Spin–Orbit Coupling in Phosphorescent Iridium(III) Complexes

We study the excited states of two iridium(III) complexes with potential applications in organic light‐emitting diodes: fac‐tris(2‐phenylpyridyl)iridium(III) [Ir(ppy)₃] and fac‐tris(1‐methyl‐5‐phenyl‐3‐n‐propyl‐[1,2,4]triazolyl)iridium(III) [Ir(ptz)₃]. Herein we report calculations of the excited states of these complexes from time‐dependent density functional theory (TDDFT) with the zeroth‐order regular approximation (ZORA). We show that results from the one‐component formulation of ZORA, with spin–orbit coupling included perturbatively, accurately reproduce both the results of the two‐component calculations and previously published experimental absorption spectra of the complexes. We are able to trace the effects of both scalar relativistic correction and spin–orbit coupling on the low‐energy excitations and radiative lifetimes of these complexes. In particular, we show that there is an indirect relativistic stabilisation of the metal‐to‐ligand charge transfer (MLCT) states. This is important because it means that indirect relativistic effects increase the degree to which SOC can hybridise singlet and triplet states and hence plays an important role in determining the optical properties of these complexes. We find that these two compounds are remarkably similar in these respects, despite Ir(ppy)₃ and Ir(ptz)₃ emitting green and blue light respectively. However, we predict that these two complexes will show marked differences in their magnetic circular dichroism (MCD) spectra.     

Density functional theory studies on structures and absorption spectra of [Au(tpy)Cl]2+ and its derivatives: Role of basis set,functional, solvent effect,and spin orbit effect

The geometries of [Au(tpy)Cl]²⁺ (tpy = 2,2′:6′,2″‐terpyridine) and its derivatives ( 1 – 4 ) were optimized using relativistic density functional theory (DFT) at both scalar and two‐component spin orbit coupling (SOC) level of theory via zero order regular approximation (ZORA). The combination of OPTX exchange, PW91c correlation functional (denoted as OP91), all‐electron ZORA TZ2P basis set was found to be the optimal combination for geometry. The results reveal that both SOC and substituents have little effect on the geometry of complexes 1 – 4 . Then, their absorption spectra were investigated by scalar relativistic time dependent DFT (TDDFT)/SAOP/TZ2P in vacuum, in CH₂Cl₂, CH₃CN solvents by means of conductor like screening model. The calculations indicate that the nature of the low‐lying spin‐allowed excited states is gold‐perturbed intraligand transition, namely charge reorganization. This fact also demonstrates that the influence of the polarity of solvent on absorption spectra of 1 – 4 is negligible. The spin orbit TDDFT was also performed to get further insight into the effect of SOC on the absorption spectra. It is found that the SOC has little influence on the simulation of electronic spectrum of complexes 1 – 4 due to no significant involvement of d‐orbitals during electronic transition. Our conclusions are reliable and are in good agreement with the previous experimental results and theoretical investigations. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

All‐electron relativistic computations on the low‐lying electronic states,bond length,and vibrational frequency of CeF diatomic molecule with spin–orbit coupling effects

Ab initio all‐electron computations have been carried out for Ce⁺ and CeF, including the electron correlation, scalar relativistic, and spin–orbit coupling effects in a quantitative manner. First, the n‐electron valence state second‐order multireference perturbation theory (NEVPT2) and spin–orbit configuration interaction (SOCI) based on the state‐averaged restricted active space multiconfigurational self‐consistent field (SA‐RASSCF) and state‐averaged complete active space multiconfigurational self‐consistent field (SA‐CASSCF) wavefunctions have been applied to evaluations of the low‐lying energy levels of Ce⁺ with [Xe]4f¹5d¹6s¹ and [Xe]4f¹5d² configurations, to test the accuracy of several all‐electron relativistic basis sets. It is shown that the mixing of quartet and doublet states is essential to reproduce the excitation energies. Then, SA‐RASSCF(CASSCF)/NEVPT2 + SOCI computations with the Sapporo(‐DKH3)‐2012‐QZP basis set were carried out to determine the energy levels of the low‐lying electronic states of CeF. The calculated excitation energies, bond length, and vibrational frequency are shown to be in good agreement with the available experimental data. © 2018 Wiley Periodicals, Inc.     

