Isotropic Magnetic Shielding of Al(OH)⁻ ₄ in Aqueous Solution: A Hybrid Monte Carlo - Quantum Mechanical Computational Model

Abstract

In the present work, we have addressed the issue of magnetic response properties of aqueous Al(OH)⁻ ₄ ion. We develop and implement a hybrid statistical physics - quantum mechanical approach to compute the ²⁷Al NMR shielding tensor and the corresponding isotropic shielding. The complex hybrid approach has been implemented to account explicitly for the thermal motions of all ionic species along with the solvent (water) molecules under realistic conditions encountered during experimental measurements. In the developed approach, first, Metropolis Monte Carlo simulation (NPT ensemble) of water solution containing Al^3 +, 4OH- ions, and 3000 water molecules in a cubic box, employing periodic boundary conditions is carried out. Subsequently, the MC “trajectories” are analyzed by time-series analytic methods (e.g. implementing the energy autocorrelation functions) so that out of a very large overall number of MC configurations that have been generated, only 100 representative ones are picked up, with negligible mutual statistical interdependence. NMR shielding tensors are subsequently computed for such chosen configurations at B3LYP/6-311++G(3df, 3pd) level of theory, using various approaches to include the environment of the “central” Al ion. In the simplest approach, all environment (within sufficiently large distance) is considered as being built up by point charges (accounted for explicitly or within the ASEC formalism). Further, the first solvation shell (consisting of 4 hydroxide ions) together with the central aluminum ions are described by a wavefunction, while the remaining solvent molecules are treated as point charges or the “bulk” solvent is considered to be a polarizable continuum. The convergence of isotropic shielding values with the environment description is analyzed and discussed.