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REVIEW 3 major objections 5 minor 67 references

Computing Hydrogen Tunneling Splittings with Nuclear-Electronic Orbital Multireference Configuration Interaction

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read This paper claims that the nuclear-electronic orbital multireference configuration interaction method computes accurate hydrogen and deuterium tunneling splittings for fixed geometries, matching numerically exact grid benchmarks across…

desk verdict First application of NEO-MRCI to tunneling splittings is credible and transparent, but 'quantitative agreement' is overstated and the protonic basis is demonstrably not converged for OCHCO+ and malonaldehyde. read the letter →

arxiv 2506.02201 v2 pith:DFUPRKVZ submitted 2025-06-02 physics.chem-ph

Rachel J. Stein , Christopher L. Malbon , Sharon Hammes-Schiffer This is my paper
classification physics.chem-ph
keywords hydrogentunnelingsplittingnuclear-electronicorbitalmultireferenceconfigurationinteractionprotontransfervibronicstatesFouriergridHamiltoniandeuteriumisotopeeffects
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 reports that the nuclear-electronic orbital multireference configuration interaction (NEO-MRCI) method, which treats the transferring proton as a quantum wavefunction together with the electrons, gives hydrogen and deuterium tunneling splittings that agree with numerically exact grid-based benchmarks at fixed geometries. The test set spans HeHHe+, OCHCO+, FHF–, and malonaldehyde, covering linear and non-linear tunneling paths over a range of donor-acceptor distances. The result is useful because tunneling splittings are extremely sensitive to the barrier and are usually hard to obtain without adjustable parameters. If the finding is correct, a parameter-free multicomponent quantum chemistry method can describe the vibronic states responsible for hydrogen tunneling.

What carries the argument

The load-bearing object is the NEO-MRCI wavefunction, a linear combination of products of electronic and protonic Slater determinants built from orbitals optimized in a state-averaged NEO-MCSCF calculation that treats the lowest two vibronic states equally. Each tunneling proton is represented by two basis function centers, placed at the donor and acceptor minima of a conventional CCSD double-well surface, each carrying a protonic and an electronic basis set. The CI expansion includes single electron, single proton, and double electron-proton excitations (MR-SDenCI), along with a full protonic active space and, for FHF–, OCHCO+, and malonaldehyde, a minimal (2e,2o) electronic active space of in-phase sigma and sigma-star orbitals; HeHHe+ uses a single-reference NEO-CASSCF treatment. This structure supplies the electron-proton correlation and the balanced treatment across the barrier that make the tunneling splitting accurate.

What would settle it

Run NEO-MRCI for a symmetric hydrogen-transfer system at a donor-acceptor distance where the CCSD-optimized proton center sits noticeably away from the maximum of the FGH ground-state proton density; if the computed tunneling splitting then deviates from the FGH benchmark by more than a few inverse centimeters, the center-placement assumption is falsified.

Watch

Extended reading notes

Core claim

The central discovery is that NEO-MRCI, expanded as single electronic, single protonic, and double electron-proton excitations from a state-averaged NEO-MCSCF reference, reproduces tunneling splittings from three-dimensional Fourier grid Hamiltonian calculations at the same fixed heavy-atom geometries. The paper reports quantitative agreement for HeHHe+, FHF–, OCHCO+, and malonaldehyde, and for deuterium-substituted FDF– and malonaldehyde, with the protonic densities showing the expected bilobal shapes and nodal structures. Because electrons and the transferring proton are treated on the same footing, the calculation avoids a Born-Oppenheimer separation for the tunneling particle and captures both the static correlation of the double well and the electron-proton dynamic correlation needed for accurate splittings.

Load-bearing premise

The method's accuracy rests on the assumption that placing the two proton basis centers at the minima found by conventional CCSD optimizations reliably represents the proton's double-well density for every system and donor-acceptor distance studied.

Editorial extensions

If this is right

  • Fixed-geometry tunneling splittings become accessible without tunable parameters in other electronically adiabatic hydrogen-transfer systems that share the two-center, double-well structure tested here.
  • Deuterium splittings follow from the same active spaces and basis sets, so kinetic isotope effects on tunneling are directly computable.
  • The method's excited vibronic states can be coupled to the other nuclear vibrations through vibronic coupling theory, a route the paper identifies toward comparing with experimental splittings such as malonaldehyde's 21.6 cm-1.
  • The small (2e,2o) electronic active space appears transferable across chemically different proton-bound systems, which keeps the cost of the NEO-MRCI step manageable despite the large protonic basis sets.

