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REVIEW 3 major objections 5 minor 65 references

MADWAVE3: a quantum time dependent wave packet code for nonadiabatic state-to-state reaction dynamics of triatomic systems

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The paper presents MADWAVE3, a parallel quantum wave-packet code that computes state-to-state probabilities for triatomic inelastic, reactive, and photodissociation processes over one or multiple coupled diabatic electronic states, and…

desk verdict Solid single-surface wave packet code with a credible J=0 ABC check; the advertised diabatic and photodissociation paths are unbenchmarked and need either demonstrations or a narrowed scope. read the letter →

arxiv 2412.10167 v1 pith:3RPZOPQD submitted 2024-12-13 physics.comp-ph physics.chem-ph

Octavio Roncero , Pablo del Mazo-Sevillano This is my paper · ORCID
classification physics.comp-phphysics.chem-ph
keywords quantumwavepacketreactivescatteringphotodissociationdiabaticrepresentationstate-to-stateprobabilitiesChebyshevpropagatortriatomicsystemsparallelcomputing
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

MADWAVE3 is a parallel Fortran 90 code for propagating quantum wave packets in triatomic systems, and the paper's claim is that it delivers converged state-to-state probabilities and cross sections for inelastic collisions, reactive collisions, and photodissociation, on one or several coupled diabatic electronic states. The authors validate this by benchmarking the H+DH(v=0,j=0) system at total angular momentum J=0: their state-to-state inelastic and reactive probabilities agree closely with results from the time-independent ABC code on the same potential. If the claim holds, the code offers a wave-packet alternative to ABC that scales more gently with channel number, supports nonadiabatic and photoinitiated processes that ABC does not implement, and parallelizes efficiently over helicity and angular grid points. The paper provides the potential surface, input files, and installation instructions so the benchmark is reproducible.

What carries the argument

The load-bearing machinery is the modified Chebyshev propagator of Mandelshtam and Taylor: the wave packet is expanded as real Chebyshev components Ψ(k) that stay real when the initial packet is real, and the Hamiltonian action is split into radial kinetic terms evaluated with FFTW sine transforms, angular kinetic terms applied via DVR-to-FBR transformations, and a potentially L-shaped grid for the potential. To extract state-to-state probabilities the code uses either reactant-coordinate-based (RCB) or product-coordinate-based (PCB) sequential coordinate transformations, and the analysis is done through flux and projection coefficients at a fixed product distance. Parallelization is done by distributing helicity Ω components (coupled only to Ω±1) and, for low J, the γ angle grid.

What would settle it

Run MADWAVE3 on a photodissociation case with published cross sections (for example the LiHF or HCN systems cited in the paper) and compare the computed absolute absorption cross section; or run a two-state nonadiabatic benchmark against MCTDH or known results. If the photodissociation autocorrelation (Eq. 24) or the state-to-state products from the diabatic coupling do not match, the central claim of multi-process capability would be contradicted.

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Extended reading notes

Core claim

The central claim is that MADWAVE3 computes correct state-to-state S-matrix elements, and hence probabilities and cross sections, for triatomic A+BC → AB+C reactions and ABC+hν → AB+C photodissociation, including multiple coupled diabatic electronic states. The machinery works in body-fixed Jacobi coordinates (r, R, γ) with the wave packet expanded in helicity Ω and electronic components; propagation uses a modified Chebyshev scheme that keeps the wave packet real, and state-to-state analysis is done by projecting onto product or reactant Jacobi coordinates via sequential transformations. The key demonstration is the H+DH(v=0,j=0) example: for J=0, the MADWAVE3 state-to-state probabilities for HD and H2 product channels are reported to be in excellent agreement with the ABC hypherspherical close-coupling code, which the authors take as evidence of convergence and accuracy of the grids, basis, and propagation parameters.

Load-bearing premise

The load-bearing premise is that the code's photodissociation and multi-diabatic-state machinery is as correct as the single-electronic-state reactive machinery, because the ABC benchmark exercises only the latter and would not expose an error in the former.

