OEP 7 — Strong-field dissociation of small molecules: the products a pulse leaves#
OEP |
7 |
Title |
Strong-field dissociation of small molecules: the products a pulse leaves |
Author |
John Travers |
Drafting agent |
Opus 5.5 (2026-10-09) |
Status |
Draft |
Review status |
Not reviewed |
Reviewers |
— |
Type |
Feature |
Created |
2026-10-09 |
Resolution |
— |
Requires |
OEP 1: model identity, digests and the declared public surface; OEP 6: the rule that array evaluation returns NaN with an availability mask at unavailable points |
Supersedes |
— |
Superseded-by |
— |
Implementation |
— |
Manual pages |
— |
Part I — Proposal#
1. Abstract#
An intense near-infrared pulse leaves more than ions and electrons in a molecular gas. It leaves molecular ions in excited states, some of which fall apart; fragment ions; dications that explode; and, in fragile molecules such as ozone, neutral fragments from absorption alone. optmat gives the strong-field ionisation rate of a molecule into its ion’s ground state only. This OEP proposes a model of the products of one molecule at the end of a pulse for O2, N2, N2O, NO2, O3 and N2O5, at 800 nm from a few cycles to 30 fs and up to about 10¹⁵ W cm⁻². It has four parts:
ionisation into each state of the ion;
each state’s fragmentation;
the dications;
neutral channels.
It also gives one labelled recombination-limited bound on the atoms the products can become. The plasma kinetics after the pulse stays outside optmat; optmat supplies its curated rate data. The model succeeds if every product yield is traceable to curated records with a stated status, if it reproduces the published model tables it is built from, and if it says plainly where it fails. It is known to fail the measured N2⁺ state populations without post-ionisation coupling (section 4), and it has no data for NO2, O3 and N2O5 ionisation.
2. Motivation and scope#
The need. A model of the atomic oxygen and nitrogen a femtosecond pulse produces needs, for each molecule, what the pulse leaves behind:
how many ions;
in which states;
how many of them dissociate;
what neutral fragments appear without ionisation.
This applies to air, to nitrogen-oxide traces, and to ozone and N2O5 in atmospheric or plasma-chemistry settings. The maintainer’s priority is the total atomic yield after the pulse, with all six molecules equally wanted.
The literature curated for this OEP (TC-954 to TC-981) shows the yield has two parts:
Within the pulse. Each molecule’s own products, including unimolecular breakup within about a picosecond.
After the pulse. Collisions and recombination over picoseconds to microseconds, which depend on pressure, electron temperature and composition.
For N2 the second part dominates. Kleine et al. see only a weak prompt N⁺ signal, and N + N⁺ appearing collisionally with a 19.8 ps time constant at 4 bar backing pressure (TC-958).
Peters et al.’s kinetics model of femtosecond-ionised N2 makes its N atoms by dissociative recombination of N2⁺ and its cluster ions (TC-977).
The first part is a property of the molecule and the pulse, which optmat can own. The second is a kinetics problem for the user’s model or a propagation code (decided by the maintainer, 2026-10-09; TC-954).
In scope:
The six molecules: O2, N2, N2O, NO2, O3 and N2O5, each with a status, and unavailable channels marked as such.
Ionisation into individual ionic states: the inner orbitals (HOMO−1, HOMO−2) as well as the HOMO, with curated vertical energies and structure coefficients.
State to products: each ionic state’s fragmentation, from curated photoionisation branching ratios and dissociation limits.
Post-ionisation laser coupling among the ion’s states, in a later phase, for the measured N2⁺ populations.
Dications: their states and Coulomb-explosion channels, with kinetic energy release.
Neutral channels: one-photon absorption into dissociative states (ozone’s Chappuis and Wulf bands), and multiphoton channels where a cross section is curated.
The products a pulse leaves per molecule, with the energy the pulse deposits.
The recombination-limited atom bound (section 4), labelled
provisional.A data accessor for the curated dissociative-recombination coefficients.
The work’s own deliverables: tests, docstrings, a manual page, a gallery example and the register entries.
Out of scope:
Plasma kinetics after the pulse: recombination dynamics, clustering, charge transfer, attachment, electron-impact dissociation, and transport. optmat states the rate data; it does not integrate them.
Focal-volume averaging and propagation (Q5).
