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%% This BibTeX bibliography file was created using BibDesk. %% This BibTeX bibliography file was created using BibDesk.
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@article{Li_2021,
author = {Li,Chenyang and Evangelista,Francesco A.},
date-added = {2022-03-17 18:25:45 +0100},
date-modified = {2022-03-17 18:25:59 +0100},
doi = {10.1063/5.0059362},
journal = {J. Chem. Phys.},
number = {11},
pages = {114111},
title = {Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics},
volume = {155},
year = {2021},
bdsk-url-1 = {https://doi.org/10.1063/5.0059362}}
@article{Li_2018,
author = {Li,Chenyang and Evangelista,Francesco A.},
date-added = {2022-03-17 18:24:46 +0100},
date-modified = {2022-03-17 18:25:16 +0100},
doi = {10.1063/1.5019793},
journal = {J. Chem. Phys.},
number = {12},
pages = {124106},
title = {Driven similarity renormalization group for excited states: A state-averaged perturbation theory},
volume = {148},
year = {2018},
bdsk-url-1 = {https://doi.org/10.1063/1.5019793}}
@article{Li_2017,
author = {Li,Chenyang and Evangelista,Francesco A.},
date-added = {2022-03-17 18:23:18 +0100},
date-modified = {2022-03-17 18:23:50 +0100},
doi = {10.1063/1.4979016},
journal = {J. Chem. Phys.},
number = {12},
pages = {124132},
title = {Driven similarity renormalization group: Third-order multireference perturbation theory},
volume = {146},
year = {2017},
bdsk-url-1 = {https://doi.org/10.1063/1.4979016}}
@article{Yanai_2007,
author = {Yanai,Takeshi and Chan,Garnet Kin-Lic},
date-added = {2022-03-17 18:22:09 +0100},
date-modified = {2022-03-17 18:22:23 +0100},
doi = {10.1063/1.2761870},
journal = {J. Chem. Phys.},
number = {10},
pages = {104107},
title = {Canonical transformation theory from extended normal ordering},
volume = {127},
year = {2007},
bdsk-url-1 = {https://doi.org/10.1063/1.2761870}}
@article{Loos_2021c,
author = {Loos, Pierre-Fran{\c c}ois and Comin, Massimiliano and Blase, Xavier and Jacquemin, Denis},
date-added = {2022-03-17 17:53:12 +0100},
date-modified = {2022-03-17 17:53:32 +0100},
doi = {10.1021/acs.jctc.1c00226},
journal = {J. Chem. Theory Comput.},
number = {6},
pages = {3666-3686},
title = {Reference Energies for Intramolecular Charge-Transfer Excitations},
volume = {17},
year = {2021},
bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.1c00226}}
@article{Loos_2021b,
author = {Loos, Pierre-Fran{\c c}ois and Jacquemin, Denis},
date-added = {2022-03-17 17:50:43 +0100},
date-modified = {2022-03-17 17:53:48 +0100},
doi = {10.1021/acs.jpca.1c08524},
journal = {J. Phys. Chem. A},
number = {47},
pages = {10174-10188},
title = {A Mountaineering Strategy to Excited States: Highly Accurate Energies and Benchmarks for Bicyclic Systems},
volume = {125},
year = {2021},
bdsk-url-1 = {https://doi.org/10.1021/acs.jpca.1c08524}}
@article{Knowles_1988,
abstract = {A new method for evaluating one-particle coupling coefficients in a general configuration interaction calculation is presented. Through repeated application and use of resolutions of the identity, two-, three- and four-body coupling coefficients and density matrices may be built in a simple and efficient way. The method is therefore of use in both multiconfiguration SCF (MC SCF) and multireference configuration interaction (MRCI) calculations. Examples show that the approach is efficient for both these applications.},
author = {Peter J. Knowles and Hans-Joachim Werner},
date-added = {2022-03-17 17:36:24 +0100},
date-modified = {2022-03-17 17:36:40 +0100},
doi = {https://doi.org/10.1016/0009-2614(88)87412-8},
journal = {Chem. Phys. Lett.},
number = {6},
pages = {514-522},
title = {An efficient method for the evaluation of coupling coefficients in configuration interaction calculations},
volume = {145},
year = {1988},
bdsk-url-1 = {https://www.sciencedirect.com/science/article/pii/0009261488874128},
bdsk-url-2 = {https://doi.org/10.1016/0009-2614(88)87412-8}}
@article{Werner_1988,
author = {Werner,Hans‐Joachim and Knowles,Peter J.},
date-added = {2022-03-17 17:35:27 +0100},
date-modified = {2022-03-17 17:35:38 +0100},
doi = {10.1063/1.455556},
journal = {J. Chem. Phys.},
number = {9},
pages = {5803-5814},
title = {An efficient internally contracted multiconfiguration--reference configuration interaction method},
volume = {89},
year = {1988},
bdsk-url-1 = {https://doi.org/10.1063/1.455556}}
@article{Wen_2018,
author = {Wen, Jin and Han, Bowen and Havlas, Zden{\v e}k and Michl, Josef},
date-added = {2022-03-17 17:14:20 +0100},
date-modified = {2022-03-17 17:14:26 +0100},
doi = {10.1021/acs.jctc.8b00136},
eprint = {https://doi.org/10.1021/acs.jctc.8b00136},
journal = {J. Chem. Theory Comput.},
number = {8},
pages = {4291--4297},
title = {An MS-CASPT2 Calculation of the Excited Electronic States of an Axial Difluoroborondipyrromethene (BODIPY) Dimer},
url = {https://doi.org/10.1021/acs.jctc.8b00136},
volume = {14},
year = {2018},
bdsk-url-1 = {https://doi.org/10.1021/acs.jctc.8b00136}}
@article{Vela_2016,