Reading between the lines

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

  • One consequence not tested here is that NEO-MRCI might serve as a benchmark generator for larger proton-transfer systems where the FGH grid calculation becomes too expensive; the current fixed-geometry benchmarks are the evidence that would justify that role.
  • The CCSD-based center placement means the method could be extended to non-symmetric systems by a second optimization near the acceptor, but the paper does not show how sensitive the splittings are to small displacements of those centers.
  • Because the wavefunction explicitly correlates the proton with electrons, the same machinery could in principle report excited protonic states beyond the lowest doublet, which would test the assumption that the (2e,2o) active space is sufficient for higher vibronic states.
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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 paper applies the recently developed NEO-MRCI method, specifically the NEO-MR-SD enCI variant, to compute hydrogen and deuterium tunneling splittings at fixed geometries for four systems: HeHHe+, FHF-, OCHCO+, and malonaldehyde. The results are benchmarked against three-dimensional Fourier Grid Hamiltonian (FGH) calculations whose potential energy surfaces are generated at the CCSD level. The authors report good qualitative agreement for the distance dependence of the splittings and conclude that NEO-MRCI can produce accurate tunneling splittings at fixed geometries, positioning the method as a parameter-free multicomponent wavefunction approach for tunneling problems.

Significance. If the central claim is upheld, NEO-MRCI would be a valuable addition to the toolbox for hydrogen tunneling because it treats the transferring proton and electrons on the same footing without a Born-Oppenheimer separation and does not rely on empirically fitted parameters. The paper provides a substantial amount of numerical data, including explicit coordinates, basis-set convergence tables, and timings, which is commendable for reproducibility. However, the reported agreement with the FGH reference is less quantitative than claimed in several cases, and the convergence of the protonic basis for two of the four systems is not demonstrated. These issues currently limit the strength of the conclusions, though they appear addressable with additional calculations and revised wording.

major comments (3)
  1. [Abstract and Fig. 2, Tables S1, S3, S4] The abstract and the discussion of Fig. 2 state that the NEO-MR-SD enCI tunneling splittings 'agree quantitatively' and are in 'excellent agreement' with the FGH benchmarks. The tabulated data contradict this wording for extended donor-acceptor distances: Table S1 gives a relative error of about 53% at He-He = 2.40 Å (2.3 vs 4.9 cm-1), Table S3 gives a relative error of about 27% at C-C = 3.10 Å (7.1 vs 5.6 cm-1), and Table S4 gives a relative error of about 23% at O-O = 2.62 Å (10.3 vs 8.4 cm-1). These are systematic overestimates that grow with distance. The claim of quantitative agreement should be replaced with an explicit error analysis, or the calculations should be improved to support such a claim.
  2. [Computational Details and Tables S3-S5] The 5s5p5d5f protonic basis used for OCHCO+ and malonaldehyde is justified by a convergence test on HeHHe+ (Table S5), but the same comparison is not reported for the two larger systems. Tables S3 and S4 show that 8s8p8d and 5s5p5d5f results differ by 15-45% for OCHCO+ and by 35-50% for malonaldehyde at the same geometries (e.g., OCHCO+ at 3.10 Å: 3.9 vs 7.1 cm-1; malonaldehyde at 2.62 Å: 5.4 vs 10.3 cm-1). Therefore the favorable agreement of the 5s5p5d5f results with FGH is not a demonstrated property of the NEO-MRCI method; it may reflect an accidental cancellation of basis-set incompleteness. The authors should either report 8s8p8d8f (or 5s5p5d5f5g) results for these systems at representative distances or explicitly state that the reported errors include an uncontrolled basis-set component.
  3. [Computational Details and Conclusion] The proton basis-function center positions are determined by conventional CCSD geometry optimizations, as described in the Computational Details section. This is a free input to the NEO-MRCI calculation, and tunneling splittings are exponentially sensitive to the barrier and thus to the placement of these centers. The paper asserts that this CCSD-based procedure 'provides a reliable method' but reports no sensitivity tests, such as perturbing the centers or comparing with centers optimized at a different level. Consequently, the statement in the Conclusion that 'NEO-MRCI does not require any parameters' is overstated; the center positions are an external parameter of the protocol. The authors should either add a numerical test of the sensitivity to the center positions or qualify the 'parameter-free' claim to mean 'no empirically fitted parameters.'
minor comments (5)
  1. [SI Section 8.1] For the entry labeled 'He-He distance 2.4 Å', the He coordinates are listed as +/- 1.120 Å, which corresponds to a separation of 2.24 Å, not 2.40 Å. Please correct either the label or the coordinates, as this affects the reproducibility of the data point with the largest reported discrepancy.
  2. [Fig. 5 caption] The word 'deterium' in the figure caption should be 'deuterium'.
  3. [Table S1 footnote] The word 'inidcated' in the footnote should be 'indicated'.
  4. [SI table headers] The SI headers contain 'V arying' and similar spacings; these should be cleaned up.
  5. [Main text] The statement 'We show that the same tunneling splitting is obtained for HeHHe+ using the 8s8p8d8f and 5s5p5d5f basis sets (Table S5)' is correct only for the single tested distance of 2.30 Å and should be phrased as a single-point comparison, not a general convergence statement.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: NEO-MRCI tunneling splittings are genuine first-principles energy differences benchmarked against independent grid-based FGH calculations, with no fitted parameters.

