Spin-flip Density Functional Theory Research Articles

Spin-Flip Density Functional Theory for the Redox Properties of Organic Photoredox Catalysts in Excited States.

Photoredox catalysts (PCs) have contributed to the advancement of organic chemistry by accelerating conventional reactions and enabling new pathways through the use of reactive electrons in excited states. With a number of successful applications, chemists continue to seek new promising organic PCs to achieve their objectives. Instead of labor-intensive manual experimentation, quantum chemical simulations could explore the enormous chemical space more efficiently. The reliability and accuracy of quantum chemical simulations have become important factors for material screening. We designed a theoretical protocol capable of predicting redox properties in excited states with high accuracy for a selected model system of dihydroquinoxalino[2,3-b]quinoxaline derivatives. Herein, three factors were considered as critical to achieving reliable predictions with accurate physics: the solvent medium effect on excited-state geometries, an adequate amount of Hartree-Fock exchange (HFX), and the consideration of double-excitation character in excited states. We determined that it is necessary to incorporate solvent medium during geometry optimizations to obtain planar excited-state structures that are consistent with the experimentally observed modest Stokes shift. While density functionals belonging to the generalized gradient approximation family perform well for the prediction of photoelectrochemical properties, an incorrect description of exciton boundedness (spontaneous dissociation of excitons or extremely weak boundedness) on small organic molecules was predicted. The inclusion of an adequate amount of Hartree-Fock exchange was suggested as one approach to obtain bound excitons, which is physically reasonable. The last consideration is the double-excitation character in S1 states. As revealed by the second-order algebraic diagrammatic construction theory, non-negligible double excitations exist in S1 states in our model systems. Time-dependent density functional theory (TDDFT) is blind to doubly excited states, and this motivated us to use spin-flip DFT (SF-DFT). We established a theoretical protocol that could provide highly accurate estimations of photophysical properties and ground-/excited-state redox properties, focusing on the three factors mentioned above. Geometry optimization with DFT and TDDFT employing the B3LYP functional (20% HFX) in solution and energy refinement by SF-DFT reproduced the experimental redox properties in the excited and ground states remarkably well with mean signed deviations (MSDs) of 0.01 and -0.15 V, respectively. This theoretical protocol is expected to contribute to the understanding of exciton behavior in organic PCs and to the efficient design of new promising PC candidates.

Singlet-triplet energy gaps and the degree of diradical character in binuclear copper molecular magnets characterized by spin-flip density functional theory.

Molecular magnets, defined here as organic polyradicals, can be used as building blocks in the fabrication of novel and structurally diverse magnetic light-weight materials. We present a theoretical investigation of the lowest spin states of several binuclear copper diradicals. In contrast to previous studies, we consider not only the energetics of the low-lying states (which are related to the exchange-coupling parameter within the Heisenberg-Dirac-van-Vleck model), but also the character of the diradical states themselves. We use natural orbitals, their occupations, and the number of effectively unpaired electrons to quantify bonding patterns in these systems. We compare the performance of spin-flip time-dependent density functional theory (SF-TDDFT) using various functionals and effective core potentials against the wave function based approach, equation-of-motion spin-flip coupled-cluster method with single and double substitutions (EOM-SF-CCSD). We find that SF-TDDFT paired with the PBE50 and B5050LYP functionals performs comparably to EOM-SF-CCSD, with respect to both singlet-triplet gaps and states' characters. Visualization of frontier natural orbitals shows that the unpaired electrons are localized on copper centers, in some cases exhibiting slight through-bond interaction via copper d-orbitals and p-orbitals of neighboring ligand atoms. The analysis reveals considerable interactions between the formally unpaired electrons in the antiferromagnetic diradicaloids, meaning that they are poorly described by the Heisenberg-Dirac-van-Vleck model. Thus, for these systems the experimentally derived exchange-coupling parameters are not directly comparable with the singlet-triplet gaps. This explains systematic discrepancies between the computed singlet-triplet energy gaps and the exchange-coupling parameters extracted from experiment.

The photoisomerization of 11‐cis‐retinal protonated schiff base in gas phase: Insight from spin‐flip density functional theory

This extensive theoretical study employed the spin-flip density functional theory (SFDFT) method to investigate the photoisomerization of 11-cis-retinal protonated Schiff base (PSB11) and its minimal model tZt-penta-3,5-dieniminium cation (PSB3). Our calculated results indicate that SFDFT can perform very well in describing the ground- and excited-state geometries of PSB3 and PSB11. We located the conical intersection (CI) point and constructed the photoisomerization reaction path of PSB3 and PSB11 by using the SFDFT method. To further verify the SFDFT results, we computed the energy profiles along the constructed linearly interpolated internal coordinate (LIIC) pathways by using high-level theoretical methods, such as the EOM-CCSD, CR-EOM-CCSD(T), CASPT2, NEVPT2, and XMCQDPT2 methods. The SFDFT method predicts that the photoisomerization of PSB3 is barrierless, in accordance with previous complete-active-space self-consistent-field (CASSCF) results. However, an energy barrier is predicted along the LIIC pathways of PSB11. This finding is different from previous CASSCF results and may indicate that the photoisomerization of PSB11 in gas phase is similar to that in solution. However, the higher spin contamination of the SFDFT method in the vicinity of the CI point caused the located CI geometry to deviate from that of the real CI. In addition, the LIIC pathways are only approximations to the minimum energy path (MEP). Thus, further experimental and theoretical studies are needed to verify the existence of an energy barrier along the photoisomerization reaction path of PSB11 in gas phase.

