DFT Studies of p-N,N-(Dimethylamino) Benzoic Acid with Para or Meta–Electron Withdrawing or Donating Moieties for Dye-Sensitized Solar Cells (DSSCs)

Abstract

Solar energy is receiving considerable attention worldwide. Our contribution here focuses on fabricating p-N,N-(dimethylamino) benzoic acid (4-DMABA) donor-π-acceptor derivatives for use in dye-sensitized solar cells (DSSCs). The gas-phase and solvated 4-DMABA and some of its electron donating or withdrawing ortho or meta derivatives were studied theoretically. Density functional theory (DFT) and time-dependent DFT (TD-DFT) were applied to visualize their structural, molecular, photoelectrical, electronic, and photophysical parameters. The parameters for monitoring DSSC efficacies include HOMOs, LUMOs, energy gaps, wavelengths, oscillator strengths, light harvesting efficiencies (LHE), electron injection driving forces (ΔG_inject), regeneration driving forces (ΔG_regen), open circuit voltages (V_OC), and short-circuit current densities (J_sc).

This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. Introduction

The rapid development and utilization of renewable energy are vital measures to provide clean energy sources. The steadily increasing global demand for energy, coupled with the depletion of harmful environmental effects, which are associated with the combustion of fossil fuels, has necessitated the rapid search for renewable energy sources [1]. At the present time, the global energy sources are mainly dependent on fossil fuels. This energy source is the main cause of global warming that brings about devastating climate changes as a result of the emitted carbon dioxide (CO₂) [2]. However, the alarming rate of depletion of the major conventional energy resources such as coal, petroleum, and natural gas, coupled with the environmental degradation caused by the process of harnessing these energy sources, has necessitated the investment in renewable energy resources that could provide sufficient power without degrading the environment through greenhouse gas emissions. These renewable energy sources include wind power, solar energy, hydropower, bioenergy, and geothermal energy.

Dye-sensitized solar cells (DSSCs) have received considerable attention due to their low-cost conversion of photovoltaic energy compared to the silicon-based semiconductor ones [3]. In particular, DSSCs are characterized by acquiring a wide bandgap semiconductor, typically titanium dioxide (TiO₂) that can be sensitized by molecular organic dyes. This architectural design, together with a transparent conductive oxide layer (TCO) and a redox electrolyte, typically iodide/triiodide, is capable of capturing light in the visible region of the spectrum [4].

Solar energy is considered the most promising renewable energy source for supplying the future with energy [5]. Consequently, dye-sensitized solar cells (DSSCs) have attracted ever-increasing attention in scientific research and in practical applications since the first report by O’Regan and Grätzel in 1991 [6] due to their low cost and high efficiency in converting sunlight into electricity. In DSSCs, the incoming light photons excite the dye electrons, which are injected into the conduction band of the nanocrystalline metal oxide. This step is followed by the regaining of electrons by the dye from the redox couple in the electrolyte solution [7]. Generally, a power-conversion efficient dye sensitizer has the following characteristics: The highest occupied molecular orbital (HOMO) energy must be below the conduction band minimum (CBM) of the semiconductor (TiO₂) and the lowest unoccupied molecular orbital (LUMO) energy should be higher than the energy of the redox electrolyte pair (I⁻/I⁻³).

The sensitizing dyes play important roles in DSSCs through maximizing the solar-to-electricity conversion efficiency [8]. In contrast to experimental results on metal-free organic dyes, the theoretical investigations are still lagging behind. Only a few research groups have studied the electronic structures and photophysical properties of the dye sensitizers [9] and the intramolecular electron dynamic process between dyes and TiO₂ nanocrystals [10, 11]. Wang et al. [11] have thoroughly studied theoretically 3-(10-butyl-8-(methylthio)-10H-phenothiazin-3-yl)-2-cyanoacrylic acid coupled with diketopyrrolopyrrole derivatives. In this context, the theoretical study of the structures of several benzoic acid derivatives has been conducted recently with considerable accuracy [12]. The structures of p-dimethylamino benzonitrile (pDMABN) [13], p-aminobenzoic acid (pANA) [14],and Ethyl-4-(dimethylamino) benzoate (4-EDMAB) were taken as references to study the effect of para-substituents on the aromatic-ring moiety. The structure of p-(dimethylamino) benzoic acid (hereinafter-DMABA), with the dimethylamino group as a para-substituent having relatively intermediate behavior as compared with the nitro and amino groups, is expected to yield more information about the cooperative electronic interaction in the para-substituted compounds.