Editorial extensions

If this is right

  • For systems where the ABC code becomes expensive—high total angular momentum, deep wells, or many channels—MADWAVE3 is claimed to be a better-scaled alternative because it computes one column of the S-matrix and parallelizes over helicity and angular grid points.
  • The code extends state-to-state wave-packet dynamics to photodissociation, using a first-order perturbation-theory initial packet built from a bound state and transition dipole moments, which ABC does not provide.
  • The diabatic multi-state treatment allows nonadiabatic reactive and photoinitiated processes to be studied in a single framework, with products' rovibrational states computed in the full electronic manifold when needed.
  • The accompanying potential grid, input files, and analysis programs (for cross sections via J-shifting interpolation) make the benchmark fully reproducible, so users can check convergence parameters before running new systems.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper's advertised nonadiabatic and photodissociation capabilities rest on untested code paths: the only benchmark is single-electronic-state J=0 reactive/inelastic scattering, so a bug in the diabatic coupling or in the Eq. (13) initial-state construction would not be caught by the ABC comparison. A natural next test is to reproduce a published photodissociation cross section (e.g., HCN or Li
  • Because the code reads user-supplied potential routines and transition dipoles, its practical accuracy for a new molecular system will depend on the quality of the diabatization, which the code itself does not build; users must supply a diabatic representation that is diagonal in the reactant asymptotic channel.
  • The J-shifting interpolation results shown for higher J indicate that approximate cross sections can be obtained from a few partial waves, so the code's advertised scaling advantage matters most when many J or many channels are needed.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript presents MADWAVE3, a Fortran90 time-dependent wave packet code for triatomic quantum dynamics. The theoretical framework uses body-fixed Jacobi coordinates, a real Chebyshev propagator with complex absorbing potentials, DVR/FBR transformations for the angular kinetic terms, and reactant- or product-coordinate-based analysis for state-to-state probabilities. The paper documents the modular structure, installation, input namelists, and auxiliary programs, and gives a case study of H+DH(v=0,j=0) at J=0: total and state-to-state probabilities are compared with the time-independent ABC code, partial-wave cross sections are shown, and MPI/OpenMP speedups are reported. The abstract advertises inelastic, reactive, and photodissociation processes over one or multiple coupled diabatic electronic states.

Significance. If the advertised capabilities are correct, MADWAVE3 is a useful open-source alternative to time-independent codes for triatomic state-to-state dynamics, and the repository with example inputs, the potential, and auxiliary analysis tools is a practical strength. The J=0 comparison against the independent ABC code is a genuinely non-circular check of the single-surface reactive/inelastic machinery, and the parallel-scaling study is informative. However, the evidence in the manuscript covers only a single-electronic-state, iphoto=0 collision benchmark; the nonadiabatic and photodissociation paths named in the abstract are not exercised. The paper would be considerably strengthened by quantitative convergence data and by at least one benchmark of the coupled-state or photodissociation code paths.

major comments (3)
  1. [§6.2 and Figure 2; §2.1 Eq. (5); §2.3.2 Eq. (13); §2.4 Eq. (18)] The only quantitative validation in the paper is for nelec=1 and iphoto=0. The off-diagonal electronic couplings in the Hamiltonian of Eq. (5), the coupled-electronic-state product basis of Eq. (18), and the photodissociation initial-state construction of Eqs. (13)-(16) are never exercised by any reported test. Since the abstract states that the code computes photodissociation processes and works over multiple coupled diabatic electronic states, the present evidence supports only the single-surface collision claim. Please add a validation case for at least one nonadiabatic or photodissociation process, or explicitly restrict the claims made in the abstract and conclusions to single-surface collisions.
  2. [§6.2 and Figure 2] The agreement with ABC is described only as 'excellent', with no numerical deviations, no maximum or mean absolute error, and no systematic convergence study over the parameters listed in Table 1 (grid sizes, absorption parameters, number of Chebyshev iterations). As written, the benchmark is visual and cannot be independently verified quantitatively. Please report numerical differences from ABC and a convergence test for the key propagation and grid parameters.
  3. [§2.5, Eq. (22)] Eq. (22) defines the cumulative probability with a free index Ω' on the S-matrix element but no sum over Ω'. For a state-to-state cross section to a final v',j', all final helicity projections must be summed. As written, the formula would omit the final-helicity degeneracy contribution and is incomplete. Please clarify whether the sum over Ω' is implicit in the code’s definition of the S-matrix files, and correct Eq. (22) accordingly.
minor comments (5)
  1. [§7, Eq. (27)] The divisibility condition in Eq. (27) appears to be reversed: if nγ angular points are distributed over nγ_proc processors, the requirement should be that nγ is divisible by nγ_proc (mod(nγ,nγ_proc)=0), not that nγ_proc is divisible by nγ. The nproc values used in Figure 5 are inconsistent with the printed condition.
  2. [Figure 2 caption and §6.2 text] The text says the inelastic probabilities are in the top panel and reactive probabilities in the bottom panel, while the caption says the reverse. The panel labels in the figure itself also disagree with the caption. Please make the text, caption, and panels consistent.
  3. [§6.1 and §8] The in-house H3 potential is described only as reproducing BKMP2 'very well', with no quantitative comparison or fitting details. Since the ABC benchmark and the presented cross sections both use this potential, please document its deviations from BKMP2 or use the published BKMP2 surface so that the physical results are reproducible and independently checkable.
  4. [§8, Conclusions] The conclusions state that 'the D + H2+ → DH+ + H is presented as an use example', but the example in Section 6 is H + DH → H2 + D. Please correct this sentence.
  5. [§6.3 and Figure 5] The state-to-state cross sections in Figure 4 are shown without any independent comparison or convergence test. Even a J>0 ABC comparison for one partial wave would help; alternatively, state explicitly that these cross sections are illustrative. Also, the notation 'nOM P proc' in Figure 5 and the statement that J=9 has Ω=0,...,10 (with nΩ=10) should be clarified, since Ω usually ranges only up to J.

