#### Dr. Christopher Stein

Theoretical Physics

University of Duisburg-Essen

##### Contact

- christopher[dot]stein[at]uni-due[dot]de
- +49 203 379 2228
- personal website

##### Hub

**A benchmark dataset for Hydrogen Combustion**

Guan, X. and Das, A. and Stein, C.J. and Heidar-Zadeh, F. and Bertels, L. and Liu, M. and Haghighatlari, M. and Li, J. and Zhang, O. and Hao, H. and Leven, I. and Head-Gordon, M. and Head-Gordon, T.*Scientific Data*9 (2022)The generation of reference data for deep learning models is challenging for reactive systems, and more so for combustion reactions due to the extreme conditions that create radical species and alternative spin states during the combustion process. Here, we extend intrinsic reaction coordinate (IRC) calculations with ab initio MD simulations and normal mode displacement calculations to more extensively cover the potential energy surface for 19 reaction channels for hydrogen combustion. A total of ∼290,000 potential energies and ∼1,270,000 nuclear force vectors are evaluated with a high quality range-separated hybrid density functional, ωB97X-V, to construct the reference data set, including transition state ensembles, for the deep learning models to study hydrogen combustion reaction. © 2022, The Author(s).view abstract 10.1038/s41597-022-01330-5 **Origin of the different reactivity of the high-valent coinage-metal complexes [RCuiiiMe3]− and [RAgiiiMe3]− (R=allyl)****

Auth, T. and Stein, C.J. and O'Hair, R.A.J. and Koszinowski, K.*Chemistry - A European Journal*28 (2022)High-valent tetraalkylcuprates(iii) and -argentates(iii) are key intermediates of copper- and silver-mediated C−C coupling reactions. Here, we investigate the previously reported contrasting reactivity of [RMiiiMe3]− complexes (M=Cu, Ag and R=allyl) with energy-dependent collision-induced dissociation experiments, advanced quantum-chemical calculations and kinetic computations. The gas-phase fragmentation experiments confirmed the preferred formation of the [RCuMe]− anion upon collisional activation of the cuprate(iii) species, consistent with a homo-coupling reaction, whereas the silver analogue primarily yielded [AgMe2]−, consistent with a cross-coupling reaction. For both complexes, density functional theory calculations identified one mechanism for homo coupling and four different ones for cross coupling. Of these pathways, an unprecedented concerted outer-sphere cross coupling is of particular interest, because it can explain the formation of [AgMe2]− from the argentate(iii) species. Remarkably, the different C−C coupling propensities of the two [RMiiiMe3]− complexes become only apparent when properly accounting for the multi-configurational character of the wave function for the key transition state of [RAgMe3]−. Backed by the obtained detailed mechanistic insight for the gas-phase reactions, we propose that the previously observed cross-coupling reaction of the silver complex in solution proceeds via the outer-sphere mechanism. © 2021 The Authors. Chemistry - A European Journal published by Wiley-VCH GmbHview abstract 10.1002/chem.202103130 **Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package**

