1
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Chibueze CS, Visscher L. Restricted open-shell time-dependent density functional theory with perturbative spin-orbit coupling. J Chem Phys 2024; 161:094112. [PMID: 39234966 DOI: 10.1063/5.0226870] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2024] [Accepted: 08/19/2024] [Indexed: 09/06/2024] Open
Abstract
When using quantum chemical methods to study electronically excited states of open-shell molecules, it is often beneficial to start with wave functions that are spin eigenfunctions. For excited states of molecules containing heavy elements, spin-orbit coupling (SOC) is important and needs to be included as well. An efficient approach is to include SOC perturbatively on top of a restricted open-shell Kohn-Sham (ROKS) time-dependent density functional theory, which can be combined with the Tamm-Dancoff approximation (TDA) to suppress numerical instabilities. We implemented and assessed the potential of such a ROKS-TDA-SOC method, also featuring the possibility of calculating transition dipole moments between states to allow for full spectrum simulation. Our study shows that the ROKS-TDA-SOC formalism yields a clear and easy-to-use method to obtain electronically excited states of open-shell molecules that are of moderate size and contain heavy elements.
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Affiliation(s)
- Chima S Chibueze
- Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit, De Boelelaan 1108, 1081 HZ Amsterdam, The Netherlands
| | - Lucas Visscher
- Department of Chemistry and Pharmaceutical Sciences, Vrije Universiteit, De Boelelaan 1108, 1081 HZ Amsterdam, The Netherlands
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2
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Holzer C. Practical Post-Kohn-Sham Methods for Time-Reversal Symmetry Breaking References. J Chem Theory Comput 2023. [PMID: 37183702 DOI: 10.1021/acs.jctc.3c00156] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
The applicability of reduced scaling algorithms based on auxiliary subspace methods for the correlation energy from the random phase approximation (RPA) as well as the correlation part of the self-energy obtained from the GW method is outlined for time-reversal symmetry breaking Kohn-Sham (KS) references. The updated algorithms allow for an efficient evaluation of RPA energies and GW quasiparticle energies for molecular systems with KS references that break time-reversal symmetry. The latter occur, for example, in magnetic fields. Furthermore, KS references for relativistic open-shell molecules also break time-reversal symmetry due to the single determinant ansatz used. Errors of the updated reduced-scaling algorithms are shown to be negligible compared to reference implementations, while the overall computational scaling is reduced by 2 orders of magnitude. Ionization energies obtained from the GW approximation are shown to be robust even for the electronically complicated group of trivalent lanthanoid ions. Starting from GW quasiparticle energies, it is subsequently shown that light-matter interactions of these systems can be calculated using the Bethe-Salpeter equation (BSE). Using the combined GW-BSE method, the absorption and emission spectra of a molecular europium(III) complex can be obtained including spin-orbit coupling.
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Affiliation(s)
- Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
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3
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Li H, Pu Z, Sun Q, Gao YQ, Xiao Y. Noncollinear and Spin-Flip TDDFT in Multicollinear Approach. J Chem Theory Comput 2023; 19:2270-2281. [PMID: 36971474 DOI: 10.1021/acs.jctc.3c00059] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/29/2023]
Abstract
Time-dependent density functional theory (TDDFT) is one of the most important tools for investigating the excited states of electrons. The TDDFT calculation for spin-conserving excitation, where collinear functionals are sufficient, has obtained great success and has become routine. However, TDDFT for noncollinear and spin-flip excitations, where noncollinear functionals are needed, is less widespread and still a challenge nowadays. This challenge lies in the severe numerical instabilities that root in the second-order derivatives of commonly used noncollinear functionals. To be free from this problem radically, noncollinear functionals with numerical stable derivatives are desired, and our recently developed approach, called the multicollinear approach, provides an option. In this work, the multicollinear approach is implemented in noncollinear and spin-flip TDDFT, and prototypical tests are given.
