Spin−Orbit Coupling Patterns Induced by Twist and Pyramidalization Modes in C2H4: A Quantitative Study and a Qualitative Analysis

Small-Occupation Density Functional Correlation Energy Correction to Wave Function Approximations

In this work, we introduce a novel hybrid approach, termed WFT-soDFT, designed to seamlessly incorporate DFT correlation into wave function ansatzes. This is achieved through a partitioning of the orbital space, distinguishing between large and small natural occupation numbers associated with wave function theory (WFT) and DFT correlation, respectively. The method uses a novel criterion for partitioning the orbital space and mapping the electron density in natural orbitals with a small occupation with the correlation energy of fast electrons within the homogeneous electron gas. Central to our approach is the introduction of a separation parameter ν, the choice of the WFT approach, and the correlation functional. Here, we combine the RASCI wave function with hole and particle truncation with a local density correlation functional to only account for small-occupation correlation energy. We investigate the performance of the method in the study of small but challenging chemical systems, for which WFT-soDFT demonstrates notable improvements over pristine wave function calculations. These findings collectively highlight the potential of the WFT-soDFT approach as a computationally affordable strategy to improve the accuracy of WFT electronic structure calculations.

SOiCISCF: Combining SOiCI and iCISCF for Variational Treatment of Spin-Orbit Coupling

It has recently been shown that the SOiCI approach [Zhang, N.; J. Phys.: Condens. Matter 2022, 34, 224007], in conjunction with the spin-separated exact two-component relativistic Hamiltonian, can provide very accurate fine structures of systems containing heavy elements by treating electron correlation and spin-orbit coupling (SOC) on an equal footing. Nonetheless, orbital relaxations/polarizations induced by SOC are not yet fully accounted for due to the use of scalar relativistic orbitals. This issue can be resolved by further optimizing the still real-valued orbitals self-consistently in the presence of SOC, as done in the spin-orbit coupled CASSCF approach [Ganyushin, D.; et al. J. Chem. Phys. 2013, 138, 104113] but with the iCISCF algorithm [Guo, Y.; J. Chem. Theory Comput. 2021, 17, 7545-7561] for large active spaces. The resulting SOiCISCF employs both double group and time reversal symmetries for computational efficiency and the assignment of target states. The fine structures of p-block elements are taken as showcases to reveal the efficacy of SOiCISCF.

Spin-Orbit Couplings of Open-Shell Systems with Restricted Active Space Configuration Interaction

In this work we perform electronic structure calculations to unravel the origin of spin-orbit couplings (SOCs) in open-shell molecules. For that, we select systems displaying di or polyradical character, e.g., trimethylene, and analyze the changes in the magnitude of SOC constants along molecular distortions of ethylene and in the presence of intermolecular interactions between open and closed-shell moieties in the O₂-C₂H₄ system. Calculations were performed by using nonrelativistic wave functions obtained with the restricted active space configuration interaction (RASCI) method, in conjunction with a recent implementation for the calculation of SOC based on the spin-orbit mean field approximation. Our results demonstrate the suitability of RASCI in the calculation of SOCs of open-shell systems, while providing a deep understanding of the relationship between couplings and the nature of the electronic states. Moreover, we introduce a new definition of the SOC constant for the study of molecular aggregates.

SOiCI and iCISO: combining iterative configuration interaction with spin-orbit coupling in two ways

