Pith. sign in

REVIEW 3 major objections 4 minor 65 references

Exact quantum dynamics background of dispersion interactions: case study for CH$_4\cdot$Ar in full (12) dimensions

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Twelve-dimensional vibrational states of CH4-Ar set the benchmark for 3D rigid-monomer models.

desk verdict A solid, first-of-its-kind 12D study with one genuine loose end: the highest 'bound' states need convergence evidence before the all-bound-states claim can stand. read the letter →

arxiv 1908.05432 v2 pith:QNC3BADI submitted 2019-08-15 physics.chem-ph quant-ph

Gustavo Avila , Dóra Papp , Gábor Czakó , Edit Mátyus This is my paper · ORCID
classification physics.chem-phquant-ph
keywords full-dimensionalpotentialenergysurfaceCH4-ArvanderWaalscomplexvariationalvibrationalboundstatesSmolyaksparsegridrigid-monomerapproximationdispersioninteractionsmonomerflexibilityeffectspredissociative
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

The paper tries to establish that the weakly bound methane–argon complex can now be treated with all twelve vibrational dimensions on a single ab initio potential surface, and that the resulting full-dimensional energies give a direct benchmark for the rigid-monomer models commonly used for such van der Waals complexes. On the new FullD-2019 surface, a 12D calculation that keeps only one nine-dimensional harmonic-oscillator basis function for the methane fragment has an rms error of $0.40~\text{cm}^{-1}$ against the converged 12D excitation energies, less than half the $0.93~\text{cm}^{-1}$ error of a rigorously constrained 3D rigid-monomer model. Adding ten methane basis functions lowers the error to $0.07~\text{cm}^{-1}$, clearly outperforming the best adjusted 3D model. A reader should care because dispersion-bound complexes are natural testbeds for how intermolecular forces distort and exchange energy with a floppy molecular fragment, and this paper supplies the quantum-dynamical reference against which reduced models can be checked.

What carries the argument

The load-bearing machinery is the FullD-2019 potential energy surface combined with the GENIUSH\textendash Smolyak variational procedure. The PES is a permutationally invariant polynomial of Morse-type variables $y_{ij}=\exp(-r_{ij}/a)$ fit to 15,995 CCSD(T)-F12b/aug-cc-pVTZ points, with terms up to degree 7; the Morse variables give smooth dissociation, and the high-order terms reproduce the intermediate-range $R^{-6}$ dispersion character without a switching function. The variational procedure builds the kinetic energy operator automatically from user-defined internal coordinates and uses Smolyak sparse grids to prune the direct product basis and grid, controlling the exponential cost of 12 dimensions. A second key ingredient is the choice of generalized normal coordinates referenced to the effective ground-state methane structure, which builds in the dominant static anharmonicity and lets a tiny methane basis capture monomer-flexibility effects. Convergence of the intermolecular excitation energies relies on error cancellation between the zero-point-dominated reference and excited states.

What would settle it

Recompute the 12D bound states with a methane basis larger than $b=3$ ($b=4$ or more) and check whether any intermolecular excitation energy shifts by more than roughly $0.05~\mathrm{cm}^{-1}$; a larger shift would mean the claimed convergence, and hence the derived 3D-model errors, is not stable.

Watch

Extended reading notes

Core claim

The central claim is that the full-dimensional bound-state vibrational energies of CH$_4$\cdot Ar computed on the new FullD-2019 PES are converged enough to serve as a reference, and that relative to this reference the standard rigid-monomer approximations are accurate to about $1~\text{cm}^{-1}$ or worse unless adjusted. The 12D computation with the smallest methane basis ($b=0$, a single 9D harmonic-oscillator function) gives intermolecular excitation energies within $0.40~\text{cm}^{-1}$ rms of the $b=3$ reference; the $b=1$ computation with ten methane functions gives $0.07~\text{cm}^{-1}$ rms. The rigorously constrained 3D model built at the ground-state average methane structure has $0.93~\text{cm}^{-1}$ rms and incorrectly predicts an extra bound state, while an adjusted 3D model that tunes the methane C\textendash H distance in the kinetic energy operator to reproduce the effective rotational constant recovers the correct count and $0.32~\text{cm}^{-1}$ rms. The PES itself matches benchmark dissociation energies at the global and secondary minima within $0.3$ and $2.6~\text{cm}^{-1}$, and its isolated-methane levels reproduce experimental values through the pentad with $2.88~\text{cm}^{-1}$ rms.

