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Jørgensen FK, Delcey MG, Hedegård ED. Perspective: multi-configurational methods in bio-inorganic chemistry. Phys Chem Chem Phys 2024; 26:17443-17455. [PMID: 38868993 DOI: 10.1039/d4cp01297f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2024]
Abstract
Transition metal ions play crucial roles in the structure and function of numerous proteins, contributing to essential biological processes such as catalysis, electron transfer, and oxygen binding. However, accurately modeling the electronic structure and properties of metalloproteins poses significant challenges due to the complex nature of their electronic configurations and strong correlation effects. Multiconfigurational quantum chemistry methods are, in principle, the most appropriate tools for addressing these challenges, offering the capability to capture the inherent multi-reference character and strong electron correlation present in bio-inorganic systems. Yet their computational cost has long hindered wider adoption, making methods such as density functional theory (DFT) the method of choice. However, advancements over the past decade have substantially alleviated this limitation, rendering multiconfigurational quantum chemistry methods more accessible and applicable to a wider range of bio-inorganic systems. In this perspective, we discuss some of these developments and how they have already been used to answer some of the most important questions in bio-inorganic chemistry. We also comment on ongoing developments in the field and how the future of the field may evolve.
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Affiliation(s)
- Frederik K Jørgensen
- Department of Physics, Chemistry, and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark.
| | - Mickaël G Delcey
- Department of Chemistry, Lund University, Naturvetarvägen 14, 221 00 Lund, Sweden
| | - Erik D Hedegård
- Department of Physics, Chemistry, and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark.
- Department of Chemistry, Lund University, Naturvetarvägen 14, 221 00 Lund, Sweden
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Soltani Nejad M, Alipour M. How does theory compare to experiment for oscillator strengths in electronic spectra? Proposing range-separated hybrids with reliable accountability. Phys Chem Chem Phys 2024; 26:879-894. [PMID: 38087910 DOI: 10.1039/d3cp04793h] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2024]
Abstract
As an important quantity in atomic and molecular spectroscopy, oscillator strength should be mentioned. Oscillator strength is linked to the transition dipole moment and consequently to the transition probability between two states, where its magnitude is directly connected to the intensity of the peaks in ultraviolet-visible spectra. However, accurately accounting for oscillator strengths still remains one of the greatest challenges in theory and experiment. Given previous efforts in the context of investigations into oscillator strengths, the related theoretical treatments are relatively limited and have proven to be challenging. In this work, the oscillator strengths in the electronic spectra of organic compounds have thoroughly been investigated with the help of optimally tuned range-separated hybrids (OT-RSHs). In particular, variants of the OT-RSHs combined with the polarizable continuum model (PCM), OT-RSHs-PCM, as well as their screened versions accounting for the screening effects by the electron correlation through the dielectric constant, OT-SRSHs-PCM, are proposed for reliable prediction of the oscillator strengths. The role of the involved ingredients in the proposed methods, namely the underlying density functional approximations, short-range and long-range Hartree-Fock (HF) exchange, as well as the range-separation parameter, has been examined in detail. It is shown that any combination of the parameters in the proposed approximations does not render the reliable oscillator strengths, but a particular compromise among them is needed to describe the experimental data well. Perusing all the results of our developed methods, the best ones are found to be the generalized gradient approximation-based OT-RSHs-PCM, coupled with the linear response theory in the non-equilibrium solvation regime, with the correct asymptotic behavior and incorporating no (low) HF exchange contributions in the short-range part. The best proposed approximations also reveal superior performances not only with respect to their standard counterparts with the default parameters but also as compared to earlier range-separated functionals. Finally, the applicability of the best approximation is also put into broader perspective, where it is used for predicting the oscillator strengths in other sets of compounds not included in the process of developing the approximations. Hopefully, our proposed method can function as an affordable alternative to the expensive wave function-based methods for both theoretical modeling and confirming the experimental observations in the field of electronic spectroscopy.
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Affiliation(s)
- Mahdi Soltani Nejad
- Department of Chemistry, School of Science, Shiraz University, Shiraz 71946-84795, Iran.
| | - Mojtaba Alipour
- Department of Chemistry, School of Science, Shiraz University, Shiraz 71946-84795, Iran.
