Spin–orbit coupling in oxygen containing diradicals

Intermediate diradicals which occur in the Paterno–Büchi photocycloaddition and in the Norrish type I photoreactions have been calculated taking into account the spin–orbit coupling (SOC) between the singlet (S) and triplet (T) states. Reaction paths for the photocycloaddition of formaldehyde to ethene and the diradical products of the α-cleavage of cyclohexanone have been optimized by the MNDO CI method for a number of different singlet and triplet states. SOC integrals are calculated by an effective one-electron approximation. Intermediate diradicals in the Paterno–Büchi reaction and the SOC effects are also studied ab initio with CAS SCF geometry optimization in a TZV basis set. Both methods predict a large SOC matrix element between the S and T states in the course of the C–C attack, while the SOC integral is two orders of magnitude smaller for the diradical produced in the C–O attack. In the Norrish type I photoreaction the oxygen atom also produces some nonzero contribution to the SOC integral which governs intersystem crossing in a ·C–C· diradical. For the diradicals produced by the α-cleavage of cyclohexanone a vibronic interaction is responsible for the SOC mixing between the lowest S and T states. The importance of one-center versus two-center SOC contributions in diradicals is briefly discussed.     

Spin–orbit coupling of spin‐frustrated systems

We have investigated the effects of spin–orbit (SO) interactions on noncollinear molecular magnetism by combining the classical Dzyaloshinsky–Moriya (DM) model and ab initio generalized spin orbital (GSO) method. We have derived an estimation scheme of the magnetic anisotropy energy (MAE) and the Dzyaloshinsky vector based on the SO first‐order perturbation theory (SOPT1) for GSO Hartree–Fock (GHF) solutions. We found that the fundamental results of GHF‐SOPT1 method can be reproduced by diagonalizing the core Hamiltonian plus SO terms, and that the spin topologies of odd‐ring systems can be determined by the topological indices of the singly occupied molecular orbitals. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Spin–orbit and dispersion energy effects in XeF

Spin–orbit and dispersion energy contributions to the energy curves of XeF are examined. A rapid variation in the spin–orbit coupling with internuclear separation is found for both the ground and excited states. This result can explain the experimentally observed ordering of the ionic excited states when the spin–orbit perturbation couples ²σ and ²π energy curves obtained by both all-electron and effective core potential (ECP ) calculations at the first-order configuration interaction (FOCI ) level of accuracy. Damped dispersion energy contributions to the ground-state energy curve are shown to be comparable to the charge transfer contribution. The energy curve for XeF is in reasonable agreement with experimental results and a calculation of the analogous XeCl curve confirms the qualitative correctness of the calculation. The energy curves and transition moments were then applied to two problems related to the efficiency of the XeF laser. Photodissociation of the X state provides a means of removing a bottlenecked vibrational level but a calculation of the radiative transition probability between the X and A states finds the cross section is too small to yield rates competitive with collisional deactivation. The bottlenecked state may also be removed by electron dissociative attachment but the calculated energy curves for the X states of XeF and XeF^? do not cross at a low energy indicating a small cross section.     

Excited biradical states in oxirane ring opening

The mechanism of oxirane ring opening was studied by ab initio [RHF, ROHF, GVB/DH, RHF/SBK(p, d)] calculations. The strained structure of oxiranes and their complexes with aliphatic alcohols and amines is characterized by low-lying biradical states whose thermal population leads to the ring opening. The examined oxirane ring opening reacitons have low activation energy (<10 kcal mol-¹) and are catalyzed by labile hydrogen atoms in hydroxy and amino groups of the reaction complex.     

Spin–other–orbit and spin–orbit interactions in ƒ2 and ƒ3 electron configurations

Expressions of the matrix elements of the spin–other–orbit and spin–orbit interactions for the various multiplets of all the states of ?²- and ?³-electron configurations are reported and used to evaluate the Hartree–Fock values of these interactions in the neutral atoms Ce(4?²), Pr(4?³), Ho(4?¹¹) and Er(4?¹²). The required values of the spin–spin parameters M, and the spin-orbit parameter ζ for these atoms were obtained using numerical Hartree–Fock wave functions.     

Spin–orbit effects on magnetically induced current densities in the () clusters

This study reports the spin–orbit effects on the aromaticity of the , , , , , and anionic clusters via the magnetically induced current‐density method. All‐electron density functional theory (DFT) calculations were carried out using the four‐component Dirac‐Coulomb (DC) hamiltonian, including scalar and spin–orbit relativistic effects. The magnetic index of aromaticity was calculated by numerical integration over the current flow between two atoms in the pentagonal ring. These values were compared to the spin‐free values (spin–orbit coupling switched off), in order to assess the spin–orbit effect on aromaticity. It was found that in the heavy anions, and , there is a significant influence of the spin–orbit coupling. © 2018 Wiley Periodicals, Inc.     