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4
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Pikulová P, Misenkova D, Marek R, Komorovsky S, Novotný J. Quadratic Spin-Orbit Mechanism of the Electronic g-Tensor. J Chem Theory Comput 2023; 19:1765-1776. [PMID: 36896579 DOI: 10.1021/acs.jctc.2c01213] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/11/2023]
Abstract
Understanding how the electronic g-tensor is linked to the electronic structure is desirable for the correct interpretation of electron paramagnetic resonance spectra. For heavy-element compounds with large spin-orbit (SO) effects, this is still not completely clear. We report our investigation of quadratic SO contributions to the g-shift in heavy transition metal complexes. We implemented third-order perturbation theory in order to analyze the contributions arising from frontier molecular spin orbitals (MSOs). We show that the dominant quadratic SO term─spin-Zeeman (SO2/SZ)─generally makes a negative contribution to the g-shift, irrespective of the particular electronic configuration or molecular symmetry. We further analyze how the SO2/SZ contribution adds to or subtracts from the linear orbital-Zeeman (SO/OZ) contribution to the individual principal components of the g-tensor. Our study suggests that the SO2/SZ mechanism decreases the anisotropy of the g-tensor in early transition metal complexes and increases it in late transition metal complexes. Finally, we apply MSO analysis to the investigation of g-tensor trends in a set of closely related Ir and Rh pincer complexes and evaluate the influence of different chemical factors (the nuclear charge of the central atom and the terminal ligand) on the magnitudes of the g-shifts. We expect our conclusions to aid the understanding of spectra in magnetic resonance investigations of heavy transition metal compounds.
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Affiliation(s)
- Petra Pikulová
- CEITEC─Central European Institute of Technology, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia.,Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia
| | - Debora Misenkova
- Institute of Inorganic Chemistry, Slovak Academy of Science, Dúbravská cesta 9, Bratislava SK-84536, Slovakia
| | - Radek Marek
- CEITEC─Central European Institute of Technology, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia.,Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia
| | - Stanislav Komorovsky
- Institute of Inorganic Chemistry, Slovak Academy of Science, Dúbravská cesta 9, Bratislava SK-84536, Slovakia
| | - Jan Novotný
- CEITEC─Central European Institute of Technology, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia.,Department of Chemistry, Faculty of Science, Masaryk University, Kamenice 5, Brno CZ-62500, Czechia.,Institute of Inorganic Chemistry, Slovak Academy of Science, Dúbravská cesta 9, Bratislava SK-84536, Slovakia
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5
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Moitra T, Konecny L, Kadek M, Rubio A, Repisky M. Accurate Relativistic Real-Time Time-Dependent Density Functional Theory for Valence and Core Attosecond Transient Absorption Spectroscopy. J Phys Chem Lett 2023; 14:1714-1724. [PMID: 36757216 PMCID: PMC9940299 DOI: 10.1021/acs.jpclett.2c03599] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2022] [Accepted: 02/03/2023] [Indexed: 06/18/2023]
Abstract
First principles theoretical modeling of out-of-equilibrium processes observed in attosecond pump-probe transient absorption spectroscopy (TAS) triggering pure electron dynamics remains a challenging task, especially for heavy elements and/or core excitations containing fingerprints of scalar and spin-orbit relativistic effects. To address this, we formulate a methodology for simulating TAS within the relativistic real-time, time-dependent density functional theory (RT-TDDFT) framework, for both the valence and core energy regimes. Especially for TAS, full four-component (4c) RT simulations are feasible but computationally demanding. Therefore, in addition to the 4c approach, we also introduce the atomic mean-field exact two-component (amfX2C) Hamiltonian accounting for one- and two-electron picture-change corrections within RT-TDDFT. amfX2C preserves the accuracy of the parent 4c method at a fraction of its computational cost. Finally, we apply the methodology to study valence and near-L2,3-edge TAS processes of experimentally relevant systems and provide additional physical insights using relativistic nonequilibrium response theory.
