{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T11:21:43Z","timestamp":1753874503227,"version":"3.41.2"},"reference-count":109,"publisher":"AIP Publishing","issue":"15","license":[{"start":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T00:00:00Z","timestamp":1681862400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2023,4,19]],"date-time":"2023-04-19T00:00:00Z","timestamp":1681862400000},"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":[[2023,4,21]]},"abstract":"<jats:p>In this work, we present a computational approach that is able to incorporate vibrational effects in the computations of magnetic circular dichroism (MCD) spectra. The method combines our previous implementations to model absorption as well as fluorescence and phosphorescence spectra in the framework of excited state dynamics with a new technique to calculate MCD intensities, where molecular orientational averages are treated via semi-numerical quadrature. The implementation relies on a path integral approach that is employed to compute nuclear dynamics under the harmonic oscillator approximation (accounting for the nuclear potential energy surface) together with quasi-degenerate perturbative theory (to include the perturbation of an external magnetic field). We evaluate our implementation with a selected molecular set consisting of five aromatic organic molecules, namely, 1,4-benzoquinone, naphthalene, 2-naphthylamine, 2-naphthaldehyde, and benzene; we also included the MnO4\u2212 and the [Co(NH3)6]3+ transition metal complexes. This set is used to validate the ability of the approach to compute MCD A- and B-terms in conjunction with time-dependent density functional theory. The computed intensities are discussed in terms of the overall quality of the electronic structure treatments, vibrational modes, and the quality of the nuclear Hessians. It is shown that in the cases in which the potential energy surface is accurately represented, electric dipole-forbidden transitions are vibrationally activated, producing intensities relative to the dipole-allowed transitions in the same order of magnitude as the experimental measurements.<\/jats:p>","DOI":"10.1063\/5.0144845","type":"journal-article","created":{"date-parts":[[2023,4,27]],"date-time":"2023-04-27T17:09:03Z","timestamp":1682615343000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":6,"title":["Including vibrational effects in magnetic circular dichroism spectrum calculations in the framework of excited state dynamics"],"prefix":"10.1063","volume":"158","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6970-0609","authenticated-orcid":false,"given":"Nicol\u00e1s","family":"Foglia","sequence":"first","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Kohlenforschung 1 , Kaiser-Wilhelm-Platz 1, 45470 M\u00fclheim an der Ruhr, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7531-021X","authenticated-orcid":false,"given":"Bernardo","family":"De Souza","sequence":"additional","affiliation":[{"name":"FAccTs GmbH 2 , K\u00f6ln, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1550-5162","authenticated-orcid":false,"given":"Dimitrios","family":"Maganas","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Kohlenforschung 1 , Kaiser-Wilhelm-Platz 1, 45470 M\u00fclheim an der Ruhr, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4691-0547","authenticated-orcid":false,"given":"Frank","family":"Neese","sequence":"additional","affiliation":[{"name":"Max-Planck-Institut f\u00fcr Kohlenforschung 1 , Kaiser-Wilhelm-Platz 1, 45470 M\u00fclheim an der Ruhr, Germany"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"317","published-online":{"date-parts":[[2023,4,19]]},"reference":[{"key":"2023081106461784000_c1","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1038\/s43586-021-00034-1","article-title":"Computational molecular spectroscopy","volume":"1","year":"2021","journal-title":"Nat. Rev. Methods Primers"},{"key":"2023081106461784000_c2","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1073\/pnas.53.3.579","article-title":"Magnetic circular dichroism studies: A preliminary report","volume":"53","year":"1965","journal-title":"Proc. Natl. Acad. Sci. U. S. A."},{"key":"2023081106461784000_c3","doi-asserted-by":"publisher","first-page":"6824","DOI":"10.1021\/ja00490a004","article-title":"Magnetic circular dichroism of cyclic .pi.-electron systems. 4. Aza analogs of benzene","volume":"100","year":"1978","journal-title":"J. Am. Chem. Soc."