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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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2
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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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3
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Gromov OI. Performance of the DLPNO-CCSD and recent DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals. J Mol Model 2021; 27:194. [PMID: 34075533 DOI: 10.1007/s00894-021-04807-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2021] [Accepted: 05/26/2021] [Indexed: 10/21/2022]
Abstract
In the present study, the performance of a set of density functionals: BP86, PBE, OLYP, BEEF, PBEpow, TPSS, SCAN, PBEGXPBE, M06L, MN15L, B3LYP, PBE0, mPW1PW, B97, BHandHLYP, mPW1PW, B98, TPSS0, PBE1KCIS, SCAN0, M06, M06-2X, MN15, CAM-B3LYP, ωB97x, B2PLYP, and the B3LYP/N07D and PBE/N07D schemes in the calculation of the 14N anisotropic hyperfine coupling (HFC) constants of a set of 23 nitroxide radicals is evaluated. The results are compared with those obtained with the DLPNO-CCSD method and experimental HFC values. Harmonic contribution to the 14N HFC vibrational correction was calculated at the revPBE0/def2-TZVPP level and included in the evaluation. With the vibrational correction, the DLPNO-CCSD method yielded HFC values in good agreement with the experiment (mean absolute deviation (MAD) = 0.3 G for the dipole-dipole contribution and MAD = 0.8 G for the contact coupling contribution). The best DFT results are obtained using the M06 functional with MAD = 0.2 G for the dipole-dipole contribution and MAD = 0.7 G for the contact coupling contribution. In general, vibrational correction significantly improved most DFT functionals' performance but did not change its overall ranking.
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Affiliation(s)
- Oleg I Gromov
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, 119991, Russia.
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4
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Auer AA, Tran VA, Sharma B, Stoychev GL, Marx D, Neese F. A case study of density functional theory and domain-based local pair natural orbital coupled cluster for vibrational effects on EPR hyperfine coupling constants: vibrational perturbation theory versus ab initio molecular dynamics. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1797916] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
| | - Van Anh Tran
- MPI für Kohlenforschung, Mülheim an der Ruhr, Germany
| | - Bikramjit Sharma
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Bochum, Germany
| | | | - Dominik Marx
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Bochum, Germany
| | - Frank Neese
- MPI für Kohlenforschung, Mülheim an der Ruhr, Germany
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5
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Gromov OI, Kuzin SV, Golubeva EN. Performance of DFT methods in the calculation of isotropic and dipolar contributions to 14N hyperfine coupling constants of nitroxide radicals. J Mol Model 2019; 25:93. [PMID: 30859325 DOI: 10.1007/s00894-019-3966-y] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2018] [Accepted: 02/07/2019] [Indexed: 10/27/2022]
Abstract
In the present study, we tested the widely used density functionals BP86, PBE, OLYP, TPSS, M06-L, B3LYP, PBE0, mPW1PW, B97, BHandHLYP, TPSS0, M06, M06-2X, CAM-B3LYP, ωB97x, and B2PLYP with the cc-pCVQZ basis set in calculations on a set of 23 nitroxide radicals with well-resolved 14N anisotropic hyperfine coupling (HFC) constants. The results were compared with those obtained using the B3LYP/N07D and PBE/N07D methods. The convergence of the HFC values to the complete basis set limit is briefly discussed. The best results were obtained using the M06/COSMO method, with a mean absolute deviation (MAD) of 0.4 G for the dipole-dipole contribution and MAD = 0.6 G for the contact coupling contribution (as compared to 1.1 G and 1.0 G, respectively, for the B3LYP/N07D/COSMO method and 1.7 G and 0.5 G, respectively, for the B3LYP/N07D method). The majority of the functionals yielded satisfactory results for the dipole-dipole contribution, but only the M06 functional yielded similar errors for both the dipole-dipole and isotropic contributions. The RIJCOSX and RI approximations introduced errors equal to or smaller than 0.01 G.