Load-bearing premise

The load-bearing premise is that the $b=3$ 12D excitation energies are converged, which relies on error cancellation between the zero-point and excited intramolecular states; if that cancellation fails, the reported rms values and the comparison with 3D models lose their reference.

Editorial extensions

If this is right

  • The $b=0$ 12D computation, with a single methane basis function, gives an rms of $0.40~\text{cm}^{-1}$ against the converged $b=3$ results, making it a cheap yet accurate alternative to 3D models.
  • The $b=1$ 12D computation (ten methane basis functions) reaches $0.07~\text{cm}^{-1}$ rms, much better than both 3D models, while taking only about 20 hours on 20 cores.
  • The rigorously constrained 3D model built at the ground-state average structure has $0.93~\text{cm}^{-1}$ rms and predicts a spurious triply degenerate bound state; the full-dimensional calculation corrects that.
  • The PES reproduces benchmark dissociation energies at the global and secondary minima within $0.3$ and $2.6~\text{cm}^{-1}$, respectively, and its isolated-methane vibrational levels match experiment to $2.88~\text{cm}^{-1}$ rms through the pentad.
  • Because the surface dissociates correctly, the method can be extended to methane-excited predissociative states, where intramolecular-to-intermolecular vibrational energy transfer becomes observable.

Reading between the lines

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

  • The paper does not state this, but the $b=0$ result implies that a rigid-monomer model using the ground-state effective structure already captures most monomer-flexibility effects, which could be tested quickly on other atom\textendash molecule complexes without running full-dimensional calculations.
  • The convergence tests are for relative excitation energies; the zero-point energy itself is estimated to be $1$\textendash$2~\text{cm}^{-1}$ too high at $b=3$, so absolute dissociation thresholds carry that uncertainty even though relative levels are stable.
  • Following the paper's stated route, repeating the 12D computation with a methane basis that includes excited normal-mode combinations ($b=6$ or $7$) and comparing predissociative line positions with measured spectra would be a sharper test of the surface and of the reduced-model assessment.
  • Because the degree-7 Morse-variable fit reproduces the $R^{-6}$ tail without an explicit dispersion term, the same fitting strategy may transfer to other dispersion-bound complexes; a direct test would be fitting a known long-range potential and checking whether the recovered asymptotic falloff matches $1/R^6$.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper reports the first full-dimensional (12D) variational bound-state computation for the CH4–Ar van der Waals complex. The authors construct a new permutationally invariant, full-dimensional ab initio PES (FullD-2019) from 15,995 CCSD(T)-F12b/aug-cc-pVTZ points, benchmark its dissociation energies at the global and secondary minima against composite CCSD(T)-F12b/CCSDT(Q)/core-correlation estimates, and then solve the 12D vibrational Schrödinger equation with the GENIUSH–Smolyak approach. Convergence of the intermolecular basis is reported at the 0.01 cm−1 level, and the methane-fragment basis is varied from pruning parameter b=0 to b=3. The resulting b=3 excitation energies are used as the reference to assess two rigid-monomer 3D models, finding rms deviations of 0.93 cm−1 (rigid-geometry model) and 0.32 cm−1 (rotationally adjusted model). The paper also shows that a 12D computation with only a single methane harmonic-oscillator function (b=0) already outperforms the purely rigid 3D model, with rms 0.40 cm−1, and that including ten methane functions (b=1) reduces the rms to 0.07 cm−1. The central claims are that the FullD-2019 PES is of near-spectroscopic quality and that the 12D calculations provide a valid benchmark for reduced-dimensionality models of this complex.

