2. Computational method
All calculations were performed using the Gaussian 09 software package
[9]. The DFT method is carried out for structural, electronic, and
optical investigations; whereas, the Becke-three-Lee-Yang-Parr (B3LYP)
hybrid functional with 6-311G(d,p) basis set is used for the optimized
process for all studied compounds in the ground state at the neutral,
the anion and the cation forms. As clear from the previous study, the
optimized geometries of the many organic compounds in the ground-state
(S0) as possessed from the B3LYP funtional are in better
agreement with the experiment [1,10]. In our study, as shown in
Table S1, regarding molecules 1 , 3 and 10 ,
the results of the theoretical calculation of bond lengths and angles
are in line with the experimental values obtained from X-ray diffraction
too. [4,8,11].
Vibrational frequencies are calculated at the same level as the correct
zero-point energy (ZPE) and confirm that the presence of ground states
without imaginary frequency.For the first excited state
(S1), the TD-DFT/B3LYP was used to optimized the excited
state geometries of the the analogues at the same level of basis set.
The absorption and emission wavelengths and oscillator strengths ofDTS and eleven compounds 1-11 are calculated by using
B3LYP, PBE0 and ωB97XD functionals with the 6-311G(d,p) basis set. The
polarizable continuum model (PCM) has been used to identify solvent
effects.
For the assessment of transfer of an electron or a hole takes place from
one charged molecule to an adjacent neutral molecule in OLED efficient
materials, the charge transport factor (kET ) is
taken into account. This expected rate of charge transport depends on
the basis of semi-classical Marcus theory and can be written in the
following equation (1) [12,13]:
\(k_{\text{ET}}=\ \frac{{4\pi}^{2}}{h}\frac{1}{\sqrt{4\pi\lambda k_{B}T}}V^{2}exp\{\ \frac{\lambda}{4k_{B}T}\ \}\)(1)
Where h , kB , T , λ , andV are Planck constant, Boltzmann constant, temperature, the
reorganization energy, and transfer integral, respectively.
Noticeably, the significant value kET will be
proportional to the maximum value of V , as well as a minimum
number of λ . In this paper, we mainly focus on investigating the
effects of several functional groups on the optoelectronic aspect of a
single molecule. Therefore, the reorganization energy λ would be
considered, in which this parameter has been resulted from the
combination of two intramolecular categories and surrounding medium
energetic values [14]. In fact, the inner reorganization energy
likely plays an important role to affect organic electronic materials.
For example, the change between the environmental distribution to the
relaxation energy of solid-state systems is small. [10,14]. Inner
reorganization energies relate to electron and hole, which are derived
from equations 2-3 [1,10,14]:
λh = (EC(N) – EC) +
(EN(C) – EN) (2)
λe = (EA(N) – EA) +
(EN(A) – EN) (3)
Where EC(N)/EA(N) is the energy of
cation/anion in the optimized geometry of neutral form.
EN(C)/EN(A) is assigned as the energy of
neutral computed with the optimized cation/anionic molecule.
EN/EC/EA could be viewed
as the energy of neutral/cation/anion in their corresponding optimized
geometries.
Ionization potential (IP), and electron affinity (EA) are the sum of
energy variations when a molecule system is donated and has accepted an
electron, respectively (equations 4a-4b, and 5a-5b) [10].
IPVertical = EC(A) –
EN; IPadiabatic = EC –
EN (4a-4b)
EAvertical = EN –
EA(N); EAadiabatic = EN– EA (5a-5b)