Quasi-Diabatic Scheme for Non-adiabatic On-the-fly Simulations

Arkajit Mandal; Pengfei Huo; Wanghuai Zhou

REVIEW 3 major objections 6 minor 72 references

Quasi-Diabatic Scheme for Non-adiabatic On-the-fly Simulations

T0 review · 3 major / 6 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The quasi-diabatic scheme lets diabatic quantum dynamics methods run directly on adiabatic ab initio data, with ethylene dynamics matching AIMS and outperforming FSSH.

desk verdict A genuinely useful first on-the-fly demonstration of the QD scheme, but the AIMS benchmark level is ambiguous and the comparison deserves a hard look before the headline claim is taken at face value. read the letter →

arxiv 1908.05219 v1 pith:5DH7NUY2 submitted 2019-08-14 physics.comp-ph cond-mat.otherphysics.chem-phquant-ph

Wanghuai Zhou , Arkajit Mandal , Pengfei Huo This is my paper · ORCID

classification physics.comp-phcond-mat.otherphysics.chem-phquant-ph

keywords quasi-diabaticschemenon-adiabaticmoleculardynamicson-the-flysimulationpartiallinearizeddensitymatrixsymmetricquasi-classicalapproachCASSCFethylenephotodynamicsconicalintersections

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

This paper claims that a 'quasi-diabatic' (QD) propagation scheme—using the adiabatic electronic states at a fixed reference geometry as a local diabatic basis over each short nuclear propagation segment—provides a seamless interface between diabatic quantum dynamics methods and conventional adiabatic electronic structure calculations. The authors demonstrate the scheme on the first ab initio on-the-fly example, the photodynamics of ethylene at the SA-3-CASSCF(2,2)/6-31G* level, running two diabatic methods, partial linearized density matrix (PLDM) and symmetric quasi-classical (SQC) dynamics. They report that QD-PLDM and QD-SQC population dynamics agree closely with the ab initio multiple spawning (AIMS) benchmark and outperform decoherence-corrected fewest-switches surface hopping (FSSH). If the claim holds, the scheme removes the need to construct global diabatic surfaces or reformulate diabatic dynamics into the adiabatic representation, giving many recently developed quantum dynamics approaches a direct route to on-the-fly ab initio simulation and realistic test cases.

What carries the argument

The central object is the quasi-diabatic basis, defined per short propagation segment by freezing the adiabatic states at the reference geometry $R_0\equiv R(t_0)$: $|\Phi_\alpha(R_0)\rangle \equiv |\Phi_\alpha(R(t_0))\rangle$ for $t\in[t_0,t_1]$. This basis makes the derivative coupling vanish inside the segment and converts the electronic Hamiltonian into a matrix with off-diagonal couplings, computed as $V_{\alpha\beta}(R(t_1))=\sum_{\lambda\nu}S_{\alpha\lambda}\,E_\lambda(R(t_1))\,\delta_{\lambda\nu}\,S^\dagger_{\beta\nu}$ with overlap matrix $S_{\alpha\lambda}=\langle\Phi_\alpha(R_0)|\Phi_\lambda(R(t_1))\rangle$, and using nuclear gradients $\nabla V_{\alpha\beta}(R(t_1))$ built from the full nuclear dependence of the adiabatic states. These quantities avoid the singular derivative couplings and non-adiabatic couplings that can destabilize other approaches near conical intersections, and they supply the mapping-Hamiltonian forces needed by PLDM and SQC. This machinery is what carries the seamless interface between diabatic dynamics and adiabatic electronic structure.

What would settle it

Run QD-PLDM ethylene photodynamics at nuclear time steps of 0.05, 0.1, and 0.5 fs and check whether the S1/S0 population curves converge; significant step-size dependence would indicate the frozen quasi-diabatic basis is not converged at the tested step sizes.

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Extended reading notes

Core claim

The central discovery is that non-adiabatic dynamics methods formulated in a diabatic representation do not need global diabatic states to run on the fly. During each short time segment $t\in[t_0,t_1]$, the QD scheme defines the quasi-diabatic basis as the adiabatic states at the segment's starting geometry, $|\Phi_\alpha(R_0)\rangle \equiv |\Phi_\alpha(R(t_0))\rangle$. In this basis derivative couplings vanish within the segment, while the electronic Hamiltonian $V_{\alpha\beta}(R(t))$ acquires off-diagonal elements obtained by linear interpolation between the diagonal values at $R(t_0)$ and the overlap-transformed values at $R(t_1)$, with gradients $\nabla V_{\alpha\beta}(R(t_1))$ computed from adiabatic energies and state overlaps. Using PLDM and SQC as diabatic dynamics engines, the paper presents the first ab initio on-the-fly ethylene photodynamics driven by CASSCF, obtains S1/S0 population dynamics in close agreement with AIMS and better than FSSH over 200 fs, and recovers the competing non-radiative pathways through the twisted-pyramidalized and ethylidene conical intersections, with about half the trajectories traversing each channel.

Load-bearing premise

The argument assumes that the adiabatic electronic states frozen at each segment's starting geometry remain an accurate local basis through the whole short propagation segment, and that the AIMS benchmark describes the same electronic-structure-level dynamics; if either fails, the reported agreement would not be meaningful.