abstract = {Complete active space self-consistent field theory (CASSCF) calculations and subsequent second-order perturbation theory treatment (CASPT2) are discussed in the evaluation of the spin-states energy difference (ΔHelec) of a series of seven spin crossover (SCO) compounds. The reference values have been extracted from a combination of experimental measurements and DFT + U calculations, as discussed in a recent article (Vela et al., Phys Chem Chem Phys 2015, 17, 16306). It is definitely proven that the critical IPEA parameter used in CASPT2 calculations of ΔHelec, a key parameter in the design of SCO compounds, should be modified with respect to its default value of 0.25 a.u. and increased up to 0.50 a.u. The satisfactory agreement observed previously in the literature might result from an error cancellation originated in the default IPEA, which overestimates the stability of the HS state, and the erroneous atomic orbital basis set contraction of carbon atoms, which stabilizes the LS states. {\copyright} 2015 Wiley Periodicals, Inc.},
author = {Vela, Sergi and Fumanal, Maria and Ribas-Ari{\~n}o, Jordi and Robert, Vincent},
date-added = {2022-03-17 17:14:06 +0100},
date-modified = {2022-03-17 17:14:12 +0100},
doi = {https://doi.org/10.1002/jcc.24283},
eprint = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.24283},
journal = {J. Comput. Chem.},
keywords = {spin crossover, molecular magnetism, computational chemistry},
number = {10},
pages = {947--953},
title = {On the Zeroth-Order Hamiltonian for CASPT2 Calculations of Spin Crossover Compounds},
url = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.24283},
volume = {37},
year = {2016},
bdsk-url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.24283},
bdsk-url-2 = {https://doi.org/10.1002/jcc.24283}}
@article{Rudavskyi_2014,
author = {Rudavskyi,Andrii and Sousa,Carmen and de Graaf,Coen and Havenith,Remco W. A. and Broer,Ria},
date-added = {2022-03-17 17:13:51 +0100},
date-modified = {2022-03-17 17:14:05 +0100},
doi = {10.1063/1.4875695},
eprint = {https://doi.org/10.1063/1.4875695},
journal = {J. Chem. Phys.},
number = {18},
pages = {184318},
title = {Computational Approach to the Study of Thermal Spin Crossover Phenomena},
url = {https://doi.org/10.1063/1.4875695},
volume = {140},
year = {2014},
bdsk-url-1 = {https://doi.org/10.1063/1.4875695}}
@article{Daku_2012,
author = {Lawson Daku, Lat{\'e}vi Max and Aquilante, Francesco and Robinson, Timothy W. and Hauser, Andreas},
date-added = {2022-03-17 17:13:29 +0100},
date-modified = {2022-03-17 17:13:42 +0100},
doi = {10.1021/ct300592w},
eprint = {https://doi.org/10.1021/ct300592w},
journal = {J. Chem. Theory Comput.},
number = {11},
pages = {4216--4231},
title = {Accurate Spin-State Energetics of Transition Metal Complexes. 1. CCSD(T), CASPT2, and DFT Study of [M(NCH)$_6$]$^{2+}$ (M = Fe, Co)},
url = {https://doi.org/10.1021/ct300592w},
volume = {8},
year = {2012},
bdsk-url-1 = {https://doi.org/10.1021/ct300592w}}
@article{Kepenekian_2009,
author = {Kepenekian,Mika{\"e}l and Robert,Vincent and Le Guennic,Boris},
date-added = {2022-03-17 17:13:14 +0100},
date-modified = {2022-03-17 17:13:29 +0100},
doi = {10.1063/1.3211020},
eprint = {https://doi.org/10.1063/1.3211020},
journal = {J. Chem. Phys.},
number = {11},
pages = {114702},
title = {What Zeroth-Order Hamiltonian for CASPT2 Adiabatic Energetics of Fe(II)N$_6$ Architectures?},
url = {https://doi.org/10.1063/1.3211020},
volume = {131},
year = {2009},
bdsk-url-1 = {https://doi.org/10.1063/1.3211020}}
@article{Suaud_2009,
author = {Suaud, Nicolas and Bonnet, Marie-Laure and Boilleau, Corentin and Lab{\`e}guerie, Pierre and Guih{\'e}ry, Nathalie},
date-added = {2022-03-17 17:12:58 +0100},
date-modified = {2022-03-17 17:13:05 +0100},
doi = {10.1021/ja805626s},
eprint = {https://doi.org/10.1021/ja805626s},
journal = {J. Am. Chem. Soc.},
number = {2},
pages = {715-722},
title = {Light-Induced Excited Spin State Trapping: Ab Initio Study of the Physics at the Molecular Level},
url = {https://doi.org/10.1021/ja805626s},
volume = {131},
year = {2009},
bdsk-url-1 = {https://doi.org/10.1021/ja805626s}}
@article{Pierloot_2008,
author = {Pierloot,Kristine and Vancoillie,Steven},
date-added = {2022-03-17 17:12:41 +0100},
date-modified = {2022-03-17 17:12:47 +0100},
doi = {10.1063/1.2820786},
eprint = {https://doi.org/10.1063/1.2820786},
journal = {J. Chem. Phys.},
number = {3},
pages = {034104},
title = {Relative Energy of the High-($^5T_{2g}$) and Low-($^1A_{1g}$) Spin states of the Ferrous Complexes [Fe(L)(NHS$_4$)]: CASPT2 versus Density Functional Theory},
url = {https://doi.org/10.1063/1.2820786},
volume = {128},
year = {2008},
bdsk-url-1 = {https://doi.org/10.1063/1.2820786}}
@article{Pierloot_2006,
author = {Pierloot,Kristine and Vancoillie,Steven},
date-added = {2022-03-17 17:12:20 +0100},
date-modified = {2022-03-17 17:12:34 +0100},
doi = {10.1063/1.2353829},
eprint = {https://doi.org/10.1063/1.2353829},
journal = {J. Chem. Phys.},
number = {12},
pages = {124303},
title = {Relative Energy of the High-($^5T_{2g}$) and low-($^1A_{1g}$) Spin States of [Fe(H$_2$O)$_6$]$^{2+}$, [Fe(NH$_3$)$_6$]$^{2+}$, and [Fe(bpy)$_3$]$^{2+}$: CASPT2 \emph{versus} Density Functional Theory},
url = {https://doi.org/10.1063/1.2353829},
volume = {125},
year = {2006},
bdsk-url-1 = {https://doi.org/10.1063/1.2353829}}
@article{Silva-Junior_2008,
author = {Silva-Junior, M. R. and Schreiber, M. and Sauer, S. P. A. and Thiel, W.},
date-added = {2022-03-17 15:19:55 +0100},
date-modified = {2022-03-17 15:20:01 +0100},
journal = JCP,
pages = {104103},
title = {Benchmarks for Electronically Excited States: Time-Dependent Density Functional Theory and Density Functional Theory Based Multireference Configuration Interaction},
volume = 129,
year = 2008}
@article{Faber_2013,
author = {Faber, C. and Boulanger, P. and Duchemin, I. and Attaccalite, C. and Blase, X.},
