Foundations

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.

The RNA-condensate interface study measures in-vitro RNA/PEG systems and compares interface behavior with molecular modeling.

Assembly, partitioning and a cellular phenotype do not alone identify whether phase separation causally produces that phenotype.

Gadd and colleagues resolved a Brd4 bromodomain–MZ1–VHL complex and combined binding, mutagenesis, proximity and cell-protein measurements.

The D statistic compares two discordant allele-sharing patterns in an ordered four-sample test.

Reaction stoichiometry relates species-amount changes to reaction and exchange fluxes.

GUIDE-seq detects tagged double-strand-break locations by oligonucleotide integration and sequencing.

EmptyDrops tests barcode expression against an ambient-RNA null rather than relying solely on total-count thresholds.

UMIs help distinguish amplified reads from captured molecules, but barcode errors and finite capture affect estimated counts.

In Lecuit’s nondimensional two-cell example, the isolated reaction Jacobian has eigenvalues −1, whereas an antisymmetric spatial mode can become unstable after unequal diffusive coupling.

Dupont and colleagues altered substrate rigidity and cell geometry and tested actomyosin/Rho and YAP/TAZ responses in specified cultured mammalian cells.