Spin–orbit coupling in the intersystem crossing of the ring-opened oxirane biradical

The intersystem crossing (ISC ) between the lowest triplet and singlet states occurring in the reaction of atomic oxygen with ethylene was studied. The importance of spin–orbit coupling (SOC ) in oxirane biradicals (?R′R″—CRR*—?) is stressed through calculations where the spin–orbit matrix elements over the full Breit–Pauli SOC operator has been obtained in the singlet–triplet crossing region. The calculations are performed with a multiconfigurational linear response approach, in which the spin–orbit couplings are obtained from triplet response functions using differently correlated singlet-reference-state wave functions. Computational results confirm earlier semiempirical predictions of the spin–orbit coupling as an important mechanism behind the ring opening of oxiranes and addition of oxygen O(³P) atoms to alkenes. © 1995 John Wiley & Sons, Inc.     

Ultrafast Decay of the Excited Singlet States of Thioxanthone by Internal Conversion and Intersystem Crossing

The experimental ultrafast photophysics of thioxanthone in several aprotic organic solvents at room temperature is presented, measured using femtosecond transient absorption together with high‐level ab initio CASPT2 calculations of the singlet‐ and triplet‐state manifolds in the gas phase, including computed state minima and conical intersections, transition energies, oscillator strengths, and spin–orbit coupling terms. The initially populated singlet ππ* state is shown to decay through internal conversion and intersystem crossing processes via intermediate nπ* singlet and triplet states, respectively. Two easily accessible conical intersections explain the favorable internal conversion rates and low fluorescence quantum yields in nonpolar media. The presence of a singlet–triplet crossing near the singlet ππ* minimum and the large spin–orbit coupling terms also rationalize the high intersystem crossing rates. A phenomenological kinetic scheme is proposed that accounts for the decrease in internal conversion and intersystem crossing (i.e. the very large experimental crescendo of the fluorescence quantum yield) with the increase of solvent polarity.     

Relativistic effects in spectroscopy and photophysics of heavy-metal complexes illustrated by spin–orbit calculations of [Re(imidazole)(CO)3(phen)]+

Spin–orbit coupling (SOC) is an essential factor in photophysics of heavy transition metal complexes. By enabling efficient population of the lowest triplet state and its strong emission, it gives rise to a very interesting photophysical behavior and underlies photonic applications such as organic light emitting diodes (OLED) or luminescent imaging agents. SOC affects excited-state characters, relaxation dynamics, radiative and nonradiative decay pathways, as well as lifetimes and reactivity. We present a new photophysical model based on mixed-spin states, illustrated by relativistic spin–orbit TDDFT and MS-CASPT2 calculations of [Re(imidazole)(CO)₃(1,10-phenanthroline)]⁺. An excited-state scheme is constructed from spin–orbit (SO) states characterized by their energies, double-group symmetries, parentages in terms of contributing spin-free singlets and triplets, and oscillator strengths of corresponding transitions from the ground state. Some of the predictions of the relativistic SO model on the number and nature of the optically populated and intermediate excited states are qualitatively different from the spin-free model. The relativistic excited-state model accounts well for electronic absorption and emission spectra of Re^I carbonyl diimines, as well as their complex photophysical behavior. Then, we discuss the SO aspects of photophysics of heavy metal complexes from a broader perspective. Qualitative SO models as well as previous relativistic excited-state calculations are briefly reviewed together with experimental manifestations of SOC in polypyridine and cyclometallated complexes of second- and third row d⁶ metals. It is shown that the relativistic SO model can provide a comprehensive and unifying photophysical picture.     

