Multi-objective optimization via equivariant deep hypervolume approximation

Optimizing multiple competing objectives is a common problem across science and industry. The inherent inextricable trade-off between those objectives leads one to the task of exploring their Pareto front. A meaningful quantity for the purpose of the latter is the hypervolume indicator, which is used in Bayesian Optimization (BO) and Evolutionary Algorithms (EAs). However, the computational complexity for the calculation of the hypervolume scales unfavorably with increasing number of objectives and data points, which restricts its use in those common multi-objective optimization frameworks. To overcome these restrictions we propose to approximate the hypervolume function with a deep neural network, which we call DeepHV. For better sample efficiency and generalization, we exploit the fact that the hypervolume is scale-equivariant in each of the objectives as well as permutation invariant w.r.t. both the objectives and the samples, by using a deep neural network that is equivariant w.r.t. the combined group of scalings and permutations. We evaluate our method against exact, and approximate hypervolume methods in terms of accuracy, computation time, and generalization. We also apply and compare our methods to state-of-the-art multi-objective BO methods and EAs on a range of synthetic benchmark test cases. The results show that our methods are promising for such multi-objective optimization tasks.Comment: Updated with camera-ready version. Accepted at ICLR 202

Reaction mechanism of hydrogen activation by frustrated Lewis pairs

Typically, a Lewis acid and a base react with each other and form classic acid base adducts. The neutralization reaction is however prevented by the introduction of bulky substitutes and this interesting finding leads to a new concept called frustrated Lewis pairs, FLPs. Since both reactivities of Lewis acids and bases are remained in the same systems, FLPs have been shown many important applications. One of them is hydrogen activation, which showed for the first time the use of a non metal catalyst for that purpose. In this mini review, we have summarized all important findings regarding the H2 activation by FLPs. This includes preorganisation of FLPs, reaction path for the activation, polarization of HH bond and the factors affected the reactivity. In light of some recent developments, we aim to clarify the reaction mechanism for the H2 actitation by FLPs, which has been under debate for decades since the first discovery of FLPs. We believe that this mini review can be served as a guideline for the future fundamental studies and industrial applications

QM/MM study of proton transport process in [FeFe] hydrogenase enzyme

Di-iron hydrogenases are a class of enzymes that are capable of reducing protons to form molecular hydrogen with high efficiency. In addition to the catalytic site, these enzymes have evolved dedicated pathways to transport protons and electrons to the reaction center. Here, we present a detailed study of the most likely proton trans- fer pathway in such an enzyme using QM/MM molecular dynamics simulations. The protons are transported through a channel lined out from the protein exterior to the di-iron active site, by a series of hydrogen-bonded, weakly acidic or basic, amino-acids and two incorporated water molecules. Proton transport takes place via a ”hole” mech- anism, rather than an excess proton mechanism, the free energy landscape of which is remarkably flat, with a highest transition state barrier of only 5 kcal/mol. These results confirm our previous assumptions that proton transport is not rate limiting in the H2 formation activity and that cystene C299 may be considered protonated at physiological pH conditions. Detailed understanding of this proton transport may aid in the ongoing attempts to design artificial bio-mimetic hydrogenases for hydrogen fuel production

Redox Properties of Flavin in BLUF and LOV Photoreceptor Proteins from Hybrid QM/MM Molecular Dynamics Simulation

Flavins play an important role in many oxidation and reduction processes in bio- logical systems. For example, flavin adenine dinucleotide (FAD) and flavin mononu- cleotide (FMN) are common cofactors found in enzymatic proteins that use the special redox properties of these flavin molecules for their catalytic or photoactive functions. The redox potential of the flavin is strongly affected by its (protein) environment, however the underlying molecular interactions of this effect are still unknown. Using hybrid Quantum Mechanics / Molecular Mechanics (QM/MM) simulation techniques, we have studied the redox properties of flavin in the gas phase, aqueous solution and two different protein environments, in particular a BLUF and a LOV photoreceptor domain. By mapping the changes in electrostatic potential and solvent structure, we gain insight in how specific polarization of the flavin by its environment tunes the re- duction potential. We find also that accurate calculation of the reduction potentials of these systems by using the hybrid QM/MM approach is hampered by a too limited sampling of the counter ion configurations and by artifacts at the QM/MM boundary. We make suggestions on how these issues can be overcome

Reactive trajectories of the Ru2+/3+ self-exchange reaction and the connection to Marcus' theory

Outer sphere electron transfer between two ions in aqueous solution is a rare event on the time scale of first principles molecular dynamics simulations. We have used transition path sampling to generate an ensemble of reactive trajectories of the self-exchange reaction between a pair of Ru and Ru ions in water. To distinguish between the reactant and product states, we use as an order parameter the position of the maximally localised Wannier center associated with the transferring electron. This allows us to align the trajectories with respect to the moment of barrier crossing and compute statistical averages over the path ensemble. We compare our order parameter with two typical reaction coordinates used in applications of Marcus theory of electron transfer: the vertical gap energy and the solvent electrostatic potential at the ions.This work is part of the Industrial Partnership Programme (IPP) ‘Computational sciences for energy research’ of the Foundation for Fundamental Research on Matter (FOM), which is part of the Netherlands Organisation for Scientific Research (NWO). This research programme is co-financed by Shell Global Solutions International B.V. The calculations were carried out on the Dutch national einfrastructure with the support of the SURF Cooperative.Peer Reviewe