Molecular alignment and its revivals. The rates are orientation-averaged, as
molecular_rate_model’s are.Circular polarisation, which has no validated molecular rate in optmat.
Higher charge states than the dication.
A change to
molecular_rate_model’s recommended total rates (section 10).
3. Context#
Manual:
Molecular ionisation rates (Ionisation rates of molecules): the PPT/MO-ADK rate of a molecule into its ion’s ground state, its Coulomb factor, the Tong–Lin correction, the electron count and its validation against static all-electron rates and measured yields.
Ionisation rates (Ionisation rates): the pulse integration (
pulse_yield,cycle_pulse).The curated data (The curated data): the vocabulary.
Propagation (Using optmat from a propagation code): the surface a propagation code builds on, OEP 1.
Modules:
optmat.gas.molecular_ionisation_rates(molecular_rate_model,MolecularRateModel,moadk_rate_au);optmat.gas._tunnelling(the structure factors and their orientation average);optmat.gas.ionisation_validation(pulse_yield,cycle_pulse);optmat.gas.raman_response(raman_response_status, the precedent for asking a gas’s status without building its model);optmat.identity(Identified,Status).
Data:
The quantities added for this work (TC-954):
dissociation_energy;ionic_state_population;fragmentation_branching_ratio;kinetic_energy_release;dissociation_time;dissociative_recombination_rate_coefficient(its law inparameters.law);photodissociation_quantum_yield;transition_dipole_moment.
Existing quantities:
ionization_energywith a final state;tunnelling_structure_coefficient;appearance_energy;absorption_cross_section.
Materials registered by reference only (TC-954): NO2, N2O5, NO, NO2⁺, NO⁺, N2²⁺ and O2²⁺.
Register:
TC-446, TC-675: Zhao et al.’s structure coefficients (2010, 2017) behind the HOMO rates. N2O has only Zhao 2017’s.
TC-508, TC-510: Talebpour et al. (1999) and Guo et al. (1998). Their measured molecular yields include dissociative channels; Talebpour gives N⁺/N2⁺ and O⁺/O2⁺ ≈ 10⁻² in their experiment.
TC-954 to TC-981: the curation for this OEP.
Roadmap: none. This is new.
4. Theory#
4.1 Ionisation into individual ionic states. Each state \(s\) of the ion is reached by removing an electron from one orbital. Its static rate is the MO-ADK/PPT rate of that orbital, with:
the state’s vertical ionisation energy \(I_s\);
its asymptotic coefficients \(C_{lm}^{(s)}\);
its electron count \(N_s\).
These are the same formulas molecular_rate_model uses for the HOMO
(Ionisation rates of molecules, The rate):
orientation-averaged as \(\langle B^2(m')\rangle = \sum_l (C^{(s)}_{l})^2 Q^2/(2l+1)\).
In the sudden limit the ion’s states are populated independently and not coupled afterwards. For neutral population \(P_0\) and ionic-state populations \(P_s\):
The HOMO channel with the existing default parameters reproduces molecular_rate_model
exactly, and the inner channels add to it (Q1, resolved).
The inner orbitals’ rates fall steeply with \(I_s\). For N2 the sudden limit puts N2⁺(B) roughly an order of magnitude below N2⁺(X); Kleine et al. state this tunnelling expectation. Kleine et al. measured instead X : A : B = 0.47 : 0.07 : 0.46 of the ions at 800 nm and 4.5×10¹⁴ W cm⁻² (TC-958). The sudden limit is therefore known to fail for N2. That is why section 4.2 exists.
4.2 Post-ionisation coupling (Phase 2). Yuen and Lin’s density-matrix model (TC-955) keeps the ion’s states coherent after ionisation. Their reduced density matrix \(\rho\) evolves under the field-dressed Hamiltonian \(H_{ss'}(t) = I_s\,\delta_{ss'} - \mathbf{d}_{ss'}\cdot\mathbf{F}(t)\), with a source from the neutral and a loss to the dication:
Here \(\Gamma^{(2)}\) holds the state-resolved rates of the second ionisation. The transition dipoles \(\mathbf{d}_{ss'}\) are curated:
N2⁺: X–A and X–B in Yuen and Lin; against bond length in Jia et al. (TC-957).
O2⁺: a–b in Yuen et al. (TC-956).
