Orbit Matrix Elements Research Articles

New definitions of the effective nuclear charge and its application to estimate the matrix element [formula omitted]

New definitions of the effective nuclear charge are proposed to evaluate the orbital wave function and the dipole matrix element ⟨n,l|r|n′,l′⟩ for the non-hydrogenic atoms or ions. It is found that the commonly used effective nuclear charge defined by the orbital energy is insufficiently precise to estimate the orbital wave functions and matrix elements ⟨n,l|r|n′,l′⟩. Instead, the effective nuclear charge defined by ⟨r⟩ or ⟨r2⟩ are more advantageous. It is shown that the effective nuclear charge method becomes increasingly precise to predict wave functions and matrix elements as the orbital angular momentum, the principle quantum number and the degree of ionization increase. Good accuracy is achieved when principal quantum numbers are identical n=n′ or when both orbital quantum numbers l and l′ are non-zero. When s-orbitals are involved (l or l′ equal to zero) the precision is decreasing.

Theoretical MRCI + Q study on electronic structure and spectroscopic properties of the HX+(X = F, Cl, Br, I) cations

In this work, we have systematacially investigated the electronic structure and spectroscopic properties of the HX+ (X = F, Cl, Br, I) cations by using the highly correlated MRCI + Q approach. This is the first comprehensive ab initio study on the electronic states of the HX+ cations. The spin–orbit coupling (SOC) effect is introduced with the state interaction approach. There are total 10 Λ-S and 18 Ω states obtained in the calculation. The results show that the potential energy curves’ (PECs) shapes and structure of the electronic states of different HX+ cations exhibit the significant distinction due to the X-dependent energy-level order of the unique dissociation channel H+(1Sg) + X(2Pu). From PECs, the spectroscopic constants of the bound electronic states are determined, which are in good agreement with available observed values. Regarding HBr+ and HI+, the good agreement has been achieved only when the SOC effect is considered. The predissociation for the first excited A2Σ+ state of HCl+, HBr+, and HI+ is analyzed based on computed spin–orbit matrix elements. Around the equilibrium position, the energy splittings of X2Π are calculated to be 288, 661, 2691, and 5137 cm−1 for HF+, HCl+, HBr+, and HI+, respectively. It has been demonstrated that SOC is substantial for HX+, leading to significant changes in PECs’ shapes as well as in electronic structure. Finally, the transition properties are predicted, including transition dipole moments, Franck–Condon factors, and radiative lifetimes. Both the Ω transitions A2Σ+ 1/2-X2Π3/2 and A2Σ+ 1/2-X2Π1/2 of the HX+ cations are determined to possess the radiative lifetimes at the microsecond (µs) level.

A new look at N[formula omitted] electronic transitions: An experimental and theoretical study

Neutral and ionic N2 species exhibit a rich spectrum as a result of the large density of couplings between states with different multiplicities. In this sense, spectra of the molecular ion N2+ are investigated combining Fourier transform spectroscopy and ab initio methods. We have reanalyzed the First Negative band System (B2Σu+→ X2Σg+) including five bands not reported previously by Fourier spectroscopy. The spectra were recorded using a resolution of 0.6 cm−1 and accuracy of 0.005 cm−1. These results are then compared with new MRCI+Q/AV6Z calculations. For the first time, transition probabilities are computed for the previously observed 22Πg-A2Πu band system. The 22Πg state (Te = 67,029 cm−1) has a dissociation energy of 24,787 cm−1 at Re = 2.7332 a0. The predicted lifetimes for the 22Πg-A2Πu emissions are of the order of 170 ns. The calculated transition probabilities A(v′=0, v′′=0) for the B2Σu+-X2Σg+ and 22Πg-A2Πu bands are 1.156 × 107 and 1.716 × 103 s−1, respectively. The role of spin–orbit (SO) matrix elements in the spectroscopic data of N2+ is discussed, including results for SO constants as a function of vibrational level of A2Πu state. Our theoretical SO constant A0(A2Πu) = −73.40 cm−1 reproduces well the experimental one (−74.67 cm−1). SO calculations are also used to investigate spin-forbidden transitions on N2+. The obtained <A2Πu|HˆSO|a4Σu+>≈ 30 cm−1. Following a sum-over-states (SOS) methodology, the best estimate for the spin-rotation constant γ0 of the X2Σg+ and B2Σu+ states are 0.0096 and 0.0211 cm−1, respectively, in quantitative agreement with the present experimental data of 0.00917(36) and 0.0206(9).