Spin–orbit and correlation effects in platinum hydride (PtH)

The low-lying electronic states of PtH were studied by all-electron one- and two-component variational calculations on the multireference CI levels. The orbital optimization is performed within a one-component formalism, whereas the further refinement of the wave functions follows two different schemes: The most demanding approach introduces spin–orbit coupling in the CI optimization step, giving a simultaneous treatment of electron correlation and spin–orbit coupling. The second, considerably less demanding approach, corresponds almost to a perturbational treatment, introducing spin–orbit coupling as a final step after the CI optimization by diagonalizing the resulting Hamiltonian matrix over CI states. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 68: 53–64, 1998     

Franck-Condon factors in intermolecular intersystem crossing

It is concluded from the energy dependence of the rate constant for intersystem crossing between guests and host molecules in mixed crystals that Franck-Condon factors for inter- and intramolecular radiationless transitions are virtually identical.     

On the intersystem crossing of pentacene in p-terphenyl

Applying methods developed for single molecule spectroscopy to small ensembles, we have recorded high-resolution fluorescence-excitation spectra for pentacene in all substitutional sites of a p-terphenyl single crystal. The difference in intersystem crossing efficiency for pentacene molecules in the various substitutional sites is discussed on the basis of these spectra and data from optically detected magnetic resonance experiments.     

Electronic spectra and intersystem spin‐orbit coupling in 1,2‐ and 1,3‐squaraines

The main photophysical properties of a series of recently synthetized 1,2‐ and 1,3‐squaraines, including absorption electronic spectra, singlet‐triplet energy gaps, and spin‐orbit matrix elements, have been investigated by means of density functional theory (DFT) and time‐dependent DFT approaches. A benchmark of three exchange‐correlation functionals has been performed in six different solvent environments. The investigated 1,2 squaraines have been found to possess two excited triplet states (T₁ and T₂) that lie below the energy of the excited singlet one (S₁). The radiationless intersystem spin crossing efficiency is thus enhanced in both the studied systems and both the transitions could contribute to the excited singlet oxygen production. Moreover, they have a singlet‐triplet energy gap higher than that required to generate the cytotoxic singlet oxygen species. According to our data, these compounds could be used in photodynamic therapy applications that do not require high tissue penetration. © 2014 Wiley Periodicals, Inc.     

Studies of intersystem crossing dynamics in acetylene

We report a new ab initio study of the acetylene T3 potential energy surface, which clarifies the nature of its energy minimum, and present computed equilibrium geometries and diabatic frequencies. This information enables the computation of harmonic vibrational overlap integrals of T3 vibrational levels with the S1 3nu3 state. The results of this calculation support the interpretation of two local perturbations of S1 3nu3, revealed in ultraviolet laser-induced fluorescence/surface electron ejection by laser excited metastables spectroscopy and Zeeman anticrossing measurements, respectively, as arising from two rotational submanifolds of a single T3 vibrational state. We present plausible assignments for this state as a guide for future experimental work.     

Mechanism of collision-induced intersystem crossing in CO

We have studied inert-gas pressure effects on the fluorescence decay in CO selectively excited to the υ = 0 to 7 vibronic levels of the A ¹Π electronic state. It is shown that the dependence of the quenching cross section σ_isc on the average value of the ST mixing coefficient (β²) has a quasi-logarithmic form. A simple two-level model describing semiquantitatively this behavior is proposed.     

Temperature dependence of intersystem crossing of pyrene

The temperature dependence of the rate constant for intersystem crossing from S₁ of pyrene was determined by means of a method proposed previously. In contrast to the conclusions of Stevens, Thomaz and Jones, and of Kropp, Dawson and Windsor, we conclude that both temperature-independent and temperature-dependent intersystem crossing processes exist. These two processes contribute equally at ≈ 150 K.     

