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WIREs Comput Mol Sci
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The DFT/MRCI method

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In the past two decades, the combined density functional theory and multireference configuration interaction (DFT/MRCI) method has developed from a powerful approach for computing spectral properties of singlet and triplet excited states of large molecules into a more general multireference method applicable to states of all spin multiplicities. In its original formulation, it shows great efficiency in the evaluation of singlet and triplet excited states which mainly originate from local one‐electron transitions. Moreover, DFT/MRCI is one of the few methods applicable to large systems that yields the correct ordering of states in extended π‐systems where double excitations play a significant role. A recently redesigned DFT/MRCI Hamiltonian extends the application range of the method to bi‐chromophores such as hydrogen‐bonded or π‐stacked dimers and loosely coupled donor–acceptor systems. In conjunction with a restricted‐open shell Kohn–Sham optimization of the molecular orbitals, even electronically excited doublet and quartet states can be addressed. After a short outline of the general ideas behind this semi‐empirical method and a brief review of alternative approaches combining density functional and multireference wavefunction theory, formulae for the DFT/MRCI Hamiltonian matrix elements are presented and the adjustments of the two‐electron contributions are discussed. The performance of the DFT/MRCI variants on excitation energies of organic molecules and transition metal compounds against experimental or ab initio reference data is analyzed and case studies are presented which show the strengths and limitations of the method. Finally, an overview over the properties available from DFT/MRCI wavefunctions and further developments is given. This article is categorized under: Electronic Structure Theory > Density Functional Theory Electronic Structure Theory > Semiempirical Electronic Structure Methods Software > Quantum Chemistry
Schematic of the low‐lying singlet and triplet excited‐state energies of (a) all‐trans‐octatetraene (b) pentacene and the leading configurations of the corresponding wave functions. Both examples stress the importance of double excitations and multiconfiguration expansions for a qualitatively correct description of the spectral properties of these compounds
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Absorption spectra of the three‐coordinate 1,3‐bis(2,6‐diisopropylphenyl)imidazol‐2‐ylidene‐Cu(I)‐1,10‐phenanthroline complex. The experimental data points were read from Figure of Reference . (a) DFT/MRCI (original parametrization), green: Scalar relativistic, gold: Including spin–orbit coupling effects; (b) TDDFT in conjunction with the PBE0 functional. All line spectra were broadened with Gaussians of 1,500/cm FWHM. Herein, no shifts were applied (Reprinted with permission from Reference . Copyright 2016 ACS Publications)
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UV/Vis spectrum of ferrocene. Experimental data had been taken from Reference . The DFT/MRCI excitation energies (original parametrization) were blue‐shifted by 0.15 eV for a better match with experiment (Reprinted with permission from Reference . Copyright 1999 AIP Publishing)
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Calculated absorption spectra of IrIII(ppy)2(acac). Green: Spin–orbit free DFT/MRCI (R2016 Hamiltonian), yellow: Spin–orbit free DFT/MRCI (original Hamiltonian), purple: DFT/MRCI (original Hamiltonian) including spin–orbit coupling effects. The envelopes of the line spectra were plotted with a Gaussian broadening of 3,000/cm FWHM. The data points of the experimental spectrum were taken from Reference
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Histogram of the error distributions (Ecalc − Eexp) of 67 DFT/MRCI and TDDFT singlet and triplet excitation energies (in eV) of 21 first‐ and second‐row transition metal complexes with respect to experimental data. DFT/MRCI results on the 27 inorganic and 40 organometal complexes were obtained with (a) standard parameters and selection threshold 1 Eh (b) tight parameters and selection threshold 0.8 Eh
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Chemical structure of m‐xylylene in the biradical ground state (a) and the first excited singlet state (b). Density plots of the 2a2 (c) and 3b2 (d) MOs are shown for an isovalue of 0.05
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Chemical structure and absorption spectrum of the Blatter radical in dichloromethane (DCM) solution. The data points of the experimental spectrum were read from Reference
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Histogram of the error (Ecalc − Eexp) of the R2017 DFT/MRCI approach with δEsel = 1.0 Eh. (a) All doublet states from a sample of 150 states, (b) all singlet, doublet and triplet states from a sample of 310 states in total (Reprinted with permission from Reference . Copyright 2017 AIP Publishing)
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Histogram of the error distributions (Ecalc − Eexp) of 160 singlet and triplet states of small‐ and medium‐sized organic molecules from experimental data using (a) the original and (b) the redesigned R2016 DFT/MRCI Hamiltonian using standard parameters and a selection threshold of δEsel = 1.0 Eh
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Sketch of the ethylene‐tetrafluorothylene dimer and the orbitals involved in the low‐lying excitations (Reprinted with permission from Reference . Copyright 2016 AIP Publishing)
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Performance of the original DFT/MRCI (DFT/MRCI‐S) and redesigned R2016 DFT/MRCI (DFT/MRCI‐R) methods on excitation energies of extended π‐systems in comparison with experimental results: (a) carotenes, (b) polyacences (Reprinted with permission from Reference . Copyright 2016 AIP Publishing)
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Frontier MOs of free‐base porphyrin. In addition to the four Gouterman orbitals (c)‐(f), at least two further high‐lying occupied orbitals (a) and (b) are required for a qualitatively correct description of the Soret band. (a) HOMO‐3, (b) HOMO‐2, (c) HOMO‐1, (d) HOMO, (e) LUMO, and (f) LUMO+1
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Damping functions used to scale down the off‐diagonal matrix elements with unequal spatial configurations in the original, R2016, R2017, and R2018 Hamiltonians for (a) the standard parametrization in conjunction with a configuration selection threshold esel = 1.0 Eh (b) the tight (or short) parametrization in conjunction with esel = 0.8 Eh
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Software > Quantum Chemistry
Electronic Structure Theory > Density Functional Theory
Electronic Structure Theory > Semiempirical Electronic Structure Methods

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