Epifanovsky, E. and Gilbert, A.T.B. and Feng, X. and Lee, J. and Mao, Y. and Mardirossian, N. and Pokhilko, P. and White, A.F. and Coons, M.P. and Dempwolff, A.L. and Gan, Z. and Hait, D. and Horn, P.R. and Jacobson, L.D. and Kaliman, I. and Kussmann, J. and Lange, A.W. and Lao, K.U. and Levine, D.S. and Liu, J. and McKenzie, S.C. and Morrison, A.F. and Nanda, K.D. and Plasser, F. and Rehn, D.R. and Vidal, M.L. and You, Z.-Q. and Zhu, Y. and Alam, B. and Albrecht, B.J. and Aldossary, A. and Alguire, E. and Andersen, J.H. and Athavale, V. and Barton, D. and Begam, K. and Behn, A. and Bellonzi, N. and Bernard, Y.A. and Berquist, E.J. and Burton, H.G.A. and Carreras, A. and Carter-Fenk, K. and Chakraborty, R. and Chien, A.D. and Closser, K.D. and Cofer-Shabica, V. and Dasgupta, S. and De Wergifosse, M. and Deng, J. and Diedenhofen, M. and Do, H. and Ehlert, S. and Fang, P.-T. and Fatehi, S. and Feng, Q. and Friedhoff, T. and Gayvert, J. and Ge, Q. and Gidofalvi, G. and Goldey, M. and Gomes, J. and González-Espinoza, C.E. and Gulania, S. and Gunina, A.O. and Hanson-Heine, M.W.D. and Harbach, P.H.P. and Hauser, A. and Herbst, M.F. and Hernández Vera, M. and Hodecker, M. and Holden, Z.C. and Houck, S. and Huang, X. and Hui, K. and Huynh, B.C. and Ivanov, M. and Jász, Á. and Ji, H. and Jiang, H. and Kaduk, B. and Kähler, S. and Khistyaev, K. and Kim, J. and Kis, G. and Klunzinger, P. and Koczor-Benda, Z. and Koh, J.H. and Kosenkov, D. and Koulias, L. and Kowalczyk, T. and Krauter, C.M. and Kue, K. and Kunitsa, A. and Kus, T. and Ladjánszki, I. and Landau, A. and Lawler, K.V. and Lefrancois, D. and Lehtola, S. and Li, R.R. and Li, Y.-P. and Liang, J. and Liebenthal, M. and Lin, H.-H. and Lin, Y.-S. and Liu, F. and Liu, K.-Y. and Loipersberger, M. and Luenser, A. and Manjanath, A. and Manohar, P. and Mansoor, E. and Manzer, S.F. and Mao, S.-P. and Marenich, A.V. and Markovich, T. and Mason, S. and Maurer, S.A. and McLaughlin, P.F. and Menger, M.F.S.J. and Mewes, J.-M. and Mewes, S.A. and Morgante, P. and Mullinax, J.W. and Oosterbaan, K.J. and Paran, G. and Paul, A.C. and Paul, S.K. and Pavošević, F. and Pei, Z. and Prager, S. and Proynov, E.I. and Rák, Á. and Ramos-Cordoba, E. and Rana, B. and Rask, A.E. and Rettig, A. and Richard, R.M. and Rob, F. and Rossomme, E. and Scheele, T. and Scheurer, M. and Schneider, M. and Sergueev, N. and Sharada, S.M. and Skomorowski, W. and Small, D.W. and Stein, C.J. and Su, Y.-C. and Sundstrom, E.J. and Tao, Z. and Thirman, J. and Tornai, G.J. and Tsuchimochi, T. and Tubman, N.M. and Veccham, S.P. and Vydrov, O. and Wenzel, J. and Witte, J. and Yamada, A. and Yao, K. and Yeganeh, S. and Yost, S.R. and Zech, A. and Zhang, I.Y. and Zhang, X. and Zhang, Y. and Zuev, D. and Aspuru-Guzik, A. and Bell, A.T. and Besley, N.A. and Bravaya, K.B. and Brooks, B.R. and Casanova, D. and Chai, J.-D. and Coriani, S. and Cramer, C.J. and Cserey, G. and Deprince, A.E., III and Distasio, R.A., Jr. and Dreuw, A. and Dunietz, B.D. and Furlani, T.R. and Goddard, W.A., III and Hammes-Schiffer, S. and Head-Gordon, T. and Hehre, W.J. and Hsu, C.-P. and Jagau, T.-C. and Jung, Y. and Klamt, A. and Kong, J. and Lambrecht, D.S. and Liang, W. and Mayhall, N.J. and McCurdy, C.W. and Neaton, J.B. and Ochsenfeld, C. and Parkhill, J.A. and Peverati, R. and Rassolov, V.A. and Shao, Y. and Slipchenko, L.V. and Stauch, T. and Steele, R.P. and Subotnik, J.E. and Thom, A.J.W. and Tkatchenko, A. and Truhlar, D.G. and Van Voorhis, T. and Wesolowski, T.A. and Whaley, K.B. and Woodcock, H.L., III and Zimmerman, P.M. and Faraji, S. and Gill, P.M.W. and Head-Gordon, M. and Herbert, J.M. and Krylov, A.I.*Journal of Chemical Physics*155 (2021)This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware"model and an increasingly modular design. © 2021 Author(s).view abstract 10.1063/5.0055522 **Stripping away ion hydration shells in electrical double-layer formation: Water networks matter**

Alfarano, S.R. and Pezzotti, S. and Stein, C.J. and Lin, Z. and Sebastiani, F. and Funke, S. and Hoberg, C. and Kolling, I. and Ma, C.Y. and Mauelshagen, K. and Ockelmann, T. and Schwaab, G. and Fu, L. and Brubach, J.-B. and Roy, P. and Head-Gordon, M. and Tschulik, K. and Gaigeot, M.-P. and Havenith, M.*Proceedings of the National Academy of Sciences of the United States of America*118 (2021)The double layer at the solid/electrolyte interface is a key concept in electrochemistry. Here, we present an experimental study combined with simulations, which provides a molecular picture of the double-layer formation under applied voltage. By THz spectroscopy we are able to follow the stripping away of the cation/anion hydration shells for an NaCl electrolyte at the Au surface when decreasing/increasing the bias potential. While Na+ is attracted toward the electrode at the smallest applied negative potentials, stripping of the Cl2 hydration shell is observed only at higher potential values. These phenomena are directly measured by THz spectroscopy with ultrabright synchrotron light as a source and rationalized by accompanying molecular dynamics simulations and electronic-structure calculations. © 2021 National Academy of Sciences. All rights reserved.view abstract 10.1073/pnas.2108568118 **Modern quantum chemistry with [open]molcas**

Aquilante, F. and Autschbach, J. and Baiardi, A. and Battaglia, S. and Borin, V.A. and Chibotaru, L.F. and Conti, I. and De Vico, L. and Delcey, M. and Galván, I.F. and Ferré, N. and Freitag, L. and Garavelli, M. and Gong, X. and Knecht, S. and Larsson, E.D. and Lindh, R. and Lundberg, M. and Malmqvist, P.Å. and Nenov, A. and Norell, J. and Odelius, M. and Olivucci, M. and Pedersen, T.B. and Pedraza-González, L. and Phung, Q.M. and Pierloot, K. and Reiher, M. and Schapiro, I. and Segarra-Martí, J. and Segatta, F. and Seijo, L. and Sen, S. and Sergentu, D.-C. and Stein, C.J. and Ungur, L. and Vacher, M. and Valentini, A. and Veryazov, V.*Journal of Chemical Physics*152 (2020)MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions. © 2020 Author(s).view abstract 10.1063/5.0004835 **Semiclassical Dispersion Corrections Efficiently Improve Multiconfigurational Theory with Short-Range Density-Functional Dynamic Correlation**

