In the current study, the reference molecule was [19] was modified with different end-capped groups and in this way five freshly fabricated molecules N1-N5 are obtained. Absorption maximum wavelength of reference molecule is obtained after its optimization using level DFT 6-31G(d,p) on four chosen functionals i.e. B3LYP, CAM-B3LYP, ωB97XD, and MPW1PW91. The λmax values obtained on these functionals are 682, 532, 514, and 646 nm, respectively. The computationally obtained λmax on B3LYP functional matched precisely to the experimental data of reference which is 682 nm. It can also be seen through Figure 1 showing the comparison between the maximum absorption wavelengths obtained computationally and experimental data. This also justifies the use of B3LYP functional for further computational analysis done on the newly designed molecules N1-N5.
3.1 Frontier molecular orbital analysis
The two-dimensional structure of the reference molecule and newly modified acceptor groups are shown in Figure 2. FMO analysis demonstrates the optical properties of reference molecules and newly tailored molecules. It related the energies of both HOMO and LUMO [20]. HOMO and LUMO of R and newly fabricated molecules obtained through FMO analysis are shown in Figure 3. HOMO influences the bonding properties while LUMO influences the anti-bonding properties in NFA molecules on the ground state and excited state. [21] If stronger electron-withdrawing groups are present within the acceptor part of the molecule then it helps to increase the λmax value. A molecular orbital having higher or lower energy also determines its stability. The more stable a molecular orbital is the more ease of electronic transportations throughout the excitation process [22].
A less stable filled HOMO plays a more effective role in electronic excitation than a more stable HOMO. It is more effective to have LUMO of higher energy along with HOMO of higher energy to have maximum absorption of solar photons for electronic excitations. [23] The LUMO should be stable enough to hold the transported electrons during the excitation process for more time and competently. The acceptor region is the LUMO in PSCs which if perfectly tuned can be useful in capturing more photons and effectively converting them into electric signals to make SCs more proficient. The electronic transportation rate between HOMO and LUMO is directly related to the percentage of electronic transitions in an excited molecule [19].
The graphic representation of molecular orbitals of R and newly fabricated molecules are shown in figure 3.
HOMO describes where the electronic population is present in the donor part of the solar cell. Whereas LUMO elaborates the possibility of transportation of electronic population towards the acceptor region of SCs. The more electron capturing ability the acceptor part has, the more it can make the electrons get transported towards the acceptor part from the donor part. In the current study, the HOMO of the reference molecule and all newly designed molecules are identical, showing the presence of an electronic population on the donor region of the SCs. However, the LUMO graphs show that the electronic density is distributed all over the molecule but is denser on the acceptor groups. In N1, the LUMO graph shows that the electronic population is spread all over but is richer on one side of the molecule. N2 LUMO shows electron density present all over the molecule but most of this density is accumulated on both acceptor sides of the molecule. In N3, N4, and N5 the electron population is present all over the molecules but is denser on the acceptor regions.
Thus, these outcomes proved the electron-deficient nature of the acceptor groups, and the best electronic flow from the donor part towards the acceptor part is shown by N2 because of the stronger electron capturing effect of its end capped groups i.e., dinitro and thiochloro groups. The computational calculations give us data about the EHOMO and ELUMO and of R and newly fabricated molecules N1-N5 which is displayed in Table 1.
Table 1
Energies of HOMO, LUMO, and band gap Eg of R as well as N1-N5
Molecules
|
HOMO energy (eV)
|
LUMO energy (eV)
|
Eg
|
R
|
-5.62
|
-3.48
|
2.14
|
N1
|
-5.85
|
-3.83
|
2.02
|
N2
|
-5.74
|
-3.73
|
2.01
|
N3
|
-5.84
|
-3.79
|
2.05
|
N4
|
-5.69
|
-3.57
|
2.12
|
N5
|
-5.77
|
-3.69
|
2.08
|
These calculations revealed that the energies of HOMO and LUMO of newly fabricated molecules are lower than that of R. The increase in energy is due to the increase in conjugation in acceptor sides connected to an asymmetric central unit. This also caused an increase in absorption maxima. Reduced the EHOMO and ELUMO, reduced are the energy losses and improved open-circuit voltage which plays a vital role to facilitate electronic transitions to give better efficiencies. [24, 25]
The energy of HOMO of the reference and five newly fabricated molecules are shown in an increasing order N1< N3< N5< N2< N4< R. While the increasing order of LUMO energy of reference and newly fabricated molecules is N1< N3< N2< N5< N4< R. As is clear that the most minimum energies of molecular orbitals are shown by N1 because of stronger electron capturing end-capped groups i.e., two dicyano groups and improved conjugation. It is followed by N3 containing one acid and three cyano groups on terminal parts which makes it more electron-deficient and stronger electron-withdrawing acceptor moiety than N2 (one thiochloro and dinitro end-capped groups), N5 (two acid and dicyano end-capped groups), and N4 (dicyano and dichloro groups). The highest values of EHOMO and ELUMO are displayed by N4 when compared to all newly fabricated molecules which are caused to relatively less strong electron capturing end-capped groups.