Yuen et al. (2023) and Jia et al. (2024) extend it to O2 and to dication-state coupling. Their published populations are figures, not tables (TC-955 to TC-957), so reproducing them needs vector digitising under rule 8.
4.3 From ionic states to products. At the end of the pulse each state \(s\) goes to products \(k\) with a branching \(B_{s\to k}\), \(\sum_k B_{s\to k} = 1\):
A state wholly below its lowest dissociation limit has \(B_{s\to\mathrm{parent}} = 1\). N2⁺ X, A and B and O2⁺ X are expected to be such states, but their limits are not yet curated (section 5). A state above it takes its branching from state-resolved photoionisation data where curated. N2O⁺ is the one held case: Berkowitz and Eland give the states’ fragments, ratios and appearance energies (TC-965).
These are photoionisation branchings, and they are taken to hold after strong-field ionisation into the same state. The assumption is checked against:
Kübel et al.’s N–N over N–O bond-breaking ratio of 3.5 (TC-966);
Zhu et al.’s NO2⁺ : NO⁺ ≈ 3 at 810 nm (TC-967; NO2 has no ionisation model yet).
The O2⁺ states above the O⁺ + O limit (b ⁴Σg⁻ and above) need their predissociation branching from a source not yet held (Q3). De et al. show that bound O2⁺ a ⁴Πu wavepackets dissociate when a later field couples them to f ⁴Πg (TC-962). That is a coupling effect, outside the sudden limit.
4.4 Dications (Phase 3). The dication’s states are populated from the ion’s states
by the second ionisation, at the effective binding energies Yuen et al. define. These are
curated as ionization_model_parameter, not ionisation energies (TC-956). The dication
states and their energies above the neutral are curated for N2 (Yuen and Lin; Jia et al.
against bond length) and for O2 (Yuen et al.). So are their dissociation limits and
kinetic energy releases. Metastable dication states count as N2²⁺ or O2²⁺; the rest give
two ions.
4.5 Neutral channels. A neutral molecule \(M\) absorbing one photon with cross section \(\sigma(\omega)\) and dissociating with quantum yield \(\phi(\omega)\) does so with probability
where \(\Phi\) is the photon fluence. For a Gaussian pulse of peak intensity \(I_0\) and intensity FWHM \(\tau\), \(\Phi = I_0\tau\sqrt{\pi/(4\ln 2)}/\hbar\omega\).
For O3 at 800 nm, optmat’s absorption model gives \(\sigma = 1.5\times10^{-22}\) cm², which agrees with El Helou et al. to about 1 % (TC-972). Ozone’s Chappuis and Wulf bands dissociate to O2 + O. The quantum yield of order one is the subject of Grebenshchikov et al.’s review; its printed yields are reviews of other work and are not curated (TC-973, Q4). At \(I_0 = 10^{14}\) W cm⁻² and \(\tau = 30\) fs, \(\Phi \approx 1.3\times10^{19}\) cm⁻² and \(P_1 \approx 2\times10^{-3}\).
Two other one-photon cases need care:
NO2 absorbs one 800 nm photon, but its NO + O dissociation energy exceeds the photon’s energy, so one photon cannot dissociate it. The limit is not yet curated (section 5) and is quoted here from general knowledge.
N2O5: its curated cross sections end at 398 nm (TC-974); no absorption at 800 nm is curated.
Multiphoton dissociation into a channel of order \(n\) would have the rate \(W_n = \sigma_n (I/\hbar\omega)^n\). No \(\sigma_n\) for these molecules is curated; Song et al. give only O2’s photon order (about 9 to 11) and timescale (TC-960). Neutral multiphoton channels are therefore unavailable, never zero (section 6).
4.6 The recombination-limited bound. Each product ion \(j\) recombining dissociatively with an electron gives \(a_{j,X}\) atoms of element \(X\), by its curated dominant channel (TC-976):
O2⁺ → O + O;
N2⁺ → N + N;
NO⁺ → N + O;
NO2⁺ → NO + O.
The bound on atoms of \(X\) per molecule is
assuming every ion recombines dissociatively and nothing else competes.
The bound fails, as an approximation, where other processes win. For example, in air at one atmosphere O2⁺ clusters to O4⁺, whose recombination gives O2 + O2. The manual will state the competing processes, with their coefficients where curated (Kossyi et al., TC-976, includes the clusters in its notes). The recombination time \(1/(k n_e)\) uses the curated \(k(T_e)\), e.g. \(2\times10^{-7}(300/T_e)\) cm³ s⁻¹ for O2⁺.