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Larsson ED, Reinholdt P, Hedegård ED, Kongsted J. Accuracy of One- and Two-Photon Intensities with the Extended Polarizable Density Embedding Model. J Phys Chem B 2023; 127:9905-9914. [PMID: 37948667 DOI: 10.1021/acs.jpcb.3c05029] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2023]
Abstract
The recently developed extended polarizable density embedding (PDE-X) model is evaluated for the spectroscopic properties of organic chromophores solvated in water, including both one- and two-photon absorption properties. The PDE-X embedding model systematically improves vertical excitation energies over the preceding polarizable density embedding model (PDE). PDE-X shows more modest improvements over existing embedding models for oscillator strengths and two-photon absorption cross-sections, which are more sensitive properties. We argue that the origin of these discrepancies is related to the description of polarization effects, suggesting directions for future development of the embedding model.
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Affiliation(s)
- Ernst Dennis Larsson
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense, Denmark
| | - Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense, Denmark
| | - Erik Donovan Hedegård
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense, Denmark
| | - Jacob Kongsted
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, DK-5230 Odense, Denmark
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Jansen M, Reinholdt P, Hedegård ED, König C. Theoretical and Numerical Comparison of Quantum- and Classical Embedding Models for Optical Spectra. J Phys Chem A 2023. [PMID: 37399130 DOI: 10.1021/acs.jpca.3c02540] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/05/2023]
Abstract
Quantum-mechanical (QM) and classical embedding models approximate a supermolecular quantum-chemical calculation. This is particularly useful when the supermolecular calculation has a size that is out of reach for present QM models. Although QM and classical embedding methods share the same goal, they approach this goal from different starting points. In this study, we compare the polarizable embedding (PE) and frozen-density embedding (FDE) models. The former is a classical embedding model, whereas the latter is a density-based QM embedding model. Our comparison focuses on solvent effects on optical spectra of solutes. This is a typical scenario where super-system calculations including the solvent environment become prohibitively large. We formulate a common theoretical framework for PE and FDE models and systematically investigate how PE and FDE approximate solvent effects. Generally, differences are found to be small, except in cases where electron spill-out becomes problematic in the classical frameworks. In these cases, however, atomic pseudopotentials can reduce the electron-spill-out issue.
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Affiliation(s)
- Marina Jansen
- Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, Callinstr. 3A, 30167 Hannover, Germany
| | - Peter Reinholdt
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark
| | - Erik D Hedegård
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, Campusvej 55, 5230 Odense, Denmark
| | - Carolin König
- Institute of Physical Chemistry and Electrochemistry, Leibniz University Hannover, Callinstr. 3A, 30167 Hannover, Germany
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Pernal K, Hapka M. Range‐separated multiconfigurational density functional theory methods. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2021. [DOI: 10.1002/wcms.1566] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Affiliation(s)
| | - Michał Hapka
- Lodz University of Technology Institute of Physics Lodz Poland
- Faculty of Chemistry University of Warsaw Warsaw Poland
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Kjellgren ER, Hedegård ED, Jensen HJA. Triplet excitation energies from multiconfigurational short-range density-functional theory response calculations. J Chem Phys 2019; 151:124113. [PMID: 31575161 DOI: 10.1063/1.5119312] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Linear response theory for the multiconfigurational short-range density functional theory (MC-srDFT) model is extended to triplet response with a singlet reference wave function. The triplet linear response equations for MC-srDFT are derived for a general hybrid srGGA functional and implemented in the Dalton program. Triplet excitation energies are benchmarked against the CC3 model of coupled cluster theory and the complete-active-space second-order perturbation theory using three different short-range functionals (srLDA, srPBE, and srPBE0), both with full linear response and employing the generalized Tamm-Dancoff approximation (gTDA). We find that using gTDA is required for obtaining reliable triplet excitations; for the CAS-srPBE model, the mean absolute deviation decreases from 0.40 eV to 0.26 eV, and for the CAS-srLDA model, it decreases from 0.29 eV to 0.21 eV. As expected, the CAS-srDFT model is found to be superior to the HF-srDFT model when analyzing the calculated triplet excitations for molecules in the benchmark set where increased static correlation is expected.
