Multireference Approaches for Excited States of Molecules Hans Lischka, Dana Nachtigallova, Adélia Aquino, Peter Szalay, Felix Plasser, Francisco Machado, Mario Barbatti To cite this version: Hans Lischka, Dana Nachtigallova, Adélia Aquino, Peter Szalay, Felix Plasser, et al.. Multireference Approaches for Excited States of Molecules. Chemical Reviews, American Chemical Society, 2018, 118 (15), pp.7293-7361. 10.1021/acs.chemrev.8b00244. hal-01965456 HAL Id: hal-01965456 https://hal-amu.archives-ouvertes.fr/hal-01965456 Submitted on 26 Dec 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Multireference Approaches for Excited States of Molecules † Hans Lischkaa,b,c*, Dana Nachtigallovád,e, Adélia J. A. Aquinoa,b,f, Péter G. Szalayg, Felix Plasserc,h, Francisco B. C. Machadoi, Mario Barbattih aSchool of Pharmaceutical Sciences and Technology, Tianjin University, Tianjin 300072, P.R. China bDepartment of Chemistry and Biochemistry, Texas Tech University, Lubbock, Texas 79409, United States cInstitute of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Straße 17, 1090 Vienna, Austria ORCID: 0000-0002-5656-3975 dInstitute of Organic Chemistry and Biochemistry v.v.i., The Czech Academy of Sciences, Flemingovo nám. 2, 160610 Prague 6, Czech Republic eRegional Centre of Advanced Technologies and Materials, Palacký University, 77146 Olomouc, Czech Republic ORCID: 0000-0002-9588-8625 fInstitute for Soil Research, University of Natural Resources and Life Sciences Vienna, Peter-Jordan- Strasse 82, A-1190 Vienna, Austria ORCID: 0000-0003-4891-6512 gELTE Eötvös Loránd University, Laboratory of Theoretical Chemistry, Pázmány Péter sétány 1/A, 1117 Budapest, Hungary ORCID: 0000-0003-1885-3557 hDepartment of Chemistry, Loughborough University, LE11 3TU, United Kingdom ORCID: 0000-0003-0751-148X iDepartamento de Química, Instituto Tecnológico de Aeronáutica, São José dos Campos 12228-900, São Paulo, Brazil ORCID: 0000-0002-2064-3463 hAix Marseille Univ, CNRS, ICR, Marseille, France ORCID: 0000-0001-9336-6607; ResearchID: F-5647-2014 † Cite this paper as: Lischka, H.; Nachtigallová, D.; Aquino, A. J. A.; Szalay, P. G.; Plasser, F.; Machado, F. B. C.; Barbatti, M. Multireference Approaches for Excited States of Molecules. Chem. Rev. 2018, DOI: 10.1021/acs.chemrev.8b00244. This document is the unedited Author’s version of a Submitted Work that was subsequently accepted for publication in Chemical Reviews, copyright © American Chemical Society after peer review. To access the final edited and published work see dx.doi.org/10.1021/acs.chemrev.8b00244 * Corresponding author: [email protected] 1 ABSTRACT .............................................................................................................................................................. 4 1. INTRODUCTION ............................................................................................................................................ 5 2. THEORY AND METHODS ............................................................................................................................... 9 2.1. CONFIGURATION INTERACTION ........................................................................................................................... 9 2.1.1. Basic concepts ........................................................................................................................................ 9 2.1.2. Single- and Multireference Spaces ....................................................................................................... 10 2.1.3. Size-extensivity Problem ...................................................................................................................... 14 2.1.4. Contracted CI ....................................................................................................................................... 16 2.1.5. Calculation of Excited States ................................................................................................................ 18 2.1.6. Individual Selection Schemes ............................................................................................................... 19 2.1.7. Local MRCI Approaches ....................................................................................................................... 19 2.1.8. Natural Orbitals for Use in MRCI ......................................................................................................... 20 2.2. MULTICONFIGURATION SELF-CONSISTENT FIELD METHOD .................................................................................... 21 2.2.1. Multiple MCSCF Solutions and Symmetry Breaking ............................................................................. 24 2.3. COUPLED CLUSTER METHODS: .......................................................................................................................... 28 2.3.1. Single reference coupled cluster methods to describe excited states .................................................. 28 2.3.2. Multireference coupled cluster Methods ............................................................................................. 32 2.3.2.1. MRCC methods based on the Jeziorski-Monkhorst ansatz ........................................................................ 34 2.3.2.2. Using multideterminantal vacuum state: internally contracted MRCC methods ...................................... 37 2.3.2.3. MRCC based on SR formalism .................................................................................................................... 41 2.3.2.4. Outlook on MRCC for excited states .......................................................................................................... 42 2.4. MUTIREFERENCE PERTURBATION THEORY ........................................................................................................... 43 2.5. MRCI WITH SEMIEMPIRICAL HAMILTONIANS ...................................................................................................... 52 2.6. MULTIREFERENCE DENSITY FUNCTIONAL THEORY ................................................................................................ 56 2.6.1. Nondynamical electron correlation in DFT........................................................................................... 56 2.6.2. Semiempirical MRCI with DFT .............................................................................................................. 57 2.6.3. Hybrid wavefunction and DFT .............................................................................................................. 59 2.6.4. Multiconfigurational DFT ..................................................................................................................... 61 2.6.5. Ensemble DFT ....................................................................................................................................... 62 2.7. EMERGING ALGORITHMS: DMRG, FCIQMC ...................................................................................................... 64 2.7.1. DMRG ................................................................................................................................................... 64 2.7.2. FCIQMC ................................................................................................................................................ 69 2.8. ASPECTS OF ANALYTIC GRADIENTS AND NONADIABATIC COUPLINGS .......................................................................... 74 2 2.9. DIAGNOSTICS OF MULTIREFERENCE CHARACTER, ANALYSIS OF EXCITED STATES ........................................................... 78 3. APPLICATIONS OF MULTIREFERENCE METHODS TO MOLECULAR EXCITED STATES ..................................... 82 3.1. DIATOMICS AND SMALL MOLECULES .................................................................................................................. 82 3.2. SINGLET OXYGEN PHOTOSENSITIZATION .............................................................................................................. 89 3.3. CONJUGATED Π SYSTEMS ................................................................................................................................. 97 3.3.1. Excited States of Polyenes: ................................................................................................................... 97 3.3.2. Protonated Schiff bases: .................................................................................................................... 107 3.3.3. Nucleic acids: from nucleobases to double strands ........................................................................... 111 3.3.3.1. Nucleobases and derivatives.................................................................................................................... 111 3.3.3.2. Interacting nucleobases and DNA/RNA fragments .................................................................................. 115 3.3.4. Aminoacids and proteins ..................................................................................................................