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A slight modification of the original Hamiltonian is introduced to avoid accumulation of small numerical errors incurred after each switching process.In this article, we report the use of randomly structured light illumination for chemical imaging of molecular distribution based on Raman microscopy with improved image resolution. Random structured basis images generated from temporal and spectral characteristics of the measured Raman signatures were superposed to perform structured illumination microscopy (SIM) with the blind-SIM algorithm. For experimental validation, Raman signatures corresponding to Rhodamine 6G (R6G) in the waveband of 730-760 nm and Raman shift in the range of 1096-1634 cm-1 were extracted and reconstructed to build images of R6G. The results confirm improved image resolution using the concept and hints at super-resolution by almost twice better than the diffraction-limit.Modeling linear absorption spectra of solvated chromophores is highly challenging as contributions are present both from coupling of the electronic states to nuclear vibrations and from solute-solvent interactions. In systems where excited states intersect in the Condon region, significant non-adiabatic contributions to absorption line shapes can also be observed. Here, we introduce a robust approach to model linear absorption spectra accounting for both environmental and non-adiabatic effects from first principles. This model parameterizes a linear vibronic coupling (LVC) Hamiltonian directly from energy gap fluctuations calculated along molecular dynamics (MD) trajectories of the chromophore in solution, accounting for both anharmonicity in the potential and direct solute-solvent interactions. The resulting system dynamics described by the LVC Hamiltonian are solved exactly using the thermalized time-evolving density operator with orthogonal polynomials algorithm (T-TEDOPA). The approach is applied to the linear absorption spectrum of methylene blue in water. We show that the strong shoulder in the experimental spectrum is caused by vibrationally driven population transfer between the bright S1 and the dark S2 states. The treatment of the solvent environment is one of many factors that strongly influence the population transfer and line shape; accurate modeling can only be achieved through the use of explicit quantum mechanical solvation. The efficiency of T-TEDOPA, combined with LVC Hamiltonian parameterizations from MD, leads to an attractive method for describing a large variety of systems in complex environments from first principles.The efficacy in 1H Overhauser dynamic nuclear polarization in liquids at ultralow magnetic field (ULF, B0 = 92 ± 0.8 µT) and polarization field (Bp = 1-10 mT) was studied for a broad variety of 26 different spin probes. Among others, piperidine, pyrrolidine, and pyrroline radicals specifically synthesized for this study, along with some well-established commercially available nitroxides, were investigated. Isotope-substituted variants, some sterically shielded reduction-resistant nitroxides, and some biradicals were included in the measurements. The maximal achievable enhancement, Emax, and the radio frequency power, P1/2, needed for reaching Emax/2 were measured. Physico-chemical features such as molecular weight, spectral linewidth, heterocyclic structure, different types of substituents, deuteration, and 15N-labeling as well as the difference between monoradicals and biradicals were investigated. For the unmodified nitroxide radicals, the Emax values correlate with the molecular weight. The P1/2 values correlate with the spectral linewidth and are additionally influenced by the type of substituents neighboring the nitroxide group. The nitroxide biradicals with high intramolecular spin-spin coupling show low performance. Nitroxides enriched with 15N and/or 2H afford significantly higher |Emax| and require lower power to do so, compared to their unmodified counterparts containing at natural abundance predominantly 14N and 1H. The results allow for a correlation of chemical features with physical hyperpolarization-related properties and indicate that small nitroxides with narrow spectral lines have clear advantages for the use in Overhauser dynamic nuclear polarization experiments. Perdeuteration and 15N-labeling can be used to additionally boost the spin probe performance.We explore how the entropic notion of depletion forces between spheres, introduced by Asakura and Oosawa, can be extended to depletion torques that affect the orientations of colloidal particles having complex shapes. In prior experimental work, systems of microscale plate-like particles in the presence of a nanoscale depletion agent have been shown to form polymer-like columnar chains; restoring depletion torques act to align lithographically-structured platelets within a chain orientationally about the chain's axis. We consider depletion torques corresponding to parallel, face-to-face, near-contact pair interactions for complex-shaped, plate-like, prismatic lithographic particles in colloidal dispersions containing a spherical nanoscale depletion agent. We calculate depletion torques for a wide variety of such particles, including rotationally symmetric, asymmetric, achiral, chiral, and elongated particles. Moreover, we determine depletion torques between two non-parallel proximate square platelets connected by a lossless hinge along a common edge. Our investigations show that depletion torques can be tailored through lithographic or synthetic design of specific geometrical features in the shapes of particles.Despite the emergence of a molecular picture of urea's protein unfolding mechanism in the past few decades, less is known about its action mechanism on protein aggregation. This is especially relevant for understanding the aggregation of amyloid proteins and peptides, implicated in several