In this study, we endeavor to monitor the characteristics of several donor-π-acceptor (D-π-A) dyes having –N(Me)₂ and –COOH moieties as donors and acceptors, respectively. The electronic structure and optical absorption properties of eight dye sensitizers (see Scheme 1) in the gas-phase and dimethyl sulphoxide (DMSO) were investigated by using density functional theory (DFT) and time-dependent density functional theory (TD-DFT). Based on the calculated results, we analyzed the role of the different electron-donor or–acceptor groups in tuning the geometries, electronic structures, and optical properties. In addition, we aim to see the effects of the donors or the acceptors of the sensitizers on the open circuit photovoltage (V_oc) and the short-circuit current density (Jsc) of the cell by discussing the key factors affecting V_oc and J_sc with the goal of finding potential sensitizers for use in solar cells.

2. Computational Details

The ab initio molecular orbital calculations were performed using the Gaussian09 suites [15] and viewed by GaussView software [16]. All calculations for structural optimization were done by density functional theory (DFT) [17] using the B3LYP (Beck three parameter Lee-Yang-Parr) [17], the Coulomb-attenuating Beck three parameter Lee-Yang-Parr (CAM-B3LYP) [18], the pure functional, Perdew, Burke, and Ernzerhof (PBEPBE) [19], and the long-range corrected hybrid ωB97XD [20] functional. All the geometrical structures of the substrates yielded global minima in their potential energy surfaces. This is achieved by performing vibrational calculations that gave no imaginary frequencies. The time-dependent density functional theory (TD-DFT) [21] was used to simulate the absorption and emission spectra of the substrates which were monitored by the Chemissian Software [22]. The effects of basis sets were investigated by using the triple-zeta without and with polarization and diffuse functions on hydrogen and heavy atom basis sets: 6-311G, 6–311++G, 6–311G${}^{\mathrm{\ast \ast }}$, 6–311+ G${}^{\mathrm{\ast \ast }}$, and 6–311++G${}^{\mathrm{\ast \ast }}$ [23]. The HOMO and LUMO, electron absorption and emission spectra, oscillator strengths (f), and light harvesting efficiency of the optimized substrates were investigated using the same methods and basis set in the gas phase. The dimethyl sulphoxide (DMSO) solvated substrates were studied using the polarizable continuum model (PCM) [24] for simulating their absorption and emission spectra.

3. Result and Discussion

3.1. The Geometry

Table 1 lists some selected bond lengths, angles, and dihedral angles of the neat 4-DMABA and Ti⁺⁴-bound complex computed by using PBEPBE, B3LYP, CAM-B3LYP, and WB97XD functionals with 6–311++G${}^{\mathrm{\ast \ast }}$ basis sets in the gas phase. The atom numbering of these two substrates are shown in Figure 1, while their standard orientations are depicted in Tables S2 and S3. A quick look at Table 1 shows that the neat 4-DMABA estimated geometrical parameters using all DFT functionals are in excellent agreement with each other. The calculated exocyclic C1–N15 and C4–C11 bond lengths of 4-DMABA of ca. 1.377 and 1.471 Å, respectively, are in excellent agreement with those of its solid-state crystal structure; while the C11–O12 and C11–O13 bonds of the former are longer (ca. 0.04 Å) and shorter (0.09 Å), respectively, compared to those of the latter as a result of dimerization in the solid-state [25]. All DFT functionals have predicted completely planar gas-phase geometries, but the crystal structures have indicated deviations from a planarity of ca. 2–4° [25]. The exocyclic C1–N15 bond length is shorter than a typical C–N single bond by 0.094 Å [26] and longer than an exemplary C=N double bond by 0.105 Å [27]. Likewise, the exocyclic C4–C11 bond length is shorter than a model C–C bond length by 0.068 Å [28] and longer by 0.134 Å compared to a representative C=C double bond [29]. The multiple bond characters of these bonds are quite important in dictating the passage of charge from donors (N–N-dimethyl amine group) to acceptors (carboxyl moiety).

Table 1

Some selected bond lengths (Å) bond angles (°) and dihedral angles (°) of gas-phase 4-DMABA (D1) and 4-DMABA-T⁺⁴(OH)₄ (D2) which were calculated by using B3LYP, CAM-B3LYB, PBEPBE, ωB97XD functionals, and 6–311++G${}^{\mathrm{\ast \ast }}$ basis set.