date-added = {2022-03-17 15:19:01 +0100},
date-modified = {2022-03-17 15:19:10 +0100},
doi = {http://dx.doi.org/10.1063/1.4830236},
journal = {J. Chem. Phys.},
number = {19},
pages = {194308},
title = {Many-Body Greens Function GW and Bethe-Salpeter Study of the Optical Excitations in a Paradigmatic Model Dipeptide},
url = {http://scitation.aip.org/content/aip/journal/jcp/139/19/10.1063/1.4830236},
volume = {139},
year = {2013},
bdsk-url-1 = {http://scitation.aip.org/content/aip/journal/jcp/139/19/10.1063/1.4830236},
bdsk-url-2 = {http://dx.doi.org/10.1063/1.4830236}}
@article{Peach_2008,
author = {Peach, M. J. G. and Benfield, P. and Helgaker, T. and Tozer, D. J.},
date-added = {2022-03-17 15:18:46 +0100},
date-modified = {2022-03-17 15:18:55 +0100},
journal = JCP,
pages = {044118},
title = {Excitation Energies in Density Functional Theory: an Evaluation and a Diagnostic Test},
volume = 128,
year = 2008}
@article{Burcl0_2002,
abstract = {Excited states of furan and pyrrole were studied by time-dependent density functional theory. The effect of basis set and density functional on the vertical excitation energies was investigated. Energy gradients and dipole moments were evaluated analytically. Stationary points on the lowest excited states were determined. Harmonic frequencies and (v′=0←v=0) excitation energies were evaluated. Many of the results agree well with the experimental values available as well as most recent theoretical ab initio values, but there remain discrepancies in the valence states. The dipole moments of many excited states show a large variation with the basis set and functional; this is due to the fact that the states have an extremely large polarisability.},
author = {Rudolf Burcl and Roger D. Amos and Nicholas C. Handy},
date-added = {2022-03-17 15:18:31 +0100},
date-modified = {2022-03-17 15:18:39 +0100},
doi = {https://doi.org/10.1016/S0009-2614(02)00122-7},
issn = {0009-2614},
journal = {Chem. Phys. Lett.},
number = {1},
pages = {8--18},
title = {Study of Excited States of Furan and Pyrrole by Time-Dependent Density Functional Theory},
url = {http://www.sciencedirect.com/science/article/pii/S0009261402001227},
volume = {355},
year = {2002},
bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0009261402001227},
bdsk-url-2 = {https://doi.org/10.1016/S0009-2614(02)00122-7}}
@article{Tozer_1999,
author = {Tozer, D. J. and Handy, N. C.},
date-added = {2022-03-17 15:18:19 +0100},
date-modified = {2022-03-17 15:18:24 +0100},
journal = {J. Comput. Chem.},
pages = {106--113},
title = {Excitation Energies of Benzene from Kohn-Sham Theory},
volume = {20},
year = {1999}}
@article{Serrano-Andres_2005,
abstract = {The present contribution contains an overview of quantum-chemical methods and strategies to compute and interpret spectroscopic and photochemical phenomena in molecular systems. The state of the art for the quantum chemistry of the excited state is reviewed, focusing in the advantages and disadvantages of the most commonly employed computational methods, from the single configurational procedures like CI-Singles (CIS), propagator approaches, and Coupled-Cluster (CC) techniques, to the more sophisticated multiconfigurational treatments, with particular emphasis on perturbation theory, the CASPT2 approach. Also, a short summary on the performance, lights, and shadows of the popular TDDFT methods is included. The role of the differential correlation effects on quantum-chemical calculations is analyzed, especially for the location of potential energy surface crossings. The contribution finally addresses the importance that theoretical constructs as conical and non-conical intersections play in non-adiabatic photochemistry. The nice photochemistry of cytosine is used as an illustrative example of theoretical photochemistry, a continuously expanding field of research.},
author = {Luis Serrano-Andr\'{e}s and Manuela Merch\'{a}n},
date-added = {2022-03-17 15:17:55 +0100},
date-modified = {2022-03-17 15:18:04 +0100},
doi = {https://doi.org/10.1016/j.theochem.2005.03.020},
issn = {0166-1280},
journal = {J. Mol. Struct. (THEOCHEM)},
keywords = {Excited states, Photochemistry, Quantum chemistry},
number = {1},
pages = {99--108},
title = {Quantum Chemistry of the Excited State: 2005 Overview},
url = {http://www.sciencedirect.com/science/article/pii/S0166128005002460},
volume = {729},
year = {2005},
bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0166128005002460},
bdsk-url-2 = {https://doi.org/10.1016/j.theochem.2005.03.020}}
@article{Serrano-Andres_2002,
author = {Serrano-Andr{\'e}s,Luis and Pou-Am{\'e}rigo,Rosendo and F{\"u}lscher,Markus P. and Borin,Antonio Carlos},
date-added = {2022-03-17 15:17:40 +0100},
date-modified = {2022-03-17 15:17:48 +0100},
doi = {10.1063/1.1482706},
eprint = {https://doi.org/10.1063/1.1482706},
journal = {J. Chem. Phys.},
number = {4},
pages = {1649--1659},
title = {Electronic Excited States of Conjugated Cyclic Ketones and Thioketones: A Theoretical Study},
url = {https://doi.org/10.1063/1.1482706},
volume = {117},
year = {2002},
bdsk-url-1 = {https://doi.org/10.1063/1.1482706}}
@article{Roos_2002,
author = {Bj{\"o}rn O. Roos and Per-{\AA}ke Malmqvist and Vincent Molina and Luis Serrano-Andr{\'e}s and Manuela Merch{\'a}n},
date-added = {2022-03-17 15:17:24 +0100},
date-modified = {2022-03-17 15:17:32 +0100},
doi = {10.1063/1.1465406},
eprint = {https://doi.org/10.1063/1.1465406},
journal = {J. Chem. Phys.},
