A Theoretical Investigation of Charge Transfer Dynamics from Sensitized Molecule D35CPDT Dye to 𝑺𝒏𝑶 𝟐 and 𝑻𝒊𝑶 𝟐 Semiconductor

In this research, the dynamics process of charge transfer from the sensitized D35CPDT dye to tin(iv) oxide( 𝑆𝑛𝑂 2 ) or titanium dioxide ( 𝑇𝑖𝑂 2 ) semiconductors are carried out by using a quantum model for charge transfer. Different chemical solvents Pyridine, 2-Methoxyethanol. Ethanol, Acetonitrile, and Methanol have been used with both systems as polar media surrounded the systems. The rate for charge transfer from photo-excitation D35CPDTdye and injection into the conduction band of 𝑆𝑛𝑂 2 or 𝑇𝑖𝑂 2 semiconductors vary from a ~10 −26 to ~10 −29 for system and from a ~10 −52 to ~10 −56 for the system, depending on the charge transfer parameters strength coupling, free energy, potential of donor and acceptor in the system. The charge transfer rate in D35CPDT / 𝑆𝑛𝑂 2 the system is larger than the rate in D35CPDT/ 𝑇𝑖𝑂 2 a system depending on transition energy and driving energy. However, the charge transfer for both systems to be large is associated with large transition energy, decreasing driving energy and potential, and increasing strength coupling with Methanol solvent.


Introduction
Recently, the energy demand becomes increasingly become one of most problems because of the increased requirements in modern life. Photovoltaic and solar cell technology is utilized to convert solar energy to electric energy [1]. The dye-sensitized solar cell DSSC is the main promising renewable device because of the low cost and good conversion efficiency [2]. The molecules electronics are cooperated with solid materials to be used in various devices IHJPAS. 5 3 (3)2022 6 because they are easily fabricated and cheap [3]. Since O'Regan and Gratzel introduced a work in1990s,dye-sensitized solar cell DSSCs are attracting more attention to convert light to electricity at a low cost [4]. The dye-sensitized had been excitation by light-induced due to absorbed light and the electrons will be transferred from the dye to the conduction band of the semiconductor [5]. The electron transfer process is an important fundamental reaction in different devices and dye-sensitized solar cell devices [6]. It occurs by thermal excitation and photo inducement [6]. A basic classical theory for the charge transfer process was introduced by Rudolph Marcus to describe the transfer between two states donor and acceptor and was awarded Nobel Prize in 1992 [7]. The dye-sensitized had been excited by light-induced due to absorbed light, and the electrons will be transferred from the dye to the semiconductor's conduction band [5]. The electron transfer process is an important fundamental reaction in different devices and dye-sensitized solar cell devices [6]. It occurs by thermal excitation and photo inducement [6]. A basic classical theory for the charge transfer process was introduced by Rudolph Marcus to describe the transfer between two states, donor and acceptor, and awarded Nobel Prize in 1992 [7]. Despite electron transfer theory developments using various tools; analytical theory methods, time-resolved, spectroscopy, and computer simulation [8]. In recent years, many modifications have been proposed to dye-sensitized solar cell DSSC, including the fabrication of indoline organic dyes as sensitizers [9]. The dynamo red dye is a sensitized dye known as D35CPDT dye, as shown in figure (1).
It is stable, low cost, and high performance to use in DSSCs devices [10]. 2 and 2 are used to be an acceptor state in two device systems, its conversion of solar energy to electricity and to chemical energy [11].
2 is one of the n-type used in dyesensitized solar cells DSSCs [12]. SnO2 is a wide band gap of about 3.6 eV and has chemical and physical steady-state properties at different temperatures [13]. On the other hand, the 2 is an important n-type semiconductor used in solar cell devices. It has a wide energy band gap of about 3.2 eV, is low cost, nontoxic in nature and stable [14].The schematic of energy levels for sensitized D35CPDT dye with 2 and 2 semiconductors is shown in Figure (1) [15]. In this paper, we utilize the quantum model to investigate charge transfer dynamics from Sensitized D35CPDT Dye to the conduction band of 2 or/and 2 Semiconductor.

