Combining Time-Dependent Density Functional Theory and the ΔSCF Approach for Accurate Core-Electron Spectra

Can ΔSCF and ROKS DFT-Based Methods Predict the Inversion of the Singlet-Triplet Gap in Organic Molecules?

Inverted singlet-triplet gap systems (INVEST) have emerged as an intriguing class of materials with potential applications as emitters in Organic Light Emitting Diodes (OLEDs). Indeed, this type of material exhibits a negative singlet-triplet energy gap (ΔEST), i.e., an inversion of the lowest singlet (S1) and triplet (T1) excited states, that goes against Hund's rule. In this study, the ΔEST of a set of 15 INVEST molecules has been computed within the framework of Restricted Open-Shell Kohn-Sham (ROKS) and Delta Self-Consistent Field (ΔSCF) methods and the results were benchmarked against wavefunction-based calculations performed at the EOM-CCSD, NEVPT2, and SCS-CC2 levels. We find that ROKS always (and wrongly) predicts a positive ΔEST with global hybrid, meta-GGA, and long-range corrected functionals and that this is almost functional-independent. We also show that the only way to obtain an inverted gap was to resort to double hybrid functionals. In contrast, using the above-mentioned functionals, ΔSCF usually gives a negative ΔEST, although the results are largely functional-dependent. Overall, applying a ΔSCF method based on the PBE0 functional provides the lowest MSD and MAD with respect to the EOM-CCSD results. We further show that the singlet-triplet inversion is driven by different degrees of orbital relaxation in the singlet versus triplet state and that this is well captured by ΔSCF calculations. As a matter of fact, this orbital relaxation in ΔSCF somehow mimics the involvement of double and higher-order excitations in EOM-CCSD, which leads to a difference in spatial localization of the α and β spins, and thus introduces (local) spin polarization effects sourcing the negative ΔEST. However, care should be taken when using the ΔSCF method to screen materials with potential INVEST behavior in view of their limited quantitative correlation with reference EOM-CCSD results on the molecular data basis used here.

N-Aromatic Complexation in Tetraphenyl Porphyrin Iron (III)-Pyridine: Evidence of Spin-Flip via Gas-Phase Electronic Spectroscopy

There is growing interest in the electronic properties of metalloporphyrins especially in relation to their interactions with other molecular species in their local environment. Here, UV-VIS laser photodissociation spectroscopy in vacuo has been applied to an iron-centred metalloporphyrin (FeTPP+) and its N-aromatic adduct with pyridine (py) to determine the electronic effect of complexation. Both the metalloporphyrin (FeTPP+) and pyridine adduct (FeTPP+⋅py) absorb strongly across the spectral region studied (652-302 nm: 1.91-4.10 eV). Notably, a large blue shift was observed for the dominant Soret band (41 nm) upon complexation (0.47±0.02 eV), indicative of strong pyridine binding. Significant differences in the profiles (i. e. number and position of bands) of the electronic spectra are evident comparing FeTPP+ and FeTPP+⋅py. Time-dependent density functional theory calculations were used to assign the spectra, revealing that the FeIII spin-state flips from S=3/2 to S=5/2 upon complexation with pyridine. For FeTPP+, all bright spectral transitions are found to be π-π* in character, with electron density variously distributed across the porphyrin and/or its phenyl substituents. Similar electronic excitations are observed for FeTPP+⋅py, with an additional bright transition which involves charge transfer from the porphyrin to the pyridine moiety.

Long-range Corrected Density Functional Theory Including a Two-Gaussian Hartree-Fock Operator for High Accuracy Core-excitation Energy Calculations of Both the Second- and Third-Row Atoms (LC2gau-core-BOP)

In the previous work, LCgau-core-BOP, which includes the short-range interelectronic Gaussian attenuating Hartree-Fock (HF) exchange to the long-range HF exchange, showed high accuracy core-excitation energies from 1s orbitals of the second-row atoms (1s → π*, 1s → σ*, 1s → n*, and 1s → Rydberg), but underestimates the core-excitation energies from 1s orbitals of the third-row atoms. To improve this, we added one more Gaussian attenuating HF exchange to LCgau-core-BOP. We named it LC2gau-core-BOP, which achieves a mean absolute error (MAE) of 0.6 and 0.3 eV for core excitation energies of the second- and third-row atoms of the tested small molecules, respectively. We found that the inclusion of the short-range interelectronic HF exchange at a distance ranging from 0.2 to 0.6 a.u. contributes to the increase of performances on 1s orbital energy calculations of the second-row atoms, while the inclusion of more short-range interelectronic HF exchange at a distance ranging from 0 to 0.2 a.u. does to the increase of performance on 1s orbital energy calculations of the third-row atoms. It is notable that all of these improvements were accomplished using flexible Gaussian attenuating HF exchange inclusion. LC2gau-core-BOP shows deviations of less than 0.8 eV from experimental values for all of the core-excitation energies of the tested medium-size molecules consisting of thymine, oxazole, glycine, and dibenzothiophene sulfone. Moreover, by optimizing one parameter of the OP correlation functional, LC2gau-core-BOP provides atomization energies over the G3 test set with an accuracy comparable to that of B3LYP.