Introducing MPEC: Massively parallel electron correlation.

We have developed a new program for carrying out improved internally contracted Multi-reference Configuration Interaction Singles and Doubles (i2cMRCISD) calculations. It is designed from the ground up to be used on distributed memory parallel computers. Tests show good scaling properties with the number of cores per node and the number nodes. This program features Gaussian basis sets with ℓ > 6; scalar special relativity via the spin-free method; convergence to C∞v, D∞v, or spherical electronic states; special code to determine Rydberg orbitals; both uncontracted and contracted MRCISD wavefunctions; one and two electron properties, including full spin-orbit matrix elements with the Breit interaction; analytic calculation of Born-Oppenheimer diagonal correction for multi-configuration Hartree-Fock wavefunctions; and analytic calculation of second order Born-Oppenheimer corrections for Hartree-Fock wavefunctions. The program can be obtained from software.nasa.gov.

Two dimensional Janus RuXY (X, Y = Br, Cl, F, I, X ≠ Y) monolayers: ferromagnetic semiconductors with spontaneous valley polarization and tunable magnetic anisotropy.

Two-dimensional (2D) ferromagnetic (FM) materials with valley polarization are highly desirable for use in valleytronic devices. The 2D Janus materials have fascinating physical properties due to their asymmetrical structures. In this work, the electronic structure and magnetic properties of Janus RuXY (X, Y = Br, Cl, F, I, X ≠ Y) monolayers are systematically studied using first-principles calculations. RuBrCl, RuBrF, and RuClF monolayers are all FM semiconductors. The valley polarization is present in the band structure and this is determined by the spin orbit coupling (SOC). The valley splitting energy of the RuClF monolayer is as large as 204 meV, with a perpendicular magnetic anisotropy (PMA) energy of 1.918 mJ m-2 and a Curie temperature of 316 K. Therefore, spontaneous valley polarization at room temperature will be seen in the RuClF monolayer. The Curie temperature of the RuBrF monolayer is higher than that of the RuClF, but the magnetic anisotropy energy (MAE) is in-plane magnetic anisotropy (IMA). The valley splitting energy of the RuBrCl monolayer is higher and the PMA energy is lower than that of the RuClF monolayer. The Curie temperature was only 197 K. The valley polarization was modulated in the RuXY monolayers at different biaxial strains, during which the semiconductor properties are still maintained. The PMA of the RuClF and RuBrCl monolayers is enhanced by the biaxial compressive strains, which are mainly attributed to the variation of the (dyz, d2z) orbital matrix elements of the Ru atoms. The MAE of the RuBrF monolayer is tuned from IMA into PMA at a biaxial strain of -6%. These results show an example of a 2D Janus ferrovalley material.

How Computations Can Assist the Rational Design of Drugs for Photodynamic Therapy: Photosensitizing Activity Assessment of a Ru(II)-BODIPY Assembly.

Ruthenium-based complexes represent a new frontier in light-mediated therapeutic strategies against cancer. Here, a density functional-theory-based computational investigation, of the photophysical properties of a conjugate BODIPY-Ru(II) complex, is presented. Such a complex was reported to be a good photosensitizer for photodynamic therapy (PDT), successfully integrating the qualities of a NIR-absorbing distyryl-BODIPY dye and a PDT-active [Ru(bpy)3]2+ moiety. Therefore, the behaviour of the conjugate BODIPY-Ru(II) complex was compared with those of the metal-free BODIPY chromophore and the Ru(II) complex. Absorptions spectra, excitation energies of both singlet and triplet states as well as spin–orbit-matrix elements (SOCs) were used to rationalise the experimentally observed different activities of the three potential chromophores. The outcomes evidence a limited participation of the Ru moiety in the ISC processes that justifies the small SOCs obtained for the conjugate. A plausible explanation was provided combining the computational results with the experimental evidences.

Spin-Orbit Matrix Elements for a Combined Spin-Flip and IP/EA approach.