Signature of Singlet Open-Shell Character on the Optically Allowed Singlet Excitation Energy and Singlet–Triplet Energy Gap

A signature of singlet open-shell character on the optically allowed singlet excitation energy and singlet-triplet energy gap is theoretically illuminated for open-shell singlet molecules. On the basis of a two-site diradical model with two electrons in two orbitals, the linear dependence of these excitation energies on the transfer integral, which is equivalent to the energy gap between the highest occupied (HOMO) and the lowest unoccupied (LUMO) molecular orbitals in the Hückel theory, is found to be broken down in the high diradical character region due to an increase in electron correlation in the open-shell singlet ground state. A series of polyacenes shows the similar behavior of the optically allowed singlet excitation energies obtained by time-dependent spin-flip density functional theory calculations and experiments, which bears testimony to the singlet open-shell character in long polyacenes.

Optimizing conical intersections of solvated molecules: The combined spin-flip density functional theory/effective fragment potential method

Solvent effects on a potential energy surface crossing are investigated by optimizing a conical intersection (CI) in solution. To this end, the analytic energy gradient has been derived and implemented for the collinear spin-flip density functional theory (SFDFT) combined with the effective fragment potential (EFP) solvent model. The new method is applied to the azomethane-water cluster and the chromophore of green fluorescent protein in aqueous solution. These applications illustrate not only dramatic changes in the CI geometries but also strong stabilization of the CI in a polar solvent. Furthermore, the CI geometries obtained by the hybrid SFDFT/EFP scheme reproduce those by the full SFDFT, indicating that the SFDFT/EFP method is an efficient and promising approach for understanding nonadiabatic processes in solution.

Photoisomerization of Stilbene: A Spin-Flip Density Functional Theory Approach

The photoisomerization process of 1,2-diphenylethylene (stilbene) is investigated using the spin-flip density functional theory (SFDFT), which has recently been shown to be a promising approach for locating conical intersection (CI) points (Minezawa, N.; Gordon, M. S. J. Phys. Chem. A2009, 113, 12749). The SFDFT method gives valuable insight into twisted stilbene to which the linear response time-dependent DFT approach cannot be applied. In contrast to the previous SFDFT study of ethylene, a distinct twisted minimum is found for stilbene. The optimized structure has a sizable pyramidalization angle and strong ionic character, indicating that a purely twisted geometry is not a true minimum. In addition, the SFDFT approach can successfully locate two CI points: the twisted-pyramidalized CI that is similar to the ethylene counterpart and another CI that possibly lies on the cyclization pathway of cis-stilbene. The mechanisms of the cis--trans isomerization reaction are discussed on the basis of the two-dimensional potential energy surface along the twisting and pyramidalization angles.

Optimizing Conical Intersections by Spin−Flip Density Functional Theory: Application to Ethylene

Conical intersections (CIs) of ethylene have been successfully determined using spin-flip density functional theory (SFDFT) combined with a penalty-constrained optimization method. We present in detail three structures, twisted-pyramidalized, hydrogen-migrated, and ethylidene CIs. In contrast to the linear response time-dependent density functional theory, which predicts a purely twisted geometry without pyramidalization as the S(1) global minimum, SFDFT gives a pyramidalized structure. Therefore, this is the first correct optimization of CI points of twisted ethylene by the DFT method. The calculated energies and geometries are in good agreement with those obtained by the multireference configuration interaction (MR-CI) method and the multistate formulation of second-order multireference perturbation theory (MS-CASPT2).

Magnetic Interactions in Alkyl Substituted Cyclohexane Diradical Systems: A Broken Symmetry Approach

Magnetic interactions in alkyl substituted cyclohexane diradical systems have been investigated within the framework of spin flip density functional theory. The investigations suggest a ferromagnetic interaction for both the alkyl substituted cyclohexane-1,3-diyls and cyclohexane-1,4-diyls. However, in the case of cyclohexane-1,3-diyls, the ferromagnetic interaction is much stronger than its 1,4 analogue. Interestingly, it has been observed that this interaction is reduced to almost half the value from the butyl to the decyl substituted unit relative to the lower homologues up to the propyl substituted unit in cyclohexane-1,3-diyls. On the other hand, in case of alkyl substituted cyclohexane-1,4-diyls, the ferromagnetic interaction for the higher homologues, i.e., butyl to decyl substituted units, substantially reduces to almost 5-6 times the value of its lower homologue (methyl and ethyl substituted unit). In both these cyclohexane diradical systems, beyond butyl substituted unit, a saturation effect in the magnetic coupling constant (J) value is observed. The rapid decrease followed by a saturation in the singlet-triplet gap and J as well may be explained by considering positive inductive effect of the alkyl substituent.