Pith. sign in

REVIEW 3 major objections 6 minor 2 cited by

Transcorrelated Methods for Multireference Problems

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read This paper argues that optimising the Jastrow factor against a multireference wavefunction, rather than a single Hartree-Fock determinant, removes the transcorrelated method's failure on strongly correlated systems, giving chemically…

desk verdict Genuine advance in transcorrelated methods: multireference Jastrow references fix the N2 curve, but the unquantified xTC cumulant error and unreleased code keep this from being fully settled. read the letter →

arxiv 2505.20187 v1 pith:OGMRJ2OI submitted 2025-05-26 physics.chem-ph physics.comp-ph

J. Philip Haupt , Evelin M. C. Christlmaier , Pablo López Ríos , Nikolay A. Bogdanov , Daniel Kats , Ali Alavi This is my paper · ORCID
classification physics.chem-phphysics.comp-ph
keywords transcorrelatedmethodJastrowfactormultireferencewavefunctionfullconfigurationinteractionquantumMonteCarloxTCapproximationnitrogenbindingcurveexcitationenergieschemicalaccuracy
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 claims that the transcorrelated workflow fails on multireference problems because the Jastrow factor is optimised against a single determinant. The fix is to optimise J against a multireference reference wavefunction, either from a small FCIQMC run or from CASSCF, and to feed the same reference's one-body density matrix into the xTC approximation. With this change, TC-FCIQMC reproduces the experimental N$_2$ binding curve to chemical accuracy across the full range of bond lengths, removes the unphysical dip and size-consistency error seen with the Hartree-Fock reference, and yields vertical excitation energies for N$_2$, CO and NH$_3$ that match much larger-basis non-transcorrelated calculations. The authors conclude that the main obstacle in the transcorrelated workflow is resolved.

What carries the argument

The load-bearing object is the multireference Jastrow optimisation: the variance objective $\sigma^2_{\mathrm{ref}}$ is built from the similarity-transformed Hamiltonian acting on the expansion $\Phi_0 = \sum_I c_I |D_I\rangle$, and the same $\Phi_0$ supplies the one-body reduced density matrix used by the xTC approximation to fold three-body terms into one- and two-body operators. The Jastrow factor is a polynomial in electron-electron, electron-nuclear, and electron-electron-nuclear distances with optimised coefficients, truncated at 100 determinants from the reference CI vector. Together these choices define a TC Hamiltonian whose FCIQMC solution is evaluated with a multi-determinant trial wavefunction to control stochastic noise.

What would settle it

Perform a TC-FCIQMC calculation at a strongly stretched N-N distance (e.g. 6 bohr) with the full three-body transcorrelated Hamiltonian instead of the xTC approximation, using the same Jastrow factor and reference; if the energy shifts by more than about 1.6 mHa relative to the xTC value, the reported chemical accuracy is an artefact of the approximation rather than a systematic result.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the choice of reference wavefunction during Jastrow optimisation is the decisive ingredient for transcorrelated calculations of strongly multireference systems. Beginning from the Jastrow ansatz $\Psi = e^{J}\Phi$, the authors show that when $\Phi$ is a single Slater determinant the optimised Jastrow carries a single-reference bias: the resulting TC-FCIQMC binding curve of N$_2$ acquires an unphysical dip near 6 bohr and a long-distance asymptote about 10 mHa below twice the atomic energy. Replacing $\Phi$ with a multireference expansion—a truncated FCIQMC wavefunction or a CASSCF(10e,8o) wavefunction—and using the corresponding one-body reduced density matrix in the xTC approximation removes these artefacts. The FCIQMC-Jastrow route gives a dissociation energy of 364.2 mHa against the experimental 363.7 mHa, with size-consistency error 0.5 mHa and non-parallelity error 4.6 mHa; the CASSCF-Jastrow route is slightly less accurate but deterministic. The workflow extends to excited states by optimising a state-specific Jastrow for each target, with accurate vertical excitation energies for N$_2$, CO and NH$_3$ using small basis sets.

Load-bearing premise

The paper relies on the xTC approximation—replacing the higher-order density matrices by antisymmetrised products of the one-body density matrix—being accurate for genuinely multireference references, yet the error from the dropped cumulant is never quantified.

Editorial extensions

If this is right

  • TC-FCIQMC with a multireference Jastrow reproduces the full experimental N$_2$ binding curve within chemical accuracy (about $\pm 1.6$ mHa), including the strongly stretched regime where single-reference methods fail.
  • The size-consistency error drops from 12.7 mHa with a Hartree-Fock reference to 0.5 mHa with the FCIQMC-Jastrow and $-$1.5 mHa with the CASSCF-Jastrow, restoring the correct long-distance asymptote.
  • Vertical excitation energies computed at aug-cc-pVDZ are comparable to extrapolated FCI at aug-cc-pVQZ, implying much faster basis-set convergence for excited states.
  • A state-specific Jastrow, aided by a spin-penalty term, lets the method target individual singlet excited states without collapsing to lower triplets.
  • The CASSCF-Jastrow variant is deterministic and available from standard quantum chemistry tools, making the workflow practical as a default choice.