4.7 Energy deposited. The pulse deposits \(\sum_s P_s I_s\) per molecule into ionic
states (the HOMO channel’s adiabatic energy, as energy_per_event). It deposits
\(\hbar\omega\) per absorbed photon in the neutral channels. The kinetic energy of
electrons is not counted, as now.
Units and conventions: SI at the interface; populations and yields per molecule; energies in J (eV in the tables). Intensity is the cycle-averaged \(I = \tfrac12 c\varepsilon_0 F_0^2\) of a linearly polarised field, as in Conventions.
5. Primary sources and data#
In hand (curated):
Need |
Sources |
Register |
|---|---|---|
Ionic-state vertical energies, inner-orbital \(C_{lm}\) |
Yuen and Lin 2022 (N2); Yuen et al. 2023 (O2, three orbitals); Jia et al. 2024 (N2, against \(R\)); Zhao et al. 2010, 2017 (HOMO) |
TC-955–957, TC-446, TC-675 |
Transition dipoles of ions and dications |
Yuen and Lin; Yuen et al.; Jia et al. |
TC-955–957 |
Dication states, limits, KER |
Yuen and Lin; Yuen et al.; Jia et al.; Wu et al. (triple ionisation KER) |
TC-955–957, TC-959 |
N2O⁺ state → fragments |
Berkowitz and Eland 1977 |
TC-965 |
Validators: measured state populations |
Kleine et al. 2022 (N2⁺ X/A/B) |
TC-958 |
Validators: strong-field channel ratios |
Kübel et al. 2014 (N2O); Zhu et al. 2006 (NO2); Singhal et al. 1998 (NO2, figures); Talebpour et al. 1999 and Guo et al. 1998 (O⁺/O2⁺, N⁺/N2⁺) |
TC-966–968, TC-508, TC-510 |
Dissociation times |
Kleine et al. (collisional N2⁺); Song et al. (O2 superexcited); Zhao et al. 2023 (N2O⁺) |
TC-958, TC-960, TC-971 |
O3 neutral channel |
El Helou et al. 2005; optmat’s O3 absorption; Grebenshchikov et al. 2007 (limits) |
TC-972, TC-973 |
N2O5 photochemistry |
Harwood et al. 1998; Ravishankara et al. 1986 (disagree at 248 nm) |
TC-974, TC-975 |
Recombination coefficients |
Kossyi et al. 1992 (and its copies in Peters et al. and Hooshyar and Dumitrache) |
TC-976, TC-977, TC-979 |
Missing, and requested: these are not curated as source records, and each is to be identified and checked before use.
O2⁺ predissociation branching. The state-resolved fragmentation of O2⁺ above the O⁺ + O limit, from threshold photoelectron–photoion coincidence data (Q3).
Structure coefficients for NO2 and O3 (weak-field asymptotic theory or MO-ADK), and for N2O’s inner orbitals. Zhao 2017 covers N2O’s HOMO only.
N2O5 ionisation: whether N2O5⁺ survives, and its fragment appearance energies.
NO2⁺ and O3⁺ state-resolved fragmentation from photoionisation.
Absolute fragment yields against intensity at 30 fs or shorter, for O2 and NO2.
Validators of the total atom yield: ozone and NOx produced by femtosecond filaments; absolute atomic O and N densities after femtosecond excitation.
The Supplemental Material of Kleine et al., for the pulse duration and polarisation of their measurement (TC-958).
Dissociation limits of N2⁺, O2⁺ and NO2 (thermochemical), to show which states are bound.
Figures to digitise (rule 8, use = "check"): the register entries of TC-955 to
TC-971 list them. The first needed are:
Yuen and Lin’s yields against intensity (Fig. 5);
Yuen et al.’s Fig. 9;
Jia et al.’s Fig. 2;
Wu et al.’s Fig. 4 channel ratios (raster).
Uncertainty. Each channel states:
its source uncertainty where printed;
the spread between curated coefficient sets. For O2’s HOMO, Yuen et al.’s 0.69/0.06 against Zhao 2010’s 0.52/0.03 and Zhao 2017’s 0.64/0.04; Jia et al.’s N2 values also differ (TC-956, TC-957; Q2).