Editorial extensions

If this is right

Any diabatic quantum dynamics method that only needs a local electronic Hamiltonian matrix and its gradients can be coupled directly to standard adiabatic electronic structure packages, without representation reformulation or global diabatization.
QD-PLDM and QD-SQC reproduce the AIMS benchmark populations for the CAS(2,2) ethylene model, while decoherence-corrected FSSH relaxes too quickly; the QD-based methods are thus more accurate than a widely used trajectory surface hopping method on this test.
Because the QD scheme replaces derivative couplings with well-behaved overlap and gradient quantities, methods built on it may be numerically robust near trivial crossings and conical intersections where derivative couplings become singular.
The scheme enables realistic ab initio test cases—such as ethylene photodynamics—to assess approximate diabatic dynamics methods, and here it correctly predicts the competing non-radiative channels (ethylidene and twisted-pyramidalized conical intersections, and H2 dissociation).

Reading between the lines

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

If the QD basis approximation is as good as this one-molecule test suggests, the same interface should work for any electronic structure method that can supply adiabatic energies, gradients, and state overlaps—for example, methods describing charge transfer or Rydberg states—provided the reference geometry is refreshed often enough to track changing electronic character.
A direct convergence test of the nuclear time step (e.g., dt = 0.05 vs 0.1 vs 0.5 fs) would isolate the error coming from the frozen-basis assumption; the paper uses dt = 0.1 fs and notes 0.5 fs works at the single-trajectory level but does not report a systematic population convergence study.
The QD scheme's replacement of derivative couplings by overlap matrices suggests a natural route for interfacing with machine-learned or otherwise approximate representations of $V_{\alpha\beta}$ and gradients, potentially extending on-the-fly diabatic dynamics to larger systems where analytic couplings are unavailable.
For systems with more than two coupled states, the scheme will need careful treatment of state-tracking phase conventions and orthonormalization (both mentioned in the SI), and a many-state generalization would be a natural next validation.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

The real news here is straightforward: this is the first ab initio on-the-fly application of the quasi-diabatic (QD) propagation scheme, and it works. The authors take two diabatic methods, PLDM and SQC, and run them on ethylene photodynamics with SA-3-CASSCF(2,2)/6-31G* surfaces, without building a global diabatic model or reformulating the dynamics into the adiabatic representation. That is a concrete capability demonstration, and the population dynamics agree reasonably with their chosen benchmark and beat decoherence-corrected FSSH in this case. The method section is honest about the local nature of the basis, and the equations for the QD potentials and gradients are standard and sound. I also appreciate that they openly note the QD scheme does not strictly avoid derivative-coupling-like quantities; it trades them for overlap matrices and gradients, which is a fair and useful framing. No fitted parameters, 120 trajectories, Wigner sampling—this is a careful simulation study, not a toy.

Now the soft spots, in proportion. The biggest one is the AIMS benchmark. The text says in one place that AIMS used CASPT2 (ref 55 is a MS-CASPT2 paper) and in another that AIMS is at CASSCF level (refs 54, 55). That is an internal inconsistency in the manuscript itself, and it matters. If the AIMS curve in Fig. 2 is from a CASPT2 calculation, then the comparison is between different electronic Hamiltonians, and close agreement between QD-PLDM and AIMS would be partly coincidental, not a clean validation of the QD interface at the CASSCF level used. The authors need to resolve this—state explicitly which electronic structure level the AIMS benchmark used and, if it was CASPT2, make clear that the comparison is illustrative rather than a strict validation. That is a load-bearing ambiguity, not a style nit.

Second, there are no error bars on the trajectory populations. With 120 trajectories, sampling noise in the nonadiabatic decay window is non-negligible, and the small reported differences between QD-PLDM and QD-SQC could be within noise. The SQC population is visibly noisy and they note the windowing issue, but they do not quantify it. A simple bootstrap over trajectories would address this.

Third, the SI is referenced but not included in the preprint. For a method paper whose whole point is enabling others to do the same thing, missing the numerical details (overlap computation, phase tracking, Löwdin steps) is a real impediment. Code release would be even better.

Is the central argument sound? The core idea—crude adiabatic states as a local diabatic basis with dynamical updating—is not new here; it is in their earlier work, and they cite it properly. The contribution is the first realistic on-the-fly test, and that is a legitimate contribution. If the AIMS level is clarified and error bars are added, the central claim should hold up. I would not desk-reject this. The community needs more real-molecule tests of diabatic methods, and this is a credible step. Send it to a referee who knows both mapping-based dynamics and ethylene photochemistry, and ask pointed questions about the benchmark level and the statistical significance of the differences. It deserves serious review, not a rubber stamp.

Who is this for? People working on nonadiabatic dynamics methods and their interfacing with electronic structure. I would bring it to a reading group focused on semiclassical dynamics, and I would probably cite it as the first on-the-fly QD application once the SI and benchmark details are settled.