number = {17},
pages = {7526--7536},
title = {Theoretical Characterization of the Lowest-Energy Absorption Band of Pyrrole},
url = {https://doi.org/10.1063/1.1465406},
volume = {116},
year = {2002},
bdsk-url-1 = {https://doi.org/10.1063/1.1465406},
bdsk-url-2 = {http://dx.doi.org/10.1063/1.1465406}}
@inbook{Merchan_1999,
abstract = { Abstract Applications of the Complete Active Space (CAS) SCF method in conjunction with multiconfigurational second-order perturbation theory (CASPT2) in electronic spectroscopy of organic molecules are reviewed. Since the first applications in spectroscopy were performed at the beginning of the present decade, the CASSCF/CASPT2 method has been used to study electronic spectra of a large number of compounds. The experience gained from this global investigation is illustrated in the present contribution through several examples. In most cases, the CASSCF reference function does characterize with sufficient accuracy the states of interest, which supports the use of a single reference perturbation theory in spectroscopic studies of organic systems. The CASSCF/CASPT2 method is capable of yielding accurate results for relative energies and other properties of excited states, provided that flexible one-electron basis sets are used and an appropriate active space can be chosen. The overall accuracy of the approach is high. The excitation energies are usually found to be within $\pm$0.2 eV of the available experimental energies for correctly assigned transitions. The review covers some of the most recent applications in the spectroscopy of organic compounds: absorption spectrum of free base porphin employing an extended treatment; vertical, nonvertical, and emission energies of long polyenals; spectra of trans- and cis-stilbene together with an analysis of certain static aspects of the photo-induced isomerization process; absorption spectra of purine DNA base monomers and related compounds, and analysis of the spectroscopic features of polypeptides based on intra- and interpeptide charge transfer transitions. In addition, the electronic spectra of organic compounds with interacting double bonds are rationalized. These studies either confirm existing experimental assignments or lead to new predictions and a novel understanding of the electronic spectra of the corresponding organic molecules. },
author = {Merchan, Manuela and Serrano-Andr\'{e}s,Luis and Roos, Bjorn O},
booktitle = {Recent Advances in Multireference Methods},
date-added = {2022-03-17 15:16:10 +0100},
date-modified = {2022-03-17 15:21:23 +0100},
doi = {10.1142/9789812812186_0006},
pages = {161--195},
publisher = {World Scientific},
series = {Recent Advances in Computational Chemistry},
title = {Multiconfigurational Perturbation Theory Applied to Excited States of Organic Compounds},
year = {1999},
bdsk-url-1 = {https://www.worldscientific.com/doi/abs/10.1142/9789812812186_0006},
bdsk-url-2 = {https://doi.org/10.1142/9789812812186_0006}}
@article{Roos_1999,
author = {Roos, Bj{\"o}rn O.},
date-added = {2022-03-17 15:15:58 +0100},
date-modified = {2022-03-17 15:16:04 +0100},
doi = {10.1021/ar960091y},
eprint = {https://doi.org/10.1021/ar960091y},
journal = {Acc. Chem. Res.},
number = {2},
pages = {137--144},
title = {Theoretical Studies of Electronically Excited States of Molecular Systems Using Multiconfigurational Perturbation Theory},
url = {https://doi.org/10.1021/ar960091y},
volume = {32},
year = {1999},
bdsk-url-1 = {https://doi.org/10.1021/ar960091y}}
@article{Serrano-Andres_1998a,
author = {Serrano-Andr{\'e}s,Luis and Forsberg,Niclas and Malmqvist,Per-{\AA}ke},
date-added = {2022-03-17 15:15:30 +0100},
date-modified = {2022-03-17 15:15:45 +0100},
doi = {10.1063/1.476138},
eprint = {https://doi.org/10.1063/1.476138},
journal = {J. Chem. Phys.},
number = {17},
pages = {7202--7216},
title = {Vibronic Structure in Triatomic Molecules: The Hydrocarbon Flame Bands of the Formyl Radical (HCO). A Theoretical Study},
url = {https://doi.org/10.1063/1.476138},
volume = {108},
year = {1998},
bdsk-url-1 = {https://doi.org/10.1063/1.476138}}
@article{Serrano-Andres_1998b,
author = {Serrano-Andr{\'e}s, Luis and F{\"u}lscher, Markus P.},
date-added = {2022-03-17 15:15:30 +0100},
date-modified = {2022-03-17 15:15:42 +0100},
doi = {10.1021/ja981148+},
eprint = {https://doi.org/10.1021/ja981148+},
journal = {J. Am. Chem. Soc.},
number = {42},
pages = {10912--10920},
title = {Theoretical Study of the Electronic Spectroscopy of Peptides. III. Charge-Transfer Transitions in Polypeptides},
url = {https://doi.org/10.1021/ja981148+},
volume = {120},
year = {1998},
bdsk-url-1 = {https://doi.org/10.1021/ja981148+}}
@article{Serrano-Andres_1996a,
author = {Serrano-Andr{\'e}s, Luis and F{\"u}lscher, Markus P.},
date-added = {2022-03-17 15:15:08 +0100},
date-modified = {2022-03-17 15:15:19 +0100},
doi = {10.1021/ja961996+},
eprint = {https://doi.org/10.1021/ja961996+},
journal = {J. Am. Chem. Soc.},
number = {48},
pages = {12190--12199},
title = {Theoretical Study of the Electronic Spectroscopy of Peptides. 1. The Peptidic Bond: Primary, Secondary, and Tertiary Amides},
url = {https://doi.org/10.1021/ja961996+},
volume = {118},
year = {1996},
bdsk-url-1 = {https://doi.org/10.1021/ja961996+}}
@article{Serrano-Andres_1996b,
author = {Serrano-Andr{\'e}s, Luis and F{\"u}lscher, Markus P. and Roos, Bj{\"o}rn O. and Merch{\'a}n, Manuela},
date-added = {2022-03-17 15:15:08 +0100},
