DFT and TD-DFT Studies of 1,3,5-Tris (Dipheny1amino) Benzene Derivatives Based Hole Transport Materials: Application for Perovskite Solar Cells

The current study examined a series of 1,3,5-tris (diphenylamino) benzene derivatives used as hole transport materials in perovskite solar cells (HTM1-HTM9). DFT and TD/DFT with the B3LYP/6-311G basis set used for all calculations. The ground state geometry, frontier molecular orbital (FMO), photoelectric properties and reorganization energies and the absorption spectra were investigated. The energy levels of HOMO and LUMO orbitals were calculated for HTM1-HTM9, compared to all of the compounds under investigation and the spiro-OMeTAD, HTM 8 has the lowest HOMO energy level, indicating a favourable overlap with the MAPbI3 perovskite active layer.


Introduction
Perovskite solar cells (PSCs) have signi cant attention for academia and industry, Due to outstanding qualities such as e ciency, low cost, and simple assembly using roll-to-roll processing [1][2][3]. In photovoltaics, perovskite materials are gamechangers. The performance of perovskite solar cells has recently increased from 3.7 % to 25.2 % in a brief period, making it a formidable competitor to silicon solar cells [4]. A light-absorbing layer is commonly placed between the electron transport material (ETM) and PSCs' hole transport material (HTM). At the interface between the HTM and the perovskite layer, the HTM's role is to allow hole extraction while preventing charge recombination. To justify their use, suitable materials should have tremendous hole transport capacity and conductivity, high mobility [5]. In addition, the HOMO orbital energy level should be well aligned with the valence band of the perovskite material [6] and good solubility to aid processability, and low cost [7].
The e ciency of a solar device is determined mainly by charge generation and passage to the appropriate electrodes. After the electrons/holes are generated and transferred to their charge transport layers, they are collected at their corresponding electrodes, resulting in a photocurrent. Solar cells are also subject to undesired processes, such as recombining charged species, which reduces e ciency [8]. The charge generation, separation, and extraction processes must occur faster than the recombination process to achieve high e ciency. Charges (holes/electrons) are better extracted and transported from the absorbing layer to the electrodes when interfacial layers are present; they also prevent the ow of oppositely charged ions.
HTMs are critical to device performance because they: i) change the energy barrier height between an electrode and the active layer; ii) form a speci c contact for carriers; iii) protect a physical and chemical reaction between the electrode and the active layer; iv) aid in charge transport and collection; and v) improve the stability of the active layer/electrode and, ultimately, the device. Perovskite solar cells use a variety of HTMs, including inorganic, polymer, and small organic molecules. Inorganic HTMs need thermal deposition, whereas solution-processable deposition destroys perovskite lm, leading to a degraded absorption layer [2]. On the other hand, polymers have been associated with poor reproducibility due to batch to batch variance in polymerization or polydispersity. Another drawback of polymer HTMs is their low hole mobility, which their weak stacking would cause compared to small molecules. Molecules, on either hand, can be used as HTM to tackle repeatability di culties since structural changes can easily change the purity, mobility, and optical properties [9].
To create smaller molecules that make good HTMs for perovskite solar cells, researchers must rst investigate the structureproperties relationship, including the electronic structure of molecules as their constituents. Useful data about any molecule can be gathered by conducting a comprehensive theoretical and experimental study to understand bandgap, HOMO, and LUMO energy levels. This knowledge is crucial for understanding and designing appropriate compounds for solar cells. It has previously been reported that using DFT theory to predict geometry, electronic structure, and properties of conjugated materials is a good and trustworthy method [10,11].
The present study focused on derivates of 1,3,5-tris (diphenylamino) benzene (TDAB) molecule. Scheme 1 depicts the design of novel 1,3,5-tris (diphenylamino) benzene (TDAB) derivatives. The computational investigation of various e cient small molecules-based HTMs in perovskite solar cells employing the DFT method with B3LYP/6-31G levels of theory is presented here. The systematic theoretical study sought a comprehensive knowledge of structure-property co-relationships and explored numerous optimal geometry properties such as bandgap, HOMO, and LUMO.