Significance. If the results hold, this is a significant methodological and systems-oriented contribution. It provides a new full-dimensional PES for a weakly bound complex of a polyatomic molecule and a rare-gas atom, and it demonstrates the feasibility of genuinely 12D variational bound-state calculations with the GENIUSH–Smolyak machinery. The PES fitting quality (rms below 1 cm−1 up to 55,000 cm−1) and the benchmark dissociation energies are carefully established, and the comparison of 3D rigid-monomer models against full-dimensional results is a direct, useful assessment of a widely used approximation. The manuscript is generally clear, with extensive convergence data for the lower states, and the reported energies and rms values are internally consistent with the tables. The main open issue concerns the highest bound state(s), whose convergence and even bound-state character are not yet fully established; this does not undermine the lower-state conclusions but does affect the claim that the table lists all bound states and the associated bound-state-count comparisons.

major comments (3)
  1. [Section III.D, Table V] The highest 12D state(s), rows #44–46 at 99.32 cm−1, are the only rows without any Δ0, Δ1, or Δ2 convergence entries, and they have no counterparts in either 3D column. The text claims that Table V lists all bound states, and later uses the bound-state count to argue that the 3D(⟨B⟩0) model reproduces the correct number of bound states. For these top states, however, there is no evidence that the b=3 energy is converged with respect to the methane-fragment basis. The state also lies close to the dissociation limit: using the b=3 numbers in the text, De(GM)=153.13 cm−1, CH4 ZPVE(b=3)=9692.41 cm−1, and complex ZPVE(b=3)=9745.40 cm−1 give D0≈100.14 cm−1, while Section III.D states that the b=3 complex ZPVE is 1–2 cm−1 too high; the correspondingly corrected D0 is 99.35–100.35 cm−1, placing the 99.32 cm−1 state inside the uncertainty of the dissociation threshold. The manuscript should provide convergence data for these states, or at least a quantitative discussion of why they are bound, before asserting that the table contains all bound states and before using the bound-state count in the 3D assessment.
  2. [Section III.D, text vs. Table V] The statement that the 3D(⟨B⟩0) model 'reproduces the correct number of bound states' is not supported by Table V as printed. Table V shows no entries for #44–46 in either 3D column, so the 3D(⟨B⟩0) model appears to have only 44 bound states, while the 12D b=3 column lists 47. If the 3D model actually has the three extra states, the table is incomplete; if it does not, the 'correct number' claim is incorrect. This discrepancy affects the central comparison between the full-dimensional and reduced-dimensional models and should be resolved in revision.
  3. [Section III.D, text] The sentence claiming that the 3D(⟨r⟩0) model 'erroneously predicts an additional, triply degenerate, bound state below the dissociation asymptote' is difficult to reconcile with Table V, in which the 3D(⟨r⟩0) column contains no state beyond the 12D list and actually shows fewer bound states than the 12D column. The reader cannot identify the additional state or the comparison basis. Please clarify which state is meant and how it relates to the 12D results, or correct the statement so that the table and text agree.
minor comments (4)
  1. [Table V, row #44–46] The row for states #44–46 lacks any assignment (j, nR, Γ). Even if the states are genuine, providing at least a symmetry or angular-momentum label would help the reader assess their character; if no assignment is possible, a brief explanation is needed.
  2. [Table V, footnote b] Footnote b states that the intermolecular radial and angular representations are 'sufficient for converging the figures shown in the table,' but the highest-state row has no convergence figures. Please qualify the statement to indicate which rows are covered.
  3. [Section III.D, ZPVE discussion] The estimate that the b=3 ZPVE is 1–2 cm−1 too high is stated without showing the underlying comparison for the complex itself. Since this estimate drives the uncertainty in D0 and thus the bound-state interpretation of the top state, a more explicit derivation or a small convergence table for the complex ZPVE would be valuable.
  4. [Abstract and Section I] The phrase 'single harmonic oscillator basis function (9D)' is slightly confusing because a single 9D function is an entire 9D Hartree-product function, not one oscillator in one dimension. A wording such as 'a single 9D harmonic-oscillator basis function (b=0)' would be clearer.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: PES is ab initio fitted, bound states are variational outputs, and the adjusted 3D model is explicitly labeled as an adjustment.