We present a practical approach for computing the Breit-Pauli spin-orbit matrix elements of multiconfigurational systems with both spin and spatial degeneracies based on our recently developed RAS-nSF-IP/EA method (Houck, S. E.; et al. J. Chem. Theory Comput. 2019, 15, 2278). The spin-orbit matrix elements over all the multiplet components are computed using a single one-particle reduced density matrix as a result of the Wigner-Eckart theorem. A mean field spin-orbit approximation was used to account for the two-electron contributions. Basis set dependence as well as the effect of including additional excitations is presented. The effect of correlating the core and semicore orbitals is also examined. Surprisingly accurate results are obtained for spin-orbit coupling constants, despite the fact that the efficient wave function approximations we explore neglect the bulk of dynamical correlation.

Low-lying electronic states of aluminum monoiodide**Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0403300), the National Natural Science Foundation of China (Grant Nos. 11874179, 11574114, and 11874177), and the Natural Science Foundation of Jilin Province, China (Grant Nos. 20180101289JC).

High-level ab initio calculations of aluminum monoiodide (AlI) molecule are performed by utilizing the multi-reference configuration interaction plus Davidson correction (MRCI+Q) method. The core-valence correlation (CV) and spin–orbit coupling (SOC) effect are considered. The adiabatic potential energy curves (PECs) of a total of 13 Λ–S states and 24 Ω states are computed. The spectroscopic constants of bound states are determined, which are in accordance with the results of the available experimental and theoretical studies. The interactions between the Λ–S states are analyzed with the aid of the spin–orbit matrix elements. Finally, the transition properties including transition dipole moment (TDM), Frank–Condon factors (FCF) and radiative lifetime are obtained based on the computed PEC. Our study sheds light on the electronic structure and spectroscopy of low-lying electronic states of the AlI molecule.

Excitation energies, singlet-triplet energy gaps, spin-orbit matrix elements and heavy atom effects in BOIMPYs as possible photosensitizers for photodynamic therapy: a computational investigation.

Bis(borondifluoride)-8-imidazodipyrromethene (BOIMPY) based molecules show interesting photophysical properties. We have undertaken a computational study at DFT and TDDFT levels of theory with the aim of verifying if the non-fluorescent BOIMPYs meet those properties necessary to be proposed as potential photosensitizers for photodynamic therapy (PDT). In particular, we have computed the absorption wavelengths, the singlet-triplet energy gaps and the spin-orbit matrix elements. The effect of halogen atom substitution (Br, I), in different amounts and positions in the BOIMPY skeleton, on the photophysical properties, has been elucidated. Some possible pathways for the population of the lowest triplet state have been examined and rationalized on the basis of Kasha rules. The results indicate that many of the studied systems can be indicated as potential photosensitizers for photodynamic therapy.

Experimental and spin-orbit coupled TDDFT predictions of photophysical properties of three-coordinate mononuclear and four-coordinate binuclear copper(I) complexes with thioamidines and bulky triarylphosphanes

Abstract The reactions of copper halides CuX with the N-heterocyclic thioamidine 5-methyl-1,3,4-thiadiazole-2-thione (mtdztH) in the presence of the sterically demanding tri(o-tolyl)phosphane (totp), depending on the halide, affords either the mononuclear compound [CuX(totp)(mtdztH)] (1), when X = I, with the thione acting as a terminal S-bound ligand or the symmetrical, thione-S-bridged binuclear compound [CuX(totp)(μ-S-mtdzt)]2 (2), when X = Cl. The steric effects of the large cone-angle phosphane ligand are further demonstrated by the distorted coordination environments of the copper centers in the solid-state structures of the two complexes. The two compounds are photoluminescent in the solid state at ambient temperature, with their emission maxima located in the blue region of the electromagnetic spectrum and influenced by the type of halide present in each case. Density Functional Theory (DFT) and Time-Dependent DFT (TDDFT) calculations were employed in order to elucidate the mechanism of the photoluminescence of the two Cu(I) complexes. The emissive T1 state exhibits a 3MLCT character and minor structural distortions compared to the S0 state. Employing self-consistent spin-orbit coupling TDDFT (SOC-TDDFT) calculations the radiative lifetimes and the zero-field splitting (ZFS) were estimated to be in the ranges 21–375 μs and 1–4 cm−1 respectively. The highest values for the Spin - Orbit matrix elements, calculated with the SOC-TDDFT method, are the and for 1 and the mononuclear counterpart of 2 (2′) indicating a thermal singlet–singlet deactivation path followed by ISC from S1 to T1. In contrast, the highest value SOC matrix element for 2 is the and therefore this complex should exhibit a direct ISC from S1 to T1 without a preceding thermal deactivation. The very small values of the energy difference between S1 and T1 states (ΔE(S1-T1)) calculated to be in the range 1–9 kcal/mol for these complexes, should also favor the ISC process between these excited states.