Stein, C.J. and Reiher, M.*Journal of Physical Chemistry A*124 (2020)Multiconfigurational wave functions are known to describe the electronic structure across a Born-Oppenheimer surface qualitatively correct. However, for quantitative reaction energies, dynamic correlation originating from the many configurations involving excitations out of the restricted orbital space, the active space, must be considered. Standard procedures involve approximations that eventually limit the ultimate accuracy achievable (most prominently, multireference perturbation theory). At the same time, the computational cost increases dramatically due to the necessity to obtain higher-order reduced density matrices. It is this disproportion that leads us here to propose an MC-srDFT-D hybrid approach of semiclassical dispersion (D) corrections to cover long-range dynamic correlation in a multiconfigurational (MC) wave function theory, which includes short-range (sr) dynamic correlation by density functional theory (DFT) without double counting. We demonstrate that the reliability of this approach is very good (at negligible cost), especially when considering that standard second-order multireference perturbation theory usually overestimates dispersion interactions. © 2020 American Chemical Society.view abstract 10.1021/acs.jpca.0c02130 **autoCAS: A Program for Fully Automated Multiconfigurational Calculations**

Stein, C.J. and Reiher, M.*Journal of Computational Chemistry*40 (2019)We present our implementation autoCAS for fully automated multiconfigurational calculations, which we also make available free of charge on our webpages. The graphical user interface of autoCAS connects a general electronic structure program with a density-matrix renormalization group program to carry out our recently introduced automated active space selection protocol for multiconfigurational calculations (Stein and Reiher, J. Chem. Theory Comput., 2016, 12, 1760). Next to this active space selection, autoCAS carries out several steps of multiconfigurational calculations so that only a minimal input is required to start them, comparable to that of a standard Kohn–Sham density-functional theory calculation, so that black-box multiconfigurational calculations become feasible. Furthermore, we introduce a new extension to the selection algorithm that facilitates automated selections for molecules with large valence orbital spaces consisting of several hundred orbitals. © 2019 Wiley Periodicals, Inc. © 2019 Wiley Periodicals, Inc.view abstract 10.1002/jcc.25869 **OpenMolcas: From Source Code to Insight**

Fdez. Galván, I. and Vacher, M. and Alavi, A. and Angeli, C. and Aquilante, F. and Autschbach, J. and Bao, J.J. and Bokarev, S.I. and Bogdanov, N.A. and Carlson, R.K. and Chibotaru, L.F. and Creutzberg, J. and Dattani, N. and Delcey, M.G. and Dong, S.S. and Dreuw, A. and Freitag, L. and Frutos, L.M. and Gagliardi, L. and Gendron, F. and Giussani, A. and González, L. and Grell, G. and Guo, M. and Hoyer, C.E. and Johansson, M. and Keller, S. and Knecht, S. and Kovačević, G. and Källman, E. and Li Manni, G. and Lundberg, M. and Ma, Y. and Mai, S. and Malhado, J.P. and Malmqvist, P.Å. and Marquetand, P. and Mewes, S.A. and Norell, J. and Olivucci, M. and Oppel, M. and Phung, Q.M. and Pierloot, K. and Plasser, F. and Reiher, M. and Sand, A.M. and Schapiro, I. and Sharma, P. and Stein, C.J. and Sørensen, L.K. and Truhlar, D.G. and Ugandi, M. and Ungur, L. and Valentini, A. and Vancoillie, S. and Veryazov, V. and Weser, O. and Wesołowski, T.A. and Widmark, P.-O. and Wouters, S. and Zech, A. and Zobel, J.P. and Lindh, R.*Journal of Chemical Theory and Computation*15 (2019)In this Article we describe the OpenMolcas environment and invite the computational chemistry community to collaborate. The open-source project already includes a large number of new developments realized during the transition from the commercial MOLCAS product to the open-source platform. The paper initially describes the technical details of the new software development platform. This is followed by brief presentations of many new methods, implementations, and features of the OpenMolcas program suite. These developments include novel wave function methods such as stochastic complete active space self-consistent field, density matrix renormalization group (DMRG) methods, and hybrid multiconfigurational wave function and density functional theory models. Some of these implementations include an array of additional options and functionalities. The paper proceeds and describes developments related to explorations of potential energy surfaces. Here we present methods for the optimization of conical intersections, the simulation of adiabatic and nonadiabatic molecular dynamics, and interfaces to tools for semiclassical and quantum mechanical nuclear dynamics. Furthermore, the Article describes features unique to simulations of spectroscopic and magnetic phenomena such as the exact semiclassical description of the interaction between light and matter, various X-ray processes, magnetic circular dichroism, and properties. Finally, the paper describes a number of built-in and add-on features to support the OpenMolcas platform with postcalculation analysis and visualization, a multiscale simulation option using frozen-density embedding theory, and new electronic and muonic basis sets. Copyright © 2019 American Chemical Society.view abstract 10.1021/acs.jctc.9b00532 **Optimization of highly excited matrix product states with an application to vibrational spectroscopy**