Circularity Check

0 steps flagged · score 0.0 of 10

No material circularity: the central numerical claim is validated against the external ABC code, and the paper's self-citations are methodological rather than load-bearing.

full rationale

The paper's central quantitative claim is that MADWAVE3 reproduces state-to-state inelastic and reactive probabilities for H+DH, and this is checked against the independent time-independent ABC code in Figure 2. That is an external benchmark: the ABC code is a different program based on hyperspherical coordinates, and the agreement is not manufactured from MADWAVE3's own outputs. The load-bearing validation sentence, "The agreement between the MADWAVE3 and ABC results is excellent, what demonstrates the convergence and accuracy achieved with the parameters used," asserts agreement with an independent implementation, so the core numerical claim is self-contained. The methodological self-citations, such as Ref. [1] for DVR/FBR transformations and Ref. [2] for the reactant-coordinate transformation used with iprod=2, are not invoked as uniqueness theorems or as substitutes for validation; the ABC comparison independently exercises the RCB path for the single-electronic-state case. The J-shifting interpolation of Eq. (23) uses a fitted rotational constant B, but the paper explicitly states that B is "previously fitted for each [J1,J2] interval" and presents this as an approximation, not as a first-principles prediction; it does not feed back into the ABC validation. The in-house H3 potential is an input, not an output of the calculation, and no circular definition links it to the reported probabilities. The advertised photodissociation and multiple-coupled-electronic-state capabilities are not benchmarked in the example, but that is a validation-scope gap, not a circularity: nothing in the paper reduces those capabilities to the ABC agreement or to a fitted parameter. Therefore no circular step can be identified with the required specific reduction, and the appropriate score is 0.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The central claim rests on standard quantum wave packet machinery, modified Chebyshev propagation, flux analysis, and reactant/product coordinate transformations, drawn from published literature, plus user-tuned numerical parameters such as absorption strengths and grid sizes. The domain-specific assumptions, the validity of the diabatic representation and the faithfulness of the user-supplied PES, are not exercised by the paper's only validation, which is single-state. No new physical entities are introduced.