Multireference configuration interaction study on the ground and excited electronic states of the AlO+ molecule

High-level ab initio calculations on the electronic states of AlO+ cation have been performed with the explicitly correlated multi-reference configuration interaction (MRCI-F12) method. The potential energy curves (PECs) of 24 electronic states have been obtained, most of which are reported for the first time. From the computed PECs, the precise spectroscopic constants of the bound states are determined. Our calculations confirm that the ground state of AlO+ cation is the X1Σ+ state. The permanent dipole moments (PDMs) functions of the selected bound states are computed. The spin–orbit (SO) matrix elements between the electronic states involved in the crossing region of the PECs are calculated to analyze the predissociation mechanisms of the X1Σ+, A1Π, and 21Σ+ states. Finally, the transition properties of four spin-allowed transitions are predicted, including the transition dipole moments (TDMs), Franck-Condon Factors (FCFs), and the radiative lifetimes. This work should enhance our understanding on the electronic structure and spectroscopy of AlO+ cation.

Electronic structures and photophysical properties of phosphorescent platinum (II) complexes with tridentate C^N*N cyclometalated ligands

To get an insight into the structure–property relationships in a series of strongly phosphorescent platinum(II) complexes with tridentate C^N*N cyclometalated ligands, their electronic structures and electroluminescence properties were systematically investigated via density functional theory and time‐dependent density functional theory. Moreover, the factors related to the radiative and non‐radiative decay process, including the transition electric dipole moment μ(Sn), the energy difference between singlet and lowest triplet excited states ΔE(Sn–T1) and the spin–orbital coupling matrix elements , as well as the energy gap between T1 and S0 states ΔE(T1–S0) and absorption–emission Stokes shifts have been calculated. Fine emission color tuning and high phosphorescence quantum yield of phosphorescent complexes may be achieved through introducing five–six‐membered metallacycle geometries and linking a substituent (such as phenyl) at bridge atoms. Additionally, phosphorescent properties of these complexes show a clear dependence on the electronegativity of bridge atoms.

Investigation of the Spin Competition in the Al6 Cluster

Small-sized aluminum clusters exhibit a possible spin competition at finite temperatures. For this reason, it is difficult to perform standard electronic structure investigations to determine the properties of the ground states of such clusters. In the particular case of Al6, a nonmagnetic ground state has been predicted at 0 K. However, singlet–triplet intercrossing could occur at laboratory temperatures, in agreement with Stern–Gerlach experiments. We have thus investigated, by means of nonadiabatic transition state theory, the possibility of such singlet–triplet spin competition. We determined the possible crossing points on the potential energy surface and then identified the most favorable minimum-energy crossing points. For these points, we evaluated the spin–orbit matrix elements, transition probabilities, and rate constants for the singlet–triplet equilibria at different temperatures using the Landau–Zener and weak-coupling formulas. The predicted equilibria at finite temperatures are consistent w...

MRCI+Q study of the low-lying electronic states of CdF including spin–orbit coupling**Project supported by the National Natural Science Foundation of China (Grant Nos. 11604052, 11404180, and 11574114 ), the Natural Science Foundation of Heilongjiang Province, China (Grant No. A2015010), the Natural Science Foundation of Anhui Province, China (Grant No. 1608085MA10), the International Science & Technology Cooperation Program of Anhui Province,

CdF molecule, which plays an important role in a great variety of research fields, has long been subject to numerous researchers. Due to the unstable nature and heavy atom Cd containing in the CdF molecule, electronic states of the molecule have not been well studied. In this paper, high accurate ab initio calculations on the CdF molecule have been performed at the multi-reference configuration interaction level including Davidson correction (MRCI+Q). Adiabatic potential energy curves (PECs) of the 14 low-lying Λ–S states correlating with the two lowest dissociation limits and have been constructed. For the bound Λ–S and Ω states, the dominant electronic configurations and spectroscopic constants are obtained, and the calculated spectroscopic constants of bound states are consistent with previous experimental results. The dipole moments (DMs) of are determined, and the spin–orbit (SO) matrix elements between each pair of are obtained. The results indicate that the sudden changes of DMs and SO matrix elements arise from the variation of the electronic configurations around the avoided crossing region. Moreover, the Franck–Condon factors (FCFs), the transition dipole moments (TDMs), and radiative lifetimes of low-lying states-the ground state are determined. Finally, the transitional properties of and are studied. Based on our computed spectroscopic information of CdF, the feasibility and challenge for laser cooling of CdF molecule are discussed.

