Enhancing the Photophysical Properties of NHC-Based Iron Sensitizers for Dye-Sensitized Solar Cells: A Computational Study

Abstract

Iron(II) complexes bearing N-heterocyclic carbene (NHC) ligands have emerged as promising earth-abundant dye sensitizers for applications in dye-sensitized solar cells (DSSCs). In this work, we present a computational study of a set of 42 Fe–NHC dyes derived from seven ligand frameworks, systematically functionalized with donor, acceptor, and donor–acceptor groups to tune or enhance their photophysical properties. The calculated geometries reveal that substitution modulates Fe–N bond lengths and ligand dihedral angles only slightly, preserving the structural integrity of the complexes. TD-DFT calculations show clear and predictable electronic trends: donor groups raise the HOMO, acceptor groups lower the LUMO, and the combined push–pull configuration produces the most pronounced HOMO–LUMO gap narrowing and largest redshifts in MLCT transitions. Key DSSC performance descriptors, including electron-injection and dye-regeneration free energies, light-harvesting efficiency, excited-state lifetimes, and hole-transport reorganization energies, collectively identify the double-acceptor and push–pull derivatives as the most promising candidates across multiple frameworks.

1. Introduction

Dye-sensitized solar cells (DSSCs) have emerged as a versatile photovoltaic technology with notable advantages over traditional silicon cells, including tunable photophysical properties and excellent performance under low-light or indoor conditions [1,2,3,4,5,6]. Over the past few decades, extensive developments in DSSC research have been reported, particularly in the design of dye sensitizers based on organic [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] and inorganic/organometallic [31,32,33,34,35,36,37,38,39,40,41,42,43,44,45] motifs. In parallel, major advances in semiconductor photoanode materials and device architectures have played a crucial role in enhancing DSSC performance [16,46,47,48,49,50,51,52,53,54,55]. Ruthenium polypyridyl complexes have played a central role in the development of dye sensitizers for high-efficiency DSSCs due to their long-lived metal–ligand charge-transfer (MLCT) states, which enable efficient electron injection into the semiconductor conduction band [56,57,58,59,60,61,62]. However, the scarcity, cost, and toxicity of ruthenium limit large-scale implementation, motivating the search for sustainable alternatives [58].

Among the earth-abundant metals being explored as alternatives to ruthenium, Fe(II) complexes have emerged as particularly attractive candidates due to their low cost, abundance, and rich coordination chemistry [63,64,65,66,67,68,69,70]. In this context, Fe(III) complexes have also been investigated for their potential application as dye sensitizers [71,72]. Unfortunately, traditional Fe(II) polypyridyl complexes have long been considered unsuitable for photoredox or photovoltaic applications [63,70]. Their key limitation lies in the ultrafast population of low-lying metal-centered (MC) states, which quench the photoactive MLCT state on a sub-picosecond timescale, several orders of magnitude shorter than those required for efficient electron injection in DSSCs [73]. A major breakthrough came with the introduction of strong $\sigma$-donor N-heterocyclic carbene (NHC) ligands, which significantly reshaped the electronic landscape of Fe(II) photosensitizers [63,70,74]. The strong ligand field exerted by NHCs destabilizes the Fe(II) MC states, thereby suppressing their unwanted population, and extending MLCT lifetimes into the picosecond scale [63,70].

