{"id":"3144d5f4-2e67-45d0-a350-abdb94928f62","arxiv_id":"2607.28845","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"TC-RPA, a random-phase approximation on a Jastrow-transformed non-Hermitian Hamiltonian with three-body terms, accelerates basis-set convergence and improves ground-state energies but does not systematically improve excitation energies.","lead":"This paper derives a random-phase approximation built on a transcorrelated Hamiltonian, which folds short-range electron correlation into the Hamiltonian itself. The method improves ground-state energies and basis-set convergence for small atoms and molecules, but leaves vertical excitation energies largely unchanged.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Ground-state accuracy claim is confounded by system-specific, ground-state-optimized Jastrow factors; the 'nearly an order of magnitude' improvement may be inherited from the Jastrow rather than intrinsic to TC-RPA.","rationale":"After reading the paper in good faith, I believe the strongest claim—that TC-RPA provides a systematic, near-order-of-magnitude improvement in ground-state energies—is most vulnerable not to the quasiboson approximation (which is inherited from standard RPA and affects both conventional and TC variants similarly) but to the circularity introduced by using system- and state-specific Jastrow factors. The quasiboson approximation is a shared assumption; even if it introduces uncontrolled error, it does not distinguish TC-RPA from conventional RPA. In contrast, the Jastrow is unique to TC-RPA, and its parameters are optimized to reproduce ground-state correlation of the exact same systems used for benchmarking. This makes the ground-state accuracy claim non-transferable and potentially a fitting artifact. The paper's own discussion of excited states confirms the Jastrow is ground-state-specific: 'the Jastrow factor ... is optimized exclusively for the ground state' (Sec. III.C). If a generic Jastrow fails to reproduce the improvement, the headline claim collapses. This is a concrete, testable concern that the authors can address. The H2CO counterexample in Fig. 2 already shows that the fitted Jastrow does not consistently help, which further undermines the blanket abstract statement. I therefore recommend the verdict remain CONDITIONAL, with an explicit condition that the authors demonstrate Jastrow independence of the ground-state accuracy claim.","tokens_in":24395,"tokens_out":6220,"duration_ms":66802,"concrete_test":"Re-run the TC-dRPA and TC-RPAx ground-state calculations for H2O, CH4, and H2CO using a fixed, system-independent Jastrow factor (e.g., the one-parameter correlation factor of Dobrautz et al., J. Chem. Phys. 156, 234108 (2022), or a Jastrow optimized once on a different molecule) instead of the system-specific Boys–Handy parameters from Refs. 184 and 185. If the error reduction versus conventional RPA at aV5Z shrinks by more than half for these systems, the accuracy claim is primarily an artifact of Jastrow fitting. Alternatively, use a state-averaged Jastrow optimized for ground and excited states and check whether ground-state accuracy degrades; if it does, the method's predictive power is Jastrow-limited.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central numerical claim—that TC-RPA reduces ground-state energy errors by nearly an order of magnitude—rests on benchmarks in Figs. 1–2 where the Jastrow factor is optimized for the ground state of each system. Section III.A states the Boys–Handy Jastrow parameters were 'optimized at the single-determinant level within a variational Monte Carlo framework' and taken from Refs. 184 (atoms) and 185 (molecules). This is not a neutral test of the TC-RPA approximation: the transcorrelated Hamiltonian already contains correlation information specific to the target ground state, so improved energies relative to conventional RPA may reflect information fed into the Jastrow rather than a better many-body treatment. The paper's own interpretation in Sec. III.C—that the lack of excitation-energy improvement is due to the Jastrow being 'optimized exclusively for the ground state'—implies that the ground-state benchmark is trained data. Without controlling for Jastrow quality, the headline 'systematic and substantial improvement' is not established. The H2CO case (errors increase from 53.9 to 74.7 mH for TC-dRPA at aV5Z) is a direct illustration that the fitted Jastrow does not consistently transfer.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript extends the random-phase approximation (RPA) to the non-Hermitian transcorrelated (TC) Hamiltonian, which contains explicit three-body interactions generated by a Boys–Handy Jastrow factor. The authors derive TC-RPA equations in a biorthogonal equation-of-motion framework, introduce a quasiboson approximation, and present spin-adapted working equations for two variants: TC-dRPA (direct) and TC-RPAx (with exchange). They apply these methods to ground-state correlation energies and vertical excitation energies of He, Ne, H2O, NH3, CH4, and H2CO. The paper claims that, for ground states, TC-RPA substantially accelerates basis-set convergence and reduces errors by nearly an order of magnitude relative to conventional RPA, while for vertical excitation energies the TC treatment gives only marginal improvements, attributed to the ground-state-optimized Jastrow