Foundations

Stefan–Maxwell transport represents friction between different species rather than independent dilute diffusion through an inert solvent.

Current–potential data can reflect charge transfer, bulk migration/diffusion, homogeneous reactions and evolving surface structure.

Molar-mass dispersity is the ratio of mass-average to number-average molar mass.

Size-exclusion results depend on column, solvent and calibration, so retention-based molar masses are not intrinsically absolute.

Branching models locate gelation when continuing connections become self-sustaining.

A Maxwell spring and dashpot in series predicts exponential stress relaxation with a characteristic time.

For linear harmonic loading, the complex modulus separates in-phase elastic storage from quadrature viscous loss.

Corrected diffraction intensities constrain squared structure-factor amplitudes, while phases remain essential for reconstructing electron density.

Phase probabilities and map weighting affect reconstructed density, and model-derived phases can bias the apparent support for that same model.

The Br2+ attosecond study reports coherent vibronic signals and interprets their evolution using electronic/nuclear modeling with anharmonic and spin–orbit contributions.

Truncated CI can retain a variational upper bound yet fail size consistency because products of fragment excitations may lie outside its excitation space.

CCSD and perturbative-triples CCSD(T) truncate correlation differently from CI; FNO variants also truncate the virtual space using MP2-derived occupations.

CAS-CI solves the configuration problem within a selected active orbital/electron space; CASSCF also optimizes the orbital partition.

EOM-EE describes target electronic states by excitation operators acting on a correlated reference.

Fewest-switches surface hopping propagates classical nuclear trajectories on individual electronic surfaces with stochastic electronic transitions.

Molecular-dynamics convergence requires checking integration step, constraints and conserved quantities for the chosen ensemble.

QM/MM uses quantum treatment in a selected reactive region and a classical environment.

ReaxFF models changing bond order and charge equilibration using fitted parameters rather than evaluating an electronic wavefunction at each step.

Same-excess reaction-progress experiments compare rates at matched reactant concentrations but different catalyst histories; differences can reveal deactivation, product effects or activation.

An abundant observed catalyst state can be a resting state or off-cycle reservoir, while a low-population intermediate may carry productive flux.

Deuterium isotope effects can constrain C–H functionalization pathways, but their interpretation depends on whether rates, competition or product distributions were measured.

Carrow and Hartwig compared isolated palladium hydroxo/halide and boronic-acid/boronate species and their rates.

The 2025 copper study combines atomistic surface/kinetic calculations with STM comparison to examine CO-induced reconstruction during CO2 reduction.

A working electrocatalyst can change structure and coverage during operation.

The 2026 device study reports separating sorbent regeneration and CO2 liberation through redox-decoupled electrolysis.

The NIST-authored XPS guide emphasizes planning the specimen, measurement and reporting together.

XANES and EXAFS constrain absorption-edge and local-neighbor structure rather than directly determining every atom in a material.

Splitting particles into independent reconstruction/refinement halves helps detect overfitting through Fourier-shell correlation.

A useful chemical probe requires potency and selectivity in the relevant biochemical and cellular context.

When microscopy, spectroscopy and chemical perturbations support different models, compare their sampled populations, detection limits and environments before combining them.