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Affiliation(s)
- Torsha Moitra
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Lukas Konecny
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Max
Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
| | - Marius Kadek
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Department
of Physics, Northeastern University, Boston, Massachusetts 02115, United States
- Algorithmiq
Ltd., Kanavakatu 3C, FI-00160 Helsinki, Finland
| | - Angel Rubio
- Max
Planck Institute for the Structure and Dynamics of Matter, Center for Free Electron Laser Science, Luruper Chaussee 149, 22761 Hamburg, Germany
- Center
for Computational Quantum Physics (CCQ), The Flatiron Institute, 162 Fifth Avenue, New York New York 10010, United States
- Nano-Bio
Spectroscopy Group, Departamento de Física de Materiales, Universidad del País Vasco, 20018 San Sebastian, Spain
| | - Michal Repisky
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Department
of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, 84104 Bratislava, Slovakia
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6
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Konecny L, Komorovsky S, Vicha J, Ruud K, Repisky M. Exact Two-Component TDDFT with Simple Two-Electron Picture-Change Corrections: X-ray Absorption Spectra Near L- and M-Edges of Four-Component Quality at Two-Component Cost. J Phys Chem A 2023; 127:1360-1376. [PMID: 36722848 PMCID: PMC9923756 DOI: 10.1021/acs.jpca.2c08307] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2022] [Revised: 01/13/2023] [Indexed: 02/02/2023]
Abstract
X-ray absorption spectroscopy (XAS) has gained popularity in recent years as it probes matter with high spatial and elemental sensitivities. However, the theoretical modeling of XAS is a challenging task since XAS spectra feature a fine structure due to scalar (SC) and spin-orbit (SO) relativistic effects, in particular near L and M absorption edges. While full four-component (4c) calculations of XAS are nowadays feasible, there is still interest in developing approximate relativistic methods that enable XAS calculations at the two-component (2c) level while maintaining the accuracy of the parent 4c approach. In this article we present theoretical and numerical insights into two simple yet accurate 2c approaches based on an (extended) atomic mean-field exact two-component Hamiltonian framework, (e)amfX2C, for the calculation of XAS using linear eigenvalue and damped response time-dependent density functional theory (TDDFT). In contrast to the commonly used one-electron X2C (1eX2C) Hamiltonian, both amfX2C and eamfX2C account for the SC and SO two-electron and exchange-correlation picture-change (PC) effects that arise from the X2C transformation. As we demonstrate on L- and M-edge XAS spectra of transition metal and actinide compounds, the absence of PC corrections in the 1eX2C approximation results in a substantial overestimation of SO splittings, whereas (e)amfX2C Hamiltonians reproduce all essential spectral features such as shape, position, and SO splitting of the 4c references in excellent agreement, while offering significant computational savings. Therefore, the (e)amfX2C PC correction models presented here constitute reliable relativistic 2c quantum-chemical approaches for modeling XAS.
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Affiliation(s)
- Lukas Konecny
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037Tromsø, Norway
- Center
for Free Electron Laser Science, Max Planck
Institute for the Structure and Dynamics of Matter, Luruper Chaussee 149, 22761Hamburg, Germany
| | - Stanislav Komorovsky
- Institute
of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536Bratislava, Slovakia
| | - Jan Vicha
- Centre
of Polymer Systems, University Institute,
Tomas Bata University in Zlín, CZ-76001Zlín, Czech Republic
| | - Kenneth Ruud
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037Tromsø, Norway
- Norwegian
Defence Research Establishment, P.O.
