Figure-03: Carbazole-Donor Based Modified Organic Dyes: (a) D1A (b) D2A (c)D3A
The molecular structures of dyes comprise of 91 atoms in D1, 89 atoms in D2, 96 atoms in D3, 98 atoms in D1A, 96 atoms in D2A and 103 atoms in D3A. The Slater type basis and fit functions were used with number of 4 for H, 9 for C, 9 for N, 13 for S, 9 for O. The entire calculations were done without enforcing any symmetry. The structures were pre-optimized using universal force field and then geometries were optimized to ensure complete relaxation of the molecules/structures at minimum possible energy. In the course of structural relaxation, the geometry updates involved ‘delocalized’ optimization coordinates with BFGS (Broyden-Fletcher-Goldfarb-Shanno) as Hessian update algorithm.
The basis functions were in the form of Slater Type Orbitals (STOs)of quality TZP (core double zeta, valence triple zeta, single polarized basis set) for all atoms used in the dye molecules. The exchange and correlation functional (XC) was separately taken as standard GGA-PBE and hybrid BELYP for all cases studied in this work. The iterative geometry improvements involved convergence criteria with changes in energy, gradients and bond length changes as 0.02 eV, 0.02 eV/Å and 0.01Å whereas the SCF updates of geometry were carried out with convergence criterion of 2.7x 10-5 eV. The numerical integrations were carried out with Becke grid quality and ZlmFit density fit Quality as ‘Good’. The precision parameters involved in numerical integration was 6.0000000000 whereas the basis and fit neglect functions were 0.1x10-7. The linear scaling parameters of cut-off radii density fit, overlap cut-off criterion for Coulomb potential and multipole terms were 0.1x10-9, 0.1x10-7, 0.1x10-9 and 0.1x10-9 respectively. The entire calculations were of all-electron type in such a way that no of core orbitals were considered for finding the orbital energies. The ADF calculates the value of bond energy by finding the difference of energy between molecule and its fragments in the form of spherically symmetric and spin restricted atoms [54].
(TiO2)96 quantum dot having 96 atoms of Ti and 192 atoms of O was prepared using DFTB by employing SCC-DFTB model. The dispersion and periodicity were set as ‘none’ and the parameter set trio/org 0-1 was used thereby setting Fermi temperature at 5 K. The default values of occupation and initial hessian were selected. The energy convergence, gradient convergence and step convergence are 10-5 eV, 10-3 eV/Å and 10-3 Ǻ respectively. The optimization method and optimization space were employed as quasi-newton method and cartesian space respectively.
After the geometry optimization of the structures, all electrons single point calculations were done, on the optimized neutral dye structures without considering symmetry, in order to study electronic and optical characteristics of photosensitizes. The UV-Vis excitation spectrum was calculated using ADF-Response code by considering the singlet-singlet allowed transitions by utilizing Davidson method [55]. The properties of the structures optimized at corresponding levels of theory were calculated using XC functionals GGA-PBE and Hybrid-B3LYP. The criterion of convergence was adopted as 10-6 eV thereby setting the numerical quality ‘good’ with basis set TZP. The excitation spectra were are also calculated using DFTB with model SCC-DFTB by selecting singlet-singlet transitions with both Davidson and exact methods.
In order to study the photoinjection, the already optimized dye molecules were adsorbed on the surface of optimized (TiO2)96 quantum dot (QD) by performing geometry optimization at DFTB level of theory using Canonical DFTB algorithm. A complete SCC convergence was ensured with gradient convergence of 0.01 Hartree/Å and charge convergence of 10-8e at Fermi temperature of 300 K.The atoms of the QD were kept fixed except the unit involved in binding with dye acceptor. Further, the entire atoms of the dyes were allowed to relax during the optimization of QD-Dye complex. The excitation spectra on the optimized QD-Dye complexes were calculated in single point runs to study the photoinjection by employing the stated parameters. The electron occupation in shells and sub shells are set as ‘default’ that include both fermi and aufbau principal and with K-space sampling as ‘gamma’. Transition charges in these calculations are pre-calculated. From excitation spectra, photoinjection energy, recombination energy and LHE were calculated.
The effects of solvation were also studied by optimizing the dyes structure in two solvents; water and methanol. The number of molecules of solvents and the polarity of solvents are important factors that should be kept in mind during these calculations. The parameters that are used in geometry optimization of dyes and dyes-TiO2were also utilized for relaxation of dyes in solvents. The solvent radius was set as 10.0 where the solute factor was set as 2.7 that comprise almost 27 solvent molecules relative to one molecule of dye. As the dyes get relaxed in solvents then their UV-Vis excitation spectrums of all the dyes were calculated in order to study the spectral shift in dyes due to solvation.