Full four‐component relativistic calculations of the one‐bond 77Se–13C spin‐spin coupling constants in the series of selenium heterocycles and their parent open‐chain selenides

Four‐component relativistic calculations of ⁷⁷Se–¹³C spin–spin coupling constants have been performed in the series of selenium heterocycles and their parent open‐chain selenides. It has been found that relativistic effects play an essential role in the selenium–carbon coupling mechanism and could result in a contribution of as much as 15–25% of the total values of the one‐bond selenium–carbon spin‐spin coupling constants. In the overall contribution of the relativistic effects to the total values of ¹J(Se,C), the scalar relativistic corrections (negative in sign) by far dominate over the spin‐orbit ones (positive in sign), the latter being of less than 5%, as compared to the former (ca 20%). A combination of nonrelativistic second‐order polarization propagator approach (CC2) with the four‐component relativistic density functional theory scheme is recommended as a versatile tool for the calculation of ¹J(Se,C). Solvent effects in the values of ¹J(Se,C) calculated within the polarizable continuum model for the solvents with different dielectric constants (ε 2.2–78.4) are next to negligible decreasing negative ¹J(Se,C) in absolute value by only about 1 Hz. The use of the locally dense basis set approach applied herewith for the calculation of ⁷⁷Se–¹³C spin‐spin coupling constants is fully justified resulting in a dramatic decrease in computational cost with only 0.1–0.2‐Hz loss of accuracy. Copyright © 2014 John Wiley & Sons, Ltd.     

Accurate spectroscopic constants of the lowest three electronic states in halonitrenes with multireference configuration interaction

Internally contracted multireference configuration interaction (icMRCI) calculations of the ground state (X³Σ⁻), the first excited state (a¹Δ) as well as the second excited state (b¹Σ⁺) have been performed for a series of halogenated nitrenes NXs (X = Cl, Br, and I). Accurate spectroscopic constants of these lowest three electronic states of each NX were obtained in this work using MRCI methods with aug‐cc‐pVXZ (X = T, Q, 5) basis sets and complete basis set (CBS) limit. In addition, various corrections, including the Davidson correction, scalar relativistic effect, core‐valence correlation, and spin‐orbit coupling effect, have been studied in calculating spectroscopic constants, especially for heavy‐atom nitrenes. Comparisons have been made with previous computational and experimental results where available. The icMRCI + Q calculations presented in this work provide a comprehensive series of results at a consistent high level of theory for all of the halogenated nitrenes.     

Description of excited states in [Re(Imidazole)(CO)3(Phen)]+ including solvent and spin‐orbit coupling effects: Density functional theory versus multiconfigurational wavefunction approach

The low‐lying electronic excited states of [Re(imidazole)(CO)₃(phen)]⁺ (phen = 1,10‐phenanthroline) ranging between 420 nm and 330 nm have been calculated by means of relativistic spin‐orbit time‐dependent density functional theory (TD‐DFT) and wavefunction approaches (state‐average‐CASSCF/CASPT2). A direct comparison between the theoretical absorption spectra obtained with different methods including SOC and solvent corrections for water points to the difficulties at describing on the same footing the bands generated by metal‐to‐ligand charge transfer (MLCT), intraligand (IL) transition, and ligand‐to‐Ligand‐ charge transfer (LLCT). While TD‐DFT and three‐roots‐state‐average CASSCF (10,10) reproduce rather well the lowest broad MLCT band observed in the experimental spectrum between 420 nm and 330 nm, more flexible wavefunctions enlarged either by the number of roots or by the number of active orbitals and electrons destabilize the MLCT states by introducing IL and LLCT character in the lowest part of the absorption spectrum. © 2016 Wiley Periodicals, Inc.     