full rationale

The paper's derivation chain is self-contained: the FullD-2019 PES is fitted to 15,995 CCSD(T)-F12b/aug-cc-pVTZ ab initio energy points, and the 12D bound-state energies are obtained by variational solution of the nuclear Schrödinger equation using the GENIUSH–Smolyak method, with no experimental or target bound-state energy used as a fitting input. The convergence of the 12D excitation energies is tested directly through increasing methane-basis pruning parameters b = 0, 1, 2, 3 (Table V). The 3D(⟨B⟩0) model does adjust a KEO C–H distance to reproduce a rotational constant, but the paper explicitly calls this an 'adjusted' model and the adjusted quantity is not the bound-state excitation energy being compared; hence it is not a fitted input renamed as a prediction. The only overlapping self-citation, Ref. [40], is an independently published methodological paper that is not used to justify a target-dependent result. The unquantified convergence of the highest states #44–46 is a correctness/convergence concern, not a circularity, because the paper does not define those energies in terms of the comparison target.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The work introduces no new physical entities. It rests on standard electronic structure levels, a high-dimensional fitted PES, and the quasi-variational numerical machinery. The free parameters listed are either PES fitting parameters or basis/adjustment parameters, none of which are fitted to the target bound-state energies.

free parameters (5)
  • PES polynomial expansion coefficients (9355) = Not listed individually (in ESI)
    The full-dimensional PES is represented by a weighted least-squares fit of 9,355 coefficients in a permutationally invariant Morse-variable polynomial to 15,995 CCSD(T)-F12b/aug-cc-pVTZ energies. These coefficients are the fitted model; the entire paper's dynamics is computed on this fitted surface.
  • Morse variable exponent a = 2.0 bohr
    Chosen by hand for the y_ij = exp(-r_ij/a) coordinate transformation; affects the distribution of fitting flexibility but not a physical parameter.
  • PES fit weights E0, E1 = E0=0.05 hartree, E1=0.5 hartree
    Chosen weight function (E0/(E0+E))*(E1/(E1+E)) in the least-squares fit; a modeling choice.
  • Morse radial basis parameters D, alpha, gamma = D=150 cm^-1, alpha=0.65, gamma=0.00033
    Parameters of the Morse tridiagonal basis for the dissociation coordinate, chosen to fit the 1D cut of the PES. The paper reports convergence with 13 functions, so these do not affect converged results.
  • 3D(⟨B⟩0) adjusted C-H distance = r_fit(C-H)=2.072988169 bohr
    Fitted so that a 2D coupled-rotor computation reproduces the ⟨B⟩0=5.212508664 cm^-1 effective rotational constant of the PES. Used only in the reduced-dimensionality test model.
assumptions (4)
  • domain assumption CCSD(T)-F12b/aug-cc-pVTZ electronic structure method provides accurate interaction energies for the CH4-Ar complex (within a few cm^-1 for dissociation energies).
    The PES and benchmark are built on this level of theory; the paper estimates ±2 cm^-1 uncertainty from basis set and correlation corrections, which is not fully validated against experiment for the PES itself.
  • domain assumption A polynomial of Morse-like variables up to degree 7, invariant under permutation of identical atoms, can represent the full-dimensional PES without significant interpolation artifacts.
    The paper shows low fitting rms and smooth 1D cuts, but the global behavior between the 15,995 sampled points is assumed.
  • standard math The variational principle holds: the computed vibrational energies are upper bounds to the exact eigenvalues of the Hamiltonian defined by the PES and the kinetic energy operator.
    GENIUSH constructs the exact kinetic energy operator numerically; the Smolyak quadrature introduces approximate integration, so the energies are quasi-variational, not strict upper bounds.
  • domain assumption Atomic masses (rather than nuclear masses) are used for the vibrational problem, neglecting the small difference from electron mass.
    Atomic masses are standard in quantum chemistry vibrational computations and give the correct rotational constants for the isolated molecule, but introduce a tiny systematic error.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Exact quantum dynamics background of dispersion interactions: case study for CH$_4\cdot$Ar in full (12) dimensions." pith.science (2026). https://pith.science/paper/QNC3BADI