Theory
The charge transfer rate (Κ ) is given by Fermi Golden Rule to transfer charge from a donor state to an acceptor state and is given by [16].
Where ℎ is Planck constant, 〈 〉 is the charge transfer strength coupling, and ( )is the active density of electrons. The activation density profile is the function of the effective density of states and effective length . It has been determined from the expression [17].
The charge transfer rate in Eq.(1) together with Eq.(2) to reduce: The total effective density of states depends on the density of the state〈̂〉 = − (Λ+∆ 0 ) 2 4Λ √(4 Λ ) for the system and can be described by [18].
Where is the atomic density of a semiconductor. The charge transfer rate in Eq.(1) will be set through Eq.( 4) by Introduce the Fermi distribution function f ( ) for electrons as a function of the conduction band energy E C and electronic energy E in the system and may be written [19]: We can insert Eq.( 6) in Eq.(5) with integration over energy E(0 → E C to obtain: The corresponding driving energy ∆ 0 in the charge transfer process are obtained as a function of the conduction band energy E C of semiconductor and electrochemical potential ϕ and is computed by [20]. The results solve integral in Eq.(9) reduce to.
The potential energy is obtained by calculating the driving energy and transition energy and is given as [21].
Therefore, we insert Eq.(10) and Eq. (11) in Eq.( 9) to result: According to the continuum model of donor -acceptor theory, the transition energy Λ(eV) can be obtained [22]: Where and ° are charge and permittivity, and are the refractive index of solvent and semiconductor, and are the dielectric constant of solvent and semiconductor, is the radius of dye and D is the distance between the dye and the semiconductor. The radius is given as a function of molecular weight and density due to the spherical approach formula [23].
Where is Avogadro number.

Results
To study the charge transfer dynamics from D35CPDT sensitized dye to conduction band 2 or 2 In a semiconductor, we can calculate the rate of the charge transfer process in this system. It can enable us to know the electronic properties. The charge transfer rate at interfaces is calculated depending on the transition energy, driving force, potential at the interface, and strong coupling of charge transfer in the system. Transition energy was calculated depending on the donor-acceptor system with polarity media of solvents. The physical properties of solvents and 2 and 2 semiconductors are shown in Tables (1) and (2), respectively. Firstly, we must calculate the radius of D35CPDT dye and the distance ( ) between D35CPDT dye and 2 and 2 . Depending on the approach of the spherical formula, the radii of the D35CPDT molecule, 2 and 2 are estimated using Eq. (14), from which we may calculate the association transition energy, driving energy coefficient, the potential at the interface and charge transfer rate of the charge transfer process in both systems.The radii are calculated using the expression in Eq. (14) with inserting the value of molecular weight MW = 1125.58 g/mol [28], 150.71g/ mol [25] and79.866 g/ mol [27]   We can also calculate the driving energy for the charge transfer process using Eq.(8) as a function of the conduction band of E cb = 3.2 eV for 2 , E cb = 4.05 eV for 2 , and the electrochemical potential energy of D35PCDT are taken in the range ϕ=3.1 eV to 2.5 eV; results are listed in Table (4). Here, we can use values of the transition energy in the table (3) and the driving energy in the table (4) to calculate the potential energy using Eq. (11). Results are listed in the table (5) for D35CPDT / 2 the system with the driving energy ∆ 0 ( ) = 0.6 eV and D35CPDT / 2 system with the driving energy∆ 0 ( ) = 1.25 , respectively .