Revealing the marked differences of phosphorescence efficiencies on C˄N˄N‐coordinated Pt(II) complexes: A theoretical study

In this study, green phosphorescent Pt(II) complexes with N,N‐diphenyl‐6‐(1H‐pyrazol‐1‐yl)pyridin‐2‐amine (Ndpp) coordinated ligands, [Pt (Ndpp)Cl] 2a , [Pt (Ndpp)Pb, Pb = (prop‐1‐ynyl)benzene] 2b , and [Pt (Ndpp)CN] 2a? CN were theoretically investigated by means of density functional theory and time‐dependent density functional theory calculations to reveal their marked distinct phosphorescence quantum yields. These complexes exhibit evident absorption bands in the 200–450 nm region but emit strong green light with marked differences of phosphorescence quantum yields. Compared with the complex 2a , the complex 2b possesses large oscillator strengths of absorption spectra, strong spin‐orbit coupling, and transition electric dipole moment, as well as small singlet‐triplet splitting energies, which conduces to enhancing its radiative decay. To illustrate the nonradiative decay process, the transition state (TS) between the triplet metal‐centered (³MC) state and the excited state (T₁) was optimized. The ³MC state is found to be the minimum energy crossing point (MECP) between the T₁ state and the S₀ state. Compared with the complex 2a , the complex 2b possesses a much larger energy barrier to the MECP state from the T₁ state, so it is strongly emissive in the green region. Besides, the introduction of ? CN substitutions on 2a is useful for enhancing the energy barrier to the thermal deactivation pathway of ³MLCT → TS → MECP. These results demonstrate that the modification of metal–ligand conjugation is an effective way to develop high‐performance phosphorescent materials.     

Cyclobutadiene automerization and rotation of ethylene: Energetics of the barriers by using Spin‐polarized wave functions

Spin‐projected spin polarized Møller–Plesset and spin polarized coupled clusters calculations have been made to estimate the cyclobutadiene automerization, the ethylene torsion barriers in their ground state, and the gap between the singlet and triplet states of ethylene. The results have been obtained optimizing the geometries at MP4 and/or CCSD levels, by an extensive Gaussian basis set. A comparative analysis with more complex calculations, up to MP5 and CCSDTQP, together with others from the literature, have also been made, showing the efficacy of using spin‐polarized wave functions as a reference wave function for Møller–Plesset and coupled clusters calculations, in such problems. © 2014 Wiley Periodicals, Inc.     

Magnitude of Finite‐Nucleus‐Size Effects in Relativistic Density Functional Computations of Indirect NMR Nuclear Spin–Spin Coupling Constants

A spherical Gaussian nuclear charge distribution model has been implemented for spin‐free (scalar) and two‐component (spin–orbit) relativistic density functional calculations of indirect NMR nuclear spin–spin coupling (J‐coupling) constants. The finite nuclear volume effects on the hyperfine integrals are quite pronounced and as a consequence they noticeably alter coupling constants involving heavy NMR nuclei such as W, Pt, Hg, Tl, and Pb. Typically, the isotropic J‐couplings are reduced in magnitude by about 10 to 15 % for couplings between one of the heaviest NMR nuclei and a light atomic ligand, and even more so for couplings between two heavy atoms. For a subset of the systems studied, viz. the Hg atom, Hg₂²⁺, and Tl? X where X=Br, I, the basis set convergence of the hyperfine integrals and the coupling constants was monitored. For the Hg atom, numerical and basis set calculations of the electron density and the 1s and 6s orbital hyperfine integrals are directly compared. The coupling anisotropies of TlBr and TlI increase by about 2 % due to finite‐nucleus effects.     

Theory of Monte Carlo simulations of the magnetic circular dichroism spectra of alkali metal/rare gas systems