Baiardi, A. and Stein, C.J. and Barone, V. and Reiher, M.*Journal of Chemical Physics*150 (2019)An efficient approximation to the full configuration interaction solution can be obtained with the density matrix renormalization group (DMRG) algorithm without a restriction to a predefined excitation level. In a standard DMRG implementation, however, excited states are calculated with a ground-state optimization in the space orthogonal to all lower lying wave function solutions. A trivial parallelization is therefore not possible, and the calculation of highly excited states becomes prohibitively expensive, especially in regions with a high density of states. Here, we introduce two variants of the DMRG algorithm that allows us to target directly specific energy regions and therefore highly excited states. The first one, based on shift-and-invert techniques, is particularly efficient for low-lying states but is not stable in regions with a high density of states. The second one, based on the folded auxiliary operator, is less efficient but more accurate in targeting high-energy states. We apply the algorithm to the solution of the nuclear Schrödinger equation but emphasize that it can be applied to the diagonalization of general Hamiltonians as well, such as the electronic Coulomb Hamiltonian to address X-ray spectra. In combination with several root-homing algorithms and a stochastic sampling of the determinant space, excited states of interest can be adequately tracked and analyzed during the optimization. We validate these algorithms by calculating several highly excited vibrational states of ethylene and demonstrate that we can accurately calculate prominent spectral features of large molecules such as the sarcosine-glycine dipeptide. © 2019 Author(s).view abstract 10.1063/1.5068747 **Orbital Entanglement Analysis of Exchange-Coupled Systems**

Stein, C.J. and Pantazis, D.A. and Krewald, V.*Journal of Physical Chemistry Letters*10 (2019)A new tool for the interpretation of multiconfigurational wave functions representing the spin states of exchange-coupled transition metal complexes is introduced. Based on orbital entanglement measures, herein derived from multiconfigurational density matrix renormalization group calculations, the complexity of the wave function is reduced, thus facilitating a connection with established concepts for the interpretation of magnetically coupled systems. We show that the entanglement of localized orbitals with a small basis set is a good representation of the magnetic coupling topology and that it is sensitive to chemical changes in homologous complexes. Furthermore, we introduce a measure for the magnetic relevance of orbitals in the active subspace and a concept for the quantitative comparison of different chemical species. The approach presented here will be easily applicable to higher nuclearity clusters, providing a direct insight into all states of the Heisenberg spin ladder for systems previously accessible only by single-configurational methods. Copyright © 2019 American Chemical Society.view abstract 10.1021/acs.jpclett.9b02417 **The Poisson-Boltzmann model for implicit solvation of electrolyte solutions: Quantum chemical implementation and assessment via Sechenov coefficients**

Stein, C.J. and Herbert, J.M. and Head-Gordon, M.*Journal of Chemical Physics*151 (2019)We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the solute. A hierarchy of approximations for this model includes a linear approximation for weak electrostatic potentials, finite size of the mobile electrolyte ions, and a Stern-layer correction. Recasting the Poisson-Boltzmann equations into Euler-Lagrange equations then significantly simplifies the derivation of the free energy of solvation for these approximate models. The parameters of the model are either fit directly to experimental observables - e.g., the finite ion size - or optimized for agreement with experimental results. Experimental data for this optimization are available in the form of Sechenov coefficients that describe the linear dependence of the salting-out effect of solutes with respect to the electrolyte concentration. In the final part, we rationalize the qualitative disagreement of the finite ion size modification to the Poisson-Boltzmann model with experimental observations by taking into account the electrolyte concentration dependence of the Stern layer. A route toward a revised model that captures the experimental observations while including the finite ion size effects is then outlined. This implementation paves the way for the study of electrochemical and electrocatalytic processes of molecules and cluster models with accurate electronic structure methods. © 2019 Author(s).view abstract 10.1063/1.5131020 **Engineering Molecular Iodine Catalysis for Alkyl-Nitrogen Bond Formation**

Duhamel, T. and Stein, C.J. and Martínez, C. and Reiher, M. and Muñiz, K.*ACS Catalysis*8 (2018)An advanced protocol for the intramolecular C-H amination of alkyl groups via amidyl radicals (Hofmann-Löffler reaction) under homogeneous iodine catalysis is reported. This protocol employs common mCPBA as terminal oxidant. It proceeds under mild conditions, with complete chemoselectivity, is compatible with radical intermediates, and allows for the selective intramolecular amination reaction of secondary and tertiary hydrocarbon bonds and is not restricted to benzylic C-H amination. The involvement of an iodine(III) catalyst state in the C-N bond formation derives from selective oxidation at the stage of the corresponding alkyl iodide with mCPBA. Its formation is corroborated by quantum-chemical calculations. This new catalysis thus proceeds within a defined iodine(I/III) catalysis manifold. © 2018 American Chemical Society.view abstract 10.1021/acscatal.8b00286 **Structure and dynamics of the radical cation of ethane arising from the Jahn-Teller and pseudo-Jahn-Teller effects**

