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Maste S, Sharma B, Pongratz T, Grabe B, Hiller W, Erlach MB, Kremer W, Kalbitzer HR, Marx D, Kast SM. The accuracy limit of chemical shift predictions for species in aqueous solution. Phys Chem Chem Phys 2024; 26:6386-6395. [PMID: 38315169 DOI: 10.1039/d3cp05471c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2024]
Abstract
Interpreting NMR experiments benefits from first-principles predictions of chemical shifts. Reaching the accuracy limit of theory is relevant for unambiguous structural analysis and dissecting theoretical approximations. Since accurate chemical shift measurements are based on using internal reference compounds such as trimethylsilylpropanesulfonate (DSS), a detailed comparison of experimental with theoretical data requires simultaneous consideration of both target and reference species ensembles in the same solvent environment. Here we show that ab initio molecular dynamics simulations to generate liquid-state ensembles of target and reference compounds, including explicitly their short-range solvation environments and combined with quantum-mechanical solvation models, allows for predicting highly accurate 1H (∼0.1-0.5 ppm) and aliphatic 13C (∼1.5 ppm) chemical shifts for aqueous solutions of the model compounds trimethylamine N-oxide (TMAO) and N-methylacetamide (NMA), referenced to DSS without any system-specific adjustments. This encompasses the two peptide bond conformations of NMA identified by NMR. The results are used to derive a general-purpose guideline set for predictive NMR chemical shift calculations of NMA in the liquid state and to identify artifacts of force field models. Accurate predictions are only obtained if a sufficient number of explicit water molecules is included in the quantum-mechanical calculations, disproving a purely electrostatic model of the solvent effect on chemical shifts.
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Affiliation(s)
- Stefan Maste
- Fakultät für Chemie und Chemische Biologie, Technische Universität Dortmund, Otto-Hahn-Straße 4a, 44227 Dortmund, Germany.
| | - Bikramjit Sharma
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany.
| | - Tim Pongratz
- Fakultät für Chemie und Chemische Biologie, Technische Universität Dortmund, Otto-Hahn-Straße 4a, 44227 Dortmund, Germany.
| | - Bastian Grabe
- Fakultät für Chemie und Chemische Biologie, Technische Universität Dortmund, Otto-Hahn-Straße 4a, 44227 Dortmund, Germany.
| | - Wolf Hiller
- Fakultät für Chemie und Chemische Biologie, Technische Universität Dortmund, Otto-Hahn-Straße 4a, 44227 Dortmund, Germany.
| | - Markus Beck Erlach
- Fakultät für Biologie und Vorklinische Medizin, Universität Regensburg, 93040 Regensburg, Germany
| | - Werner Kremer
- Fakultät für Biologie und Vorklinische Medizin, Universität Regensburg, 93040 Regensburg, Germany
| | - Hans Robert Kalbitzer
- Fakultät für Biologie und Vorklinische Medizin, Universität Regensburg, 93040 Regensburg, Germany
| | - Dominik Marx
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany.
| | - Stefan M Kast
- Fakultät für Chemie und Chemische Biologie, Technische Universität Dortmund, Otto-Hahn-Straße 4a, 44227 Dortmund, Germany.
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Imamura K, Yokogawa D, Sato H. Recent developments and applications of reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED): A hybrid model of quantum chemistry and integral equation theory of molecular liquids. J Chem Phys 2024; 160:050901. [PMID: 38341702 DOI: 10.1063/5.0190116] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/04/2023] [Accepted: 01/04/2024] [Indexed: 02/13/2024] Open
Abstract
The significance of solvent effects in electronic structure calculations has long been noted, and various methods have been developed to consider this effect. The reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED) is a hybrid model that combines the integral equation theory of molecular liquids with quantum chemistry. This method can consider the statistically convergent solvent distribution at a significantly lower cost than molecular dynamics simulations. Because the RISM theory explicitly considers the solvent structure, it performs well for systems where hydrogen bonds are formed between the solute and solvent molecules, which is a challenge for continuum solvent models. Taking advantage of being founded on the variational principle, theoretical developments have been made in calculating various properties and incorporating electron correlation effects. In this review, we organize the theoretical aspects of RISM-SCF-cSED and its distinctions from other hybrid methods involving integral equation theories. Furthermore, we carefully present its progress in terms of theoretical developments and recent applications.
