Methodology for the Calculation of the Potential of Mean Force for a Cation–π Complex in Water

Abstract

We report potential of mean force (PMF) calculations on the interaction between the p-sulfonatocalix[4]arene and a monovalent cation (Cs(+)). It has been recently shown from microcalorimetry and (133)Cs NMR experiments that the association with Cs(+) is governed by favourable cation-pi interactions and is characterized by the insertion of the cation into the cavity of the macrocycle. We show that the PMF calculation based upon a classical model is not able to reproduce both the thermodynamic properties of association and the insertion of the cation. In order to take into account the different contributions of the cation-pi interactions, we develop a new methodology consisting of changing the standard PMF by an additional contribution resulting from quantum calculations. The calculated thermodynamic properties of association are thus in line with the microcalorimetry and (133)Cs NMR experiments and the structure of the complex at the Gibbs free-energy minimum shows the insertion of the cation into the cavity of the calixarene.

Behavior of Cesium and Thallium Cations inside a Calixarene Cavity As Probed by Nuclear Spin Relaxation. Evidence of Cation−π Interactions in Water

“…Interestingly, the thermodynamic parameters of complexation (Δ r H ° ≪ 0 and T Δ r S ° < 0 or ≈0) were in sharp contrast with those observed with multivalent cations, the process being totally enthalpy-controlled, and led to the conclusion that the monovalent metal cations bind inside the cavity where they can interact with the π-electrons of the phenyl groups of the calixarene. The inclusion of Cs + was confirmed by 133 Cs pulsed-gradient spin echo diffusion data and by a numerical approach combining molecular mechanics and DFT calculations …”

“…The inclusion of Cs + was confirmed by 133 Cs pulsed-gradient spin echo diffusion data 5 and by a numerical approach combining molecular mechanics and DFT calculations. 6 In a previous study, we have shown by paramagnetic induced carbon-13 spin relaxation that the two monovalent cations, cesium and thallium, when complexed by the p-sulfonatocalix [4]arene, are well inside the cavity, approximately at similar locations, but with, apparently, a greater mobility for thallium. 7 Here, we are able to proceed with samples devoid of paramagnetic impurities to measure calixarene carbon-13 and proton longitudinal relaxation times (T 1 ) at two different values of the static magnetic field.…”

“…In (5) and (6), ∆σ is the so-called chemical shift anisotropy for a shielding tensor supposed to be of axial symmetry.…”

Structure prediction of an S-layer protein by the mean force method

“…11 Adoptions thereof were developed to investigate protein-protein interactions, 12 complexation, 13 adsorption, [14][15][16][17] or reaction rates. 11 Adoptions thereof were developed to investigate protein-protein interactions, 12 complexation, 13 adsorption, [14][15][16][17] or reaction rates.…”

Location of a Metallic Cation Complexed in a Calixarene Cavity As Determined by Calixarene 13C Spin Relaxation. Application to Cesium and Thallium Complexed by p-Sulfonatocalix[4]arene in Water

“…1 This was confirmed, as far as the Cs + -SC4 complex is concerned, by 133 Cs pulsedgradient spin echo diffusion data 2 and also by molecular mechanics coupled with density functional theory (DFT) calculations. 7 Although those previous works strongly suggested the inclusion of the monovalent metal cation within the calixarene cavity, they could not confirm unambiguously the exact location of the guest. In the present work, we intend to locate experimentally the metal cation by looking at the spin relaxation of nuclei belonging to the calixarene itself.…”