date-modified = {2022-03-17 15:15:17 +0100},
doi = {10.1021/jp952809h},
eprint = {https://doi.org/10.1021/jp952809h},
journal = {J. Phys. Chem.},
number = {16},
pages = {6484--6491},
title = {Theoretical Study of the Electronic Spectrum of Imidazole},
url = {https://doi.org/10.1021/jp952809h},
volume = {100},
year = {1996},
bdsk-url-1 = {https://doi.org/10.1021/jp952809h}}
@article{Serrano-Andres_1995,
author = {Serrano-Andres, Luis and Merchan, Manuela and Roos, Bjoern O. and Lindh, Roland},
date-added = {2022-03-17 15:14:20 +0100},
date-modified = {2022-03-17 15:14:29 +0100},
doi = {10.1021/ja00116a024},
eprint = {https://doi.org/10.1021/ja00116a024},
journal = {J. Am. Chem. Soc.},
number = {11},
pages = {3189--3204},
title = {Theoretical Study of the Internal Charge Transfer in Aminobenzonitriles},
url = {https://doi.org/10.1021/ja00116a024},
volume = {117},
year = {1995},
bdsk-url-1 = {https://doi.org/10.1021/ja00116a024}}
@article{Serrano-Andres_1993a,
author = {Serrano-Andr\'es, L. and Mech\'an, M. and Nebot-Gil, I. and Lindh, R. and Roos, B. O.},
date-added = {2022-03-17 15:13:13 +0100},
date-modified = {2022-03-17 15:13:27 +0100},
journal = JCP,
pages = {3151--3162},
title = {Towards an Accurate Molecular Orbital Theory for Excited States: Ethene, Butadiene, and Hexatriene},
volume = 98,
year = 1993}
@article{Serrano-Andres_1993b,
author = {Serrano-Andr\'es, Luis and Merch\'{a}n, Manuela and Nebot-Gil, Ignacio and Roos, Bjoern O. and Fulscher, Markus},
date-added = {2022-03-17 15:13:13 +0100},
date-modified = {2022-03-17 15:13:49 +0100},
doi = {10.1021/ja00067a038},
eprint = {https://doi.org/10.1021/ja00067a038},
journal = {J. Am. Chem. Soc.},
number = {14},
pages = {6184--6197},
title = {Theoretical Study of the Electronic Spectra of Cyclopentadiene, Pyrrole, and Furan},
url = {https://doi.org/10.1021/ja00067a038},
volume = {115},
year = {1993},
bdsk-url-1 = {https://doi.org/10.1021/ja00067a038}}
@article{Serrano-Andres_1993c,
abstract = {The electronic spectrum of thiophene has been studied using multiconfiguration second-order perturbation theory and extended ANO basis sets. The calculations comprise four singlet valence excited states and the 3s3p3rd Rydberg series. The lowest triplet states were included and some n-π* and n-σ* states. The results have been used to assign the experimental spectrum below 8.0 eV, with a maximum deviation of about 0.1 eV for vertical transition energies. The calculations place the 2 1A1 valence state at 5.33 eV, below the 1 1B2 valence state at 5.72 eV, and the most intense valence transitions at 6.69 eV (3 1A1) and 7.32 eV (4 1B2) with oscillator strengths 0.19 and 0.39, respectively.},
author = {Luis Serrano-Andr{\'e}s and Manuela Merch{\'a}n and Markus F{\"u}lscher and Bj{\"o}rn O. Roos},
date-added = {2022-03-17 15:13:13 +0100},
date-modified = {2022-03-17 15:13:54 +0100},
doi = {https://doi.org/10.1016/0009-2614(93)80061-S},
issn = {0009-2614},
journal = {Chem. Phys. Lett.},
number = {1},
pages = {125--134},
title = {A Theoretical Study of the Electronic Spectrum of Thiophene},
url = {http://www.sciencedirect.com/science/article/pii/000926149380061S},
volume = {211},
year = {1993},
bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/000926149380061S},
bdsk-url-2 = {https://doi.org/10.1016/0009-2614(93)80061-S}}
@article{Kendall_1992,
author = {Kendall, R. A. and Dunning, T. H. and Harisson, R. J.},
date-added = {2022-03-17 14:43:48 +0100},
date-modified = {2022-03-17 14:44:26 +0100},
doi = {10.1063/1.462569},
journal = {J. Chem. Phys.},
pages = {6796--6806},
title = {Electron Affinities of the First-Row Atoms Revisited. Systematic Basis Sets and Wave Functions},
volume = {96},
year = {1992},
bdsk-url-1 = {https://doi.org/10.1063/1.462569}}
@article{Angeli_2012, @article{Angeli_2012,
author = {Celestino Angeli and Renzo Cimiraglia and Mariachiara Pastore}, author = {Celestino Angeli and Renzo Cimiraglia and Mariachiara Pastore},
date-added = {2022-03-16 21:35:50 +0100}, date-added = {2022-03-16 21:35:50 +0100},
@ -48,7 +547,7 @@
bdsk-url-1 = {https://doi.org/10.1063/1.2768529}} bdsk-url-1 = {https://doi.org/10.1063/1.2768529}}
@article{Pastore_2007, @article{Pastore_2007,
author = {Pastore, M. and Angeli, C. and Cimiraglia, R. }, author = {Pastore, M. and Angeli, C. and Cimiraglia, R.},
date-added = {2022-03-16 21:28:42 +0100}, date-added = {2022-03-16 21:28:42 +0100},
date-modified = {2022-03-16 21:29:45 +0100}, date-modified = {2022-03-16 21:29:45 +0100},
doi = {10.1007/s00214-006-0239-5}, doi = {10.1007/s00214-006-0239-5},
@ -56,7 +555,8 @@
number = {35-46}, number = {35-46},
title = {A multireference perturbation theory study on the vertical electronic spectrum of thiophene}, title = {A multireference perturbation theory study on the vertical electronic spectrum of thiophene},
volume = {118}, volume = {118},
year = {2007}} year = {2007},
bdsk-url-1 = {https://doi.org/10.1007/s00214-006-0239-5}}
@article{Pastore_2006b, @article{Pastore_2006b,