full rationale

The paper's central claim is that NEO-MRCI computes accurate hydrogen and deuterium tunneling splittings at fixed geometries. The splitting is obtained as an energy difference between two NEO-MRCI vibronic states, i.e., from the wavefunction expansion in Eqs. (1)-(2), with no parameter adjusted to reproduce the FGH benchmarks. The FGH values are used only as a comparison: 'To benchmark the NEO-MRCI results, the three-dimensional Fourier Grid Hamiltonian (FGH) method was used to compute numerically exact reference tunneling splittings at fixed geometries.' The proton basis function centers are optimized with conventional CCSD, and the FGH reference potential is also generated with CCSD, but the center positions do not enter the FGH calculation and the NEO-MRCI splitting is not constructed from the CCSD double-well splitting. Thus the agreement is not forced by construction. The choice of the (2e,2o) active space and the 5s5p5d5f protonic basis for OCHCO+ and malonaldehyde is a modeling choice; Tables S3 and S4 indicate incomplete basis convergence for those systems, but that is a correctness or accuracy concern, not circularity. Self-citations to Ref. [51] establish the NEO-MRCI method itself, but the present numerical results are new and are compared to an independent numerical grid benchmark, so the self-citation is not load-bearing in a circular sense.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

No new physical entities are introduced. The method relies on established quantum chemistry approximations (CCSD for the reference potential, NEO-MRCI wavefunction ansatz, and a fixed protocol for basis centers). The main free input is the proton basis center placement, which is determined by a separate CCSD calculation rather than by fitting the tunneling splitting.

free parameters (1)
  • Proton basis function center positions = Per-system CCSD-optimized positions (given in SI), e.g., HeHHe+ at 2.30 Å: H at +/-0.336 Å
    These centers are chosen via a separate CCSD optimization, not fitted to the tunneling splitting, but they are an input that affects the results. The paper assumes this choice is unbiased, and it is a modeling choice rather than a parameter tuned to the target.
assumptions (3)
  • domain assumption Conventional CCSD potential energy surfaces provide accurate references for fixed-geometry tunneling splittings.
    The FGH benchmark is built from CCSD/aug-cc-pVTZ (or cc-pVTZ for malonaldehyde) energies at each grid point; the paper treats these as 'numerically exact' references, which presumes CCSD is accurate for these systems.
  • ad hoc to paper The NEO-MR-SD enCI expansion (single electron, single proton, and double electron-proton excitations, excluding double electronic excitations) captures the essential physics of the tunneling splittings.
    The paper assumes double electronic excitations are 'not expected to be critical' (main text) and uses a minimal (2e,2o) active space for three systems; this is an approximation specific to this study, supported only by the empirical agreement with FGH.
  • domain assumption The two proton basis function centers placed at CCSD-optimized proton positions provide an adequate basis for the tunneling wavefunction.
    The paper states that optimizing the basis function center positions at the conventional CCSD level 'provides a reliable method' (main text), but this is only tested on the four systems herein.