Each model carries an uncertainty_factor with its reason, as the molecular rates do.
A product yield’s uncertainty is not a sum in quadrature of these. It is stated per
channel, and validators decide the status.
6. Proposed interface#
A new module, optmat.gas.dissociation.
Name |
Meaning |
Units |
|---|---|---|
|
the model of one molecule at one carrier wavelength |
m |
|
the ion’s states: label, vertical energy, structure coefficients, electron count, products table, sources |
J |
|
\(w_s\) for each state, instantaneous, linear polarisation |
s⁻¹ |
|
a |
1; J |
|
each neutral channel: order, cross section or its absence, quantum yield, sources |
|
|
\(A_X^{\max}\) per element, labelled |
1 |
|
OEP 1 |
|
|
|
|
|
the curated \(k(T_e)\) and its source; no kinetics |
m³ s⁻¹ |
Warnings and refusals:
Unavailable channels: a channel without curated data is unavailable. Evaluating it returns NaN with
available = False(OEP 6’s rule), never 0. Examples are NO2’s ionisation in Phase 1, every neutral multiphoton channel, and O2⁺ b-state branching until Q3.Unknown molecule: a molecule outside the six raises
OptmatError.Range: where the HOMO model warns (
ModelRangeWarning: below 350 nm, above itscorrection_range), so does this one. The curated validators are all near 800 nm, and the manual will say so.The sudden limit’s status: any model without coupling carries status
provisional, with the reason that it fails Kleine’s N2⁺ populations.The bound: the recombination-limited bound always carries status
provisional. It is never offered as a prediction of atoms at a time.
A sketch (fenced as text until it runs; values to be generated):
>>> from optmat.gas.dissociation import fragmentation_model
>>> o2 = fragmentation_model("O2", 800e-9)
>>> [s.label for s in o2.states]
['X 2Pi_g', 'a 4Pi_u', 'b 4Sigma_g-']
>>> p = o2.pulse_products(1e18, fwhm=30e-15) # 1e14 W/cm2, in W/m2
>>> p.yields["O2+"], p.yields["O+"], p.available["O"]
...
>>> o2.recombination_limited_atoms(p)["O"] # provisional bound
...
Composition:
With
molecular_rate_model: the HOMO channel is the existing model and is not changed. The inner channels add to it. A user who wants the total ionisation keeps usingmolecular_rate_model; the fragmentation model’s total is reported beside it. Measured yields used to validate the HOMO model already include dissociative channels (TC-508, TC-510). The difference is of order 10⁻², within its uncertainty factor.With optmat’s absorption models: the O3 neutral channel uses the gas’s curated absorption cross section. It does not hold a copy.
With a propagation code: the energy deposited and the electrons are per molecule per pulse. A time-resolved loss current would come from
state_ratesand the neutral channels’ rates. The split between channels is the code’s choice.
7. Implementation strategies#
Where it belongs: the gas subpackage (optmat.gas.dissociation), beside the
molecular rates, reusing:
optmat.gas.ionisation_ratesandmolecular_ionisation_ratesfor each state’s rate, as aMolecularRateModelbuiltfrom_parameterswith the state’s energy and coefficients;ionisation_validation’s pulses for the integration.
Configuration: a TOML file per model, data/gas/dissociation.toml, in the pattern of
molecular_ionisation_rates.toml. Each state names its datasets and its reason
(TC-n). Each products table names the dataset of each branching or the reason for a
fixed value, e.g. bound below the limit, citing the dissociation_energy or
appearance_energy dataset that shows it.
Option A: sudden limit first (recommended). Phase 1 is the rate-equation model of 4.1 with the tables of 4.3. It is cheap and directly traceable. Its known failure for N2 is stated in its status and tested against Kleine as a validator that fails by design.
Option B: density matrix from the start. It is correct for N2⁺ but needs:
the transition dipoles against geometry;
the field-dressed integration;
digitised figures to check it.
It would delay a usable model for all six molecules for the sake of the two best served by data. It is recommended as Phase 2, not as the start.
Option C: empirical fragment fractions. For example, a constant 25 % of NO2⁺ dissociating, from Zhu et al. It is rejected as a default: those fractions are measured under one pulse with doubtful intensity calibration. They are kept as validators.