Jacovella, U. and Stein, C.J. and Grütter, M. and Freitag, L. and Lauzin, C. and Reiher, M. and Merkt, F.*Physical Chemistry Chemical Physics*20 (2018)The pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of C2H6 has been recorded in the region of the adiabatic ionization threshold. The partially rotationally resolved spectrum indicates the existence of several vibronic states of C2H6+ with less than 600 cm-1 of internal excitation. The analysis of the rotational structures assisted by ab initio calculations enabled the determination of the adiabatic ionization energy of C2H6 and the investigation of the structure and dynamics of C2H6+ at low energies. The ground state of C2H6+ is found to be a 2Ag state of diborane-like structure with strongly mixed (a1g)-1 and (eg)-1 configurations. The vibrational structure reveals the importance of large-amplitude nuclear motions involving the diborane distortion modes, the C-C stretching motion, and the internal rotation at elongated C-C distances. The spectrum is analyzed in the light of the information obtained in earlier studies of C2H6+ by ab initio quantum chemistry, EPR spectroscopy and photoelectron spectroscopy. © 2018 the Owner Societies.view abstract 10.1039/c7cp06907c **Automated identification of relevant frontier orbitals for chemical compounds and processes**

Stein, C.J. and Reiher, M.*Chimia*71 (2017)Quantum-chemical multi-configurational methods are required for a proper description of static electron correlation, a phenomenon inherent to the electronic structure of molecules with multiple (near-)degenerate frontier orbitals. Here, we review how a property of these frontier orbitals, namely the entanglement entropy is related to static electron correlation. A subset of orbitals, the so-called active orbital space is an essential ingredient for all multi-configurational methods. We proposed an automated selection of this active orbital space, that would otherwise be a tedious and error prone manual procedure, based on entanglement measures. Here, we extend this scheme to demonstrate its capability for the selection of consistent active spaces for several excited states and along reaction coordinates. © Swiss Chemical Society.view abstract 10.2533/chimia.2017.170 **Cooperative Light-Activated Iodine and Photoredox Catalysis for the Amination of Csp3 −H Bonds**

Becker, P. and Duhamel, T. and Stein, C.J. and Reiher, M. and Muñiz, K.*Angewandte Chemie - International Edition*56 (2017)An unprecedented method that makes use of the cooperative interplay between molecular iodine and photoredox catalysis has been developed for dual light-activated intramolecular benzylic C−H amination. Iodine serves as the catalyst for the formation of a new C−N bond by activating a remote C sp3 −H bond (1,5-HAT process) under visible-light irradiation while the organic photoredox catalyst TPT effects the reoxidation of the molecular iodine catalyst. To explain the compatibility of the two involved photochemical steps, the key N−I bond activation was elucidated by computational methods. The new cooperative catalysis has important implications for the combination of non-metallic main-group catalysis with photocatalysis. © 2017 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.view abstract 10.1002/anie.201703611 **Measuring multi-configurational character by orbital entanglement**

Stein, C.J. and Reiher, M.*Molecular Physics*115 (2017)One of the most critical tasks at the very beginning of a quantum chemical investigation is the choice of either a multi- or single-configurational method. Naturally, many proposals exist to define a suitable diagnostic of the multi-configurational character for various types of wave functions in order to assist this crucial decision. Here, we present a new orbital-entanglement-based multi-configurational diagnostic termed Zs(1). The correspondence of orbital entanglement and static (or non-dynamic) electron correlation permits the definition of such a diagnostic. We chose our diagnostic to meet important requirements such as well-defined limits for pure single-configurational and multi-configurational wave functions. The Zs(1) diagnostic can be evaluated from a partially converged, but qualitatively correct, and therefore inexpensive density matrix renormalisation group wave function as in our recently presented automated active orbital selection protocol. Its robustness and the fact that it can be evaluated at low cost make this diagnostic a practical tool for routine applications. © 2017 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.view abstract 10.1080/00268976.2017.1288934 **Quantum Chemical Spin Densities for Radical Cations of Photosynthetic Pigment Models**

Artiukhin, D.G. and Stein, C.J. and Reiher, M. and Neugebauer, J.*Photochemistry and Photobiology*93 (2017)The spin densities of radical cations of magnesium porphyrin, magnesium chlorine and a truncated chlorophyll a model are calculated with density-functional theory and multiconfigurational quantum chemical methods. The latter serve as a reference for approximate density-functional theory which yields spin densities that may suffer from the self-interaction error. We carried out complete active space self-consistent field calculations with increasing active orbital spaces to systematically converge qualitatively correct spin densities. In particular, for the magnesium chlorine and chlorophyll a model radical cations, this is not easy to achieve because of the lower symmetry compared to magnesium porphyrin. Strategies had to be employed which allowed us to consider very large active orbital spaces. We explored restricted active space self-consistent field and density-matrix renormalization group calculations. Based on these reference data, we assessed the accuracy of different density-functional approximations. We show that in particular, exchange–correlation model potentials with correct asymptotic behavior yield good spin densities, and we find, in agreement with previous studies on different classes of compounds, that hybrid functionals systematically increase spin-polarization effects with increasing amounts of exact exchange. Our results provide a starting point for investigations of spin densities of more complex systems such as the hinge model for the primary electron donor in photosystem II. © 2017 The American Society of Photobiologyview abstract 10.1111/php.12757 **Redox Activity of Oxo-Bridged Iridium Dimers in an N,O-Donor Environment: Characterization of Remarkably Stable Ir(IV,V) Complexes**

