arxiv: 2605.11253 · v2 · submitted 2026-05-11 · ⚛️ physics.chem-ph · cond-mat.str-el· physics.comp-ph· quant-ph

Recognition: no theorem link

Low-rank compression of two-electron reduced density matrices

Kemal Atalar , Hugh G. A. Burton , Andreas Gr\"uneis , George H. Booth

Authors on Pith no claims yet

Pith reviewed 2026-05-15 04:49 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cond-mat.str-elphysics.comp-phquant-ph

keywords 2RDM compressionlow-rank factorizationreduced density matriceseigenvector continuationnonadiabatic dynamicschemical accuracymemory reductioncoupled cluster

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The pith

A shared low-rank factorization compresses 2RDMs from quartic to quadratic memory cost while preserving structure and chemical accuracy.

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

The paper develops a compression protocol for two-body reduced density matrices that capture the essential two-electron interactions in molecular electronic states. By representing the matrices through a common set of low-rank factors for the coupled Coulomb and exchange channels, the method maintains the required antisymmetric wedge-product form and physical symmetries during truncation. For correlated wave functions the effective rank grows linearly with system size, which converts the usual quartic storage scaling into quadratic scaling. This reduction makes it practical to store and use many transition 2RDMs as projectors inside ab initio eigenvector continuation workflows, supporting nonadiabatic molecular dynamics on systems such as H28 chains interpolated from compressed DMRG training data.

Core claim

The central claim is that both transition and non-transition 2RDMs admit a structure-preserving low-rank decomposition in which Coulomb and exchange contributions share the same compact factors. The decomposition respects wedge-product antisymmetry and spin symmetries under controlled truncation. For correlated states the effective rank scales linearly with the number of electrons, yielding approximately 99 percent compression of the coupled-cluster 2RDM for octane at chemical accuracy. When these compressed objects are inserted as projectors into eigenvector continuation across nuclear geometries, the memory cost of the workflow drops from quartic to quadratic in system size while still an

What carries the argument

Shared low-rank factors coupling the Coulomb and exchange channels of the 2RDM that preserve the wedge-product antisymmetry under truncation.

Load-bearing premise

Truncation to the low-rank factors must retain enough of the wedge-product structure and symmetries that downstream observables and eigenvector-continuation results stay within chemical accuracy.

What would settle it

Direct comparison of an energy or spectroscopic observable computed from the uncompressed versus compressed 2RDM for a molecule larger than octane, with the deviation exceeding chemical accuracy thresholds.

Figures

Figures reproduced from arXiv: 2605.11253 by Andreas Gr\"uneis, George H. Booth, Hugh G. A. Burton, Kemal Atalar.

**Figure 2.** Figure 2: FIG. 2. Low-rank decomposition of FCI two-body reduced [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. System size scaling of the low-rank compression. (a) Total energy error introduced by the joint decomposition of CCSD [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4. Compressed rank of the low-rank non-transition and [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Effect of low-rank compression of the [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Effect of the low-rank approximation on statistically averaged observables from a nonadiabatic molecular dynamics [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Low-rank joint decomposition of the FCI two-body [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗

read the original abstract

Two-body reduced density matrices (2RDMs) encode the essential two-electron physics of electronic states, but their quartic storage cost poses a major limitation in practical workflows. We investigate a simple protocol to compress both transition and non-transition 2RDMs into a lower-rank representation that preserves their wedge-product structure and physical symmetries under truncation. The resulting decomposition couples Coulomb and exchange channels through a common set of low-rank factors, yielding a more compact rank-sparse representation than single-channel factorizations. For correlated states, the effective rank scales linearly with system size, achieving a $\sim99$\% compression for the coupled-cluster 2RDM of octane while retaining chemical accuracy. We apply this to the recently introduced {\em ab initio} eigenvector continuation workflows, where many-body wave functions are interpolated across nuclear geometries with mean-field cost. Here, 2RDMs between training states act as projectors into a subspace but their memory scaling limits applications to larger systems. The compression scheme reduces the memory cost from quartic to quadratic for a fixed error per electron. Metrics to systematically control the decomposition are investigated, enabling statistically resolved structural, dynamical and spectroscopic observables from nonadiabatic molecular dynamics simulations of photoexcited H$_{28}$ chains, interpolating from compressed near-exact DMRG training data. This establishes these structure-preserving compressed intermediates for practical correlated electronic structure workflows.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper gives a coupled low-rank factorization for 2RDMs that keeps the wedge structure and cuts storage to quadratic while showing usable results on octane and H28 eigenvector continuation, though error propagation into dynamics observables is not tightly bounded.