Moreover, the development of NHC-based iron(II) sensitizers demonstrates that targeted chemical modifications, specifically introducing or altering donor/acceptor character through substitutions on the NHC ligands, are critical for optimizing electronic properties, facilitating efficient charge separation via push-pull effects, and ultimately leading to significant advancements in photocurrent and overall efficiency [75,76,77,78,79,80]. For instance, Warnmark and coworkers demonstrated a linearly aligned push-pull design in an Fe-NHC sensitizer by functionalizing one ligand with an electron donor and the other with an electron-withdrawing carboxylic acid anchor, thereby creating a directional charge-transfer pathway [79]. A similar push-pull strategy was subsequently examined by Gros and co-workers, who likewise reported encouraging photophysical and photovoltaic behavior [77]. Additional recent studies have further highlighted the growing potential of Fe-NHC architectures as viable sensitizers for solar-energy applications [79,81,82,83,84,85,86,87,88,89]. Furthermore, recent advances by Heinze and co-workers have significantly deepened the understanding of how NHC ligands modulate MLCT lifetimes in Fe(II) chromophores. In fact, they demonstrated that combining strong $\sigma$-donating NHC donors with $\pi$-accepting pyridines and enforcing a high octahedral rigid structure through tripodal coordination can dramatically enhance the MLCT lifetime by several orders of magnitude [90,91].

Absorption of sunlight into excited electronic states is a fundamental requirement for efficient DSSCs. The operational principles of DSSCs have been extensively reviewed [92,93], and it is well established that broad, redshifted absorption into the visible region significantly enhances device performance [92,93]. In this context, time-dependent density functional theory (TD-DFT) has become an indispensable tool, offering reasonably accurate and computationally efficient predictions of excitation energies and transition character in organometallic complexes in general [94,95,96,97,98,99,100,101,102,103,104,105,106], and organoiron systems in particular [107,108,109]. By providing electronic-structure insights that are often inaccessible experimentally, computational modeling enables the rational design of new sensitizers and guides molecular modifications to improve light absorption and overall photophysical behavior [110,111,112]. Sensitizer design can rely on pure chemical intuition [112,113,114,115,116,117], or incorporating machine-learning approaches that permit rapid and cost-effective screening of molecular candidates [118,119,120]. In the same context, machine-learning approaches are also used for the predictions of excited ectronic states of molecules [121,122,123,124,125,126,127].

Push–pull chromophores featuring an electron donor–$\pi$–acceptor (D–$\pi$–A) architecture are known to enhance charge separation and redshift light absorption in DSSC applications [77,79]. Motivated by this principle, we investigate how donor and acceptor substitutions modulate the photophysical behavior of NHC-based iron(II) sensitizers. A set of 42 Fe(II) model complexes was constructed by systematically modifying seven NHC complex frameworks with electron-donating or electron-withdrawing groups, enabling us to assess how different substitution patterns influence absorption properties and overall DSSC suitability. Only a few studies, most notably those of Warnmark [79] and Gros [77], have shown that introducing push–pull character into NHC ligands in iron(II) complexes can broaden absorption and improve charge-separation directionality. In this context, the present work aims to modulate and assess key photophysical parameters that govern the performance of Fe–NHC sensitizers in DSSCs. Through donor, acceptor, and donor–acceptor substitutions, we specifically seek to tune (i) the energies of the frontier molecular orbitals and the resulting HOMO–LUMO gaps, (ii) the energies and intensities of absorption transitions, (iii) light-harvesting efficiency, and (iv) thermodynamic variables relevant to DSSC operation, including electron-injection and dye-regeneration driving forces. By correlating these parameters with systematic chemical modifications across multiple ligand frameworks, this study provides a coherent picture for the rational design of improved iron-based sensitizers.

2. Results and Discussion

2.1. Construction of the Model Fe(II)–NHC Dye Series

Iron(II), like other ${3\mathrm{d}}^6$ metals such as Cr(0), Mn(I), and Co(III), strongly favors octahedral coordination. In a strong-field environment, Fe(II) adopts a low-spin $t_{2g}^6$ configuration, which is energetically well-suited for hexacoordination and stabilizes an octahedral geometry. The classical polypyridyl complex tris(bipyridine)iron(II) [Fe(bpy)₃]²⁺ [128] (complex A in Figure 1) demonstrated ultrafast deactivation via low-lying MC states, highlights the need for stronger-field ligands to achieve longer MLCT lifetimes [128].