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Affiliation(s)
- Kosuke Imamura
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
| | - Daisuke Yokogawa
- Graduate School of Arts and Science, The University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan
| | - Hirofumi Sato
- Department of Molecular Engineering, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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3
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Tran VA, Teucher M, Galazzo L, Sharma B, Pongratz T, Kast SM, Marx D, Bordignon E, Schnegg A, Neese F. Dissecting the Molecular Origin of g-Tensor Heterogeneity and Strain in Nitroxide Radicals in Water: Electron Paramagnetic Resonance Experiment versus Theory. J Phys Chem A 2023; 127:6447-6466. [PMID: 37524058 PMCID: PMC10424240 DOI: 10.1021/acs.jpca.3c02879] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Revised: 07/01/2023] [Indexed: 08/02/2023]
Abstract
Nitroxides are common EPR sensors of microenvironmental properties such as polarity, numbers of H-bonds, pH, and so forth. Their solvation in an aqueous environment is facilitated by their high propensity to form H-bonds with the surrounding water molecules. Their g- and A-tensor elements are key parameters to extracting the properties of their microenvironment. In particular, the gxx value of nitroxides is rich in information. It is known to be characterized by discrete values representing nitroxide populations previously assigned to have different H-bonds with the surrounding waters. Additionally, there is a large g-strain, that is, a broadening of g-values associated with it, which is generally correlated with environmental and structural micro-heterogeneities. The g-strain is responsible for the frequency dependence of the apparent line width of the EPR spectra, which becomes evident at high field/frequency. Here, we address the molecular origin of the gxx heterogeneity and of the g-strain of a nitroxide moiety (HMI: 2,2,3,4,5,5-hexamethylimidazolidin-1-oxyl, C9H19N2O) in water. To treat the solvation effect on the g-strain, we combined a multi-frequency experimental approach with ab initio molecular dynamics simulations for structural sampling and quantum chemical EPR property calculations at the highest realistically affordable level, including an explicitly micro-solvated HMI ensemble and the embedded cluster reference interaction site model. We could clearly identify the distinct populations of the H-bonded nitroxides responsible for the gxx heterogeneity experimentally observed, and we dissected the role of the solvation shell, H-bond formation, and structural deformation of the nitroxide in the creation of the g-strain associated with each nitroxide subensemble. Two contributions to the g-strain were identified in this study. The first contribution depends on the number of hydrogen bonds formed between the nitroxide and the solvent because this has a large and well-understood effect on the gxx-shift. This contribution can only be resolved at high resonance frequencies, where it leads to distinct peaks in the gxx region. The second contribution arises from configurational fluctuations of the nitroxide that necessarily lead to g-shift heterogeneity. These contributions cannot be resolved experimentally as distinct resonances but add to the line broadening. They can be quantitatively analyzed by studying the apparent line width as a function of microwave frequency. Interestingly, both theory and experiment confirm that this contribution is independent of the number of H-bonds. Perhaps even more surprisingly, the theoretical analysis suggests that the configurational fluctuation broadening is not induced by the solvent but is inherently present even in the gas phase. Moreover, the calculations predict that this broadening decreases upon solvation of the nitroxide.