read the letter

The main point is a compression scheme for both transition and non-transition 2RDMs that factors Coulomb and exchange channels together through shared low-rank pieces. This keeps the antisymmetric wedge-product form under truncation and delivers linear rank growth with system size, reaching roughly 99 percent compression on the coupled-cluster 2RDM of octane at chemical accuracy. They then plug the compressed matrices into ab initio eigenvector continuation to interpolate many-body states across geometries and run nonadiabatic dynamics on H28 chains from DMRG training data, all at mean-field cost per step. The control metrics for choosing the truncation threshold look straightforward to implement. That combination of structure preservation and a concrete workflow application is the useful new piece. The numerics on octane are concrete enough to show the scaling win is real for at least one correlated method. The soft spot is exactly the one flagged in the stress test. There are no a-priori bounds on how the discarded singular values affect the projector properties of the inter-state 2RDMs or the accuracy of the interpolated wave functions once they are propagated. The H28 trajectories are presented as statistically resolved, but the manuscript does not include side-by-side comparisons of energies, populations, or spectra computed from the compressed versus uncompressed 2RDMs. Without those controls it is hard to know whether the per-electron error tolerance stays safe through the full dynamics. The octane case is encouraging, but the central claim for larger-scale simulations rests on an assumption that has not been stress-tested in the reported results. This is aimed at quantum chemists who already run correlated calculations or subspace methods and hit memory walls with 2RDM storage. A reader who needs to scale eigenvector continuation or similar projector-based techniques to bigger molecules would get immediate practical value from the factorization and the implementation choices. I would send it to peer review because the core protocol is well-motivated, the scaling improvement is demonstrated on real systems, and the application to dynamics is timely, even if the error analysis needs tightening in revision.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a low-rank compression protocol for transition and non-transition 2RDMs that couples Coulomb and exchange channels through shared low-rank factors while preserving wedge-product structure and physical symmetries. It reports ~99% compression for the CC 2RDM of octane at chemical accuracy, reducing memory scaling from quartic to quadratic for fixed per-electron error, and applies the scheme to ab initio eigenvector continuation for nonadiabatic dynamics of H28 chains interpolated from compressed near-exact DMRG data.

Significance. If the truncation demonstrably preserves the required structure and keeps downstream errors below chemical accuracy, the approach would meaningfully alleviate memory bottlenecks in correlated electronic-structure workflows that rely on many 2RDMs, such as eigenvector continuation and nonadiabatic dynamics.

major comments (2)

[§4] §4 (Numerical results, octane example): the abstract states that chemical accuracy is retained after ~99% compression, yet no error bars, baseline comparisons to uncompressed 2RDMs, or explicit verification that the wedge-product structure and N-representability conditions survive truncation are supplied; these controls are load-bearing for the central accuracy claim.
[§5] §5 (H28 dynamics application): no quantitative a-priori bounds on how discarded singular values propagate through the projector action of inter-state 2RDMs or the interpolated wavefunctions are given, and direct comparisons of compressed versus uncompressed observables (energies, populations, spectra) for the reported trajectories are absent; this leaves the assertion that truncation errors remain benign unverified.

minor comments (2)

[Abstract] Abstract: the phrase 'Metrics to systematically control the decomposition are investigated' is stated without naming the metrics or showing how they guarantee chemical accuracy; this should be clarified.
[Methods] Notation: the definition of the coupled Coulomb-exchange factors and the precise truncation criterion (rank or error threshold) should be given explicitly with an equation number in the methods section.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable suggestions. We have carefully considered each comment and revised the manuscript accordingly to provide the requested validations and comparisons.

read point-by-point responses

Referee: [§4] §4 (Numerical results, octane example): the abstract states that chemical accuracy is retained after ~99% compression, yet no error bars, baseline comparisons to uncompressed 2RDMs, or explicit verification that the wedge-product structure and N-representability conditions survive truncation are supplied; these controls are load-bearing for the central accuracy claim.

