Notes

Wilson's Condition: Dealing with task regarding Figuring out a Rare Condition.
Motivated by renewed interest in the physics of branched polymers, we present here a detailed characterization of the connectivity and spatial properties of 2- and 3-dimensional single-chain conformations of randomly branching polymers under θ-solvent conditions obtained by Monte Carlo computer simulations. The first part of the work focuses on polymer average properties, such as the average polymer spatial size as a function of the total tree mass and the typical length of the average path length on the polymer backbone. In the second part, we move beyond average chain behavior and we discuss the complete distribution functions for tree paths and tree spatial distances, which are shown to obey the classical Redner-des Cloizeaux functional form. Our results were rationalized first by the systematic comparison to a Flory theory for branching polymers and next by generalized Fisher-Pincus relationships between scaling exponents of distribution functions. For completeness, the properties of θ-polymers were compared to their ideal (i.e., no volume interactions) as well as good-solvent (i.e., above the θ-point) counterparts. The results presented here complement the recent work performed in our group [A. Rosa and R. Everaers, J. Phys. A Math. Theor. 49, 345001 (2016); J. Chem. Phys. 145, 164906 (2016); and Phys. Rev. E 95, 012117 (2017)] in the context of the scaling properties of branching polymers.In order to study the spin-orbit charge transfer induced intersystem crossing (SOCT-ISC), Bodipy (BDP)-carbazole (Cz) compact electron donor/acceptor dyads were prepared. Charge transfer (CT) emission bands were observed for dyads showing strong electronic coupling between the donor and the acceptor (coupling matrix elements VDA, 0.06 eV-0.18 eV). Depending on the coupling magnitude, the CT state of the dyads can be either dark or emissive. Equilibrium between the 1LE (locally excited) state and the 1CT state was confirmed by temperature-dependent fluorescence studies. Efficient ISC was observed for the dyads with Cz connected at the meso-position of the BDP. Interestingly, the dyad with non-orthogonal geometry shows the highest ISC efficiency (ΦΔ = 58%), which is different from the previous conclusion. The photo-induced charge separation (CS, time constant 0.7 ps) and charge recombination (CR, ∼3.9 ns) were studied by femtosecond transient absorption spectroscopy. Nanosecond transient absorption spectroscopy indicated that the BDP-localized triplet state was exceptionally long-lived (602 µs). Using pulsed laser excited time-resolved electron paramagnetic resonance spectroscopy, the SOCT-ISC mechanism was confirmed, and we show that the electron spin polarization of the triplet state is highly dependent on the mutual orientation of the donor and acceptor. The dyads were used as triplet photosensitizers for triplet-triplet-annihilation (TTA) upconversion, and the quantum yield is up to 6.7%. TTA-based delayed fluorescence was observed for the dyads (τDF = 41.5 µs). The dyads were also used as potent photodynamic therapy reagents (light toxicity of IC50 = 0.1 µM and dark toxicity of IC50 = 70.8 µM).A Machine-Learning based Deep Potential (DP) model for Al clusters is developed through training with an extended database including ab initio data of both bulk and several clusters in only 6 CPU/h. This DP model has good performance in accurately predicting the low-lying candidates of Al clusters in a broad size range. Based on our developed DP model, the low-lying structures of 101 different sized Al clusters are extensively searched, among which the lowest-energy candidates of 69 sized clusters are updated. Our calculations demonstrate that machine-learning is indeed powerful in generating potentials to describe the interaction of atoms in complex materials.Until now, the potential energy surfaces (PESs) of the ArNO complex found in the literature were two-dimensional, with the NO interatomic distance being fixed. In this work, we present the first accurate three-dimensional ground state X̃ 2Π PESs (both A' and A″) of ArNO computed at the CCSD(T)/CBS level of theory. The equilibrium geometries and the well depths (De) are compared to several other electronic structure methods. We found that using the multireference method, MRCI-F12 makes the surfaces much shallower (by 25%) and the depth of the surfaces does not agree with experimental data. The explicitly correlated coupled-cluster method underestimates the well depth as well. Analytic representations for both A' and A″ surfaces were fit to 4380 ab initio points to within 2.71 cm-1. A three-dimensional Numerov propagator method in Delves coordinates is used to compute the bound state spectrum up to Jtot = 6.5. The recommended dissociation energies are D0 = 97.2 cm-1 for the adiabatic ground state and De = 133.7 (128.1) cm-1 for A' (A″).A fractional Fokker-Planck equation based on the continuous time random walk Ansatz is written via the Langevin equations for the dynamics of a dipole interacting with its surroundings, as represented by a cage of dipolar molecules. This equation is solved in the frequency domain using matrix continued fractions, thus yielding the linear dielectric response for extensive ranges of damping, dipole moment ratio, and cage-dipole inertia ratio, and hence the complex susceptibility. The latter comprises a low frequency band with width depending on the anomalous parameter and a far infrared (THz) band with a comb-like structure of peaks. Several physical consequences of the model relevant to anomalous diffusion in the presence of interactions are discussed. The entire calculation may be regarded as an extension of the cage model interpretation of the dynamics of polar molecules to anomalous diffusion, taking into account inertial effects.The time-independent eigenstate-free Raman wavefunction approach for calculating anharmonic vibronic spectra has been extended for the calculation of Herzberg-Teller contributions on the basis of an n-mode expansion of the transition electric dipole moment surface. This allows for the efficient simulation of Franck-Condon dark vibronic spectra. check details In addition, vibrational angular momentum terms have been implemented into this formalism, as they are important for an accurate description of vibrational wavefunctions spanning double-well potentials. This approach has been used to compute the FC-forbidden vibronic spectrum of the n → π* transition of formaldehyde based on a potential energy and transition dipole moment surfaces obtained from explicitly correlated multi-reference configuration interaction calculations. An extensive analysis of the resulting vibronic structure is provided, which allows for a detailed assignment and interpretation of the experimental spectrum.
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