Sinha, S.B. and Shopov, D.Y. and Sharninghausen, L.S. and Stein, C.J. and Mercado, B.Q. and Balcells, D. and Pedersen, T.B. and Reiher, M. and Brudvig, G.W. and Crabtree, R.H.*Journal of the American Chemical Society*139 (2017)Chemical and electrochemical oxidation or reduction of our recently reported Ir(IV,IV) mono-μ-oxo dimers results in the formation of fully characterized Ir(IV,V) and Ir(III,III) complexes. The Ir(IV,V) dimers are unprecedented and exhibit remarkable stability under ambient conditions. This stability and modest reduction potential of 0.99 V vs NHE is in part attributed to complete charge delocalization across both Ir centers. Trends in crystallographic bond lengths and angles shed light on the structural changes accompanying oxidation and reduction. The similarity of these mono-μ-oxo dimers to our Ir "blue solution" water-oxidation catalyst gives insight into potential reactive intermediates of this structurally elusive catalyst. Additionally, a highly reactive material, proposed to be a Ir(V,V) μ-oxo species, is formed on electrochemical oxidation of the Ir(IV,V) complex in organic solvents at 1.9 V vs NHE. Spectroelectrochemistry shows reversible conversion between the Ir(IV,V) and proposed Ir(V,V) species without any degradation, highlighting the exceptional oxidation resistance of the 2-(2-pyridinyl)-2-propanolate (pyalk) ligand and robustness of these dimers. The Ir(III,III), Ir(IV,IV) and Ir(IV,V) redox states have been computationally studied both with DFT and multiconfigurational calculations. The calculations support the stability of these complexes and provide further insight into their electronic structures. © 2017 American Chemical Society.view abstract 10.1021/jacs.7b04874 **Vibrational Density Matrix Renormalization Group**

Baiardi, A. and Stein, C.J. and Barone, V. and Reiher, M.*Journal of Chemical Theory and Computation*13 (2017)Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. Here, we demonstrate how the density matrix renormalization group (DMRG) can be exploited to optimize vibrational wave functions (vDMRG) expressed as matrix product states. We study the convergence of these calculations with respect to the size of the local basis of each mode, the number of renormalized block states, and the number of DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for small molecules that were intensively studied in the literature. We then proceed to show that the complete fingerprint region of the sarcosyn-glycin dipeptide can be calculated with vDMRG. © 2017 American Chemical Society.view abstract 10.1021/acs.jctc.7b00329 **Automated Selection of Active Orbital Spaces**

Stein, C.J. and Reiher, M.*Journal of Chemical Theory and Computation*12 (2016)One of the key challenges of quantum-chemical multi-configuration methods is the necessity to manually select orbitals for the active space. This selection requires both expertise and experience and can therefore impose severe limitations on the applicability of this most general class of ab initio methods. A poor choice of the active orbital space may yield even qualitatively wrong results. This is obviously a severe problem, especially for wave function methods that are designed to be systematically improvable. Here, we show how the iterative nature of the density matrix renormalization group combined with its capability to include up to about 100 orbitals in the active space can be exploited for a systematic assessment and selection of active orbitals. These benefits allow us to implement an automated approach for active orbital space selection, which can turn multi-configuration models into black box approaches. © 2016 American Chemical Society.view abstract 10.1021/acs.jctc.6b00156 **New approaches for ab initio calculations of molecules with strong electron correlation**

Knecht, S. and Hedegård, E.D. and Keller, S. and Kovyrshin, A. and Ma, Y. and Muolo, A. and Stein, C.J. and Reiher, M.*Chimia*70 (2016)Reliable quantum chemical methods for the description of molecules with dense-lying frontier orbitals are needed in the context of many chemical compounds and reactions. Here, we review developments that led to our new computational toolbox which implements the quantum chemical density matrix renormalization group in a second-generation algorithm. We present an overview of the different components of this toolbox. © Swiss Chemical Society.view abstract 10.2533/chimia.2016.244 **The Delicate Balance of Static and Dynamic Electron Correlation**

Stein, C.J. and Von Burg, V. and Reiher, M.*Journal of Chemical Theory and Computation*12 (2016)Multi-configurational approaches yield universal wave function parametrizations that can qualitatively well describe electronic structures along reaction pathways. For quantitative results, multi-reference perturbation theory is required to capture dynamic electron correlation from the otherwise neglected virtual orbitals. Still, the overall accuracy suffers from the finite size and choice of the active orbital space and peculiarities of the perturbation theory. Fortunately, the electronic wave functions at equilibrium structures of reactants and products can often be well described by single-reference methods and hence are accessible to accurate coupled cluster calculations. Here, we calculate the heterolytic double dissociation energy of four 3d-metallocenes with the complete active space self-consistent field method and compare to highly accurate coupled cluster data. Our coupled cluster data are well within the experimental error bars. This accuracy can also be approached by complete active space calculations with an orbital selection based on information entropy measures. The entropy based active space selection is discussed in detail. We find a very subtle balance between static and dynamic electron correlation effects that emphasizes the need for algorithmic active space selection and that differs significantly from restricted active space results for identical active spaces reported in the literature. © 2016 American Chemical Society.view abstract 10.1021/acs.jctc.6b00528 **Accurate calculation of the dissociation energy of the highly anharmonic system ClHCl-**