The incorporation of N-heterocyclic carbene (NHC) ligands into Fe(II) coordination spheres is highly advantageous, as their strong $\sigma$-donor character effectively increases the ligand-field splitting and raises the energy of low-lying metal-centered (MC) states. This stabilization suppresses ultrafast MC-mediated deactivation pathways, thereby creating more favorable conditions for sustaining MLCT excited states. However, the design of an efficient DSSC sensitizer must also consider the overall photoinduced electron-transfer process. In particular, the ligand framework must facilitate the directional flow of electron density from the photoexcited dye into the semiconductor. Introducing a $\pi$-accepting unit into the coordination environment enhances this charge-separation process by providing a low-lying orbital manifold capable of accepting electron density upon excitation. At the same time, increasing $\pi$-deficiency within the ligand system contributes to lowering the MLCT energy, enabling broader and more redshifted absorption [63].

Pyridyl–NHC architectures naturally satisfy these requirements: the pyridine ring acts as a $\pi$-acceptor, while the NHC moieties provide strong $\sigma$-donation, resulting in a push-pull electronic arrangement that promotes both MLCT stabilization and excited-state directionality. Within this context, Warnmark and co-workers reported the synthesis of a tridentate bis-imidazolium-pyridine ligand and its corresponding homoleptic Fe(II) complex [Fe(bpmi)₂]²⁺, (complex B in Figure 1), establishing an early example of such a donor-acceptor motif in Fe–NHC sensitizers [74]. Additional improvements to NHC ligands have been pursued by extending $\pi$-conjugation and by introducing electron-donating alkyl substituents on the carbene units. These modifications led to the development of complex C [Fe(pbmbi)₂]²⁺ [129], and complex D [Fe(pbbi)₂]²⁺ [74], respectively.

Beyond the meridional tetracarbene architectures featured in complexes such as B, C, and D, Heinze and co-workers have developed tripodal NHC ligands that coordinate to the iron center in a facial arrangement: Complex E cis-[Fe(dpmi)₂]²⁺ [90], complex F trans-[Fe(pdmi)₂]²⁺ [91], and complex G cis-[Fe(pdmi)₂]²⁺ [91]. The iron atom in E is coordinated to four nitrogen atoms (four pyridines) and two carbon atoms (2 NHCs); while that of F and G is coordinated with two nitrogen atoms (two pyridines) and four carbon atoms (4 NHCs); see Figure 1. Using variable-temperature ultrafast transient absorption spectroscopy, Heinze and co-workers revealed that the MLCT → MC population transfer can involve significant activation barriers in the cis isomer (complex G), which lead to nanosecond MLCT lifetimes at 77 K [91].

Linear push–pull chromophores featuring an electron donor–$\pi$–acceptor (D–$\pi$–A) architecture have demonstrated strong performance in DSSC applications, owing to their enhanced charge-separation character and redshifted absorption profiles [70,77,79]. In particular, both Warnmark and co-workers and Gros and co-workers have shown that introducing push–pull substituents can substantially modify the electronic structure of complex B Fe–NHC-based sensitizer, promoting more efficient charge separation and leading to enhanced photocurrent and overall device performance [77,79]. A broader discussion of these effects can be found in a recent review [70]. Motivated by these design principles, the present work explores how targeted donor and acceptor functionalization can modulate the photophysical properties of different NHC-based iron(II) sensitizers. We have constructed a set of 42 Fe(II) model complexes derived from seven NHC frameworks A to G (Figure 1), each systematically modified at the four-position of the pyridine rings. Six functionalization patterns were examined: 1. unmodified ligands; 2. single-donor substitution; 3. double-donor substitution; 4. single-acceptor substitution; 5. double-acceptor substitution; and 6. donor-acceptor substitution that explicitly generates a linear D–$\pi$–A motif; see Figure 2. These combinations (A1, A2, …, G6) enable a comprehensive evaluation of how donor/acceptor placement influences absorption profiles and overall suitability for light-harvesting applications. In all model compounds, a carboxylic acid moiety was employed as the electron acceptor, while a di(p-tolyl)amino unit served as the electron donor.