The energy band gap of R and the newly tailored molecules is shown below in decreasing order R >N4 >N5 >N3 >N1 >N2. The energy bandgap is the difference between ELUMO and EHOMO. By comparing the energy band gap exhibited by all newly fabricated molecules and R molecules, we deduced that the energy band gap of N1-N5 molecules is smaller than the R molecule because of the more electron-withdrawing effect influenced by the terminal groups. The least energy band gap is displayed by the N2 molecule that has an acceptor region containing dichloro and thiochloro functional groups. N1 has a higher bandgap than N2 but lesser than N3, N5, and N4 because of its two dicyano groups. N3 containing one acid and three cyano groups in acceptor moiety exhibits a greater energy band gap than N2 and N1. N3 is followed by N5 (two acid and dicyano electron-withdrawing groups), and N4 (dicyano and dichloro terminal groups). The bar chart representation of ELUMO and EHOMO, and their difference (Eg) is shown in Figure 4.
The FMO studies gave us conclusion that all the newly fabricated molecules N1-N5 shows better electron capturing nature than R. And among all the newly fabricated molecules, most appropriate results are displayed by N2 making it a good choice to give a proficient SCs.
3.2 Partial density of states
The partial density of states (PDOS) technique relates the bonding, anti-bonding atoms, and molecular orbitals. The PDOS graphs of reference and newly fabricated molecules N1-N5 are displayed in figure 5. From the graphs, the change in terminal groups of acceptor parts shifted the electronic density towards itself. The overall study of the electronic distribution revealed that all the new NFAs showed proficient electronic distribution along with improved charge transportation from the donor part of the SCs to the acceptor part relative to the R molecule.
This technique is used for further clarifying the results obtained from FMO analysis. The density of states calculations of reference and all newly fabricated molecules are done on the same functional level B3LYP using a basis set 6-31G(d,p). The left side of the PDOS plots symbolizes the HOMO region while the right side is symbolizing the LUMO region of R and N1-N5 molecules. The red lines characterize the comparative intensity of the donor part while the green lines are of the acceptor part. The HOMO of all the fabricated molecules shows that the electronic population is mainly on the core unit while in the LUMO, this electronic population is shifted on the acceptor region more than the reference molecule. The proficient electronic intensity transition of reference and all the newly designed molecules are shown in decreasing order N2 >N3 >N5 >N1 >N4 >R.
3.3 Molecular Electrostatic Potential (MEP)
Molecular electrostatic potential analyzes the electron’s distribution in the molecule indicating its electron-deficient and electron-rich regions. [26] MEP plots of reference and newly fabricated molecules N1-N5 are shown in Figure 6. The molecules are colored showing different regions according to electronic distribution and the scale indicates how electronic distribution relates to the colors.
Three major colors are present in the plots as well as in scales i.e., red, blue, and green which indicates an abundance of positive charge, an abundance of a negative charge, and a neutral region respectively. The reference and all newly fabricated molecules N1-N5 showed a similar trend in MEP plots indicating the donor part in blue color showing its electron-rich and electron-donating nature while the acceptor end-capped groups are in red proving their electron-deficient and electron-withdrawing nature.
3.4 Optical Properties
Optical properties of R and newly fabricated molecules N1-N5 are analyzed using TD-SCF with basis set 6-31G(d,p) and solvent chloroform along with model CPCM. This analysis gives information about the absorption maximum in the electromagnetic spectrum. [27] Optical properties include maximum absorption wavelength (nm), transition energy (eV), oscillation strength (f), and major contributing orbitals.