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Pith. "Pith review of Computing Hydrogen Tunneling Splittings with Nuclear-Electronic Orbital Multireference Configuration Interaction." pith.science (2026). https://pith.science/paper/DFUPRKVZ

@misc{pith2026250602201,
  author       = {Pith},
  title        = {Pith review of: Computing Hydrogen Tunneling Splittings with Nuclear-Electronic Orbital Multireference Configuration Interaction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DFUPRKVZ}},
  note         = {Machine review of arXiv:2506.02201}
}
read the original abstract

Hydrogen tunneling is an important process that impacts reaction rates and molecular spectra. Describing and understanding this process requires a quantum mechanical treatment of the transferring hydrogen. The nuclear-electronic orbital (NEO) approach treats specified nuclei quantum mechanically on the same level as electrons and has recently been implemented at the multireference configuration interaction (MRCI) wavefunction level. The NEO-MRCI method includes both the static correlation necessary to describe hydrogen tunneling and the electron-proton dynamic correlation required for computing quantitatively accurate nuclear-electronic vibronic states. Herein, the NEO-MRCI method is used to compute the nuclear-electronic wavefunctions and corresponding vibronic energies for four hydrogen tunneling systems at fixed geometries for a range of donor-acceptor distances. Comparison of the NEO-MRCI results to numerically exact grid-based calculations shows that the NEO-MRCI method can be used to obtain accurate hydrogen and deuterium tunneling splittings at fixed geometries. Thus, this work presents an important component for studying hydrogen tunneling systems.

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Works this paper leans on

67 extracted references · 65 canonical work pages

  1. [1]

    J.; Klinman, J

    Cha, Y.; Murray, C. J.; Klinman, J. P. Hydrogen Tunneling in Enzyme Reactions. Science 1989, 243, 1325--1330

    work page 1989

  2. [2]

    W.; Babcock, G

    Hoganson, C. W.; Babcock, G. T. A Metalloradical Mechanism for the Generation of Oxygen from Water in Photosynthesis. Science 1997, 277, 1953--1956

    work page 1997

  3. [3]

    J.; Rickert, K.; Klinman, J

    Knapp, M. J.; Rickert, K.; Klinman, J. P. Temperature-Dependent Isotope Effects in Soybean Lipoxygenase-1: Correlating Hydrogen Tunneling with Protein Dynamics. J. Am. Chem. Soc. 2002, 124, 3865--3874

    work page 2002

  4. [4]

    G.; Yee, C

    Stubbe, J.; Nocera, D. G.; Yee, C. S.; Chang, M. C. Y. Radical Initiation in the Class I Ribonucleotide Reductase: Long-Range Proton-Coupled Electron Transfer? Chem. Rev. 2003, 103, 2167--2202

    work page 2003

  5. [5]

    Magnuson, A.; Anderlund, M.; Johansson, O.; Lindblad, P.; Lomoth, R.; Polivka, T.; Ott, S.; Stensjö, K.; Styring, S.; Sundström, V. et al. Biomimetic and Microbial Approaches to Solar Fuel Generation. Acc. Chem. Res. 2009, 42, 1899--1909

    work page 2009

  6. [6]

    Hammes-Schiffer, S.; Stuchebrukhov, A. A. Theory of Coupled Electron and Proton Transfer Reactions. Chem. Rev. 2010, 110, 6939--6960

    work page 2010

  7. [7]

    J.; Tronic, T

    Warren, J. J.; Tronic, T. A.; Mayer, J. M. Thermochemistry of Proton-Coupled Electron Transfer Reagents and its Implications. Chem. Rev. 2010, 110, 6961--7001

    work page 2010

  8. [8]

    L.; Bullock, R

    DuBois, D. L.; Bullock, R. M. Molecular Electrocatalysts for the Oxidation of Hydrogen and the Production of Hydrogen – The Role of Pendant Amines as Proton Relays. Eur. J. Inorg. Chem. 2011, 2011, 1017--1027

    work page 2011

Show all 67 references
  1. [9]

    L.; Smith, Z.; Wilson, E

    Baughcum, S. L.; Smith, Z.; Wilson, E. B.; Duerst, R. W. Microwave spectroscopic study of malonaldehyde. 3. Vibration-rotation interaction and one-dimensional model for proton tunneling. J. Am. Chem. Soc. 1984, 106, 2260--2265

    1984

  2. [10]

    W.; Beyer, K.; Dvorak, M

    Firth, D. W.; Beyer, K.; Dvorak, M. A.; Reeve, S. W.; Grushow, A.; Leopold, K. R. Tunable far‐infrared spectroscopy of malonaldehyde. J. Chem. Phys. 1991, 94, 1812--1819

    1991

  3. [11]

