{"id":"1a51db97-f9e8-4b48-a13f-f2ee1334d2ff","arxiv_id":"2507.17960","paper_version":1,"verdict":"ACCEPT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The EAS additive-screening method is adapted to the mixed-product basis of the (L)APW all-electron method, enabling lower-cost G0W0 and BSE calculations of weakly bound heterostructures with accuracy close to exact references.","lead":"This paper extends an efficient approximation for electronic screening, called expansion and addition screening (EAS), to all-electron calculations that treat core electrons explicitly. It implements the method in the exciting code and shows that it reproduces exact G0W0 and BSE results for a WSe2 bilayer and a pyridine-on-MoS2 hybrid while cutting the polarizability cost by more than half.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claim holds for the demonstrated weakly bound, unrelaxed regime; the load-bearing additive/identical-radial-function assumption is untested for relaxed or more strongly coupled heterostructures, so no verdict change is needed.","rationale":"The reader's weakest assumption correctly identifies the additive polarizability ansatz and the identical radial-function assumption as the load-bearing approximation. My stress-test agrees with that identification. The paper is honest about the exact-replica condition and the weakly bound scope, and both validation examples fall squarely inside that scope, with gap errors of 0.02-0.04 eV. No mathematical inconsistency was found in the derivation of the expansion and addition steps, and the CPU-time comparison is reported transparently, including the less impressive total savings for G0W0. The only genuine gap is that realistic heterostructures are usually relaxed, so the expansion step is not exact in the intended use case; the paper does not quantify the resulting error. This does not invalidate the central claim as written, but it is worth a verification test and a small qualification in the conclusion. Therefore the ACCEPT verdict stands unchanged.","tokens_in":12638,"tokens_out":25704,"duration_ms":265012,"concrete_test":"Repeat the pyridine@MoS2 comparison with the heterostructure geometry fully relaxed using the same PBE+TS setup, keeping all other computational parameters identical, and compare the EAS and exact fundamental gaps and optical gaps. If the gap differences remain below roughly 0.1 eV, the relaxation caveat is not a practical limitation; if they grow appreciably, the paper should restrict its claims to rigid-lattice or exact-replica interfaces.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that EAS in the mixed-product basis reproduces exact G0W0/BSE results for weakly bound heterostructures. The load-bearing assumption, stated in Section III.B and explicitly delimited in Section IV.B, is that P_HS is approximately the sum of the individual polarizabilities with the same radial muffin-tin basis functions, and that the expansion step is exact only when the supercell is an exact replica of the unit cell. The WSe2 bilayer test exercises only the addition step; the pyridine@MoS2 test exercises the expansion but with MoS2 fixed at ideal lattice sites, enforcing the exact-replica condition. The paper provides no estimate of how errors grow when the heterostructure geometry is relaxed, which is the typical practical use case, or when interlayer hybridization is non-negligible. This is a boundary-of-applicability gap rather than an internal inconsistency: the in-regime agreement for both test systems supports the claim as stated. The residual risk is that the conclusion's phrasing about 'heterostructures much larger than those considered so far' invites application outside the validated exact-replica/weak-coupling regime.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper extends the expansion-and-addition screening (EAS) method, previously developed in a planewave representation, to the mixed-product basis used in the all-electron (L)APW method. It derives the basis transformations for both the expansion step (folding a component's polarizability from its unit cell to a supercell) and the addition step (superposing the polarizabilities of two components), and implements them in the G0W0 and BSE modules of the exciting code. The method is validated on bilayer WSe2 and pyridine@MoS2 against exact reference calculations, showing quasi-particle gap differences of at most 0.04 eV and optical-gap differences of at most 0.02 eV, with reductions in total runtime of about 25% for G0W0 and 46% for BSE.","tokens_in":12844,"tokens_out":14048,"duration_ms":134458,"significance":"If the reported accuracy