Referee Report

3 major / 6 minor

Summary. The paper presents the first on-the-fly ab initio application of the quasi-diabatic (QD) propagation scheme, in which adiabatic states at a reference geometry are used as local diabatic states during each short nuclear propagation segment and are dynamically updated along the trajectory. The authors interface this QD scheme with two diabatic quantum dynamics methods, PLDM and SQC, and use it to simulate the nonadiabatic photodynamics of ethylene at the SA-3-CASSCF(2,2)/6-31G* level. The central claim, stated in the abstract and conclusions, is that QD-PLDM and QD-SQC produce adiabatic population dynamics in close agreement with an AIMS benchmark and that both outperform decoherence-corrected FSSH. In addition, the paper analyzes representative reactive trajectories and product populations, arguing that the QD-based simulations correctly capture the competing nonradiative decay pathways through different conical intersections. The manuscript also provides the formal expressions for the quasi-diabatic potential and gradient matrix elements (Eqs. 3-7), emphasizing that no global diabatic surfaces or representation reformulation of the dynamics methods are required.

Significance. If the central claim holds, the paper is a significant methodological advance: it demonstrates that a broad class of diabatic quantum dynamics approaches can be coupled directly to adiabatic electronic structure calculations, eliminating the need to construct global diabatic potentials or rederive equations of motion in the adiabatic representation. The demonstration uses a realistic, non-model test case (ethylene photodynamics) and compares against an independent wavepacket benchmark rather than fitting parameters, which is a strong validation strategy for a methods paper. The formal QD equations in Eqs. 3-7 are internally consistent, and the absence of trajectory-specific fitted parameters (the SQC square-window parameter being a fixed methodological constant) strengthens the credibility of the reported comparison. The reactive-trajectory and product-population analyses also add mechanistic value beyond the population curves. However, the benchmark-level ambiguity and the lack of statistical uncertainties mean that the quantitative strength of the headline comparison is not yet established.

major comments (3)

[Results and Discussion, Fig. 2] The level of electronic structure behind the AIMS benchmark is ambiguous and this ambiguity is load-bearing. The text attributes Ref. 55 to AIMS using CASPT2, yet the same paragraph calls the benchmark 'the almost exact quantum dynamics of the CAS(2,2) ethylene model' provided by AIMS, and the later discussion refers to 'AIMS results performed at the CASSCF level of theory (54, 55)'. If the filled circles in Fig. 2 come from MS-CASPT2 rather than CASSCF, the comparison is between different electronic Hamiltonians and the close agreement in Fig. 2B/C would not validate the QD interface at the SA-3-CASSCF level actually used in the QD simulations. The authors should state explicitly which electronic structure level produced the AIMS curves in Fig. 2, cite the correct reference, and, if the benchmark is CASPT2, provide the corresponding CASSCF-level AIMS result for a consistent comparison.
[Fig. 2 and Calculation Details] No statistical uncertainties are reported for the 120-trajectory population curves, although the QD-SQC curve is visibly noisy and the differences among methods in the bottom panels are comparable in size to the apparent noise. The claims of 'close agreement with AIMS' and of outperforming FSSH should be supported by error bars or confidence intervals obtained from trajectory statistics, and ideally by a convergence test with respect to the number of trajectories for at least one of the QD methods.
[Eq. 2 and Calculation Details] The central quasi-diabatic approximation, namely that the crude adiabatic states at a fixed reference geometry form a valid local diabatic basis over the propagation segment, is only tested indirectly through agreement with AIMS. The statement that dt = 0.5 fs reproduces the single-trajectory result is not a convergence test of the ensemble population dynamics. A direct convergence study with respect to the nuclear time step (e.g., dt = 0.05, 0.1, and 0.2 fs) would substantiate the finite-step approximation embodied in Eqs. 3-5 and rule out the possibility that the close agreement in Fig. 2 is accidental.

minor comments (6)

[Eq. 4] Equation 4 contains typographical errors: 'Vαβ(R0))' should read 'Vαβ(R0)' in both occurrences.
[Abstract and Significance Statement] The phrase 'ab-inito' should be 'ab initio', and the term 'dibabatic' near the end of the Introduction should be 'diabatic'.
[Fig. 4] The y-axis label 'Strucutre proportion' is misspelled and should read 'Structure proportion'.
[Fig. 3 caption] The sentence 'Fig. 3 presets three representative reactive trajectories' should read 'presents'.
[Calculation Details] The sentence 'a much larger time-step dt = 0.5 fs can be used and generates the same results at the single trajectory level' is vague; the reference time step and the metric used to compare single trajectories should be specified.
[Materials and Methods] The supporting information is referenced several times but is not included in the manuscript; if it is not part of the submission package, the key technical details (phase tracking of adiabatic states and Löwdin orthonormalization) should be summarized in the main text.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: QD population dynamics are independent predictions benchmarked against external AIMS data; self-citations to the authors' QD scheme are not load-bearing.

full rationale

The central quantitative claims (QD-PLDM and QD-SQC population dynamics, product branching fractions) are generated by forward non-adiabatic simulation with no parameters fitted to the AIMS benchmark or to the target populations. The quasi-diabatic Hamiltonian matrix elements and gradients (Eqs. 3-7) are evaluated from on-the-fly SA-3-CASSCF(2,2)/6-31G* electronic structure data and overlap matrices, not defined in terms of the quantities being predicted. The only self-citations (Refs. 40, 41, 48, 49) are to the authors' own earlier QD-scheme papers, but the present paper restates and re-derives the local quasi-diabatic construction, and it does not invoke any uniqueness theorem to forbid alternatives. The AIMS benchmark is external (Ref. 55), so the agreement or disagreement is an empirical outcome rather than a construction. The manuscript's internal ambiguity about whether the AIMS reference data use CASSCF or CASPT2 is a benchmark-consistency concern that could affect the validity of the comparison, but it is a correctness/technical issue and not a circularity: the QD results are not defined in terms of the AIMS results. No step was found where a prediction reduces by construction to an input, a fitted parameter, or a self-citation chain.