Parameters	B3LYP		CAM-B3LYB		PBEPBE		WB97XD		Expt.${}^{\ast }$	Expt.#
	D1	D2	D1	D2	D1	D2	D1	D2
C1–N15(14)	1.377	1.375	1.378	1.370	1.387	1.377	1.378	1.372	1.376	1.368
C4–C11	1.472	1.463	1.470	1.461	1.473	1.464	1.473	1.464	1.472	1.475
C11–O12	1.212	1.274	1.207	1.268	1.224	1.285	1.208	1.275	1.248	1.271
C11–O13	1.365	1.284	1.354	1.275	1.376	1.295	1.376	1.267	1.282	1.278
O12–C11–O13	121.2	116.2	121.2	116.2	121.3	116.6	121.4	116.6	121.9	119.2
C6–C1– N15 –C20(19)	−180	−175.2	−180	−177.2	−180	−176.5	−180	−173.5	−178	−178.3
O12–C11– C4–C3	180	179.5	180	179.2	−180.0	179.6	180.0	178.9	176	179.2

${}^{\ast }$Taken from Ref.26 #Taken from Ref.31.

[figure(s) omitted; refer to PDF]

In comparison, the calculated gas-phase geometrical parameters of the Ti⁺⁴-bound complex using all DFT functionals are in complete coincidence with each other and agree satisfactorily with those of a DMABA-Zn bond complex [30] as shown in Table 1. Noticeably, the planarity of the neat dye is hardly lifted upon chelation with the titanium hydroxide. Here, again, the exocyclic C1–N15 and C4–C11 bonds have witnessed a slight shortening as a result of the bidentate binding of 4-DMABA with Ti(OH)₄. In addition, the parent dye O12–C11–O13 bond angle is closed by ca. 5° to facilitate the bidentate complexation. These observations could be harnessed as indicators for the existence of more charge transfer from the donor to the acceptor. As the charge transfer is a cornerstone in the functioning of solar cells; this parameter will be investigated more thoroughly in the upcoming sections.

3.2. Frontier Molecular Orbitals (FMO)

The Frontier molecular orbitals (FMOs) include some of the lowest unoccupied molecular orbitals (LUMOs) and a few of the highest occupied molecular orbitals (HOMOs). The HOMO-LUMO energy gap is an ideal quantum mechanical descriptor that plays a major role in governing a wide range of chemical interactions [31]. In Figure 2 are depicted the FMOs of the parent dye and its Ti⁺⁴-bound complex were computed by using the B3LYP/6311++G${}^{\mathrm{\ast \ast }}$ level of theory. As shown in Table 2, all the FMOs of the parent dye are stabilized upon chelation with Ti(OH)₄. The LUMO+2 for the neat dye is a π${}^{\ast }$-antibonding orbital spreading all over the dye skeleton, while that of the Ti⁺⁴-bound complex is crowding around the Ti-atom. The LUMO+1 is 0.07 and 0.24 eV below the LUMO+2 of the parent dye and its Ti⁺⁴-boud complex, respectively. Both of them are benzene ring π${}^{\ast }$-antibonding orbitals. The LUMOs are concentrated around the carboxylate chelating acceptor moiety as π${}^{\ast }$-antibonding orbitals. The LUMO of the neat dye is stabilized by 0.74 eV upon chelation. The HOMOs of both species are π-bonding orbitals engulfing the donor dimethylamino group. The complexation effect has decreased the energy gap of the neat dye by 0.6 to 0.7 eV, which means more charge flow [32]. The HOMO-1 and HOMO-2 of the neat dye are oxygen atom’s nonbonding orbitals and benzene π-bonding orbitals, respectively. Upon chelation, both of them characterize the π-bonding orbitals on the benzene moiety. They are 1.428 and 1.800 eV below the HOMO of the parent species, respectively: and 1.409 and 2.215 eV underneath the HOMO of the Ti⁺⁴-bound complex, respectively.

[figure(s) omitted; refer to PDF]

Table 2

The FMOs (eV), energy gaps (∆E/eV), dipole moments (µ/Debye), and absorption spectra maxima (λ_max/nm) of the gas-phase neat 4-DMABA and 4-DMABA-T⁺⁴(OH)₄ complex which was calculated by using different DFT functionals with 6–311++G${}^{\mathrm{\ast \ast }}$ basis set.