The coefficient sets: where Yuen et al. or Jia et al. and Zhao et al. differ, the model takes one set per orbital and records the other as a comparison model (Q2, resolved: the HOMO on the default’s set, the inner orbitals on the defining paper’s).
Cost: the sudden limit integrates a handful of rates over a pulse: milliseconds per intensity. The density matrix is a few-state ODE per pulse: well under a second.
Vocabulary: done (TC-954). The species of products are strings from a controlled list in the module (O, N, NO, NO2, NO3, O2, N2 and their ions). Atoms are not registered materials (Q9).
8. Verification and validation#
Reproductions:
The HOMO channel equals
molecular_rate_model’s default to floating-point tolerance, for every molecule that has one.Each state’s static rate reproduces
moadk_rate_auwith that state’s curated \(I_s\) and \(C_{lm}\).Phase 2 reproduces Yuen et al.’s and Jia et al.’s published populations (digitised, vector). The tolerance is the digitising uncertainty, combined with the difference between their MO-ADK form and optmat’s (Tong–Lin and Coulomb factor). That difference is stated and switched off for the comparison where possible.
Invariants:
\(P_0 + \sum_s P_s + \sum_d P_d = 1\).
\(\sum_k B_{s\to k} = 1\) for every state.
Element balance: atoms in equal atoms out, for every products record.
The bound is at least the prompt atoms.
Analytic limits:
The neutral one-photon channel against \(1-\exp(-\phi\sigma\Phi)\) for a Gaussian pulse.
The weak-field limit of each state’s rate.
Validators:
Kleine’s N2⁺ X : A : B. Phase 1 reports the miss; Phase 2 is judged on it, within Kleine’s stated errors and the unknown pulse duration (Q7).
Talebpour et al.’s fragment-to-parent ratios of about 10⁻² for O2 and N2.
Kübel’s N2O channel ratios, and Zhu’s NO2 ratio once NO2 ionises.
Ozone: the linear probability against El Helou’s cross section at its tabulated maxima, interpolated with optmat’s own model.
solprop: no parity target exists. A paired solprop proposal, if any, consumes
Productsandstate_rates.
9. Documentation#
A new manual page, Strong-field dissociation. It covers:
the two parts of the atom yield and the boundary;
the sudden limit and why it fails for N2;
the products tables, with their sources;
the neutral channels;
the bound and its failure modes, with the recombination coefficients;
a table of each molecule’s status and its unavailable channels;
open questions.
Docstrings with units and ranges.
A gallery example: O2 and N2 products against intensity at 30 fs, with the bound.
Links: the molecular-rates page links to the new page, and the data page’s quantities are already documented (TC-954).
10. Compatibility and impact#
No recommended value changes.
molecular_rate_modeland every default are untouched.No stored fit is re-run.
New public names only:
optmat.gas.dissociationand its config file.No solprop parity fixture changes.
No register entry is superseded.
11. Alternatives considered#
A kinetics solver in optmat. Declined by the maintainer (TC-954). Its result depends on pressure, mixture and electron temperature, which are the user’s conditions, not the material’s. Its rate data would be mostly secondary compilations.
Fitting fragment fractions to measured ratios against intensity. The measured ratios carry estimated or unstated intensity calibrations (TC-967, TC-508), and some would be digitised from raster figures, which optmat never fits.
Taking published strong-field model curves (e.g. Yuen et al.’s) as data. Those curves are model outputs. They are used as reproductions of the method, not as references, as for the ionisation rates (TC-439’s tiers).
Leaving the triatomics out. Rejected by the maintainer’s priority (all six equally). They are included with explicit unavailable channels instead, so that a user sees what is missing.
12. Phases#
The sudden-limit framework. Deliverables:
optmat.gas.dissociationwith the interface of section 6;data/gas/dissociation.toml;the state channels for O2 (X, a, b) and N2 (X, A, B), and N2O (X only, until its inner orbitals are curated);
the products tables from section 4.3, with unavailable entries for O2⁺’s b state until Q3;
the O3 neutral one-photon channel;
NO2, O3 and N2O5 models whose ionisation is unavailable, with their status
untested;the recombination accessor and bound;
tests of section 8 except Phase 2’s;
the manual page, the gallery example, register entries and a changelog line.
Post-ionisation coupling. Deliverables:
the density-matrix evolution of 4.2 for N2⁺ and O2⁺, with the curated dipoles;
the digitised populations of Yuen and Lin, Yuen et al. and Jia et al. as checks.