Assumptions & free parameters 1 free parameters · 8 assumptions · 0 invented entities

The paper uses no fitted parameters or invented entities. The QD scheme, PLDM, SQC, and AIMS are all established methods. The central claim rests on the local-diabatic approximation, the chosen electronic structure level, and the validity of the benchmarks.

free parameters (1)

SQC square window parameter = Standard square window (Cotton and Miller, ref 50)
The SQC method's window width is taken from prior work, not fitted here; the authors state they use the simplest square window function.

assumptions (8)

domain assumption The crude adiabatic basis at a reference geometry is a valid local diabatic basis for a short-time propagation segment (Eq. 2).
Core premise of the QD scheme; if the electronic states rotate significantly within dt, the quasi-diabatic potential and dynamics are inaccurate.
domain assumption The dynamics is confined to the S0/S1 subspace; Rydberg and higher states are ignored.
Used for CASSCF(2,2)/6-31G* model; ethylene Rydberg states could participate at high energies.
domain assumption CASSCF(2,2)/6-31G* provides accurate potentials, gradients, and overlaps for the dynamics in this model.
Adopted from prior ethylene studies; basis set may not describe Rydberg states.
domain assumption The potential matrix can be linearly interpolated between t0 and t1 (Eq. 4).
Approximation for on-the-fly dynamics; tested indirectly with dt=0.5 fs.
domain assumption Overlap integrals between adiabatic states at different geometries are computed accurately with the method of ref 71.
Needed for transformation matrices; numerical errors in overlaps would propagate to populations.
domain assumption PLDM's linearization approximation and MMST mapping are valid for this system.
Standard approximate quantum dynamics method; accuracy depends on system.
domain assumption AIMS provides a near-exact benchmark for the CAS model.
Used as reference; if the AIMS results are at a different electronic structure level, the benchmark is mismatched.
domain assumption SQC square window function is a valid approximation.
Standard method with a parameter; results may vary with window choice.

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Cite this review

Pith. "Pith review of Quasi-Diabatic Scheme for Non-adiabatic On-the-fly Simulations." pith.science (2026). https://pith.science/paper/5DH7NUY2

@misc{pith2026190805219,
  author       = {Pith},
  title        = {Pith review of: Quasi-Diabatic Scheme for Non-adiabatic On-the-fly Simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5DH7NUY2}},
  note         = {Machine review of arXiv:1908.05219}
}

read the original abstract

This paper provides the first ab-initio on-the-fly example of using the Quasi-Diabatic (QD) scheme for non-adiabatic simulations with diabatic dynamics approaches. The QD scheme provides a seamless interface between diabatic quantum dynamics approaches and {\it adiabatic} electronic structure calculations. It completely avoids additional theoretical efforts to reformulate the equation of motion from diabatic to adiabatic representation, or construct global diabatic surfaces. This scheme enables many recently developed diabatic quantum dynamics approaches for ab-inito on-the-fly simulations, providing the non-adiabatic community a wide variety of approaches (such as the real-time path integral method and symmetric quasi-classical approach) beyond the well-explored methods (like trajectory surface-hopping or ab-initio multiple-spawning). The QD scheme also enables using realistic test cases (like ethylene photodynamics) that go beyond simple model systems to assess the accuracy and limitation of recently developed quantum dynamics approaches.

Figures

Figures reproduced from arXiv: 1908.05219 by the authors.

**Figure 1.** CASSCF potential energy surface of S1 (upper surface) and S0 (lower surface) along two main reaction coordinates of photo-dissociation pathways in ethylene. Upon photo-excitation, the system quickly relax to the minimum along the twist angle on the S1 surface, then pyramidalized and relax back to the S0 through the twistedpyramidalized conical intersection. of the electronic structure of ethylene, we follow the pre… view at source ↗

**Figure 2.** B presents the comparison of the population dynamics obtained from QD-PLDM (solid lines) and the decoherence corrected FSSH (dashed lines), and AIMS (filled circles). The population differences between the trajectory based approaches and AIMS are presented in the bottom panel. All three approaches provide the same plateau of the S1 population (t = 0 ∼20 fs), which corresponds to the initial adiabatic nuclear rela… view at source ↗

**Figure 3.** Representative QD-PLDM reactive trajectories for (A) hydrogen transfer (B) pyramidalization, and (C) H2 dissociation pathways, respectively. The C-H bond lengths are defined in the inset of panel A, and used in both panels A and C. The pyramidalization angle is defined in the inset of panel B. through the ethylidene-like conical intersection (55) (which is different than the twisted-pyramidalized conical intersectio… view at source ↗

Figures from the paper (1 more)

**Figure 4.** Figure 4: presents the population of various nuclear configurations obtained from QD-PLDM through the ensemble average of trajectories. These nuclear configurations are defined based on the criteria in Ref. (65), with the representative geometries provided on top of this figur…

Discussion (0). Continue with ORCID to comment.