},{"key":"2023081106461784000_c4","doi-asserted-by":"publisher","first-page":"6828","DOI":"10.1021\/ja00490a005","article-title":"Magnetic circular dichroism of cyclic .pi.-electron systems. 5. Derivatives of pyridine","volume":"100","year":"1978","journal-title":"J. Am. Chem. Soc."},{"key":"2023081106461784000_c5","doi-asserted-by":"publisher","first-page":"6834","DOI":"10.1021\/ja00490a006","article-title":"Magnetic circular dichroism of cyclic .pi.-electron systems. 6. Pyridones and related heterocycles","volume":"100","year":"1978","journal-title":"J. Am. Chem. Soc."},{"key":"2023081106461784000_c6","doi-asserted-by":"publisher","first-page":"6838","DOI":"10.1021\/ja00490a007","article-title":"Magnetic circular dichroism of cyclic .pi.-electron systems. 7. Aza analogs of naphthalene","volume":"100","year":"1978","journal-title":"J. Am. Chem. Soc."},{"key":"2023081106461784000_c7","doi-asserted-by":"publisher","first-page":"6844","DOI":"10.1021\/ja00490a008","article-title":"Magnetic circular dichroism of cyclic .pi.-electron systems. 8. Derivatives of naphthalene","volume":"100","year":"1978","journal-title":"J. Am. Chem. Soc."},{"key":"2023081106461784000_c8","doi-asserted-by":"publisher","first-page":"3845","DOI":"10.1016\/s0040-4020(01)99999-5","article-title":"Magnetic circular dichroism of aromatic molecules","volume":"40","year":"1984","journal-title":"Tetrahedron"},{"key":"2023081106461784000_c9","doi-asserted-by":"publisher","first-page":"1549","DOI":"10.1351\/pac198052061549","article-title":"Electronic structure of aromatic \u03c0-electron systems as reflected in their MCD spectra","volume":"52","year":"1980","journal-title":"Pure Appl. Chem."},{"key":"2023081106461784000_c10","doi-asserted-by":"publisher","first-page":"5730","DOI":"10.1021\/ja01023a013","article-title":"Magnetic circular dichroism of d8 square-planar complexes","volume":"90","year":"1968","journal-title":"J. Am. Chem. Soc."},{"key":"2023081106461784000_c11","doi-asserted-by":"publisher","first-page":"386","DOI":"10.1016\/0009-2614(76)80102-9","article-title":"Use of semi-empirical models for calculation of B terms in MCD spectra. Aromatic hydrocarbons: Prediction of substituent and heteroatom effects from PPP model","volume":"39","year":"1976","journal-title":"Chem. Phys. Lett."},{"key":"2023081106461784000_c12","doi-asserted-by":"publisher","first-page":"6801","DOI":"10.1021\/ja00490a001","article-title":"Magnetic circular dichroism of cyclic .pi.-electron systems. 1. Algebraic solution of the perimeter model for the A and B terms of high-symmetry systems with a (4N + 2)-electron [n]annulene perimeter","volume":"100","year":"1978","journal-title":"J. Am. Chem. Soc."},{"key":"2023081106461784000_c13","doi-asserted-by":"publisher","first-page":"3754","DOI":"10.1073\/pnas.70.12.3754","article-title":"Molecular orbital calculations of magnetic circular dichroism spectra: A benzene-indole sequence","volume":"70","year":"1973","journal-title":"Proc. Natl. Acad. Sci."},{"key":"2023081106461784000_c14","doi-asserted-by":"publisher","first-page":"6198","DOI":"10.1021\/ja00540a004","article-title":"Theoretical study of the optical absorption and magnetic circular dichroism spectra of cyclopropane","volume":"102","year":"1980","journal-title":"J. Am. Chem. Soc."},{"key":"2023081106461784000_c15","doi-asserted-by":"publisher","first-page":"164113","DOI":"10.1063\/1.2080027","article-title":"Theoretical studies on magnetic circular dichroism by the finite perturbation method with relativistic corrections","volume":"123","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c16","doi-asserted-by":"publisher","first-page":"1531","DOI":"10.1002\/jcc.23277","article-title":"Computation of magnetic circular dichroism by sum-over-states summations","volume":"34","year":"2013","journal-title":"J. Comput. Chem."