abstract = {The vertical electronic spectrum of furan is investigated by second and third-order multireference perturbation theory (NEVPT). The excitation energies of the three lowest-energy valence states, as well as the 3l Rydberg states are reported. The effects of the size of the active space and the valence--Rydberg mixing are discussed. The application of the quasi-degenerate NEVPT approach has proved to be necessary in order to handle the consistent valence--Rydberg interactions occurring for the two 1A1+and1B2+ valence states. For the three valence states and the low-lying Rydberg states, the computed excitation energies agree with those computed in the more recent high-level theoretical studies.}, abstract = {The vertical electronic spectrum of furan is investigated by second and third-order multireference perturbation theory (NEVPT). The excitation energies of the three lowest-energy valence states, as well as the 3l Rydberg states are reported. The effects of the size of the active space and the valence--Rydberg mixing are discussed. The application of the quasi-degenerate NEVPT approach has proved to be necessary in order to handle the consistent valence--Rydberg interactions occurring for the two 1A1+and1B2+ valence states. For the three valence states and the low-lying Rydberg states, the computed excitation energies agree with those computed in the more recent high-level theoretical studies.},
@ -2295,18 +2795,6 @@
year = {2001}, year = {2001},
bdsk-url-1 = {https://doi.org/10.1063/1.1416173}} bdsk-url-1 = {https://doi.org/10.1063/1.1416173}}
@article{Li_2018,
author = {J. Li and M. Otten and A. A. Holmes and S. Sharma and C. J. Umrigar},
date-added = {2021-05-06 15:31:25 +0200},
date-modified = {2021-05-06 15:31:25 +0200},
doi = {10.1063/1.5055390},
journal = {J. Chem. Phys.},
pages = {214110},
title = {Fast semistochastic heat-bath configuration interaction},
volume = {149},
year = {2018},
bdsk-url-1 = {https://doi.org/10.1063/1.5055390}}
@article{Li_2020, @article{Li_2020,
author = {Li, Junhao and Yao, Yuan and Holmes, Adam A. and Otten, Matthew and Sun, Qiming and Sharma, Sandeep and Umrigar, C. J.}, author = {Li, Junhao and Yao, Yuan and Holmes, Adam A. and Otten, Matthew and Sun, Qiming and Sharma, Sandeep and Umrigar, C. J.},
date-added = {2021-05-06 15:31:25 +0200}, date-added = {2021-05-06 15:31:25 +0200},

80
Manuscript/CASPT3.tex
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@ -85,7 +85,8 @@
% Abstract % Abstract
\begin{abstract} \begin{abstract}
The present study assesses the performance of the third-order multireference perturbation theory, CASPT3, in the context of molecular excited states. The present study assesses the performance of the third-order multireference perturbation theory, CASPT3, in the context of molecular excited states.
Based on 284 vertical excitation energies of various natures extracted from the QUEST database, we show that... Based on 284 vertical excitation energies of various natures extracted from the QUEST database, we show that CASPT3 provides a significant improvement compared to its second-order counterpart, CASPT2.
As already reported, we have also observed that the accuracy of CASPT3 is much less sensitive to the infamous ionization-potential-electron-affinity (IPEA) shift.
%\bigskip %\bigskip
%\begin{center} %\begin{center}
% \boxed{\includegraphics[width=0.4\linewidth]{TOC}} % \boxed{\includegraphics[width=0.4\linewidth]{TOC}}
@ -110,53 +111,76 @@ This has led, in certain specific contexts, to the development of empirical stra
Extension of single-reference perturbation theory to electronic excited states is far from being trivial, and the algebraic diagrammatic Extension of single-reference perturbation theory to electronic excited states is far from being trivial, and the algebraic diagrammatic
construction (ADC) approximation of the polarization propagator is probably the most natural. \cite{Schirmer_1982,Schirmer_1991,Barth_1995,Schirmer_2004,Schirmer_2018,Trofimov_1997,Trofimov_1997b,Trofimov_2002,Trofimov_2005,Trofimov_2006,Harbach_2014,Dreuw_2015} construction (ADC) approximation of the polarization propagator is probably the most natural. \cite{Schirmer_1982,Schirmer_1991,Barth_1995,Schirmer_2004,Schirmer_2018,Trofimov_1997,Trofimov_1997b,Trofimov_2002,Trofimov_2005,Trofimov_2006,Harbach_2014,Dreuw_2015}
However, the ADC series naturally inherits some of the drawbacks of its MP parent and it has been shown to be not particularly rapidly convergent in the context of vertical excitation energies. \cite{Veril_2021} However, the ADC series naturally inherits some of the drawbacks of its MP parent and it has been shown to be not particularly rapidly convergent in the context of vertical excitation energies. \cite{Loos_2018a,Loos_2020a,Veril_2021}
This has led some of the authors to recently propose the ADC(2.5) composite approach, where, in the same spirit as MP2.5, one averages the second-order [ADC(2)] and third-order [ADC(3)] vertical transition energies. \cite{Loos_2020d} This has led some of the authors to recently propose the ADC(2.5) composite approach, where, in the same spirit as MP2.5, one averages the second-order [ADC(2)] and third-order [ADC(3)] vertical transition energies. \cite{Loos_2020d}
Multi-reference perturbation theory is somewhat easier to generalize to excited states as one selects the states of interest to include in the reference (zeroth-order) space via the so-called complete-active-space self-consistent field (CASSCF) formalism, hence catching effectively static correlation in the zeroth-order wave function. Multi-reference perturbation theory is somewhat easier to generalize to excited states as one selects the states of interest to include in the reference (zeroth-order) space via the so-called complete-active-space self-consistent field (CASSCF) formalism, hence catching effectively static correlation in the zeroth-order wave function.