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Works this paper leans on

72 extracted references · 72 canonical work pages

[1]

John C. Tully. Perspective: Nonadiabatic dynamics theory. J. Chem. Phys., 137(22):22A301, 2012

work page 2012
[2]

Subotnik, Ethan C

Joseph E. Subotnik, Ethan C. Alguire, Qi Ou, Brian R. Landry, and Shervin Fatehi. The req- uisite electronic structure theory to describe photoexcited nonadiabatic dynamics: Nonadia- batic derivative couplings and diabatic electronic couplings.Acc. Chem. Res., 48:1340–1350, 2015

work page 2015
[3]

B. G. Levine and T. J. Martinez. Isomerization through conical intersections. Annu. Rev. Phys. Chem., 58:613–634, 2007

work page 2007
[4]

Nelson, S

T. Nelson, S. Fernandez-Alberti, A. E. Roitberg, , and S. Tretiak. Nonadiabatic excited-state molecular dynamics: Modeling photophysics in organic conjugated materials. Acc. Chem. Res., 47:1155–1164, 2014. Zhou et al. —- | August 15, 2019 | vol. XXX | no. XX | 5

work page 2014
[5]

Mi Kyung Lee, Pengfei Huo, and David F . Coker. Semiclassical path integral dynamics: Pho- tosynthetic energy transfer with realistic environment interactions. Annu. Rev. Phys. Chem. , 67(1):639–668, 2016

work page 2016
[6]

Crespo-Otero and M

R. Crespo-Otero and M. Barbatti. Recent advances and perspectives on nonadiabatic mixed quantum-classical dynamics. Chem. Rev., 118:7026–7068, 2018

work page 2018
[7]

B. F . E. Curchod and T. J. Martinez. Ab initio nonadiabatic quantum molecular dynamics. Chem. Rev., 118:3305–3336, 2018

work page 2018
[8]

John C. Tully. Molecular dynamics with electronic transitions. J. Chem. Phys. , 93(2):1061– 1071, 1990

work page 1990

Show all 72 references

[9]

Nonadiabatic processes in condensed matter: Semi-classical theory and implementation

Frank Webster, P .J.Rossky, and R.A.Friesner. Nonadiabatic processes in condensed matter: Semi-classical theory and implementation. Comput. Phys. Commun., 63(1):494–522, 1991

1991
[10]

Nonadiabatic dynamics of excited excess electrons in simple ﬂuids

B Space and DF Coker. Nonadiabatic dynamics of excited excess electrons in simple ﬂuids. J. Chem. Phys., 94(3):1976–1984, 1991

1976
[11]

Sharon Hammes-Schiffer and John C. Tully. Proton transfer in solution: Molecular dynamics with quantum transitions. J. Chem. Phys., 12:4657–4667, 1994

1994
[12]

Understanding the surface hopping view of electronic transitions and decoherence

Joseph E Subotnik, Amber Jain, Brian Landry, Andrew Petit, Wenjun Ouyang, and Nicole Bellonzi. Understanding the surface hopping view of electronic transitions and decoherence. Annu. Rev. Phys. Chem., 67:387–417, 2016

2016
[13]

Subotnik

Amber Jain, Ethan Alguire, and Joseph E. Subotnik. An efﬁcient, augmented surface hopping algorithm that includes decoherence for use in large-scale simulations. J. Chem. Theory Comput., 12:5256–5268, 2016

2016
[14]

Recent progress in surface hopping: 2011–2015

Linjun Wang, Alexey Akimov, and Oleg V Prezhdo. Recent progress in surface hopping: 2011–2015. J. Phys. Chem. Lett. , 7(11):2100–2112, 2016

2011
[15]

Nonadiabatic dynamics with trajectory surface hopping method

Mario Barbatti. Nonadiabatic dynamics with trajectory surface hopping method. Wiley Int. Rev. Comp. Mol. Sci., 1:620–633, 2011

2011
[16]

Quenneville M

J. Quenneville M. Ben-Nun and T. J. Martinez. Ab initio multiple spawning: Photochemistry from ﬁrst principles quantum molecular dynamics. J. Phys. Chem. A , 104(22):5161–5175, 2000

2000
[17]

Saita and D

K. Saita and D. V. Shalashilin. On-the-ﬂy ab initio molecular dynamics with multiconﬁgura- tional ehrenfest method. J. Chem. Phys., 137:22A506, 2012

2012
[18]

Makhov, William J

Dmitry V. Makhov, William J. Glover, Todd J. Martinez, and Dmitrii V. Shalashilin. Ab initio multiple cloning algorithm for quantum nonadiabatic molecular dynamics. J. Chem. Phys. , 141(5):054110, 2014

2014
[19]

Makhov, Sergei Tretiak, and Dmitrii V

Sebastian Fernandez-Alberti, Dmitry V. Makhov, Sergei Tretiak, and Dmitrii V. Shalashilin. Non-adiabatic excited state molecular dynamics of phenylene ethynylene dendrimer using a multiconﬁgurational ehrenfest approach. Phys. Chem. Chem. Phys. , 18:10028, 2016

2016
[20]