Polysulfides in Magnesium-Sulfur Batteries

Mg-S batteries hold great promise as a potential alternative to Li-based technologies. Their further development hinges on solving a few key challenges, including the lower capacity and poorer cycling performance when compared to Li counterparts. At the heart of the issues is the lack of knowledge on polysulfide chemical behaviors in the Mg-S battery environment. In this Review, a comprehensive overview of the current understanding of polysulfide behaviors in Mg-S batteries is provided. First, a systematic summary of experimental and computational techniques for polysulfide characterization is provided. Next, conversion pathways for Mg polysulfide species within the battery environment are discussed, highlighting the important role of polysulfide solubility in determining reaction kinetics and overall battery performance. The focus then shifts to the negative effects of polysulfide shuttling on Mg-S batteries. The authors outline various strategies for achieving an optimal balance between polysulfide solubility and shuttling, including the use of electrolyte additives, polysulfide-trapping materials, and dual-functional catalysts. Based on the current understanding, the directions for further advancing knowledge of Mg polysulfide chemistry are identified, emphasizing the integration of experiment with computation as a powerful approach to accelerate the development of Mg-S battery technology.

Toward a correct treatment of core properties with local hybrid functionals

In local hybrid functionals (LHs), a local mixing function (LMF) determines the position-dependent exact-exchange admixture. We report new LHs that focus on an improvement of the LMF in the core region while retaining or partly improving upon the high accuracy in the valence region exhibited by the LH20t functional. The suggested new pt-LMFs are based on a Padé form and modify the previously used ratio between von Weizsäcker and Kohn-Sham local kinetic energies by different powers of the density to enable flexibly improved approximations to the correct high-density and iso-orbital limits relevant for the innermost core region. Using TDDFT calculations for a set of K-shell core excitations of second- and third-period systems including accurate state-of-the-art relativistic orbital corrections, the core part of the LMF is optimized, while the valence part is optimized as previously reported for test sets of atomization energies and reaction barriers (Haasler et al., J Chem Theory Comput 2020, 16, 5645). The LHs are completed by a calibration function that minimizes spurious nondynamical correlation effects caused by the gauge ambiguities of exchange-energy densities, as well as by B95c meta-GGA correlation. The resulting LH23pt functional relates to the previous LH20t functional but specifically improves upon the core region.

Core-Projected Hybrids Fix Systematic Errors in Time-Dependent Density Functional Theory Predicted Core-Electron Excitations

Linear response time-dependent density functional theory (TDDFT) is widely applied to valence, Rydberg, and charge-transfer excitations but, in its current form, makes large errors for core-electron excitations. This work demonstrates that the admixture of nonlocal exact exchange in atomic core regions significantly improves TDDFT-predicted core excitations. Exact exchange admixture is accomplished using projected hybrid density functional theory [ J. Chem. Theory Comput. 2023, 19, 837-847]. Scalar relativistic TDDFT calculations using core-projected B3LYP accurately model core excitations of second-period elements C-F and third-period elements Si-Cl, without sacrificing performance for the relative shifts of core excitation energies. Predicted K-edge X-ray near absorption edge structure (XANES) of a series of sulfur standards highlight the value of this approach. Core-projected hybrids appear to be a practical solution to TDDFT's limitations for core excitations, in the way that long-range-corrected hybrids are a practical solution to TDDFT's limitations for Rydberg and charge-transfer excitations.

Fractional-Electron and Transition-Potential Methods for Core-to-Valence Excitation Energies Using Density Functional Theory

Methods for computing X-ray absorption spectra based on a constrained core hole (possibly containing a fractional electron) are examined. These methods are based on Slater's transition concept and its generalizations, wherein core-to-valence excitation energies are determined using Kohn-Sham orbital energies. Methods examined here avoid promoting electrons beyond the lowest unoccupied molecular orbital, facilitating robust convergence. Variants of these ideas are systematically tested, revealing a best-case accuracy of 0.3-0.4 eV (with respect to experiment) for K-edge transition energies. Absolute errors are much larger for higher-lying near-edge transitions but can be reduced below 1 eV by introducing an empirical shift based on a charge-neutral transition-potential method, in conjunction with functionals such as SCAN, SCAN0, or B3LYP. This procedure affords an entire excitation spectrum from a single fractional-electron calculation, at the cost of ground-state density functional theory and without the need for state-by-state calculations. This shifted transition-potential approach may be especially useful for simulating transient spectroscopies or in complex systems where excited-state Kohn-Sham calculations are challenging.

Slater transition methods for core-level electron binding energies

Methods for computing core-level ionization energies using self-consistent field (SCF) calculations are evaluated and benchmarked. These include a "full core hole" (or "ΔSCF") approach that fully accounts for orbital relaxation upon ionization, but also methods based on Slater's transition concept in which the binding energy is estimated from an orbital energy level that is obtained from a fractional-occupancy SCF calculation. A generalization that uses two different fractional-occupancy SCF calculations is also considered. The best of the Slater-type methods afford mean errors of 0.3-0.4 eV with respect to experiment for a dataset of K-shell ionization energies, a level of accuracy that is competitive with more expensive many-body techniques. An empirical shifting procedure with one adjustable parameter reduces the average error below 0.2 eV. This shifted Slater transition method is a simple and practical way to compute core-level binding energies using only initial-state Kohn-Sham eigenvalues. It requires no more computational effort than ΔSCF and may be especially useful for simulating transient x-ray experiments where core-level spectroscopy is used to probe an excited electronic state, for which the ΔSCF approach requires a tedious state-by-state calculation of the spectrum. As an example, we use Slater-type methods to model x-ray emission spectroscopy.