{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,16]],"date-time":"2026-10-16T23:38:30Z","timestamp":1792193910755,"version":"4.4.0"},"reference-count":111,"publisher":"American Chemical Society (ACS)","issue":"16","license":[{"start":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T00:00:00Z","timestamp":1785974400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000928","name":"Welch Foundation","doi-asserted-by":"publisher","award":["C-2212"],"award-info":[{"award-number":["C-2212"]}],"id":[{"id":"10.13039\/100000928","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000928","name":"Welch Foundation","doi-asserted-by":"publisher","award":["R-C-0002-20240404"],"award-info":[{"award-number":["R-C-0002-20240404"]}],"id":[{"id":"10.13039\/100000928","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,8,25]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) has emerged as a promising electronic structure method for correlated electronic systems. However, the quality of its predictions depends critically on the choice of trial wave function, and it is not obvious how to make an optimal choice, especially for strongly correlated states of large systems. Mean-field wave functions are compelling trial wave function candidates, as they map directly to chemical concepts and can be obtained withO(N4) cost. Yet in the strongly correlated regime, one faces a symmetry dilemma and the existence of multiple nearly degenerate solutions. In this work, we investigate active space models of [2Fe\u20132S]2+, mixed-valent [4Fe\u20134S]2+, and [4Fe\u20134S]4+ and explore the sensitivity of ph-AFQMC to the choice of unrestricted Hartree\u2013Fock trial wave function. We find that surprisingly accurate ground-state energies for these systems can be obtained when trial selection is guided by chemical properties and physical symmetries, rather than the variational energy. However, in all cases, we find a rapidly decaying overlap between the stochastic wave function and the UHF trial, indicating that the trials are acting as suboptimal importance functions. By analogy to a similar situation in the stretched helium dimer cation, we show how this sampling bias pushes ph-AFQMC with UHF trials toward artificially negative energies, which evidently can be compensated for by the phaseless bias in certain cases.<\/jats:p>","DOI":"10.1021\/acs.jctc.6c00899","type":"journal-article","created":{"date-parts":[[2026,8,6]],"date-time":"2026-08-06T15:01:50Z","timestamp":1786028510000},"page":"8274-8287","source":"Crossref","is-referenced-by-count":1,"title":["Selecting Optimal\nUnrestricted Hartree\u2013Fock\nTrial Wave Functions for Phaseless Auxiliary-Field Quantum Monte Carlo:\nAccuracy and Limitations in Modeling Three Iron\u2013Sulfur Clusters"],"prefix":"10.1021","volume":"22","author":[{"given":"Don","family":"Danilov","sequence":"first","affiliation":[{"name":"Rice University , , , ,","place":["Houston, Texas, United States, 77005-1892"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Brad","family":"Ganoe","sequence":"additional","affiliation":[{"name":"Rice University , , , ,","place":["Houston, Texas, United States, 77005-1892"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4079-8347","authenticated-orcid":true,"given":"Leon","family":"Otis","sequence":"additional","affiliation":[{"name":"Rice University , , , ,","place":["Houston, Texas, United States, 77005-1892"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1316-4675","authenticated-orcid":true,"given":"Zhi","family":"Gong","sequence":"additional","affiliation":[{"name":"Rice University , , , ,","place":["Houston, Texas, United States, 77005-1892"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zixiang","family":"Lu","sequence":"additional","affiliation":[{"name":"University of Illinois Urbana\u2212champaign , , ,","place":["Urbana, Illinois, United States, 61801"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8333-8151","authenticated-orcid":true,"given":"James","family":"Shee","sequence":"additional","affiliation":[{"name":"Rice University , , , ,","place":["Houston, Texas, United States, 77005-1892"]},{"name":"Rice University , , , ,","place":["Houston, Texas, United States, 77005-1892"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2026,8,6]]},"reference":[{"key":"2026083118573194600_cit1","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1007\/978-1-4684-3779-9","volume-title":"Biochemistry\nof Nonheme Iron","author":"Bezkorovainy","year":"1980"},{"key":"2026083118573194600_cit2","doi-asserted-by":"publisher","first-page":"247","DOI":"10.1146\/annurev.biochem.74.082803.133518","article-title":"Structure,\nFunction,\nand Formation of biological iron-sulfur clusters","volume":"74","author":"Johnson","year":"2005","journal-title":"Annu. 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Chem.\nPhys."},{"key":"2026083118573194600_cit32","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2601.04621","article-title":"Classical\ncomputational simulation of the FeMo-cofactor model to chemical accuracy\nand its implications","author":"Zhai","year":"2026","journal-title":"arXiv"},{"key":"2026083118573194600_cit33","doi-asserted-by":"publisher","first-page":"11335","DOI":"10.1021\/acs.jctc.5c01038","article-title":"A Perspective\non Quantum Computing Applications in Quantum Chemistry\nUsing 25\u2013100 Logical Qubits","volume":"21","author":"Alexeev","year":"2025","journal-title":"J. Chem.\nTheory Comput."},{"key":"2026083118573194600_cit34","doi-asserted-by":"publisher","first-page":"7555","DOI":"10.1073\/pnas.1619152114","article-title":"Elucidating\nreaction mechanisms on quantum computers","volume":"114","author":"Reiher","year":"2017","journal-title":"Proc.