The history of magnetic circular dichroism (MCD) spectroscopy in the study of alkali metal/rare gas (M/Rg) cryogenic systems is reviewed in the context of developing a better understanding of alkali metal/hydrogen systems of current interest to the U.S. Air Force as enhanced‐performance cryogenic rocket propellants. A new theory for simulating the MCD spectra of M/Rg systems is presented together with a careful discussion of the theory's implicit and explicit approximations and their implications. This theory uses a classical Monte Carlo (MC) simulation scheme to model the perturbing effects of the Rg environment on the ²S → ²P MCD‐active transition of the M atom. The theory sets up the MC–MCD simulation as a 6 × 6 matrix eigenvalue/eigenvector problem in the ²P manifold in which are included the effects of M–Rg interactions, metal atom spin‐orbit coupling in the ²P manifold, magnetic Zeeman perturbations of the ²S and ²P manifolds, Boltzmann temperature factors, and electric dipole transition moment integrals for left circularly polarized (LCP) and right circularly polarized (RCP) light. The theory may be applied to any type of trapping site of the host M in the guest Rg matrix; a single atom substitutional metal atom trapping site (one host Rg atom is replaced by one guest M atom) is modeled in this study for M = Na and Rg = Ar. Two temperature factors are used in these simulations; a lattice temperature to model the mobility of the Rg lattice and a magnetic temperature to model Boltzmann factors in the ²S ground manifold. The 6 × 6 eigenvalue/eigenvector problem is solved for a number of randomly generated and suitably averaged Rg configurations to yield the simulated MC‐MCD spectrum for the single substitutional Na/Ar system. The MC–MCD simulations of Na/Ar give the characteristic triplet MCD spectrum with the correct Boltzmann temperature dependence. The simulated MC–MCD spectrum correctly inverts when the direction of the applied magnetic field is reversed. Addition of the LCP and RCP absorbances gives rise to a characteristic ²S → ²P triplet absorption feature. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the C?H Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

The Kinetic Isotope Effect as a Probe of Spin Crossover in the CH Activation of Methane by the FeO+ Cation

Two‐state reactivity (TSR) is often used to explain the reaction of transition‐metal–oxo reagents in the bare form or in the complex form. The evidence of the TSR model typically comes from quantum‐mechanical calculations for energy profiles with a spin crossover in the rate‐limiting step. To prove the TSR concept, kinetic profiles for C? H activation by the FeO⁺ cation were explored. A direct dynamics approach was used to generate potential energy surfaces of the sextet and quartet H‐transfers and rate constants and kinetic isotope effects (KIEs) were calculated using variational transition‐state theory including multidimensional tunneling. The minimum energy crossing point with very large spin–orbit coupling matrix element was very close to the intrinsic reaction paths of both sextet and quartet H‐transfers. Excellent agreement with experiments were obtained when the sextet reactant and quartet transition state were used with a spin crossover, which strongly support the TSR model.     

Ab initio quasirelativistic calculations on electronic transitions in ICl by the multireference many‐body perturbation theory

A quasirelativistic perturbative method of ab initio calculations on ground and excited molecular electronic states and transition properties within the relativistic effective core potential approximation is presented and discussed. The method is based on the construction of a state‐selective many‐electron effective Hamiltonian in the model space spanned by an appropriate set of Slater determinants by means of the second‐order many‐body multireference perturbation theory. The neglect of effective spin–orbit interactions outside of the model space allows the exploitation of relatively high nonrelativistic symmetry during the evaluation of perturbative corrections and therefore dramatic reduction of the cost of computations without any contraction of the model‐space functions. One‐electron transition properties are evaluated via the perturbative construction of spin‐free transition density matrices. Illustrative calculations on the X0⁺ ? A1, B0⁺, and (ii)1 transitions in the ICl molecule are reported. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

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Spin-inversion dynamics in O₂ binding to a model heme complex, which consisted of Fe(II)-porphyrin and imidazole, were studied using nonadiabatic wave packet dynamics calculations. We considered three active nuclear degrees of freedom in the dynamics, including the motions along the Fe–O distance, Fe–O–O angle, and Fe out-of-plane distance. Spin-free potential energy surfaces for the singlet, triplet, quintet, and septet states were developed using density functional theory calculations, and spin–orbit coupling elements were obtained from CASSCF-level electronic structure calculations. The spin-inversion mainly occurred between the singlet state and one of the triplet states due to large spin–orbit couplings and the contributions of other states were extremely small. The present quantum dynamics calculations suggested that the narrow crossing region model plays a dominant role in the O₂ binding dynamics. In addition, the one-dimensional Landau–Zener model underestimated the nonadiabatic transition probability.     