Time-dependent approaches for the calculation of intersystem crossing rates

We present three formulas for calculating intersystem crossing rates in the Condon approximation to the golden rule by means of a time-dependent approach: an expression using the full time correlation function which is exact for harmonic oscillators, a second-order cumulant expansion, and a short-time approximation of this expression. While the exact expression and the cumulant expansion require numerical integration of the time correlation function, the integration of the short-time expansion can be performed analytically. To ensure convergence in the presence of large oscillations of the correlation function, we use a Gaussian damping function. The strengths and weaknesses of these approaches as well as the dependence of the results on the choice of the technical parameters of the time integration are assessed on four test examples, i.e., the nonradiative S(1) ? T(1) transitions in thymine, phenalenone, flavone, and porphyrin. The obtained rate constants are compared with previous results of a time-independent approach. Very good agreement between the literature values and the integrals over the full time correlation functions are observed. Furthermore, the comparison suggests that the cumulant expansion approximates the exact expression very well while allowing the interval of the time integration to be significantly shorter. In cases with sufficiently high vibrational density of states also the short-time approximation yields rates in good agreement with the results of the exact formula. A great advantage of the time-dependent approach over the time-independent approach is its excellent computational efficiency making it the method of choice in cases of large energy gaps, large numbers of normal modes, and high densities of final vibrational states.     

Inverse deuterium isotope effect in the intersystem crossing of diphenylcarbene

The singlet-to-triplet intersystem crossing rate (k_st) of diphenylcarbene (DPC) is found to exhibit an inverse isotope effect in various solvents. An off-resonance coupling model between the initial singlet state and a sparse triplet vibronic manifold accounts for k_ST showing both an inverse isotope effect in a given solvent as well as an inverse energy gap effect in a solvent series.     

Influence of solvent on carbene intersystem crossing rates

The influence of coordinating solvents on singlet-to-triplet carbene intersystem crossing (ISC) rates has been studied with diphenylcarbene (DPC) and para-biphenyltrifluoromethylcarbene (BpCCF 3) by using ultrafast time-resolved spectroscopy. DPC has a triplet ground state in all of the solvents considered, and the concentration of singlet carbene at equilibrium is too small to be measured. It is found that the lifetime of (1)DPC is extended in acetonitrile, benzene, tetrahydrofuran, dichloromethane, and halobenzene solvents relative to cyclohexane. The solvent effect does not well correlate with bulk measures of solvent polarity. The singlet-triplet energy separation of BpCCF 3 is close to zero. The data demonstrates that BpCCF 3 has a triplet ground state in benzene, fluorobenzene, and hexafluorobenzene. Halogenated solvents are found to dramatically retard the rate of ISC in (1)BpCCF 3. We postulate that the empty p orbital of a singlet carbene coordinates with a nonbonding pair of electrons of a halogen atom of the solvent to form a pseudoylide solvent complex, stabilize the singlet carbene, and decrease the singlet-triplet (S-T) energy gap. The "golden rule" of radiationless transitions posits that the smaller the energy gap between the two states, the faster their rate of interconversion. To explain the apparent violation of the golden rule of radiationless transitions for the carbene ISC processes monitored in this study, we propose that the significantly different specific solvation of the singlet and triplet carbenes imposes a Franck-Condon-like factor on the ISC process. Those solvents that most solvate the singlet carbene will also have the greatest structural difference between singlet carbene-solvent complex and their triplet spin isomer-solvent complex, the smallest S-T gap, and the slowest ISC rate. Alternatively, one can propose that a highly solvated singlet carbene must desolvate prior to ISC, and that this requirement decelerates the radiationless transition.     

Ab initio calculation of the Dzyaloshinskii–Moriya parameters: Spin–orbit GSO‐HF,DFT, and CI approaches

We present ab initio methods to determine the Dzyaloshinskii–Moriya (DM) parameter, which provides the anisotropic effects of noncollinear spin systems. For this purpose, we explore various general spin orbital (GSO) approaches, such as Hartree–Fock (HF), density functional theory (DFT), and configuration interaction (CI), with one‐electron spin–orbit coupling (SOC1). As examples, two simple D_3h‐symmetric models, H₃ and B(CH₂)₃, are examined. Implications of the computational results are discussed in relation to as isotropic and anisotropic interactions of molecular‐based magnets. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Reduced equations of motion for collision-induced intersystem crossing

A model is proposed for collision-induced intersystem crossing in “intermediate case” and small molecules. The collisions are assumed to cause dephasing (T₂) among the zero order singlet and triplet molecular states. The combined effect of the intramolecular spin-orbit coupling (μ) and the collisional dephasing, results in the experimentally observable relaxation of populations (T₁). The basic assumption of the present model is that the duration of a collision τ_c is short compared to the intramolecular coupling (μτ_c ? 1). Reduced equations of motion for the molecular density matrix are derived and conditions for observing nonexponential relaxations are discussed. The model demonstrates the equivalence of T₁ and T₂ processes, depending on our choice of a basis set.