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Affiliation(s)
- Van Anh Tran
- Max-Planck-Institut
für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Markus Teucher
- Max-Planck-Institut
für Chemische Energiekonversion, Stiftstraße 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Laura Galazzo
- Department
of Physical Chemistry, University of Geneva, Quai Ernest Ansermet 30, 1211 Geneva, Switzerland
- Faculty
of Chemistry and Biochemistry, Ruhr-Universität
Bochum, 44780 Bochum, Germany
| | - Bikramjit Sharma
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44780 Bochum, Germany
| | - Tim Pongratz
- Fakultät
für Chemie und Chemische Biologie, Technische Universität Dortmund, Otto-Hahn-Str. 4a, 44227 Dortmund, Germany
| | - Stefan M. Kast
- Fakultät
für Chemie und Chemische Biologie, Technische Universität Dortmund, Otto-Hahn-Str. 4a, 44227 Dortmund, Germany
| | - Dominik Marx
- Lehrstuhl
für Theoretische Chemie, Ruhr-Universität
Bochum, 44780 Bochum, Germany
| | - Enrica Bordignon
- Department
of Physical Chemistry, University of Geneva, Quai Ernest Ansermet 30, 1211 Geneva, Switzerland
- Faculty
of Chemistry and Biochemistry, Ruhr-Universität
Bochum, 44780 Bochum, Germany
| | - Alexander Schnegg
- Max-Planck-Institut
für Chemische Energiekonversion, Stiftstraße 34-36, 45470 Mülheim an der Ruhr, Germany
| | - Frank Neese
- Max-Planck-Institut
für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
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Szczuka C, Eichel RA, Granwehr J. Gauging the importance of structural parameters for hyperfine coupling constants in organic radicals. RSC Adv 2023; 13:14565-14574. [PMID: 37188254 PMCID: PMC10177955 DOI: 10.1039/d3ra02476h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 05/08/2023] [Indexed: 05/17/2023] Open
Abstract
The identification of fundamental relationships between atomic configuration and electronic structure typically requires experimental empiricism or systematic theoretical studies. Here, we provide an alternative statistical approach to gauge the importance of structure parameters, i.e., bond lengths, bond angles, and dihedral angles, for hyperfine coupling constants in organic radicals. Hyperfine coupling constants describe electron-nuclear interactions defined by the electronic structure and are experimentally measurable, for example, by electron paramagnetic resonance spectroscopy. Importance quantifiers are computed with the machine learning algorithm neighborhood components analysis using molecular dynamics trajectory snapshots. Atomic-electronic structure relationships are visualized in matrices correlating structure parameters with coupling constants of all magnetic nuclei. Qualitatively, the results reproduce common hyperfine coupling models. Tools to use the presented procedure for other radicals/paramagnetic species or other atomic structure-dependent parameters are provided.
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Affiliation(s)
- Conrad Szczuka
- Institute of Energy and Climate Research (IEK-9), Forschungszentrum Jülich GmbH 52425 Jülich Germany
| | - Rüdiger-A Eichel
- Institute of Energy and Climate Research (IEK-9), Forschungszentrum Jülich GmbH 52425 Jülich Germany
- Institute of Physical Chemistry, RWTH Aachen University 52056 Aachen Germany
| | - Josef Granwehr
- Institute of Energy and Climate Research (IEK-9), Forschungszentrum Jülich GmbH 52425 Jülich Germany
- Institute of Technical and Macromolecular Chemistry, RWTH Aachen University 52056 Aachen Germany
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5
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Giovannini T, Marrazzini G, Scavino M, Koch H, Cappelli C. Integrated Multiscale Multilevel Approach to Open Shell Molecular Systems. J Chem Theory Comput 2023; 19:1446-1456. [PMID: 36780359 PMCID: PMC10018740 DOI: 10.1021/acs.jctc.2c00805] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/14/2023]
Abstract
We present a novel multiscale approach to study the electronic structure of open shell molecular systems embedded in an external environment. The method is based on the coupling of multilevel Hartree-Fock (MLHF) and Density Functional Theory (MLDFT), suitably extended to the unrestricted formalism, to Molecular Mechanics (MM) force fields (FF). Within the ML region, the system is divided into active and inactive parts, thus describing the most relevant interactions (electrostatic, polarization, and Pauli repulsion) at the quantum level. The surrounding MM part, which is formulated in terms of nonpolarizable or polarizable FFs, permits a physically consistent treatment of long-range electrostatics and polarization effects. The approach is extended to the calculation of hyperfine coupling constants and applied to selected nitroxyl radicals in an aqueous solution.
