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It is broadly recognized that intramolecular electric fields, produced by the protein scaffold and acting on the active site, facilitate enzymatic catalysis. This field effect can be described by several theoretical models, each of which is intuitive to varying degrees. In this contribution, we show that a fundamental effect of electric fields is to generate electrostatic potentials that facilitate the energetic alignment of reactant frontier orbitals. We apply this model to demystify the impact of electric fields on high-valent iron–oxo heme proteins: catalases, peroxidases, and peroxygenases/monooxygenases. Specifically, we show that this model easily accounts for the observed field-induced changes to the spin distribution within peroxidase active sites and explains the transition between epoxidation and hydroxylation pathways seen in Cytochrome P450 active site models. Thus, for the intuitive interpretation of the chemical effect of the field, the strategy involves analyzing the response of the orbitals of active site fragments, and their energetic alignment. We note that the energy difference between fragment orbitals involved in charge redistribution acts as a measure for the chemical hardness/softness of the reactive complex. This measure, and its sensitivity to electric fields, offers a single parameter model from which to quantitatively assess the effects of electric fields on reactivity and selectivity. Thus, the model provides an additional perspective to describe electrostatic preorganization and offers ways for its manipulation. 

By leveraging the fundamental doctrine of the quantum theory of atoms in molecules — the partitioning of the electron charge density (ρ) into regions bounded by surfaces of zero flux — we map the gradient field of ρ onto a two-dimensional space called the gradient bundle condensed charge density ([Formula: see text]). The topology of [Formula: see text] appears to correlate with regions of chemical significance in ρ. The bond wedge is defined as the image in ρ of the basin of attraction in [Formula: see text], analogous to the Bader atom, which is the basin of attraction in ρ. A bond bundle is defined as the union of bond wedges that share interatomic surfaces. We show that maxima in [Formula: see text] typically map to bond paths in ρ, though this is not necessarily always true. This observation addresses many of the concerns regarding the chemical significance of bond critical points and bond paths in the quantum theory of atoms in molecules. 

Abstract Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counterintuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfvén waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold,α= 2 as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed >600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: preflare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine thatα= 1.63 ± 0.03. This is below the critical threshold, suggesting that Alfvén waves are an important driver of coronal heating.