The variational fitting of the Fock potential employing localized molecular orbitals requires either the inversion of the local two-center Coulomb matrices or alternatively the solution of corresponding linear equation systems with these matrices. In both cases, the method of choice is the Cholesky decomposition of the formally positive definite local two-center Coulomb matrices. However, due to finite-precision round-off errors, the local Coulomb matrices may be indefinite, and thus, the Cholesky decomposition is not applicable. To overcome this problem, we propose to make use of a modified Cholesky decomposition based on the indefinite factorization of local two-center Coulomb matrices. To this end, the working equations for the use of the modified Cholesky decomposition within the variational fitting of the Fock potential are presented. Benchmark calculations with global and range-separated hybrid functionals show that the proposed method can improve considerably the workload balance in parallel calculations.The swap Monte Carlo algorithm allows the preparation of highly stable glassy configurations for a number of glass-formers but is inefficient for some models, such as the much studied binary Kob-Andersen (KA) mixture. We have recently developed generalizations to the KA model where swap can be very effective. Here, we show that these models can, in turn, be used to considerably enhance the stability of glassy configurations in the original KA model at no computational cost. We successfully develop several numerical strategies both in and out of equilibrium to achieve this goal and show how to optimize them. We provide several physical measurements indicating that the proposed algorithms considerably enhance mechanical and thermodynamic stability in the KA model, including a transition toward brittle yielding behavior. Our results thus pave the way for future studies of stable glasses using the KA model.Many linear inversion problems involving Fredholm integrals of the first kind are frequently encountered in the field of magnetic resonance. One important application is the direct inversion of a solid-state nuclear magnetic resonance (NMR) spectrum containing multiple overlapping anisotropic subspectra to obtain a distribution of the tensor parameters. Because of the ill-conditioned nature of this inverse problem, we investigate the use of the truncated singular value decomposition and the smooth least absolute shrinkage and selection operator based regularization methods, which (a) stabilize the solution and (b) promote sparsity and smoothness in the solution. We also propose an unambiguous representation for the anisotropy parameters using a piecewise polar coordinate system to minimize rank deficiency in the inversion kernel. To obtain the optimum tensor parameter distribution, we implement the k-fold cross-validation, a statistical learning method, to determine the hyperparameters of the regularized inverse problem. In this article, we provide the details of the linear-inversion method along with numerous illustrative applications on purely anisotropic NMR spectra, both synthetic and experimental two-dimensional spectra correlating the isotropic and anisotropic frequencies.Molecular interactions are essential for regulation of cellular processes from the formation of multi-protein complexes to the allosteric activation of enzymes. Identifying the essential residues and molecular features that regulate such interactions is paramount for understanding the biochemical process in question, allowing for suppression of a reaction through drug interventions or optimization of a chemical process using bioengineered molecules. In order to identify important residues and information pathways within molecular complexes, the dynamical network analysis method was developed and has since been broadly applied in the literature. However, in the dawn of exascale computing, this method is frequently limited to relatively small biomolecular systems. In this work, we provide an evolution of the method, application, and interface. All data processing and analysis are conducted through Jupyter notebooks, providing automatic detection of important solvent and ion residues, an optimized and parallel generalized correlation implementation that is linear with respect to the number of nodes in the system, and subsequent community clustering, calculation of betweenness of contacts, and determination of optimal paths. Using the popular visualization program visual molecular dynamics (VMD), high-quality renderings of the networks over the biomolecular structures can be produced. Our new implementation was employed to investigate three different systems, with up to 2.5M atoms, namely, the OMP-decarboxylase, the leucyl-tRNA synthetase complexed with its cognate tRNA and adenylate, and respiratory complex I in a membrane environment. Our enhanced and updated protocol provides the community with an intuitive and interactive interface, which can be easily applied to large macromolecular complexes.Two or more liquid states may exist even for single-component substances, which is known as liquid polymorphism, and the transition between them is called liquid-liquid transition (LLT). On the other hand, the existence of two or more amorphous states is called polyamorphism, and the transition between them is called amorphous-amorphous transition (AAT). Recently, we have accumulated a lot of experimental and numerical evidence for LLT and AAT. These intriguing phenomena provide crucial information on the fundamental nature of liquid and amorphous states. Here, we review the recent progress in this field and discuss how we can physically rationalize the existence of two or more liquids (glasses) for a single-component substance. We also discuss the relationship between liquid-, amorphous-, and crystal-polymorphisms, putting a particular focus on the roles of thermodynamics, mechanics, and kinetics.The low temperature transport of electron, or vibrational or electronic exciton toward polymer chains, turns out to be dramatically sensitive to its interaction with transverse acoustic vibrations.  https://www.selleckchem.com/  We show that this interaction leads to a substantial polaron effect and decoherence, which are generally stronger than those associated with longitudinal vibrations. For site-dependent interactions, transverse phonons form subohmic bath leading to the quantum phase transition accompanied by full suppression of the transport at zero temperature and fast decoherence characterized by temperature dependent rate k2 ∝ T3/4 at low temperature, while k2 ∝ T2 for site-independent interactions. The latter dependence was used to interpret recent measurements of temperature dependent vibrational energy transport in polyethylene glycol oligomers.