Spin–Orbit Contributions in High‐Spin Nitrenes/Carbenes: A Hybrid CASSCF/MRMP2 Study of Zero‐Field Splitting Tensors

Zero‐field splitting (ZFS) tensors ( D tensors) of organic high‐spin oligonitrenes/oligocarbenes up to spin‐septet are quantitatively determined on the basis of quantum chemical calculations. The spin–orbit contributions, D ^SO tensors are calculated in terms of a hybrid CASSCF/MRMP2 approach, which was recently proposed by us. The spin–spin counterparts, D ^SS tensors are computed based on McWeeny–Mizuno’s equation in conjunction with the RODFT spin densities. The present calculations show that more than 10 % of ZFS arises from spin–orbit interactions in the high‐spin nitrenes under study. Contributions of spin‐bearing site–site interactions are estimated with the aid of a semi‐empirical model for the D tensors and found to be ca. 5 % of the D ^SO tensor. The analysis of intermediate states reveal that the largest contributions to the calculated D ^SO tensors are attributed to intra‐site spin flip excitations and delocalized π and π* orbitals play an important role in the inter‐site spin–orbit interactions.     

Photophysics of Push–Pull Distyrylfurans,Thiophenes and Pyridines by Fast and Ultrafast Techniques

Time‐resolved transient absorption and fluorescence spectroscopy with nano‐ and femtosecond time resolution were used to investigate the deactivation pathways of the excited states of distyrylfuran, thiophene and pyridine derivatives in several organic solvents of different polarity in detail. The rate constant of the main decay processes (fluorescence, singlet–triplet intersystem crossing, isomerisation and internal conversion) are strongly affected by the nature [locally excited (LE) or charge transfer (CT)] and selective position of the lowest excited singlet states. In particular, the heteroaromatic central ring significantly enhances the intramolecular charge‐transfer process, which is operative even in a non‐polar solvent. Both the thiophene and pyridine moieties enhance the S₁→T₁ rate with respect to the furan one. This is due to the heavy‐atom effect (thiophene compounds) and to the ¹(π,π)*→³(n,π)* transition (pyridine compounds), which enhance the spin‐orbit coupling. Moreover, the solvent polarity also plays a significant role in the photophysical properties of these push–pull compounds: in fact, a particularly fast ¹LE*→¹CT* process was found for dimethylamino derivatives in the most polar solvents (time constant, τ≤400 fs), while it takes place in tens of picoseconds in non‐polar solvents. It was also shown that the CT character of the lowest excited singlet state decreased by replacing the dimethylamino side group with a methoxy one. The latter causes a decrease in the emissive decay and an enhancement of triplet‐state formation. The photoisomerisation mechanism (singlet/triplet) is also discussed.     

Coordination Complexes of a Neutral 1,2,4‐Benzotriazinyl Radical Ligand: Synthesis,Molecular and Electronic Structures,and Magnetic Properties

A series of d‐block metal complexes of the recently reported coordinating neutral radical ligand 1‐phenyl‐3‐(pyrid‐2‐yl)‐1,4‐dihydro‐1,2,4‐benzotriazin‐4‐yl ( 1 ) was synthesized. The investigated systems contain the benzotriazinyl radical 1 coordinated to a divalent metal cation, Mn^II, Fe^II, Co^II, or Ni^II, with 1,1,1,5,5,5‐hexafluoroacetylacetonato (hfac) as the auxiliary ligand of choice. The synthesized complexes were fully characterized by single‐crystal X‐ray diffraction, magnetic susceptibility measurements, and electronic structure calculations. The complexes [Mn( 1 )(hfac)₂] and [Fe( 1 )(hfac)₂] displayed antiferromagnetic coupling between the unpaired electrons of the ligand and the metal cation, whereas the interaction was found to be ferromagnetic in the analogous Ni^II complex [Ni( 1 )(hfac)₂]. The magnetic properties of the complex [Co( 1 )(hfac)₂] were difficult to interpret owing to significant spin–orbit coupling inherent to octahedral high‐spin Co^II metal ion. As a whole, the reported data clearly demonstrated the favorable coordinating properties of the radical 1 , which, together with its stability and structural tunability, make it an excellent new building block for establishing more complex metal–radical architectures with interesting magnetic properties.     

