{"id":"d4edb53b-2b16-4a84-98ac-f5b463f7fb56","arxiv_id":"2507.19876","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Multi-reference generalizations of RPAx and ppRPA are derived via diagrammatic resummation and benchmarked on small molecules.","lead":"Researchers extend a diagrammatic multi-reference framework to two new random phase approximation channels, particle-hole with exchange and particle-particle. These new methods target strongly correlated molecules where single-reference methods fail.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"MR-ppRPA's eigenvalue formula (50) rests on an unproven positive-definiteness condition for E_alpha = Delta + alpha V; the heuristic mu (Eq. 51) is not shown to guarantee it, so the method may be unjustified for some systems.","rationale":"The reader's weakest_assumption identifies exactly this unproven positive-definiteness condition for MR-ppRPA, and I agree that it is the most load-bearing concern. The central claim that Eqs. (45) and (50) define a valid, unified MR-ppRPA correlation energy depends on the contour integration and eigenvalue pairing, both of which require E_alpha positive definite. The paper is transparent about the restriction but does not establish that its chosen mu (Eq. 51) always meets it; the numerical section reports no verification. This is a correctness risk, not merely a 'consensus differs' issue, because a failure of the condition would invalidate the computed energies. The MR-RPAx imaginary-root instability is also a real limitation, but it is acknowledged and partially mitigated by the '-e' variant, and it does not threaten the internal validity of the derivation for the stable regime. The positive-definiteness gap, by contrast, is an unproven mathematical precondition on the main ppRPA result. Since the reader already assigned CONDITIONAL based on this concern, my stress-test does not change the verdict. The proposed numerical check (smallest eigenvalue of E_1 and the equality of the two traces in Eq. (50)) would either confirm the assumption for the test set or reveal a concrete failure mode, and a broader scan would assess the generality of the heuristic mu.","tokens_in":31052,"tokens_out":23131,"duration_ms":212578,"concrete_test":"For every molecule and geometry in Tables S5-S8, compute with mu from Eq. (51) the smallest eigenvalue of E_1 = Delta + V (Eq. S27 at alpha = 1) and verify it is positive; also confirm numerically that tr(Omega_+) - tr(A_+) equals -tr(Omega_-) - tr(A_-) from Eq. (50), which would fail if the spectral representation is invalid. Then scan a broader set of systems (small HOMO-LUMO gap, open-shell, transition-metal, or larger active spaces) to see whether E_1 can become indefinite; if a counterexample appears, the paper must either prove a bound on V or replace Eq. (51) with a mu-selection strategy that guarantees positive definiteness.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The MR-ppRPA derivation in the Supplemental Material (Eqs. S27-S34) requires that E_alpha = Delta + alpha V be positive definite for all alpha in [0,1], so that the generalized eigenvalue problem (Eq. S28) has N_pp positive and N_hh negative eigenvalues and the contour integration leading to Eq. (50) is valid. The paper explicitly states two restrictions on the chemical potential mu (positive diagonals of Delta and positive definiteness of E_1) but provides no proof that the heuristic choice in Eq. (51), mu = (min{omega^{N+1}_A} - min{omega^{N-1}_I})/2, satisfies them for arbitrary systems. In the single-reference limit, the condition follows because two-particle addition energies are sums of orbital energies and 2mu is the HOMO-LUMO midpoint, guaranteeing Delta > 0; however, for the MR case, omega^{N+2}_P - 2mu and omega^{N-2}_H + 2mu involve interacting active-space energies with no such algebraic relation. If E_1 is not positive definite, the spectral representation (S31) and the sign-pairing used in the contour integrals (S33)-(S34) break down, so Eq. (50) is not equivalent to the defining integral (45). The numerical benchmarks do not report any check of this condition or a comparison of the two equivalent expressions in Eq. (50), leaving open the possibility that the method silently fails outside the tested molecules.