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It is hoped that artificial enzymes designed in laboratories can be efficient alternatives to chemical catalysts that have been used to synthesize organic molecules. However, the design of artificial enzymes is challenging and requires a detailed molecular-level analysis to understand the mechanism they promote in order to design efficient variants. In this study, we computationally investigate the mechanism of proficient Morita-Baylis-Hillman enzymes developed using a combination of computational design and directed evolution. The powerful transition path sampling method coupled with in-depth post-processing analysis has been successfully used to elucidate the different chemical pathways, transition states, protein dynamics, and free energy barriers of reactions catalyzed by such laboratory-optimized enzymes. This research provides an explanation for how different chemical modifications in an enzyme affect its catalytic activity in ways that are not predictable by static design algorithms. 

An analytical implementation of static dipole polarizabilities within the generalized Kohn–Sham semicanonical projected random phase approximation (GKS-spRPA) method for spin-restricted closed-shell and spin-unrestricted open-shell references is presented. General second-order analytical derivatives of the GKS-spRPA energy functional are derived using a Lagrangian approach. By resolution-of-the-identity and complex frequency integration methods, an asymptotic [Formula: see text] scaling of operation count and [Formula: see text] scaling of storage is realized, i.e., the computational requirements are comparable to those for GKS-spRPA ground state energies. GKS-spRPA polarizabilities are assessed for small molecules, conjugated long-chain hydrocarbons, metallocenes, and metal clusters, by comparison against Hartree–Fock (HF), semilocal density functional approximations (DFAs), second-order Møller–Plesset perturbation theory, range-separated hybrids, and experimental data. For conjugated polydiacetylene and polybutatriene oligomers, GKS-spRPA effectively addresses the “overpolarization” problem of semilocal DFAs and the somewhat erratic behavior of post-PBE RPA polarizabilities without empirical adjustments. The ensemble averaged GKS-spRPA polarizabilities of sodium clusters (Na n for n = 2, 3, …, 10) exhibit a mean absolute deviation comparable to PBE with significantly fewer outliers than HF. In conclusion, analytical second-order derivatives of GKS-spRPA energies provide a computationally viable and consistent approach to molecular polarizabilities, including systems prohibitive for other methods due to their size and/or electronic structure.