Reading between the lines

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

  • The same workflow is a testable candidate for other strongly correlated curves (e.g. O$_2$, C$_2$, or stretched CH bonds), where the single-reference dip should reappear with an RHF Jastrow and disappear with a multireference one.
  • Because the FCIQMC reference is a single imaginary-time snapshot, averaging the CI vector and 1RDM over a period of imaginary time would likely reduce the remaining noise in the binding curve; the authors note this option but do not implement it.
  • The apparent success raises the question of whether the xTC approximation's neglect of the 2RDM cumulant is benign for multireference references; a cumulant-corrected or exact-three-body TC calculation at one stretched geometry would settle whether the chemical accuracy is systematic.
  • Iterating the workflow self-consistently—using the TC-FCIQMC output as the next reference for Jastrow optimisation—points toward a fully correlated TC-MCSCF method, an outlook the authors sketch.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper proposes a multireference extension of the transcorrelated workflow by optimizing the Jastrow factor in the presence of a multireference reference wavefunction (CASSCF or a truncated, unconverged FCIQMC CI vector) and using the corresponding multireference 1RDM in the xTC approximation. The central demonstrations are the N2 binding curve with aug-cc-pVTZ compared against the experimental potential of Le Roy et al., and vertical excitation energies for N2, CO, and NH3 compared against extrapolated FCI references and experiment. The authors report that the multireference Jastrow optimization removes the unphysical dip and large size-consistency error seen with an RHF-based Jastrow, yielding dissociation energies close to experiment (CASSCF-Jastrow 361.2 mHa, FCIQMC-Jastrow 364.2 mHa vs. experimental 363.7 mHa).

Significance. If the results hold, the paper provides a practical and general workflow for applying transcorrelated methods to strongly multireference problems, which is an important step for the field. The strengths are that the energies are benchmarked against external experimental and high-level theoretical data (LeRoy N2 potential, HEAT, extrapolated FCI from reference [43]), and the Jastrow parameters are variance-minimized rather than fitted to the target energies. The clean contrast between the RHF-Jastrow baseline (size-consistency error 12.7 mHa, non-parallelity error 8.0 mHa) and the two multireference variants (errors of -1.5/0.5 mHa and 3.1/4.6 mHa, respectively) directly supports the main methodological claim. However, the reported energies are all computed from the xTC Hamiltonian, whose multireference generalization still lacks a quantified error bound, and the FCIQMC-based Jastrow reference introduces uncontrolled stochastic noise.

major comments (3)
  1. [Section 2.1-2.2, Eqs. (6)-(8)] The xTC approximation replaces higher-order density matrices by antisymmetrized products of the 1RDM, which the paper itself states is exact only for single-determinant references. In Section 2.2 the same approximation is then used with CASSCF and FCIQMC multireference 1RDMs, silently neglecting the connected (cumulant) part of the 2RDM. Since all reported TC-FCIQMC energies are obtained from this approximate Hamiltonian, the authors must quantify the error introduced by this neglect, for example by comparing xTC results against a full TC treatment that retains the three-body operator or explicitly includes the 2RDM cumulant, at representative geometries (e.g., N2 at equilibrium and at 10 bohr, and at least one excited state). Without such a numerical bound, the claimed chemical accuracy could be coincidental rather than systematic.
  2. [Section 3.1 and Section 3.2] The FCIQMC-based Jastrow reference is described as a single imaginary-time snapshot from a 3×10^7-walker calculation, truncated to the 100 most important determinants, and the paper notes in Section 3.2 that this is a source of noise. No statistical error bars or convergence tests are reported for the resulting Jastrow parameters or for the final TC-FCIQMC energies, such as the FCIQMC-Jastrow dissociation energy of 364.2 mHa in Table 1. The authors should provide error bars from independent repetitions or show that the optimized Jastrow and final energies are stable with respect to snapshot length and determinant cutoff, particularly for the stretched geometries where the method is most stochastic.
  3. [Section 3.2, Table 1 and Figure 4] The abstract claims chemical accuracy across the entire binding curve, but the non-parallelity errors reported in Table 1 are 3.1 mHa (CASSCF-Jastrow) and 4.6 mHa (FCIQMC-Jastrow), both larger than the ±1.6 mHa chemical-accuracy window. A non-parallelity error larger than 3.2 mHa necessarily means at least one point lies outside that window, so the paper should report the maximum absolute deviation from experiment for each curve, or qualify the chemical-accuracy claim accordingly. This does not undermine the main methodological improvement, but it affects the precision of the abstract's central claim.
minor comments (6)
  1. [Section 2.1, Eq. (6)] Equation (6) states that the Hamiltonian is normal ordered with respect to Φ_SD, while Section 2.2 uses the same xTC expressions with multireference 1RDMs; the notation should be revised to make clear that the reference in the normal-ordering formalism is not restricted to a single determinant.
  2. [Reference [38]] The pytchint library is cited as 'to be released'; if the code is not yet public, the authors should state its availability or provide a stable reference, since the reproducibility of the xTC integrals is relevant to the reader.
  3. [Figures 5-7] The horizontal axis in Figures 5-7 is labeled with expressions such as '1 avdz' and '1 CBS' rather than a clear axis title; the figures should explicitly label the abscissa as 1/n_orb and define the basis-set abbreviations in the captions.
  4. [Section 3.3] For ammonia, the paper states that the excitations were treated as vertical, which is likely the cause of the large discrepancy with experiment, but the corresponding experimental values should be identified as adiabatic (or the comparison should be explicitly stated as vertical-theory versus adiabatic-experiment) to avoid ambiguity in the figure.
  5. [Section 3.3] The phrase 'state-averaged CASSCF Jastrow ansatzes' is potentially confusing because the Jastrow factors are optimized state-specifically; the text should clarify that the orbitals come from state-averaged CASSCF while the CI vector and Jastrow are optimized for each target state individually.
  6. [Section 3.1] The initiator parameter n_add = 3 is mentioned but not defined; for reproducibility, the authors should briefly define the initiator approximation parameter or cite the relevant equation in reference [18].