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper develops a diagrammatic multi-reference generalization of two RPA variants, RPAx and ppRPA, building on the authors' earlier cumulant-based generalized Feynman diagram framework. For each method the authors derive three formally equivalent expressions for the correlation energy: an imaginary-frequency integral, a plasmon-type eigenvalue formula, and a coupled-cluster-like Riccati equation, and they show that these reduce to the standard single-reference formulas. The methods are implemented with a CASSCF/Dyall zeroth-order Hamiltonian and benchmarked on the Li4 size-extensivity model and on potential energy curves for HF, ScH, H2O, and N2 against DMRG and SC-NEVPT2 data. A perturbative analysis up to fifth order attributes the numerical behavior of the three MR-RPA variants to error cancellation between second and higher orders. The paper reports that MR-dRPA offers the most balanced treatment, MR-ppRPA performs best at the dissociated limit but underestimates correlation near equilibrium, and MR-RPAx suffers from imaginary roots at stretched geometries, which is partially rescued by the active-space-screening-neglected variant MR-RPAx-e.","tokens_in":31300,"tokens_out":4550,"duration_ms":42872,"significance":"If the derivations are valid, the paper extends the diagrammatic MR many-body framework to two additional RPA channels and provides a unified set of equations that hold at both single- and multi-reference levels, which is a genuine methodological step beyond the previous MR-dRPA work. The treatment of the second-order diagrams in RPAx with the correction term is a careful and nontrivial detail that the authors handle correctly. The perturbative analysis, the size-extensivity test, and the benchmark data against DMRG and SC-NEVPT2 are useful contributions, and the paper is clearly written. However, the MR-ppRPA eigenvalue formula rests on an unproven positive-definiteness condition for the matrix E_α, and the instability of MR-RPAx at strong correlation limits the scope of the central claim that the methods provide accurate energies for strongly correlated systems. These issues are fixable but currently leave the MR-ppRPA derivation incomplete and the MR-RPAx claim overstated.","major_comments":[{"comment":"The derivation of the MR-ppRPA eigenvalue formula Eq. (50) requires that E_α = Δ + αV be positive definite for α in [0,1], so that the eigenpairs in Eq. (S28) split into N_pp positive and N_hh negative branches and the normalization (S30) and spectral representation (S31) hold. The paper states two restrictions on the chemical potential μ (positive diagonals of Δ and positive definiteness of E_1) but provides no proof that the heuristic choice in Eq. (51) satisfies them in the multi-reference case. The single-reference guarantee, where 2μ is the HOMO-LUMO midpoint, does not carry over because ω^{N+2}_P - 2μ and ω^{N-2}_H + 2μ involve interacting active-space energies. If E_1 is not positive definite, the sign pairing and the contour integration used to obtain Eq. (50) break down, and Eq. (50) is not equivalent to the defining integral in Eq. (45). The numerical sections do not report any check of positive definiteness or a direct comparison of tr(Ω+) - tr(A+) with -tr(Ω-) - tr(A-), leaving this load-bearing gap unaddressed.","section":"Sec. II.C and Supplemental Material, Eqs. (S27)-(S34)"},{"comment":"The central claim that MR-RPAx provides accurate correlation energies for strongly correlated systems is contradicted by the paper's own data: at stretched geometries, Eq. (25) gives imaginary roots and MR-RPAx fails for all four molecules. The rescue via MR-RPAx-e drops the active-space screening terms and is a different approximation, not the resummation of generalized ring diagrams with antisymmetrized vertices that defines MR-RPAx. The abstract and introduction should therefore be tempered: the numerical evidence supports MR-RPAx only in the regime where Eq. (25) has real paired eigenvalues, and the strong-correlation performance claim should be restricted accordingly.","section":"Sec. III.B and Fig. 5"},{"comment":"The paper uses the plasmon formula Eq. (28) for all numerical results, but the equivalence between Eq. (28) and the defining imaginary-frequency expression Eq. (20) relies on the non-Hermitian eigenvalue problem (25) having real paired eigenvalues. The paper reports imaginary roots at stretched geometries but does not discuss whether Eq. (20) remains meaningful in that