Several of the model structures generated in this work correspond to Fe–NHC sensitizers that have already been synthesized and evaluated experimentally in DSSC applications. Examples include derivatives of complex B, such as B1 and B5 [75,76,129], B4 [76], and B3 and B6 [79], as well as related analogues of complex C, including C1 and C5 [129]. In contrast, the substituted derivatives derived from the tripodal frameworks E, F, and G, specifically the donor- and/or acceptor-functionalized complexes E2–E6, F2–F6, and G2–G6 have not been previously synthesized or investigated for DSSC applications. These species, therefore, represent genuinely new molecular designs, constructed to explore how systematic donor/acceptor substitution patterns affect the electronic structure, absorption properties, and overall light-harvesting potential within these less experimentally explored ligand environments.

2.2. Optimized Geometries

The selected bond lengths and dihedral angles used to characterize the optimized geometries of the proposed dyes are reported in

Table 1. Selected bond lengths and dihedral angles of all complexes in their ground state, optimized at the CPCM-B3LYP/def2-TZVP level in acetonitrile solvent. Bond lengths (L1–L6) in (Å) and dihedral angles (DH1–DH4) in degrees (°). All bond lengths and bond angles are defined in Figure 3.

	L1	L2	L3	L4	L5	L6	DH1	DH2	DH3	DH4
	(Dn)	(Ac)	(Dn)	(Dn)	(Ac)	(Ac)	(Dn)	(Dn)	(Ac)	(Ac)
A1	2.019	2.020
A2	2.019	2.020	1.372				14.3
A3	2.019	2.019	1.372	1.373			13.9	15.0
A4	2.019	2.014			1.497				0.465
A5	2.014	2.014			1.497	1.496			0.684	0.684
A6	2.019	2.011	1.371		1.496		15.1		0.980
B1	1.955	1.955
B2	1.958	1.950	1.374				15.0
B3	1.955	1.955	1.379	1.378			21.7	17.8
B4	1.959	1.941			1.495				0.679
B5	1.945	1.944			1.496	1.496			1.36	0.099
B6	1.998	1.972	1.369		1.493		11.1		4.50
C1	1.925	1.926
C2	1.954	1.949	1.370				11.1
C3	1.954	1.954	1.372	1.374			14.2	16.1
C4	1.954	1.939			1.497				1.794
C5	1.942	1.943			1.497	1.497			1.785	0.848
C6	1.957	1.936	1.370		1.496		11.6		0.237
D1	1.959	1.959
D2	1.963	1.958	1.373				17.2
D3	1.962	1.963	1.373	1.375			15.8	18.0
D4	1.961	1.946			1.496				0.515
D5	1.949	1.949			1.496	1.496			0.404	0.122
D6	1.965	1.944	1.370		1.495		12.5		1.941
E1	2.051	2.051
E2	2.053	2.050	1.373				14.5
E3	2.052	2.055	1.373	1.374			14.0	15.		1
E4	2.051	2.037			1.494				2.538
E5	2.037	2.041			1.495	1.495			2.316	3.127
E6	2.053	2.033	1.372		1.494		13.3		2.351
F1	2.070	2.070
F2	2.079	2.069	1.375				17.8
F3	2.078	2.076	1.375	1.375			15.3	15.		5
F4	2.075	2.049			1.493				0.156
F5	2.055	2.055			1.493	1.494			1.709	1.6
F6	2.083	2.044	1.373		1.492		17.4		0.406
G1	2.106	2.107
G2	2.114	2.105	1.374				14.3
G3	2.105	2.109	1.375	1.375			13.6	13.7
G4	2.106	2.088			1.493				3.498
G5	2.090	2.088			1.494	1.494			0.642	0.605
G6	2.109	2.079	1.374		1.493		14.4		0.203