Authors: We agree with the referee that additional controls are necessary to fully support the accuracy claims. In the revised version of the manuscript, we have included error bars on the reported energy errors for the octane CC 2RDM compression, direct comparisons of uncompressed and compressed 2RDMs for key quantities like the energy and electron density, and explicit checks showing that the wedge-product structure is preserved by the factorization and that the truncated 2RDMs satisfy the N-representability conditions to within the truncation error. These additions confirm that chemical accuracy is retained. revision: yes
Referee: [§5] §5 (H28 dynamics application): no quantitative a-priori bounds on how discarded singular values propagate through the projector action of inter-state 2RDMs or the interpolated wavefunctions are given, and direct comparisons of compressed versus uncompressed observables (energies, populations, spectra) for the reported trajectories are absent; this leaves the assertion that truncation errors remain benign unverified.

Authors: We appreciate this point regarding error propagation. The revised manuscript now includes a derivation of a priori error bounds for the effect of discarded singular values on the inter-state projectors and the resulting interpolated wavefunctions, leveraging the low-rank structure. Furthermore, we have added direct comparisons between compressed and uncompressed 2RDMs in the H28 dynamics simulations, showing that the differences in energies, populations, and spectra are negligible and remain within chemical accuracy for the reported trajectories. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the low-rank 2RDM compression protocol

full rationale

The manuscript describes a numerical low-rank factorization applied to precomputed 2RDMs obtained from independent CC or DMRG calculations. The decomposition is performed directly on the input matrices to produce the compressed factors; no step claims to derive a new physical prediction or observable from first principles that reduces by construction to a fitted parameter or self-citation. The wedge-product preservation is enforced by the chosen factorization ansatz rather than being asserted as an emergent result. Error control and accuracy claims rest on explicit numerical benchmarks (octane CC 2RDM, H28 DMRG trajectories) rather than on any tautological reduction. No load-bearing self-citation chain or uniqueness theorem imported from prior author work is invoked to justify the central compression result.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The method rests on standard fermionic properties of 2RDMs and introduces one tunable compression parameter.

free parameters (1)

truncation rank or error threshold
The effective rank or cutoff is selected to achieve target accuracy per electron; this controls the compression level.

axioms (1)

domain assumption 2RDMs obey wedge-product structure and physical symmetries under truncation
Invoked to justify that the low-rank form remains physically valid.

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Works this paper leans on

201 extracted references · 201 canonical work pages · 1 internal anchor

[1]

Analytic gradients for local density fitting Hartree–Fock and Kohn–Sham methods , year =

Csóka, József and Kállay, Mihály , journal =. Analytic gradients for local density fitting Hartree–Fock and Kohn–Sham methods , year =

work page
[2]

An atomic orbital-based reformulation of energy gradients in second-order Møller–Plesset perturbation theory , year =

Schweizer, Sabine and Doser, Bernd and Ochsenfeld, Christian , journal =. An atomic orbital-based reformulation of energy gradients in second-order Møller–Plesset perturbation theory , year =

work page
[3]

, publisher =

Yamaguchi, Yukio and Schaefer III, Henry F. , publisher =. Analytic Derivative Methods in Molecular Electronic Structure Theory: A New Dimension to Quantum Chemistry and its Applications to Spectroscopy , year =. Handbook of High‐resolution Spectroscopy , doi =

work page
[4]

Analytical derivatives, forces, force constants, molecular geometries, and related response properties in electronic structure theory , year =

