DFT and TD-DFT Study of Structure and Properties of Semiconductive Hybrid Networks Formed by Bismuth Halides and Different Polycyclic Aromatic Ligands

The structure and spectroscopic properties of polycyclic aromatic ligands of 2,3,6,7,10,11-hexakis (alkylthio) triphenylene (alkyl: methyl, ethyl, and isopropyl; corresponding to the abbreviations of the molecules: HMTT, HETT and HiPTT) were studied using density functional theory (DFT) and time dependent density functional theory (TD-DFT) methods with triple-zeta valence polarization (TZVP) basis set. It was shown that the type of functional theory used, Becke-Perdew (BP) and Leeuwen-Baerends (LB94) implemented in Amsterdam Density functional (ADF) program package, does not have essential influence on the geometry of studied compounds in both ground and excited states. However, significant differences were obtained for the band gap values with relativistic effects of the zero order regular approximation scalar corrections (ZORA) and LB94 functional seems to reproduce better the experimental optical band gap of these systems.


Introduction
Molecular conductors based on radical cations of tetrathiafulvalene (TTF) 1 and its derivatives have been of major interest in the last decades 2 .The structures of molecular materials type donor-acceptor 3 , are built on stacks of organic cation with large transfer integrals between nearest neighbours to result in band formation, where partial filling due to removal of some electrons provide superconducting, metallic, spin density wave 4 , charge density wave and semiconducting states.The properties of these salts depend on structures of chemical modification of the organic cation or inorganic anion.The charge transport pathway in organic semiconductors [5][6][7] is considered to be along the direction of maximum π orbital overlap between the organic molecules subsystems.Some semi-empirical theoretical studies 8 have been done on the dimensionality of these salts, which is generally imposed by the overlap mode developed in the organic subsystems.Among the numerous TTF ligand systems investigated in these last twenty years, the most extensively studied are those containing pyridine and bipyridine for the elaboration of metal complexes 9 .Like the first cobalt complexe containing TTF-pyridines based on the coordination of the CoBr 2 fragment by tetradendate 4,5 bis(2-pyridyl-methylsulfanyl)-4',5'-ethylenedithio-TTF 10,11 .A variety of such class of compounds have been prepared by varying the included guest organic molecule, which leads to a new family of hybrid semiconductive coordination network [12][13][14][15] .
These extended structures based on organic-inorganic hybrids have been synthesized and reported by zhengtao Xu 16 .They are based on the coordination between bismuth trichloride and tribromide (BiX 3 , X= Cl, Br) and the different polycyclic aromatic ligands within multiple chelating thioether groups, that leads to the corresponding abbreviations: HMTT, HETT and HiPTT (Scheme 1).Scheme 1. Structure of the organic ligands with atom labelling Do the solid-state electronic properties depend on nature of bond coordination of Bi-S and Bi-X of such systems.What is the correlation between band gap and dimensionality 17 .A large number of density functional theory (DFT) studies have treated excited state properties based on the time-dependent (TD) method.Most of these studies employ the geometric structure of the electronic ground state 18,19 .DFT and TD-DFT methods are the most widely used tool for theoretically evaluating excited state energies and simulating the UV-vis spectra of organic and hybrids compounds in molecular and solid state level 20 .In this paper we present results of our studies of structure of polycyclic aromatic ligands of 2,3,6,7,10,11-hexakis (alkylthio) triphenylene in the molecular level with ADF.

Experimental
The problem of large organic materials is the inefficient predicting of the band gap.The π-π interactions are one of the important noncovalent intermolecular forces especially when they involve aromatic rings, these weak bonds are problematic for DFT calculations and commonly used exchange-correlation functionals do not include effects such as dispersion interactions.The studied compounds are large systems and the electron correlation methods such as MP2 and CCSD(T) generally treat such interactions accurately, but these computations are difficult due to their high computational cost.DFT based methods, provide reasonable approximations with better computational efficiency.DFT method 21 for ground state and TD-DFT [22][23][24] for excited states calculations have been carried out with the Amsterdam Density Functional (ADF) program package 25,26 .Several pure and hybrid functionals were used but globally pure functionals (BP and LB94) gave better results.We also used pure meta-GGA functional M06-L for noncovalent interactions.The electronic configurations of all atoms were described by a valence-triple-polarized Slater-type orbitals (TVZP-STO) basis set 27 .For systems containing Bismuth atoms, the scalar relativistic effects of zero order regular approximation (ZORA) 28,29 are considered.The core electrons were kept frozen.The geometries of studied compounds based on experimental X-ray were optimized in solid state and calculated at LB94 and BP level theory without any symmetry constraints.