    Baba, T.; Tanaka, T.; Morino, I.; Yamada, K. M. T.; Tanaka, K. Detection of the tunneling-rotation transitions of malonaldehyde in the submillimeter-wave region. J. Chem. Phys. 1999, 110, 4131--4133

    1999

  4. [12]

    High-Resolution Infrared Spectroscopy of the Formic Acid Dimer

    Birer, \"O .; Havenith, M. High-Resolution Infrared Spectroscopy of the Formic Acid Dimer. Annu. Rev. Phys. Chem. 2009, 60, 263--275

    2009

  5. [13]

    Mode-Selective Promotion and Isotope Effects of Concerted Double-Hydrogen Tunneling in Porphycene Embedded in Superfluid Helium Nanodroplets

    Vdovin, A.; Waluk, J.; Dick, B.; Slenczka, A. Mode-Selective Promotion and Isotope Effects of Concerted Double-Hydrogen Tunneling in Porphycene Embedded in Superfluid Helium Nanodroplets. ChemPhysChem 2009, 10, 761--765

    2009

  6. [14]

    J.; Yang, N.; Huang, M.; Duong, C

    Talbot, J. J.; Yang, N.; Huang, M.; Duong, C. H.; McCoy, A. B.; Steele, R. P.; Johnson, M. A. Spectroscopic Signatures of Mode-Dependent Tunnel Splitting in the Iodide–Water Binary Complex. J. Phys. Chem. A. 2020, 124, 2991--3001

    2020

  7. [15]

    Enzymatic tunneling and kinetic isotope effects: chemistry at the crossroads

    Sen, A.; Kohen, A. Enzymatic tunneling and kinetic isotope effects: chemistry at the crossroads. J. Phys. Org. Chem. 2010, 23, 613--619

    2010

  8. [16]

    Quantum tunneling observed without its characteristic large kinetic isotope effects

    Hama, T.; Ueta, H.; Kouchi, A.; Watanabe, N. Quantum tunneling observed without its characteristic large kinetic isotope effects. Proc. Natl. Acad. Sci. U.S.A. 2015, 112, 7438--7443

    2015

  9. [17]

    P.; Offenbacher, A

    Klinman, J. P.; Offenbacher, A. R. Understanding Biological Hydrogen Transfer Through the Lens of Temperature Dependent Kinetic Isotope Effects. Acc. Chem. Res. 2018, 51, 1966--1974

    2018

  10. [18]

    Explaining Kinetic Isotope Effects in Proton-Coupled Electron Transfer Reactions

    Hammes-Schiffer, S. Explaining Kinetic Isotope Effects in Proton-Coupled Electron Transfer Reactions. Acc. Chem. Res. 2025, 58, 1335--1344

    2025

  11. [19]

    V.; Nakamura, H

    Mil’nikov, G. V.; Nakamura, H. Practical implementation of the instanton theory for the ground-state tunneling splitting. J. Chem. Phys. 2001, 115, 6881--6897

    2001

  12. [20]

    O.; Althorpe, S

    Richardson, J. O.; Althorpe, S. C. Ring-polymer instanton method for calculating tunneling splittings. J. Chem. Phys. 2011, 134, 054109

    2011

  13. [21]

    Trenins, G.; Meuser, L.; Bertschi, H.; Vavourakis, O.; Flütsch, R.; Richardson, J. O. Exact tunneling splittings from symmetrized path integrals. J. Chem. Phys. 2023, 159, 034108

    2023

  14. [22]

    K.; Clary, D

    Gregory, J. K.; Clary, D. C. Calculations of the tunneling splittings in water dimer and trimer using diffusion Monte Carlo. J. Chem. Phys. 1995, 102, 7817--7829

    1995

  15. [23]

    C.; Yu, Q.; Mancini, J

    Fortenberry, R. C.; Yu, Q.; Mancini, J. S.; Bowman, J. M.; Lee, T. J.; Crawford, T. D.; Klemperer, W. F.; Francisco, J. S. Communication: Spectroscopic consequences of proton delocalization in OCHCO+. J. Chem. Phys. 2015, 143, 071102

    2015

  16. [24]

    J.; Finney, J

    DiRisio, R. J.; Finney, J. M.; McCoy, A. B. Diffusion Monte Carlo approaches for studying nuclear quantum effects in fluxional molecules. Wiley Interdiscip. Rev. Comput. Mol. Sci. 2022, 12, e1615

    2022

  17. [25]

    M.; McCoy, A

    Finney, J. M.; McCoy, A. B. Correlations between the Structures and Spectra of Protonated Water Clusters. J. Phys. Chem. A 2024, 128, 868--879