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: energies are benchmarked against external data and Jastrow parameters are variance-minimized, not fitted to target energies.

full rationale

The paper's derivation chain is self-contained in the sense required by the circularity review. The TC-FCIQMC energies are eigenvalues of a transcorrelated Hamiltonian whose Jastrow parameters are optimized by minimizing the variance of a reference wavefunction (Eqs. 16-17), not by fitting any reported energy; no fitted constant enters the dissociation energies or excitation energies. The xTC approximation (Eqs. 6-8) is imported from same-group prior work (refs 20, 22), but in this paper it is used as a computational method and the resulting numbers are checked against the external LeRoy experimental N2 curve and against Loos et al. extrapolated FCI benchmarks (refs 27, 43). The multireference 1RDM enters the Hamiltonian definition rather than being tuned to reproduce the target values, so the central claims do not reduce by construction to their inputs. The main caveat, namely that the neglected 2RDM cumulant in the xTC approximation is not quantified for multireference references, is an accuracy and robustness concern, not a circularity. Similarly, the stochastic FCIQMC snapshot used as Jastrow reference introduces noise but does not make the prediction identical to an input by construction.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central claims rest on: stochastically optimized Jastrow parameters (DTN form), the xTC normal-ordering approximation which is exact only for single-determinant references, and the transferability of a variance-minimized Jastrow to an accurate TC-FCIQMC solution. No attackable invented entities. The most honest accounting: the paper contributes a workflow and a benchmark demonstration whose foundations (xTC, DTN Jastrow, FCIQMC) come from prior same-group work, plus variational Jastrow parameters that are fitted per geometry and per state.

free parameters (3)
  • DTN Jastrow coefficients (a_k, b_k, c_klm) = not tabulated in main text (per-geometry, per-state VMC optimization)
    Eqs. (9)-(12): the Jastrow factor is optimized by stochastic variance minimization against the reference wavefunction, separately for each geometry and state. These parameters shape the TC Hamiltonian, and their optimization noise contributes to the scatter in the binding curve (Section 3.2).
  • Determinant cutoff for the reference CI vector = 100 determinants
    Section 3.1: the FCIQMC or CASSCF CI vector used for Jastrow optimization is truncated to 100 determinants, a hand-chosen truncation that defines the reference wavefunction.
  • NDet for the trial wavefunction in projected energies = 20 determinants (Fig. 2 example)
    Section 2.3: the multi-determinant trial wavefunction reduces statistical fluctuations of the projected energy; the chosen size affects variance, not the converged energy.
assumptions (5)
  • standard math The BCH expansion of e^{-J} H e^{J} terminates exactly at the second commutator for a Jastrow depending only on spatial coordinates.
    Eq. (3): the kinetic operator is second-order, so its nested commutators with J exhaust the derivatives; standard and correct.
  • standard math The similarity transformation preserves the spectrum, so the TC eigenvalue problem has the same eigenvalues as the original Hamiltonian.
    e^{J} is invertible; used throughout to justify solving for Phi instead of Psi.
  • domain assumption xTC approximation: explicit three-body terms are neglected and higher-order density matrices are replaced by antisymmetrized products of the 1RDM (Eqs. 6-8).
    Exact for single-determinant references; the paper applies it with multireference CASSCF/FCIQMC references without quantifying the dropped 2RDM cumulant. This is the load-bearing approximation identified in the review.
  • domain assumption A Jastrow optimized by variance minimization against a qualitatively correct reference transfers to accurate TC-FCIQMC energies for that state.
    Methodological premise of the paper: the reference supplies static correlation and the Jastrow supplies dynamic correlation. Supported only empirically via comparisons to experiment and extrapolated FCI.
  • domain assumption Experimental N2 potential (ref [27]), HEAT benchmark (ref [44]), and experimental excitation energies (refs [45-49]) are valid ground truth for the computed electronic energies.
    Standard benchmarking practice; the NH3 comparison is acknowledged as vertical versus adiabatic, which limits that benchmark.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Transcorrelated Methods for Multireference Problems." pith.science (2026). https://pith.science/paper/OGMRJ2OI