The wavelength of maximum absorption (λmax) of R and new fabricated molecules N1-N5 are 682, 729, 735, 714, 696, and 708 nm respectively. All newly tailored molecules have greater λmax as compared to R while all the values are within visible spectral range with N2 having the highest λmax value due to electron-withdrawing effect caused by thiochloro group along with dinitro group present in its acceptor moiety. It is followed by N1, N3, N5, and N4 respectively. N1 shows higher λmax than N3, N5, and N4 due to the presence of two dicyano groups in its acceptor part. The difference in acceptor groups of N1 and other molecules with lower λmax is that in N3 one cyano group is replaced by an acid group, in N5 two cyano groups are replaced by two acid groups while in N4 two cyano groups are replaced by two chloro groups. The increase in absorption maximum is known as redshift. The difference between λmax of newly fabricated molecules from the reference molecules gives us the value of the red shift shown by our designed molecules. The redshift shown by N1-N5 compared to R is 47, 53, 32, 14, and 26 nm respectively. It is clear from this difference that acceptor groups D1-D5 present on molecules N1-N5 show more electron-withdrawing properties and among all these newly fabricated molecules, N2 is showing maximum redshift.
Excitation energy is also known as transition energy is also an important optical property that defines the charge transportation trend in the desired molecules. Smaller excitation energy makes the faster electronic transition from HOMO to LUMO making the molecules have greater charge mobilities and conversion efficiencies. In our study, all the tailored molecules have smaller transition energy than R which makes them have higher charge mobilities and PCE values than that of the R molecule. N2 has the lowest excitation energy value than the other tailored molecules i.e., 1.69 eV followed by N1 (1.70 eV), N3 (1.73 eV), N5 (1.75 eV), and N4 (1.78 eV), respectively as shown in Table 2. Thus, it is concluded that N2 molecule having D2 terminal group is proved to be the best choice among the newly fabricated molecules while all the N1-N5 NFAs show better results than the reference molecule.
Table 2
The computationally calculated and experimentally recorded λmax (nm), Excitation energy (eV), oscillator strength, major contribution of molecular orbitals
Molecules
|
Calculated λmax (nm)
|
Experimental λmax(nm)
|
Energy (eV)
|
Osc. Strength
(f)
|
Assignment
|
Dipole Moment
|
R
|
682
|
682
|
1.82
|
2.1932
|
HOMO→LUMO (99%)
|
6.71
|
N1
|
729
|
---
|
1.70
|
1.8572
|
HOMO→LUMO (98%)
|
6.87
|
N2
|
735
|
---
|
1.69
|
1.8184
|
HOMO→LUMO (98%)
|
3.60
|
N3
|
714
|
---
|
1.73
|
2.0238
|
HOMO→LUMO (98%)
|
7.40
|
N4
|
696
|
---
|
1.78
|
2.0189
|
HOMO→LUMO (98%)
|
7.07
|
N5
|
708
|
---
|
1.75
|
1.9664
|
HOMO→LUMO (98%)
|
5.44
|
3.5 Dipole Moment
The dipole moment is an important factor having a great effect on the efficiency of PSCs. Systematically calculated dipole moment values of R and N1-N5 molecules have been shown in Table 2.
It gives information about the solubility of the investigated molecule in an organic solvent i.e., chloroform in our case. A higher dipole moment indicates greater solubility in the solvent. The N3 molecule has the highest dipole moment of 7.40 D followed by N4, N1, R, N5, and N2 respectively. Greater dipole moment helps molecules to be self-arranged for better charge mobilities.
3.6 Reorganization Energy
Reorganization energy is used for the systematic calculation of electrons and holes mobilities. The holes and charge mobilities calculated systematically help in elaborating the working of SCs. Charge mobility has an inverse relation with reorganization energy in a way that the greater the reorganization energy smaller the charge mobilities. This depends on many aspects including structural properties of anions and cations.
The geometry of anion defines the transportation of electrons from a donor while the geometry of cations describes the hole accumulation in the acceptor part of SCs. So, reorganization is used to study the electron transportation between the donor and acceptor. It is categorized into two classes i.e., external, and internal reorganization energy. We focused only on the latter type and neglected the external reorganization energy because of no environmental factor affecting investigated molecules.
Reorganization energy calculations as shown in Table 3 revealed that N1 and N3 showed the lowest energy values which makes these two molecules have the highest electron mobilities. All other molecules show comparable results.