    2024

  18. [26]

    D.; Viel, A.; Manthe, U

    Coutinho-Neto, M. D.; Viel, A.; Manthe, U. The ground state tunneling splitting of malonaldehyde: Accurate full dimensional quantum dynamics calculations. J. Chem. Phys. 2004, 121, 9207--9210

    2004

  19. [27]

    Theoretical studies of the tunneling splitting of malonaldehyde using the multiconfiguration time-dependent Hartree approach

    Schröder, M.; Gatti, F.; Meyer, H.-D. Theoretical studies of the tunneling splitting of malonaldehyde using the multiconfiguration time-dependent Hartree approach. J. Chem. Phys. 2011, 134, 234307

    2011

  20. [28]

    A Structure-Based Gaussian Expansion for Quantum Reaction Dynamics in Molecules: Application to Hydrogen Tunneling in Malonaldehyde

    Suzuki, K.; Kanno, M.; Koseki, S.; Kono, H. A Structure-Based Gaussian Expansion for Quantum Reaction Dynamics in Molecules: Application to Hydrogen Tunneling in Malonaldehyde. J. Phys. Chem. A. 2023, 127, 4152--4165

    2023

  21. [29]

    P.; Iordanov, T.; Hammes-Schiffer, S

    Webb, S. P.; Iordanov, T.; Hammes-Schiffer, S. Multiconfigurational nuclear-electronic orbital approach: Incorporation of nuclear quantum effects in electronic structure calculations. J. Chem. Phys. 2002, 117, 4106--4118

    2002

  22. [30]

    Nuclear–electronic orbital methods: Foundations and prospects

    Hammes-Schiffer, S. Nuclear–electronic orbital methods: Foundations and prospects. J. Chem. Phys. 2021, 155, 030901

    2021

  23. [31]

    V.; Chakraborty, A.; Hammes-Schiffer, S

    Pak, M. V.; Chakraborty, A.; Hammes-Schiffer, S. Density Functional Theory Treatment of Electron Correlation in the Nuclear-Electronic Orbital Approach. J. Phys. Chem. A 2007, 111, 4522--4526

    2007

  24. [32]

    R.; Culpitt, T.; Pak, M

    Yang, Y.; Brorsen, K. R.; Culpitt, T.; Pak, M. V.; Hammes-Schiffer, S. Development of a practical multicomponent density functional for electron-proton correlation to produce accurate proton densities. J. Chem. Phys. 2017, 147, 114113

    2017

  25. [33]

    R.; Yang, Y.; Hammes-Schiffer, S

    Brorsen, K. R.; Yang, Y.; Hammes-Schiffer, S. Multicomponent Density Functional Theory: Impact of Nuclear Quantum Effects on Proton Affinities and Geometries. J. Phys. Chem. Lett. 2017, 8, 3488--3493

    2017

  26. [34]

    Multicomponent Time-Dependent Density Functional Theory: Proton and Electron Excitation Energies

    Yang, Y.; Culpitt, T.; Hammes-Schiffer, S. Multicomponent Time-Dependent Density Functional Theory: Proton and Electron Excitation Energies. J. Phys. Chem. Lett. 2018, 9, 1765--1770

    2018

  27. [35]

    Enhancing the applicability of multicomponent time-dependent density functional theory

    Culpitt, T.; Yang, Y.; Pavošević, F.; Tao, Z.; Hammes-Schiffer, S. Enhancing the applicability of multicomponent time-dependent density functional theory. J. Chem. Phys. 2019, 150, 201101

    2019

  28. [36]

    Multicomponent Coupled Cluster Singles and Doubles Theory within the Nuclear-Electronic Orbital Framework

    Pavošević, F.; Culpitt, T.; Hammes-Schiffer, S. Multicomponent Coupled Cluster Singles and Doubles Theory within the Nuclear-Electronic Orbital Framework. J. of Chem. Theory Comput. 2019, 15, 338--347

    2019

  29. [37]

    Multicomponent Coupled Cluster Singles and Doubles with Density Fitting: Protonated Water Tetramers with Quantized Protons

    Pavošević, F.; Tao, Z.; Hammes-Schiffer, S. Multicomponent Coupled Cluster Singles and Doubles with Density Fitting: Protonated Water Tetramers with Quantized Protons. J. Chem. Phys. Lett. 2021, 12, 1631--1637