case, whether Eq. (28) is undefined, or what stability condition would guarantee real roots. This is a load-bearing point for the applicability of MR-RPAx as defined, and the authors should either provide a stability analysis or explicitly state that Eq. (20) itself is only defined when Eq. (25) is well-behaved.","section":"Sec. II.B, Eqs. (20) and (28)"}],"minor_comments":[{"comment":"The symbol '/' appears in the SR-RPAx and MR-RPAx columns at large bond distances without explanation; presumably these entries are absent because the eigenvalue problem has imaginary roots, but this should be stated explicitly in the table captions or in the main text.","section":"Tables S5-S8"},{"comment":"The second term in Eq. (22) sums over states labeled |Φ^{N-1}_I>, whereas the first term uses |Φ^{N-1}_H>; the index naming should be made consistent throughout the equation and the following definitions.","section":"Eq. (22)"},{"comment":"The abbreviation MR-phRPA is introduced in the abstract and used in Sec. III.C, but it is defined only later in Sec. II.A; please define the abbreviation at first use in the abstract or restructure the introduction.","section":"Abstract and Sec. III.C"},{"comment":"The caption contains the stray text '79' in the sentence describing the interaction vertices; this appears to be a citation artifact and should be removed or properly formatted as a reference.","section":"Fig. 1 caption"}],"recommendation":"major_revision","confidential_remarks":"This is a solid and readable contribution from a group that has established the diagrammatic MR framework. The main issue is the unproven positive-definiteness assumption in the MR-ppRPA derivation; this is fixable either by a proof under stated conditions or by numerical verification of the condition and of the equivalence of the two traces in Eq. (50). The MR-RPAx instability is honestly reported, but the abstract and conclusions should be recalibrated so that the claimed scope matches the evidence. I recommend major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a genuine extension of the authors' diagrammatic MR framework to the exchange-corrected particle-hole channel (RPAx) and the particle-particle channel (ppRPA), and the derivations look careful. The one thing to probe is the MR-ppRPA eigenvalue formula: it rests on a positive-definiteness condition that is stated but not proven, and the tests never check it.\n\nWhat's new and good: MR-RPAx and MR-ppRPA are new. The paper derives the same set of equations at SR and MR levels, with the special treatment of the second-order RPAx diagram handled correctly. The perturbative analysis, done to fifth order for HF, is a good addition and gives a plausible account of the error cancellation that explains the numerical behavior. The PEC benchmarks compare against independent DMRG and SC-NEVPT2 data, and the size-extensivity check on Li4 is a nice detail. The derivations are internally consistent, the citation pattern is solid (SR ppRPA and prior MR-RPA work are covered), and the authors are honest about the limitations of MR-RPAx.\n\nThe soft spots, in proportion: the ppRPA issue is real but not fatal. In the supplemental derivation (S27–S34), the contour integration requires E_alpha = Delta + alpha V to be positive definite for all alpha, and the chemical potential must keep the N±2 addition/removal energies positive. The paper states these restrictions and proposes the heuristic mu of Eq. (51), but no proof that mu always satisfies them. In the single-reference limit this is fine; in the MR case, interacting N±2 energies have no algebraic guarantee. The benchmarks don't report the check, so it is possible the method silently fails outside the tested molecules. A numerical comparison of the two equivalent forms in Eq. (50) would close the gap. Also, MR-RPAx suffers from imaginary roots at stretched geometries; the proposed MR-RPAx-e fix is ad hoc but clearly labeled. No code is released, so independent verification is limited.\n\nWho this is for: people working on multi-reference correlation methods, especially RPA variants. The central claim—unified equations for all three channels—is credible and the honest reporting of limitations makes it a workable starting point. It deserves a serious referee, but the referee should ask for a check of the positive-definiteness condition or a revised mu strategy, and for the stability of MR-RPAx to be discussed rather than patched.