Low‐lying singlet excited states of isocyanogen

Recent photofragment fluorescence excitation (PHOFEX) spectroscopy experiments have observed the ùA″ singlet excited state of isocyanogen (CNCN) for the first time. The observed spectrum is not completely assigned and significant questions remain about the excited states of this system. To provide insight into the energetically accessible excited states of CNCN, optimized geometries, harmonic vibrational frequencies, and excitation energies for the first three singlet excited states are determined using equation‐of‐motion coupled‐cluster theory with singles and doubles (EOM‐CCSD) and correlation‐consistent basis sets. Additionally, excited state coupled‐cluster methods which approximate the contributions from triples (CC3) are utilized to estimate the effect of higher‐order correlation on the energy of each excited state. For the ùA″ state, our best estimate for T₀ is about 42,200 cm^?1, in agreement with the experimentally estimated upper limit for the zero‐point level of 42,523 cm^?1. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

An Investigation of Lanthanum Coordination Compounds by Using Solid‐State 139La NMR Spectroscopy and Relativistic Density Functional Theory

Lanthanum‐139 NMR spectra of stationary samples of several solid La^III coordination compounds have been obtained at applied magnetic fields of 11.75 and 17.60 T. The breadth and shape of the ¹³⁹La NMR spectra of the central transition are dominated by the interaction between the ¹³⁹La nuclear quadrupole moment and the electric field gradient (EFG) at that nucleus; however, the influence of chemical‐shift anisotropy on the NMR spectra is non‐negligible for the majority of the compounds investigated. Analysis of the experimental NMR spectra reveals that the ¹³⁹La quadrupolar coupling constants (C_Q) range from 10.0 to 35.6 MHz, the spans of the chemical‐shift tensor (Ω) range from 50 to 260 ppm, and the isotropic chemical shifts (δ_iso) range from ?80 to 178 ppm. In general, there is a correlation between the magnitudes of C_Q and Ω, and δ_iso is shown to depend on the La coordination number. Magnetic‐shielding tensors, calculated by using relativistic zeroth‐order regular approximation density functional theory (ZORA‐DFT) and incorporating scalar only or scalar plus spin–orbit relativistic effects, qualitatively reproduce the experimental chemical‐shift tensors. In general, the inclusion of spin–orbit coupling yields results that are in better agreement with those from the experiment. The magnetic‐shielding calculations and experimentally determined Euler angles can be used to predict the orientation of the chemical‐shift and EFG tensors in the molecular frame. This study demonstrates that solid‐state ¹³⁹La NMR spectroscopy is a useful characterization method and can provide insight into the molecular structure of lanthanum coordination compounds.     

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     

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.     

Excited-State Reactivity of [Mn(im)(CO)3(phen)]+: A Structural Exploration

The electronic excited state reactivity of [Mn(im)(CO)₃(phen)]⁺ (phen = 1,10-phenanthroline; im = imidazole) ranging between 420 and 330 nm have been analyzed by means of relativistic spin–orbit time-dependent density functional theory and wavefunction approaches (state-average-complete-active-space self-consistent-field/multistate CAS second-order perturbation theory). Minimum energy conical intersection (MECI) structures and connecting pathways were explored using the artificial force induced reaction (AFIR) method. MECIs between the first and second singlet excited states (S₁/S₂-MECIs) were searched by the single-component AFIR (SC-AFIR) algorithm combined with the gradient projection type optimizer. The structural, electronic, and excited states properties of [Mn(im)(CO)₃(phen)]⁺ are compared to those of the Re(I) analogue [Re(im)(CO)₃(phen)]⁺. The high density of excited states and the presence of low-lying metal-centered states that characterize the Mn complex add complexity to the photophysics and open various dissociative channels for both the CO and imidazole ligands. © 2018 Wiley Periodicals, Inc.     