Stein, C. and Oswald, R. and Botschwina, P. and Peterson, K.A.*Journal of Physical Chemistry A*119 (2015)Accurate bond dissociation energies (D0) are reported for different isotopologues of the highly anharmonic system ClHCl-. The mass-independent equilibrium dissociation energy De was obtained by a composite method with frozen-core (fc) CCSD(T) as the basic contribution. Basis sets as large as aug-cc-pV8(+d)Z were employed, and extrapolation to the complete basis set (CBS) limit was carried out. Explicitly correlated calculations with the CCSD(T)-F12b method were also performed to support the conventionally calculated values. Core-core and core-valence correlation, scalar relativity, and higher-order correlation were considered as well. Two mass-dependent contributions, namely, the diagonal Born-Oppenheimer correction and the difference in zero-point energies between the complex and the HCl fragment, were then added in order to arrive at precise D0 values. Results for 35ClH35Cl- and 35ClD35Cl- are 23.81 and 23.63 kcal/mol, respectively, with estimated uncertainties of 0.05 kcal/mol. In contrast to FHF- (Stein, C.; Oswald, R.; Sebald, P.; Botschwina, P.; Stoll, H., Peterson, K. A. Mol. Phys. 2013, 111, 2647-2652), the D0 values of the bichloride species are larger than their De counterparts, which is an unusual situation in hydrogen-bonded systems. © 2014 American Chemical Society.view abstract 10.1021/jp509711g **Challenging High-Level ab initio Rovibrational Spectroscopy: The Nitrous Oxide Molecule**

Schröder, B. and Sebald, P. and Stein, C. and Weser, O. and Botschwina, P.*Zeitschrift fur Physikalische Chemie*229 (2015)The equilibrium structure and rovibrational energies of nitrous oxide (N2O) in its electronic ground state (X1Σ+) are derived from a high-level ab initio potential energy function (PEF). This PEF is based on a composite approach with the basic contribution given by explicitly correlated coupled-cluster (CC) calculations. Smaller contributions include corrections due to inner-shell correlation, scalar-relativistic effects and higher-order correlation up to iterative pentuple excitations (CCSDTQP in CC nomenclature). The high importance of higher-order correlation in order to reach the desired accuracy led to the use of an extrapolation scheme to approximately account for the effect of hextuple and some pentuple excitations. A reasoning for the soundness of the method is given in this work. The results of the rovibrational calculations are compared to those of two multi-reference (MR) based composite PEFs, where the basic contribution is given by MR configuration interaction and MR average coupled-pair functional calculations. A highly accurate electric dipole moment function is also computed by the three composite methods in excellent agreement with the experimental values available. Subtle irregularities in the intensity pattern are reproduced in great detail and several kinds of resonances are analyzed without the need to empirically adjust our best ab initio PEF. The equilibrium bond lengths were determined by a mixed experimental/theoretical approach yielding Re(NN) = 1.12695(10)Å and Re(NO) = 1.18539(5)Å. © 2015 Walter de Gruyter Berlin/Boston.view abstract 10.1515/zpch-2015-0622 **High-level theoretical spectroscopic parameters for three ions of astrochemical interest**

Stein, C. and Weser, O. and Schröder, B. and Botschwina, P.*Molecular Physics*113 (2015)The equilibrium geometry and rovibrational spectroscopic parameters of the three astrochemical ions l-C3H+, l-SiC2H+, and C3N- and some of their isotopologues are obtained from high-level quantum chemical calculations. A composite approach based on the explicitly correlated coupled-cluster method CCSD(T)-F12b, that further includes core correlation, scalar-relativistic effects and most importantly higher order correlation beyond CCSD(T) is used to set-up the near-equilibrium potential energy surface (PES). The spectroscopic parameters of these linear tetra-atomic ions are then extracted from these PESs by vibrational perturbation theory of second order (VPT2). Calculation of absolute intensities is also carried out for the stretching frequencies of the cations in order to identify the bands that are most likely to be detected. The importance of the accurate calculation of the rotational constants B0 and D0 for astrochemistry is discussed as well as the limits of VPT2 in this context and reasons for these limitations. © 2015 Taylor & Francis.view abstract 10.1080/00268976.2015.1017019 **Theoretical rovibrational spectroscopy of NO2+**

Botschwina, P. and Bargholz, A. and Sebald, P. and Stein, C. and Schröder, B. and Oswald, R.*Journal of Molecular Spectroscopy*311 (2015)Accurate near-equilibrium potential energy functions (PEFs) have been constructed for the nitronium ion (NO2+) by composite methods using either CCSD(T)-F12b or explicitly correlated multi-reference methods (MRCI-F12+Q or MRACPF-F12) as dominant contributions. Up to pentuple substitutions are required in the coupled-cluster based approach to reach convergence in the wavenumbers of the fundamentals to ca. 1 cm-1. These are predicted to be ν1=1386.0cm-1,ν1=621.1 cm-1 and ν3=2342.8 cm-1. All values differ significantly from the results of previous studies by zero-kinetic energy (ZEKE) spectroscopy and reanalysis or remeasurement is suggested. Compared to neon-matrix IR spectroscopic work of Jacox and coworkers the present calculations yield smaller wavenumbers of Δν3=-5.4 cm-1 and Δ(ν1+ν3)=-7.9 cm-1 so that blueshifting is predicted for those absorptions. The calculated isotopic shifts for both bands are in excellent agreement with the corresponding experimental values. Accurate values for rotational and centrifugal distortion constants of NO2+ in different vibrational states are predicted which should be of help in the search for forthcoming high-resolution spectra of that cation. © 2014 Elsevier Inc. All rights reserved.view abstract 10.1016/j.jms.2014.11.005 **Strong theoretical support for the assignment of B11244 to l-C 3H+**