Parameters	B3LYP		CAM-B3LYB		PBEPBE		ωB97XD
	D1	D2	D1	D2	D1	D2	D1	D2
LUMO+2	−0.477	−1.279	0.583	0.094	−0.838	−1.966	1.260	0.715
LUMO+1	−0.543	−1.520	0.131	−0.057	−1.217	−2.222	0.858	0.597
LUMO	−1.165	−1.906	0.104	−0.486	−1.860	−2.592	0.751	0.157
HOMO	−5.759	−5.812	−7.067	−7.087	−5.006	−5.081	−7.580	−7.615
HOMO-1	−7.187	−7.221	−8.672	−8.682	−6.129	−6.418	−9.210	−9.222
HOMO-2	−7.556	−8.027	−9.359	−9.630	−6.366	−6.587	9.811	−10.123
∆E	4.594	3.906	7.171	6.601	3.146	2.489	8.331	7.772
µ	5.164	6.277	4.883	5.829	5.356	6.686	4.822	5.705
λ max	290.1	356.6	267.2	275.2	321.5	470.5	265.2	270.2

As a conclusion, all the as-investigated functionals have yielded narrower energy gaps and larger dipole moments upon chelation, in excellent agreement with that of Wang et al. [11]. This means that an easy charge flow occurs when the dye preys on the Ti (OH)₄ molecule. It is apparent that the pure PBEPBE functional has given the straight energy gap and larger dipole moment; while the dispersion ωB97XD functional produced the colossal energy gap and smaller dipole moments. The order of decreasing energy gaps among the applied functionals is as follows: ωB97XD > CAM-B3LYP > B3LYP > PBEPBE [33]. This trend is inverted by the calculated dipole moments. The pure PBEPBE functional yielded the narrowest energy gap by stabilizing the LUMO and destabilizing the HOMO; while the ωB97XD functional gave the widest energy gaps through destabilizing the LUMO and stabilizing the HOMO [34]. As the hybrid B3LYP functional gave energy gap suitable for reasonable charge flow; it was adopted for simulating the absorption and emission spectra and the theoretical testing of DSSCs [35].

3.3. Electronic Excitations of 4-DMABA Derivatives

The π⟶π${}^{\ast }$ and n⟶π${}^{\ast }$ electronic transitions in π-conjugated organic compounds are recognized for leading to UV-visible spectra [36, 37]. Table 2 lists the maximum absorption wavelengths of gas-phase 4-DMABA dye (D1) using the as-investigated functionals with 6–311++G${}^{\mathrm{\ast \ast }}$ basis set. The parent (D1) absorption UV-visible bands calculated by B3LYP functional are in excellent agreement with its experimental ones [38]. In Table S1 (Supplementary Information), the electronic transitions of D1 are registered using B3LYP and PBEPBE functionals with different basis sets. The polarization functions have a propensity to underestimate the maximum absorption wavelengths [39], while the diffuse functions are liable to overestimating them [40]. That is, when the polarization [6-311G${}^{\mathrm{\ast \ast }}$] and the diffuse [6–311++G] basis sets were applied with B3LYP and PBEPBE functionals, the maximum absorption wavelengths were blue-shifted and red-shifted, respectively, compared with the values obtained by using the 6-311G basis set with these two functionals (See Table S1). Hence, it is recommended to use both the polarization and diffuse functions in simulating UV-Vis spectra [41].

Normally, molecules with large dipole moments have strong asymmetric electronic charge distribution and thus become more reactive and sensitive to external electric fields [42]. The theoretical UV-visible spectra of 4-DMABA using TD-B3LYP and TD-PBEPBE functionals with a 6–311++G${}^{\mathrm{\ast \ast }}$ basis set of theory are shown in Figures S1 and S2. TD-B3LYP/6-311++G${}^{\mathrm{\ast \ast }}$ predicted intense electronic transition bands at λ_max = 290 nm (f = 0.5297) which is red-shifted by ca. 11 nm compared to the experimental value of 310 nm [11, 38]. The calculations showed that these bands originate mainly from a HOMO- > LUMO transition (See Table S1). Moreover, the computed dipole moment using this level of theory of 5.164 Debye is in line with the values of the predicted electronic bands (See Table 2).

We have also investigated some D1 derivatives (D1.1-D1.7) by replacing the hydrogen atoms at the ortho or meta positions by two or four CH₃, OH, NH₂, F, CN, and NO₂ as electron donating or withdrawing moieties (cf. Scheme 1). Figure 3 depicts their optimized geometries using the B3LYP/6-311++G${}^{\mathrm{\ast \ast }}$ level of theory. Their standard orientations are registered in Tables S4–S10. Figure 4(a) depicts the absorption spectra of the DMSO-solvated D1-D1.7 dyes which have been simulated by using TD-B3LYP/6-311++G${}^{\mathrm{\ast \ast }}$ level of theory.