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Affiliation(s)
| | - Gioia Marrazzini
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Marco Scavino
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Henrik Koch
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy.,Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - Chiara Cappelli
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
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6
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Eschenbach P, Artiukhin DG, Neugebauer J. Reliable Isotropic Electron-Paramagnetic-Resonance Hyperfine Coupling Constants from the Frozen-Density Embedding Quasi-Diabatization Approach. J Phys Chem A 2022; 126:8358-8368. [DOI: 10.1021/acs.jpca.2c04959] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Patrick Eschenbach
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Simulation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
| | - Denis G. Artiukhin
- Institut für Chemie und Biochemie, Freie Universität Berlin, Arnimallee 22, 14195 Berlin, Germany
| | - Johannes Neugebauer
- Theoretische Organische Chemie, Organisch-Chemisches Institut and Center for Multiscale Theory and Simulation, Westfälische Wilhelms-Universität Münster, Corrensstraße 36, 48149 Münster, Germany
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7
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Falbo E, Fusè M, Lazzari F, Mancini G, Barone V. Integration of Quantum Chemistry, Statistical Mechanics, and Artificial Intelligence for Computational Spectroscopy: The UV-Vis Spectrum of TEMPO Radical in Different Solvents. J Chem Theory Comput 2022; 18:6203-6216. [PMID: 36166322 PMCID: PMC9558374 DOI: 10.1021/acs.jctc.2c00654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
The ongoing integration of quantum chemistry, statistical
mechanics,
and artificial intelligence is paving the route toward more effective
and accurate strategies for the investigation of the spectroscopic
properties of medium-to-large size chromophores in condensed phases.
In this context we are developing a novel workflow aimed at improving
the generality, reliability, and ease of use of the available computational
tools. In this paper we report our latest developments with specific
reference to unsupervised atomistic simulations employing non periodic
boundary conditions (NPBC) followed by clustering of the trajectories
employing optimized feature spaces. Next accurate variational computations
are performed for a representative point of each cluster, whereas
intracluster fluctuations are taken into account by a cheap yet reliable
perturbative approach. A number of methodological improvements have
been introduced including, e.g., more realistic reaction field effects
at the outer boundary of the simulation sphere, automatic definition
of the feature space by continuous perception of solute–solvent
interactions, full account of polarization and charge transfer in
the first solvation shell, and inclusion of vibronic contributions.
After its validation, this new approach has been applied to the challenging
case of solvatochromic effects on the UV–vis spectra of a prototypical
nitroxide radical (TEMPO) in different solvents. The reliability,
effectiveness, and robustness of the new platform is demonstrated
by the remarkable agreement with experiment of the results obtained
through an unsupervised approach characterized by a strongly reduced
computational cost as compared to that of conventional quantum mechanics
and molecular mechanics models without any accuracy reduction.
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Affiliation(s)
- Emanuele Falbo
- Scuola Normale Superiore di Pisa, piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Marco Fusè
- Scuola Normale Superiore di Pisa, piazza dei Cavalieri 7, 56126 Pisa, Italy.,Dipartimento di Medicina Molecolare e Traslazionale, Università di Brescia, Viale Europa 11, 25123 Brescia, Italy
| | - Federico Lazzari
- Scuola Normale Superiore di Pisa, piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Giordano Mancini
- Scuola Normale Superiore di Pisa, piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Vincenzo Barone
- Scuola Normale Superiore di Pisa, piazza dei Cavalieri 7, 56126 Pisa, Italy
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8
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Jung KA, Markland TE. 2D spectroscopies from condensed phase dynamics: Accessing third-order response properties from equilibrium multi-time correlation functions. J Chem Phys 2022; 157:094111. [DOI: 10.1063/5.0107087] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The third-order response lies at the heart of simulating and interpreting nonlinear spectroscopies ranging from two dimensional infrared (2D-IR) to 2D electronic (2D-ES), and 2D sum frequency generation (2D-SFG). The extra time and frequency dimensions in these spectroscopies provides access to rich information on the electronic and vibrational states present, the coupling between them, and the resulting rates at which they exchange energy that are obscured in linear spectroscopy, particularly for condensed phase systems that usually contain many overlapping features. While the exact quantum expression for the third-order response is well established it is incompatible with the methods that are practical for calculating the atomistic dynamics of large condensed phase systems. These methods, which include both classical mechanics and quantum dynamics methods that retain quantum statistical properties while obeying the symmetries of classical dynamics, such as LSC-IVR, Centroid Molecular Dynamics (CMD) and Ring Polymer Molecular Dynamics (RPMD) naturally provide short-time approximations to the multi-time symmetrized Kubo transformed correlation function. Here, we show how the third-order response can be formulated in terms of equilibrium symmetrized Kubo transformed correlation functions. We demonstrate the utility and accuracy of our approach by showing how it can be used to obtain the third-order response of a series of model systems using both classical dynamics and RPMD. In particular, we show that this approach captures features such as anharmonically induced vertical splittings and peak shifts while providing a physically transparent framework for understanding multidimensional spectroscopies.