The near-exact iCIPT2 approach for strongly correlated systems of electrons, which stems from the combination of iterative configuration interaction (iCI, an exact solver of full CI) with configuration selection for static correlation and second-order perturbation theory (PT2) for dynamic correlation, is extended to the relativistic domain. In the spirit of spin separation, relativistic effects are treated in two steps: scalar relativity is treated by the infinite-order, spin-free part of the exact two-component (X2C) relativistic Hamiltonian, whereas spin-orbit coupling (SOC) is treated by the first-order, Douglas-Kroll-Hess-like SOC operator derived from the same X2C Hamiltonian. Two possible combinations of iCIPT2 with SOC are considered, i.e., SOiCI and iCISO. The former treats SOC and electron correlation on an equal footing, whereas the latter treats SOC in the spirit of state interaction, by constructing and diagonalizing an effective spin-orbit Hamiltonian matrix in a small number of correlated scalar states. Both double group and time reversal symmetries are incorporated to simplify the computation. Pilot applications reveal that SOiCI is very accurate for the spin-orbit splitting (SOS) of heavy atoms, whereas the computationally very cheap iCISO can safely be applied to the SOS of light atoms and even of systems containing heavy atoms when SOC is largely quenched by ligand fields.

Impact of fluorination on the photophysics of the flavin chromophore: a quantum chemical perspective

10-Methylisoalloxazine (MIA) and its fluorinated derivatives (6-9F-MIA) were investigated by means of quantum chemistry, looking into the influence of fluorination on fluorescence, absorption and inter-system crossing (ISC) in vacuum and in aqueous solution.

Theoretical Study on the Reaction Mechanism of Ti with CH3CN in the Gas Phase

To gain a deeper understanding of the reaction mechanisms of Ti with acetonitrile molecules, the triplet and singlet spin-state potential energy surfaces (PESs) has been investigated at B3LYP level of density functional theory (DFT). Crossing points between the different PESs and possible spin inversion processes are discussed by spin-orbit coupling (SOC) calculation. In addition, the bonding properties of the species along the reaction were analyzed by electron localization function (ELF), atoms in molecules (AIM) and natural bond orbital (NBO). The results showed that acetonitrile activation by Ti is a typical spin-forbidden process; larger SOC (by 220.12 cm(-1)) and the possibility of crossing between triplet and singlet imply that intersystem crossing (ISC) would occur near the minimum energy crossing point (MECP) during the transfer of the hydrogen atom.

A Local CC2 and TDA-DFT Double Hybrid Study on BODIPY/aza-BODIPY Dimers as Heavy Atom Free Triplet Photosensitizers for Photodynamic Therapy Applications

A series of 11 different boron-dipyrromethene (BODIPY) dimers is carefully examined by means of ab initio and Tamm-Dancoff approximated density functional theory methods. Vertical and 0-0 excitation energies along with the tetraradical character of these dimers are determined. Possible application of a series of linked dimers for photodynamic therapy (PDT) was investigated through computing their excitation energies, spin-orbit coupling matrix elements, and singlet-triplet energy gaps. Finally through a systematic investigation of a series of 36 different BODIPY and aza-BODIPY dimers, a new class of near-IR heavy atom free photosensitizers for PDT action is introduced.

Photophysics of flavin derivatives absorbing in the blue-green region: thioflavins as potential cofactors of photoswitches

The purpose of this study was to find flavin derivatives with absorption maxima in the blue-green region of the visible spectrum that might be used as alternative cofactors in blue-light photoreceptors. To this end, the vertical absorption spectra of eight lumiflavin-related compounds were calculated by means of quantum chemical methods. The compounds differ from lumiflavin by the subsitution of an S atom for an O atom at the 2- and/or 4-positions of the isoalloxazine core, the substitution of an N atom for a CH group in the 6- and/or 9-positions, or an extension of the π system at the 7- and 8-positions. For the three most promising compounds, 2-thio-lumiflavin, 4-thio-lumiflavin, and 2,4-dithio-lumiflavin, the quantum chemical investigations were extended to include geometry relaxations in the excited states, rates for spin-forbidden transitions and an estimate of spectral shifts brought about by polar protic environments. We find these thiocarbonyl compounds to have very promising excited-state properties. They absorb in the blue-green wavelength regime around 500 nm, i.e., substantially red-shifted with respect to lumiflavin that is the cofactor of natural blue-light photoreceptors. Their triplet quantum yields are predicted to be close to unity while their triplet lifetimes are long enough to enable bimolecular photochemical reactions. The combination of these properties makes the thioflavins potentially suitable candidates as cofactors in biomimetic photoswitches.

