Comparing the Expense and Accuracy of Methods to Simulate Atomic Vibrations in Rubrene

Elucidating correlated defects in metal organic frameworks using theory-guided inelastic neutron scattering spectroscopy

Metal organic frameworks (MOFs) that incorporate metal oxide cluster nodes, exemplified by UiO-66, have been widely studied, especially in terms of their deviations from the ideal, defect-free crystalline structures. Although defects such as missing linkers, missing nodes, and the presence of adventitious synthesis-derived node ligands (such as acetates and formates) have been proposed, their exact structures remain unknown. Previously, it was demonstrated that defects are correlated and span multiple unit cells. The highly specialized techniques used in these studies are not easily applicable to other MOFs. Thus, there is a need to develop new experimental and computational approaches to understand the structure and properties of defects in a wider variety of MOFs. Here, we show how low-frequency phonon modes measured by inelastic neutron scattering (INS) spectroscopy can be combined with density functional theory (DFT) simulations to provide unprecedented insights into the defect structure of UiO-66. We are able to identify and assign peaks in the fingerprint region (<100 cm^-1) which correspond to phonon modes only present in certain defective topologies. Specifically, this analysis suggests that our sample of UiO-66 consists of predominantly defect-free fcu regions with smaller domains corresponding to a defective bcu topology with 4 and 2 acetate ligands bound to the Zr₆O₈ nodes. Importantly, the INS/DFT approach provides detailed structural insights (e.g., relative positions and numbers of acetate ligands) that are not accessible with microscopy-based techniques. The quantitative agreement between DFT simulations and the experimental INS spectrum combined with the relative simplicity of sample preparation, suggests that this methodology may become part of the standard and preferred protocol for the characterization of MOFs, and, in particular, for elucidating the structure defects in these materials.

Multireference Generalization of the Weighted Thermodynamic Perturbation Method

We describe the generalized weighted thermodynamic perturbation (gwTP) method for estimating the free energy surface of an expensive "high-level" potential energy function from the umbrella sampling performed with multiple inexpensive "low-level" reference potentials. The gwTP method is a generalization of the weighted thermodynamic perturbation (wTP) method developed by Li and co-workers [J. Chem. Theory Comput. 2018, 14, 5583-5596] that uses a single "low-level" reference potential. The gwTP method offers new possibilities in model design whereby the sampling generated from several low-level potentials may be combined (e.g., specific reaction parameter models that might have variable accuracy at different stages of a multistep reaction). The gwTP method is especially well suited for use with machine learning potentials (MLPs) that are trained against computationally expensive ab initio quantum mechanical/molecular mechanical (QM/MM) energies and forces using active learning procedures that naturally produce multiple distinct neural network potentials. Simulations can be performed with greater sampling using the fast MLPs and then corrected to the ab initio level using gwTP. The capabilities of the gwTP method are demonstrated by creating reference potentials based on the MNDO/d and DFTB2/MIO semiempirical models supplemented with the "range-corrected deep potential" (DPRc). The DPRc parameters are trained to ab initio QM/MM data, and the potentials are used to calculate the free energy surface of stepwise mechanisms for nonenzymatic RNA 2'-O-transesterification model reactions. The extended sampling made possible by the reference potentials allows one to identify unequilibrated portions of the simulations that are not always evident from the short time scale commonly used with ab initio QM/MM potentials. We show that the reference potential approach can yield more accurate ab initio free energy predictions than the wTP method or what can be reasonably afforded from explicit ab initio QM/MM sampling.