@misc{pith2026190805432,
  author       = {Pith},
  title        = {Pith review of: Exact quantum dynamics background of dispersion interactions: case study for CH$_4\cdot$Ar in full (12) dimensions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/QNC3BADI}},
  note         = {Machine review of arXiv:1908.05432}
}
abstract

A full-dimensional \emph{ab initio} potential energy surface of spectroscopic quality is developed for the van-der-Waals complex of a methane molecule and an argon atom. Variational vibrational states are computed on this surface including all twelve (12) vibrational degrees of freedom of the methane-argon complex using the GENIUSH computer program and the Smolyak sparse grid method. The full-dimensional computations make it possible to study fine details of the interaction and distortion effects and to make a direct assessment of the reduced-dimensionality models often used in the quantum dynamics study of weakly-bound complexes. A 12-dimensional (12D) vibrational computation including only a single harmonic oscillator basis function (9D) to describe the methane fragment (for which we use the ground-state effective structure as the reference structure) has a 0.40 cm$^{-1}$ root-mean-square error (rms) with respect to the converged 12D bound-state excitation energies, which is less than half of the rms of the 3D model set up with the $\langle r \rangle_0$ methane structure. Allowing 10 basis functions for the methane fragment, the rms of the bound state vibrational energies is reduced to 0.07 cm$^{-1}$, which is much better than the 3D models. The full-dimensional potential energy surface correctly describes the dissociation of the system, which together with further development of the variational (ro)vibrational methodology opens the route for the study of the role of dispersion forces on the excited methane vibrations and the energy transfer from the intra- to the intermolecular vibrational modes.

Figures

Figures reproduced from arXiv: 1908.05432 by the authors.

Figure 1
Figure 1. FIG. 1. Potential energy curves along the [PITH_FULL_IMAGE:figures/full_fig_p009_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Geometric parameters of the global (top) and the secondary (bottom) minimum structures [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Potential energy curve along one C–H bond of the CCSD(T)-F12b/aug-cc-pVTZ global [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Long-range interactions: potential energy representations of CH [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Vibrational states along the dissociation coordinate (1D model) using (a) the Morse fit, [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

65 extracted references · 64 canonical work pages

  1. [1]

    Benchmark dissociation energies Geometries of the global (GM) and secondary minima (SM) of the CH 4·Ar complex are optimized using the explicitly-correlated coupled cluster singles, doubles, and perturbative triples electronic structure method, CCSD(T)-F12b [41], with the aug-cc-pVQZ correlation- consistent basis set [42], followed by harmonic frequency c...

    work page

  2. [2]

    Note that previous test computations by one of us showed that the standard augmented and F12 correlation-consistent basis sets provide similar accuracy for PES devel- opments [48]

    Full-dimensional PES development A full-dimensional analytic ab initio PES, named FullD-2019 PES, is developed based on 15 995 energy points computed at the CCSD(T)-F12b/aug-cc-pVTZ level of theory at geometries covering the configuration space relevant for the interaction between methane and argon. Note that previous test computations by one of us showed ...