holds, this is a valuable contribution: it transfers the EAS idea to an all-electron framework, where the mixed-product basis makes the addition and expansion steps nontrivial, and it provides a way to reduce the O(N^4) polarizability cost for weakly bound heterostructures. The paper is commendable for deriving the transformation matrices in Appendix B, for validating against independent exact calculations, and for explicitly stating the exact-replica condition for the expansion step. The main limitation is that the demonstrated accuracy covers the weakly bound, unrelaxed (or replica-exact) regime; the authors acknowledge this, and it does not undermine the stated central claim.","major_comments":[],"minor_comments":[{"comment":"The sentence 'This results in a total runtime of 2962 CPU hours, corresponding to a reduction of almost 70% of the computational time' refers only to the polarizability step; the total BSE runtime is reduced by 46% (7661 vs 14161 CPU hours). Please reword to avoid implying a 70% total reduction.","section":"IV B / Table I"},{"comment":"The final sentence of the Conclusions is broader than the validated regime: 'heterostructures much larger than those considered so far' invites application to relaxed geometries, for which the expansion step is not exact. Please add a caveat or soften the sentence.","section":"V"},{"comment":"The derivation of the MT-MT expansion formula, Eq. (9), is very terse; the origin of the prefactor N_sc/N_uc and the phase factor in the second equality is not self-evident. Please expand the derivation or provide a reference.","section":"III A"},{"comment":"There are minor typos: 'the the exact calculation' should be 'the exact calculation' and 'the obtained result show' should be 'the obtained results show'.","section":"IV A"}],"recommendation":"accept","confidential_remarks":null},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe genuinely new thing here is the translation of the EAS polarizability trick from planewave codes to the mixed-product basis of the (L)APW method. That is not trivial because the basis splits into muffin-tin and interstitial pieces, and the expansion and addition steps need separate treatments. The authors derive the transformations in detail (Section III and Appendix B) and implement them in the exciting code. They also apply the same additive idea to BSE, which is a new application. The validation is solid: WSe2 bilayer fundamental gap 2.39 vs 2.41 eV exact, pyridine@MoS2 gap 2.32 vs 2.36 eV, optical gaps within 0.02 eV. Those numbers support the claim that EAS works for weakly bound heterostructures.\n\nWhat the paper does well: the derivation is self-contained, the limitations are stated explicitly (expansion exact only for exact replicas, additive ansatz assumes weak coupling), and the CPU-hour table gives a realistic picture—the polarizability part is cut by more than half, but total time by only a quarter to a half. That is honest.\n\nThe soft spots are real but proportionate. The additive ansatz and the assumption that radial muffin-tin functions are the same in the components and the heterostructure are untested for relaxed geometries or stronger interlayer hybridization. The pyridine@MoS2 test uses MoS2 fixed at ideal lattice sites, which satisfies the exact-replica condition but is not the typical practical use case. The paper does not estimate how errors grow when the structure is relaxed. That is a boundary-of-applicability gap, not an internal inconsistency. I would ask the authors to add a paragraph on this and maybe a test with a slightly relaxed geometry, but it does not undermine the demonstrated results.\n\nA minor point: no input files or commit hash are provided, which makes reproduction harder. That is common for methods papers in this field, so not a blocker.\n\nThe central claim holds within the demonstrated regime. The citation pattern looks appropriate, and there is no circularity: EAS is an approximation, not a target quantity, and the validation uses independent exact references. The paper is a useful contribution for anyone doing all-electron GW/BSE on heterostructures, especially for benchmarking.