An effective set of Hartree-Fock (HF) equations are derived for electrons of muonic systems, i.e., molecules containing a positively charged muon, conceiving the muon as a quantum oscillator, which are completely equivalent to the usual two-component HF equations used to derive stationary states of the muonic molecules. In these effective equations, a non-Coulombic potential is added to the orthodox coulomb and exchange potential energy terms, which describes the interaction of the muon and the electrons effectively and is optimized during the self-consistent field cycles. While in the two-component HF equations a muon is treated as a quantum particle, in the effective HF equations it is absorbed into the effective potential and practically transformed into an effective potential field experienced by electrons. The explicit form of the effective potential depends on the nature of muon's vibrations and is derivable from the basis set used to expand the muonic spatial orbital. The resulting effective Hartree-Fock equations are implemented computationally and used successfully, as a proof of concept, in a series of muonic molecules containing all atoms from the second and third rows of the Periodic Table. To solve the algebraic version of the equations muon-specific Gaussian basis sets are designed for both muon and surrounding electrons and it is demonstrated that the optimized exponents are quite distinct from those derived for the hydrogen isotopes. The developed effective HF theory is quite general and in principle can be used for any muonic system while it is the starting point for a general effective electronic structure theory that incorporates various types of quantum correlations into the muonic systems beyond the HF equations.
The molecular docking simulation is a key computational tool in modern drug discovery research that its predictive performance strongly depends on the employed scoring functions. Many recent studies have shown that the application of machine learning algorithms in the development of scoring functions has led to a significant improvement in docking performance. In this work, we introduce a new machine learning (ML) based scoring function called ET-Score, which employs the distanceweighted interatomic contacts between atom type pairs of the ligand and the protein for featurizing protein À ligand complexes and Extremely Randomized Trees algorithm for the training process. The performance of ET-Score is compared with some successful ML-based scoring functions and several popular classical scoring functions on the PDBbind 2016v core set. It is shown that our ET-Score model (with Pearson's correlation of 0.827 and RMSE of 1.332) achieves very good performance in comparison with most of the ML-based scoring functions and all classical scoring functions despite its extremely low computational cost. ET-Score's codes are freely available on the web at https://github.com/miladrayka/ET_Score.
A set of effective electronic-only Kohn-Sham (EKS) equations are derived for the muonic molecules (containing a positively charged muon), which are completely equivalent to the coupled electronic-muonic Kohn-Sham equations derived previously within the framework of the nuclear-electronic orbital density functional theory (NEO-DFT). The EKS equations contain effective non-coulombic external potentials depending on parameters describing the muon's vibration, which are optimized during the solution of the EKS equations making the muon's KS orbital reproducible. It is demonstrated that the EKS equations are derivable from a certain class of effective electronic Hamiltonians through applying the usual Hohenberg-Kohn theorems revealing a "duality" between the NEO-DFT and the effective electronic-only DFT methodologies. The EKS equations are computationally applied to a small set of muoniated organic radicals and it is demonstrated that a mean effective potential may be derived for this class of muonic species while an electronic basis set is also designed for the muon. These computational ingredients are then applied to muoniated ferrocenyl radicals, which had been previously detected experimentally through adding a muonium atom to ferrocene. In line with previous computational studies, from the six possible species, the staggered conformer, where the muon is attached to the exo position of the cyclopentadienyl ring, is deduced to be the most stable ferrocenyl radical.
In recent years, thanks to advances in computer hardware and dataset availability, data-driven approaches (like machine learning) have become one of the essential parts of the drug design framework to accelerate drug discovery procedures. Constructing a new scoring function, a function that can predict the binding score for a generated protein-ligand pose during docking procedure or a crystal complex, based on machine and deep learning has become an active research area in computer-aided drug design. GB-Score is a state-ofthe-art machine learning-based scoring function that utilizes distance-weighted interatomic contact features, PDBbind-v2019 general set, and Gradient Boosting Trees algorithm to the binding affinity prediction. The distanceweighted interatomic contact featurization method used the distance between different ligand and protein atom types for numerical representation of the protein-ligand complex. GB-Score attains Pearson's correlation 0.862 and RMSE 1.190 on the CASF-2016 benchmark test in the scoring power metric. GB-Score's codes are freely available on the web at https://github.com/miladrayka/GB_Score.
In recent years, thanks to advances in computer hardware and dataset availability, data-driven approaches (like machine learning) have become one of the essential parts of the drug design framework to accelerate drug discovery procedures. Constructing a new scoring function, a function that can predict the binding score for a generated protein-ligand pose during docking procedure or a crystal complex, based on machine and deep learning has become an active research area in computer-aided drug design. GB-Score is a state-of-the-art machine learning-based scoring function that utilizes distance-weighted interatomic contact features, PDBbind-v2019 general set, and Gradient Boosting Trees algorithm to the binding affinity prediction. The distance-weighted interatomic contact featurization method used the distance between different ligand and protein atom types for numerical representation of the protein-ligand complex. GB-Score attains Pearson’s correlation 0.862 and RMSE 1.190 on the CASF-2016 benchmark test in the scoring power metric. GB-Score’s codes are freely available on the web at https://github.com/miladrayka/GB_Score.
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