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)