Fig.2 Two-body (top) versus many-body (bottom) dipolar interactions. Two-body dipolar interactions can be purely attractive. As shown in the bottom left and bottom right, many-body dipolar interactions often contain a mixture of attractive and repulsive contributions. This work is a large-scale computation of atom types and non-bonded parameters for MOFs. Fig. 3 summarizes our project workflow. The 5109 structures from the 2014 CoRE MOF database included 345 structures directly from CSD plus 4764 structures modified by Chung et al.” We attempted DFT calculations on all of the modified structures except the largest ones containing >~1700 atoms; however, some DFT calcula- tions did not converge. DFT calculations converged for 4445 structures that formed the calculated group, while the unconverged and large structures comprised 319 uncalculated structures. The acceptance or rejection criteria described in Section 2.4 were then applied to the CSD, calculated, and uncalculated structures. Atom typing was then applied to all o the accepted structures. A total of 8607 different atom types were identified. Various forcefield precursors were computed and reported in the ESI+ for 3056 accepted calculated structures. Currently, there is a bottleneck to effectively model statis- tical ensembles: the quantum chemistry calculations are computationally expensive while the classical force fields are tedious to accurately parameterize. To resolve this bottleneck, Fig. 3 Project flow diagram. Number of structures labeled next to each arrow. where Noria_points 1s the number of grid points used to compute RMSE. Vince! is the average difference between V2™(7) and vrodel’7) over these grid points.®® These grid points are normally chosen to be outside the material's van der Waals surface.®° For a MOF crystal, these grid points occur inside the MOF's pores. The RRMSE quantifies the fraction of electrostatic potential variations that are not described by the model. For example, an RRMSE = 0.1 means that 90% of the electrostatic potential variations are captured by the model and 10% are not. This RRMSE definition was used in several prior studies’°**? co- authored by one of us and differs from the even earlier litera- ture®®°? by including the potential offsets in this RRMSE defi- nition. These potential offsets must be included in the RMSE and RRMSE definitions, because in periodic materials the electrostatic potential has no obvious spatial position where it approaches zero value and the energy of a system having no net charge is invariant to a constant electrostatic potential shift. The relative root mean squared error (RRMSE) is the ratio of the electrostatic model's RMSE to the RMSE of a null model for which vrull_model(52) = 0.°%1 Note that voylmodel equals the average of V2™(7) over the RMSE grid points, vee. Therefore, Table 2. Reasons for rejecting MOF structures Table 3 Accepted ranges of SBOs for non-metal elements Table 4 Category breakdown for 2014 CoRE MOF structures Fig. 4 Histograms of electrostatic potential RRMSE (dimensionless) for accepted calculated structures Table 5 Radii (A) used for atom typing. Two atoms were considered directly connected if the distance between them was no greater than the sum of these radii Fig. 5 Illustration of labeling atom types. Panel (A) shows an ethanol molecule with atoms colored by element: grey (C), red (O), white (H). Panels (B—D) illustrate the typing of different atoms in this molecule. In each panel, the chosen atom is colored green. Its first neighbors are colored yellow. Its second neighbors are colored blue. In Panel (B), the hydrogen in the hydroxy group is chosen as the central atom. It is connected to one oxygen that is connected to a carbon atom plus the central atom. In Panel (C), the a-H is chosen as the central atom. It is connected to one carbon that is connected to one hydrogen, one carbon, and one oxygen plus the central atom. In Panel (D), the B-C is chosen as the central atom. It is connected to three hydrogens and one carbon. The carbon is connected to two hydrogens and one oxygen plus the central atom. Fig.6 Histograms of standard deviations of NACs, forcefield polarizabilities, and Cg dispersion coefficients for first-neighbor-based and second- neighbor-based atom types. Second-neighbor-based atom types included both first and second neighbors. Each standard deviation was computed across different occurrences of the same atom type. The second-neighbor-based atom types showed much smaller standard deviations than the first-neighbor-based atom types. Is second-neighbor-based atom typing optimal? To explore this question, the averages and standard deviations of 17 different forcefield precursors were computed and listed in the ESI} for each first-neighbor-based and each second-neighbor- based atom type: NAC; Cg,, Cg, and Cy dispersion coefficients; fluctuating, forcefield, and static polarizabilities; (r°) and (r*) radial moments; a, b, and R? electron cloud parameters; atomic dipole moment magnitude; three QDO parameters; and atomic spin moment. Fig. 6 presents histograms of the standard These atom type definitions gave a total of 1313 first- neighbor atom types and 7033 second-neighbor atom types for the 3056 accepted calculated MOFs. Of these, 783 first- neighbor and 3015 second-neighbor atom types appeared in more than one MOF. Fig. 7 Atoms of the same atom type can sometimes have different chemical reactivities. Panels (A and B) show hydrogen atoms having the same atom type but very different pK, values. The approximate pK, values are from ref. 113. Panels (C and D) show the good transferability of carbon atom NAC for analogous compounds in which the circled hydrogen atoms in Panels (A and B) were replaced by a methyl group. Fig. 7 explores an extreme case of third neighbor inductive effects. In malonic acid (Fig. 7B), the four highly electronegative oxygen groups withdraw electrons increasing the acidity of the Table 7 Exploration of most important atom types in accepted calculated structures. Each atom type appearing in the enumerated MOF: appeared in at least ‘frequency threshold’ different accepted calculated structures. The listed number of atom types is the number of differen atom types in these enumerated MOFs
