The effect of reversible energy hopping between different local environments on the properties of spin-polarized excited states is investigated theoretically using a two-site model. The kinetic equations for the populations of the spin sublevels of the excited state are derived and then used to obtain analytical expressions for the evolution of the spin polarization of excited triplet states under specific conditions. The time dependence of the triplet state polarization patterns is also obtained by numerical solution of the kinetic equations. It is shown that the reversible energy hopping can lead to significant changes in the properties of the triplet state, including changes in the shape of the observed spectrum and, in some cases, the inversion of the sign of the polarization, the generation of the net polarization, and anisotropic spin-lattice relaxation. The relations between the parameters that can be observed experimentally by time-resolved electron paramagnetic resonance spectroscopy and the kinetic and dynamic parameters of the system are discussed.Due to the intrinsic complexity and nonlinearity of chemical reactions, direct applications of traditional machine learning algorithms may face many difficulties. In this study, through two concrete examples with biological background, we illustrate how the key ideas of multiscale modeling can help to greatly reduce the computational cost of machine learning, as well as how machine learning algorithms perform model reduction automatically in a time-scale separated system. Our study highlights the necessity and effectiveness of an integration of machine learning algorithms and multiscale modeling during the study of chemical reactions.In this work, we present a relativistic quantum embedding formalism capable of variationally treating relativistic effects, including scalar-relativity and spin-orbit coupling. We extend density functional theory (DFT)-in-DFT projection-based quantum embedding to a relativistic two-component formalism, where the full spin magnetization vector form is retained throughout the embedding treatment. To benchmark various relativistic embedding schemes, spin-orbit splitting of the nominally t2g valence manifold of W(CO)6, exchange coupling of [(H3N)4Cr(OH)2Cr(NH3)4]4+, and the dissociation potential curve of WF6 are investigated. The relativistic embedding formalism introduced in this work is well suited for efficient modeling of open-shell systems containing late transition metal, lanthanide, and actinide molecular complexes.Elusive [S, S, N, O] isomers including the perthiyl radical •SSNO are S/N hybrid species in the complex bioinorganic chemistry of signaling molecules H2S and •NO. By mixing thermally generated disulfur (S2) with •NO in the gas phase, •SSNO was generated and subsequently isolated in cryogenic Ar- and N2-matrices at 10.0 K and 15.0 K, respectively. Upon irradiation with a 266 nm laser, •SSNO isomerizes to novel sulfinyl radicals cis-NSSO• and trans-NSSO• as well as thiyl radicals cis-OSNS• and trans-OSNS•, which have been characterized by combining matrix-isolation IR (15N-labeling) and UV/Vis spectroscopy and quantum chemical calculations at the CCSD(T)-F12/cc-pVTZ-F12 level of theory. The photo-induced reversible interconversion between NSSO• and OSNS• has also been observed.Evolution of quantum mechanical systems under time-dependent Hamiltonians has remained a challenging problem of interest across all disciplines. Through suitable approximations, different averaging methods have emerged in the past for modeling the time-evolution under time-dependent Hamiltonians. To this end, the development of analytic methods in the form of time-averaged effective Hamiltonians has gained prominence over other methods. In particular, the advancement of spectroscopic methods for probing molecular structures has benefited enormously from such theoretical pursuits. Nonetheless, the validity of the approximations and the exactness of the proposed effective Hamiltonians have always remained a contentious issue. Here, in this report, we reexamine the equivalence between the effective Hamiltonians derived from the Magnus formula and Floquet theory through suitable examples in magnetic resonance.Stereodynamics of cold collisions has become a fertile ground for sensitive probe of molecular collisions and control of the collision outcome. A benchmark system for stereodynamic control of rotational transition is He + HD. This system was recently probed experimentally by Perreault et al.  https://www.selleckchem.com/products/sj6986.html  by examining quenching from j = 2 to j' = 0 state in the v = 1 vibrational manifold of HD. Here, through explicit quantum scattering calculations on a highly accurate ab initio interaction potential for He + H2, we reveal how a combination of two shape resonances arising from l = 1 and l = 2 partial waves controls the stereodynamic outcome rather than a single l = 2 partial wave attributed in the experiment. Furthermore, for collision energies below 0.5 cm-1, it is shown that stereodynamic preference for the integral cross section follows a simple universal trend.Hydrodynamic flow can have complex and far-reaching consequences on the rate of homogeneous nucleation. We present a general formalism for calculating the nucleation rates of simply sheared systems. We have derived an extension to the conventional Classical Nucleation Theory, explicitly embodying the shear rate. Seeded molecular dynamics simulations form the backbone of our approach. The framework can be used for moderate supercooling, at which temperatures brute-force methods are practically infeasible. The competing energetic and kinetic effects of shear arise naturally from the equations. We show how the theory can be used to identify shear regimes of ice nucleation behavior for the mW water model, unifying disparate trends reported in the literature. At each temperature, we define a crossover shear rate in the limit of 1000 s-1-10 000 s-1, beyond which the nucleation rate increases steadily up to a maximum, at the optimal shear rate. For 235 K, 240 K, 255 K, and 260 K, the optimal shear rates are in the range of ≈106 s-1-107 s-1.