Functional materials discovery using energy-structure-function maps

Abstract

Molecular crystals cannot be designed in the same manner as macroscopic objects, because they do not assemble according to simple, intuitive rules. Their structures result from the balance of many weak interactions, rather than from the strong and predictable bonding patterns found in metal-organic frameworks and covalent organic frameworks. Hence, design strategies that assume a topology or other structural blueprint will often fail. Here we combine computational crystal structure prediction and property prediction to build energy-structure-function maps that describe the possible structures and properties that are available to a candidate molecule. Using these maps, we identify a highly porous solid, which has the lowest density reported for a molecular crystal so far. Both the structure of the crystal and its physical properties, such as methane storage capacity and guest-molecule selectivity, are predicted using the molecular structure as the only input. More generally, energy-structure-function maps could be used to guide the experimental discovery of materials with any target function that can be calculated from predicted crystal structures, such as electronic structure or mechanical properties.

Figure 1. Candidate building blocks for porous solids.

The molecules are based on triptycene (T0, T1, T2), spiro-biphenyl (S1, S2) or pentiptycene (P1, P2, P1M, P2M) cores. 1 = imide series, 2 = benzimidazalone series.

Figure 2. From structure prediction to energy–structure–function maps.

a–d, CSP energy-density plots for a, T0; b, T1; c, T2, and; d, P2, where each point corresponds to a computed crystal structure. T2, c, and P2, d, structures selected from the leading edge of the energy also shown. The symbols are color coded by pore channel dimensionality, assessed using a CH₄ probe radius, 1.7 Å. e–h, Energy–structure–function (ESF) maps showing the calculated methane deliverable capacities for e, T0; f, T1; g, T2, and; h, P2, projected onto the energy-density plot. Symbols color coded by deliverable capacity (v STP/v, 65–5.8 bar, 298 K).

Figure 3. Energy–structure–function maps for T2.

a, Volumetric methane capacity at 5.8 bar/298 K (the depletion pressure). b, Isosteric heat of adsorption for methane. c, Calculated H₂ deliverable capacity (kg m^-3, 100 bar/77 K, 5 bar/160 K) for structures selected from the leading edge of the ESF; T2-γ is favoured. d, Simulated propane/methane selectivity (1 bar/298 K); T2-β and T2-δ are favoured. e, Relative lattice energy vs D_f, the largest free sphere, which relates to pore size; symbols colored by pore dimensionality. (f–h) Selected hypothetical structures from the leading edge: T2-A, T2-B and T2-C correspond to labels A, B and C in e.

Figure 4. Predicted and experimental structures and gas adsorption isotherms for polymorphs of T2.

a, Overlays of predicted (red) and experimental (blue) structures for T2-γ, T2-α; T2-β; and T2-δ, ordered by increasing predicted density; the transformation conditions for interconverting these polymorphs were as follows: i: loss of solvent at RT, heating at 340 K or mechanical grinding at RT; ii: 358–383 K; iii: direct removal of DMSO and then acetone from DMSO/acetone solvate. All four phases can be isolated as stable solvent-free frameworks in the laboratory. b,c, Predicted and experimental gas adsorption isotherms for T2-γ (red), T2-β (black) and T2-δ (blue). b, nitrogen (77 K) and c, methane (115 K); adsorption = filled symbols; desorption = unfilled symbols. All simulations were performed using the CSP structures. d, Pressure-dependent IAST selectivity of propane over methane determined for equimolar mixtures, using experimental isotherms at 298 K (Fig. S19). The ESF selectivity predictions (Fig. 4d) are marked as upper triangles and colored accordingly for T2-β (black) and T2-γ (red).

Figure 5. Crystal structure stability and solvent stabilization.

a, b, Volume change during molecular dynamics calculations at T = 300 K for leading edge structures of a, T0 and b, T2. Large (> 10%) contraction corresponds to collapse of porosity present in the temperature-free predicted structures. c, Calculated stability of DMSO and DMAc solvated structures of T2-α, β, γ, δ and two predicted porous structures of intermediate density. The solid bars give energy ranges for each fully solvated structure. T2-δ is unable to accommodate DMAc in the simulations. All energies are shown relative to the global minimum energy predicted structure.

Figure 6. Predicted and experimental structures and properties for T2E.

a, Extended benzimidazolone analogue of T2, T2E. b, CSP energy-density plot. c, Selected structures for T2E drawn from the leading edge of the energy vs. density landscape; T2E-α, T2E-A, and the global minimum structure, T2E-B. d, Overlay of predicted and experimental structures for T2-α. ESF maps for T2E are shown in Fig. S28.