{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,9]],"date-time":"2026-10-09T22:46:14Z","timestamp":1791585974539,"version":"4.3.4"},"reference-count":59,"publisher":"AIP Publishing","issue":"8","license":[{"start":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T00:00:00Z","timestamp":1740441600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T00:00:00Z","timestamp":1740441600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2025,2,28]]},"abstract":"<jats:p>A comprehensive description of photo-chemical processes in materials, comprising spin-forbidden processes such as intersystem crossing and phosphorescence, implies taking into account spin\u2013orbit coupling. We present an efficient implementation of a perturbative spin\u2013orbit coupling correction for the Tamm\u2013Dancoff approximation of linear-response time-dependent density functional theory within a mixed Gaussian and plane wave framework relying on spin\u2013orbit coupling corrected pseudopotentials. The implementation is validated for a benchmark set of small aromatic molecules, with mean errors in excitation energies and spin\u2013orbit coupling matrix elements being in the range of 0.1\u20130.6\u00a0eV and 1.0\u201314.4 cm\u22121, respectively, in comparison with density functional theory and density functional theory multi-reference configuration interaction reference results. Computational timings are given for a bismuth-containing metal\u2013organic framework.<\/jats:p>","DOI":"10.1063\/5.0242940","type":"journal-article","created":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T08:09:14Z","timestamp":1740470954000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Perturbative spin\u2013orbit couplings for the simulation of extended framework materials"],"prefix":"10.1063","volume":"162","author":[{"given":"Jan-Robert","family":"Vogt","sequence":"first","affiliation":[{"name":"Institute of Physical Chemistry, Christian-Albrechts-University Kiel 1 , Max-Eyth-Strasse 1, 24118 Kiel,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8678-8246","authenticated-orcid":false,"given":"Jan","family":"Wilhelm","sequence":"additional","affiliation":[{"name":"Institute of Theoretical Physics, University of Regensburg 2 , 93053 Regensburg,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0498-740X","authenticated-orcid":false,"given":"Anna-Sophia","family":"Hehn","sequence":"additional","affiliation":[{"name":"Institute of Physical Chemistry, Christian-Albrechts-University Kiel 1 , Max-Eyth-Strasse 1, 24118 Kiel,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"317","published-online":{"date-parts":[[2025,2,25]]},"reference":[{"key":"2025022513085472700_c1","doi-asserted-by":"publisher","first-page":"187","DOI":"10.1002\/wcms.83","article-title":"Spin\u2013orbit coupling and intersystem crossing in molecules","volume":"2","year":"2012","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2025022513085472700_c2","doi-asserted-by":"publisher","first-page":"044108","DOI":"10.1063\/1.5012041","article-title":"Perturbative treatment of spin-orbit-coupling within spin-free exact two-component theory using equation-of-motion coupled-cluster methods","volume":"148","year":"2018","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c3","first-page":"664","article-title":"Chapter 12 Perturbation theory of relativistic effects","volume-title":"Relativistic Electronic Structure Theory","author":"Schwerdtfeger","year":"2002"},{"key":"2025022513085472700_c4","doi-asserted-by":"publisher","first-page":"105","DOI":"10.1016\/0009-2614(96)00530-1","article-title":"The fine-structure splitting of the thallium atomic ground state: LS- versus jj-coupling","volume":"257","year":"1996","journal-title":"Chem. Phys. Lett."},{"key":"2025022513085472700_c5","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1007\/s002140050268","article-title":"Ab initio calculations of the 2P12-2P32 splitting in the thallium atom","volume":"97","year":"1997","journal-title":"Theor. Chim. Acta"},{"key":"2025022513085472700_c6","doi-asserted-by":"publisher","first-page":"1215","DOI":"10.1002\/qua.24891","article-title":"A general method to describe intersystem crossing dynamics in trajectory surface hopping","volume":"115","year":"2015","journal-title":"Int. J. Quantum Chem."