The superposition of atomic potentials (SAP) approach has recently been shown to be a simple and efficient way to initialize electronic structure calculations [S. Lehtola, J. Chem. Theory Comput. 15, 1593-1604 (2019)]. Here, we study the differences between effective potentials from fully numerical density functional and optimized effective potential calculations for fixed configurations. click here We find that the differences are small, overall, and choose exchange-only potentials at the local density approximation level of theory computed on top of Hartree-Fock densities as a good compromise. The differences between potentials arising from different atomic configurations are also found to be small at this level of theory. Furthermore, we discuss the efficient Gaussian-basis implementation of SAP via error function fits to fully numerical atomic radial potentials. The guess obtained from the fitted potentials can be easily implemented in any Gaussian-basis quantum chemistry code in terms of two-electron integrals. Fits covering the whole periodic table from H to Og are reported for non-relativistic as well as fully relativistic four-component calculations that have been carried out with fully numerical approaches.Determining the influence of the solvent on electrochemical reaction energetics is a central challenge in our understanding of electrochemical interfaces. To date, it is unclear how well existing methods predict solvation energies at solid/liquid interfaces, since they cannot be assessed experimentally. Ab initio molecular dynamics (AIMD) simulations present a physically highly accurate, but also a very costly approach. In this work, we employ extensive AIMD simulations to benchmark solvation at charge-neutral metal/water interfaces against commonly applied continuum solvent models. We consider a variety of adsorbates including *CO, *CHO, *COH, *OCCHO, *OH, and *OOH on Cu, Au, and Pt facets solvated by water. The surfaces and adsorbates considered are relevant, among other reactions, to electrochemical CO2 reduction and the oxygen redox reactions. We determine directional hydrogen bonds and steric water competition to be critical for a correct description of solvation at the metal/water interfaces. As a consequence, we find that the most frequently applied continuum solvation methods, which do not yet capture these properties, do not presently provide more accurate energetics over simulations in vacuum. We find most of the computed benchmark solvation energies to linearly scale with hydrogen bonding or competitive water adsorption, which strongly differ across surfaces. Thus, we determine solvation energies of adsorbates to be non-transferable between metal surfaces, in contrast to standard practice.Minimum-energy conical intersection (MECI) geometries play an important role in photophysics, photochemistry, and photobiology. In a previous study [Nakai et al., J. Phys. Chem. A 122, 8905 (2018)], frozen orbital analysis at the MECI geometries between the ground and first electronic excited states (S0/S1 MECI), which considers the main configurations contributing to the excitation, inductively clarified two controlling factors. First, the exchange integral between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) approximately becomes zero. Second, the HOMO-LUMO gap becomes close to the HOMO-LUMO Coulomb integral. This study applies the controlling factors to the penalty function method, which is the standard MECI optimization technique, and minimizes the energy average of the two states with the constraint that the energy gap between the states vanishes. Numerical assessments clarified that the present method could obtain the S0/S1 MECI geometries more efficiently than the conventional one.Stochastic models are key to understanding the intricate dynamics of gene expression. However, the simplest models that only account for active and inactive states of a gene fail to capture common observations in both prokaryotic and eukaryotic organisms. Here, we consider multistate models of gene expression that generalize the canonical Telegraph process and are capable of capturing the joint effects of transcription factors, heterochromatin state, and DNA accessibility (or, in prokaryotes, sigma-factor activity) on transcript abundance. We propose two approaches for solving classes of these generalized systems. The first approach offers a fresh perspective on a general class of multistate models and allows us to “decompose” more complicated systems into simpler processes, each of which can be solved analytically. This enables us to obtain a solution of any model from this class. Next, we develop an approximation method based on a power series expansion of the stationary distribution for an even broader class of multistate models of gene transcription. We further show that models from both classes cannot have a heavy-tailed distribution in the absence of extrinsic noise. The combination of analytical and computational solutions for these realistic gene expression models also holds the potential to design synthetic systems and control the behavior of naturally evolved gene expression systems in guiding cell-fate decisions.When a dilute aqueous solution freezes at 1 atm, it is segregated into water-rich ice Ih and solute-rich freeze-concentrated glassy solution. A similar segregation is observed at the crystallization of homogeneous glassy aqueous solutions by heating. The influence of solutes on the nucleation of solvent water and the solute discharge process from the crystalline ice are not clear. In this study, I made a homogeneous dilute glassy glycerol aqueous solution (0.07 mol fraction) using pressure liquid cooling vitrification (PLCV), measured the specific volume and the sample temperature during the compression and decompression processes, and examined the polyamorphic and crystallization behaviors. It is found that the sample crystallized slightly above the crystallization temperature is amorphized homogeneously under pressure, and that the amorphized sample is equivalent to the homogeneous glassy sample made by PLCV. This indicates that glycerol solutes in the crystalline sample are dispersed homogeneously and the crystalline sample does not segregate.