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Affiliation(s)
- Oleg I Gromov
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, Russia, 119991.
| | - Sergei V Kuzin
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, Russia, 119991
| | - Elena N Golubeva
- Chemistry Department, Lomonosov Moscow State University, Leninskiye Gory 1-3, Moscow, Russia, 119991
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6
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Massolle A, Dresselhaus T, Eusterwiemann S, Doerenkamp C, Eckert H, Studer A, Neugebauer J. Towards reliable references for electron paramagnetic resonance parameters based on quantum chemistry: the case of verdazyl radicals. Phys Chem Chem Phys 2018; 20:7661-7675. [PMID: 29497710 DOI: 10.1039/c7cp05657e] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We present an efficient and accurate computational procedure to calculate properties measurable by EPR spectroscopy. We simulate a molecular dynamics (MD) trajectory by employing the quantum mechanically derived force field (QMDFF) [S. Grimme, J. Chem. Theory Comput., 2014, 10, 4497] and sample the trajectory at different time steps. For each snapshot EPR properties are calculated with a hybrid density functional theory (DFT) method. EPR spectra are simulated based on the averaged results. We applied the strategy to a number of previously published and novel verdazyl radicals, for which we recorded EPR spectra. The resulting simulated spectra are compatible with experiment already before employing an additional fitting step, in contrast to those from single point electronic-structure calculations. After the refinement, the experimental data are excellently reproduced, and the fitted EPR parameters do not deviate much from the calculated ones. This provides confidence in ascribing a direct physical meaning to the refined data in terms of experimental EPR parameters rather than merely considering them as mathematical fit parameters. We also find that couplings to hydrogen nuclei have a significant influence on the spectra of verdazyl radicals.
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Affiliation(s)
- Anja Massolle
- Organisch-Chemisches Institut, Westfälische Wilhelms-Universität Münster, Corrensstraße 40, 48149 Münster, Germany.
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7
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Egidi F, Williams-Young DB, Baiardi A, Bloino J, Scalmani G, Frisch MJ, Li X, Barone V. Effective Inclusion of Mechanical and Electrical Anharmonicity in Excited Electronic States: VPT2-TDDFT Route. J Chem Theory Comput 2017; 13:2789-2803. [PMID: 28453287 DOI: 10.1021/acs.jctc.7b00218] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We present a reliable and cost-effective procedure for the inclusion of anharmonic effects in excited-state energies and spectroscopic intensities by means of second-order vibrational perturbation theory. This development is made possible thanks to a recent efficient implementation of excited-state analytic Hessians and properties within the time-dependent density functional theory framework. As illustrated in this work, by taking advantage of such algorithmic developments, it is possible to perform calculations of excited-state infrared spectra of medium-large isolated molecular systems, with anharmonicity effects included in both the energy and property surfaces. We also explore the use of this procedure for the inclusion of anharmonic effects in the simulation of vibronic bandshapes of electronic spectra and compare the results with previous, more approximate models.
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Affiliation(s)
- Franco Egidi
- Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - David B Williams-Young
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Alberto Baiardi
- Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Julien Bloino
- Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti OrganoMetallici (ICCOM-CNR) , UOS di Pisa, Area della Ricerca CNR, Via G. Moruzzi 1, Pisa 56124, Italy
| | - Giovanni Scalmani
- Gaussian, Inc. , 340 Quinnipiac St., Bldg. 40, Wallingford, Connecticut 06492, United States
| | - Michael J Frisch
- Gaussian, Inc. , 340 Quinnipiac St., Bldg. 40, Wallingford, Connecticut 06492, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington , Seattle, Washington 98195, United States
| | - Vincenzo Barone
- Scuola Normale Superiore , Piazza dei Cavalieri 7, 56126 Pisa, Italy
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8
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Egidi F, Segado M, Koch H, Cappelli C, Barone V. A benchmark study of electronic excitation energies, transition moments, and excited-state energy gradients on the nicotine molecule. J Chem Phys 2015; 141:224114. [PMID: 25494739 DOI: 10.1063/1.4903307] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In this work, we report a comparative study of computed excitation energies, oscillator strengths, and excited-state energy gradients of (S)-nicotine, chosen as a test case, using multireference methods, coupled cluster singles and doubles, and methods based on time-dependent density functional theory. This system was chosen because its apparent simplicity hides a complex electronic structure, as several different types of valence excitations are possible, including n-π(*), π-π(*), and charge-transfer states, and in order to simulate its spectrum it is necessary to describe all of them consistently well by the chosen method.