Joubert-Doriol and A

L. Joubert-Doriol and A. F . Izmaylov. Variational nonadiabatic dynamics in the moving crude adiabatic representation: Further merging of nuclear dynamics and electronic structure. J. Chem. Phys., 148:114102, 2018

2018
[21]

Meek and Benjamin G

Garrett A. Meek and Benjamin G. Levine. The best of both reps-diabatized gaussians on adiabatic surfaces. J. Chem. Phys., 145:184103, 2016

2016
[22]

Seung Kyu Min, Federica Agostini, OrcidIvano Tavernelli, and E. K. U. Gross. Ab initio nona- diabatic dynamics with coupled trajectories: A rigorous approach to quantum (de)coherence. J. Phys. Chem. Lett. , 8:3048–3055, 2017

2017
[23]

Curchod, Federica Agostini, and Ivano Tavernelli

Basile F .E. Curchod, Federica Agostini, and Ivano Tavernelli. Ct-mqc-a coupled-trajectory mixed quantum/classical method including nonadiabatic quantum coherence effects. Eur. Phys. J. B, 91:168, 2018

2018
[24]

Sato, Aaron Kelly, and Angel Rubio

Shunsuke A. Sato, Aaron Kelly, and Angel Rubio. Coupled forward-backward trajectory ap- proach for nonequilibrium electron-ion dynamics. Phys. Rev. B, 97:134308, 2018

2018
[25]

Craig C. Martens. Surface hopping by consensus. J. Phys. Chem. Lett. , 7:2610?2615, 2016

2016
[26]

G. W. Richings and S. Habershon. Mctdh on-the-ﬂy: Efﬁcient grid-based quantum dynamics without pre-computed potential energy surfaces. J. Chem. Phys., 148:134116, 2018

2018
[27]

G. W. Richings, C. Robertson, and S. Habershon. Improved on-the-ﬂy mctdh simulations with many-body-potential tensor decomposition and projection diabatisation. J. Chem. Theory Comput., 15:857–870, 2018

2018
[28]

J. R. Schmidt, Priya V. Parandekar, and John C. Tully. Mixed quantum-classical euilibrium: Surface hopping. J. Chem. Phys., 129:044104, 2008

2008
[29]

Mapping Quantum-Classical Liouville Equation: Projectors and Trajectories

A Kelly, R van Zon, J Schoﬁeld, and R Kapral. Mapping Quantum-Classical Liouville Equation: Projectors and Trajectories. J. Chem. Phys., 136:084101, 2012

2012
[30]

Pengfei Huo and David F . Coker. Communication: Partial linearized density matrix dynamics for dissipative, non-adiabatic quantum evolution. J. Chem. Phys., 135(20):201101, 2011

2011
[31]

Analysis of the Forward-Backward Trajectory Solution for the Mixed Quantum-Classical Liouville Equation

C-Y Hsieh and R Kapral. Analysis of the Forward-Backward Trajectory Solution for the Mixed Quantum-Classical Liouville Equation. J. Chem. Phys., 138:134110, 2013

2013
[32]

P . L. Walters and N. Makri. Iterative quantum-classical path integral with dynamically consis- tent state hopping. J. Chem. Phys., 144:044108, 2016

2016
[33]

Mapping variable ring polymer molecular dynamics: A path-integral based method for nonadiabatic processes

N Ananth. Mapping variable ring polymer molecular dynamics: A path-integral based method for nonadiabatic processes. J. Chem. Phys., 139:124102, 2013

2013
[34]

Richardson and Michael Thoss

Jeremy O. Richardson and Michael Thoss. Communication: Nonadiabatic ring-polymer molecular dynamics. J. Chem. Phys., 139:031102, 2013

2013
[35]

S. N. Chowdhury and P . Huo. Coherent state mapping ring-polymer molecular dynamics for non-adiabatic quantum propagations. J. Chem. Phys., 147:214109, 2017

2017
[36]

Miller and Stephen J

William H. Miller and Stephen J. Cotton. Classical molecular dynamics simulation of electron- ically non-adiabatic processes. Faraday Discuss., 195:9–30, 2016

2016
[37]

W. H. Miller and S. J. Cotton. Communication: Note on detailed balance in symmetrical quasi- classical models for electronically non-adiabatic dynamics. J. Chem. Phys. , 142:131103, 2015

2015
[38]

Dunietz, and Eitan Geva

Ellen Mulvihill, Alexander Schubert, Xiang Sun, Barry D. Dunietz, and Eitan Geva. A modiﬁed approach for simulating electronically nonadiabatic dynamics via the generalized quantum master equation. J. Chem. Phys., 150:034101, 2019

2019
[39]

Maximilian A. C. Saller, Aaron Kelly, and Jeremy O. Richardson. On the identity of the identity operator in nonadiabatic linearized semiclassical dynamics. J. Chem. Phys. , 150:071101, 2019

2019
[40]

Mandal, S

A. Mandal, S. Y amijala, and P . Huo. Quasi diabatic representation for nonadiabatic dynamics propagation. J. Chem. Theory Comput , 14:1828–1840, 2018

2018
[41]