\nNatl. Acad. Sci. U. S. 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Phys."},{"key":"2026083118573194600_cit40","doi-asserted-by":"publisher","first-page":"4727","DOI":"10.1021\/acs.jpca.1c00397","article-title":"Resolution of low-energy states in spin-exchange transition-metal\nclusters: Case study of singlet states in [Fe (III) 4S4] cubanes","volume":"125","author":"Li Manni","year":"2021","journal-title":"J. Phys. Chem. A"},{"key":"2026083118573194600_cit41","doi-asserted-by":"publisher","first-page":"7210","DOI":"10.1021\/acs.jctc.4c00578","article-title":"Combined Multireference\u2013Multiscale\nApproach to the Description of Photosynthetic Reaction Centers","volume":"20","author":"Drosou","year":"2024","journal-title":"J. Chem. Theory Comput."},{"key":"2026083118573194600_cit42","doi-asserted-by":"publisher","first-page":"136401","DOI":"10.1103\/PhysRevLett.90.136401","article-title":"Quantum Monte Carlo method using phase-free random\nwalks with Slater determinants","volume":"90","author":"Zhang","year":"2003","journal-title":"Phys. Rev. Lett."},{"key":"2026083118573194600_cit43","doi-asserted-by":"publisher","DOI":"10.1002\/wcms.1364","article-title":"Ab initio computations\nof molecular systems by the auxiliary\u2013field\nquantum Monte Carlo method","volume":"8","author":"Motta","year":"2018","journal-title":"WIREs Comput. Mol.\nSci."},{"key":"2026083118573194600_cit44","doi-asserted-by":"publisher","first-page":"024107","DOI":"10.1063\/5.0031024","article-title":"Some recent developments in auxiliary-field quantum Monte Carlo for\nreal materials","volume":"154","author":"Shi","year":"2021","journal-title":"J. Chem. Phys."},{"key":"2026083118573194600_cit45","doi-asserted-by":"publisher","first-page":"7024","DOI":"10.1021\/acs.jctc.2c00802","article-title":"Twenty Years of Auxiliary-Field Quantum\nMonte Carlo in Quantum Chemistry: An Overview and Assessment on Main\nGroup Chemistry and Bond-Breaking","volume":"18","author":"Lee","year":"2022","journal-title":"J. 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Theory Comput."},{"key":"2026083118573194600_cit48","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2510.06486","article-title":"Systematic\nimprovement of trial states in phaseless auxiliary-field quantum Monte\nCarlo","author":"Kj\u00f8nstad","year":"2025","journal-title":"arXiv"},{"key":"2026083118573194600_cit49","doi-asserted-by":"publisher","first-page":"2861","DOI":"10.1021\/acs.jctc.5c01936","article-title":"Evaluating multiconfigurational trials\nfor accurate\nphaseless auxiliary-field quantum Monte Carlo on 3d transition metal\ncomplexes","volume":"22","author":"Vuong","year":"2026","journal-title":"J. Chem. Theory Comput."},{"key":"2026083118573194600_cit50","doi-asserted-by":"publisher","DOI":"10.48550\/arXiv.2406.08314","article-title":"GPU-accelerated Auxiliary-field\nquantum\nMonte Carlo with multi-Slater determinant trial states","author":"Huang","year":"2024","journal-title":"arXiv"},{"key":"2026083118573194600_cit51","doi-asserted-by":"publisher","first-page":"174111","DOI":"10.1063\/5.0087047","article-title":"Selected configuration\ninteraction wave functions in\nphaseless auxiliary field quantum Monte Carlo","volume":"156","author":"Mahajan","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2026083118573194600_cit52","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1021\/acs.jctc.2c00934","article-title":"ipie: A Python-Based\nAuxiliary-Field Quantum Monte Carlo Program with Flexibility and Efficiency\non CPUs and GPUs","volume":"19","author":"Malone","year":"2023","journal-title":"J. Chem. 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Acta, Bioenerg."},{"key":"2026083118573194600_cit76","doi-asserted-by":"publisher","first-page":"1237","DOI":"10.1021\/ja00004a025","article-title":"Proton NMR spectroscopy and the electronic\nstructure of the high\npotential iron-sulfur protein from Chromatium vinosum","volume":"113","author":"Bertini","year":"1991","journal-title":"J. Am. Chem. Soc."},{"key":"2026083118573194600_cit77","doi-asserted-by":"publisher","first-page":"2644","DOI":"10.1021\/ja00815a071","article-title":"Equivalence of metal centers in the\niron-sulfur protein active site analogs [Fe4S4(SR)4]2-","volume":"96","author":"Holm","year":"1974","journal-title":"J. Am. Chem. Soc."},{"key":"2026083118573194600_cit78","doi-asserted-by":"publisher","first-page":"440","DOI":"10.1103\/PhysRev.81.440","article-title":"Interaction\nBetween the d Shells in the Transition Metals","volume":"81","author":"Zener","year":"1951","journal-title":"Phys. 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Sci."},{"key":"2026083118573194600_cit87","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1002\/qua.560230203","article-title":"Towards a\n\u201cchemical\u201d Hamiltonian","volume":"23","author":"Mayer","year":"1983","journal-title":"Int. J.\nQuantum Chem."},{"key":"2026083118573194600_cit88","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1002\/qua.560260111","article-title":"Bond order\nand valence: Relations to Mulliken\u2019s population analysis","volume":"26","author":"Mayer","year":"1984","journal-title":"Int. J. Quantum Chem."},{"key":"2026083118573194600_cit89","doi-asserted-by":"publisher","first-page":"72","DOI":"10.1007\/s002140050239","article-title":"A comparative study of high-spin manganese and iron\ncomplexes","volume":"97","author":"Blomberg","year":"1997","journal-title":"Theor. Chem. 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