[figure(s) omitted; refer to PDF]

Table 3 lists the calculated HOMO, LUMO, bandgaps, absorption wavelengths, oscillator strengths, light harvesting efficiencies (LHE), and electronic transition assignments of the gas-phase D1-D1.7 derivatives using the B3LYP/6-311++G${}^{\mathrm{\ast \ast }}$ level of theory. On the one hand, the electron donating groups (CH₃, NH₂, and OH) at the ortho positions have widened the band gaps and hence blueshifted the wavelengths compared to those of the parent dye (D1). On the other hand, the electron withdrawing groups (F, CN, and NO₂) at the meta positions have straitened the bandgaps and accordingly redshifted the wavelengths [11]. When both electron donating (CH₃) and withdrawing (CN) ligands are used (D1.7); moderate results are obtained for both the band gap and absorption wavelength. These UV spectra originate mostly from HOMO to LUMO transitions.

Table 3

The calculated HOMO (eV), LUMO (eV), bandgap (∆E/eV), absorption wavelengths (λ_max/nm), oscillator strengths (f), light harvesting efficiencies (LHE), and electronic transition assignments of the gas-phase D1-D1.7 derivatives using B3LYP/6-311++G${}^{\mathrm{\ast \ast }}$.

Dye	HOMO	LUMO	∆E	λmax	f	LHE	Major transition assignment
D1	−5.759	−1.165	4.594	290	0.530	0.705	HOMO- > LUMO (97%)
D1.1	−5.624	−0.993	4.631	287	0.400	0.602	HOMO- > LUMO (91%)
D1.2	−5.227	−0.771	4.456	282	0.171	0.326	H-1- > LUMO (48%), H-1- > L+1 (46%)
D1.3	−5.870	−1.078	4.792	275	0.412	0.613	HOMO- > LUMO (77%)
D1.4	−5.310	−1.894	3.415	300	0.406	0.607	HOMO- > LUMO (92%)
D1.5	−6.709	−2.392	4.317	305	0.311	0.512	HOMO- > LUMO (72%)
D1.6	−6.691	−3.232	3.459	435	0.024	0.055	HOMO- > LUMO (99%)
D1.7	−6.599	−2.315	4.284	244	0.145	0.284	H1>L+1(60%), H3>LUMO(28%),

In Table 4 are registered the HOMO, LUMO, bandgaps (∆E), absorption and emission wavelengths, the emission oscillator strengths of D1.1–D1.7 solvated (DMSO (ε = 46)) derivatives which were obtained by using TD-B3LYP functional with 6–311++G${}^{\mathrm{\ast \ast }}$ basis set. Apart from D1.4, all the energy gaps of the elected dyes (D1.1-D1.7) are smaller than that of the parent dye(D1). The derivatives D1.6, D1.7 and D1.5 gave the smallest energy gaps amongst them. The absorption wavelength (λ_abs/nm) of D1.1 to D1.7 derivatives are slightly shifted compared to that of D1. The absorption wavelength of the derivatives having–I (inductive) with +R (resonance) effects (NH₂, OH, and F) were generally blueshifted compared to that of the parent D1; while those for the ones with–I effect (CN) were redshifted. In the methyl derivative (D1.1), the methyl groups with +I effect have redshifted the peaks. Similar trends have been shown by the emission spectra.

Table 4

The calculated excitation energy (E), absorption wavelengths (λ_max), emission wavelength (λ_em), emission oscillator strength (f), light harvesting efficiency (LHE), excited-state lifetime (τ), and Stokes shift (SS) of dye D1 and its derivatives (D1.1-D1.7) in a DMSO solvent medium. They were calculated by using the TD-B3LYP/6-311++G${}^{\mathrm{\ast \ast }}$ level of theory.

Dyes	HOMO	LUMO	E∆	E (cm−1)	λabs(nm)	λem(nm)	f	LHE	τ(ns)	Stokes shift (SS)
D1	−5.764	−1.423	4.341	31475	306	318	0.671	0.787	2.3	12
D1.1	−5.762	−1.669	4.093	31775	305	315	0.546	0.715	2.7	10
D1.2	−5.791	−1.655	4.136	31876	293	314	0.577	0.735	2.6	21
D1.3	−5.707	−1.749	3.958	32925	294	304	0.626	0.763	2.2	10
D1.4	−6.088	−1.541	4.547	32817	294	305	0.688	0.795	2.0	11
D1.5	−6.341	−2.425	3.916	28435	342	352	0.454	0.648	4.1	10
D1.6	−6.314	−3.300	3.014	30797	280	325	0.080	0.168	19.7	45
D1.7	−6.091	−2.383	3.708	25339	388	395	0.192	0.357	12.2	7