Botschwina, P. and Stein, C. and Sebald, P. and Schröder, B. and Oswald, R.*Astrophysical Journal*787 (2014)Highly accurate quantum chemical calculations beyond CCSD(T) have been used to study the molecular cation l-C3H+ which is the carrier of harmonically related radio lines observed in the Horsehead photodissociation region and toward Sgr B2(N). Excellent agreement with spectroscopic and radioastronomical measurements is obtained for the rotational constant, with the calculated value of B 0 = 11246.4 MHz only 1.5 MHz or 0.01% above the experimental value. The unusually large ratio of centrifugal distortion constants D 0(exp.)De(theor.) = 1.80 is attributed to the shallow CCC bending potential of l-C3H+ and is quantitatively reproduced by variational calculations within a pseudo-triatomic model. A comparative study of centrifugal distortion constants in a series of four linear interstellar molecules (C3N-, C3O, l-C3H+, and C3) is made and some general conclusions are drawn. © 2014. The American Astronomical Society. All rights reserved.view abstract 10.1088/0004-637X/787/1/72 **Accurate bond dissociation energies (D0) for FHF- isotopologues**

Stein, C. and Oswald, R. and Sebald, P. and Botschwina, P. and Stoll, H. and Peterson, K.A.*Molecular Physics*111 (2013)Accurate bond dissociation energies (D 0) are determined for three isotopologues of the bifluoride ion (FHF-). While the zero-point vibrational contributions are taken from our previous work (P. Sebald, A. Bargholz, R. Oswald, C. Stein, P. Botschwina, J. Phys. Chem. A, DOI: 10.1021/jp3123677), the equilibrium dissociation energy (D e ) of the reaction FHF-→ F-+ HF was obtained by a composite method including frozen-core (fc) CCSD(T) calculations with basis sets up to cardinal number n = 7 followed by extrapolation to the complete basis set limit. Smaller terms beyond fc-CCSD(T) cancel each other almost completely. The D 0 values of FHF-, FDF-, and FTF- are predicted to be 15,176, 15,191, and 15,198 cm-1, respectively, with an uncertainty of ca. 15 cm-1. © 2013 Taylor and Francis Group, LLC.view abstract 10.1080/00268976.2013.809165 **FHF- isotopologues: Highly anharmonic hydrogen-bonded systems with strong coriolis interaction**

Sebald, P. and Bargholz, A. and Oswald, R. and Stein, C. and Botschwina, P.*Journal of Physical Chemistry A*117 (2013)Explicitly correlated coupled cluster theory at the CCSD(T*)-F12b level in conjunction with the aug-cc-pV5Z basis set has been used in the calculation of three-dimensional potential energy and dipole moment surfaces for the bifluoride ion (FHF-). An empirically corrected analytical potential energy function (PEF) was obtained by fit to four pieces of accurate spectroscopic information. That PEF was used in variational calculations of energies and wave functions for a variety of rovibrational states of the isotopologues FHF-, FDF-, and FTF-. Excellent agreement with available data from IR laser diode spectroscopy is observed and many predictions are being made. Unusual isotope effects among the spectroscopic constants and unusual features of the calculated line spectra are discussed. © 2013 American Chemical Society.view abstract 10.1021/jp3123677 **Rovibrational states of N 3 - And CO2 up to high J: A theoretical study beyond fc-CCSD(T)**

Sebald, P. and Stein, C. and Oswald, R. and Botschwina, P.*Journal of Physical Chemistry A*117 (2013)An accurate near-equilibrium potential energy surface (PES) has been constructed for the azide ion (N3-) on the basis of coupled cluster calculations up to CCSDTQ (Kállay, M.; Surján, P. R. J. Chem. Phys. 2001, 115, 2945.), with contributions from inner-shell correlation and special relativity being taken into account as well. A larger number of rovibrational states has been investigated by variational calculations with Watson's isomorphic Hamiltonian for linear molecules. Analogous calculations for CO2 demonstrate the high quality of this type of calculations. The Gv values of the symmetric stretching and bending vibration of 14N3- are predicted to be ν1 = 1307.9 cm-1 and ν2 = 629.3 cm-1, with an uncertainty of ca. 1 cm-1. Fermi resonance is less pronounced for the lower polyads of 14N3- compared with 12C 16O2 but is as strong as in CO2 for the lowest diad of isotopologue 15-14-15. The band origin of the antisymmetric stretching vibration of 14N3- is calculated to be ν3 = 1986.4 cm-1, only 0.1 cm-1 lower than the experimental value. The corresponding vibrational transition dipole moment is predicted to be as large as μ = 0.476 D, 46% higher than calculated for CO2. The perturbed combination tone (0111), which was accessible through diode laser IR spectroscopy, undergoes anharmonic interaction with at least two other vibrational states. © 2013 American Chemical Society.view abstract 10.1021/jp4081806

#### modelling and simulation

#### numerical methods

#### quantum theory