Guided examples#
The guided examples follow interaction problems that recur in localized-state models of two-dimensional systems: screened direct interactions, exchange between distinct orbitals, orientation dependence, numerically sampled wavefunctions, complex transition fields, dielectric-environment sweeps, and long-range matrix elements. Each example keeps the field definitions simple enough that the physical content remains visible while exercising the same PETAL2D → QUARTIC2D workflow used for numerical orbitals.
- Localized-state interactions in a 2D dielectric environment
- Direct and exchange couplings in a two-orbital localized basis
- Orientation-dependent interactions of anisotropic localized states
- Sampled transition fields on a Cartesian grid
- Complex localized orbitals and off-diagonal Coulomb matrix elements
- Dielectric screening of multiorbital interaction channels
- Long-range Coulomb matrix elements between distant localized states
The progression is deliberate:
Localized-state interactions in a 2D dielectric environment establishes the end-to-end workflow and the distinction between self-convergence and an analytic reference.
Direct and exchange couplings in a two-orbital localized basis introduces distinct orbital products and a sign-changing exchange transition field.
Orientation-dependent interactions of anisotropic localized states resolves orientation dependence into harmonic pair contributions.
Sampled transition fields on a Cartesian grid replaces analytic callables by sampled Cartesian arrays and carries them through a complete four-center interaction.
Complex localized orbitals and off-diagonal Coulomb matrix elements treats genuinely complex off-diagonal transition fields and multiorbital channels.
Dielectric screening of multiorbital interaction channels demonstrates calibrated parameter reuse across a bounded family of radial kernels.
Long-range Coulomb matrix elements between distant localized states examines a strongly oscillatory displacement regime against an analytic long-distance reference.
Benchmark stress fields, publication-sized sweeps, method coverage, and timing measurements are defined separately in Validation and benchmarks. They are evidence for validated capability, not the identity of the guided examples.