@misc{pith2026250520187,
  author       = {Pith},
  title        = {Pith review of: Transcorrelated Methods for Multireference Problems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OGMRJ2OI}},
  note         = {Machine review of arXiv:2505.20187}
}
abstract

We apply the transcorrelated method to problems of multireference character. For this, we show that the choice of reference wavefunction during the Jastrow optimisation procedure is vital, and we propose a workflow wherein we use conventional multi-configurational methods to provide a reference wavefunction for Jastrow factor optimisation. This Jastrow function is subsequently used with transcorrelated-full configuration interaction quantum Monte Carlo within the xTC approximation (TC-FCIQMC) to yield highly accurate transcorrelated energies. This is demonstrated for N$_2$ using the aug-cc-pVTZ basis set, achieving chemical accuracy across the entire binding curve compared with experiment. We also apply the method to compute excitation energies of dinitrogen, CO and the ammonia molecule, where accurate results, comparable to the best available theoretical predictions, are obtained with modest basis sets.

Figures

Figures reproduced from arXiv: 2505.20187 by the authors.

Figure 1
Figure 1. The TC-FCIQMC binding curve for N2 with the aug-cc-pVTZ basis set. An unphysical dip in the TC-FCIQMC calculation at large bond lengths is apparent when zooming in on the curve, as shown in the inset. For reference we also include the MRCI-D-F12 curve. 2.2 Multireference TC Ansatzes Based on the discussion in the previous section, it is plausible that the transcorrelated workflow suffers from a single-reference bias… view at source ↗
Figure 2
Figure 2. The HF-projected and trial-projected energy trajectories in imaginary time for N [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. TC-FCIQMC energies for the nitrogen dimer for various points along its binding curve, between [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: The difference between the theoretical binding curve and the experimental binding curve [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]
Figure 5
Figure 5. Figure 5: Excitation energies for dinitrogen compared with experiment [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]
Figure 6
Figure 6. Figure 6: Excitation energies for carbon monoxide compared with experiment [PITH_FULL_IMAGE:figures/full_fig_p010_6.png]
Figure 7
Figure 7. Figure 7: Excitation energies for ammonia compared with experiment [PITH_FULL_IMAGE:figures/full_fig_p011_7.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Deterministic Optimisation of Jastrow Factors

    physics.chem-ph 2025-06 conditional novelty 7.0 of 10

    A deterministic finite-basis method for optimizing Jastrow factors is derived and validated, yielding noise-free Jastrows with energies close to VMC energy-optimized results.

  2. Transcorrelated Theory for Transition Metal Atoms

    physics.chem-ph 2025-06 conditional novelty 5.0 of 10

    Transcorrelated pseudopotential calculations yield ionization and excitation energies for Sc-Zn that are mostly within 1 kcal/mol of experiment using aug-cc-pVQZ, without complete basis set extrapolation.

Reference graph

Works this paper leans on

54 extracted references · 22 canonical work pages · cited by 2 Pith papers

  1. [43]

    A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks.Journal of Chemical Theory and Computation, 14(8):4360–4379, 2018

    Pierre-Fran¸ cois Loos, Anthony Scemama, Aymeric Blondel, Yann Garniron, Michel Caffarel, and Denis Jacquemin. A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks.Journal of Chemical Theory and Computation, 14(8):4360–4379, 2018. ISSN 1549-

    work page 2018

  2. [1]

    On the eigenfunctions of many-particle systems in quantum mechanics.Communica- tions on Pure and Applied Mathematics, 10(2):151–177, January 1957

    Tosio Kato. On the eigenfunctions of many-particle systems in quantum mechanics.Communica- tions on Pure and Applied Mathematics, 10(2):151–177, January 1957. ISSN 00103640. doi: 10. 11 1002/cpa.3160100201. URLhttps://onlinelibrary.wiley.com/doi/10.1002/cpa.3160100201. Publisher: John Wiley & Sons, Ltd

    doi:10.1002/cpa.3160100201 1957

  3. [2]

    J. C. Slater. Central Fields and Rydberg Formulas in Wave Mechanics.Physical Review, 31(3): 333–343, March 1928. doi: 10.1103/PhysRev.31.333. URLhttps://link.aps.org/doi/10.1103/ PhysRev.31.333. Publisher: American Physical Society

    work page doi:10.1103/physrev.31.333 1928

  4. [3]

    Hylleraas

    Egil A. Hylleraas. Neue Berechnung der Energie des Heliums im Grundzustande, sowie des tiefsten Terms von Ortho-Helium.Zeitschrift f¨ ur Physik, 54(5):347–366, May 1929. ISSN 0044-3328. doi: 10.1007/BF01375457

    doi:10.1007/bf01375457 1929

  5. [4]