\n\nThis deserves a serious referee. I would send it to peer review and suggest minor revision: add a discussion of error behavior outside the tested regime and provide reproducibility artifacts if possible. Read it if you work on all-electron many-body methods; otherwise it is still a clean methods paper worth skimming.","headline":"A careful, well-validated extension of EAS to all-electron (L)APW with clear derivation; the boundary assumptions are honestly stated, so the paper deserves peer review.","tokens_in":13385,"tokens_out":3162,"would_cite":true,"duration_ms":31118,"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":"The expansion-and-addition screening method, ported to the mixed-product basis of (L)APW all-electron codes, reproduces exact $G_0W_0$ and BSE results for weakly bound heterostructures at a fraction of the polarizability cost.","keywords":["G0W0","Bethe-Salpeter equation","expansion and addition screening (EAS)","mixed-product basis","(L)APW all-electron method","polarizability","van der Waals heterostructures","two-dimensional materials"],"falsifier":"Take a heterostructure whose geometry is optimized after stacking and compute the exact polarizability matrix blocks; compare them with the EAS sum $P^1+P^2$ and with exact $G_0W_0$ gaps. If the difference in fundamental gaps exceeds the roughly $0.04$ eV seen here, the additivity premise fails.","tokens_in":12433,"feed_emoji":"⚛️","tokens_out":9455,"duration_ms":94700,"temperature":0.7,"pith_summary":"All-electron $G_0W_0$ and Bethe-Salpeter calculations of van der Waals heterostructures are normally very expensive because building the polarizability of the combined supercell grows steeply with atom number. This paper establishes that for weakly bound stacks the polarizability can be treated additively: each component is computed in its own small unit cell, folded into the heterostructure supercell, and then summed. The authors derive the folding and summation transformations for the mixed-product basis of the (L)APW all-electron method and implement them in both the $G_0W_0$ and BSE screening steps. Benchmarks on bilayer WSe$_2$ and pyridine@MoS$_2$ reproduce exact fundamental gaps within $0.04$ eV and optical gaps within $0.02$ eV while cutting the polarizability cost by roughly half to two-thirds. This makes reference-quality all-electron calculations of much larger interfaces feasible.","feed_headline":"Additive screening cuts polarizability cost by half","feed_subtitle":"Weakly bound stacks match exact gaps within 0.04 eV, at 50–70% lower polarizability cost.","key_machinery":"The machinery is the EAS identity $P^{HS}=P^1+P^2$ together with two basis-aware steps. In the expansion step, a polarizability computed in a component's smallest unit cell is folded into the heterostructure supercell using the mapping of reciprocal vectors; in the addition step, the two expanded polarizabilities are superposed by transforming each into the heterostructure's basis via overlap matrices $C^\\mu_{aA}$. The mixed-product basis makes this nontrivial: inside muffin-tin spheres it consists of radial functions times spherical harmonics, while in the interstitial region it consists of orthonormalized planewave combinations. The paper shows how each block of the polarizability matrix—muffin-tin, interstitial, and mixed—must be transformed separately, and how the disjointness of the two muffin-tin regions simplifies the addition to a small set of block expressions.","core_discovery":"The central claim is that the expansion-and-addition screening (EAS) ansatz—$P^{HS}=P^1+P^2$, with each component polarizability first folded from its primitive cell to the heterostructure supercell—can be implemented exactly in the mixed-product basis used by all-electron (L)APW codes. The paper derives the required transformations blockwise: muffin-tin matrix elements are folded through a real-to-reciprocal-space sum, interstitial elements through the planewave mapping $\\mathbf{q}_{uc}+\\mathbf{G}_{uc}=\\mathbf{q}+\\mathbf{G}$, and mixed blocks by applying the corresponding transformation to rows or columns. For the addition step, the component polarizabilities are transformed into the heterostructure basis with overlap matrices $C^\\mu_{aA}=\\langle\\chi^\\mu_a|\\chi_A\\rangle$, using the fact that muffin-tin spheres of different components are disjoint and their radial functions are assumed identical. The same additive screening is used for the electron-hole interaction in BSE as for $W$ in $G_0W_0$. On bilayer WSe$_2$ and pyridine@MoS$_2$, the method reproduces the exact quasi-particle and optical spectra: fundamental gaps of 2.39 vs 2.41 eV and 2.32 vs 2.36 eV, and optical gaps of 2.63 vs 2.64 eV and 2.00 vs 2.02 eV.","pith_inferences":["A natural stress test would be a heterostructure that is relaxed after stacking or binds more strongly; there the exact-replica and additivity assumptions weaken, so the tens-of-meV agreement should degrade, and quantifying this would map the method's validity boundary.","Since only the polarizability is accelerated, the self-energy and BSE Hamiltonian still