},{"key":"2025022513085472700_c7","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1021\/acs.jctc.6b00915","article-title":"Evaluation of spin-orbit couplings with linear-response time-dependent density functional methods","volume":"13","year":"2017","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2025022513085472700_c8","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1021\/jacsau.2c00659","article-title":"State interaction linear response time-dependent density functional theory with perturbative spin\u2013orbit coupling: Benchmark and perspectives","volume":"3","year":"2023","journal-title":"JACS Au"},{"key":"2025022513085472700_c9","doi-asserted-by":"publisher","first-page":"676","DOI":"10.1016\/j.cpc.2013.10.014","article-title":"MolSOC: A spin\u2013orbit coupling code","volume":"185","year":"2014","journal-title":"Comput. Phys. Commun."},{"key":"2025022513085472700_c10","doi-asserted-by":"publisher","first-page":"224105","DOI":"10.1063\/1.4936864","volume":"143","year":"2015","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c11","doi-asserted-by":"publisher","first-page":"144103","DOI":"10.1063\/1.4870010","volume":"140","year":"2014","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c12","doi-asserted-by":"publisher","first-page":"5809","DOI":"10.1021\/acs.jctc.0c00512","article-title":"Pragmatic approach to photodynamics: Mixed Landau\u2013Zener surface hopping with intersystem crossing","volume":"16","year":"2020","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2025022513085472700_c13","doi-asserted-by":"publisher","first-page":"15445","DOI":"10.1039\/c8cp01852a","article-title":"Incorporating spin\u2013orbit effects into surface hopping dynamics using the diagonal representation: A linear-response time-dependent density functional theory implementation with applications to 2-thiouracil","volume":"20","year":"2018","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2025022513085472700_c14","doi-asserted-by":"publisher","first-page":"953","DOI":"10.1021\/acs.jctc.2c01036","article-title":"Accurate spin\u2013orbit coupling by relativistic mixed-reference spin-flip-tddft","volume":"19","year":"2023","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2025022513085472700_c15","doi-asserted-by":"publisher","first-page":"22A501","DOI":"10.1063\/1.4707737","article-title":"Surface hopping trajectory simulations with spin-orbit and dynamical couplings","volume":"137","year":"2012","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c16","doi-asserted-by":"publisher","first-page":"6505","DOI":"10.1063\/1.472460","article-title":"The zero-order regular approximation for relativistic effects: The effect of spin\u2013orbit coupling in closed shell molecules","volume":"105","year":"1996","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c17","doi-asserted-by":"publisher","first-page":"392","DOI":"10.1063\/1.476576","volume":"109","year":"1998","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c18","doi-asserted-by":"publisher","first-page":"2630","DOI":"10.1103\/physrevb.21.2630","article-title":"Relativistic norm-conserving pseudopotential","volume":"21","year":"1980","journal-title":"Phys. Rev. B"},{"key":"2025022513085472700_c19","doi-asserted-by":"publisher","first-page":"2103","DOI":"10.1103\/physrevb.25.2103","article-title":"Relativistic norm-conserving pseudopotentials","volume":"25","year":"1982","journal-title":"Phys. Rev. B"},{"key":"2025022513085472700_c20","doi-asserted-by":"publisher","first-page":"2920","DOI":"10.1103\/physrevb.34.2920","article-title":"Spin-orbit splitting in semiconductors and insulators from the ab\u00a0initio pseudopotential","volume":"34","year":"1986","journal-title":"Phys. Rev. B"},{"key":"2025022513085472700_c21","doi-asserted-by":"publisher","first-page":"3641","DOI":"10.1103\/physrevb.58.3641","volume":"58","year":"1998","journal-title":"Phys. Rev. B"},{"key":"2025022513085472700_c22","first-page":"1704","volume":"54","year":"1996","journal-title":"Phys. Rev. B"},{"key":"2025022513085472700_c23","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/s00214-005-0655-y","article-title":"Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals","volume":"114","year":"2005","journal-title":"Theor. Chem. Acc."},{"key":"2025022513085472700_c24","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/s0009-2614(02)00837-0","article-title":"Spin\u2013orbit coupling with model core potentials","volume":"360","year":"2002","journal-title":"Chem. Phys. Lett."