qscat

Validated quantum-scattering numerics for electron–diatomic collisions.

qscat is a CPU-first Python library for electron–molecule scattering with the FEM-DVR method and exterior complex scaling (ECS): vibrational-excitation (VE), dissociative-attachment (DA), and dissociative-recombination (DR) cross sections, by time-independent and time-dependent routes. Everything is in atomic units, and every method is validated against an analytic benchmark, a conservation law, a convergence study, or an independent reference.

This site is the API reference and the theory notes. For the project overview — what the methods are and what they have measured — see https://qscat.org; the source, issues and changelog are at https://github.com/VanaMartin/qscat, and the published computed artifacts are served from https://data.qscat.org.

Contents

• Getting started
  • Install
  • Your first cross section
  • Choosing a grid
  • The config CLI
• API reference
  • What is public
  • The layers
• Published artifacts
  • Three tiers, by who reads the number
  • Fetching
  • What a pointer may say
  • Referencing an artifact directly
  • Publishing
• Related work
  • Summary
  • The closest relative: quantumGrid
  • Other implementations of the same numerical ingredients
  • Electron–molecule scattering codes with a different method and scope
  • The resonance-model literature releases data, not solvers
  • What appears to have no released counterpart
  • How this survey was done, and what it cannot see
  • On the name

Theory — technical

• Theory notes
• Validation harnesses
  • The harnesses
  • What each one actually establishes
  • Where the @slow boundary falls
  • Reading a NOTE row
• Discretisation
  • FEM-DVR-ECS: finite-element DVR with exterior complex scaling
  • The N-dimensional tensor-product Hamiltonian
  • FEM-DVR-ECS discretisation tuner: design, calibration, and gate
• Linear algebra and solvers
  • The MUMPS complex-symmetric sparse backend
  • TI energy-sweep symbolic reuse + the dense σ(E) cross-section curve
  • Sparse shift-invert eigensolver
• The scattering engine
  • qscat.core + qscat.model: the electron–diatomic VE-scattering engine
  • N₂ electron-impact ²Π_g shape resonance: fixed-R pole search
  • N₂ vibrationally-elastic/inelastic cross section: TI resolvent/driven-equation method
  • N₂ vibrationally-elastic/inelastic cross section: exact 2-D driven-equation method
  • NRM vibrational excitation
• Time-dependent routes
  • N₂ vibrationally-elastic/inelastic cross section: time-dependent (Crank-Nicolson) method
  • N₂ vibrationally-elastic/inelastic cross section: time-dependent (Crank-Nicolson) route to the exact 2-D solution
  • Alternative TD energy extractors: Dirac (delta) and Flux (flow)
  • Time-dependent dissociative attachment (TD-DA): the nuclear-axis extractors
  • The time-dependent nonlocal resonance model
  • Watching the nonlocal kernel run — a walkthrough
• Dissociation and approximations
  • NO and F₂ exact-2D VE cross sections (the model port)
  • The nonlocal resonance model (NRM)
  • H₂⁺ dissociative recombination (the first ionic model)
• Resonances and levels
  • BO/LCP resonance levels — quasi-bound vibrational states of the anion
  • Exact (non-Born-Oppenheimer) resonance states of the 2-D model
  • Exact resonance states of H₂⁺, against the Born–Oppenheimer picture
  • Potential factory — fitting model surfaces to target curves
  • Coupled partial waves in the NO shape resonance: does the fixed-l reduction hold?
• Open directions
  • Angular (θ) extension: coupled partial-wave channels — research direction
  • Potential factory: building model surfaces that match real molecules — options survey
  • Optimization targets (measured)

Theory — molecules

• N₂ — the benchmark target
• NO and F₂ — no independent data
• O₂ — the first fitted target
• H₂⁺ — the first ionic target

Quick links

• Install & first cross section: Getting started

• API reference: API reference

• How this relates to existing codes: Related work

• Fetching published sweep results: Published artifacts

• Theory notes: Theory notes

• Design decisions: the docs/adr/ directory (ADRs)

Citing

If you use qscat in research, citation is required — see CITATION.cff in the repository and the “Citing qscat” section of the package README.

Indices

• Index

• Module Index