    2021

  30. [38]

    Triple electron–electron–proton excitations and second-order approximations in nuclear–electronic orbital coupled cluster methods

    Pavošević, F.; Hammes-Schiffer, S. Triple electron–electron–proton excitations and second-order approximations in nuclear–electronic orbital coupled cluster methods. J. of Chem. Phys. 2022, 157, 074104

    2022

  31. [39]

    Nuclear-electronic all-particle density matrix renormalization group

    Muolo, A.; Baiardi, A.; Feldmann, R.; Reiher, M. Nuclear-electronic all-particle density matrix renormalization group. The Journal of Chemical Physics 2020, 152, 204103

    2020

  32. [40]

    Quantum Proton Effects from Density Matrix Renormalization Group Calculations

    Feldmann, R.; Muolo, A.; Baiardi, A.; Reiher, M. Quantum Proton Effects from Density Matrix Renormalization Group Calculations. J. Chem. Theory Comput. 2022, 18, 234--250

    2022

  33. [41]

    J.; Brorsen, K

    Fajen, O. J.; Brorsen, K. R. Multicomponent CASSCF Revisited: Large Active Spaces Are Needed for Qualitatively Accurate Protonic Densities. J. Chem. Theory Comput. 2021, 17, 965--974

    2021

  34. [42]

    V.; Hammes-Schiffer, S

    Pak, M. V.; Hammes-Schiffer, S. Electron-Proton Correlation for Hydrogen Tunneling Systems. Phys. Rev. Lett. 2004, 92, 103002

    2004

  35. [43]

    V.; Swalina, C.; Webb, S

    Pak, M. V.; Swalina, C.; Webb, S. P.; Hammes-Schiffer, S. Application of the nuclear–electronic orbital method to hydrogen transfer systems: multiple centers and multiconfigurational wavefunctions. Chem. Phys. 2004, 304, 227--236

    2004

  36. [44]

    V.; Hammes-Schiffer, S

    Swalina, C.; Pak, M. V.; Hammes-Schiffer, S. Analysis of the nuclear-electronic orbital method for model hydrogen transfer systems. J. Chem. Phys. 2005, 123, 014303

    2005

  37. [45]

    H.; Pak, M

    Skone, J. H.; Pak, M. V.; Hammes-Schiffer, S. Nuclear-electronic orbital nonorthogonal configuration interaction approach. J. Chem. Phys. 2005, 123, 134108

    2005

  38. [46]

    Nuclear-Electronic Orbital Multistate Density Functional Theory

    Yu, Q.; Hammes-Schiffer, S. Nuclear-Electronic Orbital Multistate Density Functional Theory. J. Phys. Chem. Lett. 2020, 11, 10106--10113

    2020

  39. [47]

    A.; Yu, Q.; Hammes-Schiffer, S

    Dickinson, J. A.; Yu, Q.; Hammes-Schiffer, S. Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory for Multiple Proton Transfer Processes. J. Phys. Chem. Lett. 2023, 14, 6170--6178

    2023

  40. [48]

    M.; Upadhyay, S.; Li, X.; Hammes-Schiffer, S

    Garner, S. M.; Upadhyay, S.; Li, X.; Hammes-Schiffer, S. Nuclear–Electronic Orbital Time-Dependent Configuration Interaction Method. J. Phys. Chem. Lett. 2024, 15, 6017--6023

    2024

  41. [49]

    Nonadiabatic Dynamics of Hydrogen Tunneling with Nuclear-Electronic Orbital Multistate Density Functional Theory

    Yu, Q.; Roy, S.; Hammes-Schiffer, S. Nonadiabatic Dynamics of Hydrogen Tunneling with Nuclear-Electronic Orbital Multistate Density Functional Theory. J. Chem. Theory Comput. 2022, 18, 7132--7141

    2022

  42. [50]

    A.; Hammes-Schiffer, S

    Dickinson, J. A.; Hammes-Schiffer, S. Nonadiabatic Hydrogen Tunneling Dynamics for Multiple Proton Transfer Processes with Generalized Nuclear-Electronic Orbital Multistate Density Functional Theory. J. Chem. Theory Comput. 2024, 20, 7716--7727

    2024

  43. [51]

    L.; Hammes-Schiffer, S

    Malbon, C. L.; Hammes-Schiffer, S. Nuclear-Electronic Orbital Multireference Configuration Interaction for Ground and Excited Vibronic States and Fundamental Insights into Multicomponent Basis Sets. Journal of Chemical Theory and Computation 2025, 21, 3968--3980