Symmetric quasi classical dy- namics with quasi diabatic propagation scheme

Juan Sebastian Sandoval, Arkajit Mandal, and Pengfei Huo. Symmetric quasi classical dy- namics with quasi diabatic propagation scheme. J. Chem. Phys., 149(4):044115, 2018

2018
[42]

M. Baer. Adiabatic and diabatic representations for atom-diatom collisions: Treatment of the three-dimensional case. Chem. Phys., 18(1):49–57, 1976

1976
[43]

Alden Mead and Donald G

C. Alden Mead and Donald G. Truhlar. Conditions for the deﬁnition of a strictly diabatic electronic basis for molecular systems. J. Chem. Phys., 77:6090, 1982

1982
[44]

Cave and Marshall D

Robert J. Cave and Marshall D. Newton. Calculation of electronic coupling matrix elements for ground and excited state electron transfer reactions: Comparison of the generalized mulliken- hush and block diagonalization methods. J. Chem. Phys., 106(1):9213, 1997

1997
[45]

J. E. Subotnik, S. Y egenah, R. J. Cave, and M. A. Ratner. Constructing diabatic states from adiabatic states: Extending generalized mulliken-hush to multiple charge centers with boys localization. J. Chem. Phys., 128(1):244101, 2008

2008
[46]

The diabatic picture of electron transfer, reaction barriers, and molecular dynamics

Troy Van Voorhis, Tim Kowalczyk, Benjamin Kaduk, Lee-Ping Wang, Chiao-Lun Cheng, and Qin Wu. The diabatic picture of electron transfer, reaction barriers, and molecular dynamics. Annu. Rev. Phys. Chem., 61(1):149–170, 2010

2010
[47]

Y arkony

Hua Guo and David R. Y arkony. Accurate nonadiabatic dynamics.Phys. Chem. Chem. Phys., 18(1):26335–26352, 2016

2016
[48]

Mandal, F

A. Mandal, F . A. Shakib, and P . Huo. Investigating photoinduced proton coupled electron transfer reaction using quasi diabatic dynamics propagation. J. Chem. Phys. , 148:244102, 2018

2018
[49]

Sandoval, Farnaz A

Arkajit Mandal, Juan S. Sandoval, Farnaz A. Shakib, and Pengfei Huo. Quasi-diabatic prop- agation scheme for direct simulation of protoncoupled electron transfer reaction. J. Phys. Chem. A, 123:2470–2482, 2019

2019
[50]

Cotton and William H

Stephen J. Cotton and William H. Miller. Symmetrical windowing for quantum states in quasi-classical trajectory simulations: Application to electronically non-adiabatic processes. J. Chem. Phys., 139(23):234112, 2013

2013
[51]

Ben-Nun and T

M. Ben-Nun and T. J. Martínez. Ab initio molecular dynamics study of cis-trans photoisomer- ization in ethylene. Chem. Phys. Lett., 298:57–65, 1998

1998
[52]

Barbatti, J

M. Barbatti, J. Paier, and H. Lischka. Photochemistry of ethylene: A multireference conﬁgura- tion interaction investigation of the excited-state energy surface. J. Chem. Phys., 121:11614, 2004

2004
[53]

Barbatti, G

M. Barbatti, G. Grannucci, M. Persico, and H. Lischka. Semiempirical molecular dynamics investigation of the excited state lifetime of ethylene. Chem. Phys. Lett., 401:276–281, 2005

2005
[54]

B. G. Levine, J. D. Coe, A. M. Virshup, and T. J. Martínez. Implementation of ab initio multiple spawning in the MOLPRO quantum chemistry package. Chem. Phys., 347:3–16, 2008

2008
[55]

H. Tao, B. G. Levine, and T. J. Martínez. Ab initio multiple spawning dynamics using multi- state second-order perturbation theory. J. Phys. Chem. A , 113:13656–13662, 2009

2009
[56]

T. Mori, W. J. Glover, M. S. Schuurman, and T. J. Martínez. Role of Rydberg states in the photochemical dynamics of ethylene. J. Chem. Phys. A. , 116:2808–2818, 2011

2011
[57]

Kosma, S

K. Kosma, S. A. Trushin, W. Fuss, and W. E. Schmid. Ultrafast dynamics and coherent oscillations in ethylene and ethylene-d4 excited at 162 nm. J. Chem. Phys. A. , 112:7514– 7529, 2008

2008
[58]

Kobayashi, T

T. Kobayashi, T. Horio, and T. Suzuki. Ultrafast deactivation of theππ∗(V ) state of ethylene studied using sub-20 fs time-resolved photoelectron imaging. J. Chem. Phys. A. , 119:9518– 9523, 2015

2015
[59]

H. Tao, T. K. Allison, T. W. Wright, A. M. Stooke, C. Khurmi, J. van Tilborg, Y . Liu, R. W. Falcone, A. Belkacem, and T. J. Martínez. Ultrafast internal conversion in ethylene. I. the excited state lifetime. J. Chem. Phys., 134:224306, 2011

2011
[60]

T. K. Allison, H. Tao, W. J. Glover, T. W. Wright, A. M. Stooke, C. Khurmi, J. van Tilborg, Y . Liu, R. W. Falcone, T. J. Martínez, and A. Belkacem. Ultrafast internal conversion in ethylene. II. mechanisms and pathways for quenching and hydrogen elimination. J. Chem. Phys. , ...

