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While great progress has been made for certain types of resonances\ue5f8for example, temporary anions created by attaching one excess electron to a closed shell neutral\ue5f8resonances in general remain a great challenge of quantum chemistry because a successful description of the decay requires a balanced description of the bound and continuum aspect of the resonance. Here, a smoothed Voronoi complex absorbing potential (CAP) is combined with the XMS-CASPT2 method, which enables us to address the balance challenge by appropriate choice of the CAS space. To reduce the computational cost, the method is implemented in the projected scheme. In this pilot application, three temporary anions serve as benchmarks: the \u03c0* resonance state of formaldehyde; the \u03c0* and \u03c3* resonance states of chloroethene as functions of the C\u2013Cl bond dissociation coordinate; and the 4\u03a0u and 2\u03a0u resonance states of N2\u2013. The convergence of the CAP\/XMS-CASPT2 results has been systematically examined with respect to the size of the active space. Resonance parameters predicted by the CAP\/XMS-CASPT2 method agree well with CAP\/SAC-CI results (deviations of about 0.15 eV); however, as expected, CAP\/XMS-CASPT2 has clear advantages in the bond dissociation region. The advantages of CAP\/XMS-CASPT2 are further demonstrated in the calculations of 4\u03a0u and 2\u03a0u resonance states of N2\u2013 including their 3\u03a3u+ and 3\u0394u parent states. Three of the involved states (2\u03a0u, 3\u03a3u+, and 3\u0394u) possess multireference character, and CAP\/XMS-CASPT2 can easily describe these states with a relatively modest active space.<\/jats:p>","DOI":"10.1021\/acs.jctc.9b01032","type":"journal-article","created":{"date-parts":[[2020,2,27]],"date-time":"2020-02-27T12:26:42Z","timestamp":1582806402000},"page":"2606-2616","source":"Crossref","is-referenced-by-count":25,"title":["Combination of a Voronoi-Type Complex Absorbing Potential\nwith the XMS-CASPT2 Method and Pilot Applications"],"prefix":"10.1021","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8205-5328","authenticated-orcid":true,"given":"Quan Manh","family":"Phung","sequence":"first","affiliation":[{"name":"Nagoya University , , Furo-cho, Chikusa-ku, , ,","place":["Nagoya, Aichi, Japan, 464-8602"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yuki","family":"Komori","sequence":"additional","affiliation":[{"name":"Nagoya University , , Furo-cho, Chikusa-ku, , ,","place":["Nagoya, Aichi, Japan, 464-8602"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Takeshi","family":"Yanai","sequence":"additional","affiliation":[{"name":"Nagoya University , , Furo-cho, Chikusa-ku, , ,","place":["Nagoya, Aichi, Japan, 464-8602"]},{"name":"Nagoya University , , Furo-cho, Chikusa-ku, , ,","place":["Nagoya, Aichi, Japan, 464-8602"]},{"name":"Japan Science and Technology Agency, PRESTO , 4-1-8 Honcho , , ,","place":["Kawaguchi, Saitama, Japan, 332-0012"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8105-5414","authenticated-orcid":true,"given":"Thomas","family":"Sommerfeld","sequence":"additional","affiliation":[{"name":"Southeastern Louisiana University , , SLU 10878 , , ,","place":["Hammond, Louisiana, United States, 70402"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2185-0077","authenticated-orcid":true,"given":"Masahiro","family":"Ehara","sequence":"additional","affiliation":[{"name":"Institute for Molecular Science and Research Center for Computational Science , 38 Nishigonaka, Myodaiji , ,","place":["Okazaki, Japan, 444-8585"]},{"name":"Kyoto University , , Katsura, ,","place":["Kyoto, Japan, 615-8520"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"316","published-online":{"date-parts":[[2020,2,27]]},"reference":[{"key":"2026081721163252500_cit1","doi-asserted-by":"publisher","first-page":"557","DOI":"10.1021\/cr00079a005","article-title":"Temporary Anion\nStates of Polyatomic Hydrocarbons","volume":"87","author":"Jordan","year":"1987","journal-title":"Chem. 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Lett."},{"key":"2026081721163252500_cit18","doi-asserted-by":"publisher","first-page":"218","DOI":"10.1002\/qua.1042","article-title":"Efficient Method to\nPerform CAP\/CI Calculations for\nTemporary Anions","volume":"82","author":"Sommerfeld","year":"2001","journal-title":"Int. J. Quantum Chem."},{"key":"2026081721163252500_cit19","doi-asserted-by":"publisher","first-page":"5511","DOI":"10.1063\/1.1501903","article-title":"Complex Absorbing Potentials in the Framework of Electron\nPropagator Theory. I. General Formalism","volume":"117","author":"Santra","year":"2002","journal-title":"J.\nChem. Phys."},{"key":"2026081721163252500_cit20","doi-asserted-by":"publisher","first-page":"6188","DOI":"10.1063\/1.1557452","article-title":"Complex\nAbsorbing Potentials in the Framework of Electron Propagator Theory.\nII. Application to Temporary Anions","volume":"118","author":"Feuerbacher","year":"2003","journal-title":"J. Chem.\nPhys."},{"key":"2026081721163252500_cit21","doi-asserted-by":"publisher","first-page":"2267","DOI":"10.1080\/00268970500084158","article-title":"A General Formalism\nof the Fock Space Multireference Coupled Cluster\nMethod for Investigating Molecular Electronic Resonances","volume":"103","author":"Sajeev","year":"2005","journal-title":"Mol. Phys."