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.     

The modified all-valence INDO method with the inclusion of spin–orbit coupling

The all-valence INDO method has been modified for the inclusion of spin–orbit coupling effects. In the method presented, the Hamiltonian includes spin–orbit coupling and the basis set constitutes the singlet and triplet determinental wave functions constructed from molecular orbitals resulting from nonrelativistic calculations. Eigenvectors obtained are later used for the evaluation of transition probabilities among different states. The results presented include lifetimes of different states of organic molecules and transition energies for halogen molecules and they are in a good agreement with experimental results. © 1992 John Wiley & Sons, Inc.     

Theoretical study of the mechanism for spin‐forbidden quenching process O(1D) + CO2(1Σ) → O(3P) + CO2(1Σ)

The mechanism of the spin‐forbidden quenching process O(¹D) + CO₂(¹Σ) → O(³P) + CO₂(¹Σ) was investigated by ab initio quantum chemistry methods. The calculations showed the singlet potential surface [O(¹D)+CO₂] is attractive where a strongly bound intermediate complex CO₃ is formed in the potential basin without a transition state, whereas the complex CO₃ that is formed on the triplet surface [O(³P)+CO₃] must overcome a barrier. The complex channel was documented by searching minimum energy intersection points in the region of the bound complex CO₃ and calculating spin‐orbit coupling at the point. A direct channel was proposed by a study of cross point of singlet and triplet PESs with different collision angles and calculations of spin‐orbit coupling at those cross points in a nonbound region of the [O(¹D)+CO₃] system. The mechanism of the energy transfer is discussed on the basis of the theoretical results. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

GRECP/5e‐MRD‐CI calculation of the electronic structure of PbH

The correlation calculation of the electronic structure of PbH is carried out with the generalized relativistic effective core potential (GRECP) and multireference single‐ and double‐excitation configuration interaction (MRD‐CI) methods. The 22‐electron GRECP for Pb is used and the outer core 5s, 5p, and 5d pseudospinors are frozen using the level‐shift technique, so only five external electrons of PbH are correlated. A new configuration selection scheme with respect to the relativistic multireference states is employed in the framework of the MRD‐CI method. The [6, 4, 3, 2] correlation spin–orbit basis set is optimized in the coupled cluster calculations on the Pb atom using a recently proposed procedure, in which functions in the spin–orbital basis set are generated from calculations of different ionic states of the Pb atom and those functions are considered optimal that provide the stationary point for some energy functional. Spectroscopic constants for the two lowest‐lying electronic states of PbH (²Π_1/2, ²Π_3/2) are found to be in good agreement with the experimental data. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Two‐component calculations of spin–orbit effects for a van der Waals molecule Rn2

Electronic structures of the weakly bound Rn₂ were calculated by the two‐component Møller–Plesset second‐order perturbation and coupled‐cluster methods with relativistic effective core potentials including spin–orbit operators. The calculated spin–orbit effects are small, but depend strongly on the size of basis sets and the amount of electron correlations. Magnitudes of spin–orbit effects on D_e (0.7–3.0 meV) and R_e (−0.4∼−2.2 Å) of Rn₂ are comparable to previously reported values based on configuration interaction calculations. A two‐component approach seems to be a promising tool to investigate spin–orbit effects for the weak‐bonded systems containing heavy elements. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 72: 139–143, 1999