Molecular mechanism of diaminomaleonitrile to diaminofumaronitrile photoisomerization: an intermediate step in the prebiotic formation of purine nucleobases

The photoinduced isomerization of diaminomaleonitrile (DAMN) to diaminofumaronitrile (DAFN) was suggested to play a key role in the prebiotically plausible formation of purine nucleobases and nucleotides. In this work we analyze two competitive photoisomerization mechanisms on the basis of state-of-the-art quantum-chemical calculations. Even though it was suggested that this process might occur on the triplet potential-energy surface, our results indicate that the singlet reaction channel should not be disregarded either. In fact, the peaked topography of the S1 /S0 conical intersection suggests that the deexcitation should most likely occur on a sub-picosecond timescale and the singlet photoisomerization mechanism might effectively compete even with a very efficient intersystem crossing. Such a scenario is further supported by the relatively small spin-orbit coupling of the S1 and T2 states in the Franck-Condon region, which does not indicate a very effective triplet bypass for this photoreaction. Therefore, we conclude that the triplet reaction channel in DAMN might not be as prominent as was previously thought.

Quantum Chemical Investigation of Spin-Forbidden Transitions in Dithiosuccinimide

The vertical and adiabatic electronic spectra of dithiosuccinimide have been investigated by means of multi-reference Møller–Plesset perturbation theory and combined densitiy functional/multi-reference configuration interaction methods. Geometries of the electronic ground state and several low-lying excited states have been optimised at the level of time-dependent density functional theory. We have determined spin-orbit coupling for correlated wavefunctions utilising a non-empirical spin-orbit mean-field approach. Because of the two thiocarbonyl groups present in the molecule, dithiosuccinimide exhibits a dense spectrum of low-lying valence states. The first two excited singlet states (S 1 and S 2) originate from n → π* excitations. Nearby, three triplet states are located, two n → π* states (T 1 and T 2), and a π → π* triplet excitation (T 3). The experimentally observed strong absorption band with maximum at 3.96 eV arises from the π → π* excited 1 B 2 (S 3) state. Computed radiative lifetimes are presented for the experimentally known phosphorescence from the n → π* excited T 1 state. Further, we find nearly equal probabilities for the spin-forbidden S 0 → T 2 and the spin-allowed S 0 → S 1 transitions in absorption. On these grounds, we assign band number 3 in the spectra measured by Meskers et al. [J. Phys. Chem. 99 (1995) 1134] to this spin-forbidden transition.

SPOCK.CI: A multireference spin-orbit configuration interaction method for large molecules

We present SPOCK.CI, a selecting direct multireference spin-orbit configuration interaction (MRSOCI) program based on configuration state functions. It constitutes an extension of the spin-free density functional theory/multireference configuration interaction (DFT/MRCI) code by Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] and includes spin-orbit interaction on the same footing with electron correlation. Key features of SPOCK.CI are a fast determination of coupling coefficients between configuration state functions, the use of a nonempirical effective one-electron spin-orbit atomic mean-field Hamiltonian, the application of a resolution-of-the-identity approximation to computationally expensive spin-free four-index integrals, and the use of an efficient multiroot Davidson diagonalization scheme for the complex Hamiltonian matrix. SPOCK.CI can be run either in ab initio mode or as semiempirical procedure combined with density functional theory (DFT/MRSOCI). The application of these techniques and approximations makes it possible to compute spin-dependent properties of large molecules in ground and electronically excited states efficiently and with high confidence. Second-order properties such as phosphorescence rates are known to converge very slowly when evaluated perturbationally by sum-over-state approaches. We have investigated the performance of SPOCK.CI on these properties in three case studies on 4H-pyran-4-thione, dithiosuccinimide, and free-base porphin. In particular, we have studied the dependence of the computed phosphorescence lifetimes on various technical parameters of the MRSOCI wave function such as the size of the configuration space, selection of single excitations, diagonalization thresholds, etc. The results are compared to the outcome of extensive quasidegenerate perturbation theory (QDPT) calculations as well as experiment. In all three cases, the MRSOCI approach is found to be superior to the QDPT expansion and yields results in very good agreement with experimental findings. For molecules up to the size of free-base porphin, MRSOCI calculations can easily be run on a single-processor personal computer. Total CPU times for the evaluation of the electronic excitation spectrum and the phosphorescence lifetime of this molecule are below 40 h.