Computational Methodology
The structural, electronic, and optical properties of the studied hole transport materials HTM1-HTM9 have been explored using density functional theory (DFT) and time-dependent density functional theory (TD-DFT). S 0 and S 1 geometries of all HTMs were optimized using Beckethree-Lee-Yang-Parr (B3LYP) [12,13]. For forecasting such geometries and attributes, functional analysis is effective [14][15][16]. The optimizations were carried out using the standard 6-31G basis set. [17][18][19] The polarizable continuum model (PCM) has been used to study the in uence of acetonitrile ( = 35.09) solvation. Gaussian 09W was used to calculate the geometries and electrical characteristics of neutral (ground and rst excited states), cationic, and anionic forms, as well as reorganization energies [20]. Gauss View (version 5.0.8) [21] was used to do visual checks as part of this process. As a result, none of the HTM1-HTM9 geometries has imaginary frequencies, ensuring energy minima.

Geometry parameters-Dihedral angles
Six dihedral angles of the three connecting units to the central benzene ring were selected for the TDAB and HTM1-HTM9 at the ground state for gas and solvent optimization and are presented in Table 1. The optimized structures ( Fig. 1) in the gas and solvent phase show that all molecules are non-planar with selected dihedral angles between 20 o and 50 o , and the non-planarity is due to the presence of sp 3 hybridized nitrogen a connecting atom [22]. Removal or addition of an electron from a molecule causes a noticeable effect on the value of dihedral angle as observed in the gas phase in Fig. 2, where the larger dihedral angle of anion optimized molecules for the angle C 1 -C 6 -N 7 -C 12 was observed compared to the dihedral angle of the cation indicating that much higher reorganization energy is required for the formation of anion from neutral molecule compared to the formation of cation from the neutral molecule. The TDAB and HTM1-HTM9 quickly form cation than anion molecule, thus e ciently transporting holes than an electron.

Ionization potential and electron a nity
According to the following equations [23], to determine the ionization potential and electron a nity using the DFT approach. (1) EA = E anion − E neutral (2) During the working of the perovskite solar cell, after an electron has been excited from the valence band of the perovskite active layer, an electron from the HOMO of the HTM has to drop and ll the hole left in the valence band of the perovskite; thus the ionization potential of the HTM has to be considerably lower to favour the process of electron transfer the HTM to the perovskite active layer, hence hole transfer from perovskite material to the HTM [24]. The lower the IP value, the easy formation of holes in the molecules under study; From Fig. 3 the lowest IP value was obtained by HTM 9; thus, tri addition of -NH 2 having a much contribution to the HOMO energy level has led to lower IP value [25].

Frontier molecular orbitals (HOMO-LUMO)
The HOMO and LUMO distributions and the energy levels of the structures examined are presented in Fig. 4 to help comprehend the electronic structure. In general, a good HOMO delocalization and an appropriate HOMO energy level relative to the valence band of perovskite are advantageous for improving the hole transfer integral and hole transport. The HOMO of the structures is estimated to be distributed over the entire molecule, whereas the LUMO is concentrated on the substitution core. It turns out that the HOMO is more broadly dispersed than the LUMO in the two derivatives, indicating that the derivatives have a good chance of being used as hole transport materials. Thus, energy and distribution of frontier molecular orbitals (FMOs) could be used to explain carrier transport features.
HOMO originated mainly from the entire molecule, while LUMO was primarily given by fragment A. As seen by the FMOs, HOMO delocalized approximately over the complete molecule for both molecules, while LUMO delocalized principally over fragment A for both. Hole transport is aided by the strengthening of the delocalization effect. There was also an increase in HTM/valence band overlaps between the HOMO of the TDAB as the HTM and the perovskite material, leading to enhanced charge extraction [24]. HTM9, which is produced by adding -NH2 to TDAB in tri addition, has the greatest HOMO level, as seen in Figure 2.  When the sun illuminates the PSC, electrons must be ejected from the perovskite active layer whose band energy gap is 2eV or less. For the HTM, the band energy gap has to be more than 2eV to avoid the parasitic loss of energy from the sun. The TDAB and HTM 1-9 show a band energy gap of between 4.0 to 4.3eV; thus, the low parasitic loss is expected to occur when used with the perovskite material. The solvent acetonitrile does not affect the band energy gap, as observed in Figure 6. On the other hand, HTM3, HTM6and HTM9, which mono, di, and tri substitution of -NH 2 respectively, were have lower values of band energy gaps.
This has been due to the highest HOMO energy levels attained because the -NH 2 is the most in uential electron-donating group among the selected groups and with a smaller bandgap, a redshift is expected to occur [29].