Discussion
The transition energy in Table (3) for both systems have been calculated in room temperature. It increases upon decreasing the refractive index and increases the dielectric constant (Ɛ) of solvents. Also, the transition energy increases with the decrease of the refractive index and dielectric constant of the semiconductor which is shown in Table (3). Table (3) shows the transition energy increasing with 2 which has low dielectric constant 2.19 and a low refractive index 1.45 compared with 2 has a large dielectric constant 55 and large refractive index 2.609.
According the results in Table (2), we can find the transition energy for both D35CPDT/ 2 and D35CPDT/ 2 systems has large values with Methanol solvent but the D35CPDT/ 2 system has smaller transition energy than D35CPDT/ 2 that has large transition energy. Table (3) shows the transition energy for D35CPDT / 2 system is larger than the transition energy for D35CPDT / 2 by 0.1 eV with the same solvent; this is because of the effect of dielectric and refrective index of semiconductor. However, the transition energy can be noted to be large; it has about 0.40022eV for D35CPDT / 2 and 0.51046eV for D35CPDT / 2 with Methanol and about 0.39569 eV for D35CPDT / 2 and 0.50434 eV for D35CPDT / 2 Acetonitrile solvents comparing to the low transition energy around 0.27036 eV for D35CPDT / 2 and 0.35762 eV for D35CPDT / 2 with the Pyridine solvent. Table (6) shows the charge transfer rate in range 1.6692E-47 to 4.3922E-26 with the strength |〈 〉| 2 = 1.25 × 10 −1 (eV/ state) 2 associated with the transition energy in the range 0.35762 -0.51046eV for D35CPDT /SnO2system. Table (7) shows the charge transfer rate in the range 1.2631E-52 to 3.9436E-45with strength |〈 〉| 2 = 1.25 × 10 −1 (eV/ state) 2 associated with the transition energy in the range 0.27036-0.40022 eV for D35CPDT / 2 system. A large charge transition rate of the D35CPDT/ 2 system is achieved 4.3922E-26 with the transition energy 0.51046 eV and the Methanol solvent. On the other hand, it can be seen that the charge transfer for D35CPDT/ 2 is to be large 3.9436E-45 associated with the transition energy 0.40022eV and the Methanol solvent. It is influenced by the transition energy and increased with the increased transition energy and polarity media with the increased dielectric constant. It decreases the refractive index in both systems. The results of the charge transfer rate found that the charge transfer process depends on the driving force. Hence, in both systems, there are the same values of electrochemical potential ϕ (.1-2.5eV) which are taken with different conduction band energy.  2 in the case of D35CPDT / 2 at ∆ 0 = 0.6 eV with Pyridine solvents. Also, we note, that the charge transfer rate is large from4.3922E-26 at coupling 1.25× 10 −1 (eV/ state) 2 to reach 1.8447E-29 at coupling 1.25× 10 −5 (eV/ state) 2 for D35CPDT / 2 with Methanol solvents. However, the charge transfer rate has become minimum at coupling 11.25× 10 −5 (eV/ state) 2 with Pyridine solvents at ∆ 0 = 1.25eV and to reach to 5.3049E-56 . On the other hand ,charge transfer rate reach to maximum 1.6563E-48 at strength coupling 1.25× 10 −5 (eV/ state) 2 for D35CPDT / 2 with Methanol solvent. The other parameter that is affected and limits the charge transfer process is potential energy. The other parameter that is affected and limits the charge transfer process is the potential energy. It further influences on charge transfer rate. Furthermore, we find the results in  (5) shows the potential in both systems increasing with the decrease of the transition energy and the charge transfer rate will be increasing tremendously with the decrease of the potential energy. The results in Table (6) indicate that D35CPDT contact to 2 with Methanol solvents at driving energy 0.6eV giving us a large rate compared to the results in a table (7) or D35CPDT contact to 2 with Methanol solvent and the D35CPDT / 2 is a good system and can be used in electronic devices.

Conclusion
In conclusion, the influence of transition energy in both systems can show the charge transfer rate, the rate increases with the transition energy increase. In contrast, the driving energy in both systems increases with the decreased electrochemical potential and substantially reduces the charge transfer rate. It can be concluded that the charge transfer for both systems increases with decreases in the potential, and the rate is large for D35CPDT / 2 compared to D35CPDT / 2 . A large charge transfer rate is observed from a charge donating D35CPDT dye attached to the 2 surface compared to the small rate of charge transfer from D35CPDT dye attached to the 2 surface with the same solvents. The results of the charge transfer rate allow for further systematic analysis of the influence of transfer parameters on the flow of electronic transfer from donor to an acceptor in the device's system and to know the influences on the efficiency of devices