    R12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l.Theoretica chimica acta, 68(6):445–469, December 1985

    Werner Kutzelnigg. R12-Dependent terms in the wave function as closed sums of partial wave amplitudes for large l.Theoretica chimica acta, 68(6):445–469, December 1985. ISSN 1432-2234. doi: 10.1007/BF00527669

    work page doi:10.1007/bf00527669 1985

  6. [5]

    Bischoff, and Edward F

    Liguo Kong, Florian A. Bischoff, and Edward F. Valeev. Explicitly Correlated R12/F12 Methods for Electronic Structure.Chemical Reviews, 112(1):75–107, January 2012. ISSN 0009-2665. doi: 10.1021/cr200204r

    doi:10.1021/cr200204r 2012

  7. [6]

    N. C. Handy. Energies and expectation values for be by the transcorrelated method.The Journal of Chemical Physics, 51(8):3205–3212, October 1969. ISSN 00219606. doi: 10.1063/1.1672496. URL http://aip.scitation.org/doi/10.1063/1.1672496. Publisher: American Institute of Physic- sAIP

    doi:10.1063/1.1672496 1969

  8. [7]

    A calculation for the energies and wavefunctions for states of neon with full electronic correlation accuracy.Proceedings of the Royal Society of London

    Samuel Francis Boys, Nicholas Charles Handy, and John Wilfrid Linnett. A calculation for the energies and wavefunctions for states of neon with full electronic correlation accuracy.Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 310(1500):63–78, January

    work page

Show all 54 references
  1. [8]

    Many-Body Problem with Strong Forces.Physical Review, 98(5):1479, June 1955

    Robert Jastrow. Many-Body Problem with Strong Forces.Physical Review, 98(5):1479, June 1955. ISSN 0031899X. doi: 10.1103/PhysRev.98.1479. URLhttps://journals.aps.org/pr/abstract/ 10.1103/PhysRev.98.1479. Publisher: American Physical Society

    1955 doi

  2. [9]

    Transcorrelated method for electronic systems coupled with variational Monte Carlo calculation.The Journal of Chemical Physics, 119(19):10015–10031, 2003

    Naoto Umezawa and Shinji Tsuneyuki. Transcorrelated method for electronic systems coupled with variational Monte Carlo calculation.The Journal of Chemical Physics, 119(19):10015–10031, 2003. ISSN 0021-9606. doi: 10.1063/1.1617274. URLhttps://doi.org/10.1063/1.1617274

    2003 doi

  3. [10]

    Transcorrelated Method: Another Possible Way towards Electronic Structure Calculation of Solids.Progress of Theoretical Physics Supplement, 176:134–142, 2008

    Shinji Tsuneyuki. Transcorrelated Method: Another Possible Way towards Electronic Structure Calculation of Solids.Progress of Theoretical Physics Supplement, 176:134–142, 2008. ISSN 0375-

    2008

  4. [11]

    A feasible transcorrelated method for treating electronic cusps using a frozen Gaussian geminal.Chemical Physics Letters, 330(1):169–174, 2000

    Seiichiro Ten-no. A feasible transcorrelated method for treating electronic cusps using a frozen Gaussian geminal.Chemical Physics Letters, 330(1):169–174, 2000. ISSN 0009-2614. doi: 10.1016/S0009-2614(00)01066-6. URLhttps://www.sciencedirect.com/science/article/pii/ S0009261400010666

    doi

  5. [12]

    Electronic Structure Calculations of Solids with a Similarity- Transformed Hamiltonian.Journal of the Physical Society of Japan, 75(10):103705, 2006

    Rei Sakuma and Shinji Tsuneyuki. Electronic Structure Calculations of Solids with a Similarity- Transformed Hamiltonian.Journal of the Physical Society of Japan, 75(10):103705, 2006. ISSN 0031-9015. doi: 10.1143/JPSJ.75.103705. URLhttps://journals.jps.jp/doi/10.1143/JPSJ. 75.103705

    2006 doi

  6. [13]

    Nicholas Lee and Alex J. W. Thom. Studies on the Transcorrelated Method.Journal of Chemical Theory and Computation, 19(17):5743–5759, 2023. ISSN 1549-9618. doi: 10.1021/acs.jctc.3c00046. URLhttps://doi.org/10.1021/acs.jctc.3c00046

    2023 doi

  7. [14]

    Application of the transcorrelated Hamiltonian to the linearized coupled cluster singles and doubles model.Chemical Physics Let- ters, 353(3):317–323, 2002

    Osamu Hino, Yoshitaka Tanimura, and Seiichiro Ten-no. Application of the transcorrelated Hamiltonian to the linearized coupled cluster singles and doubles model.Chemical Physics Let- ters, 353(3):317–323, 2002. ISSN 0009-2614. doi: 10.1016/S0009-2614(02)00042-8. URLhttps: //ww...