\n\nRecommendation: send to peer review with a request for revision, focused on the ppRPA condition.","headline":"A credible, careful extension of the authors' MR-dRPA framework to RPAx and ppRPA; the open unresolved point is the unproven positive-definiteness condition behind the MR-ppRPA eigenvalue formula.","tokens_in":31891,"tokens_out":4737,"would_cite":true,"duration_ms":39069,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper defines multi-reference RPA with exchange (MR-RPAx) and particle-particle RPA (MR-ppRPA) as infinite diagram resummations whose energy equations unify with — and reduce to — their single-reference counterparts.","keywords":["multi-reference RPA","particle-particle RPA","RPA with exchange","cumulant Green's functions","diagrammatic resummation","strong correlation","correlation energy","non-Hermitian eigenvalue problem"],"falsifier":"Take a molecule with a small or ill-defined highest-occupied/lowest-unoccupied gap (the case where the chemical-potential rule of Eq. (51) is most strained), build the matrix $E_{\\alpha} = \\Delta + \\alpha V$ of Eq. (S27) from its MR-ppRPA data, and track its smallest eigenvalue for $\\alpha\\in[0,1]$ while verifying that $\\omega^{N+2}_P - 2\\mu$ and $\\omega^{N-2}_H + 2\\mu$ stay positive: if any eigenvalue crosses zero or any shifted gap turns negative, the eigenvalue formula (50) is silent about the correct energy, and the method should visibly break or jump there. For MR-RPAx, the analogous test is to diagonalize the generalized eigenvalue problem (25) along the dissociation curve of a molecule not among the four tested and look for the imaginary roots that already appear for HF, ScH, and $\\mathrm{N_2}$ at stretched geometries.","tokens_in":30785,"feed_emoji":"⚛️","tokens_out":20362,"duration_ms":165253,"temperature":0.7,"pith_summary":"Single-reference random phase approximation (RPA) starts from one determinant, so its perturbation series diverges when bonds stretch. This paper defines two multi-reference generalizations — RPA with exchange (MR-RPAx) and particle-particle RPA (MR-ppRPA) — by resumming generalized 'ring' and 'ladder' Feynman diagrams to infinite order, with the diagrams rebuilt from the cumulant (connected) two-body Green's functions of an active space. The central claim is that the resulting correlation-energy formulas, Eqs. (20) and (45), take exactly the same mathematical form for single- and multi-reference starting points, so the standard single-reference methods are special cases. A perturbative analysis attributes the numerical success to error cancellation between the second and third orders, and the tested molecules show the two channels err in opposite directions, pointing to a combined treatment.","feed_headline":"RPA correlation energies go multi-reference in two channels","feed_subtitle":"The two channels make opposite errors, so combining them is the natural next step.","key_machinery":"The load-bearing object is the generalized Feynman diagram of a multi-reference many-body perturbation theory in which Wick's theorem is replaced by a cumulant expansion of time-ordered Green's functions: diagram lines are zeroth-order Green's functions of an interacting $\\hat{H}_0$, and four-legged vertices can meet at a connected two-body cumulant (the red square in the paper's figures) that carries the active-space correlation. Two generalized propagators do the work: the particle-hole polarizability $i\\Pi^{0}_{pr,qs} = G^{0}_{rq}G^{0}_{sp} - G^{0,c}_{rs,pq}$ feeding the RPAx ring sum, and the particle-particle pair propagator $K^{0}_{rs,pq} = G^{0}_{rq}G^{0}_{sp} - G^{0}_{rp}G^{0}_{sq} - G^{0,c}_{rs,pq}$ feeding the ppRPA ladder sum. Substituting these into logarithm-of-determinant energy integrals and evaluating the frequency integrals analytically converts each resummation into a paired-eigenvalue ('plasmon') trace from a non-Hermitian generalized eigenvalue problem, Eqs. (25) and (46), or into a coupled-cluster-like Riccati equation whose order-by-order solution provides the perturbative energy analysis. With a Dyall Hamiltonian as $\\hat{H}_0$ and a CASSCF wavefunction as the reference, the eigenvalue problems take a block form whose elements are written through active-space transition density matrices.","core_discovery":"The central discovery is a unified set of energy expressions for two further RPA