Box 25, 2027Kjeller, Norway
| | - Michal Repisky
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037Tromsø, Norway
- Department
of Physical and Theoretical Chemistry, Faculty of Natural Sciences, Comenius University, Ilkovicova 6, SK-84215Bratislava, Slovakia
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7
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Knecht S, Repisky M, Jensen HJA, Saue T. Exact two-component Hamiltonians for relativistic quantum chemistry: Two-electron picture-change corrections made simple. J Chem Phys 2022; 157:114106. [PMID: 36137811 DOI: 10.1063/5.0095112] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Based on self-consistent field (SCF) atomic mean-field (amf) quantities, we present two simple yet computationally efficient and numerically accurate matrix-algebraic approaches to correct both scalar-relativistic and spin-orbit two-electron picture-change effects (PCEs) arising within an exact two-component (X2C) Hamiltonian framework. Both approaches, dubbed amfX2C and e(xtended)amfX2C, allow us to uniquely tailor PCE corrections to mean-field models, viz. Hartree-Fock or Kohn-Sham DFT, in the latter case also avoiding the need for a point-wise calculation of exchange-correlation PCE corrections. We assess the numerical performance of these PCE correction models on spinor energies of group 18 (closed-shell) and group 16 (open-shell) diatomic molecules, achieving a consistent ≈10-5 Hartree accuracy compared to reference four-component data. Additional tests include SCF calculations of molecular properties such as absolute contact density and contact density shifts in copernicium fluoride compounds (CnFn, n = 2,4,6), as well as equation-of-motion coupled-cluster calculations of x-ray core-ionization energies of 5d- and 6d-containing molecules, where we observe an excellent agreement with reference data. To conclude, we are confident that our (e)amfX2C PCE correction models constitute a fundamental milestone toward a universal and reliable relativistic two-component quantum-chemical approach, maintaining the accuracy of the parent four-component one at a fraction of its computational cost.
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Affiliation(s)
- Stefan Knecht
- Algorithmiq Ltd, Kanavakatu 3C, FI-00160 Helsinki, Finland
| | - Michal Repisky
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT-The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Hans Jørgen Aagaard Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
| | - Trond Saue
- Laboratoire de Chimie et Physique Quantiques (CNRS UMR 5626), Université Toulouse III - Paul Sabatier, 118 Route de Narbonne, F-31062 Toulouse Cedex, France
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8
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Ye L, Wang H, Zhang Y, Liu W. Self-Adaptive Real-Time Time-Dependent Density Functional Theory for X-ray Absorptions. J Chem Phys 2022; 157:074106. [DOI: 10.1063/5.0106250] [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
Real-time time-dependent density functional theory (RT-TDDFT) can in principle access the whole absorption spectrum of a many-electron system exposed to a narrow pulse. However, this requires an accurate and efficient propagator for the numerical integration of the time-dependent Kohn-Sham equation. While a low-order time propagator is already sufficient for the low-lying valence absorption spectra, it is no longer the case for the X-ray absorption spectra (XAS) of systems composed even only of light elements, for which the use of a high-order propagator is indispensable. It is then crucial to choose a largest possible time step and a shortest possible simulation time, so as to minimize the computational cost. To this end, we propose here a robust AutoPST approach to determine automatically (Auto) the propagator (P), step (S), and time (T) for relativistic RT-TDDFT simulations of XAS.
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Affiliation(s)
| | - Hao Wang
- Shandong University - Qingdao Campus, China
| | | | - Wenjian Liu
- Qingdao Institue for Theoretical and Computational Sciences, Shandong University, China
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9
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Nascimento DR, Govind N. Computational approaches for XANES, VtC-XES, and RIXS using linear-response time-dependent density functional theory based methods. Phys Chem Chem Phys 2022; 24:14680-14691. [PMID: 35699090 DOI: 10.1039/d2cp01132h] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Abstract
The emergence of state-of-the-art X-ray light sources has paved the way for novel spectroscopies that take advantage of their atomic specificity to shed light on fundamental physical, chemical, and biological processes both in the static and time domains. The success of these experiments hinges on the ability to interpret and predict core-level spectra, which has opened avenues for theory to play a key role. Over the last two decades, linear-response time-dependent density functional theory (LR-TDDFT), despite various theoretical challenges, has become a computationally attractive and versatile framework to study excited-state spectra including X-ray spectroscopies. In this context, we focus our discussion on LR-TDDFT approaches for the computation of X-ray Near-Edge Structure (XANES), Valence-to-Core X-ray Emission (VtC-XES), and Resonant Inelastic X-ray Scattering (RIXS) spectroscopies in molecular systems with an emphasis on Gaussian basis set implementations. We illustrate these approaches with applications and provide a brief outlook of possible new directions.