    work page 2019

  3. [3]

    The correction terms listed in Table I allow for estimating the accuracy of the benchmark dissociation energies

    Benchmark dissociation energies In Table I, we present the benchmark dissociation energies corresponding to the global and secondary minimum geometries of the CH4·Ar complex and compare them to the dissociation energies determined on the newly developed analytic FullD-2019 PES. The correction terms listed in Table I allow for estimating the accuracy of th...

    work page 2019

  4. [4]

    Accuracy of the analytic PES The newly developed full-dimensional analytic PES of the CH 4·Ar complex, FullD-2019 PES features extremely low root mean square (rms) fitting deviations, listed in Table II, with 7 rms values being lower than 1 cm−1 up to 55 000 cm−1 relative to the global minimum of the PES. In accord with these low rms values the one-dimensi...

    work page 2019

  5. [5]

    J. N. Murrell, S. Carter, S. C. Farantos, P. Huxley, and A. J. C. Varandas, Molecular Potential Energy Functions (Wiley, New York, 1984)

    work page 1984

  6. [6]

    Quack and M

    M. Quack and M. A. Suhm, J. Chem. Phys. 95, 28 (1991)

    work page 1991

  7. [7]

    Quack, J

    M. Quack, J. Stohner, and M. A. Suhm, J. Mol. Struct. 294, 33 (1993). 24

    work page 1993

  8. [8]

    G. C. Groenenboom, E. M. Mas, R. Bukowski, K. Szalewicz, P. E. S. Wormer, and A. van der Avoird, Phys. Rev. Lett. 84, 4072 (2000)

    work page 2000

Show all 65 references
  1. [9]

    Cencek, K

    W. Cencek, K. Szalewicz, C. Leforestier, R. van Harrevelt, and A. van der Avoird, Phys. Chem. Chem. Phys. 10, 4716 (2008)

    2008

  2. [10]

    Wang and J

    Y. Wang and J. M. Bowman, J. Chem. Phys. 134, 154510 (2011)

    2011

  3. [11]

    G. R. Medders, V. Babin, and F. Paesani, J. Chem. Theory Comput. 9, 1103 (2013)

    2013

  4. [12]

    Babin, G

    V. Babin, G. R. Medders, and F. Paesani, J. Chem. Theory Comput. 10, 1599 (2014)

    2014

  5. [13]

    Jankowski, G

    P. Jankowski, G. Murdachaew, R. Bukowski, O. Akin-Ojo, C. Leforestier, and K. Szalewicz, J. Phys. Chem. A 119, 2940 (2015)

    2015

  6. [14]

    G´ ora, W

    U. G´ ora, W. Cencek, R. Podeszwa, A. van der Avoird, and K. Szalewicz, J. Chem. Phys. 140, 194101 (2014)

    2014

  7. [15]

    T. G. A. Heijmen, P. E. S. Wormer, A. van der Avoird, R. E. Miller, and R. Moszynski, J. Chem. Phys. 110, 5639 (1999)

    1999

  8. [16]

    Sarka, A

    J. Sarka, A. G. Cs´ asz´ ar, S. C. Althorpe, D. J. Wales, and E. M´ atyus, Phys. Chem. Chem. Phys. 18, 22816 (2016)

    2016

  9. [17]

    Sarka, A

    J. Sarka, A. G. Cs´ asz´ ar, and E. M´ atyus, Phys. Chem. Chem. Phys.2, 15335 (2017)

    2017

  10. [18]

    M. P. Metz, K. Szalewicz, J. Sarka, R. T´ obi´ as, A. G. Cs´ asz´ ar, and E. M´ atyus, Phys. Chem. Chem. Phys. 21, 13504 (2019)

    2019

  11. [19]

    Jeziorska, P

    M. Jeziorska, P. Jankowski, K. Szalewicz, and B. Jeziorski, J. Chem. Phys. 113, 2957 (2000)

    2000

  12. [20]