free parameters (5)
  • Absorption parameters for r (absr1, absalp1, n1expo) = not reported; user-tuned in the example
    The complex absorbing potential in Eq. (7) must be tuned to suppress reflection, and the paper states these parameters need optimization (Section 2.2). The reported results depend on this choice.
  • Absorption parameters for R (absr2, absalp2, n2expo) = not reported; user-tuned in the example
    Same as above for the R coordinate; the paper gives no default that guarantees convergence across systems.
  • Grid sizes (npun1, npun2, nangu) = example: 256, 256, 140
    Chosen by hand through convergence checks (Section 6.2); the central results depend on the grids being large enough to converge the dynamics.
  • Energy cutoffs (vcutmaxeV, radcutmaxeV, rotcutmaxeV) = example: 2.5, 2.5, 5.0 eV
    Chosen to limit the L-shaped grid; these cutoffs prune the Hamiltonian and must be large enough not to affect the dynamics (Section 2.1, Table 1).
  • J-shifting rotational constant B = not reported; fitted per [J1,J2] interval
    Eq. (23) uses a B fitted for each interval to interpolate probabilities to intermediate J values (Section 2.5). This fit is not used in the primary ABC comparison.
assumptions (5)
  • standard math The modified Chebyshev propagator (Eq. 6) correctly yields the wave packet and S-matrix via Eqs. (8) and (9).
    Taken from Mandelshtam and Taylor (ref 22) and Tal-Ezer and Kosloff (ref 23); the paper does not re-derive the convergence of the series.
  • domain assumption A diabatic electronic representation with no kinetic coupling terms is adequate for the systems treated.
    Section 2.1 states kinetic couplings are neglected; the validity depends on the user-supplied diabatic PES, and the paper's only benchmark is a single-state case where the issue does not arise.
  • standard math The incoming half of the real initial wave packet fully determines reaction probabilities.
    Eqs. (11) and (12) follow ref 28; the outgoing half is asserted to not contribute to products.
  • standard math The total flux through a surface at r* equals the sum over S-matrix elements.
    Eq. (17) relies on refs 32 to 35 and on the standard flux formula for real wave packets.
  • domain assumption The in-house H3 potential used in the example faithfully represents the H+DH interaction.
    Section 6.1 says this PES reproduces very well the BKMP2 surface, but no fitting details or independent validation are given; the physical cross sections inherit any PES error, though the code-to-code comparison with ABC is largely insensitive to it if the same potential is used.

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Cite this review

Pith. "Pith review of MADWAVE3: a quantum time dependent wave packet code for nonadiabatic state-to-state reaction dynamics of triatomic systems." pith.science (2026). https://pith.science/paper/3RPZOPQD

@misc{pith2026241210167,
  author       = {Pith},
  title        = {Pith review of: MADWAVE3: a quantum time dependent wave packet code for nonadiabatic state-to-state reaction dynamics of triatomic systems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/3RPZOPQD}},
  note         = {Machine review of arXiv:2412.10167}
}
read the original abstract

We present MADWAVE3, a FORTRAN90 code designed for quantum time dependent wave packet propagation in triatomic systems. This program allows the calculation of state-to-state probabilities for inelastic and reactive collisions, as well as photodissociation processes, over one or multiple coupled diabatic electronic states. The code is highly parallelized using MPI and OpenMP. The execution requires the potential energy surfaces of the different electronic states involved, as well as the transition dipole moments for photodissociation processes. The formalism underlying the code is presented in section 2, together with the modular structure of the code. This is followed by the installation procedures and a comprehensive list and explanation of the parameters that control the code, organized within their respective namelists. Finally, a case study is presented, focusing on the prototypical reactive collision H+DH(v,j) -> H2(v',j') + D. Both the potential energy surface and the input files required to reproduce the calculation are provided and are available on the repository main page. This example is used to study the parallelization speedup of the code.

Figures

Figures reproduced from arXiv: 2412.10167 by the authors.

Figure 1
Figure 1. Left panel presents the total flux in black (column 3 of files S2prod.v00.J000.k [PITH_FULL_IMAGE:figures/full_fig_p030_1.png] view at source ↗
Figure 2
Figure 2. State-to-state probabilities for the HD( [PITH_FULL_IMAGE:figures/full_fig_p032_2.png] view at source ↗
Figure 3
Figure 3. Total H2 reaction probabilities for several J. Solid lines are MADWAVE3 results, while dashed lines correspond to J-shifting results, i.e., obtained from that of J = 0 as P J (E) = P J=0(E + J(J + 1)) [39], where B= 1.7 meV is an effective rotational constant. 33 [PITH_FULL_IMAGE:figures/full_fig_p033_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: State-to-state cross section for reactive (bottom panel) and inelastic (top panel) [PITH_FULL_IMAGE:figures/full_fig_p035_4.png]
Figure 5
Figure 5. Figure 5: Parallel speedup obtained for J=0 (nΩ = 1) and J=9 (nΩ = 1), for different number of processors, nproc and , n OMP proc The speedup for J = 0 (blue line) increases continuously up to nproc 20, presenting an extra-speedup from 20 to 28, just when two nodes are used. In …

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Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.