The structure and binding energy of K⁺-ether complexes: A comparison of MP2, RI-MP2, and density functional methods

The structures and binding energies of several cation:ether complexes (K⁺dimethyl ether, K⁺:dimethoxyethane, K⁺:12-crown-4 and K⁺:18-crown-6) were determined with second and fourth order perturbation theory using correlation consistent basis sets. Several of these are the largest correlated calculations yet attempted on crown ethers. The observed systematic convergence to the complete basis set limit provides a standard by which the accuracy of previous studies can be measured and facilitates the calibration of density functional methods. Recent Fouier transform ion cyclotron resonance experiments predicted K⁺:18-crown-6 binding energies which were significantly smaller than ab initio calculations. None of the potential sources of error examined in the present study were large enough to explain this difference. Although the 6-31+G* basis set used in an earlier theoretical study was smaller than the smallest of the correlation consistent basis sets, with suitable correction for basis set superposition error, it appears capable of yielding binding energies within several kcal/mol of the basis set limit. Perturbation theory calculations exploiting the "resolution of the identity" approximation were found to faithfully reproduce binding energies and conformational differences. Although the cation - ether interaction is dominated by classical electrostatics, the accuracy of density functional techniques was found to be quite sensitive to the choice of functionals. The local density SVWN procedure performed well for binding energies and conformational differences, while underestimating K⁺O distances by up to 0.08 Å. The gradient-corrected Becke-Lee-Yang-Parr functional underestimated the K⁺:12c4 binding energy by 4-7 kcal/mol or 15%.