Table 3
Reorganization energy of electrons and holes of R and N1-N5 calculated at B3LYP, 6-31G(d,p) level of DFT
Molecules
|
λe (eV)
|
λh (eV)
|
R
|
0.0087
|
0.0069
|
N1
|
0.0073
|
0.0074
|
N2
|
0.0119
|
0.0076
|
N3
|
0.0075
|
0.0091
|
N4
|
0.0091
|
0.0076
|
N5
|
0.0094
|
0.0084
|
3.7 Transition Density Matrix and Binding Energy
The transition density matrix technique is utilized for assessing the electronic transitions within the reference and newly fabricated molecules (N1-N5). It is done also on the same functional as above i.e. B3LYP with basis set 6-31G(d,p). As hydrogen atoms have little effect on transition, so it was neglected. The TDM graphs of R and new molecules N1-N5 are displayed in Figure 7.
TDM analysis is used to study the excitations, electron-hole localization, and relation between the donor and acceptor part within the molecule. For this study, we differentiated the reference and newly designed molecules into two main parts i.e., donor and acceptor region. It can be seen through the plots that the holes and electrons of exciton are accumulated in the donor and acceptor region respectively. In R and N1-N5 molecules, most of the electron density is accumulated in the acceptor region with a little density on the donor part. This proved that the electronic transportation from the donor region to the acceptor region is improved efficiently by fabricating the end-capped groups within the SCs.
Binding energy (Eb) is an important factor influencing dissociation potential thus affecting the performance of a polymer solar cell. Binding energy has an inverse relation with charge mobilities. Molecules having greater binding energies have lower charge mobilities and lower current densities. This analysis is used to relate the Columbic force among the holes and electrons in a molecule. This interaction between holes and electrons is directly dependent upon the binding energy and binding energy is inversely dependent upon exciton breakdown in an excited state. Thus, it is concluded that greater forces of attraction between holes and electrons lead to higher columbic forces leading to higher binding energies causing smaller exciton dissociation energy at the excited state. The below-mentioned equation has been used to calculate the binding energies of R and newly fabricated molecules N1-N5. [28]
$${E}_{b}={E}_{H-L}-{E}_{opt}$$
3
\({E}_{H-L}\) is band gap between the bonding and anti-bonding molecular orbital, \({E}_{opt}\)is minimum first excitation energy. The binding energies of R and all the newly fabricated molecules are tabulated in Table 4. All the molecules show relatively smaller binding energies making them efficient molecules.
Table 4
Band gap(eV), excitation energy (eV), and Binding energy values of R and N1-N5
Molecules
|
EH−L
|
Eopt
|
Eb
|
R
|
2.14
|
1.82
|
0.32
|
N1
|
2.02
|
1.70
|
0.32
|
N2
|
2.01
|
1.69
|
0.32
|
N3
|
2.05
|
1.73
|
0.32
|
N4
|
2.12
|
1.78
|
0.34
|
N5
|
2.08
|
1.75
|
0.33
|
3.8 Open Circuit Voltage
Open circuit voltage is significant for evaluating the SC's efficiency. When light falls on SCs, the electron gets excited from the donor’s HOMO to the donor’s LUMO. Then this electron moves from the donor’s LUMO to the acceptor’s LUMO. Open circuit voltage (Voc) is the difference between EHOMO of the donor and ELUMO of the acceptor. It is also shown below in equation form.
$${V}_{OC}=\left({E}_{HOMO}^{D}-{E}_{LUMO}^{A}\right)-0.3$$
4
All our new molecules N1-N5 are NFA based, so we calculated the \({V}_{OC}\) using commonly used polymer donors i.e., PTB7-Th. The outcomes can be visualized in Figure 8. For more charge transportation from donor to an acceptor molecule, the energies of HOMO and LUMO play a significant role. HOMO with higher energy and LUMO with lower energy facilitate more charge transportation. [29]
3.9 Charge Transfer (CT) analysis through N2/PTB7-Th Complex
All newly fabricated molecules are acceptor type thus for the charge transfer analysis, we used PTB7-Th polymer donor. As the N2 acceptor molecule is proved to be the best choice among all newly fabricated molecules due to its lowest bandgap along with higher λmax, therefore we used this N2 molecule for CT analysis. The optimization of PTB7-Th and N2 complex was done on DFT along B3LYP with a basis set 6-31G(d,p). The interface interaction suggested that the electron population is on the boundary of acceptor and donor maximizing the charge transfer within the complex. The optimized structure is displayed in Figure 9. [30]
The charge distribution in the molecular orbitals is also studied at function B3LYP with basis set 6-31G(d,p). The outcomes as displayed in Figure 10 conclude that in HOMO, the donor has most of the electron population but in LUMO most of the electronic density resides on the acceptor molecule. This proves the electronic shifting from the donor part towards the acceptor part. [31–43] It also confirms the acceptor-type nature of our designed molecule N2.