},{"key":"2023081106461784000_c17","doi-asserted-by":"publisher","first-page":"5586","DOI":"10.1039\/c8cp07849a","article-title":"Magnetic circular dichroism spectra of transition metal complexes calculated from restricted active space wavefunctions","volume":"21","year":"2019","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023081106461784000_c18","doi-asserted-by":"publisher","first-page":"17300","DOI":"10.1039\/c7cp02572f","article-title":"Magnetic circular dichroism of UCl6\u2212 in the ligand-to-metal charge-transfer spectral region","volume":"19","year":"2017","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023081106461784000_c19","doi-asserted-by":"publisher","first-page":"3124","DOI":"10.1021\/acs.organomet.9b00315","article-title":"Insight into the electronic structure of formal lanthanide(II) complexes using magnetic circular dichroism spectroscopy","volume":"38","year":"2019","journal-title":"Organometallics"},{"key":"2023081106461784000_c20","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/s0009-2614(98)01315-3","article-title":"Ab initio determinations of magnetic circular dichroism","volume":"300","year":"1999","journal-title":"Chem. Phys. Lett."},{"key":"2023081106461784000_c21","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s00214-006-0235-9","article-title":"An IEF-PCM study of solvent effects on the Faraday {\\mathcal {B}} term of MCD","volume":"119","year":"2008","journal-title":"Theor. Chem. Acc."},{"key":"2023081106461784000_c22","doi-asserted-by":"publisher","first-page":"10942","DOI":"10.1063\/1.1747828","article-title":"Calculation of the A term of magnetic circular dichroism based on time dependent-density functional theory I. Formulation and implementation","volume":"120","year":"2004","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c23","doi-asserted-by":"publisher","first-page":"094112","DOI":"10.1063\/1.1856453","article-title":"Ab initio calculation of the C\u2215D ratio of magnetic circular dichroism","volume":"122","year":"2005","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c24","doi-asserted-by":"publisher","first-page":"144105","DOI":"10.1063\/1.2901967","article-title":"Application of magnetically perturbed time-dependent density functional theory to magnetic circular dichroism: Calculation of B terms","volume":"128","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c25","doi-asserted-by":"publisher","first-page":"1847","DOI":"10.1021\/ic981264d","article-title":"MCD C-term signs, saturation behavior, and determination of band polarizations in randomly oriented systems with spin S \u2265 1\/2. Applications to S = 1\/2 and S = 5\/2","volume":"38","year":"1999","journal-title":"Inorg. Chem."},{"key":"2023081106461784000_c26","doi-asserted-by":"publisher","first-page":"114117","DOI":"10.1063\/1.2894297","article-title":"First-principles calculations of magnetic circular dichroism spectra","volume":"128","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c27","doi-asserted-by":"publisher","first-page":"6021","DOI":"10.1039\/b902743b","article-title":"Multireference ab\u00a0initio studies of zero-field splitting and magnetic circular dichroism spectra of tetrahedral Co(II) complexes","volume":"30","year":"2009","journal-title":"Dalton Trans."},{"key":"2023081106461784000_c28","doi-asserted-by":"publisher","first-page":"2909","DOI":"10.1039\/c4sc03268c","article-title":"Magnetic circular dichroism and computational study of mononuclear and dinuclear iron(IV) complexes","volume":"6","year":"2015","journal-title":"Chem. Sci."},{"key":"2023081106461784000_c29","doi-asserted-by":"publisher","first-page":"14312","DOI":"10.1021\/jacs.6b07708","article-title":"Magnetic circular dichroism evidence for an unusual electronic structure of a tetracarbene\u2013oxoiron(IV) complex","volume":"138","year":"2016","journal-title":"J. Am. Chem. Soc."},{"key":"2023081106461784000_c30","doi-asserted-by":"publisher","first-page":"3102","DOI":"10.1021\/acs.inorgchem.7b00097","article-title":"Magneto-structural correlations in pseudotetrahedral forms of the [Co(SPh)4]2\u2013 complex probed by magnetometry, MCD spectroscopy, advanced EPR techniques, and ab\u00a0initio electronic structure calculations","volume":"56","year":"2017","journal-title":"Inorg. Chem."},{"key":"2023081106461784000_c31","doi-asserted-by":"publisher","first-page":"6421","DOI":"10.1021\/acs.inorgchem.8b00486","article-title":"Investigations of the magnetic and spectroscopic properties of V(III) and V(IV) complexes","volume":"57","year":"2018","journal-title":"Inorg. Chem."