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Affiliation(s)
- Daniel R Nascimento
- Department of Chemistry, The University of Memphis, Memphis, TN, 38152, USA.
| | - Niranjan Govind
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, USA.
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10
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Pausch A, Holzer C, Klopper W. Efficient Calculation of Magnetic Circular Dichroism Spectra Using Spin-Noncollinear Linear-Response Time-Dependent Density Functional Theory in Finite Magnetic Fields. J Chem Theory Comput 2022; 18:3747-3758. [PMID: 35576504 DOI: 10.1021/acs.jctc.2c00232] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Excited-state calculations in finite magnetic fields are presented in the framework of spin-noncollinear linear-response time-dependent density functional theory. To ensure gauge-origin invariance, London atomic orbitals are employed throughout. An efficient implementation into the Turbomole package, which also includes the resolution of the identity approximation, allows for the investigation of excited states of large molecular systems. The implementation is used to investigate the magnetic circular dichroism spectra of sizable organometallic molecules such as a zinc tetraazaporphyrin with two fused naphthalene units, which is a molecule with 57 atoms.
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Affiliation(s)
- Ansgar Pausch
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany
| | - Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Strasse 1, 76131 Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Fritz-Haber-Weg 2, 76131 Karlsruhe, Germany.,Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen, Germany
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11
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Konecny L, Vicha J, Komorovsky S, Ruud K, Repisky M. Accurate X-ray Absorption Spectra near L- and M-Edges from Relativistic Four-Component Damped Response Time-Dependent Density Functional Theory. Inorg Chem 2022; 61:830-846. [PMID: 34958215 PMCID: PMC8767545 DOI: 10.1021/acs.inorgchem.1c02412] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2021] [Indexed: 11/27/2022]
Abstract
The simulation of X-ray absorption spectra requires both scalar and spin-orbit (SO) relativistic effects to be taken into account, particularly near L- and M-edges where the SO splitting of core p and d orbitals dominates. Four-component Dirac-Coulomb Hamiltonian-based linear damped response time-dependent density functional theory (4c-DR-TDDFT) calculates spectra directly for a selected frequency region while including the relativistic effects variationally, making the method well suited for X-ray applications. In this work, we show that accurate X-ray absorption spectra near L2,3- and M4,5-edges of closed-shell transition metal and actinide compounds with different central atoms, ligands, and oxidation states can be obtained by means of 4c-DR-TDDFT. While the main absorption lines do not change noticeably with the basis set and geometry, the exchange-correlation functional has a strong influence with hybrid functionals performing the best. The energy shift compared to the experiment is shown to depend linearly on the amount of Hartee-Fock exchange with the optimal value being 60% for spectral regions above 1000 eV, providing relative errors below 0.2% and 2% for edge energies and SO splittings, respectively. Finally, the methodology calibrated in this work is used to reproduce the experimental L2,3-edge X-ray absorption spectra of [RuCl2(DMSO)2(Im)2] and [WCl4(PMePh2)2], and resolve the broad bands into separated lines, allowing an interpretation based on ligand field theory and double point groups. These results support 4c-DR-TDDFT as a reliable method for calculating and analyzing X-ray absorption spectra of chemically interesting systems, advance the accuracy of state-of-the art relativistic DFT approaches, and provide a reference for benchmarking more approximate techniques.