dominate; combining EAS with low-rank factorization of those steps could bring total wall-time reductions far beyond the 25–46% reported here.","The block structure of the addition step should extend recursively to three or more components, so multilayer stacks and multi-molecule hybrid interfaces could reuse the same component polarizabilities without additional screening calculations."],"forward_implications":["The polarizability step for pyridine@MoS$_2$ drops from 3511 to 1545 CPU hours in $G_0W_0$ and from 9462 to 2962 CPU hours in BSE, so weakly bound interfaces with large supercells become tractable in all-electron reference calculations.","Optical absorption spectra inherit the screening from the same additive construction, so BSE exciton physics, not just quasi-particle gaps, is reproduced to within tens of meV.","Because the expansion step is exact only for exact replicas, one primitive-cell polarizability can be reused for many heterostructures containing the same unrelaxed component, amortizing the cost across a family of interfaces.","All-electron benchmarks can now target heterostructures too large for direct $G_0W_0$ or BSE reference runs, giving pseudopotential and planewave results a more demanding comparison point."],"supporting_citations":[{"why":"Introduced the additive polarizability ansatz in a planewave basis, the approach that this paper extends to the mixed-product basis.","marker":"[12]"},{"why":"Developed the expansion and addition screening formalism for energy-level alignment, whose folding and summation steps are ported here.","marker":"[13]"},{"why":"Constructed the mixed-product basis used to represent products of Kohn-Sham states in all-electron $G_0W_0$ calculations.","marker":"[25]"},{"why":"Provides the $G_0W_0$ module with the mixed-product basis into which the new EAS transformations are inserted.","marker":"[26]"},{"why":"Describes the BSE implementation that receives the analogous additive screening for optical spectra.","marker":"[32]"}],"fun_headline_variants":["Additive polarizability cuts cost for 2D heterostructures","All-electron G0W0 and BSE with 50–70% lower cost","Folded screening speeds up bilayer WSe2 and MoS2","Exact gaps within 0.04 eV at half the screening cost","Mixed-product basis enables cheap polarizability addition"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The whole construction rests on the assumption that a heterostructure's polarizability is exactly the sum of its two components' polarizabilities, with atoms sitting at exact replica positions and identical atom-centered basis functions used in both calculations.","fun_headline_variants_meta":{"raw":{"variants":["Additive polarizability cuts cost for 2D heterostructures","All-electron G0W0 and BSE with 50–70% lower cost","Folded screening speeds up bilayer WSe2 and MoS2","Exact gaps within 0.04 eV at half the screening cost","Mixed-product basis enables cheap polarizability addition"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000684,"raw_usage":{"total_tokens":3159,"prompt_tokens":1059,"completion_tokens":2100,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":675,"completion_tokens_details":{"reasoning_tokens":2009}},"tokens_in":675,"tokens_out":2100,"duration_ms":17066,"temperature":1.0,"reasoning_tokens":2009,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T14:39:34.134368+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take a heterostructure whose geometry is optimized after stacking and compute the exact polarizability matrix blocks; compare them with the EAS sum $P^1+P^2$ and with exact $G_0W_0$ gaps. If the difference in fundamental gaps exceeds the roughly $0.04$ eV seen here, the additivity premise fails.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduced the additive polarizability ansatz in a planewave basis, the approach that this paper extends to the mixed-product basis."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Developed the expansion and addition screening formalism for energy-level alignment, whose folding and summation steps are ported here."},{"cited_title":"Jiang, R","cited_arxiv_id":null,"evidence_quote":"Constructed the mixed-product basis used to represent products of Kohn-Sham states in all-electron $G_0W_0$ calculations."},{"cited_title":"Nabok, A","cited_arxiv_id":null,"evidence_quote":"Provides the $G_0W_0$ module with the mixed-product basis into which the new EAS transformations are inserted."},{"cited_title":"Vorwerk, B","cited_arxiv_id":null,"evidence_quote":"Describes the BSE implementation that receives the analogous additive screening for optical spectra."}],"review_version":1}