},{"key":"2023081106461784000_c32","doi-asserted-by":"publisher","first-page":"114107","DOI":"10.1063\/1.5129029","article-title":"Mechanism of L2,3-edge x-ray magnetic circular dichroism intensity from quantum chemical calculations and experiment\u2014A case study on V(IV)\/V(III) complexes","volume":"152","year":"2020","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c33","doi-asserted-by":"publisher","first-page":"084120","DOI":"10.1063\/5.0094709","article-title":"Going beyond the electric-dipole approximation in the calculation of absorption and (magnetic) circular dichroism spectra including scalar relativistic and spin\u2013orbit coupling effects","volume":"157","year":"2022","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c34","doi-asserted-by":"publisher","first-page":"57","DOI":"10.1098\/rspa.1976.0163","article-title":"Study of vibronic, spin-orbit and vibronic-spin-orbit couplings of formaldehyde with applications to radiative and non-radiative processes","volume":"352","year":"1976","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2023081106461784000_c35","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1098\/rspa.1973.0113","article-title":"On the theory of non-radiative transfer of electronic excitation","volume":"335","year":"1973","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2023081106461784000_c36","doi-asserted-by":"publisher","first-page":"7188","DOI":"10.1063\/1.1607311","article-title":"Effects of the Duschinsky mode-mixing mechanism on temperature dependence of electron transfer processes","volume":"119","year":"2003","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c37","doi-asserted-by":"publisher","first-page":"7778","DOI":"10.1021\/jp037739q","article-title":"Photoinduced cooling of polyatomic molecules in an electronically excited state in the presence of dushinskii rotations","volume":"108","year":"2004","journal-title":"J. Phys. Chem. A"},{"key":"2023081106461784000_c38","doi-asserted-by":"publisher","first-page":"164303","DOI":"10.1063\/1.2895041","article-title":"Ab initio spectroscopy and photoinduced cooling of the trans-stilbene molecule","volume":"128","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c39","doi-asserted-by":"publisher","first-page":"7817","DOI":"10.1021\/jp101568f","article-title":"Theory of excited state decays and optical spectra: Application to polyatomic molecules","volume":"114","year":"2010","journal-title":"J. Phys. Chem. A"},{"key":"2023081106461784000_c40","doi-asserted-by":"publisher","first-page":"215","DOI":"10.1016\/j.chemphys.2010.03.004","article-title":"Vibration correlation function formalism of radiative and non-radiative rates for complex molecules","volume":"370","year":"2010","journal-title":"Chem. Phys. Lett."},{"key":"2023081106461784000_c41","doi-asserted-by":"publisher","first-page":"4097","DOI":"10.1021\/ct400450k","article-title":"General time dependent approach to vibronic spectroscopy including Franck\u2013Condon, Herzberg\u2013Teller, and Duschinsky effects","volume":"9","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"2023081106461784000_c42","doi-asserted-by":"publisher","first-page":"476","DOI":"10.1002\/qua.22197","article-title":"Computational approach to the study of the lineshape of absorption and electronic circular dichroism spectra","volume":"110","year":"2010","journal-title":"Int. J. Quantum Chem."},{"key":"2023081106461784000_c43","doi-asserted-by":"publisher","first-page":"457","DOI":"10.1002\/andp.19273892002","article-title":"Zur Quantentheorie der Molekeln","volume":"389","year":"1927","journal-title":"Ann. Phys."},{"key":"2023081106461784000_c44","doi-asserted-by":"publisher","first-page":"259","DOI":"10.1016\/0009-2614(88)87441-4","article-title":"Vibronic activity in MCD spectra: Calculation of the induced B terms in the \u201corbital following\u201d framework","volume":"146","year":"1988","journal-title":"Chem. Phys. Lett."},{"key":"2023081106461784000_c45","doi-asserted-by":"publisher","first-page":"1557","DOI":"10.1021\/ct301101h","article-title":"First principles studies of the vibrationally resolved magnetic circular dichroism spectra of biphenylene","volume":"9","year":"2013","journal-title":"J. Chem. Theory Comput."},{"key":"2023081106461784000_c46","doi-asserted-by":"publisher","first-page":"540","DOI":"10.1021\/ct8004744","article-title":"Fully integrated approach to compute vibrationally resolved optical spectra: From small molecules to macrosystems","volume":"5","year":"2009","journal-title":"J. Chem. Theory Comput."