Performance of TD-DFT for Excited States of Open-Shell Transition Metal Compounds

Abstract

Time-dependent density functional theory (TD-DFT) has been very successful in accessing low-lying excited states of closed-shell systems. However, it is much less so for excited states of open-shell systems: unrestricted Kohn-Sham based TD-DFT (U-TD-DFT) often produces physically meaningless excited states due to heavy spin contaminations, whereas restricted Kohn-Sham based TD-DFT often misses those states of lower energies. A much better variant is the explicitly spin-adapted TD-DFT (X-TD-DFT) [J. Chem. Phys. 2011, 135, 194106] that can capture all the spin-adapted singly excited states yet without computational overhead over U-TD-DFT. While the superiority of X-TD-DFT over U-TD-DFT has been demonstrated for open-shell systems of main group elements, it remains to be seen if this is also the case for open-shell transition metal compounds. Taking as benchmark the results by MS-CASPT2 (multistate complete active space second-order perturbation theory) and ic-MRCISD (internally contracted multireference configuration interaction with singles and doubles), it is shown that X-TD-DFT is indeed superior to U-TD-DFT for the vertical excitation energies of ZnH, CdH, ScH, YH, YO, and NbO. Admittedly, there exist a few cases where U-TD-DFT appears to be better than X-TD-DFT. However, this is due to a wrong reason: the underestimation (due to spin contamination) and the overestimation (due to either the exchange-correlation functional itself or the adiabatic approximation to the exchange-correlation kernel) happen to be compensated in the case of U-TD-DFT. As for [Cu(CH)], which goes beyond the capability of both MS-CASPT2 and ic-MRCISD, X-TD-DFT revises the U-TD-DFT assignment of the experimental spectrum.

Design of Perchlorotriphenylmethyl (PTM) Radical‐Based Compounds for Optoelectronic Applications: The Role of Orbital Delocalization

“…The main goal of our theoretical study is to assess how the absorption properties of PTM‐based compounds are influenced by the nature and number of substituents and the type of connection in order to formulate useful design rules for tailoring the properties of these compounds. We stress that we are mostly interested in trends than in absolute values knowing the limitations of TD‐DFT to deal with open‐shell systems, partially due to the introduction of spin contamination ,,…”

“…We stress that we are mostly interested in trends than in absolute values knowing the limitations of TD-DFT to deal with open-shell systems, partially due to the introduction of spin contamination. [39,40,41]…”

Electronic, optical, and charge transfer properties of porphyrin and metallated porphyrins in different media

“…appearing in the Marcus-Hush equation given by Equation (1) should be used. [101,102] In this article, to overcome this difficulty, emission wavelength estimation is made by using the energy difference between the ground state and the lowest excited state. The calculated W values of porphyrin and metallated porphyrin complexes in the parallel geometry at 298.15 K are given in Table 4 (see also Table S5).…”

“…Although the emission calculations can be easily made for the closed-shell system, [99,100] these calculations are challenging for the open-shell systems. [101,102] In this article, to overcome this difficulty, emission wavelength estimation is made by using the energy difference between the ground state and the lowest excited state. The reason for this approach is that the possibility of emission corresponding to the lowest energy state can be high.…”

Spin State Energetics of VGen−/0 (n = 5–7) Clusters and New Assignments of the Anion Photoelectron Spectra

“…In the cases of VGe 3 −/0 and VGe 4 −/0 , the hybrid B3LYP, B3PW91, and PBE0 functionals were shown to underestimate the energies of the high‐spin states due to the large contribution of the Hartree–Fock exact exchange as compared to the pure GGA BP86 and PBE functionals . Also, density functional theory cannot access to all the relevant excited states, while time‐dependent density functional theory (TD‐DFT) is less successful in accessing the low‐lying excited states of open‐shell because of the heavy spin contamination problem. That is the reason why only the first bands in the photoelectron spectra of VGe n − ( n = 3–12) clusters are interpreted based on the B3PW91 functional results.…”