Furthermore, the emission spectra of the DMSO-solvated dyes D1.1–D1.7 are depicted in Figure 4(b), while the corresponding values for the orbitals responsible for the first excited singlet state (HOMO-LUMO contribution), excitation energy (cm⁻¹), maximum emission wavelength (λ_em), emission oscillator strength (f), excited-state lifetime (τ), and Stokes shift (SS) are presented in Table 4. The emission spectra arising from the S₁–S₀ transitions were assigned π${}^{\ast }$ ⟶ π character for all the studied dyes. Similar to the absorption spectrum, the emission bands were found to be related to the HOMO-to-LUMO transitions. It is noteworthy that the small values of the Stokes shift (SS) were obtained for all dyes. It is known that dyes with weak Stokes shifts present minimal conformational reorganization between the ground and excited state [43]. Our results showed that the spectral properties of the derivatives D1-D1.7 are weakly affected by these structural changes.

3.4. The Life Time of the Singlet Excited State (τ)

The first excited state (S₁) to the ground--state (S₀) decay step is extremely important for injecting the excited electron into the conduction band minimum (CBM) of the TiO₂ semiconductor. Thus, the lifetime (τ) of the excited state is an extremely crucial parameter for evaluating the charge transfer efficiency [44]. A dye sensitizer having an excited state with a longer τ value is expected to facilitate the charge transfer [45]. In Table 4 are listed the decay time (τ/nm) of the derivatives. They are obtained using $$\begin{array}{}\text{(1)}& \tau =\frac{1.499}{{E_{\text{em}}}^{2}f},\end{array}$$where $E_{em}$ is the emission energy in cm⁻¹ and f is the oscillator strength of the transition state [46]. As Table 4 shows, apart from D1.3 and D1.4, the τ values for all the derivatives are much longer than that for the parent D1. They increase in the order D1<d1.6.>2, CH₃ with CN, and CN groups, respectively, display substantially dynamic charge transfer and electron admission to the conduction band minimum of the TiO₂ semiconductor substrate. In addition, these three dyes could hinder the charge recombination process and boost the performance of DSSCs in comparison to D1. It is worth noting that the excited states of derivatives, in the more polar solvent (DMSO), live longer compared to the less polar ones [47].

3.5. The Overall Performance

The power conversion efficiency (PCE) of DSSCs is investigated by the short-circuit current density (J_SC), open-circuit photovoltage (V_OC), and fill factor (FF) values, as well as the intensity of the incident light (P_IN). It is estimated by applying Equation (2) [48]:$$\begin{array}{}\text{(2)}& \text{PCE}=\frac{1}{P_{\text{IN}}}\text{FF}\times V_{\text{OC}}\times J_{\text{SC}},\end{array}$$where FF is the ratio of the maximum power of the DSSC and the product of V_OC, J_SC, and P_IN [49]. As (2) shows, the impact of the electron withdrawing or donating groups on the product of V_OC and J_SC should be optimized to enhance the performance. V_OC can be computed by applying (3) [50],$$\begin{array}{}\text{(3)}& V_{\text{OC}}=\frac{E_{\text{CB}}}{q}+\frac{k_{B}T}{q}ln\frac{n_C}{N_{\text{CB}}}-\frac{E_{\text{redox}}}{q},\end{array}$$where k_BT is the thermal energy, q is the unit charge, and n_C is the number of electrons in the conduction band, N_CB is the conduction band attainable density of states, and E_redox is the electrolyte oxidation potential. V_OC is computed as an energy difference between the conduction band minimum of the TiO₂ semiconductor and the iodide/triiodide ($I^{-}/I_3^{-}$) electrolyte redox potential, which is assumed to be constant.

It is known that the value of J_SC in a DSSC can be computed by applying (4) [51]$$\begin{array}{}\text{(4)}& J_{\text{SC}}={\displaystyle \int LHE\lambda {\Phi }_{\text{inject}}{\eta }_{\text{collect}}d\lambda },\end{array}$$where LHE denotes the light-harvesting efficiency with respect to a given wavelength (λ_max), Φ_inject gives the electron insertion efficacy, and η_collect is related to the charge collection performance. In our proposed DSSCs, the electrode ($I^{-}/I_3^{-}$) is kept constant while the dye sensitizers are varied. Accordingly, η_collect turns out to be a constant.