    2025

  44. [52]

    Lischka, H.; Nachtigallová, D.; Aquino, A. J. A.; Szalay, P. G.; Plasser, F.; Machado, F. B. C.; Barbatti, M. Multireference Approaches for Excited States of Molecules. Chem. Rev. 2018, 118, 7293--7361

    2018

  45. [53]

    Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

    Matsika, S. Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections. Chem. Rev. 2021, 121, 9407--9449

    2021

  46. [54]

    Terrill, K.; Nesbitt, D. J. Ab initio anharmonic vibrational frequency predictions for linear proton-bound complexes OC–H+–CO and N2–H+–N2. Phys. Chem. Chem. Phys. 2010, 12, 8311--8322

    2010

  47. [55]

    F.; Almlöf, J

    Shida, N.; Barbara, P. F.; Almlöf, J. E. A theoretical study of multidimensional nuclear tunneling in malonaldehyde. J. Chem. Phys. 1989, 91, 4061--4072

    1989

  48. [56]

    Mizukami, W.; Habershon, S.; Tew, D. P. A compact and accurate semi-global potential energy surface for malonaldehyde from constrained least squares regression. J. Chem. Phys. 2014, 141, 144310

    2014

  49. [57]

    L.; Wales, D

    Vaillant, C. L.; Wales, D. J.; Althorpe, S. C. Tunneling splittings from path-integral molecular dynamics using a Langevin thermostat. J. Chem. Phys. 2018, 148, 234102

    2018

  50. [58]

    E.; Dušek, J.; Richardson, J

    Lawrence, J. E.; Dušek, J.; Richardson, J. O. Perturbatively corrected ring-polymer instanton theory for accurate tunneling splittings. J. Chem. Phys. 2023, 159, 014111

    2023

  51. [59]

    Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality

    Lauvergnat, D.; Nauts, A. Smolyak Scheme for solving the Schrödinger equation: Application to Malonaldehyde in Full Dimensionality. ChemPhysChem 2023, 24, e202300501

    2023

  52. [60]

    Baumann, J.; Trenins, G.; Richardson, J. O. The exact tunnelling splitting of malonaldehyde from symmetrized path-integral molecular dynamics. Mol. Phys. 2025, e2474202

    2025

  53. [61]

    C.; Balint‐Kurti, G

    Marston, C. C.; Balint‐Kurti, G. G. The Fourier grid Hamiltonian method for bound state eigenvalues and eigenfunctions. J. Chem. Phys. 1989, 91, 3571--3576

    1989

  54. [62]

    P.; Hammes-Schiffer, S

    Webb, S. P.; Hammes-Schiffer, S. Fourier grid Hamiltonian multiconfigurational self-consistent-field: A method to calculate multidimensional hydrogen vibrational wavefunctions. J. Chem. Phys. 2000, 113, 5214--5227

    2000

  55. [63]

    A.; Dunning, J., Thom H.; Harrison, R

    Kendall, R. A.; Dunning, J., Thom H.; Harrison, R. J. Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions. J. Chem. Phys. 1992, 96, 6796--6806

    1992

  56. [64]

    Gaussian basis sets for use in correlated molecular calculations

    Dunning, J., Thom H. Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen. J. Chem. Phys. 1989, 90, 1007--1023

    1989

  57. [65]

    H.; Hammes-Schiffer, S

    Hazra, A.; Skone, J. H.; Hammes-Schiffer, S. Combining the nuclear-electronic orbital approach with vibronic coupling theory: Calculation of the tunneling splitting for malonaldehyde. J. Chem. Phys. 2009, 130, 054108

    2009

  58. [66]

    Molecular Electronic‐Structure Theory; John Wiley & Sons, Ltd, 2000; Chapter 8, pp 287--335

    Helgaker, T.; Jørgensen, P.; Olsen, J. Molecular Electronic‐Structure Theory; John Wiley & Sons, Ltd, 2000; Chapter 8, pp 287--335

    2000

  59. [67]

    Birer, \

    Tautermann, C. S.; Voegele, A. F.; Loerting, T.; Liedl, K. R. The optimal tunneling path for the proton transfer in malonaldehyde. J. Chem. Phys. 2002, 117, 1962--1966 mcitethebibliography neo_multirefci.bib0000664000000000000000000026147615034217374013266 0ustar rootroot@arti...

    2001

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