A normalized product of two identical bonding orbitals built from separated orthogonal centers has finite weight in configurations with both electrons on one center. Repulsion penalizes that ionic weight even when hopping disappears. Mixing configurations can instead approach one electron per center while preserving the required spin and exchange symmetries.

The exact ground-state energy minus the minimum Hartree-Fock energy for the same Hamiltonian and variational constraints. It is nonpositive when compared with the unrestricted variational minimum. Correlations beyond a single determinant can substantially change phase boundaries at low density.

Adjustment of exposure dose or shape to compensate for energy deposited outside the intended write location.

Small-angle scattering that broadens an incident electron probe as it travels through resist.

Unintended exposure near a written feature caused by electron scattering in the resist and substrate. The deposited-energy distribution is broader than the incident probe, requiring dose or geometry correction for dense and isolated patterns.

For a uniform plane-wave beam of cross section $A$, mean intensity is $P/A=c{B}_{\mathrm{rms}}^2/{\mu }_0$. Hence $B_{\mathrm{rms}}=\sqrt{{\mu }_{0}P/(cA)}$. A sinusoidal peak amplitude is $\sqrt{2}$ times the rms amplitude. A Gaussian beam requires a stated waist or diameter convention before inferring its on-axis field from total power.

The distribution of emitted or received electromagnetic power, radiative flux or specific intensity across frequency or wavelength. The spectral quantity and interval convention must be specified: $F_{\nu }$ and $F_{\lambda }$ differ by the change-of-variable factor, while $\nu F_{\nu }$ gives energy flux per logarithmic frequency interval. This physical spectrum is distinct from the spectrum of a linear operator or a spectrum in topology.

Braking caused by induced currents whose magnetic force opposes motion. energy removed from mechanical motion can become resistive heat; the force depends on magnetic-field gradients or boundary crossing, resistance and inductance.

Terminal rotation in the same rotational sense under a common viewing convention during an electrocyclic reaction. It is distinguished from disrotatory motion; looking from opposite ends without changing conventions can reverse an apparent clockwise label.

Terminal rotation in opposite senses under a common viewing convention during an electrocyclic reaction.

For ordinary closed-shell systems, a thermal $4n$-electron electrocyclic process is conrotatory and a thermal $4n+2$-electron process is disrotatory. The corresponding simple photochemical rules are reversed. These rules relate terminal orbital phases and occupation to allowed concerted bond formation or cleavage.

Ring closure of a seven-carbon conjugated anion with eight pi electrons; thermal orbital-symmetry selection favors disrotatory motion.

Formation of a ring by concerted conversion of terminal pi-system overlap into a new sigma bond. Thermal four-pi closure is conrotatory, subject to the appropriate electronic-state assumptions.

The fraction of an operating cycle spent in a specified active state. For two constant-current states, average current is $\bar{I}=D{I}_a+(1-D)I_s$; wake-up transients require an additional energy term.

In temporal gauge, a spatially uniform step $\mathbf{A}(t)={\mathbf{A}}_0\Theta (t)$ gives $\mathbf{E}=-{\mathbf{A}}_0\delta (t)$. A charged scalar Fourier mode retains its canonical wavevector while its kinetic momentum changes from $\hslash \mathbf{k}$ to $\hslash \mathbf{k}-e{\mathbf{A}}_0$. The resulting frequency jump mixes positive- and negative-frequency modes.

Electron repulsion is the repulsive electrostatic interaction between electrons. In a metal complex it affects pairing costs and many-electron transition energies, so a measured absorption maximum is not always identical to a one-electron orbital splitting.

Loss of stability of a loaded configuration toward a bent or folded form. The threshold and deformation mode depend on geometry, material properties and boundary conditions.

A coefficient relating an appropriate stress and strain in the linear elastic regime. Young's modulus, shear modulus and bulk modulus describe different deformation modes.

When $B_{12}$ and $B_{21}$ multiply radiation energy density per unit angular frequency, they differ by a factor $2\pi$ from coefficients multiplying the density per ordinary frequency. For nondegenerate levels, Boltzmann distribution populations and thermal equilibrium give $B_{12}=B_{21}$ and the free-space ratio in the title. Specifically $B_{\omega }=2\pi B_{\nu }$ while $A$ is unchanged. Polarization restrictions and level degeneracy must be specified separately.