channels. For the particle-hole channel, the infinite resummation of ring diagrams with antisymmetrized Coulomb vertices, corrected at second order by subtracting one diagram with the wrong symmetry factor, yields $\\Delta E_{\\mathrm{RPAx}} = \\int \\frac{d\\omega}{2\\pi} \\frac{1}{2}\\mathrm{tr}\\,[\\ln(I - \\bar{v}\\Pi^{0}(i\\omega)) + \\bar{v}\\Pi^{0}(i\\omega)] - \\Delta E^{(2),a}$, which is also the plasmon formula $\\frac{1}{2}(\\mathrm{tr}\\,\\bar{\\Omega} - \\mathrm{tr}\\,\\bar{A}) - \\Delta E^{(2),a}$ from the non-Hermitian generalized eigenvalue problem (25) and, equivalently, a coupled-cluster-like Riccati equation. For the particle-particle channel, the resummation of generalized ladder diagrams built from the pair propagator $K^{0}$ gives $\\Delta E_{\\mathrm{ppRPA}} = \\int \\frac{d\\omega}{2\\pi} \\mathrm{tr}\\,[\\ln(I - \\tfrac{1}{4}\\bar{g}K^{0}(i\\omega)) + \\tfrac{1}{4}\\bar{g}K^{0}(i\\omega)] = \\mathrm{tr}\\,\\Omega_{+} - \\mathrm{tr}\\,A_{+}$, evaluated from the eigenvalue problem (46) in the $(N+2)$- and $(N-2)$-electron spaces. All of these reduce to the standard single-reference dRPA, RPAx, and ppRPA formulas when the reference is a single determinant, because each generalized propagator then collapses to products of ordinary one-body Green's functions. On HF, ScH, $\\mathrm{H_2O}$, and $\\mathrm{N_2}$, MR-ppRPA gives the most accurate dissociation limits among the three MR variants but underestimates correlation near equilibrium; full MR-RPAx develops imaginary roots at stretched geometries, an instability avoided by leaving out active-space screening (MR-RPAx-e); MR-dRPA remains the most balanced overall.","pith_inferences":["Editorial inference: because the particle-hole and particle-particle channels over- and under-estimate correlation, a unified resummation mixing ring and ladder diagrams is a natural next method; a concrete check is whether the opposite-signed errors persist for larger active spaces, open-shell ground states, and molecules beyond the four tested, all of which the paper leaves open.","Editorial inference: the same cumulant-diagram prescription is not tied to RPA, so it could define multi-reference generalizations of other single-reference resummable methods (for example GW self-energies or coupled-cluster doubles style sums) by the same route of replacing propagator lines with cumulant-corrected ones.","Editorial inference: the order-by-order sign pattern is a cheap diagnostic — RPAx contributes negatively at every order and diverges, while dRPA and ppRPA alternate and decay; watching the first few perturbative orders of a new RPA variant could predict whether the full resummation will be stable before running it.","Editorial inference: Eq. (50) predicts the MR-ppRPA energy is exactly independent of the chemical potential, so computing the same molecule with several different $\\mu$ values that satisfy the two restrictions would simultaneously validate the contour-integration derivation and stress the positive-definiteness assumption."],"forward_implications":["Any existing single-reference RPAx or ppRPA implementation can be promoted to a multi-reference one by redefining diagram lines through the active-space cumulant Green's functions, with the algebraic structure of the equations unchanged.","MR-ppRPA gives the most accurate correlation energies at dissociation among the three MR variants, beating SC-NEVPT2 for $\\mathrm{H_2O}$ and $\\mathrm{N_2}$ at large bond lengths, though it underestimates correlation near equilibrium.","Full MR-RPAx inherits the imaginary-root instability of single-reference RPAx at stretched geometries, but omitting active-space screening (MR-RPAx-e) removes the instability and yields qualitatively correct dissociation curves.","Error cancellation between the second and third orders is the reason both SR-RPA and MR-RPA succeed, so accurate correlation energies do not require each perturbative order to be small.","Because the particle-hole and particle-particle channels err in opposite directions, combining the two channels into a single method is the paper's concrete route to better accuracy."],"supporting_citations":[{"why":"Establishes the generalized multi-reference MBPT with cumulant diagrams and defines MR-dRPA; the present MR-RPAx and MR-ppRPA are built on this framework and inherit its unified SR/MR equations.","marker":"[10]"},{"why":"Supplies the