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Affiliation(s)
- Franco Egidi
- Scuola Normale Superiore, Piazza dei Cavalieri, 7 I-56126 Pisa, Italy
| | - Mireia Segado
- Scuola Normale Superiore, Piazza dei Cavalieri, 7 I-56126 Pisa, Italy
| | - Henrik Koch
- Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway
| | - Chiara Cappelli
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via G. Moruzzi, 3 I-56124 Pisa, Italy
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri, 7 I-56126 Pisa, Italy
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9
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Egidi F, Russo R, Carnimeo I, D'Urso A, Mancini G, Cappelli C. The electronic circular dichroism of nicotine in aqueous solution: a test case for continuum and mixed explicit-continuum solvation approaches. J Phys Chem A 2015; 119:5396-404. [PMID: 25568940 DOI: 10.1021/jp510542x] [Citation(s) in RCA: 28] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
In this paper, we extend an integrated QM/MM/polarizable continuum model (PCM) method, which combines a fluctuating charge (FQ) approach to the MM polarization with the PCM, to describe electronic circular dichroism (ECD) spectra of systems in aqueous solution. The main features of the approach are presented, and then applications to the UV and ECD spectra of neutral (S)-nicotine in aqueous solution are reported. The performance of the QM/FQ/PCM is compared with that of the PCM against newly measured UV ECD spectra, which are in agreement with previous findings. The inclusion of specific solvation effects via the QM/FQ/PCM method leads to an improvement in the calculated spectra compared to the experimental findings, though the pure PCM results are still qualitatively correct and are a useful tool for the characterization of the states.
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Affiliation(s)
- Franco Egidi
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy.,Compunet, Istituto Italiano di Tecnologia (IIT), via Morego 30, I-16163 Genova, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Department of Chemical Sciences, University of Catania, Viale A. Doria 6, I-95125 Catania, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy
| | - Rosario Russo
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy.,Compunet, Istituto Italiano di Tecnologia (IIT), via Morego 30, I-16163 Genova, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Department of Chemical Sciences, University of Catania, Viale A. Doria 6, I-95125 Catania, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy
| | - Ivan Carnimeo
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy.,Compunet, Istituto Italiano di Tecnologia (IIT), via Morego 30, I-16163 Genova, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Department of Chemical Sciences, University of Catania, Viale A. Doria 6, I-95125 Catania, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy
| | - Alessandro D'Urso
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy.,Compunet, Istituto Italiano di Tecnologia (IIT), via Morego 30, I-16163 Genova, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Department of Chemical Sciences, University of Catania, Viale A. Doria 6, I-95125 Catania, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy
| | - Giordano Mancini
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy.,Compunet, Istituto Italiano di Tecnologia (IIT), via Morego 30, I-16163 Genova, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Department of Chemical Sciences, University of Catania, Viale A. Doria 6, I-95125 Catania, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy
| | - Chiara Cappelli
- Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy.,Compunet, Istituto Italiano di Tecnologia (IIT), via Morego 30, I-16163 Genova, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Department of Chemical Sciences, University of Catania, Viale A. Doria 6, I-95125 Catania, Italy.,Scuola Normale Superiore, Piazza dei Cavalieri 7, I-56126 Pisa, Italy.,Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Giuseppe Moruzzi 3, I-56124 Pisa, Italy
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10
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Egidi F, Giovannini T, Piccardo M, Bloino J, Cappelli C, Barone V. Stereo-electronic, vibrational, and environmental contributions to polarizabilities of large molecular systems: a feasible anharmonic protocol. J Chem Theory Comput 2014; 10:2456-2464. [PMID: 26550004 DOI: 10.1021/ct500210z] [Citation(s) in RCA: 32] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Abstract
Reliable computations of linear and non-linear optical properties of molecular systems in condensed phases require a proper account of stereo-electronic, vibrational, and environmental effects. In the framework of density functional theory, these effects can be accurately introduced using second-order vibrational perturbation theory in conjunction with polarizable continuum models. We illustrate the combination of an anharmonic description of the ground-state potential energy surface with solvation effects treated with the polarizable continuum model (PCM) in the calculation of the electronic, zero-point, and pure vibrational polarizabilities of selected systems. The description of the solvation environment is enriched by taking into account the dynamical aspects of the solute-solvent interactions through the inclusion of both electronic and vibrational non-equilbrium effects, as well as the direct effect of the solvent on the electric field that generates the molecular response (local field effect). This treatment yields accurate results which can be directly compared with experimental findings without the need of empirical corrections.
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Affiliation(s)
- Franco Egidi
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | | | - Matteo Piccardo
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
| | - Julien Bloino
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy ; Consiglio Nazionale delle Ricerche, Istituto di Chimica dei Composti Organometallici, UOS di Pisa, Via G. Moruzzi 1, 56124 Pisa, Italy
| | - Chiara Cappelli
- Dipartimento di Chimica e Chimica Industriale, Università di Pisa, via Risorgimento 35, 56126 Pisa, Italy
| | - Vincenzo Barone
- Scuola Normale Superiore, Piazza dei Cavalieri 7, 56126 Pisa, Italy
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