The missing dynamical correlation can then be recovered via low-order multi-reference perturbation theory, as performed in the complete-active-space second-order perturbation theory (CASPT2) of Roos and The missing dynamical correlation can then be recovered via low-order perturbation theory, as performed in the complete-active-space second-order perturbation theory (CASPT2) of Roos and
coworkers, \cite{Andersson_1990,Andersson_1992,Roos_1995a} Hirao's multireference second-order M{\o}llet-Plesset (MRMP2) approach, \cite{Hirao_1992} or the $N$-electron valence state second-order perturbation theory (NEVPT2) developed by Angeli, Malrieu, and coworkers. \cite{Angeli_2001a,Angeli_2001b,Angeli_2002} coworkers, \cite{Andersson_1990,Andersson_1992,Roos_1995a} Hirao's multireference second-order M{\o}llet-Plesset (MRMP2) approach, \cite{Hirao_1992} or the $N$-electron valence state second-order perturbation theory (NEVPT2) developed by Angeli, Malrieu, and coworkers. \cite{Angeli_2001a,Angeli_2001b,Angeli_2002,Angeli_2006}
%However, the equations are much more involved than their single-reference counterparts and many schemes have been developed. However, these multi-reference formalisms and their implementation are much more involved and costly than their single-reference counterparts.
Although it has well-document weaknesses, CASPT2 is indisputably the most popular of the three approaches mentioned above.
As such, it has been employed in countless computational studies involving electronic excited states. \cite{Serrano-Andres_1993a,Serrano-Andres_1993b,Serrano-Andres_1993c,Serrano-Andres_1995,Roos_1996,Serrano-Andres_1996a,Serrano-Andres_1996b,Serrano-Andres_1998b,Roos_1999,Merchan_1999,Roos_2002,Serrano-Andres_2002,Serrano-Andres_2005,Tozer_1999,Burcl0_2002,Peach_2008,Faber_2013,Schreiber_2008,Silva-Junior_2008,Sauer_2009,Silva-Junior_2010a,Silva-Junior_2010b,Silva-Junior_2010c}
From the three methods mentioned above, CASPT2 is the most popular approach although it has well-document weaknesses. In the context of excited states, its most severe drawback is certainly the intruder state problem (which is, by construction, absent in NEVPT2) that describes a situation where one or several determinants of the outer (first-order) space, known as perturbers, have an energy close to the zeroth-order CASSCF wave function, hence producing divergences in the denominators of the second-order perturbative energy.
In the context of excited states, its most severe drawback is certainly the intruder state problem which describes a situation where one or several determinants of the outer (first-order) space, known as perturbers, has an energy close to the zeroth-order CASSCF wave function, hence producing divergences in the denominators of the second-order perturbative energy.
One can then introduce a shift in the denominators to avoid such situations, and correcting afterwards the second-order energy for the use of this shift. One can then introduce a shift in the denominators to avoid such situations, and correcting afterwards the second-order energy for the use of this shift.
The use of real-valued \cite{Roos_1995b,Roos_1996} or imaginary \cite{Forsberg_1997} level shift has been successfully tested and is now routine in excited-state calculations. \cite{Schapiro_2013,Zobel_2017,Sarka_2022} The use of real-valued \cite{Roos_1995b,Roos_1996} or imaginary \cite{Forsberg_1997} level shifts has been successfully tested and is now routine in excited-state calculations. \cite{Schapiro_2013,Zobel_2017,Sarka_2022}
%NEVPT2 which is an improvement of CASPT2 that does not suffer from the intruder state problem.
\titou{The second drawback was found in evaluating a large number of chemical problems for which systematic errors were noticed \cite{Andersson_1993,Andersson_1995} and ascribed to the unbalanced description of the zeroth-order Hamiltonian for the open- and closed-shell electronic configurations. A second drawback was revealed by Andersson \textit{et al.} \cite{Andersson_1993,Andersson_1995} and explained by the unbalanced treatment in the zeroth-order Hamiltonian of the open- and closed-shell electronic configurations.
This systematic error can be attenuated by introducing an additional parameter, the so-called ionization-potential-electron-affinity (IPEA) shift, in the zeroth-order A cure was quickly proposed via the introduction of an additional parameter in the zeroth-order Hamiltonian, the infamous ionization-potential-electron-affinity (IPEA) shift. \cite{Ghigo_2004}
Hamiltonian. \cite{Ghigo_2004}} Although the introduction of an IPEA shift can provide a better agreement between experiment and theory, \cite{Pierloot_2006,Pierloot_2008,Suaud_2009,Kepenekian_2009,Daku_2012,Rudavskyi_2014,Vela_2016,Wen_2018} it has been shown by Zobel \textit{et al.} that the application of an IPEA shift is not systematically justified and has been found to be fairly basis set dependent. \cite{Zobel_2017}
Recently, based on the highly-accurate vertical excitation energies of the QUEST database, we have reported an exhaustive benchmark of CASPT2 and NEVPT2 for 284 excited states of diverse nature computed in 35 small- and medium-sized organic molecules containing from three to six non-hydrogen atoms. \cite{Sarka_2022} Recently, based on the highly-accurate vertical excitation energies of the QUEST database, \cite{Loos_2018a,Loos_2019,Loos_2020a,Loos_2020b,Loos_2020c,Veril_2021,Loos_2021c,Loos_2021b} we have reported an exhaustive benchmark of CASPT2 and NEVPT2 for 284 excited states of diverse natures (singlets, triplets, valence, Rydberg, $n\to\pis$, $\pi\to\pis$, and double excitations) computed in 35 small- and medium-sized organic molecules containing from three to six non-hydrogen atoms. \cite{Sarka_2022}
Our main take-home message was that both CASPT2 with IPEA shift and partially-contracted version of NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of \SI{0.11}{} and \SI{0.13}{\eV}, respectively. Our main take-home message was that both CASPT2 with IPEA shift and the partially-contracted version of NEVPT2 provide fairly reliable vertical transition energy estimates, with slight overestimations and mean absolute errors of \SI{0.11}{} and \SI{0.13}{\eV}, respectively.
These values were found to be rather uniform for the various subgroups of transitions. Importantly, the introduction of the IPEA shift in CASPT2 was found to lower the mean absolute errors from \SI{0.27}{} to \SI{0.11}{eV}.