    2002 doi

  8. [15]

    Extension of selected configuration interaction for transcorrelated methods.The Journal of Chemical Physics, 157(13):134107, 2022

    Abdallah Ammar, Anthony Scemama, and Emmanuel Giner. Extension of selected configuration interaction for transcorrelated methods.The Journal of Chemical Physics, 157(13):134107, 2022. ISSN 0021-9606. doi: 10.1063/5.0115524. URLhttps://doi.org/10.1063/5.0115524

    2022 doi

  9. [16]

    Compactification of determinant expansions via transcorrelation.The Journal of Chemical Physics, 161(8):084104,

    Abdallah Ammar, Anthony Scemama, Pierre-Fran¸ cois Loos, and Emmanuel Giner. Compactification of determinant expansions via transcorrelation.The Journal of Chemical Physics, 161(8):084104,

  10. [17]

    Booth, Alex J.W

    George H. Booth, Alex J.W. Thom, and Ali Alavi. Fermion monte carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space.Journal of Chemical Physics, 131(5):054106, August 2009. ISSN 00219606. doi: 10.1063/1.3193710. URLhttp://scitation. aip...

    2009 doi

  11. [18]

    Booth, and Ali Alavi

    Deidre Cleland, George H. Booth, and Ali Alavi. Communications: Survival of the fittest: Ac- celerating convergence in full configuration-interaction quantum Monte Carlo.Journal of Chem- ical Physics, 132(4):041103, January 2010. ISSN 00219606. doi: 10.1063/1.3302277. URL http...

    2010 doi

  12. [19]

    Hongjun Luo and Ali Alavi. Combining the Transcorrelated Method with Full Configuration Inter- action Quantum Monte Carlo: Application to the Homogeneous Electron Gas.Journal of Chemical Theory and Computation, 14(3):1403–1411, March 2018. ISSN 15499626. doi: 10.1021/acs.jctc....

    2018 arXiv

  13. [20]

    Philip Haupt, Seyed Mohammadreza Hosseini, Pablo L´ opez R ´ ıos, Werner Dobrautz, Aron Cohen, and Ali Alavi

    J. Philip Haupt, Seyed Mohammadreza Hosseini, Pablo L´ opez R ´ ıos, Werner Dobrautz, Aron Cohen, and Ali Alavi. Optimizing Jastrow factors for the transcorrelated method. The Journal of Chemical Physics, 158(22):224105, June 2023. ISSN 0021-9606, 1089-7690. doi: 10.1063/5.014...

    2023 doi

  14. [21]

    L´ opez R ´ ıos, P

    P. L´ opez R ´ ıos, P. Seth, N. D. Drummond, and R. J. Needs. Framework for constructing generic Jastrow correlation factors.Physical Review E, 86(3):036703, 2012. doi: 10.1103/PhysRevE.86. 036703. URLhttps://link.aps.org/doi/10.1103/PhysRevE.86.036703

    2012 doi

  15. [22]

    xTC: An efficient treatment of three-body interactions in transcorrelated meth- ods.The Journal of Chemical Physics, 159(1):014113, July 2023

    Evelin Martine Corvid Christlmaier, Thomas Schraivogel, Pablo L´ opez R ´ ıos, Ali Alavi, and Daniel Kats. xTC: An efficient treatment of three-body interactions in transcorrelated meth- ods.The Journal of Chemical Physics, 159(1):014113, July 2023. ISSN 0021-9606, 1089-7690. ...

    2023 doi

  16. [23]

    S. F. Boys and N. C. Handy. A calculation for the energies and wavefunctions for states of neon with full electronic correlation accuracy. InProceedings of the Royal Society of London. A. Mathematical and Physical Sciences, volume 310, pages 63–78. The Royal Society London, Ap...

    1969

  17. [24]

    Cohen, Hongjun Luo, Kai Guther, Werner Dobrautz, David P

    Aron J. Cohen, Hongjun Luo, Kai Guther, Werner Dobrautz, David P. Tew, and Ali Alavi. Similarity transformation of the electronic Schr¨ odinger equation via Jastrow factorization.The Journal of Chemical Physics, 151(6):061101, August 2019. ISSN 0021-9606. doi: 10.1063/1.5116024

    2019 doi

  18. [25]

    Normal order and extended Wick theorem for a multiconfiguration reference wave function.The Journal of Chemical Physics, 107(2):432–449, 1997

    Werner Kutzelnigg and Debashis Mukherjee. Normal order and extended Wick theorem for a multiconfiguration reference wave function.The Journal of Chemical Physics, 107(2):432–449, 1997. ISSN 0021-9606. doi: 10.1063/1.474405. URLhttps://doi.org/10.1063/1.474405

    1997 doi

  19. [26]

    Cumulant expansion of the reduced density matrices

    Werner Kutzelnigg and Debashis Mukherjee. Cumulant expansion of the reduced density matrices. The Journal of Chemical Physics, 110(6):2800–2809, 1999. ISSN 0021-9606. doi: 10.1063/1.478189. URLhttps://doi.org/10.1063/1.478189. 13

    1999 doi

  20. [27]

    Le Roy, Yiye Huang, and Calvin Jary

    Robert J. Le Roy, Yiye Huang, and Calvin Jary. An accurate analytic potential function for ground- state N2 from a direct-potential-fit analysis of spectroscopic data.The Journal of Chemical Physics, 125(16):164310, 2006. ISSN 0021-9606. doi: 10.1063/1.2354502. URLhttps://doi....