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Jaworski A, Hedin N. Electron correlation and vibrational effects in predictions of paramagnetic NMR shifts. Phys Chem Chem Phys 2022; 24:15230-15244. [PMID: 35703010 DOI: 10.1039/d2cp01206e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Electronic structure calculations are fundamentally important for the interpretation of nuclear magnetic resonance (NMR) spectra from paramagnetic systems that include organometallic and inorganic compounds, catalysts, or metal-binding sites in proteins. Prediction of induced paramagnetic NMR shifts requires knowledge of electron paramagnetic resonance (EPR) parameters: the electronic g tensor, zero-field splitting D tensor, and hyperfine A tensor. The isotropic part of A, called the hyperfine coupling constant (HFCC), is one of the most troublesome properties for quantum chemistry calculations. Yet, even relatively small errors in calculations of HFCC tend to propagate into large errors in the predicted NMR shifts. The poor quality of A tensors that are currently calculated using density functional theory (DFT) constitutes a bottleneck in improving the reliability of interpretation of the NMR spectra from paramagnetic systems. In this work, electron correlation effects in calculations of HFCCs with a hierarchy of ab initio methods were assessed, and the applicability of different levels of DFT approximations and the coupled cluster singles and doubles (CCSD) method was tested. These assessments were performed for the set of selected test systems comprising an organic radical, and complexes with transition metal and rare-earth ions, for which experimental data are available. Severe deficiencies of DFT were revealed but the CCSD method was able to deliver good agreement with experimental data for all systems considered, however, at substantial computational costs. We proposed a more computationally tractable alternative, where the A was computed with the coupled cluster theory exploiting locality of electron correlation. This alternative is based on the domain-based local pair natural orbital coupled cluster singles and doubles (DLPNO-CCSD) method. In this way the robustness and reliability of the coupled cluster theory were incorporated into the modern formalism for the prediction of induced paramagnetic NMR shifts, and became applicable to systems of chemical interest. This approach was verified for the bis(cyclopentadienyl)vanadium(II) complex (Cp2V; vanadocene), and the metal-binding site of the Zn2+ → Co2+ substituted superoxide dismutase (SOD) metalloprotein. Excellent agreement with experimental NMR shifts was achieved, which represented a substantial improvement over previous theoretical attempts. The effects of vibrational corrections to orbital shielding and hyperfine tensor were evaluated and discussed within the second-order vibrational perturbation theory (VPT2) framework.
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Affiliation(s)
- Aleksander Jaworski
- Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden.
| | - Niklas Hedin
- Department of Materials and Environmental Chemistry, Stockholm University, SE-106 91 Stockholm, Sweden.
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10
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Barone V, Fusè M, Pinto SMV, Tasinato N. A Computational Journey across Nitroxide Radicals: From Structure to Spectroscopic Properties and Beyond. Molecules 2021; 26:molecules26237404. [PMID: 34885980 PMCID: PMC8659111 DOI: 10.3390/molecules26237404] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2021] [Revised: 11/25/2021] [Accepted: 12/02/2021] [Indexed: 11/17/2022] Open
Abstract
Nitroxide radicals are characterized by a long-lived open-shell electronic ground state and are strongly sensitive to the chemical environment, thus representing ideal spin probes and spin labels for paramagnetic biomolecules and materials. However, the interpretation of spectroscopic parameters in structural and dynamic terms requires the aid of accurate quantum chemical computations. In this paper we validate a computational model rooted into double-hybrid functionals and second order vibrational perturbation theory. Then, we provide reference quantum chemical results for the structures, vibrational frequencies and other spectroscopic features of a large panel of nitroxides of current biological and/or technological interest.
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