},{"key":"2023081106461784000_c47","doi-asserted-by":"publisher","first-page":"2348","DOI":"10.1002\/cphc.201600313","article-title":"Resolving electronic transitions in synthetic fluorescent protein chromophores by magnetic circular dichroism","volume":"17","year":"2016","journal-title":"ChemPhysChem"},{"key":"2023081106461784000_c48","doi-asserted-by":"publisher","first-page":"9064","DOI":"10.1021\/acs.jpca.7b10120","article-title":"Vibrational structure in magnetic circular dichroism spectra of polycyclic aromatic hydrocarbons","volume":"121","year":"2017","journal-title":"J. Phys. Chem. A"},{"key":"2023081106461784000_c49","doi-asserted-by":"publisher","first-page":"144301","DOI":"10.1063\/1.4979570","article-title":"On the magnetic circular dichroism of benzene. A density-functional study","volume":"146","year":"2017","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c50","doi-asserted-by":"publisher","first-page":"5483","DOI":"10.1039\/d1dt00513h","article-title":"Near-infrared C-term MCD spectroscopy of octahedral uranium(V) complexes","volume":"50","year":"2021","journal-title":"Dalton Trans."},{"key":"2023081106461784000_c51","doi-asserted-by":"publisher","first-page":"034104","DOI":"10.1063\/1.5010895","article-title":"On the theoretical prediction of fluorescence rates from first principles using the path integral approach","volume":"148","year":"2018","journal-title":"J. Chem. Phys."},{"first-page":"e1606","volume-title":"Software Update: The ORCA Program System\u2014Version 5.0","year":"2022","key":"2023081106461784000_c52"},{"key":"2023081106461784000_c53","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":"WIREs Comput. Mol. Sci."},{"key":"2023081106461784000_c54","doi-asserted-by":"publisher","first-page":"224108","DOI":"10.1063\/5.0004608","article-title":"The ORCA quantum chemistry program package","volume":"152","year":"2020","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c55","doi-asserted-by":"publisher","first-page":"73","DOI":"10.1002\/wcms.81","article-title":"The ORCA program system","volume":"2","year":"2012","journal-title":"Wiley Interdiscip. Rev.: Comput. Mol. Sci."},{"key":"2023081106461784000_c56","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. Chem. Theory Comput."},{"key":"2023081106461784000_c57","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1080\/00268976.2016.1187773","article-title":"Rotationally averaged linear absorption spectra beyond the electric-dipole approximation","volume":"115","year":"2017","journal-title":"Mol. Phys."},{"key":"2023081106461784000_c58","doi-asserted-by":"publisher","first-page":"234107","DOI":"10.1063\/1.4771959","article-title":"Efficient and automatic calculation of optical band shapes and resonance Raman spectra for larger molecules within the independent mode displaced harmonic oscillator model","volume":"137","year":"2012","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c59","doi-asserted-by":"publisher","first-page":"3098","DOI":"10.1103\/physreva.38.3098","article-title":"Density-functional exchange-energy approximation with correct asymptotic behavior","volume":"38","year":"1988","journal-title":"Phys. Rev. A"},{"key":"2023081106461784000_c60","doi-asserted-by":"publisher","first-page":"5648","DOI":"10.1063\/1.464913","article-title":"Density-functional thermochemistry. III. The role of exact exchange","volume":"98","year":"1993","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c61","doi-asserted-by":"publisher","first-page":"785","DOI":"10.1103\/physrevb.37.785","article-title":"Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density","volume":"37","year":"1988","journal-title":"Phys. Rev. B"},{"journal-title":"Version 2.8.0, Github","article-title":"Libint: A library for the evaluation of molecular integrals of many-body operators over Gaussian functions","year":"2022","key":"2023081106461784000_c62"},{"key":"2023081106461784000_c63","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.softx.2017.11.002","article-title":"Recent developments in LIBXC\u2014A comprehensive library of functionals for density functional theory","volume":"7","year":"2018","journal-title":"SoftwareX"},{"key":"2023081106461784000_c64","doi-asserted-by":"publisher","first-page":"3297","DOI":"10.1039\/b508541a","article-title":"Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy","volume":"7","year":"2005","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023081106461784000_c65","doi-asserted-by":"publisher","first-page":"1057","DOI":"10.1039\/b515623h","article-title":"Accurate Coulomb-fitting basis sets for H to Rn","volume":"8","year":"2006","journal-title":"Phys. Chem. Chem. Phys."},{"key":"2023081106461784000_c66","doi-asserted-by":"publisher","first-page":"652","DOI":"10.1016\/0009-2614(95)00838-u","article-title":"Auxiliary basis sets to approximate Coulomb potentials (Chem. Phys. Letters 240, 283\u2013290 (1995)","volume":"242","year":"1995","journal-title":"Chem. Phys. Lett."