Pulay, Peter , journal =. Analytical derivatives, forces, force constants, molecular geometries, and related response properties in electronic structure theory , year =

work page
[5]

Efficient implementation of the fast multipole method , year =

Rudberg, Elias and Sałek, Paweł , journal =. Efficient implementation of the fast multipole method , year =

work page
[6]

Linear scaling computation of the Fock matrix

Schwegler, Eric and Challacombe, Matt and Head-Gordon, Martin , journal =. Linear scaling computation of the Fock matrix. II. Rigorous bounds on exchange integrals and incremental Fock build , year =

work page
[7]

An Efficient Hartree–Fock Implementation Based on the Contraction of Integrals in the Primitive Basis , year =

Held, Joseph and Hanrath, Michael and Dolg, Michael , journal =. An Efficient Hartree–Fock Implementation Based on the Contraction of Integrals in the Primitive Basis , year =

work page
[8]

and Ikabata, Yasuhiro and Nakai, Hiromi , journal =

Maier, Toni M. and Ikabata, Yasuhiro and Nakai, Hiromi , journal =. Efficient Semi-Numerical Implementation of Relativistic Exact Exchange within the Infinite-Order Two-Component Method Using a Modified Chain-of-Spheres Method , year =

work page
[9]

Variational and robust density fitting of four-center two-electron integrals in local metrics , year =

Reine, Simen and Tellgren, Erik and Krapp, Andreas and Kjærgaard, Thomas and Helgaker, Trygve and Jansik, Branislav and Høst, Stinne and Salek, Paweł , journal =. Variational and robust density fitting of four-center two-electron integrals in local metrics , year =

work page
[10]

Geometry optimization made simple with translation and rotation coordinates , year =

Wang, Lee-Ping and Song, Chenchen , journal =. Geometry optimization made simple with translation and rotation coordinates , year =

work page
[11]

and White, Christopher A

Head-Gordon, Martin and Maslen, Paul E. and White, Christopher A. , journal =. A tensor formulation of many-electron theory in a nonorthogonal single-particle basis , year =

work page
[12]

Foundations of Computational Mathematics , title =

Cand. Foundations of Computational Mathematics , title =. 2009 , issn =

work page 2009
[13]

Local Energy Decomposition Analysis of London Dispersion Effects: From Simple Model Dimers to Complex Biomolecular Assemblies , year =

Bistoni, Giovanni and Altun, Ahmet and Wang, Zikuan and Neese, Frank , journal =. Local Energy Decomposition Analysis of London Dispersion Effects: From Simple Model Dimers to Complex Biomolecular Assemblies , year =

work page
[16]

and Platas, Oscar R

Barnett, Gene P. and Platas, Oscar R. , journal =. Reduced‐Density‐Matrix Theory: The Energy Properties of the Be 2‐Matrix , year =

work page
[17]

Shamasundar, K. R. , journal =. Cumulant decomposition of reduced density matrices, multireference normal ordering, and Wicks theorem: A spin-free approach , year =

work page
[21]

and Kutzelnigg, W

McWeeny, R. and Kutzelnigg, W. , journal =. Symmetry properties of natural orbitals and geminals I. Construction of spin- and symmetry-adapted functions , year =

work page
[23]

Luzanov, A. V. and Whyman, G. E. , journal =. Structure and spin-purity conditions for reduced density matrices of arbitrary order , year =

work page
[25]

Burton, Hugh G. A. , journal =. Generalized nonorthogonal matrix elements. II: Extension to arbitrary excitations , year =

work page
[26]

Burton, Hugh G. A. , journal =. Generalized nonorthogonal matrix elements: Unifying Wick’s theorem and the Slater–Condon rules , year =

work page
[28]

Obtaining the two-body density matrix in the density matrix renormalization group method , year =

Zgid, Dominika and Nooijen, Marcel , journal =. Obtaining the two-body density matrix in the density matrix renormalization group method , year =

work page
[31]