Results and Discussion
Structural studies These compounds 16 (Figure 1) feature different dimensionalities 30,31 architectures framework from 0D to 2D.The experimental measurements of the electronic band gap of all compounds vary between 1.64 eV for the 2D network of 3-HMTT•2BiBr 3 to 2.98 eV for the isolated (0D) HMTT, suggesting that Bi-S and Bi-X bonds improve the electronic interactions rather than π-π stacks interactions between organic molecules.We notice, in all structures, the intermolecular packing of columns of organic ligands which is dominated by π-π stacking 32 of the large aromatic molecules.The calculated bond lengths from optimized structures, are listed in Table 1 and compared with the corresponding values from the X-ray data.

DFT calculations
At non-relativistic level using BP 33 and LB94 34 functionals, we notice that BP functional gives good estimation of the gap, as mentioned in Table 2.The relativistic effects of the ZORA scalar corrections doesn't influence substantially the band gap values obtained, except for 3-HMTT•2BiBr 3 .For the compounds 0-HMTT, 2-HMTT•BiBr 3 and 4-HETT•2BiBr 3 , the deviations from experimental values are 0.23 eV, 0.18 and 0.17 respectively.The use of LB94 functional at relativistic level, provide a better agreement with experimental values.LB94 functional satisfy the asymptotic conditions and improves the performance of computing long range behaviour.We also carried out calculations on first compound (0-HMTT) using the M06-L 35 functional, which yields good results, but M06 36 family of functionals is not well tested for large systems containing heavy elements.Therefore, the results obtained for other compounds are not reliable.

TD-DFT calculations
Single point time dependent density functional theory [37][38][39] calculations including ten lowest singlet-singlet transitions were performed by employing the GGA-BP functional at non relativistic level, in order to obtain the character of electronic transition and oscillator strength of 0-HMTT, 1-HMTT•BiCl 3 (1-A).The results are listed in Table 3.Only the singlet-singlet transitions are mentioned, singlet-triplet transitions are not optically forbidden but they correspond to zero strength oscillator.We can notice that the calculated energies of S 0 state which correspond to the lowest excitation energy occur at equivalent energies with those of DFT level.The highest occupied molecular orbital (HOMO) of the system involved in the transition is mainly localized on the organic part, while the lowest unoccupied molecular orbital (LUMO) is entirely confined by the BiCl 3 entity as illustrated in the molecular orbital (MO) plots and displayed in Figure 2. Similar conclusions are obtained for compound 1-HMTT•BiBr 3 (1-A).Two major electronic transitions for the compound 0-HMTT exhibiting a large oscillator strength and assigned to S 0 ---S 4 and S 0 ---S 5 correspond essentially to HOMO-LUMO+1, HOMO-1-LUMO, and HOMO-1-LUMO+2, HOMO-LUMO and their energies are close to the experimental gap.These excitations are local type within 0-HMTT.The visibility of the S 0 ---S 1,2,3 transitions seems highly improbable, since the oscillator strength is very weak.However, for 1-HMTT•BiCl 3 (1-A), the S 0 ---S 1 transition which correspond to HOMO-LUMO excitation, is pure charge transfer type.The frontier orbitals 40 of the studied compounds, calculated at the GGA-LB94 41,42 /TZP and relativistic level of theory are shown in Figure 2. The HOMO's show contributions exclusively from the organic ligands in almost constant percentage and are generally of bonding character, while the LUMO's are most of antibonding character and essentially delocalized over the inorganic chain.It is interesting to notice that the frontier orbitals of compound 1-HMTT•BiCl 3 and 2-HMTT•BiBr 3 are quite the same, producing a similar band gap, 1.82 and 1.75 respectively and similar electronic transitions.The interactions between orbitals of Bi and S atoms are of antibonding character, they increase the band gap value whereas major interactions between Bi and Br atoms of bonding character are getting shorter and decrease the band gap.

Conclusion
In this paper, the structural and band gap of a semiconductive network hybrid compounds were computationally explored.Their vertical singlet-singlet electronic excitations were calculated and characterized by employing TD-DFT methods.We have assessed the efficiency of different methods and functionals for calculating the optical band gaps.It was found that theoretical calculations at molecular level were adequate to provide a reliable accuracy for estimation of the band gap, notably when using rationalized functionals such LB94 in the aim of reproducing the experimental values.The TD-DFT calculations point out that the most probable two transitions of HMTT belong to the local excitations, and the S 0 ---S 1 transitions for 1-HMTT•BiCl 3 and 2-HMTT•BiBr 3 belong to the charge transfert excitations.
For the present structures, the LUMO, which consists essentially of Bi-X bonds of the inorganic networks, is the key issue in determining the band gap, and the variations of the frontier orbital energies resulting in reduced band gaps correlates well with the increase of dimensionality.
•2BiBr 3 DFT and TD-DFT Study of Structure and Properties S197

Table 1 .
Structural and electronic parameters of all described compounds

Table 2 .
Band gap calculated energies at DFT molecular level

Table 3 .
TDDFT calculation of excitation energies (E) and oscillator strengths (f) of the