    2006 doi

  21. [28]

    Density matrix renormalization group for transcorrelated hamil- tonians: Ground and excited states in molecules.Journal of Chemical Theory and Computation, 19 (6):1734–1743, 2023

    Ke Liao, Huanchen Zhai, Evelin Martine Corvid Christlmaier, Thomas Schraivogel, Pablo L´ opez R ´ ıos, Daniel Kats, and Ali Alavi. Density matrix renormalization group for transcorrelated hamil- tonians: Ground and excited states in molecules.Journal of Chemical Theory and Com...

    2023 doi

  22. [29]

    Philip Haupt, Daniel Kats, Pablo Lopez-Rios, and Ali Alavi

    Kristoffer Simula, Evelin Martine Corvid Christlmaier, Maria-Andreea Filip, J. Philip Haupt, Daniel Kats, Pablo Lopez-Rios, and Ali Alavi. Transcorrelated theory with pseudopotentials.Journal of Chemical Theory and Computation, 2025. doi: 10.1021/acs.jctc.5c00343

    2025 doi

  23. [30]

    Unbiased reduced density matrices and electronic properties from full configuration interaction quan- tum Monte Carlo.The Journal of Chemical Physics, 141:244117, 2014

    Catherine Overy, George H Booth, N S Blunt, James J Shepherd, Deidre Cleland, and Ali Alavi. Unbiased reduced density matrices and electronic properties from full configuration interaction quan- tum Monte Carlo.The Journal of Chemical Physics, 141:244117, 2014. doi: 10.1063/1....

    2014 doi

  24. [31]

    F. R. Petruzielo, A. A. Holmes, Hitesh J. Changlani, M. P. Nightingale, and C. J. Umrigar. Semis- tochastic Projector Monte Carlo Method.Physical Review Letters, 109(23):230201, December 2012. doi: 10.1103/PhysRevLett.109.230201. URLhttps://link.aps.org/doi/10.1103/PhysRevLett...

    2012 doi

  25. [32]

    N. S. Blunt, Simon D. Smart, J. A. F. Kersten, J. S. Spencer, George H. Booth, and Ali Alavi. Semi- stochastic full configuration interaction quantum monte carlo: Developments and application.The Journal of Chemical Physics, 142(18):184107, 05 2015. ISSN 0021-9606. doi: 10.106...

    2015 doi

  26. [33]

    Kendall, Jr

    Rick A. Kendall, Jr. Dunning, Thom H., and Robert J. Harrison. Electron affinities of the first-row atoms revisited. systematic basis sets and wave functions.J. Chem. Phys., 96(9):6796–6806, 05

  27. [34]

    Anderson, Nick S

    Kai Guther, Robert J. Anderson, Nick S. Blunt, Nikolay A. Bogdanov, Deidre Cleland, Nike Dattani, Werner Dobrautz, Khaldoon Ghanem, Peter Jeszenszki, Niklas Liebermann, Giovanni Li Manni, Alexander Y. Lozovoi, Hongjun Luo, Dongxia Ma, Florian Merz, Catherine Overy, Markus Ramp...

    2020 arXiv

  28. [35]

    Berkelbach, Nick S

    Qiming Sun, Timothy C. Berkelbach, Nick S. Blunt, George H. Booth, Sheng Guo, Zhendong Li, Junzi Liu, James D. McClain, Elvira R. Sayfutyarova, Sandeep Sharma, Sebastian Wouters, and Garnet Kin Lic Chan. Pyscf: the python-based simulations of chemistry framework. Wiley Interdi...

    2018 doi

  29. [36]

    Blunt, Nikolay A

    Qiming Sun, Xing Zhang, Samragni Banerjee, Peng Bao, Marc Barbry, Nick S. Blunt, Nikolay A. Bogdanov, George H. Booth, Jia Chen, Zhi Hao Cui, Janus J. Eriksen, Yang Gao, Sheng Guo, Jan Hermann, Matthew R. Hermes, Kevin Koh, Peter Koval, Susi Lehtola, Zhendong Li, Junzi Liu, Na...

    2020

  30. [37]

    R. J. Needs, M. D. Towler, N. D. Drummond, P. L´ opez R ´ ıos, and J. R. Trail. Variational and diffusion quantum Monte Carlo calculations with the CASINO code.Journal of Chemical Physics, 152(15):154106, April 2020. ISSN 00219606. doi: 10.1063/1.5144288. URLhttps://doi.org/10...

