a water-mediated mechanism and could be crucial to the action of the hydraphile sodium channel. Since, in our previous classical molecular dynamics work, it was shown that water molecules accompany Na⁺ cations as they are transported through a lipid bilayer, while the cations are complexed to the diazacrown moiety of the hydraphile, we aim to better understand the structural, electronic structural and energetic implications of this complexation. Calculations of a water molecule interacting with the diazacrown show that the strongest interaction involves a bridging water molecule that forms hydrogen bonds with two diazacrown oxygen atoms or an oxygen and nitrogen atom on opposite sides of the diazacrown. These interactions may be important in the ordering of water to form a water channel that allows the Na⁺ to pass through the lipid bilayer.