},{"key":"2023081106461784000_c67","doi-asserted-by":"publisher","first-page":"98","DOI":"10.1016\/j.chemphys.2008.10.036","article-title":"Efficient, approximate and parallel Hartree\u2013Fock and hybrid DFT calculations. A \u2018chain-of-spheres\u2019 algorithm for the Hartree\u2013Fock exchange","volume":"356","year":"2009","journal-title":"Chem. Phys."},{"key":"2023081106461784000_c68","doi-asserted-by":"publisher","first-page":"144105","DOI":"10.1063\/1.3646921","article-title":"An overlap fitted chain of spheres exchange method","volume":"135","year":"2011","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c69","doi-asserted-by":"publisher","first-page":"104109","DOI":"10.1063\/5.0058766","article-title":"An improved chain of spheres for exchange algorithm","volume":"155","year":"2021","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c70","doi-asserted-by":"publisher","first-page":"1995","DOI":"10.1021\/jp9716997","article-title":"Quantum calculation of molecular energies and energy gradients in solution by a conductor solvent model","volume":"102","year":"1998","journal-title":"J. Phys. Chem. A"},{"key":"2023081106461784000_c71","doi-asserted-by":"publisher","first-page":"11060","DOI":"10.1021\/jp992097l","article-title":"A smooth solvation potential based on the conductor-like screening model","volume":"103","year":"1999","journal-title":"J. Phys. Chem. A"},{"key":"2023081106461784000_c72","doi-asserted-by":"publisher","first-page":"922","DOI":"10.1002\/jcc.26139","article-title":"Effect of the solute cavity on the solvation energy and its derivatives within the framework of the Gaussian charge scheme","volume":"41","year":"2020","journal-title":"J. Comput. Chem."},{"key":"2023081106461784000_c73","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/0041-5553(75)90133-0","article-title":"Values of the nodes and weights of ninth to seventeenth order gauss-markov quadrature formulae invariant under the octahedron group with inversion","volume":"15","year":"1975","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"2023081106461784000_c74","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1016\/0041-5553(76)90100-2","article-title":"Quadratures on a sphere","volume":"16","year":"1976","journal-title":"USSR Comput. Math. Math. Phys."},{"key":"2023081106461784000_c75","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1090\/s0025-5718-1965-0178586-1","article-title":"An algorithm for the machine calculation of complex Fourier series","volume":"19","year":"1965","journal-title":"Math. Comput."},{"key":"2023081106461784000_c76","doi-asserted-by":"publisher","first-page":"702","DOI":"10.1007\/s00775-006-0138-1","article-title":"A critical evaluation of DFT, including time-dependent DFT, applied to bioinorganic chemistry","volume":"11","year":"2006","journal-title":"JBIC, J. Biol. Inorg. Chem."},{"key":"2023081106461784000_c77","doi-asserted-by":"publisher","first-page":"526","DOI":"10.1016\/j.ccr.2008.05.014","article-title":"Prediction of molecular properties and molecular spectroscopy with density functional theory: From fundamental theory to exchange-coupling","volume":"253","year":"2009","journal-title":"Coord. Chem. Rev."},{"key":"2023081106461784000_c78","doi-asserted-by":"publisher","first-page":"134110","DOI":"10.1063\/1.2889385","article-title":"Benchmarks for electronically excited states: CASPT2, CC2, CCSD, and CC3","volume":"128","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c79","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/0301-0104(87)80156-8","article-title":"The long-wavelength MCD of some quinones and its interpretation by semi-empirical MO methods","volume":"113","year":"1987","journal-title":"Chem. Phys. Lett."},{"key":"2023081106461784000_c80","doi-asserted-by":"publisher","first-page":"5358","DOI":"10.1063\/1.1677047","article-title":"Electronic states and spectra of p-benzoquinone","volume":"56","year":"1972","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c81","doi-asserted-by":"publisher","first-page":"1604","DOI":"10.1063\/1.436734","article-title":"Distant intramolecular interaction between identical chromophores: The n-\u03c0* excited states of p-benzoquinone","volume":"69","year":"1978","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c82","doi-asserted-by":"publisher","first-page":"275","DOI":"10.1016\/s0301-0104(01)00241-5","article-title":"Excited electronic states of p-benzoquinone","volume":"264","year":"2001","journal-title":"Chem. Phys. Lett."