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Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method that increases convergence in systems composed of many metastable states. This method aims to connect metastable regions directly using generative neural networks in order to propose new configurations in the Markov chain and optimizes the acceptance probability of large jumps between modes in the configuration space. We provide a comprehensive theory as well as a training scheme for the network and demonstrate the method on example systems.Minor structural modifications to the DNA and RNA nucleobases have a significant effect on their excited state dynamics and electronic relaxation pathways. In this study, the excited state dynamics of 7-deazaguanosine and guanosine 5'-monophosphate are investigated in aqueous solution and in a mixture of methanol and water using femtosecond broadband transient absorption spectroscopy following excitation at 267 nm. The transient spectra are collected using photon densities that ensure no parasitic multiphoton-induced signal from solvated electrons. The data can be fit satisfactorily using a two- or three-component kinetic model. By analyzing the results from steady-state, time-resolved, computational calculations, and the methanol-water mixture, the following general relaxation mechanism is proposed for both molecules, Lb → La → 1πσ*(ICT) → S0, where the 1πσ*(ICT) stands for an intramolecular charge transfer excited singlet state with significant πσ* character. In general, longer lifetimes for internal conversion are obtained for 7-deazaguanosine compared to guanosine 5'-monophosphate. Internal conversion of the 1πσ*(ICT) state to the ground state occurs on a similar time scale of a few picoseconds in both molecules. learn more Collectively, the results demonstrate that substitution of a single nitrogen atom for a methine (C-H) group at position seven of the guanine moiety stabilizes the 1ππ* Lb and La states and alters the topology of their potential energy surfaces in such a way that the relaxation dynamics in 7-deazaguanosine are slowed down compared to those in guanosine 5'-monophosphate but not for the internal conversion of 1πσ*(ICT) state to the ground state.Comprehensive calculations were performed to predict the phase behavior of large spherical colloids mixed with small spherical colloids that act as a depletant. To this end, the free volume theory (FVT) of Lekkerkerker et al. [Europhys. Lett. 20, 559 (1992)] is used as a basis and is extended to explicitly include the hard-sphere character of colloidal depletants into the expression for the free volume fraction. Taking the excluded volume of the depletants into account in both the system and the reservoir provides a relation between the depletant concentration in the reservoir and that in the system that accurately matches with computer simulation results of Dijkstra et al. [Phys. Rev. E 59, 5744 (1999)]. Moreover, the phase diagrams for highly asymmetric mixtures with size ratios q ≲ 0.2 obtained by using this new approach corroborate simulation results significantly better than earlier FVT applications to binary hard-sphere mixtures. The phase diagram of a binary hard-sphere mixture with a size ratio of q = 0.4, where a binary interstitial solid solution is formed at high densities, is investigated using a numerical free volume approach. At this size ratio, the obtained phase diagram is qualitatively different from previous FVT approaches for hard-sphere and penetrable depletants but again compares well with simulation predictions.Recently, it has been proved that a set of spherically symmetric non-degenerate densities determines uniquely the Coulomb external potential. This theory is now extended to degenerate states. Euler equations and Kohn-Sham equations are derived and a novel form of the virial theorem is presented. It is emphasized that degenerate states of atoms can be rigorously treated as spherically symmetric when a subspace density is used with equal weighting factors.We propose a novel class of responsive polymer brushes, where the effective grafting density can be controlled by external stimuli. This is achieved by using end-grafted polymer chains that have an affinity to the substrate. For sufficiently strong surface interactions, a fraction of chains condenses into a near-surface layer, while the remaining ones form the outer brush. The dense layer and the more tenuous outer brush can be seen as coexisting microphases. The effective grafting density of the outer brush is controlled by the adsorption strength and can be changed reversibly and in a controlled way as a response to changes in environmental parameters. The effect is demonstrated by numerical self-consistent field calculations and analyzed by scaling arguments. Since the thickness of the denser layer is about a few monomer sizes, its capacity to form a microphase is limited by the product of the brush chain length and the grafting density. We explore the range of chain lengths and grafting densities where the effect is most pronounced. In this range, the SCF studies suggest that individual chains inside the brush show large rapid fluctuations between two states that are separated by only a small free energy barrier. The behavior of the brush as a whole, however, does not reflect these large fluctuations, and the effective grafting density varies smoothly as a function of the control parameters.The equilibrium cluster fluid state of a symmetric binary mixture of particles interacting through short-ranged attractive and long-ranged repulsive interactions is investigated through Monte Carlo simulations. We find that the clustering behavior of this system is controlled by the cross-interaction between the two types of particles. For a weak cross-attraction, the system displays a behavior that is a composite of the behavior of individual components, i.e., the two components can both form giant clusters independently and the clusters distribute evenly in the system. For a strong cross-attraction, we instead find that the resulting clusters are mixtures of both components. Between these limits, both components can form relatively pure clusters, but unlike clusters can join at their surfaces to form composite clusters. These insights should help to understand the mechanisms for clustering in experimental binary mixture systems and help tailor the properties of novel nanomaterials.
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