The T(1) (3)(pi-pi*)/S(0) intersections and triplet lifetimes of cyclic alpha,beta-enones

The ground and triplet excited states of cycloheptenone, cyclohexenone, and cyclopentenone have been studied using CASSCF calculations. For these three molecules, the difference in energy (DeltaE) between the twisted T(1) (3)(pi-pi*) minimum and T(1) (3)(pi-pi*)/S(0) intersection increases as the flexibility of the ring decreases. A strong positive correlation between DeltaE and the natural logarithm of the experimentally determined triplet lifetimes (ln tau) is found, suggesting that DeltaE predominantly determines the relative radiationless decay rates of T(1).

Photodissociation of ethylene sulfide at 193 nm: a photofragment translational spectroscopy study with VUV synchrotron radiation and ab initio calculations

Photodissociation of ethylene sulfide at 193 nm has been studied using photofragment translational spectroscopy and ab initio theoretical calculations. Tunable synchrotron radiation was used as a universal but selective probe of the reaction products to reveal new aspects of the photodissociation dynamics. The channel giving S + C2H4 was found to be dominated by production of ground-state sulfur atoms (S(3P):S(1D) = 1.44:1), mostly through a spin-forbidden process. The results also suggest the presence of a channel giving S(3P) in conjunction with triplet ethylene C2H4 (3B(1u)) and allow insight into the energy of the latter species near its equilibrium geometry, in which the two methylene groups occupy perpendicular planes. In addition, a channel leading to the production of H2S with C2H2 also has been observed. Our experimental results are supported and elaborated by theoretical calculations.

On the Z-E photoisomerization of chiral 2-pentenoate esters: stationary irradiations, laser-flash photolysis studies, and theoretical calculations

Chiral pentenoates 1-3 in both Z and E isomeric forms underwent stationary irradiations in several solvents and in the presence of different photosensitizers. The photostationary-state ratio has been determined for each Z/E couple showing a predominance of the thermodynamically more stable isomer for 1 and 3. Moreover, transient species were generated by pulsed laser excitation and detected by their characteristic ultraviolet absorptions, being the first time that enoate-originated triplets are detected. Stern-Volmer quenching studies afforded a quantitative measure for the efficiency of the photosensitization processes induced by benzophenone or acetophenone and allowed the determination of the corresponding quenching rate constants. Density functional calculations permitted the determination of the geometries and the energies of the diastereomeric excited states. Two diastereomeric orthogonal and two diastereomeric planar structures result as a consequence of the presence of a chiral substituent. The orthogonal triplets are the energy minima in all cases, whereas the planar triplets are the transition states linking these orthogonal structures, the corresponding energy barriers being 8-10 kcal mol(-1) for enoates 1-3. The computed S(0) to T(1) excitation energies show a trend which is consistent with the quenching rate constants. On the other hand, the triplet lifetimes determined for 1 and 2 are unusually long (1-20 micros) if compared with the data already described for several enones, in the range of nanoseconds. This fact has been rationalized from calculations of spin-orbit coupling at several points of the T(1) potential energy surface. This coupling is maximum for structures with a torsional angle close to 45 degrees, which are 4-5 kcal mol(-1) above the minima of T(1). Calculations done on the hypothetical aldehyde 4 and methyl vinyl ketone show much lower energy barriers, thus accounting for the shorter lifetimes reported for enone triplets.