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     

The effect of the iterative triple and quadruple cluster amplitudes on the adiabatic potential curve in the coupled cluster calculations of the ground electronic state of the Yb dimer

The dissociation energy, equilibrium internuclear distance, and spectroscopic constants for the ¹Σ ground state of the Yb₂ molecule are calculated. The relativistic effects are introduced through generalized relativistic effective core potentials with very high precision. The scalar relativistic coupled cluster method particularly well suited for closed‐shell van der Waals systems is used for the correlation treatment. Extensive generalized correlation basis sets were constructed and used. The relatively small corrections for high‐order cluster amplitudes and spin—orbit interactions are taken into account using smaller basis sets and the spin—orbit density functional theory. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Ionization potential of excited states of Be‐like sequence in the concept of iso‐spectrum‐level series

With the introduction of the concept of the iso‐spectrum‐level series, a linear relationship is found between the first differences of the ionization potential of excited states and nuclear charge Z along an iso‐spectrum‐level series, and the ionization potential of excited states of Be‐like sequence are studied systematically on the basis of the weakest bound electron potential model theory. The expression of nonrelativistic ionization potential is derived from the weakest bound electron potential model theory, and relativistic effects are included by using a fourth‐order polynomial in Z. As a demonstration, the ionization potentials of [He]2s2p ³P, [He]2s3s ¹S₀, [He]2s3p ¹P, [He]2s3d ¹D₂, and [He]2s4d ¹D₂ series for a range of Be‐like sequence from Z = 4–23 are calculated. The results are compared with the experimental data and the recent sophisticated ab initio results. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem 93: 344–350, 2003     

First example of the correlated calculation of the one‐bond tellurium–carbon spin–spin coupling constants: Relativistic effects,vibrational corrections,and solvent effects

This work reports on the comprehensive calculation of the NMR one‐bond spin–spin coupling constants (SSCCs) involving carbon and tellurium, ¹J(¹²⁵Te,¹³C), in four representative compounds: Te(CH₃)₂, Te(CF₃)₂, Te(C?CH)₂, and tellurophene. A high‐level computational treatment of ¹J(¹²⁵Te,¹³C) included calculations at the SOPPA level taking into account relativistic effects evaluated at the 4‐component RPA and DFT levels of theory, vibrational corrections, and solvent effects. The consistency of different computational approaches including the level of theory of the geometry optimization of tellurium‐containing compounds, basis sets, and methods used for obtainig spin–spin coupling values have also been discussed in view of reproducing the experimental values of the tellurium–carbon SSCCs. Relativistic corrections were found to play a major role in the calculation of ¹J(¹²⁵Te,¹³C) reaching as much as almost 50% of the total value of ¹J(¹²⁵Te,¹³C) while relativistic geometrical effects are of minor importance. The vibrational and solvent corrections account for accordingly about 3–6% and 0–4% of the total value. It is shown that taking into account relativistic corrections, vibrational corrections and solvent effects at the DFT level essentially improves the agreement of the non‐relativistic theoretical SOPPA results with experiment. © 2016 Wiley Periodicals, Inc.     

Relativistic effects on inversion barriers of pyramidal group 15 hydrides

Quantum chemistry is an important tool for determining general molecular properties, although relativistic corrections are usually required for systems containing heavy and super heavy elements. Non‐relativistic along with relativistic two‐ and four‐component electronic structure calculations done with the CCSD‐T method and the new RPF‐4Z basis set have therefore been applied for determining inversion barriers, corresponding to the change from a pyramidal (C_3v) ground‐state structure to the trigonal planar (D_3h) transition state, TS, of group 15 hydrides, XH₃ (X= N, P, As, Sb, and Bi). The ground‐state structure of the McH₃ molecule, which contains the super heavy element Moscovium, is also predicted as pyramidal (C_3v), with an atomization energy of 90.8 kcal mol⁻¹. However, although non‐relativistic calculations still provided a D_3h planar TS for McH₃, four‐component relativistic calculations based on single‐reference wave functions are unable to elucidate the definitive TS geometry in this case. Hence, the results show that relativistic effects are crucial for this barrier determination in those hydrides containing Bi and Mc. Moreover, while the scalar relativistic effects predominate, increasing barrier heights by as much as 17.6 kcal mol⁻¹ (32%) in BiH₃, the spin‐orbit coupling cannot be disregarded in those hydrides containing the heaviest group 15 elements, decreasing the barrier by 2.5 kcal mol⁻¹ (4.5%) in this same molecule.     

Fine structure in the hydrogen atom boxed in a spherical impenetrable cavity

The spectrum of the hydrogen atom confined in a spherical impenetrable box of radius R_c has been investigated by many authors up to date, but not at the level of relativistic corrections. It is well known that, as R_c diminishes, all energy levels and the pressure increase very rapidly, whereas the polarizability goes to zero. In this report, we have computed the relativistic corrections that underlie the fine structure of the confined hydrogen atom, as a function of R_c. Such corrections correspond to relativistic kinetic energy, spin‐orbit coupling and the Darwin term, which are calculated in the frame of time‐independent perturbation theory, for which, use was made of the exact confined hydrogen atom wave functions. We show that for a confinement radius of 0.5 au the relativistic corrections increase up to three orders of magnitude with respect to those corresponding to the free atom. As R_c decreases, the kinetic energy correction and the spin‐orbit coupling for become negative whereas their absolute value and the Darwin term, which is positive, increase very rapidly.     

A superatomic molecule under the spin‐orbit coupling: Insights from the electronic properties in the thiolate‐protected Au38(SR)24 cluster

The role of the spin‐orbit coupling in Au₃₈(SR)₂₄, as a representative case for a superatomic molecules is studied to offer a complete view of the relativistic effect in heavy elements clusters. Its core can be described in as an analog to a diatomic molecule, such as F₂, allowing the electronic structure to be depicted in terms of the D_∞h point group. First, we showed the electronic structure under the spin‐orbit framework using total angular momentum representations ( j = ℓ ± s ; spinors), which allows us to characterize the expected splitting of certain levels derived from the cluster core. Accordingly, the optical properties are evaluated under spin‐orbit coupling regime, revealing differences in the low‐energy region of the absorption spectrum. Lastly, the variation of electron affinity (EA) and ionization potential (IP) properties is evaluated. This reveals characteristic consequences of the inclusion of spin‐orbit coupling in Au₃₈(SR)₂₄, as a bridge to larger thiolate‐protected gold clusters.     

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     

Singlet and Triplet Excited States and Intersystem Crossing in Free‐Base Porphyrin: TDDFT and DFT/MRCI Study

Extensive time-dependent DFT (TDDFT) and DFT/multireference configuration interaction (MRCI) calculations are performed on the singlet and triplet excited states of free-base porphyrin, with emphasis on intersystem crossing processes. The equilibrium geometries, as well as the vertical and adiabatic excitation energies of the lowest singlet and triplet excited states are determined. Single and double proton-transfer reactions in the first excited singlet state are explored. Harmonic vibrational frequencies are calculated at the equilibrium geometries of the ground state and of the lowest singlet and triplet excited states. Furthermore, spin–orbit coupling matrix elements of the lowest singlet and triplet states and their numerical derivatives with respect to nuclear displacements are computed. It is shown that opening of an unprotonated pyrrole ring as well as excited-state single and double proton transfer inside the porphyrin cavity lead to crossings of the potential energy curves of the lowest singlet and triplet excited states. It is also found that displacements along out-of-plane normal modes of the first excited singlet state cause a significant increase of the 2|H_so|S₁>, 1|H_so|S₁>, and 1|H_so|S₀> spin–orbit coupling matrix elements. These phenomena lead to efficient radiationless deactivation of the lowest excited states of free-base porphyrin via intercombination conversion. In particular, the S₁→T₁ population transfer is found to proceed at a rate of ≈10⁷ s⁻¹ in the isolated molecule.