    2020

  31. [38]

    Philip Haupt, Pablo L´ opez R ´ ıos, Evelin M

    J. Philip Haupt, Pablo L´ opez R ´ ıos, Evelin M. C. Christlmaier, Maria-Andreea Filip, Kristoffer Simula, Johannes Hauskrecht, Ke Liao, Werner Dobrautz, Kai Guther, Aron J. Cohen, and A. Alavi. pytchint: Transcorrelated hamiltonian integrals library, 2025. to be released

    2025

  32. [39]

    Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach.The Journal of Physical Chemistry A, 126(12):2050–2060, 2022

    Oskar Weser, Niklas Liebermann, Daniel Kats, Ali Alavi, and Giovanni Li Manni. Spin Purification in Full-CI Quantum Monte Carlo via a First-Order Penalty Approach.The Journal of Physical Chemistry A, 126(12):2050–2060, 2022. ISSN 1089-5639. doi: 10.1021/acs.jpca.2c01338. URL h...

    2022 doi

  33. [40]

    Werner, P

    H.-J. Werner, P. J. Knowles and P. Celani, W. Gy¨ orffy, A. Hesselmann, D. Kats, G. Knizia, A. K¨ ohn, T. Korona, D. Kreplin, R. Lindh, Q. Ma, F. R. Manby, A. Mitrushenkov, G. Rauhut, M. Sch¨ utz, K. R. Shamasundar and T. B. Adler, R. D. Amos, S. J. Bennie, A. Bernhardsson, A....

  34. [41]

    Werner, P

    H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, and M. Sch¨ utz. Molpro: A general-purpose quantum chemistry program package.Wiley Interdisciplinary Reviews: Computational Molecular Science, 2:242–253, 2012

    2012

  35. [42]

    Werner, P

    H.-J. Werner, P. J. Knowles, et al. MOLPRO, version , a package of ab initio programs,

  36. [44]

    Peterson, and David A

    David Feller, Kirk A. Peterson, and David A. Dixon. A survey of factors contributing to accurate theoretical predictions of atomization energies and molecular structures.The Journal of Chemical Physics, 129(20):204105, 2008. ISSN 0021-9606. doi: 10.1063/1.3008061. URLhttps://d...

    2008 doi

  37. [45]

    Gr¯ uner, and Geerd H

    Jens Oddershede, Norbert E. Gr¯ uner, and Geerd H. F. Diercksen. Comparison between equation of motion and polarization propagator calculations.Chemical Physics, 97(2):303–310, August 1985. ISSN 0301-0104. doi: 10.1016/0301-0104(85)87039-7

    1985 doi

  38. [46]

    K. P. Huber and G. Herzberg. Constants of diatomic molecules. In K. P. Huber and G. Herzberg, editors,Molecular Spectra and Molecular Structure: IV. Constants of Diatomic Molecules, pages 8–

  39. [47]

    Nielsen, Poul Jo/rgensen, and Jens Oddershede

    Egon S. Nielsen, Poul Jo/rgensen, and Jens Oddershede. Transition moments and dynamic polarizabilities in a second order polarization propagator approach.The Journal of Chemical Physics, 73(12):6238–6246, 12 1980. ISSN 0021-9606. doi: 10.1063/1.440119. URLhttps: //doi.org/10.1...

    1980 doi

  40. [48]

    Lassettre

    Ausma Skerbele and Edwin N. Lassettre. Electron-impact spectra.The Journal of Chemical Physics, 42(1):395–401, 01 1965. ISSN 0021-9606. doi: 10.1063/1.1695705. URLhttps://doi.org/10.1063/ 1.1695705

    1965 doi

  41. [49]

    Harshbarger

    William R. Harshbarger. Identification of the ˜C state of ammonia by electron impact spectroscopy. The Journal of Chemical Physics, 54(6):2504–2509, 03 1971. ISSN 0021-9606. doi: 10.1063/1. 1675207. URLhttps://doi.org/10.1063/1.1675207. 16

    1971 doi

  42. [689]

    ISBN 978-1-4757-0961-2

    Springer US, Boston, MA, 1979. ISBN 978-1-4757-0961-2. doi: 10.1007/978-1-4757-0961-2 2

    1979 doi

  43. [1992]

    doi: 10.1063/1.462569

    doi

  44. [2024]

    doi: 10.1063/5.0217650

    ISSN 0021-9606. doi: 10.1063/5.0217650. URLhttps://doi.org/10.1063/5.0217650

    doi

  45. [9618]

    URLhttps://doi.org/10.1021/acs.jctc.8b00406

    doi: 10.1021/acs.jctc.8b00406. URLhttps://doi.org/10.1021/acs.jctc.8b00406

    doi

  46. [9687]

    URLhttps://doi.org/10.1143/PTPS.176.134

    doi: 10.1143/PTPS.176.134. URLhttps://doi.org/10.1143/PTPS.176.134

    doi

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.