2 COMPUTATIONAL METHODS
The geometry optimization of mesogenic Eu(III) complexes in the ground
state was performed by the DFT method using the Prirоdа 06
software.[28,29] According to our previous
studies[8,9,11,27,30] we used generalized gradient
approximation with the Perdew-Burke-Ernzerhof (PBЕ) exchange-correlation
functional.[31] Relativistic basis sets rL11 for
Eu(III) and rL1 for other atoms within the scalar relativistic
approximation were used.[32] These sets are
analogues of the cc-pVDZ and cc-pCVDZ double-zeta basis sets of Dunning,
respectively.[33] Calculations were performed for
isolated molecules without symmetry constraints. Optimization ended when
the gradient value reached 3∙106 eV/Å, the SCF
convergence accuracy was set to 3∙105 eV.
The types of coordination polyhedra were determined using the SHAPE
software.[34-36] This program uses sets of points
of continuous shape which correspond to the positions of atoms in
optimized geometries of molecules and determines polyhedra by the
smallest deviations of these sets from the vertices of ideal reference
polyhedra.
Experimental IR spectra were observed for pressed thin tablets of
Eu(III) complexes with potassium bromide on ALPHA FT-IR spectrometer
(Bruker) with a spectral of range 375-7500 cm-1 and
resolution 4 cm-1. The vibrational modes of the IR
spectra were calculated by the DFT method and PBE0 functional, as well
as the NMR chemical shifts with the gauge-independent atomic orbital
method. Experimental chemical shifts were taken from other
publications.[8,9,30,37]
TDDFT method with various density functionals was unable to separately
localize triplet excitation on each of the ligands in the studied
Eu(III) complexes during the optimization of the excited state
structures. The obtained excited states were intraligand or delocalized.
Unlike density functional-based methods, configuration interaction
singles method (CIS) correctly predicted excitation localization on
separate ligands. Therefore, in this work the triplet excited state
structures were optimized by the CIS method using the Firefly v. 8
software which is partially based on the GAMESS
code.[38,39] For Eu(III) ions the scalar
quasirelativistic 4f-in-core pseudopotential ECP52MWB with the
associated valence basis set was used,[40,41] for
other atoms - 6-31G(d,p). Then TDDFT/PBE0 method was applied for CIS
optimized geometries to calculate the values of triplet excited states.
Empirical dispersion correction (DFT-D version 4 with Becke-Johnson
damping)[42] was used to improve the long-range
behavior of DFT.
To determine the experimental values of the triplet excited states, we
used the phosphorescence spectra of gadolinium(III) (Gd(III)) complexes
with the corresponding ligands which are characterized by a clear
phosphorescence band of ligands.[8,43,44]
In order to evaluate the emission efficiency of the studied Eu(III)
complexes, the intramolecular energy transfer rates from the triplet
levels of ligands to the resonance levels of Eu(III) were calculated
according to the procedure described in [45, 46]. The theoretical
values of quantum yields were compared to the previously obtained
experimental absolute quantum yields.[47]
The structure-topological software package ToposPro V. 5.3.3.4 was used
for the analysis of Voronoi-Dirichlet polyhedra (VDP) after optimization
of the ground and excited state structures.[48]