},{"key":"2025022513085472700_c25","doi-asserted-by":"publisher","first-page":"164105","DOI":"10.1063\/1.2072927","article-title":"On the accuracy of one-component pseudopotential spin-orbit calculations","volume":"123","year":"2005","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c26","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1063\/1.1330208","article-title":"Study of relativistic effects on nuclear shieldings using density-functional theory and spin\u2013orbit pseudopotentials","volume":"114","year":"2001","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c27","doi-asserted-by":"publisher","first-page":"4238","DOI":"10.1103\/physrevb.47.4238","article-title":"First-principles calculations of spin-orbit splittings in solids using nonlocal separable pseudopotentials","volume":"47","year":"1993","journal-title":"Phys. Rev. B"},{"key":"2025022513085472700_c28"},{"key":"2025022513085472700_c29","doi-asserted-by":"publisher","first-page":"4736","DOI":"10.1039\/d0cp06164f","article-title":"Efficient and low-scaling linear-response time-dependent density functional theory implementation for core-level spectroscopy of large and periodic systems","volume":"23","year":"2021","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2025022513085472700_c30","doi-asserted-by":"publisher","first-page":"034108","DOI":"10.1063\/5.0058124","article-title":"First-principles correction scheme for linear-response time-dependent density functional theory calculations of core electronic states","volume":"155","year":"2021","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c31","doi-asserted-by":"publisher","first-page":"4071","DOI":"10.1021\/acs.jctc.0c00372","article-title":"Trajectory surface hopping nonadiabatic molecular dynamics with Kohn\u2013Sham \u0394SCF for condensed-phase systems","volume":"16","year":"2020","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2025022513085472700_c32","doi-asserted-by":"publisher","first-page":"4082","DOI":"10.1021\/acs.jctc.1c01046","article-title":"Spin\u2013orbit couplings for nonadiabatic molecular dynamics at the \u0394SCF level","volume":"18","year":"2022","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2025022513085472700_c33","doi-asserted-by":"publisher","first-page":"e1327","DOI":"10.1002\/wcms.1327","article-title":"Software update: The orca program system, version 4.0","volume":"8","year":"2018","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2025022513085472700_c34","doi-asserted-by":"publisher","first-page":"477","DOI":"10.1080\/00268979709482119","volume":"92","year":"1997","journal-title":"Mol. Phys."},{"key":"2025022513085472700_c35","doi-asserted-by":"publisher","first-page":"194103","DOI":"10.1063\/5.0007045","article-title":"CP2K: An electronic structure and molecular dynamics software package\u2014Quickstep: Efficient and accurate electronic structure calculations","volume":"152","year":"2020","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c36","doi-asserted-by":"publisher","first-page":"044702","DOI":"10.1063\/1.5078682","volume":"150","year":"2019","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c37","doi-asserted-by":"publisher","first-page":"499","DOI":"10.2533\/000942905777676164","article-title":"Ground and excited state density functional calculations with the Gaussian and augmented-plane-wave method","volume":"59","year":"2005","journal-title":"Chimia Int. J. Chem."},{"key":"2025022513085472700_c38","doi-asserted-by":"publisher","first-page":"749","DOI":"10.1021\/acs.jctc.6b01122","volume":"13","year":"2017","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2025022513085472700_c39","doi-asserted-by":"publisher","first-page":"8658","DOI":"10.1039\/c7dt01744h","article-title":"Synthesis, functionalisation and post-synthetic modification of bismuth metal\u2013organic frameworks","volume":"46","year":"2017","journal-title":"Dalton Trans."},{"key":"2025022513085472700_c40","doi-asserted-by":"publisher","first-page":"10373","DOI":"10.1002\/anie.201204963","volume":"51","year":"2012","journal-title":"Angew. Chem., Int. Ed."},{"key":"2025022513085472700_c41","doi-asserted-by":"publisher","first-page":"18822","DOI":"10.1039\/c6dt03852b","article-title":"Synthesis and structure of Zr(IV)- and Ce(IV)-based CAU-24 with 1,2,4,5-tetrakis(4-carboxyphenyl)benzene","volume":"45","year":"2016","journal-title":"Dalton Trans."},{"key":"2025022513085472700_c42","doi-asserted-by":"publisher","first-page":"6252","DOI":"10.1039\/c9ce01347d","volume":"21","year":"2019","journal-title":"CrystEngComm"},{"key":"2025022513085472700_c43","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1016\/s0009-2614(99)01149-5","volume":"314","year":"1999","journal-title":"Chem. Phys. Lett."},{"key":"2025022513085472700_c44","doi-asserted-by":"publisher","first-page":"3928","DOI":"10.1063\/1.1540109","volume":"118","year":"2003","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c45","doi-asserted-by":"publisher","first-page":"124107","DOI":"10.1063\/1.3097192","volume":"130","year":"2009","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c46","doi-asserted-by":"publisher","first-page":"196101","DOI":"10.1063\/1.3265858","volume":"131","year":"2009","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c47","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.theochem.2009.08.018","volume":"914","year":"2009","journal-title":"J.