However, LHE(λ) can be estimated by (5) [52]:$$\begin{array}{}\text{(5)}& \text{LHE}\lambda =1-{10}^{-f},\end{array}$$where f denotes the oscillator strength of the absorption wavelength (λ_max). It is known that the LHE and the free energy for electron injection (∆G_inject) are the two important elements that impact J_SC. The values of LHE of the elected DMABA derivatives should be high to maximize the performance of the DSSCs. Higher oscillator strengths enhance the light harvesting efficiencies and maximize the overlap with the solar light, especially over the whole UV–visible spectral region. The light harvesting efficiencies (LHE) using TD-B3LYP/6-311++G${}^{\mathrm{\ast \ast }}$ listed in Table 4 of the different DMSO-solvated DMABA derivatives (D1.1-D1.7) range between 0.168 and 0.795, indicating that these derivatives provide different photocurrent performances. J_SC can also be increased through enhancing the electron injection free energy ($\mathrm{\Delta }{G}_{\text{inject}}$) which can be computed by Equation (6) [53]$$\begin{array}{}\text{(6)}& \Delta G_{\text{inject}}=\underset{\text{OX}}{\overset{\text{dye}\ast }{E}}-\underset{\text{CB}}{\overset{{\text{TiO}}_2}{E}},\end{array}$$where $E_{CB}^{Ti{O}_2}$ denotes the reduction potential energy level of the TiO₂ conduction band and $E_{OX}^{dye\ast }$ gives the oxidation potential energy of the excited state DMABA derivatives, and $E_{CB}^{Ti{O}_2}$ which can be estimated by (7) [54–56]:$$\begin{array}{}\text{(7)}& \underset{OX}{\overset{dye\ast }{E}}=\underset{OX}{\overset{dye}{E}}-E,\end{array}$$where $E_{OX}^{dye}$ denotes the ground-state energy of the DMABA derivatives in the oxidation potential energy, while E is the lowest vertical electronic excitation energy, related to λ_max.

As registered in Table 5, all the elected DMABA derivatives give negative ∆G_inject values, where D1.2 gives the most negative value; while D1.7 shows the least negative one. In addition, the electron donating groups CH₃, OH, and NH₂ represented by D1.1, D1,2, and D1.3, respectively, yield more negative values compared to that of the parent D1; while the electron-withdrawing moieties F, CN, NO_2, and CN with CH₃ represented by D1.4, D1.5, D1.6, and D1.17, respectively, give less negative ones relative to that of their predecessor D1 (See Table 5). The absolute values of ∆G_inject for all DMABA derivatives understudy are much greater than the 0.2 eV threshold necessary for an efficient electron injection [57]. It is noteworthy that the large energy difference between the LUMOs of the DMABA derivatives and the CBM of TiO₂ of −4.0 eV is large enough to secure efficient electron injections (See Figure 5).

Table 5

The calculated band gap (∆E), ground ($E_{\text{ox}}^{\text{dye}}$) and excited state ($E_{\text{ox}}^{\text{dye}\ast }$) oxidation potentials, vertical transition energy (${\lambda }_{\max }^{\text{ICT}}$), driving force for dye regeneration (∆G_reg), electron injection efficiency (∆G_inject), open circuit photovoltage (V_OC), and binding energy (E_b) of the dye D1 and its derivatives D1.1–D1.7 in a DMSO solvent medium. They were calculated by using the TD-B3LYP/6-311++G${}^{\ast \ast }$ level of theory.

Dyes	∆E	$E_{\text{ox}}^{\text{dye}}$	${\lambda }_{\max }^{\text{ICT}}$	$E_{\text{ox}}^{\text{dye}\ast }$	$\mathrm{\Delta }{G}_{\text{reg}}$	$\mathrm{\Delta }{G}_{\text{injec}}$	$V_{\text{OC}}$	$E_b$
D1	4.341	5.765	4.055	1.718	0.965	−2.282	2.577	0.352
D1.1	4.093	5.629	4.068	1.569	0.829	−2.431	2.811	0.372
D1.2	4.136	5.517	4.235	1.283	0.717	−2.717	2.931	0.245
D1.3	3.958	5.885	4.220	1.669	1.085	−2.331	2.679	0.344
D1.4	4.547	6.089	4.220	1.870	1.289	−2.130	2.459	0.344
D1.5	3.916	6.342	3.639	2.703	1.542	−1.297	1.574	0.277
D1.6	3.014	6.314	4.431	1.893	1.514	−2.107	0.699	−1.418
D1.7	3.708	6.086	3.198	2.890	1.286	−1.110	1.615	0.503