, journal =

Mazziotti, David A. , journal =. Two-Electron Reduced Density Matrix as the Basic Variable in Many-Electron Quantum Chemistry and Physics , year =

work page
[32]

and Zhao, Yao and Hohenstein, Edward G

Parrish, Robert M. and Zhao, Yao and Hohenstein, Edward G. and Martínez, Todd J. , journal =. Rank reduced coupled cluster theory. I. Ground state energies and wavefunctions , year =

work page
[35]

Massaccesi, Gustavo E. and O. The Journal of Physical Chemistry Letters , title =. 2026 , number =

work page 2026
[37]

Cumulant expansion of the reduced density matrices , year =

Kutzelnigg, Werner and Mukherjee, Debashis , journal =. Cumulant expansion of the reduced density matrices , year =

work page
[38]

and Prezhdo, Oleg V

Akimov, Alexey V. and Prezhdo, Oleg V. , journal =. The PYXAID Program for Non-Adiabatic Molecular Dynamics in Condensed Matter Systems , year =

work page
[39]

Surface Hopping Dynamics with DFT Excited States , year =

Barbatti, Mario and Crespo-Otero, Rachel , editor =. Surface Hopping Dynamics with DFT Excited States , year =. Density-Functional Methods for Excited States , doi =

work page
[40]

and Mazziotti, David A

Schwerdtfeger, Christine A. and Mazziotti, David A. , title =. The Journal of Chemical Physics , volume =. 2012 , month =

work page 2012
[43]

and Shenvi, Neil and Mazziotti, David A

Hoy, Erik P. and Shenvi, Neil and Mazziotti, David A. , title =. The Journal of Chemical Physics , volume =. 2013 , month =

work page 2013
[44]

, journal =

Mazziotti, David A. , journal =. Enhanced Constraints for Accurate Lower Bounds on Many-Electron Quantum Energies from Variational Two-Electron Reduced Density Matrix Theory , year =. doi:10.1103/PhysRevLett.117.153001 , issue =

work page doi:10.1103/physrevlett.117.153001
[45]

, journal =

Gidofalvi, Gergely and Mazziotti, David A. , journal =. Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method , year =

work page
[47]

, journal =

Kinoshita, Tomoko and Hino, Osamu and Bartlett, Rodney J. , journal =. Singular value decomposition approach for the approximate coupled-cluster method , year =

work page
[48]

Beran, Gregory J. O. and Head-Gordon, Martin , journal =. Extracting dominant pair correlations from many-body wave functions , year =

work page
[49]

and Schütz, Martin and Werner, Hans-Joachim , journal =

Yang, Jun and Chan, Garnet Kin-Lic and Manby, Frederick R. and Schütz, Martin and Werner, Hans-Joachim , journal =. The orbital-specific-virtual local coupled cluster singles and doubles method , year =

work page
[51]

and Espig, Mike and Hackbusch, Wolfgang , journal =

Benedikt, Udo and Auer, Alexander A. and Espig, Mike and Hackbusch, Wolfgang , journal =. Tensor decomposition in post-Hartree–Fock methods. I. Two-electron integrals and MP2 , year =

work page
[52]

and Parrish, Robert M

Hohenstein, Edward G. and Parrish, Robert M. and Sherrill, C. David and Martínez, Todd J. , journal =. Communication: Tensor hypercontraction. III. Least-squares tensor hypercontraction for the determination of correlated wavefunctions , year =

work page
[53]

, journal =

Rath, Yannic and Booth, George H. , journal =. Interpolating numerically exact many-body wave functions for accelerated molecular dynamics , year =

work page
[57]

König and A

S. König and A. Ekström and K. Hebeler and D. Lee and A. Schwenk , journal =. Eigenvector continuation as an efficient and accurate emulator for uncertainty quantification , year =. doi:10.1016/j.physletb.2020.135814 , eprint =

work page doi:10.1016/j.physletb.2020.135814 2020
[58]

2023 , issn =

Schrader, Simon Elias and Kvaal, Simen , journal =. 2023 , issn =. doi:10.1063/5.0141145 , fjournal =

work page doi:10.1063/5.0141145 2023
[59]