It is judged against Kleine’s populations. It changes N2’s status only if it passes.
Dications. Deliverables:
the second ionisation from the ion’s states;
the dication states, channels and KER from the curated tables;
Wu et al.’s and Kübel et al.’s ratios as validators.
Triatomic ionisation and neutral multiphoton channels. Each of these follows its curation:
NO2, O3 and N2O5 ionisation, once their structure coefficients and ionic fragmentation are curated;
the neutral multiphoton channels, once a cross section is.
13. Open questions#
Q1 (the total; resolved). The fragmentation model’s total ionisation is the HOMO model plus the inner channels; the inner channels are not renormalised to keep the total equal to
molecular_rate_model’s. The difference is the inner orbitals’ share, small in the sudden limit, and it is reported beside the HOMO model’s total (the maintainer, 2026-10-09; TC-982).Q2 (structure coefficients; resolved). Yuen et al. cite Zhao et al. 2010 for O2’s coefficients but print different values, and Jia et al.’s N2 values differ from both of Zhao’s sets (TC-956, TC-957). Decided (the maintainer, 2026-10-09; TC-982):
the HOMO stays on the default model’s set, so that its channel is
molecular_rate_modelunchanged;the inner orbitals take the set of the paper that defines them: Yuen et al. (2023) for O2’s HOMO−1 and HOMO−2; Jia et al. (2024) for N2’s, at R = 1.10 Å, the tabulated distance nearest equilibrium;
the other sets are offered as comparison models.
Q3 (O2⁺ above the dissociation limit; before Phase 1 completes O2). The branching of O2⁺ b ⁴Σg⁻ and higher states into O⁺ + O needs a curated photoionisation source. Until then those entries are unavailable.
Q4 (ozone’s quantum yield; Phase 1). The Chappuis/Wulf quantum yield is taken as one, from the predissociative character of the bands. Grebenshchikov et al. review but do not measure it. Accept 1 with a stated reason, or wait for a curated measurement?
Q5 (focal-volume averaging; resolved recommendation). Leave it downstream. A helper may be offered in a later phase if a validator needs it.
Q6 (a kinetics validator; resolved). None in optmat (TC-954).
Q7 (Kleine’s pulse; Phase 2). The duration and polarisation of the measurement are only in the Supplemental Material, which is not held (TC-958). Request it before Phase 2 is judged.
Q8 (pulse dependence; Phase 1). Singhal et al. report that shorter pulses favour NO2⁺ over NO⁺ (TC-968). The sudden limit’s branching does not depend on the pulse. Record this as a limitation, or wait for Phase 2’s coupling?
Q9 (product species; Phase 1). Products are named by a controlled list of species strings. Should atoms and radicals (O, N, NO3) become registered materials instead? Recommended: no, until data are curated for them.
14. References#
Curated as source records unless marked (the record’s id in brackets).
C. H. Yuen and C. D. Lin, “Density-matrix approach for sequential dissociative double ionization of molecules,” Phys. Rev. A 106, 023120 (2022). doi:10.1103/PhysRevA.106.023120 [yuen_2022]
C. H. Yuen, P. Modak, Y. Song, S.-F. Zhao and C. D. Lin, “Modeling the sequential dissociative double ionization of O2 by ultrashort intense infrared laser pulses,” Phys. Rev. A 107, 013112 (2023). doi:10.1103/PhysRevA.107.013112 [yuen_2023]
Y.-W. Jia, C. H. Yuen, W.-Q. Jing, Z.-Y. Zhou, C. D. Lin and S.-F. Zhao, “Improved model for the dissociative sequential double ionization of nitrogen molecules by an intense few-cycle infrared laser pulse,” Phys. Rev. A 110, 023112 (2024). doi:10.1103/PhysRevA.110.023112 [jia_2024]