[figure(s) omitted; refer to PDF]

J _SC of the DSSC is affected by the regeneration efficiency (η_reg) of the DMABA derivatives, which can be computed from the regeneration force represented by ∆G_reg shown by (8) [58],$$\begin{array}{}\text{(8)}& \Delta G_{\text{reg}}=\underset{\text{redox}}{\overset{\text{electrolyte}}{E}}-\underset{\text{OX}}{\overset{\text{dye}}{E}}.\end{array}$$

Table 5 lists the computed values of $\mathrm{\Delta }{G}_{\text{reg}}$ for the derivatives D1.1–D1.7 of 0.829, 0.717, 1.085, 1.289, 1.542, 1.514, and 1.286 eV, respectively. It is clear that D1.1 and D1.2 offer relatively smaller driving forces for dye regeneration, which may enhance η_reg compared with the parent D1 (0.965 eV). In particular, derivative D1.2 could present the fastest regeneration, promoting the DSSC efficacy. In addition, V_OC is computed as an energy difference between E_LUMO of the DMABA derivative and E_CB of the TiO₂ semiconductor [59]:$$\begin{array}{}\text{(9)}& V_{\text{OC}}=E_{\text{LUMO}}-\underset{\text{CB}}{\overset{Ti{O}_2}{E}}.\end{array}$$

Our theoretical protocol has yielded V_OC values for the DMSO-solvated derivatives that spread between 0.699 and 2.931 eV (see Table 5). These values are quite appropriate for enabling efficacious electron injection into the LUMO of the carboxylate moiety as an electron acceptor. Thus, all the elected derivatives could be applied as sensitizers. This is because the carboxylate (COOH) acceptor group is quite propitious for electron injection from the dye into the CBM of the TiO₂ semiconductor, a situation that results in improved V_OC values. The derivative D1.2 characterized by the NH₂ moiety as an electron donating group, showed the highest V_OC value and hence could acquire an outstanding potential for application in DSSCs.

3.6. The Binding Energy (E_b)

For a high power conversion efficiency (PCE), the electron-hole entities must be kept separate as positive and negative charges to avoid recombination as a result of the attractive Coulombic forces. To achieve this crucial process, the binding energy (E_b) should be overcome, i.e., the derivatives should have lower binding energy to yield high PCE values. The binding energy (E_b) could be computed by (10) [60, 61],$$\begin{array}{}\text{(10)}& E_b=E_g-E_x=E_{H-L}-{\lambda }_{\max },\end{array}$$where $E_g$ is the HOMO–LUMO energy gap and E_x is the optical energy, calculated with reference to λ_max. Table 5 lists the exciton computed binding energies for the parent D1 and its derivatives D1.1-D1.7. It reveals the lowest value for D1.6 compared with the remaining derivatives. These findings reconfirm that the derivative D1.6 characterized by the NO₂ group is the most preferable for fabricating DSSCs.

4. Conclusion

We attempted to explore the optimized geometry, electronic structure, and their related optical absorption and emission properties of eight D–π–A-type chromophores with different ortho or para electron withdrawing or donating moieties. Our findings demonstrate that the ortho electron donating NH₂, the meta electron withdrawing CN, and the ortho electron donating CH₃ with meta electron withdrawing CN groups applied in D1.2, D1.5, and D1.7, respectively, are favorable for implication in the D–π–A design. The coplanar environment of the dimethylamine donor, benzene ring, and carboxylate acceptor together with the ortho or meta groups boosts efficacious injection of electrons from the donor [(CH₃)₂N-] to the acceptor [-COOH] of the elected dyes. Our findings show that the electron- withdrawing or donating moieties implicated in D1.2, D1.5 and D1.7 have generated relatively strong absorptions for maintaining stable charge transfer pathways for prompt electron grouting and dye regeneration, first singlet excited-state lifetime, and exciton binding energy. In addition, the elected dyes D1.5, D1.6, and D1.7 show small HOMO-LUMO energy gaps and clear red shifts in absorption and emission, compared with the parent dye (D1). It could be concluded that the elected dyes D1.2, D1.5, D1.6, and D1.7 are more favorable nominees for applications in relatively potent organic DSSCs.

Authors’ Contributions

O.I.O. planned the research. S.A.E. and S.G.A. provided the necessary literature, and M.A.H. performed some calculations and proofread the manuscript. M.Y.A reset of the calculation, analyzed the results, and wrote the first version of the manuscript.

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