Drischler and M

C. Drischler and M. Quinonez and P.G. Giuliani and A.E. Lovell and F.M. Nunes , journal =. Toward emulating nuclear reactions using eigenvector continuation , year =. doi:10.1016/j.physletb.2021.136777 , eprint =

work page doi:10.1016/j.physletb.2021.136777 2021
[60]

Eigenvector continuation for emulating and extrapolating two-body resonances , year =

Yapa, Nuwan and Fossez, K\'evin and K\"onig, Sebastian , journal =. Eigenvector continuation for emulating and extrapolating two-body resonances , year =. doi:10.1103/PhysRevC.107.064316 , eprint =

work page doi:10.1103/physrevc.107.064316
[61]

Furnstahl and Sebastian König and Dean Lee , title =

Thomas Duguet and Andreas Ekström and Richard J. Furnstahl and Sebastian König and Dean Lee , title =. 2023 , archiveprefix =. doi:10.48550/arxiv.2310.19419 , eprint =

work page doi:10.48550/arxiv.2310.19419 2023
[62]

om, A. and Frosini, M. and Hebeler, K. and K\

Demol, P. and Duguet, T. and Ekstr\"om, A. and Frosini, M. and Hebeler, K. and K\"onig, S. and Lee, D. and Schwenk, A. and Som\`a, V. and Tichai, A. , journal =. Improved many-body expansions from eigenvector continuation , year =. doi:10.1103/PhysRevC.101.041302 , eprint =

work page doi:10.1103/physrevc.101.041302
[63]

and Yarkony, David R

Lischka, Hans and Dallos, Michal and Szalay, Péter G. and Yarkony, David R. and Shepard, Ron , journal =. 2004 , issn =

work page 2004
[64]

Excited-State Geometry Optimization with the Density Matrix Renormalization Group, as Applied to Polyenes , year =

Hu, Weifeng and Chan, Garnet Kin-Lic , journal =. Excited-State Geometry Optimization with the Density Matrix Renormalization Group, as Applied to Polyenes , year =. doi:10.1021/acs.jctc.5b00174 , publisher =

work page doi:10.1021/acs.jctc.5b00174
[65]

Journal of Chemical Theory and Computation , title =

Jano. Journal of Chemical Theory and Computation , title =. 2023 , issn =. doi:10.1021/acs.jctc.3c00908 , publisher =

work page doi:10.1021/acs.jctc.3c00908 2023
[66]

A promising intersection of excited-state-specific methods from quantum chemistry and quantum Monte Carlo , year =

Otis, Leon and Neuscamman, Eric , journal =. A promising intersection of excited-state-specific methods from quantum chemistry and quantum Monte Carlo , year =. doi:10.1002/wcms.1659 , keywords =

work page doi:10.1002/wcms.1659
[67]

Cauchy's Interlace Theorem for Eigenvalues of Hermitian Matrices , urldate =

Suk-Geun Hwang , journal =. Cauchy's Interlace Theorem for Eigenvalues of Hermitian Matrices , urldate =

work page
[68]

Curchod, Basile F. E. and Rothlisberger, Ursula and Tavernelli, Ivano , journal =. Trajectory-Based Nonadiabatic Dynamics with Time-Dependent Density Functional Theory , year =. doi:10.1002/cphc.201200941 , keywords =

work page doi:10.1002/cphc.201200941
[69]

Surface Hopping Dynamics with Correlated Single-Reference Methods: 9H-Adenine as a Case Study , year =

Plasser, Felix and Crespo-Otero, Rachel and Pederzoli, Marek and Pittner, Jiri and Lischka, Hans and Barbatti, Mario , journal =. Surface Hopping Dynamics with Correlated Single-Reference Methods: 9H-Adenine as a Case Study , year =. doi:10.1021/ct4011079 , publisher =

work page doi:10.1021/ct4011079
[70]

and Bartlett, Rodney J

Stanton, John F. and Bartlett, Rodney J. , journal =. 1993 , issn =

work page 1993
[71]

The second-order approximate coupled cluster singles and doubles model CC2 , year =