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Affiliation(s)
- Lukas Konecny
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø − The Arctic University
of Norway, 9037 Tromsø, Norway
| | - Jan Vicha
- Centre
of Polymer Systems, Tomas Bata University, tř. Tomáše
Bati 5678, 760 01 Zlín, Czech Republic
| | - Stanislav Komorovsky
- Institute
of Inorganic Chemistry, Slovak Academy of
Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovakia
| | - Kenneth Ruud
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø − The Arctic University
of Norway, 9037 Tromsø, Norway
| | - Michal Repisky
- Hylleraas
Centre for Quantum Molecular Sciences, Department of Chemistry, University of Tromsø − The Arctic University
of Norway, 9037 Tromsø, Norway
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12
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Holzer C, Pausch A, Klopper W. The GW/BSE Method in Magnetic Fields. Front Chem 2021; 9:746162. [PMID: 34900932 PMCID: PMC8655096 DOI: 10.3389/fchem.2021.746162] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 10/19/2021] [Indexed: 11/16/2022] Open
Abstract
The GW approximation and the Bethe–Salpeter equation have been implemented into the Turbomole program package for computations of molecular systems in a strong, finite magnetic field. Complex-valued London orbitals are used as basis functions to ensure gauge-invariant computational results. The implementation has been benchmarked against triplet excitation energies of 36 small to medium-sized molecules against reference values obtained at the approximate coupled-cluster level (CC2 approximation). Finally, a spectacular change of colour from orange to green of the tetracene molecule is induced by applying magnetic fields between 0 and 9,000 T perpendicular to the molecular plane.
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Affiliation(s)
- Christof Holzer
- Institute of Theoretical Solid State Physics, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Ansgar Pausch
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany
| | - Wim Klopper
- Institute of Physical Chemistry, Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany.,Institute of Nanotechnology, Karlsruhe Institute of Technology (KIT), Eggenstein-Leopoldshafen, Germany
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13
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Li Z. Structured eigenvalue problems in electronic structure methods from a unified perspective. CHINESE J CHEM PHYS 2021. [DOI: 10.1063/1674-0068/cjcp2107119] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Zhendong Li
- Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, College of Chemistry, Beijing Normal University, Beijing 100875, China
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14
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Desmarais JK, Erba A, Flament JP, Kirtman B. Perturbation Theory Treatment of Spin-Orbit Coupling II: A Coupled Perturbed Kohn-Sham Method. J Chem Theory Comput 2021; 17:4712-4732. [PMID: 34286577 DOI: 10.1021/acs.jctc.1c00460] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A noncanonical coupled perturbed Kohn-Sham density functional theory (KS-DFT)/Hartree-Fock (HF) treatment of spin-orbit coupling (SOC) is provided. We take the scalar-relativistic KS-DFT/HF solution, obtained with a relativistic effective core potential, as the zeroth-order approximation. Explicit expressions are given for the total energy through the 4th order, which satisfy the 2n + 1 rule. Second-order expressions are provided for orbital energies and density variables of spin-current DFT. Test calculations are carried out on the halogen homonuclear diatomic and hydride molecules, including 6p and 7p elements, as well as open-shell negative ions. The computed properties through second or third order match well with those from reference two-component self-consistent field calculations for total and orbital energies as well as spin-current densities. In only one case (At2-) did a significant deviation occur for the remaining density variables. Our coupled perturbation theory approach provides an efficient way of adding the effect of SOC to a scalar-relativistic single-reference KS-DFT/HF treatment, in particular because it does not require diagonalization in the two-component spinor basis, leading to saving factors on the number of required floating-point operations that may exceed one order of magnitude.