    Wang and T

    X.-G. Wang and T. Carrington, Jr., J. Chem. Phys. 146, 104105 (2017)

    2017

  13. [21]

    Wang and T

    X.-G. Wang and T. Carrington, Jr., J. Chem. Phys. 148, 074108 (2018)

    2018

  14. [22]

    Avila and E

    G. Avila and E. Matyus, J. Chem. Phys. 151, 154301 (2019)

    2019

  15. [23]

    F´ abri, A

    C. F´ abri, A. G. Cs´ asz´ ar, and G. Czak´ o, J. Phys. Chem. A117, 6975 (2013)

    2013

  16. [24]

    Wodraszka, J

    R. Wodraszka, J. Palma, and U. Manthe, J. Phys. Chem. A 116, 11249 (2012)

    2012

  17. [25]

    D. Papp, J. Sarka, T. Szidarovszky, A. G. Cs´ asz´ ar., E. M´ atyus, M. Hochlaf, and T. Stoecklin, Phys. Chem. Chem. Phys. 19, 8152 (2017)

    2017

  18. [26]

    P. M. Felker and Z. Bacic, J. Chem. Phys. 151, 024305 (2019)

    2019

  19. [27]

    J. M. Bowman, S. Carter, and X. Huang, International Reviews in Physical Chemistry 22, 533 (2003)

    2003

  20. [28]

    Avila and J

    G. Avila and J. T. Carrington, J. Chem. Phys. 131, 174103 (2009)

    2009

  21. [29]

    Avila and J

    G. Avila and J. T. Carrington, J. Chem. Phys. 134, 054126 (2011). 25

    2011

  22. [30]

    Avila and J

    G. Avila and J. T. Carrington, J. Chem. Phys. 134, 064101 (2011)

    2011

  23. [31]

    Leclerc and T

    A. Leclerc and T. Carrington, J. Chem. Phys. 140, 174111 (2014)

    2014

  24. [32]

    P. S. Thomas and T. Carrington, J. Chem. Phys. 146, 204110 (2017)

    2017

  25. [33]

    Halverson and B

    T. Halverson and B. Poirier, The Journal of Physical Chemistry A 119, 12417 (2015)

    2015

  26. [34]

    Brown and T

    J. Brown and T. Carrington, J. Chem. Phys. 145, 144104 (2016)

    2016

  27. [35]

    N. K. Madsen, I. H. Godtliebsen, S. A. Losilla, and O. Christiansen, J. Chem. Phys. 148, 024103 (2018)

    2018

  28. [36]

    Baiardi and M

    A. Baiardi and M. Reiher, J. Chem. Theory Comput. 15, 3481 (2019)

    2019

  29. [37]

    W. H. Miller, N. C. Handy, and J. E. Adams, J. Chem. Phys. 72, 99 (1980)

    1980

  30. [38]

    J. M. Bowman, X. Huang, N. C. Handy, and S. Carter, J. Phys. Chem. A 111, 7317 (2007)

    2007

  31. [39]

    Lauvergnat and A

    D. Lauvergnat and A. Nauts, 119, 18 (2014)

    2014

  32. [40]

    Leforestier, Phil

    C. Leforestier, Phil. Trans. R. Soc. A 370, 2675 (2012)

    2012

  33. [41]

    T. G. A. Heijmen, T. Korona, R. Moszynski, P. E. S. Wormer, and A. van der Avoird, J. Chem. Phys. 107, 902 (1997)

    1997

  34. [42]

    R. E. Miller, T. G. A. Heijmen, P. E. S. Wormer, A. van der Avoird, and R. Moszynski, J. Chem. Phys. 110, 5651 (1999)

    1999

  35. [43]

    Wangler, D

    M. Wangler, D. A. Roth, I. Pak, G. Winnewisser, P. E. S. Wormer, and A. van der Avoird, J. Mol. Spectrosc. 222, 109 (2003)