},{"key":"2026081721163252500_cit22","doi-asserted-by":"publisher","first-page":"107","DOI":"10.1016\/j.cplett.2012.03.104","article-title":"CAP\/SAC-CI\nMethod for Calculating Resonance States\nof Metastable Anions","volume":"537","author":"Ehara","year":"2012","journal-title":"Chem. Phys. Lett."},{"key":"2026081721163252500_cit23","doi-asserted-by":"publisher","first-page":"17915","DOI":"10.1039\/c3cp52552j","article-title":"CAP\/EOM-CCSD Method\nfor the Study of Potential Curves of Resonant States","volume":"15","author":"Ghosh","year":"2013","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2026081721163252500_cit24","doi-asserted-by":"publisher","first-page":"310","DOI":"10.1021\/jz402482a","article-title":"A Fresh Look at Resonances and Complex\nAbsorbing Potentials:\nDensity Matrix-Based Approach","volume":"5","author":"Jagau","year":"2014","journal-title":"J. Phys. Chem.\nLett."},{"key":"2026081721163252500_cit25","doi-asserted-by":"publisher","first-page":"024102","DOI":"10.1063\/1.4885056","article-title":"Complex Absorbing Potentials within\nEOM-CC Family of\nMethods: Theory, Implementation, and Benchmarks","volume":"141","author":"Zuev","year":"2014","journal-title":"J. Chem. Phys."},{"key":"2026081721163252500_cit26","doi-asserted-by":"publisher","first-page":"184107","DOI":"10.1063\/1.4982950","article-title":"CAP-XMCQDPT2 Method for Molecular\nElectronic Resonances","volume":"146","author":"Kunitsa","year":"2017","journal-title":"J. Chem. Phys."},{"key":"2026081721163252500_cit27","doi-asserted-by":"publisher","first-page":"3223","DOI":"10.1021\/acs.jpca.9b01134","article-title":"Visualizing Complex-Valued Molecular\nOrbitals","volume":"123","author":"Al-Saadon","year":"2019","journal-title":"J. Phys. Chem. A"},{"key":"2026081721163252500_cit28","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/s0009-2614(98)00252-8","article-title":"The Multi-state\nCASPT2 Method","volume":"288","author":"Finley","year":"1998","journal-title":"Chem. Phys. Lett."},{"key":"2026081721163252500_cit29","doi-asserted-by":"publisher","first-page":"142","DOI":"10.1016\/j.cplett.2004.08.032","article-title":"A\nModified Definition of the Zeroth-Order\nHamiltonian in Multiconfigurational Perturbation Theory (CASPT2)","volume":"396","author":"Ghigo","year":"2004","journal-title":"Chem. Phys. Lett."},{"key":"2026081721163252500_cit30","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1016\/s0009-2614(97)00669-6","article-title":"Multiconfiguration\nPerturbation Theory with Imaginary\nLevel Shift","volume":"274","author":"Forsberg","year":"1997","journal-title":"Chem. Phys. Lett."},{"key":"2026081721163252500_cit31","doi-asserted-by":"publisher","first-page":"5483","DOI":"10.1021\/j100377a012","article-title":"Second-Order\nPerturbation Theory with a CASSCF Reference Function","volume":"94","author":"Andersson","year":"1990","journal-title":"J. Phys. Chem."},{"key":"2026081721163252500_cit32","doi-asserted-by":"publisher","first-page":"1218","DOI":"10.1063\/1.462209","article-title":"Second-Order Perturbation Theory\nwith a Complete Active Space Self-Consistent Field Reference Function","volume":"96","author":"Andersson","year":"1992","journal-title":"J. Chem. 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Theory Comput."},{"key":"2026081721163252500_cit39","doi-asserted-by":"publisher","first-page":"034105","DOI":"10.1063\/1.4905560","article-title":"Short-Range Stabilizing Potential\nfor Computing Energies and Lifetimes\nof Temporary Anions with Extrapolation Methods","volume":"142","author":"Sommerfeld","year":"2015","journal-title":"J. Chem. Phys."},{"key":"2026081721163252500_cit40","doi-asserted-by":"publisher","first-page":"4627","DOI":"10.1021\/acs.jctc.5b00465","article-title":"Complex Absorbing Potentials\nwith Voronoi Isosurfaces Wrapping Perfectly\nAround Molecules","volume":"11","author":"Sommerfeld","year":"2015","journal-title":"J. Chem. Theory Comput."},{"key":"2026081721163252500_cit41","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1002\/jcc.24010","article-title":"Projected\nCAP\/SAC-CI Method with\nSmooth Voronoi Potential for Calculating Resonance States","volume":"37","author":"Ehara","year":"2016","journal-title":"J. Comput. Chem."},{"key":"2026081721163252500_cit42","doi-asserted-by":"publisher","first-page":"2580","DOI":"10.1021\/acs.jpca.7b12669","article-title":"Temporary\nAnion States of Ethene\nInteracting with Single Molecules of Methane, Ethane, and Water","volume":"122","author":"Sommerfeld","year":"2018","journal-title":"J. Phys. Chem. A"},{"key":"2026081721163252500_cit43","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1002\/qua.24808","article-title":"Density Matrix Renormalization Group\nfor Ab Initio Calculations and Associated Dynamic Correlation Methods:\nA Review of Theory and Applications","volume":"115","author":"Yanai","year":"2015","journal-title":"Int. J.\nQuantum Chem."},{"key":"2026081721163252500_cit44","doi-asserted-by":"publisher","first-page":"204","DOI":"10.1007\/bf01343196","article-title":"Zur Quantentheorie\ndes Atomkernes","volume":"51","author":"Gamow","year":"1928","journal-title":"Z. 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