C. Kleine et al., “Electronic state population dynamics upon ultrafast strong field ionization and fragmentation of molecular nitrogen,” Phys. Rev. Lett. 129, 123002 (2022). doi:10.1103/PhysRevLett.129.123002 [kleine_2022]
J. Berkowitz and J. H. D. Eland, “Photoionization of N2O: Mechanisms of photoionization and ion dissociation,” J. Chem. Phys. 67, 2740 (1977). doi:10.1063/1.435188 [berkowitz_1977]
M. Kübel et al., “Strong-field control of the dissociative ionization of N2O with near-single-cycle pulses,” New J. Phys. 16, 065017 (2014). doi:10.1088/1367-2630/16/6/065017 [kubel_2014]
J. Zhu, W. Guo, Y. Wang and L. Wang, “Dissociation of NO2 in femtosecond intense fields,” Chin. Sci. Bull. 51, 1185 (2006). doi:10.1007/s11434-006-1185-2 [zhu_2006]
R. P. Singhal et al., “Comment on ‘On the ionisation and dissociation of NO2 by short intense laser pulses’,” Chem. Phys. Lett. 292, 643 (1998). doi:10.1016/S0009-2614(98)00718-0 [singhal_1998]
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D. Song et al., “Neutral dissociation of superexcited oxygen molecules in intense laser fields,” J. Phys. Chem. A 114, 3087 (2010). doi:10.1021/jp907662z [song_2010]
S. De et al., “Following dynamic nuclear wave packets in N2, O2, and CO with few-cycle infrared pulses,” Phys. Rev. A 84, 043410 (2011). doi:10.1103/PhysRevA.84.043410 [de_2011]
X. Zhao et al., “Probing electron localization during molecular dissociation by femtosecond strong-field ion momentum spectroscopy,” Commun. Phys. 6, 124 (2023). doi:10.1038/s42005-023-01248-3 [zhao_2023]
A. Talebpour, J. Yang and S. L. Chin, “Semi-empirical model for the rate of tunnel ionization of N2 and O2 molecule in an intense Ti:sapphire laser pulse,” Opt. Commun. 163, 29 (1999). doi:10.1016/S0030-4018(99)00113-3 [talebpour_1999]
C. Guo, M. Li, J. P. Nibarger and G. N. Gibson, “Single and double ionization of diatomic molecules in strong laser fields,” Phys. Rev. A 58, R4271 (1998). doi:10.1103/PhysRevA.58.R4271 [guo_1998]
S.-F. Zhao, C. Jin, A.-T. Le, T. F. Jiang and C. D. Lin, “Determination of structure parameters in strong-field tunneling ionization theory of molecules,” Phys. Rev. A 81, 033423 (2010). doi:10.1103/PhysRevA.81.033423 [zhao_2010]
S.-F. Zhao, J.-K. Li, G.-L. Wang, P.-C. Li and X.-X. Zhou, “Accurate structure parameters for tunneling ionization rates of gas-phase linear molecules,” Commun. Theor. Phys. 67, 289 (2017). doi:10.1088/0253-6102/67/3/289 [zhao_2017]
Z. El Helou et al., “Absolute cross sections of ozone at atmospheric temperatures for the Wulf and the Chappuis bands,” J. Chem. Phys. 122, 244311 (2005). doi:10.1063/1.1937369 [el_helou_2005]
S. Yu. Grebenshchikov, Z.-W. Qu, H. Zhu and R. Schinke, “New theoretical investigations of the photodissociation of ozone in the Hartley, Huggins, Chappuis, and Wulf bands,” Phys. Chem. Chem. Phys. 9, 2044 (2007). doi:10.1039/b701020f [grebenshchikov_2007]
M. H. Harwood, J. B. Burkholder and A. R. Ravishankara, “Photodissociation of BrONO2 and N2O5: Quantum yields for NO3 production at 248, 308, and 352.5 nm,” J. Phys. Chem. A 102, 1309 (1998). doi:10.1021/jp9729829 [harwood_1998]
A. R. Ravishankara, P. H. Wine, C. A. Smith, P. E. Barbone and A. Torabi, “N2O5 photolysis: Quantum yields for NO3 and O(3P),” J. Geophys. Res. 91, 5355 (1986). doi:10.1029/JD091iD05p05355 [ravishankara_1986]
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C. J. Peters, M. N. Shneider and R. B. Miles, “Kinetics model of femtosecond laser ionization in nitrogen and comparison to experiment,” J. Appl. Phys. 125, 243301 (2019). doi:10.1063/1.5098306 [peters_2019]
Part II — Implementation record#
None yet.
Part III — History#
2026-10-09: Drafted, after the curation of TC-954 to TC-981.
2026-10-09: Q1 and Q2 resolved by the maintainer, as recommended (TC-982).