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Affiliation(s)
- Erik Rosendahl Kjellgren
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
| | - Erik Donovan Hedegård
- Division of Theoretical Chemistry, Lund University, Kemicentrum P.O. Box 124, SE-221 00 Lund, Sweden
| | - Hans Jørgen Aagaard Jensen
- Department of Physics, Chemistry and Pharmacy, University of Southern Denmark, DK-5230 Odense M, Denmark
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Abstract
The accuracy of three different complete active space (CAS) self-consistent field (CASSCF) methods is investigated for the electronically excited-state benchmark set of Schreiber , M. ; et al. J. Chem. Phys. 2008 , 128 , 134110 . Comparison of the CASSCF linear response (LR) methods MC-RPA and MC-TDA and the state-averaged (SA) CASSCF method is made for 122 singlet excitation energies and 69 oscillator strengths. Of all CASSCF methods, when considering the complete test set, MC-RPA performs best for both excitation energies and oscillator strengths with a mean absolute error (MAE) of 0.74 eV and 51%, respectively. MC-TDA and SA-CASSCF show a similar accuracy for the excitation energies with a MAE of ∼1 eV with respect to more accurate coupled cluster (CC3) excitation energies. The opposite trend is observed for the subset of n → π* excitation energies for which SA-CASSCF exhibits the least deviations (MAE 0.65 eV). By looking at s-tetrazine in more detail, we conclude that better performance for the n → π* SA-CASSCF excitation energies can be attributed to a fortunate error compensation. For oscillator strengths, SA-CASSCF performs worst for the complete test set (MAE 100%) as well as for the subsets of n → π* (MAE 192%) and π → π* excitations (MAE 84.9%). In general, CASSCF gives the worst performance for excitation energies of all excited-state ab initio methods considered so far due to lacking the major part of dynamic electron correlation, though MC-RPA and TD-DFT (BP86) show similar performance. Among all LR-type methods, LR-CASSCF oscillator strengths are the ones with the least accuracy for the same reason. As state-specific orbital relaxation effects are accounted for in LR-CASSCF, oscillator strengths are significantly more accurate than those of MS-CASPT2. Our findings should encourage further developments of response theory-based multireference methods with higher accuracy and feasibility.
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Affiliation(s)
- Benjamin Helmich-Paris
- Max-Planck-Institut für Kohlenforschung , Kaiser-Wilhelm-Platz 1 , D-45470 Mülheim an der Ruhr , Germany
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Hedegård ED, Toulouse J, Jensen HJA. Multiconfigurational short-range density-functional theory for open-shell systems. J Chem Phys 2018; 148:214103. [DOI: 10.1063/1.5013306] [Citation(s) in RCA: 30] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/25/2022] Open
Affiliation(s)
- Erik Donovan Hedegård
- Department of Theoretical Chemistry, Lund University, Kemicentrum P.O. Box 124, SE-221 00 Lund, Sweden
| | - Julien Toulouse
- Laboratoire de Chimie Théorique, Sorbonne Université and CNRS, Paris, France
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Dong G, Ryde U, Aa. Jensen HJ, Hedegård ED. Exploration of H2 binding to the [NiFe]-hydrogenase active site with multiconfigurational density functional theory. Phys Chem Chem Phys 2018; 20:794-801. [DOI: 10.1039/c7cp06767d] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
The combination of density functional theory (DFT) with a multiconfigurational wave function is an efficient way to include dynamical correlation in calculations with multiconfiguration self-consistent field wave functions.
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Affiliation(s)
- Geng Dong
- Department of Theoretical Chemistry
- Lund University
- Chemical Centre
- SE-221 00 Lund
- Sweden
| | - Ulf Ryde
- Department of Theoretical Chemistry
- Lund University
- Chemical Centre
- SE-221 00 Lund
- Sweden
| | - Hans Jørgen Aa. Jensen
- Department of Physics, Chemistry and Pharmacy
- University of Southern Denmark
- DK-5230 Odense M
- Denmark
| | - Erik D. Hedegård
- Department of Theoretical Chemistry
- Lund University
- Chemical Centre
- SE-221 00 Lund
- Sweden
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Olsen JMH, Hedegård ED. Modeling the absorption spectrum of the permanganate ion in vacuum and in aqueous solution. Phys Chem Chem Phys 2017; 19:15870-15875. [DOI: 10.1039/c7cp01194f] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
The absorption spectrum of MnO4− in vacuum and aqueous solution is modeled using the range-separated complete active space short-range density functional theory method (CAS-srDFT) combined with either implicit (PCM) or explicit (PE) solvent models. The experimental vacuum-to-water solvent shift of the lowest intense transition is reproduced by PE-CAS-srDFT.
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Tuna D, Lu Y, Koslowski A, Thiel W. Semiempirical Quantum-Chemical Orthogonalization-Corrected Methods: Benchmarks of Electronically Excited States. J Chem Theory Comput 2016; 12:4400-22. [DOI: 10.1021/acs.jctc.6b00403] [Citation(s) in RCA: 44] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Deniz Tuna
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
| | - You Lu
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
| | - Axel Koslowski
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
| | - Walter Thiel
- Max-Planck-Institut für Kohlenforschung, 45470 Mülheim an der Ruhr, Germany
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