},{"key":"2023081106461784000_c83","doi-asserted-by":"publisher","first-page":"9536","DOI":"10.1063\/1.478918","article-title":"Theoretical study of the electronic spectrum of p-benzoquinone","volume":"110","year":"1999","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c84","doi-asserted-by":"publisher","first-page":"1520","DOI":"10.1246\/bcsj.35.1520","article-title":"Electronic states of p-benzoquinone. VIII. Vibrational analysis of the vapor absorption spectrum around 2900 \u00c5","volume":"35","year":"1962","journal-title":"Bull. Chem. Soc. Jpn."},{"key":"2023081106461784000_c85","doi-asserted-by":"publisher","first-page":"932","DOI":"10.1063\/1.1696084","article-title":"Molecular vibrations of quinones. V. Normal coordinate analysis of p-benzoquinone and its isotopic derivatives","volume":"42","year":"1965","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c86","doi-asserted-by":"publisher","first-page":"464","DOI":"10.1016\/0009-2614(72)80401-9","article-title":"Electron energy-loss spectroscopy of naphthalene vapor","volume":"16","year":"1972","journal-title":"Chem. Phys. Lett."},{"key":"2023081106461784000_c87","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/0022-2852(68)90143-4","article-title":"The intensity of absorption of naphthalene from 30 000\u00a0cm\u22121 to 53 000\u00a0cm\u22121","volume":"26","year":"1968","journal-title":"J. Mol. Spectrosc."},{"key":"2023081106461784000_c88","doi-asserted-by":"publisher","first-page":"104103","DOI":"10.1063\/1.2973541","article-title":"Benchmarks for electronically excited states: Time-dependent density functional theory and density functional theory based multireference configuration interaction","volume":"129","year":"2008","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c89","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/BF01113865","article-title":"A CASPT2 study of the valence and lowest Rydberg electronic states of benzene and phenol","volume":"91","year":"1995","journal-title":"Theor. Chim. Acta"},{"key":"2023081106461784000_c90","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1016\/0009-2614(86)80420-1","article-title":"Vacuum ultraviolet MCD and absorption spectra of benzene isolated in an Ar matrix using synchrotron radiation","volume":"130","year":"1986","journal-title":"Chem. Phys. Lett."},{"volume-title":"Advanced Inorganic Chemistry","year":"1962","key":"2023081106461784000_c91"},{"key":"2023081106461784000_c92","doi-asserted-by":"publisher","first-page":"1614","DOI":"10.1021\/ic50055a002","article-title":"Magnetic optical activity of d .fwdarw. d transitions. Octahedral chromium (III), cobalt (III), cobalt (II), nickel (II), and manganese (II) complexes","volume":"6","year":"1967","journal-title":"Inorg. Chem."},{"journal-title":"Molecular Electronic Structures of Transition Metal Complexes II,","article-title":"Chronicle about the development of electronic structure theories for transition metal complexes","key":"2023081106461784000_c93","doi-asserted-by":"publisher","DOI":"10.1007\/430_2011_47"},{"key":"2023081106461784000_c94","doi-asserted-by":"publisher","first-page":"1168","DOI":"10.1021\/jp0456990","article-title":"Vibronic structure of the permanganate absorption spectrum from time-dependent density functional calculations","volume":"109","year":"2005","journal-title":"J. Phys. Chem. A"},{"key":"2023081106461784000_c95","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/bf00537508","article-title":"Low temperature absorption spectra of KMnO4 in KClo4","volume":"7","year":"1967","journal-title":"Theor. Chim. Acta"},{"key":"2023081106461784000_c96","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1098\/rspa.1970.0203","article-title":"Ab initio molecular orbital calculations of the ground and excited states of the permanganate and chromate ions","volume":"320","year":"1970","journal-title":"Proc. R. Soc. London, Ser. A"},{"key":"2023081106461784000_c97","doi-asserted-by":"publisher","first-page":"219","DOI":"10.1016\/0009-2614(71)85034-0","article-title":"Ab initio calculations of the excited states of the permanganate and chromate ions","volume":"9","year":"1971","journal-title":"Chem. Phys. Lett."