\u00a0Mol. Struct.: Theochem"},{"key":"2025022513085472700_c48","doi-asserted-by":"publisher","first-page":"1242","DOI":"10.1103\/physreva.3.1242","article-title":"Length and velocity formulas in approximate oscillator-strength calculations","volume":"3","year":"1971","journal-title":"Phys. Rev. A"},{"key":"2025022513085472700_c49","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1016\/j.cplett.2004.03.126","article-title":"Gauge invariance of oscillator strengths in the approximate coupled cluster triples model CC3","volume":"389","year":"2004","journal-title":"Chem. Phys. Lett."},{"key":"2025022513085472700_c50","doi-asserted-by":"publisher","first-page":"8059","DOI":"10.1063\/1.473814","article-title":"Coupled cluster response functions revisited","volume":"106","year":"1997","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c51","doi-asserted-by":"publisher","first-page":"1896","DOI":"10.1021\/acs.jctc.8b00841","article-title":"Predicting phosphorescence rates of light organic molecules using time-dependent density functional theory and the path integral approach to dynamics","volume":"15","year":"2019","journal-title":"J.\u00a0Chem. Theory Comput."},{"key":"2025022513085472700_c52","doi-asserted-by":"publisher","first-page":"034107","DOI":"10.1063\/1.1829047","article-title":"Efficient and accurate approximations to the molecular spin-orbit coupling operator and their use in molecular g-tensor calculations","volume":"122","year":"2005","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c53","doi-asserted-by":"publisher","first-page":"6158","DOI":"10.1063\/1.478522","volume":"110","year":"1999","journal-title":"J.\u00a0Chem. Phys."},{"key":"2025022513085472700_c54","doi-asserted-by":"publisher","first-page":"138548","DOI":"10.1016\/j.cplett.2021.138548","article-title":"All-electron triple zeta basis sets for ZORA calculations: Application in studies of atoms and molecules","volume":"771","year":"2021","journal-title":"Chem. Phys. Lett."},{"key":"2025022513085472700_c55","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1007\/s002140050523","article-title":"The Gaussian and augmented-plane-wave density functional method for ab\u00a0initio molecular dynamics simulations","volume":"103","year":"1999","journal-title":"Theor. Chim. Acta"},{"key":"2025022513085472700_c56","doi-asserted-by":"publisher","first-page":"2105","DOI":"10.1039\/b001167n","article-title":"All-electron ab-initio molecular dynamics","volume":"2","year":"2000","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2025022513085472700_c57","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1016\/s0009-2614(96)01343-7","article-title":"Calculation of excitation energies within time-dependent density functional theory using auxiliary basis set expansions","volume":"264","year":"1997","journal-title":"Chem. Phys. Lett."},{"key":"2025022513085472700_c58","doi-asserted-by":"publisher","first-page":"5633","DOI":"10.1021\/acsami.9b21692","article-title":"Biocompatible, crystalline, and amorphous bismuth-based metal\u2013organic frameworks for drug delivery","volume":"12","year":"2020","journal-title":"ACS Appl. Mater. Interfaces"},{"key":"2025022513085472700_c59","doi-asserted-by":"publisher","first-page":"6065","DOI":"10.1039\/d0cs01414a","article-title":"The uptake of metal\u2013organic frameworks: A journey into the cell","volume":"51","year":"2022","journal-title":"Chem. Soc. Rev."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0242940\/20409918\/082502_1_5.0242940.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0242940\/20409918\/082502_1_5.0242940.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0242940\/20409918\/082502_1_5.0242940.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T16:20:54Z","timestamp":1748362854000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/162\/8\/082502\/3337065\/Perturbative-spin-orbit-couplings-for-the"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,2,25]]},"references-count":59,"journal-issue":{"issue":"8","published-print":{"date-parts":[[2025,2,28]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0242940","relation":{"has-preprint":[{"id-type":"doi","id":"10.26434\/chemrxiv-2024-tqgnv","asserted-by":"object"}]},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"value":"0021-9606","type":"print"},{"value":"1089-7690","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2025,2,28]]},"published":{"date-parts":[[2025,2,25]]},"article-number":"082502"}}