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Affiliation(s)
- Jacques K Desmarais
- Dipartimento di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy.,Université de Pau et des Pays de l'Adour, E2S UPPA, CNRS, IPREM, 64000 Pau, France
| | - Alessandro Erba
- Dipartimento di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
| | - Jean-Pierre Flament
- Université de Lille, CNRS, UMR 8523-PhLAM-Physique des Lasers, Atomes et Molécules, 59000 Lille, France
| | - Bernard Kirtman
- Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106, United States
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15
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Desmarais JK, Komorovsky S, Flament JP, Erba A. Spin–orbit coupling from a two-component self-consistent approach. II. Non-collinear density functional theories. J Chem Phys 2021; 154:204110. [DOI: 10.1063/5.0051447] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Jacques K. Desmarais
- Dipartimento di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
- Université de Pau et des Pays de l’Adour, E2S UPPA, CNRS, IPREM, Pau, France
| | - Stanislav Komorovsky
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dúbravská cesta 9, SK-84536 Bratislava, Slovakia
| | - Jean-Pierre Flament
- Université de Lille, CNRS, UMR 8523—PhLAM—Physique des Lasers, Atomes et Molécules, 59000 Lille, France
| | - Alessandro Erba
- Dipartimento di Chimica, Università di Torino, via Giuria 5, 10125 Torino, Italy
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16
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Mell B, Rust J, Lehmann CW, Berger RJF, Otte D, Ertl M, Monkowius U, Mohr F. Arylamidoethyl-Functionalized Imidazolium Salts: Precursors for Dianionic [C,N,C]2– Carbene Ligands at a Platinum Center. Organometallics 2021. [DOI: 10.1021/acs.organomet.1c00013] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Affiliation(s)
- Bernd Mell
- Fakultät für Mathematik und Naturwissenschaften, Anorganische Chemie, Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany
| | - Jörg Rust
- Chemische Kristallographie und Elektronenmikroskopie, Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Christian W. Lehmann
- Chemische Kristallographie und Elektronenmikroskopie, Max-Planck-Institut für Kohlenforschung, Kaiser-Wilhelm-Platz 1, 45470 Mülheim an der Ruhr, Germany
| | - Raphael J. F. Berger
- Fachbereich für Chemie und Physik der Materialien, Paris-Lodron Universität Salzburg, 5020 Salzburg, Austria
| | - Daniela Otte
- School of Education, MINT Didactics, Chemistry, Johannes Kepler University, 4040 Linz, Austria
| | - Martin Ertl
- School of Education, MINT Didactics, Chemistry, Johannes Kepler University, 4040 Linz, Austria
| | - Uwe Monkowius
- School of Education, MINT Didactics, Chemistry, Johannes Kepler University, 4040 Linz, Austria
| | - Fabian Mohr
- Fakultät für Mathematik und Naturwissenschaften, Anorganische Chemie, Bergische Universität Wuppertal, Gaußstraße 20, 42119 Wuppertal, Germany
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17
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Ghiasi R, Zandiyeh Z. Theoretical study of the influence of solvent polarity on the 31P and 13C NMR parameters of the Ru(PH3)4(η2-benzyne) complex. INORG CHEM COMMUN 2021. [DOI: 10.1016/j.inoche.2020.108412] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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18
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Moitra T, Karak P, Chakraborty S, Ruud K, Chakrabarti S. Behind the scenes of spin-forbidden decay pathways in transition metal complexes. Phys Chem Chem Phys 2021; 23:59-81. [PMID: 33319894 DOI: 10.1039/d0cp05108j] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
The interpretation of the ultrafast photophysics of transition metal complexes following photo-absorption is quite involved as the heavy metal center leads to a complicated and entangled singlet-triplet manifold. This opens up multiple pathways for deactivation, often with competitive rates. As a result, intersystem crossing (ISC) and phosphorescence are commonly observed in transition metal complexes. A detailed understanding of such an excited-state structure and dynamics calls for state-of-the-art experimental and theoretical methodologies. In this review, we delve into the inability of non-relativistic quantum theory to describe spin-forbidden transitions, which can be overcome by taking into account spin-orbit coupling, whose importance grows with increasing atomic number. We present the quantum chemical theory of phosphorescence and ISC together with illustrative examples. Finally, a few applications are highlighted, bridging the gap between theoretical studies and experimental applications, such as photofunctional materials.