2012
[61]

Hollas, L

D. Hollas, L. Šištík, E. G. Hohenstein, T. J. Martínez, and P . Slaví ˇcek. Nonadiabatic ab initio molecular dynamics with the ﬂoating occupation molecular orbital-complete active space conﬁguration interaction method. J. Chem. Theory Comput. , 14:339–350, 2018

2018
[62]

Werner, P

H.-J. Werner, P . J. Knowles, G. Knizia, F . R. Manby, and M. Schütz. Molpro: a general- purpose quantum chemistry program package. WIREs Comput Mol Sci , 2:242–253, 2012

2012
[63]

Nonadiabatic dynamics: The sharc approach

Sebastian Mai, Philipp Marquetand, and Leticia Gonzalez. Nonadiabatic dynamics: The sharc approach. WIREs Comput Mol Sci. , page e1370, 2018

2018
[64]

General method to describe inter- system crossing dynamics in trajectory surface hopping

Sebastian Mai, Philipp Marquetand, and Leticia Gonzalez. General method to describe inter- system crossing dynamics in trajectory surface hopping. International Journal of Quantum Chemistry, 115:1215–1231, 2015

2015
[65]

Barbatti, M

M. Barbatti, M. Ruckenbauer, and H. Lischka. The photodynamics of ethylene: A surface- hopping study on structural aspects. J. Chem. Phys., 122:174307, 2005

2005
[66]

Critical appraisal of the fewest switches algorithm for surface hopping

Giovanni Granucci and Maurizio Persico. Critical appraisal of the fewest switches algorithm for surface hopping. J. Chem. Phys., 126(13):134114, 2007

2007
[67]

Lipeng Sun and William L. Hase. Comparisons of classical and wigner sampling of transition state energy levels for quasiclassical trajectory chemical dynamics simulations. J. Chem. Phys., 133:044313, 2010

2010
[68]

Ben-Nun and T

M. Ben-Nun and T. J. Martínez. Nonadiabatic molecular dynamics: Validation of the multiple spawning method for a multidimensional problem. J. Chem. Phys., 108:7244–7257, 1998

1998
[69]

S.J Cotton and W.H. Miller. A symmetrical quasi-classical windowing model for the molecular dynamics treatment of non-adiabatic processes involving many electronic states. J. Chem. Phys., 150:104101, 2019

2019
[70]

S.J Cotton and W.H. Miller. Trajectory-adjusted electronic zero point energy in classical meyer-miller vibronic dynamics: Symmetrical quasiclassical application to photodissociation. J. Chem. Phys., 150:194110, 2019

2019
[71]

Efﬁcient and ﬂexible computation of many-electron wave function overlaps

Felix Plasser, Matthias Ruckenbauer, Sebastian Mai, Markus Oppel, Philipp Marquetand, and Leticia Gonzàlez. Efﬁcient and ﬂexible computation of many-electron wave function overlaps. J. Chem. Theory Comput. , 12:1207–1219, 2016

2016
[72]

Mapping approach to the semiclassical description of nonadiabatic quantum dynamics

Michael Thoss and Gerhard Stock. Mapping approach to the semiclassical description of nonadiabatic quantum dynamics. Phys. Rev. A, 59:64–79, 1999. 6 | Zhou et al

1999

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

John C. Tully. Perspective: Nonadiabatic dynamics theory. J. Chem. Phys., 137(22):22A301, 2012

work page 2012

[2] [2]

Subotnik, Ethan C

Joseph E. Subotnik, Ethan C. Alguire, Qi Ou, Brian R. Landry, and Shervin Fatehi. The req- uisite electronic structure theory to describe photoexcited nonadiabatic dynamics: Nonadia- batic derivative couplings and diabatic electronic couplings.Acc. Chem. Res., 48:1340–1350, 2015

work page 2015

[3] [3]

B. G. Levine and T. J. Martinez. Isomerization through conical intersections. Annu. Rev. Phys. Chem., 58:613–634, 2007

work page 2007

[4] [4]

Nelson, S

T. Nelson, S. Fernandez-Alberti, A. E. Roitberg, , and S. Tretiak. Nonadiabatic excited-state molecular dynamics: Modeling photophysics in organic conjugated materials. Acc. Chem. Res., 47:1155–1164, 2014. Zhou et al. —- | August 15, 2019 | vol. XXX | no. XX | 5

work page 2014

[5] [5]

Mi Kyung Lee, Pengfei Huo, and David F . Coker. Semiclassical path integral dynamics: Pho- tosynthetic energy transfer with realistic environment interactions. Annu. Rev. Phys. Chem. , 67(1):639–668, 2016

work page 2016

[6] [6]

Crespo-Otero and M

R. Crespo-Otero and M. Barbatti. Recent advances and perspectives on nonadiabatic mixed quantum-classical dynamics. Chem. Rev., 118:7026–7068, 2018

work page 2018

[7] [7]

B. F . E. Curchod and T. J. Martinez. Ab initio nonadiabatic quantum molecular dynamics. Chem. Rev., 118:3305–3336, 2018

work page 2018

[8] [8]

John C. Tully. Molecular dynamics with electronic transitions. J. Chem. Phys. , 93(2):1061– 1071, 1990

work page 1990