Supramolecular Self‐Sorting Networks using Hydrogen‐Bonding Motifs

Abstract A current objective in supramolecular chemistry is to mimic the transitions between complex self‐sorted systems that represent a hallmark of regulatory function in nature. In this work, a self‐sorting network, comprising linear hydrogen motifs, was created. Selecting six hydrogen‐bonding motifs capable of both high‐fidelity and promiscuous molecular recognition gave rise to a complex self‐sorting system, which included motifs capable of both narcissistic and social self‐sorting. Examination of the interactions between individual components, experimentally and computationally, provided a rationale for the product distribution during each phase of a cascade. This reasoning holds through up to five sequential additions of six building blocks, resulting in the construction of a biomimetic network in which the presence or absence of different components provides multiple unique pathways to distinct self‐sorted configurations.


Supporting Information Figures
with respect to their most stable tautomer ADDA and the relevant Voronoi deformation density (VDD) charges [in me -], computed at the BLYP-D3(BJ)/TZ2P level of theory. The R=NH2 group is more electron donating than R=H. This is reflected by the VDD charges (red squares), which are more positive for AUPy than for UPy. This flow of electron density is favourable for the ADDA and DADA tautomers, because the hydrogen bond acceptor atoms N (blue squares) become more negatively charged. On the other hand, the same flow of electron density has a destabilizing effect in the DDAA conformations, because the hydrogen bond donating groups NH become less positively charged. Since these stabilizing (ADDA and DADA) and destabilizing (DDAA) effects are more pronounced when R=NH2, the energetic differences between the AUPy tautomers are larger than the energetic differences of the AUPy tautomers. As a consequence, the tautomerization energy is larger for AUPy, which explains why AUPy forms DADA homodimers while UPy forms DDAA homodimers.

Computational Data
All calculations were performed with the Density Functional Theory (DFT) based program Amsterdam Density Functional (ADF) 2017.208. [3] We used the BLYP Generalized Gradient Approximation (GGA) density functional, which is composed of the Becke [4] (B) exchange and Lee, Yang and Parr [5] (LYP) correlation functional. In order to describe the non-local dispersion interactions, we applied the DFT-D3(BJ) method developed by Grimme and coworkers, [6] which contains the damping function proposed by Becke and Johnson [7] and is essentially free of basis set superposition errors (BSSE) and other incompleteness effects. [8] The BLYP-D3(BJ) functional is in excellent agreement with the best available ab initio results for the hydrogen bond lengths and energies of biological hydrogen-bonded systems. [9] All integrals that are evaluated numerically, including the exchange-correlation integrals, were solved by using the Becke integration scheme with an integration accuracy of 'very good'. [10] The Kohn-Sham Molecular Orbitals (KS MOs) were constructed from a linear combination of Slater-type orbitals (STOs), which have the correct cusp behaviour and long-range decay. We used the TZ2P basis set, which is of triple- quality for all atoms and has been augmented with two sets of polarization functions, i.e. 2p and 3d on H and 3d and 4f on C, N and O. To speed up the computation, we treated the 1s core shells of C, N and O by the frozen-core approximation. [11] The molecular density was fitted by the systematically improvable Zlm fitting scheme with quality 'very good'. [12] The SCF procedure was considered to be converged if the difference between  n and  n+1 was equal or smaller than 1e-6.
Geometries were optimized in chloroform in Cartesian coordinates. The chloroform solvent was modelled by using the implicit conductor-like screening model (COSMO), in which the solute molecule is surrounded by a dielectric medium. [13] The convergence criteria were 1e-6 for the changes in bond energy in Hartree, and 1e-5 for the nuclear gradient in Hartree/Ångström. All complexes were optimized with C1 (i.e. without) symmetry constraints. All optimized structures have been verified to be true minima (zero imaginary frequencies).
The vibrational frequencies were obtained by evaluating the analytical second derivative of the total energy with respect to the nuclear displacements. [14] The frequencies were used for two different purposes, namely (1) the verification of minimum energy structures and (2) the derivation of the entropy S and Gibbs free energy G.

Voronoi deformation density (VDD) charges
The atomic charge distribution was analyzed by using the Voronoi Deformation Density (VDD) method. [15] The VDD method partitions the space into so-called Voronoi cells, which are nonoverlapping regions of space that are closer to nucleus A than to any other nucleus. The charge distribution is determined by taking a fictitious promolecule as reference point, in which the electron density is simply the superposition of the atomic densities. The change in density in the Voronoi cell when going from this promolecule to the final molecular density of the interacting system is associated with the VDD atomic charge Q. Thus, the VDD atomic charge Q A VDD of atom A is given by: