Symmetry adapted formulation of the generalized Brillouin theorem

The singly excited functions satisfying Brillouin theorem are expressed as linear combinations of configuration-state functions for any spin and spatial symmetries (atomic or molecular) and for any reference wave function. The generality of the formulation is ensured by the use of the irreducible tensor method that can be adapted to any symmetry point group of interest. The expansion coefficients are simply written as products of fractional parentage coefficients, spin- and orbit-recoupling coefficients, and phase factors. The formalism is illustrated for some atomic (K_h) and molecular (C_∞v, C_3v, and T_d) configurations. Group theoretical techniques are also used to correlate the Brillouin conditions within a chain of groups.     

DFT and TD-DFT investigation of the ground and excited states for dinuclear and mononuclear copper(I) and silver(I) complexes of 3,5-bis(trifluoromethyl)pyrazole and related bis(pyrazolyl)borate

The ground-state and low-lying excited electronic states in mononuclear, {H₂B[3,5-(CF₃)₂Pz]₂M(2,4,6-Cn)} (M₁) and dinuclear {[3,5-(CF₃)₂Pz]M(2,4,6-Cn)}₂, (M₂) (Pz = pyrazole, Cn = collidine and M = Cu, Ag), are studied using DFT approach. Electronic properties are calculated using B3LYP, while excited singlet and triplet-states are examined using TD-B3LYP. All the calculated low-lying transitions are categorized as ¹MLCT transitions. A good agreement was found between experimental spectra and predicted emission wavelengths (λ_em), the corresponding emissive states being assigned as ³MLCT for Cu₁ and Ag₂, ³MLLCT for Ag₁ and ³LLCT for Cu₂.     

"CH"/N substituted mer-Gaq3 and mer-Alq3 derivatives: an effective approach for the tuning of emitting color

Equilibrium geometry configurations of the "CH"/N substituted Alq3 and Gaq3 derivatives are calculated by density functional theory (B3LYP/6-31G). The frontier molecular orbital and gap energy calculations for all complexes have been performed at the HF/6-31G level. It was shown that, compared to the pristine molecules, the HOMO and LUMO are stabilized, the net effect being however an increasing/decreasing of the gap (Eg) depending on the position of the substituted group. On the basis of the equilibrium geometries, the effect of the substitution on the absorption and emission spectra was evaluated using TDB3LYP/3-21G. It was shown that the change of "CH"/N substituted position on 8-hydroxyquinoline ligand is a powerful approach for the tuning of emitting color. An important blue shift was predicted for 5-substituted 8-hydroxyquinoline derivatives, an important red one being observed for 4-substituted ones. Interestingly, relatively significant blue and red shifts were also predicted for the 7- and 2-substituted derivatives. In this work, the correlation between the spectrum shifts and the metal-ligand bonding is also discussed.     

From atoms to biomolecules: a fruitful perspective

We present a summary of the research activities of the “Quantum Chemistry and Atomic Physics” theoretical group of the “Chimie Quantique et Photophysique” Laboratory at Université Libre de Bruxelles. We emphasize the links between the three orientations of the group: theoretical atomic spectroscopy, structure, and molecular dynamics and list the perspectives of our collaboration.     

Optical properties of the phosphorescent trinuclear copper(I) complexes of pyrazolates: insights from theory

Theoretical investigations have been performed to explore the optical properties of {[3,5-(CF3)(2)Pz]Cu}3 in monomeric and dimeric forms using TD-DFT approaches. The emission of all complexes originates from the lowest triplet excited-states (T1), and the corresponding emissive states are assigned as the mixture of the metal-centered charge transfer and ligand-to-metal charge transfer. The features of the emission spectrum are clarified in detail. The bulk emission spectrum of complex is mainly determined by the stacked dimers rather than the individual monomers. The predicted maximum emission wavelength (lambda(em)) are in good agreement with experimental values, indicating that the phosphorescence bands can be assigned to two different conformations for the neighboring stacked dimers sharing the same monomer in the complex. Energy transfer from T1 of one stacked dimer to the neighboring one is responsible for the disappearance of the shoulder, leaving only the main peak upon heating. With the aim to reveal the conformational dependence for the triplet excited-state emission spectrum, the optical properties of various stacked dimers with different conformations are investigated by varying the relative arrangements through changing inter-monomer distance or rotational angles for the dimer which is responsible for the main peak emission. Calculation results suggest that the shortest intermolecular Cu...Cu distance plays an important role in the emission spectra of the vertical- and tilting-movement dimers, which is ascribed to the variation of the energy gap for the frontier molecular orbitals involved in the main emitting transition. The blue shift of lambda(em) in parallel-movement and rotational dimers can be traced back to the variation of the mutual spatial orientation. Therefore, the modulation of the extent of movement or rotational angles for stacked dimers by external perturbations creates new possibilities for the design of molecular light-emitting devices.     

Shedding light on unusual photophysical properties of bis-cyclometalated iridium(iii) complexes containing 2,5-diaryl-1,3,4-oxadiazole-based and acetylacetonate ligands

A DFT/TDDFT investigation was conducted on a series of cyclometalated iridium(iii) complexes with 2,5-diaryl-1,3,4-oxadiazole (oxd(n)) derivatives to shed light on the effects of the stereoisomeric and steric factors on the photophysical properties. On the basis of the results reported herein, we attempt to explain the experimental observations according to which complexes N,N-trans [Ir(oxd(0))(2)(acac)] (1a) and N,N-trans [Ir(oxd(1))(2)(acac)] (2a) [with oxd(0) = 2,5-diphenyl-1,3,4-oxadiazole, oxd(1) = 2,5-bis(4-fluorophenyl)-1,3,4-oxadiazole and acac = acetylacetonate] show high quantum phosphorescence efficiencies (Φ(PL)) of 35 and 44%, while an extremely low Φ(PL) (<1%) was observed for a number of oxd(n) based complexes including N,N-cis [Ir(oxd(3))(2)(acac)] (4b) [with oxd(3) = 2-(4-fluorophenyl)-5-(2,4,6-triisopropylphenyl)-1,3,4-oxadiazole]. While new insights were gained on structural and electronic properties, the unusual photophysical properties recently reported for 4b were found to be not inherent to spin-orbit coupling (SOC) effects, but determined by both the S(1)-T(1) splitting energy (ΔE(S1-T1)) and the transition dipole moment (μ(S1)) upon the S(0)→ S(1) transition. Drastically large ΔE(S1-T1) and small μ(S1) for 4b (0.70 eV and 0.23 D, respectively) comparative to those for 2a (0.38 eV and 2.76 D, respectively) and 1a (0.58 eV and 2.44 D, respectively) were found to be tightly linked to the twisting degree of the oxd(n) ligand and to the trans-cis structural isomerism. On the basis of these parameters, the unusual physical properties of 4b were interpreted with respect to 1a and 2a, and the higher Φ(PL) of 2a with respect to that for 1a was explained.     

Large-scale MCHF calculations of hyperfine structures in nitrogen and oxygen

The hyperfine structure constants for the 1s ²2s ²2p ³ -⁴ S ^o ground state in nitrogen and the 1s ²2s ²2p ³3s ⁵ S ^o excited state in oxygen are calculated using the MCHF Atomic Structure Package. The single excitation picture is explored through the use of compact wave functions allowing radial non-orthogonalities. Electron correlation is described through numerical multiconfiguration Hartree-Fock calculations for configuration expansions obtained by allowing all single and double excitations from the reference configuration to an active set of orbitals. The latter is increased in a systematic way allowing the convergence of the hyperfine parameters to be studied. Three- and four-particle effects are shown to be important and are taken into account in a sequence of large configuration interaction calculations. The final results are in good agreement with experiment.     

Theoretical study on the influence of different NˆN ligands on the electronic structures and optoelectronic properties of heteroleptic Iridium(III) complexes

DFT/TDDFT calculations were carried out to investigate the electronic structures, absorption and phosphorescence properties of a series of heteroleptic Ir(III) complexes consisting of two N-heterocyclic carbene ligands and a conjugated bicyclic N,N′-heteroaromatic (N?N) ligand. On the basis of the results reported herein, we attempt to explain the experimental observations according to which complex (mpmi)₂Ir(pybi) (1) [Hmpmi = 1-(4-tolyl)-3-methyl-imidazole; Hpybi = 2-(pyridin-2-yl)-1H-benzo[d]imidazole] emits green light with an extremely high-quantum phosphorescence efficiency (Φ _PL ) of 79.3%, while a relatively lower Φ _PL (only 11%) was measured for (fpmi)₂Ir(tfpypz) (2) [fpmi = 1-(4-fluorophenyl)-3-methylimdazolin-2-ylidene-C, C^2′; tfpypz = 2-(3-(trifluoromethyl)-1H-pyrazol-5-yl)pyridinato] emitting blue light by tuning the N?N ligands. Besides, we also designed (fpmi)₂Ir(pyN3) (3) [pyN3H = 2-(5-(trifluoromethyl)-2H-1,2,4-triazol-3-yl)pyridine] and (fpmi)₂Ir(pyN4) (4) [pyN4H = 2-(1H-tetrazol-5-yl)pyridine] to explore the influence of electron-withdrawing substituents on N?N ligands on the electronic and optical properties of these Ir(III) complexes. The results revealed that electron-withdrawing substituents can stabilise both HOMOs and LUMOs and induce HOMO–LUMO energy gap change. Moreover, the emission properties can be significantly tuned by introducing different N?N ligands. While new insights were gained on structural and electronic properties, the extremely high Φ _PL of 1 was found to be not inherent to spin-orbital coupling effects, but determined by its large transition dipole moment (μ_{S 1}) upon S ₀–S ₁ transition compared with that of 2. On the basis of these results, the designed complexes 3 and 4 are considered to be the promising candidates for blue-emitting phosphorescence materials with higher Φ _PL than the complex 2.     

Theoretical study on the influence of ancillary and cyclometalated ligands on the electronic structures and optoelectronic properties of heteroleptic iridium(III) complexes

We report a theoretical analysis of a series of heteroleptic iridium(III) complexes (dox)(2)Ir(acac) [dox = 2,5-diphenyl-1,3,4-oxadiazolato-N,C(2), acac = acetylacetonate] (1a), (fox)(2)Ir(acac) [fox = 2,5-bis(4-fluorophenyl)-1,3,4-oxadiazolato-N,C(2)] (1b), (fox)(2)Ir(Et(2)dtc) [Et(2)dtc = N,N'-diethyldithiocarbamate] (2), (fox)(2)Ir(Et(2)dtp) [Et(2)dtp = O,O'-diethyldithiophosphate] (3), (pypz)(2)Ir(acac) [pypz = 3,5-di(2-pyridyl)pyrazole] (4a), (O-pypz)(2)Ir(acac) (4b), (S-pypz)(2)Ir(acac) (4c) and (bptz)(2)Ir(acac) [bptz = 3-tert-butyl-5-(2-pyridyl)triazole] (5) by using the density functional theory (DFT) method to investigate their electronic structures and photophysical properties and obtain further insights into the phosphorescent efficiency mechanism. Meanwhile, we also investigate the influence of ancillary and cyclometalated ligands on the properties of the above complexes. The results reveal that the nature of the ancillary ligands can influence the electron density distributions of frontier molecular orbitals and their energies, resulting in change in transition character and emission color, while the different cyclometalated ligands have a large impact on the charge transfer performances of the studied complexes. The calculated absorption and luminescence properties of the four complexes 1a, 1b, 2 and 3 are compared with the available experimental data and a good agreement is obtained. Further, the assumed complexes 4a and 4b possess better charge transfer abilities and more balanced charge transfer rates, and they are potential candidates as blue-emitting materials.     

Saturation spectra of low lying states of Nitrogen: reconciling experiment with theory

The hyperfine constants of the levels 2p ² \((^{3}\)P)3s ⁴P _J , 2p ² \((^3\)P)3p ⁴P\(^o_J\) and 2p ² \((^3\)P)3p ⁴D\(^o_J\), deduced by Jennerich et al. [Eur. Phys. J. D 40, 81 (2006)] from the observed hyperfine structures of the transitions 2p ² \((^3\)P)3s ⁴P _J \(\rightarrow\) 2p ² \((^3\)P)3p ⁴P\(^o_{J'}\) and 2p ² \((^3\)P)3s ⁴P _J \(\rightarrow\) 2p ² \((^3\)P)3p ⁴D\(^o_{J'}\) recorded by saturation spectroscopy in the near-infrared,strongly disagree with the ab initio values of Jönsson et al. [J. Phys. B: At. Mol.Opt. Phys. 43, 115006 (2010)].We propose a new interpretation of the recorded weak spectral lines. If the latter are indeed reinterpreted as crossover signals, a new set of experimental hyperfine constants is deduced, in very good agreement with the ab initio predictions.