cumulant expansion of time-ordered many-body Green's functions that substitutes for Wick's theorem when $\\hat{H}_0$ is interacting, the mathematical foundation of the generalized diagrams.","marker":"[8]"},{"why":"Provides the analytic contour-integration technique and the positive-definiteness and eigenvalue-pairing argument for single-reference ppRPA that the MR-ppRPA derivation in the Supplemental Material follows.","marker":"[85]"},{"why":"Introduces single-reference ppRPA with a chemical potential and the particle-particle/hole-hole channel that MR-ppRPA generalizes.","marker":"[66]"},{"why":"Develops the single-reference ppRPA theory whose correct antisymmetry and absence of instabilities motivate the multi-reference generalization.","marker":"[67]"},{"why":"Formulates single-reference RPA with exchange using antisymmetrized interactions, the limit to which MR-RPAx reduces.","marker":"[47]"},{"why":"Contains the analogous second-order subtraction needed when antisymmetrized ring diagrams are resummed, the same symmetry-factor subtlety handled for MR-RPAx.","marker":"[82]"},{"why":"Defines the Dyall Hamiltonian used as the interacting zeroth-order $\\hat{H}_0$, the choice that makes the multi-reference implementation accurate and efficient.","marker":"[84]"},{"why":"Defines the CASSCF reference wavefunction, including its multi-determinantal active-space part, on which all three MR-RPA methods are built.","marker":"[83]"}],"fun_headline_variants":["Unified RPA extends to multi-reference in two channels","Two-channel RPA: opposite errors point to combined theory","Multi-reference RPA unified for particle-hole and particle-particle","RPA channels unified, errors cancel in combination","One set of equations for both RPA channels and references"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the auxiliary matrix $E_{\\alpha} = \\Delta + \\alpha V$ stays positive definite for all $\\alpha\\in[0,1]$ and that the two-electron addition and removal energies $\\omega^{N+2}_P - 2\\mu$ and $\\omega^{N-2}_H + 2\\mu$ remain positive for the chosen chemical potential, so that the ppRPA summation can be evaluated as a paired-eigenvalue trace; the paper proposes a practical rule for $\\mu$ but does not prove it always enforces these conditions for arbitrary systems, and the RPAx variant separately assumes the generalized eigenvalue problem (25) has real roots, which the paper reports fails at stretched geometries of several molecules.","fun_headline_variants_meta":{"raw":{"variants":["Unified RPA extends to multi-reference in two channels","Two-channel RPA: opposite errors point to combined theory","Multi-reference RPA unified for particle-hole and particle-particle","RPA channels unified, errors cancel in combination","One set of equations for both RPA channels and references"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00027,"raw_usage":{"total_tokens":1808,"prompt_tokens":1308,"completion_tokens":500,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":924,"completion_tokens_details":{"reasoning_tokens":421}},"tokens_in":924,"tokens_out":500,"duration_ms":4872,"temperature":1.0,"reasoning_tokens":421,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T17:50:45.546231+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a molecule with a small or ill-defined highest-occupied/lowest-unoccupied gap (the case where the chemical-potential rule of Eq. (51) is most strained), build the matrix $E_{\\alpha} = \\Delta + \\alpha V$ of Eq. (S27) from its MR-ppRPA data, and track its smallest eigenvalue for $\\alpha\\in[0,1]$ while verifying that $\\omega^{N+2}_P - 2\\mu$ and $\\omega^{N-2}_H + 2\\mu$ stay positive: if any eigenvalue crosses zero or any shifted gap turns negative, the eigenvalue formula (50) is silent about the correct energy, and the method should visibly break or jump there. For MR-RPAx, the analogous test is to diagonalize the generalized eigenvalue problem (25) along the dissociation curve of a molecule not among the four tested and look for the imaginary roots that already appear for HF, ScH, and $\\mathrm{N_2}$ at stretched geometries.","supporting_citations":[{"cited_title":"Heßelmann ,\\ https://doi.org/10.1063/1.3590916 journal journal J","cited_arxiv_id":null,"evidence_quote":"Formulates single-reference RPA with exchange using antisymmetrized interactions, the limit to which MR-RPAx reduces."}],"review_version":1}