factor.","tokens_in":24662,"tokens_out":2601,"duration_ms":34590,"significance":"The formal contribution is valuable: extending RPA to a non-Hermitian Hamiltonian with three-body terms is a nontrivial step, and the presented block structure, spin adaptation, and correlation-energy formula are plausible and likely useful for future work in transcorrelated many-body methods. The use of the Quantum Package code and the inclusion of raw data in the Supplementary Materials are positive features. However, the headline numerical claim for ground-state energies is not convincingly established by the benchmarks as presented, because the Jastrow factors are optimized against each system's ground state, and because the H2CO results contradict a systematic improvement. The excited-state results, while negative, are honestly reported and usefully delineate the limitations of the approach.","major_comments":[{"comment":"The central ground-state accuracy claim is confounded by the origin of the Jastrow parameters. Section III.A states that the Boys–Handy parameters were 'optimized at the single-determinant level within a variational Monte Carlo framework' and taken from Refs. 184 and 185. These are ground-state-specific, system-specific fits. The transcorrelated Hamiltonian therefore already contains correlation information tailored to the target ground state, so the improved energies relative to conventional RPA may largely reflect information fed into the Jastrow rather than a superior many-body treatment. The H2CO case at aV5Z directly contradicts the 'nearly an order of magnitude' claim: the dRPA error increases from 53.9 mH to 74.7 mH for TC-dRPA, and the RPAx error from 140.1 mH to 146.3 mH. This outlier is acknowledged in a sentence but is not reconciled with the abstract's sweeping claim. A contr","section":"§II.C, Eq. (17)"},{"comment":"The quasiboson approximation is the step that reduces the many-body problem to the finite non-Hermitian RPA matrix of Eq. (19). Replacing particle-hole commutators by delta functions and correlated ground-state expectation values by Hartree–Fock expectation values is already known to be uncontrolled in Hermitian RPA; for a non-Hermitian, biorthogonal TC Hamiltonian, the justification is even weaker. The paper itself notes that this approximation 'can lead to an artificial lowering of the ground-state energy' but does not quantify the effect for the TC Hamiltonian. Since this approximation feeds directly into the correlation energy formula Eq. (32) and into the excitation energies, the numerical results are not yet supported. A concrete test would be to compare TC-RPA against near-exact TC-FCI or TC-selected-CI in a small basis for one of the benchmark systems, which would isolate errors","section":"§II and Supplementary Materials"},{"comment":"The main-text derivation is condensed, with key algebraic steps—the reduction of Eqs. (15)–(16) to the block matrix (19), the eigenvector structure of Eqs. (23)–(24), and the correlation-energy formula (32)—deferred to the Supplementary Materials. As presented, the reader cannot verify these load-bearing equations without reconstructing the derivation. For a methodological paper, this is acceptable only if the supplementary derivation is complete and self-contained; the manuscript should state explicitly that all working equations are derived there and should provide cross-references to the specific supplementary sections. If the supplementary material is not available to the referee or the reader, the equations must be moved into the main text or the paper revised to make the derivation auditable.","section":"§II and Supplementary Materials"}],"minor_comments":[{"comment":"The summation notation in Eq. (1) is typographically unclear ('N X i N X j,i' and 'k<{i,j}'); please use standard restricted sums over distinct indices.","section":"Eq. (1)"},{"comment":"The legend label 'estim exact' should be 'estimated exact' for clarity.","section":"Fig. 1"},{"comment":"For H2CO, the dRPA and TC-dRPA curves are visually close at aV5Z, but the text reports a 53.9 vs 74.7 mH error. Consider adding error annotations or a separate error plot to make the outlier more transparent.","section":"Fig. 2"},{"comment":"The TBE values are CBS estimates, while the RPA values are raw finite-basis results. For a fairer comparison, CBS extrapolated values for the RPA methods (or at least the aV5Z values) should be tabulated alongside the TBEs, especially because basis-set convergence rates differ strongly between methods.","section":"Tables I–III"},{"comment":"The phrase 'nearly an order of magnitude' is an overstatement given the H2CO results; consider replacing it with 'often substantially' or provide a statistical summary that excludes or flags the outlier.","section":"Abstract"}],"recommendation":"major_revision","confidential_remarks":"The paper's formal framework is likely sound and may be a useful contribution to the transcorrelated literature. The main problem is the interpretation of the ground-state benchmarks: because the Jastrow parameters are system- and state-specific, the numerical claims are not a neutral test of TC-RPA. I would encourage the editor to request a revision that either provides a Jastrow-quality-controlled benchmark (e.g., a fixed Jastrow across systems, or a comparison with TC-MP2/TC-CC) or substantially softens the abstract's claims. The H2CO outlier is not merely a local blemish; it undermines the phrase 'systematic and substantial improvement' used in the conclusion."