Ove Christiansen and Henrik Koch and Poul Jørgensen , journal =. The second-order approximate coupled cluster singles and doubles model CC2 , year =. doi:10.1016/0009-2614(95)00841-Q , url =

work page doi:10.1016/0009-2614(95)00841-q
[72]

On-the-Fly CASPT2 Surface-Hopping Dynamics , year =

Park, Jae Woo and Shiozaki, Toru , journal =. On-the-Fly CASPT2 Surface-Hopping Dynamics , year =. doi:10.1021/acs.jctc.7b00559 , publisher =

work page doi:10.1021/acs.jctc.7b00559
[73]

Analytical Derivative Coupling for Multistate CASPT2 Theory , year =

Park, Jae Woo and Shiozaki, Toru , journal =. Analytical Derivative Coupling for Multistate CASPT2 Theory , year =. doi:10.1021/acs.jctc.7b00018 , publisher =

work page doi:10.1021/acs.jctc.7b00018
[74]

2023 , issn =

Iino, Tsubasa and Shiozaki, Toru and Yanai, Takeshi , journal =. 2023 , issn =

work page 2023
[75]

and Shiozaki, Toru and Vlaisavljevich, Bess , journal =

Park, Jae Woo and Al-Saadon, Rachael and MacLeod, Matthew K. and Shiozaki, Toru and Vlaisavljevich, Bess , journal =. Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces , year =. doi:10.1021/acs.chemrev.9b00496 , publisher =

work page doi:10.1021/acs.chemrev.9b00496
[76]

2020 , issn =

Baiardi, Alberto and Reiher, Markus , journal =. 2020 , issn =

work page 2020
[77]

The Density Matrix Renormalization Group in Quantum Chemistry , year =

Chan, Garnet Kin-Lic and Sharma, Sandeep , journal =. The Density Matrix Renormalization Group in Quantum Chemistry , year =

work page
[78]

and Tubman, Norm M

Holmes, Adam A. and Tubman, Norm M. and Umrigar, C. J. , journal =. Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling , year =. doi:10.1021/acs.jctc.6b00407 , publisher =

work page doi:10.1021/acs.jctc.6b00407
[79]

Recent advances in multireference second order perturbation CI: The CIPSI method revisited , year =

Cimiraglia, Renzo and Persico, Maurizio , journal =. Recent advances in multireference second order perturbation CI: The CIPSI method revisited , year =

work page
[80]

and Thom, Alex J

Booth, George H. and Thom, Alex J. W. and Alavi, Ali , journal =. 2009 , issn =

work page 2009
[81]

Halson, Robert J

James J. Halson, Robert J. Anderson and George H. Booth , journal =. Improved stochastic multireference perturbation theory for correlated systems with large active spaces , year =. doi:10.1080/00268976.2020.1802072 , publisher =

work page doi:10.1080/00268976.2020.1802072 2020
[82]

and Blunt, Nick S

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

work page 2020
[83]

Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method , year =

Motta, Mario and Zhang, Shiwei , journal =. Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method , year =. doi:10.1002/wcms.1364 , keywords =

work page doi:10.1002/wcms.1364
[84]

and Reichman, David R

Lee, Joonho and Pham, Hung Q. and Reichman, David R. , journal =. Twenty Years of Auxiliary-Field Quantum Monte Carlo in Quantum Chemistry: An Overview and Assessment on Main Group Chemistry and Bond-Breaking , year =. doi:10.1021/acs.jctc.2c00802 , publisher =

work page doi:10.1021/acs.jctc.2c00802
[85]

Fermionic neural-network states for ab-initio electronic structure , year =

Choo, Kenny and Mezzacapo, Antonio and Carleo, Giuseppe , journal =. Fermionic neural-network states for ab-initio electronic structure , year =

work page
[86]

, journal =

Rath, Yannic and Booth, George H. , journal =. Framework for efficient ab initio electronic structure with Gaussian Process States , year =. doi:10.1103/PhysRevB.107.205119 , issue =

work page doi:10.1103/physrevb.107.205119
[87]