neurodegenerative diseases. While urea is believed to weaken the hydrophobic effect, a picture consistent with the decrease in the excess chemical potential of sufficiently large alkanes, interactions with protein polar side chains and backbone atoms are also important. Here, we study, through molecular dynamics, the hydration and aggregation of several alkanes and amphiphilic "mutants" of n-dodecane, in an 8M aqueous urea solution, aiming at getting insight into urea's mode of action. A size-dependent crossover temperature is found, above which the hydration of the alkanes is favored in the aqueous urea solution. The hydration of the alkanes is enhanced via entropy, with the enthalpy opposing hydration, consistent with experiments. The reason is that although solute-solvent interactions are favorable, these are overwhelmed by urea-water and urea-urea interactions. In contrast, water-water interactions and entropy are favored by a water depletion around the solute and a reduced water depletion around methane explains its exceptional solubility decrease. Furthermore, we show that while urea favors the hydration of n-dodecane and the amphiphilic mutants, it slightly enhances and reduces, respectively, the aggregation of the alkanes and the amphiphilic mutants. Thus, opposite to the common view, our results show that urea does not necessarily weaken hydrophobic interactions despite solvation being favored.The strong-correlation factor of the recent KP16/B13 exchange-correlation functional has been adapted and applied to the framework of local hybrid (LH) functionals. selleck compound The expression identifiable as nondynamical (NDC) and dynamical (DC) correlations in LHs is modified by inserting a position-dependent KP16/B13-style strong-correlation factor qAC(r) based on a local version of the adiabatic connection. Different ways of deriving this factor are evaluated for a simple one-parameter LH based on the local density approximation. While the direct derivation from the LH NDC term fails due to known deficiencies, hybrid approaches, where the factor is determined from the B13 NDC term as in KP16/B13 itself, provide remarkable improvements. In particular, a modified B13 NDC expression using Patra's exchange-hole curvature showed promising results. When applied to the simple LH as a first attempt, it reduces atomic fractional-spin errors and deficiencies of spin-restricted bond dissociation curves to a similar extent as the KP16/B13 functional itself while maintaining the good accuracy of the underlying LH for atomization energies and reaction barriers in weakly correlated situations. The performance of different NDC expressions in deriving strong-correlation corrections is analyzed, and areas for further improvements of strong-correlation corrected LHs and related approaches are identified. All the approaches evaluated in this work have been implemented self-consistently into a developers' version of the Turbomole program.Finite Markov chains, memoryless random walks on complex networks, appear commonly as models for stochastic dynamics in condensed matter physics, biophysics, ecology, epidemiology, economics, and elsewhere. Here, we review exact numerical methods for the analysis of arbitrary discrete- and continuous-time Markovian networks. We focus on numerically stable methods that are required to treat nearly reducible Markov chains, which exhibit a separation of characteristic timescales and are therefore ill-conditioned. In this metastable regime, dense linear algebra methods are afflicted by propagation of error in the finite precision arithmetic, and the kinetic Monte Carlo algorithm to simulate paths is unfeasibly inefficient. Furthermore, iterative eigendecomposition methods fail to converge without the use of nontrivial and system-specific preconditioning techniques. An alternative approach is provided by state reduction procedures, which do not require additional a priori knowledge of the Markov chain. Macroscopic dynamical quantities, such as moments of the first passage time distribution for a transition to an absorbing state, and microscopic properties, such as the stationary, committor, and visitation probabilities for nodes, can be computed robustly using state reduction algorithms. The related kinetic path sampling algorithm allows for efficient sampling of trajectories on a nearly reducible Markov chain. Thus, all of the information required to determine the kinetically relevant transition mechanisms, and to identify the states that have a dominant effect on the global dynamics, can be computed reliably even for computationally challenging models. Rare events are a ubiquitous feature of realistic dynamical systems, and so the methods described herein are valuable in many practical applications.Lattice models are a useful tool to simulate the kinetics of surface reactions. Since it is expensive to propagate the probabilities of the entire lattice configurations, it is practical to consider the occupation probabilities of a typical site or a cluster of sites instead. This amounts to a moment closure approximation of the chemical master equation. Unfortunately, simple closures, such as the mean-field and the pair approximation (PA), exhibit weaknesses in systems with significant long-range correlation. In this paper, we show that machine learning (ML) can be used to construct accurate moment closures in chemical kinetics using the lattice Lotka-Volterra model as a model system. We trained feedforward neural networks on kinetic Monte Carlo (KMC) results at select values of rate constants and initial conditions. Given the same level of input as PA, the ML moment closure (MLMC) gave accurate predictions of the instantaneous three-site occupation probabilities. Solving the kinetic equations in conjunction with MLMC gave drastic improvements in the simulated dynamics and descriptions of the dynamical regimes throughout the parameter space.