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a genuinely new piece of work—the first RPA derivation for a transcorrelated Hamiltonian with explicit three-body interactions, including a non-Hermitian Fock operator and a four-block response matrix. The spin-adapted working equations in Sec. II.G are practical, and the explicit three-body contraction in Eq. (39) is non-trivial. For most systems, the ground-state benchmarks do show faster basis-set convergence and smaller errors than conventional RPA. If I worked on RPA or transcorrelation, I would want this on my desk.\n\nNow the soft spots. The abstract says \"nearly an order of magnitude\" error reduction. That does not survive the H2CO numbers: at aV5Z, TC-dRPA error is 74.7 mH versus 53.9 mH for dRPA, and TC-RPAx is 146.3 versus 140.1. The authors acknowledge H2CO in the text, but the abstract still overstates. Second, the Jastrow parameters were taken from ground-state single-determinant VMC optimizations (Sec. III.A). So the TC Hamiltonian already carries system-specific ground-state correlation information. That does not make the method wrong, but it means the comparison to conventional RPA is not a clean test of the TC-RPA approximation—it tests Jastrow-plus-RPA. Their own explanation for the lack of excitation-energy gain (\"optimized exclusively for the ground state\") makes that clear. A careful reader should ask what happens with a fixed, non-system-optimized Jastrow. Third, the non-Hermitian eigenvalue structure is hand-waved: the paper assumes real eigenvalues and opposite-sign pairs without proving the needed symplectic relation for the non-symmetric A block. The derivation and quadrature convergence details are deferred to the SI, so the main text is not fully self-contained. The quasiboson approximation (Eq. 17) is the usual uncontrolled step; they note it can lower ground-state energies but do not quantify it in the TC setting.\n\nThe excited-state section is honest: TC barely moves the dRPA excitation energies, and the RPAx improvements are modest. That negative result is worth reporting.\n\nBottom line: a serious method paper with a load-bearing benchmark claim that needs rephrasing. It deserves a real referee, not a desk reject. The authors should be asked to fix the abstract, address H2CO explicitly, discuss the spectral structure, and put the convergence and quadrature results in the main text or a detailed SI. I would send it to review.","headline":"Genuinely new TC-RPA derivation with useful working equations, but the headline accuracy claim overstates the data and the ground-state benchmark is partly confounded by system-optimized Jastrow factors.","tokens_in":25189,"tokens_out":4809,"would_cite":true,"duration_ms":52761,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Applying the random-phase approximation to a Jastrow-transformed Hamiltonian cuts ground-state energy errors by roughly an order of magnitude and accelerates basis-set convergence, while leaving excitation energies nearly unchanged.","keywords":["transcorrelated Hamiltonian","random-phase approximation","Jastrow factor","basis set convergence","correlation energy","vertical excitation energies","non-Hermitian quantum chemistry","three-body interactions"],"falsifier":"Compute TC-dRPA and TC-RPAx correlation energies for a small molecule in a small basis where full configuration interaction is feasible and compare with the exact correlation energy in that basis: if the near-order-of-magnitude improvement over conventional RPA does not survive, the ground-state claim fails. For the excitation claim, re-optimize the Jastrow factor for each excited state and recompute vertical excitation energies: if they still barely move, the ground-state-optimization explanation is wrong.","tokens_in":24264,"feed_emoji":"⚛️","tokens_out":10145,"duration_ms":101948,"temperature":0.7,"pith_summary":"This paper tries to show that the slow basis-set convergence long associated with RPA correlation energies can be attacked at the Hamiltonian level: instead of simply enlarging the orbital basis, one first applies a Jastrow similarity transformation that builds the electron-electron cusp into the Hamiltonian, then runs RPA on that non-Hermitian, three-body object. For helium, neon, water, ammonia, methane, and formaldehyde, the resulting TC-dRPA and TC-RPAx methods reach near-asymptotic ground-state energies with much smaller basis sets, and their complete-basis limits sit closer to exact non-relativistic energies—often by nearly an order of magnitude in error. The practical payoff would be accurate correlation energies for small molecules at a fraction of the basis-set cost. The same treatment barely changes vertical excitation energies, which the paper reads as evidence that the ground-state-optimized Jastrow factor does not capture the correlation character of excited states.","feed_headline":"Transcorrelation cuts RPA energy errors by about 10x","feed_subtitle":"Adding a Jastrow factor at the Hamiltonian level makes small-basis ground-state energies near-exact; excitations barely move.","key_machinery":"The key object is the non-Hermitian transcorrelated Hamiltonian, obtained by a similarity transformation with a Jastrow correlation factor, and the effective interaction U-bar = V-bar + sum_k L-bar that fills the