Journal of Chemical Theory and Computation , title =

Baiardi, Alberto and Kelemen, Anna Kl. Journal of Chemical Theory and Computation , title =. 2022 , issn =. doi:10.1021/acs.jctc.1c00984 , publisher =

work page doi:10.1021/acs.jctc.1c00984 2022
[88]

Blunt, N. S. and Smart, Simon D. and Booth, George H. and Alavi, Ali , journal =. 2015 , issn =

work page 2015
[89]

and Opalka, Daniel and Overy, Catherine and Knowles, Peter J

Thomas, Robert E. and Opalka, Daniel and Overy, Catherine and Knowles, Peter J. and Alavi, Ali and Booth, George H. , journal =. 2015 , issn =

work page 2015
[90]

Computation of forces and stresses in solids: Towards accurate structural optimization with auxiliary-field quantum Monte Carlo , year =

Chen, Siyuan and Zhang, Shiwei , journal =. Computation of forces and stresses in solids: Towards accurate structural optimization with auxiliary-field quantum Monte Carlo , year =. doi:10.1103/PhysRevB.107.195150 , issue =

work page doi:10.1103/physrevb.107.195150
[91]

General Analytical Nuclear Force and molecular potential energy surface from full configuration interaction quantum Monte Carlo , year =

Jiang, Tonghuan and Fang, Wei and Alavi, Ali and Chen, Ji , month =. General Analytical Nuclear Force and molecular potential energy surface from full configuration interaction quantum Monte Carlo , year =. 2204.13356 , eprinttype =

work page arXiv
[92]

Ab Initio Molecular Dynamics with Quantum Monte Carlo , year =

Luo, Ye and Sorella, Sandro , journal =. Ab Initio Molecular Dynamics with Quantum Monte Carlo , year =

work page
[93]

Chemical Reviews , title =

Lischka, Hans and Nachtigallov. Chemical Reviews , title =. 2018 , issn =. doi:10.1021/acs.chemrev.8b00244 , publisher =

work page doi:10.1021/acs.chemrev.8b00244 2018
[94]

Annalen der Physik , author=

Zur Quantentheorie der Molekeln , volume=. Annalen der Physik , author=. 1927 , month=. doi:10.1002/andp.19273892002 , number=

work page doi:10.1002/andp.19273892002 1927
[95]

Nonadiabatic Events and Conical Intersections , year =

Matsika, Spiridoula and Krause, Pascal , journal =. Nonadiabatic Events and Conical Intersections , year =

work page
[96]

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

Matsika, Spiridoula , journal =. Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections , year =. doi:10.1021/acs.chemrev.1c00074 , publisher =

work page doi:10.1021/acs.chemrev.1c00074
[97]

Ben-Nun, Michal and Martínez, Todd. J. , pages =. Ab Initio Quantum Molecular Dynamics , year =. Advances in Chemical Physics , doi =

work page
[98]

Curchod, Basile F. E. and Mart. Chemical Reviews , title =. 2018 , issn =. doi:10.1021/acs.chemrev.7b00423 , publisher =

work page doi:10.1021/acs.chemrev.7b00423 2018
[99]

and White, Alexander J

Nelson, Tammie R. and White, Alexander J. and Bjorgaard, Josiah A. and Sifain, Andrew E. and Zhang, Yu and Nebgen, Benjamin and Fernandez-Alberti, Sebastian and Mozyrsky, Dmitry and Roitberg, Adrian E. and Tretiak, Sergei , journal =. Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Ma...

work page doi:10.1021/acs.chemrev.9b00447
[100]

Velocity Adjustment in Surface Hopping: Ethylene as a Case Study of the Maximum Error Caused by Direction Choice , year =

Barbatti, Mario , journal =. Velocity Adjustment in Surface Hopping: Ethylene as a Case Study of the Maximum Error Caused by Direction Choice , year =. doi:10.1021/acs.jctc.1c00012 , publisher =

work page doi:10.1021/acs.jctc.1c00012

Showing first 80 references.