},{"key":"2023081106461784000_c98","doi-asserted-by":"publisher","first-page":"791","DOI":"10.1063\/1.432225","article-title":"Calculations on the permanganate ion in the ground and excited states","volume":"64","year":"1976","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c99","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1016\/0301-0104(76)80056-0","article-title":"The electronic structures of tetrahedral oxo-complexes. The nature of the \u201ccharge transfer\u201d transitions","volume":"16","year":"1976","journal-title":"Chem. Phys."},{"key":"2023081106461784000_c100","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1016\/0301-0104(83)80009-3","article-title":"Limited configuration interaction calculation of the optical spectrum for the permanganate ion","volume":"74","year":"1983","journal-title":"Chem. Phys."},{"key":"2023081106461784000_c101","doi-asserted-by":"publisher","first-page":"1209","DOI":"10.1080\/00268978300101881","article-title":"Analysis of a configuration interaction calculation for a charge transfer transition in MnO4\u2212","volume":"49","year":"1983","journal-title":"Mol. Phys."},{"key":"2023081106461784000_c102","doi-asserted-by":"publisher","first-page":"8287","DOI":"10.1063\/1.461308","article-title":"Theoretical study on the ground and excited states of MnO\u22124","volume":"95","year":"1991","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c103","doi-asserted-by":"publisher","first-page":"10815","DOI":"10.1063\/1.480445","article-title":"Combining coupled cluster and perturbation theory","volume":"111","year":"1999","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c104","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1063\/1.481828","article-title":"Extended similarity transformed equation-of-motion coupled cluster theory (extended-STEOM-CC): Applications to doubly excited states and transition metal compounds","volume":"113","year":"2000","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c105","doi-asserted-by":"publisher","first-page":"9867","DOI":"10.1021\/ic4009625","article-title":"Theoretical studies on the photoelectron and absorption spectra of MnO4\u2013 and TcO4\u2013","volume":"52","year":"2013","journal-title":"Inorg. Chem."},{"key":"2023081106461784000_c106","doi-asserted-by":"publisher","first-page":"4606","DOI":"10.1063\/1.474821","article-title":"Excited-state energies and distortions of d0 transition metal tetraoxo complexes: A density functional study","volume":"107","year":"1997","journal-title":"J. Chem. Phys."},{"key":"2023081106461784000_c107","doi-asserted-by":"publisher","first-page":"681","DOI":"10.1002\/(sici)1097-461x(1996)58:6&lt;681::aid-qua10&gt;3.0.co;2-0","article-title":"A density functional study of the electronic spectrum of permanganate","volume":"58","year":"1996","journal-title":"Int. J. Quantum Chem."},{"key":"2023081106461784000_c108","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1021\/cr00005a001","article-title":"Approximate density functional theory as a practical tool in molecular energetics and dynamics","volume":"91","year":"1991","journal-title":"Chem. Rev."},{"key":"2023081106461784000_c109","doi-asserted-by":"publisher","first-page":"722","DOI":"10.1063\/1.1727633","article-title":"Faraday effect of charge-transfer transitions in Fe(CN)63\u2212, MnO4\u2212, and CrO42\u2212","volume":"45","year":"1966","journal-title":"J. Chem. Phys."}],"container-title":["The Journal of Chemical Physics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0144845\/16974904\/154108_1_5.0144845.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0144845\/16974904\/154108_1_5.0144845.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/pubs.aip.org\/aip\/jcp\/article-pdf\/doi\/10.1063\/5.0144845\/16974904\/154108_1_5.0144845.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T20:20:42Z","timestamp":1748377242000},"score":1,"resource":{"primary":{"URL":"https:\/\/pubs.aip.org\/jcp\/article\/158\/15\/154108\/2883455\/Including-vibrational-effects-in-magnetic-circular"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,19]]},"references-count":109,"journal-issue":{"issue":"15","published-print":{"date-parts":[[2023,4,21]]}},"URL":"https:\/\/doi.org\/10.1063\/5.0144845","relation":{},"ISSN":["0021-9606","1089-7690"],"issn-type":[{"type":"print","value":"0021-9606"},{"type":"electronic","value":"1089-7690"}],"subject":[],"published-other":{"date-parts":[[2023,4,21]]},"published":{"date-parts":[[2023,4,19]]},"article-number":"154108"}}