    2003

  36. [44]

    Avila and E

    G. Avila and E. M´ atyus, J. Chem. Phys. 150, 174107 (2019)

    2019

  37. [45]

    T. B. Adler, G. Knizia, and H.-J. Werner, J. Chem. Phys. 127, 221106 (2007)

    2007

  38. [46]

    T. H. Dunning, Jr., J. Chem. Phys. 90, 1007 (1989)

    1989

  39. [47]

    Raghavachari, G

    K. Raghavachari, G. W. Trucks, J. A. Pople, and M. Head-Gordon, Chem. Phys. Lett. 157, 479 (1989)

    1989

  40. [48]

    K´ allay and J

    M. K´ allay and J. Gauss, J. Chem. Phys. 123, 214105 (2005)

    2005

  41. [49]

    D. E. Woon and T. H. Dunning Jr., J. Chem. Phys. 103, 4572 (1995)

    1995

  42. [50]

    Werner, P

    Molpro, version 2015.1, a package of ab initio programs, H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Sch¨ utz, and others, see http://www.molpro.net

    2015

  43. [51]

    K´ allay, Z

    MRCC, a quantum chemical program suite written by M. K´ allay, Z. Rolik, I. Ladj´ anszki, L. Szegedy, B. Lad´ oczki, J. Csontos and B. Kornis, See also Z. Rolik, M. K´ allay, J. Chem. Phys., 2011, 135, 104111, as well as: www.mrcc.hu

    2011

  44. [52]

    Czak´ o, I

    G. Czak´ o, I. Szab´ o, and H. Telekes, J. Phys. Chem. A118, 646 (2014). 26

    2014

  45. [53]

    B. J. Braams and J. M. Bowman, Int. Rev. Phys. Chem. 28, 577 (2009)

    2009

  46. [54]

    J. M. Bowman, G. Czak´ o, and B. Fu, Phys. Chem. Chem. Phys. 13, 8094 (2011)

    2011

  47. [55]

    M´ atyus, G

    E. M´ atyus, G. Czak´ o, and A. G. Cs´ asz´ ar, J. Chem. Phys.130, 134112 (2009)

    2009

  48. [56]

    F´ abri, E

    C. F´ abri, E. M´ atyus, and A. G. Cs´ asz´ ar, J. Chem. Phys.134, 074105 (2011)

    2011

  49. [57]

    Wang and T

    X.-G. Wang and T. Carrington Jr, J. Chem. Phys. 141, 154106 (2014)

    2014

  50. [58]

    J. S. Coursey, D. J. Schwab, J. J. Tsai, and R. A. Dragoset, Atomic Weights and Isotopic Compositions (version 4.1): http://physics.nist.gov/Comp [last accessed on 12 May 2018]. National Institute of Standards and Technology, Gaithersburg, MD. (2015)

    2015

  51. [59]

    D. W. Schwenke and H. Partridge, Spectrochim. Acta 57, 887 (2001)

    2001

  52. [60]

    A. V. Nikitin, M. Rey, and V. G. Tyuterev, Chem. Phys. Lett. 501, 179 (2011)

    2011

  53. [61]

    Ferenc and E

    D. Ferenc and E. M´ atyus, Mol. Phys.117, 1694 (2019)

    2019

  54. [62]

    Wei and T

    H. Wei and T. Carrington, Jr., J. Chem. Phys. 97, 3029 (1992)

    1992

  55. [63]

    B. R. Johnson and W. P. Reinhardt, J. Chem. Phys. 85, 4538 (1986)

    1986

  56. [64]

    Tennyson and B

    J. Tennyson and B. T. Sutcliffe, J. Chem. Phys. 77, 4061 (1982)

    1982

  57. [65]

    Schiffel and U

    G. Schiffel and U. Manthe, Chemical Physics 374, 118 (2010). 27

    2010

Pith tools

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