Model study of the electron-phonon coupling in graphene; relative importance of intraband and interband scattering

The aim of this model study of the electron-phonon coupling in graphene was to find out about the relative importance of the inter- and intraband scattering and which phonon modes are the most active. This was achieved by analyzing the electron-phonon matrix element of the carbon dimer in the unit cell. We found that for the intra molecular orbital matrix elements the longitudinal optical phonon mode is the active phonon mode. The matrix element corresponding to σ→σ is greater than the matrix element for π→π. The inter molecular orbital scattering π→σ is driven by the out-of-plane acoustic phonon mode, while the out-of-plane optical mode does not contribute for symmetry reasons. We found the unexpected result that the magnitude of matrix element of the inter molecular orbital scattering π→σ exceeds the intra molecular orbital scattering π→π. These results indicate that the in general not considered inter-band scattering has to be taken into account when analyzing e.g. photo-hole lifetimes and the electron-phonon coupling constant λ from photoemission data of graphene.

On the performance of DFT/MRCI-R and MR-MP2 in spin–orbit coupling calculations on diatomics and polyatomic organic molecules

ABSTRACTWe have investigated the performance of different multi-reference quantum chemical methods with regard to electronic excitation energies and spin–orbit matrix elements (SOMES). Among these methods are two variants of the combined density functional theory and multi-reference configuration interaction method (DFT/MRCI and DFT/MRCI-R) and a multi-reference second-order Møller–Plesset perturbation theory (MR-MP2) approach. Two variants of MR-MP2 have been tested based on either Hartree–Fock orbitals or Kohn–Sham orbitals of the BH-LYP density functional. In connection with the MR-MP2 approaches, the first-order perturbed wave functions have been employed in the evaluation of spin–orbit coupling. To validate our results, we assembled experimental excitation energies and SOMES of eight diatomic and fifteen polyatomic molecules. For some of the smaller molecules, we carried out calculations at the complete active space self-consistent field (CASSCF) level to obtain SOMEs to compare with. Excitation energies of the experimentally unknown states were assessed with respect to second-order perturbation theory corrected (CASPT2) values where available. Overall, we find a very satisfactory agreement between the excitation energies and the SOMEs obtained with the four approaches. For a few states, outliers with regard to the excitation energies and/or SOMEs are observed. These outliers are carefully analysed and traced back to the wave function composition.

Extensive spin–orbit multi-reference computations on the excited states of the phosphorus monochloride molecule

Total 34 Λ-S states of the PCl molecule have been studied by using the multi-reference configuration interaction plus the Davidson correction (MRCI+Q) method with the correlation consistent quadruple-zeta quality basis set. These states are correlated to three dissociation limits P(4Su)+Cl(2Pu), P(2Du)+Cl(2Pu), and P(2Pu)+Cl(2Pu), respectively. The potential energy curves (PECs) of the Λ-S states have been calculated, from which the spectroscopic constants of the bound states are determined. The calculated spectroscopic results well reproduce the available measurements. The spin–orbit matrix elements between the Λ-S states have been calculated, which indicate that the perturbations exist in the interacting system 11Π−23Π and 11Π−23Σ−. And the excited a1Δ, b1Σ+, 21Σ+ states could be predissociated induced by the spin–orbit coupling (SOC) effect. The SOC calculation on the PCl molecule has been performed with the state interaction method. This is the first time that the SOC effect of the PCl has been studied theoretically. The SOC effect leads to the 34 Λ-S states split into the 74Ω states. The ground state X3Σ− splits into the X3Σ0−+(X10+) and X3Σ1−(X21) states. For the zero-field splitting of the X3Σ− state, the spin–orbit contribution of 6cm−1 is much larger than spin-spin contribution of 0.32cm−1. Under the influence of the SOC effect, the spectroscopic results of the a1Δ and b1Σ+ states have very small changes, but the dissociation energies strongly decrease. The transition properties of PCl are also predicted, including the E1, M1, and E2 transition moments, the Franck–Condon factors, the transition probabilities, and the radiative lifetimes. For the transitions from a1Δ-X3Σ− and b1Σ+−X3Σ−, the transition probabilities are in order of AE1 > AM1 ≫ AE2. The lifetimes for the b1Σ+(v׳=0) state are 4.87ms (E1) and 4.57ms (E1+M1), in good agreement with the available experimental result of 4.9±0.8ms.