Here, going one step further in the perturbative expansion, we propose to assess the performances of complete-active-space third-order perturbation theory (CASPT3). In the electronic structure community, third-order perturbation theory has a fairly bad reputation especially within MP perturbation theory where it is rarely worth its extra cost. \cite{Rettig_2020}
Pioneering work along these lines is due to Werner which develops a CASPT3 code in MOLPRO \cite{Werner_2020} based on a hack of the MRCI module. \cite{Werner_1996} Nonetheless, going against popular believes and one step further in the perturbative expansion, we propose here to assess the performance of the complete-active-space third-order perturbation theory (CASPT3) method developed by Werner \cite{Werner_1996} and implemented in MOLPRO. \cite{Werner_2020}
There is also the NEVPT3 method of Angeli and coworkers, \cite{Angeli_2006} which has been used in several applications, \cite{Pastore_2006a,Pastore_2006b,Pastore_2007,Angeli_2007,Camacho_2010,Angeli_2011,Angeli_2012} but, as far as we are aware of, only standalone implementation of NEVPT3 exists. Very few CASPT3 calculations have been reported in the literature \cite{Angeli_2006,Yanai_2007,Grabarek_2016,Li_2017,Li_2018,Li_2021} with only a single work reporting CASPT3 vertical excitation energies. \cite{Grabarek_2016}
Third-order perturbation theory has a bad reputation especially within MP perturbation theory because of it does not always yield to an significant improvement compared to its cheaper second-order version. \cite{Rettig_2020} Based on the same 284 vertical excitation energies from the QUEST database, we show that CASPT3 provides a significant improvement compared to CASPT2.
Third-order version have been developed but rarely used and accuracy still need to be assessed. Moreover, as already reported, \cite{Grabarek_2016} we also observe that the accuracy of CASPT3 is much less sensitive to the IPEA shift.
except in the case of rhodopsin. \cite{Grabarek_2016} Note that, although a third-order version of NEVPT has been developed \cite{Angeli_2006} and has been used in several applications \cite{Pastore_2006a,Pastore_2006b,Pastore_2007,Angeli_2007,Camacho_2010,Angeli_2011,Angeli_2012} by Angeli and coworkers, as far as we are aware of, only standalone implementation of NEVPT3 exists.
\begin{figure}
\includegraphics[width=\linewidth,viewport=1.cm 10cm 18cm 27cm,clip]{mol.pdf}
\caption{Various molecular systems considered in this study.
\label{fig:mol}}
\end{figure}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Computational details} \section{Computational details}
\label{sec:compdet} \label{sec:compdet}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
All the CASPT2 and CASPT3 calculations have been carried out with MOLPRO within the RS2 and RS3 schemes. \cite{Werner_2020}
%%% FIGURE 1 %%%
\begin{figure}
\includegraphics[width=\linewidth,viewport=1.cm 10cm 18cm 27cm,clip]{mol.pdf}
\caption{Various molecular systems considered in this study.
\label{fig:mol}}
\end{figure}
%%% %%% %%% %%%
For each compounds represented in Fig.~\ref{fig:mol}, we have computed the CASPT2 and CASPT3 vertical excitation energies with Dunning's aug-cc-pVTZ
basis set. \cite{Kendall_1992}
Geometries have been extracted from the QUEST database \cite{Veril_2021} and can be downloaded at \url{https://lcpq.github.io/QUESTDB_website}.
All the CASPT2 and CASPT3 calculations have been carried out with MOLPRO within the RS2 and RS3 contraction schemes as described in Refs.~\onlinecite{Werner_1996} and \onlinecite{Werner_2020}.
Both methods have been tested with and without IPEA (labeled as NOIPEA). Both methods have been tested with and without IPEA (labeled as NOIPEA).
The MOLPRO implementation of CASPT3 is based on a modification of the multi-reference configuration interaction (MRCI) module. \cite{Werner_1988,Knowles_1988}
For the sake of computational efficiency, the doubly-excited external configurations are internally contracted while the singly-excited internal and semi-internal configurations are left uncontracted. \cite{Werner_1996}
When an IPEA shift is applied, its value is set to the default value of \SI{0.25}{\hartree} as discussed in Ref.~\onlinecite{Ghigo_2004}.
These perturbative calculations have been performed by considering a state-averaged (SA) CASSCF wave function where we have included the ground state and (at least) the excited states of interest.
In several occasions, we have included additional excited states to avoid convergence and/or root-flipping issues.
For each system and transition, we report in the {\SupInf} the exhaustive description of the active spaces for each symmetry sector.
Additionally, for the challenging transitions, we have steadily increased the size of the active space to carefully assess the convergence of the vertical excitation energies of interest.
Finally, to alleviate the intruder state problem, a level shift of \SI{0.3}{\hartree} has been systematically applied. \cite{Roos_1995b,Roos_1996}
This value has been slightly increased in particularly difficult cases, and is specifically reported.
The usual statistical indicators are used in the following, namely, the mean signed error (MSE), the mean absolute error (MAE), the root-mean-square error (RMSE), the standard
deviation of the errors (SDE), as well as largest positive and negative deviations [Max($+$) and Max($-$), respectively].
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Results and discussion} \section{Results and discussion}
\label{sec:res} \label{sec:res}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
A detailed discussion of each individual molecule can be found in Ref.~\onlinecite{Sarka_2022} where we report relevant values from the literature.
Here, we focus on global trends.
The exhaustive list of CASPT2 and CASPT3 transitions can be found in Table \ref{tab:BigTab} and are represented in Fig.~\ref{fig:}.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Conclusion} \section{Conclusion}
\label{sec:ccl} \label{sec:ccl}

2
Manuscript/sup_CASPT3.tex
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@ -100,7 +100,7 @@ The composition of the active space is specified in terms of number of active or
The state-averaging procedure used is also described in terms of number of states per irreducible representation. The state-averaging procedure used is also described in terms of number of states per irreducible representation.
Note that, for all calculations, the ground state is systematically included in the state averaging Note that, for all calculations, the ground state is systematically included in the state averaging
procedure even if it does not belong to the same irreducible representation. procedure even if it does not belong to the same irreducible representation.
The cartesian coordinates have been extracted from the QUEST database \cite{Veril_2021} and can be download at \url{https://lcpq.github.io/QUESTDB_website}. The cartesian coordinates have been extracted from the QUEST database \cite{Veril_2021} and can be downloaded at \url{https://lcpq.github.io/QUESTDB_website}.
\begin{table*} \begin{table*}
\caption{Vertical transition energies (eV) of acetaldehyde.} \caption{Vertical transition energies (eV) of acetaldehyde.}