Charge transport properties
The reorganization energy (λ h/e ) refers to the energy change of the system, which is caused by the structural relaxation after the gain or loss of electrons. After a molecule has gained or lost an electron to form an anion or cation, the energy required for geometry modi cation is called reorganization energy. A change in dihedral angle gives a good prediction of a molecule's reorganization energy, but the reorganization energy of a molecule is inversely proportional to the charge mobility of the molecule. Thus lower reorganization energy of holes is a relevant factor for a hole transport material [30]. The reorganization energy is of two types: reorganization energy for the hole(λ h ) and electronic reorganization energy(λ e ). To optimize the anions and cations of the TDAB molecule and its derivatives to get the reorganization energies. The λ h and λ e energies calculated using the following equations [31][32][33]:  Table 3 and show in Fig. 7. From the Table 3, the order of hole reorganization energies are as follows: HTM8 > HTM9 > HTM3 > HTM5 > HTM6 > HTM2 > HTM7 > TDAB ≈ HTM1 > HTM4.  [39][40], but the level-splitting approach gives good accessibility to face-to-face stacking [40], and this con guration can improve − coupling [41]. V h is the hole transfer integral, and it can be calculated as follows [42][43][44][45][46]: V h is hole transport integral, E HOMO and E HOMO−1 are the HOMO level and HOMO-1 level of face-to-face model HTMs dimer [40].
For a good HTM, the hole transfer rate must be more than the electron transfer rate in magnitude to ensure effective charge extraction and transfer to prevent electron and hole recombination. From Table 3 and Fig. 8, HTM 9, having the highest hole transfer rate compared to other molecules, is not suitable as HTM because of its higher magnitude of the electron transfer rate.
Thus HTM6 showed the highest hole transfer rate of 1888.5 x 10 −10 s −1 with a minimum magnitude of the electron transfer rate.

Absorption spectra
The absorption properties were characterized using the TD-DFT method with a 6-311G basis set on the ground state optimized structures in both gas and solvent (acetonitrile) to obtain information about the involved in the electronic transitions. The calculated maximum absorption wavelength (λ max )of TDAB and HTM1-HMT9 in the gas and solvent state are listed in Table 4.

Figure 1
Optimized structures of the TDAB and HTM 1-9 in gas phase by using DFT/B3LYP method with 6-311G basis set.

Figure 2
Page 13/18 The dihedral angles of neutral, cation, and anion optimized structures of TDAB and HTM 1-9 in the gas phase.

Figure 3
Ionization potentials of TDAB and HTM 1-9 in gas phase by using DFT/B3LYP method with 6-311G basis set.
Page 14/18 Figure 4 HOMO and LUMO surface plots of the TDAB and HTM 1-9 in gas phase by using DFT/B3LYP method with 6-311G basis set.  Band energy gaps for TDAB and HTM 1-9 in gas and acetonitrile solvent by using DFT/B3LYP method with 6-311G basis set. Reorganization energy of holes and electrons for TDAB and HTM 1-9 in gas phase by using DFT/B3LYP method with 6-311G basis set.

Figure 8
Page 17/18 Charge transport rate diagram for holes and electrons of TDAB and HTM 1-9 in the gas by using TD-DFT/B3LYP method with 6-311G basis set.

Figure 9
Charge transport rate diagram for holes and electrons of TDAB and HTM 1-9 in the gas by using TD-DFT/B3LYP method with 6-311G basis set.

Figure 10
Charge transport rate diagram for holes and electrons of TDAB and HTM 1-9 in the solvent by using TD-DFT/B3LYP method with 6-311G basis set.