Ab initio MRCI + Q calculations on the low-lying excited states of the MgBr radical including spin–orbit coupling

Accurate theoretical calculations on the MgBr radical have been carried out by using the high-level relativistic multireference configuration interaction method with Davidson correction (MRCI+Q) using correlation-consistent Quintuple-ζ quality basis set. The potential energy curves (PECs) of the 14 Λ-S states of MgBr have been computed. In order to improve the PECs, the core–valence correlation, scalar relativistic effect, and spin–orbit coupling effect are taken into account in the computations. The spectroscopic constants of the bound states have been determined from the computed PECs. The results of the ground state X2Σ+ and the first excited state A2Π are in good agreement with those from the available experiments, while spectroscopic constants of the other electronic states are firstly reported. The low-lying ion-pair state B2Σ+ correlated to ion-pair dissociation limit Mg+ (2Sg)+Br− (1Sg) is characterized. The permanent dipole moments (PDMs) of Λ-S states and the R-dependent spin–orbit (SO) matrix elements are computed. The results indicate that the abrupt changes of PDMs and the SO matrix elements are attributed to the changes of the electronic configurations near the avoided crossing point. After taking the SOC effect into account, the 14 Λ-S states split into 30Ω states, and the SOC splitting for the A2Π is calculated to be 102.58cm−1. The SOC effect, leading to the double-well potential of the Ω=(3)1/2 state, is found to be substantial for MgBr. In order to further illustrate the SOC effect and the avoided crossing phenomenon of the PECs, the Λ-S compositions in the Ω state wavefunctions are analyzed in detail. Finally, the transition dipole moments (TDMs) of several transitions from upper Ω states to the ground X2Σ+1/2 state and the corresponding radiative lifetimes have been studied. It is shown that the (1)3/2–X2Σ+1/2 and (2)3/2–X2Σ+1/2 are particularly important to the observed transitions A2Π–X2Σ+ and C2Π–X2Σ+. The present study should shed more light on the electronic structures and transition properties of electronic states of the MgBr radical.

PDT-correlated photophysical properties of thienopyrrole BODIPY derivatives. Theoretical insights

Absorption electronic spectra, singlet-triplet energy gaps and spin–orbit matrix elements of thienopyrrole BODIPY derivatives, recently synthesized and proposed as potential photosensitizers in photodynamic therapy (PDT), have been computed by means of density functional theory (DFT) and time-dependent DFT approaches. A benchmark on structural parameters and maximum absorption wavelengths of different exchange-correlation functionals in combination with two basis set has been performed. The singlet-triplet energy gaps found are consistent with their possible application in PDT. The investigated molecules possess two excited triplet states (T1 and T2) that lie below and approximately at the same energy of the excited singlet one (S1), respectively. Both the radiationless transitions between S1 and triplet states contribute to the intersystem spin crossing efficiency, which in turn increases the production of singlet oxygen. Comparing their properties with those of agents currently used in PDT, one of them could be potentially used as photosensitizer for singlet oxygen production.

Photophysical properties prediction of selenium- and tellurium-substituted thymidine as potential UVA chemotherapeutic agents

Density functional theory and time-dependent density functional theory calculation for a series of photophysical properties (absorption spectra, singlet and triplet excitation energies and spin–orbit matrix elements) have been performed on the sulfur-, selenium- and tellurium-substituted thymine. The heavy atoms have been substituted in 2 or 4 and in both 2,4 position of the thymine ring. Different pathways for the population of the lowest triplet state have been considered. We find that all the considered systems are potential UVA chemotherapeutic agents since the lowest triplet states lie above the energy required for the production of the highly cytotoxic 1Δg excited oxygen molecule and due to the possible and efficient intersystem crossings ensured by high spin–orbit coupling values.