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Affiliation(s)
- Torsha Moitra
- DTU Chemistry, Technical University of Denmark, Kemitorvet Bldg 207, DK-2800 Kongens Lyngby, Denmark
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19
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Komorovsky S, Jakubowska K, Świder P, Repisky M, Jaszuński M. NMR Spin–Spin Coupling Constants Derived from Relativistic Four-Component DFT Theory—Analysis and Visualization. J Phys Chem A 2020; 124:5157-5169. [DOI: 10.1021/acs.jpca.0c02807] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Stanislav Komorovsky
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska cesta 9, Bratislava 845 36, Slovakia
| | | | - Paweł Świder
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warszawa 01-224, Poland
| | - Michal Repisky
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT − The Arctic University of Norway, Tromsø N-9037, Norway
| | - Michał Jaszuński
- Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, Warszawa 01-224, Poland
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20
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Sun S, Li X. Relativistic Effects in Magnetic Circular Dichroism: Restricted Magnetic Balance and Temperature Dependence. J Chem Theory Comput 2020; 16:4533-4542. [DOI: 10.1021/acs.jctc.0c00287] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Shichao Sun
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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21
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Repisky M, Komorovsky S, Kadek M, Konecny L, Ekström U, Malkin E, Kaupp M, Ruud K, Malkina OL, Malkin VG. ReSpect: Relativistic spectroscopy DFT program package. J Chem Phys 2020; 152:184101. [DOI: 10.1063/5.0005094] [Citation(s) in RCA: 47] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Michal Repisky
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Stanislav Komorovsky
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska cesta 9, SK-84536 Bratislava, Slovakia
| | - Marius Kadek
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Lukas Konecny
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Ulf Ekström
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, N-0315 Oslo, Norway
| | - Elena Malkin
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Martin Kaupp
- Technische Universität Berlin, Institute of Chemistry, Strasse des 17 Juni 135, D-10623 Berlin, Germany
| | - Kenneth Ruud
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, UiT The Arctic University of Norway, N-9037 Tromsø, Norway
| | - Olga L. Malkina
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska cesta 9, SK-84536 Bratislava, Slovakia
| | - Vladimir G. Malkin
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Dubravska cesta 9, SK-84536 Bratislava, Slovakia
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22
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Belpassi L, De Santis M, Quiney HM, Tarantelli F, Storchi L. BERTHA: Implementation of a four-component Dirac–Kohn–Sham relativistic framework. J Chem Phys 2020; 152:164118. [PMID: 32357778 DOI: 10.1063/5.0002831] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/30/2023] Open
Affiliation(s)
- Leonardo Belpassi
- Istituto di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Matteo De Santis
- Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Harry M. Quiney
- ARC Centre of Excellence for Advanced Molecular Imaging, School of Physics, The University of Melbourne, 3010 Victoria, Australia
| | - Francesco Tarantelli
- Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Loriano Storchi
- Dipartimento di Farmacia, Università degli Studi ‘G. D’Annunzio’, Via dei Vestini 31, 66100 Chieti, Italy
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23
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De Santis M, Storchi L, Belpassi L, Quiney HM, Tarantelli F. PyBERTHART: A Relativistic Real-Time Four-Component TDDFT Implementation Using Prototyping Techniques Based on Python. J Chem Theory Comput 2020; 16:2410-2429. [PMID: 32101419 DOI: 10.1021/acs.jctc.0c00053] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Matteo De Santis
- Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
- Istituto di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Loriano Storchi
- Istituto di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
- Dipartimento di Farmacia, Università degli Studi ‘G. D’Annunzio’, Via dei Vestini 31, 66100 Chieti, Italy
| | - Leonardo Belpassi
- Istituto di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
| | - Harry M. Quiney
- ARC Centre of Excellence for Advanced Molecular Imaging, School of Physics, The University of Melbourne, 3010 Victoria, Australia
| | - Francesco Tarantelli
- Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
- Istituto di Scienze e Tecnologie Chimiche (SCITEC), Consiglio Nazionale delle Ricerche c/o Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Via Elce di Sotto 8, 06123 Perugia, Italy
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24
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Konecny L, Repisky M, Ruud K, Komorovsky S. Relativistic four-component linear damped response TDDFT for electronic absorption and circular dichroism calculations. J Chem Phys 2019; 151:194112. [DOI: 10.1063/1.5128564] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022] Open
Affiliation(s)
- Lukas Konecny
- Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, 9037 Tromsø, Norway
- Department of Inorganic Chemistry, Faculty of Natural Sciences, Comenius University, Bratislava, Slovakia
| | - Michal Repisky
- Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Kenneth Ruud
- Hylleraas Centre for Quantum Molecular Sciences, UiT The Arctic University of Norway, 9037 Tromsø, Norway
| | - Stanislav Komorovsky
- Institute of Inorganic Chemistry, Slovak Academy of Sciences, Bratislava, Slovakia
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