A, B, and C blocks of the RPA matrix. The contraction of the three-body term into an effective two-body kernel, together with TC orbital energies from the biorthogonal Fock equation, is what carries short-range correlation into the linear-response problem; the quasiboson approximation then collapses the many-body problem to the finite symplectic eigenvalue problem whose eigenvalues Omega enter the correlation energy formula E = 1/2 Tr(Omega - A).","core_discovery":"The central claim is that transcorrelation changes RPA by redefining the effective many-body space, not by adding a small correction. TC orbital energies are already dressed by short-range correlation through the non-symmetric Fock operator, and the particle-hole interaction kernel is built from Jastrow-dressed two-body integrals plus a contraction of the explicit three-body term; the RPA matrix therefore has four independent blocks and separate left and right eigenvectors, and the correlation energy is 1/2 Tr(Omega - A). Numerically, TC-dRPA and TC-RPAx converge with triple- to quadruple-zeta bases while conventional RPA still drifts at quintuple- and sextuple-zeta, and the TC limits are ge","pith_inferences":["Beyond the paper: if Hamiltonian-level dressing is the mechanism, the same biorthogonal RPA derivation could be coupled to better response kernels (Bethe-Salpeter or equation-of-motion coupled-cluster style), combining Jastrow short-range correlation with a more accurate treatment of excitations.","Beyond the paper: the small net TC shifts in excitation energies probably hide large canceling changes in absolute ground- and excited-state energies; optimizing the Jastrow factor state by state would test whether that cancellation is the true obstacle.","Beyond the paper: the paper's distinction between angular cusp incompleteness (fixed by TC) and radial diffuseness (needed for Rydberg states) predicts a larger TC benefit for valence excitations; the n to pi* case in formaldehyde is a single hint, and a valence-transition benchmark would settle the question.","Beyond the paper: because the quasiboson approximation can artificially lower ground-state energies and its size for the TC Hamiltonian is left unquantified, comparing TC-RPA against full configuration interaction correlation energies in small basis sets would separate the Jastrow benefit from the bosonization error."],"forward_implications":["TC-dRPA and TC-RPAx offer a practical ground-state route: near-converged energies for small molecules are obtained at triple- or quadruple-zeta quality, avoiding the need for very large basis sets.","Because the TC transformation and the RPA approximation do not commute, conventional and transcorrelated RPA have different complete-basis limits; CBS extrapolations of conventional RPA are therefore not the right reference for TC-RPA energies.","The ground-state improvement is systematic for TC-dRPA on the molecules tested (errors drop from roughly 44-54 mH to 8-17 mH at the largest basis for water, ammonia, and methane), while TC-RPAx is less uniformly improved and formaldehyde is an outlier.","For excited states, TC-RPAx shifts are negligible for water, slightly adverse for ammonia, and helpful for formaldehyde; TC should not be assumed to improve vertical excitation energies.","The paper's proposed path to better excitation energies is state-specific or state-averaged Jastrow optimization combined with an improved response kernel, not larger basis sets alone."],"fun_headline_variants":["TC-RPA cuts ground-state energy errors ~10x","Transcorrelated RPA: near-exact ground states, small bases","RPA with Jastrow factor: 10x smaller ground-state errors","TC-RPA: ground states gain 10x, excitations barely move"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The load-bearing premise is the quasiboson approximation (Eq. 17)—replacing particle-hole pairs with bosons and correlated ground-state averages with Hartree-Fock ones—which the paper's own text notes can artificially lower ground-state energies (Sections I and II.C), but whose magnitude for the transcorrelated Hamiltonian is never quantified.","fun_headline_variants_meta":{"raw":{"variants":["TC-RPA cuts ground-state energy errors ~10x","Transcorrelated RPA: near-exact ground states, small bases","RPA with Jastrow factor: 10x smaller ground-state errors","TC-RPA: ground states gain 10x, excitations barely move"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000674,"raw_usage":{"total_tokens":2906,"prompt_tokens":746,"completion_tokens":2160,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":490,"completion_tokens_details":{"reasoning_tokens":2082}},"tokens_in":490,"tokens_out":2160,"duration_ms":20932,"temperature":1.0,"reasoning_tokens":2082,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T01:30:41.627087+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute TC-dRPA and TC-RPAx correlation energies for a small molecule in a small basis where full configuration interaction is feasible and compare with the exact correlation energy in that basis: if the near-order-of-magnitude improvement over conventional RPA does not survive, the ground-state claim fails. For the excitation claim, re-optimize the Jastrow factor for each excited state and recompute vertical excitation energies: if they still barely move, the ground-state-optimization explanation is wrong.","supporting_citations":[],"review_version":1}