, and their definitions are illustrated in Figure 3. Bond lengths L1 and L2 correspond to the Fe–N distances between the iron center and the two pyridyl nitrogen atoms. For the donor-substituted systems, L3 and L4 denote the distances between the C4 position of the pyridine ring and the nitrogen atom of the di(p-tolyl)amino donor group. For the acceptor-substituted systems, L5 and L6 represent the analogous distances between C4 and the carbonyl carbon of the carboxylic acid acceptor. Dihedral angles are defined to quantify the relative orientation of the substituents with respect to the pyridine ring. DH1 and DH2 measure the dihedral angle between the pyridine plane and the plane of the donor (diarylamino) group, whereas DH3 and DH4 describe the corresponding angles between the pyridine plane and the plane of the carboxylic acid group. The definitions apply to all six substitution patterns (configurations 1–6) across complexes A–G, noting that complexes G3, G5, and G6 possess cis arrangements of the two pyridine units.

Within each framework, introduction of a carboxylic acid acceptor at the para position leads to a systematic, albeit small, shortening of the Fe–N(pyridine) bonds (by ≈0.005–0.03 Å), whereas donor substitution has only a minor impact and in some cases slightly elongates these distances. In contrast, the C4–N(diarylamino) and C4–C(carboxyl) bond lengths remain essentially invariant (1.37 and 1.49–1.50 Å, respectively) across all dyes. Donor substituents adopt a moderately twisted orientation with respect to the pyridine ring (DH1/DH2 ≈ 11–18°), while carboxylic acid groups stay nearly coplanar (DH3/DH4 ≤ 3°), preserving conjugation into the acceptor arm.

For a given substitution pattern, the Fe–N(pyridine) distances display a clear framework dependence, following approximately C ≲ B ≈ D < A < E < F < G. The meridional tetracarbene complexes B–D, and in particular pbmbi-based complex C, exhibit the shortest Fe–N bonds, consistent with a strong ligand field and rigid chelation, whereas the tripodal systems E–G feature significantly longer Fe–N distances. Notably, the donor and acceptor dihedral angles vary only slightly between frameworks, indicating that the overall push–pull geometry, with twisted donors and nearly planar acceptors, is largely preserved across the entire series.

2.3. Electronic Structure

The electronic structure of the 42 Fe–NHC model dyes was examined through their frontier-orbital HOMO and LUMO energies, HOMO–LUMO gaps, and the evolution of these quantities with respect to both the substitution patterns (configurations 1–6) and the frameworks (A–G). The results, collected in

Table 2. Frontier molecular orbital energies and HOMO–LUMO gap energies, in eV.

Dye	HOMO − 2	HOMO − 1	HOMO	LUMO	LUMO + 1	LUMO + 2	H-L Gap
	(eV)	(eV)	(eV)	(eV)	(eV)	(eV)	(eV)
A1	−6.279	−6.277	−6.195	−2.472	−2.470	−2.469	3.724
A2	−6.192	−6.144	−5.808	−2.459	−2.454	−2.294	3.349
A3	−6.058	−5.776	−5.728	−2.413	−2.271	−2.259	3.315
A4	−6.399	−6.392	−6.321	−2.890	−2.521	−2.511	3.431
A5	−6.482	−6.469	−6.403	−2.904	−2.904	−2.542	3.498
A6	−6.281	−6.234	−5.842	−2.853	−2.483	−2.316	2.989
B1	−5.925	−5.923	−5.584	−1.778	−1.775	−1.500	3.806
B2	−5.787	−5.539	−5.482	−1.723	−1.445	−1.421	3.759
B3	−5.441	−5.414	−5.391	−1.446	−1.420	−1.413	3.945
B4	−6.047	−6.038	−5.688	−2.600	−1.823	−1.613	3.088
B5	−6.152	−6.150	−5.781	−2.637	−2.637	−1.675	3.144
B6	−6.178	−5.750	−5.531	−2.753	−1.785	−1.674	2.778
C1	−6.185	−6.181	−5.880	−1.886	−1.880	−1.567	3.994
C2	−6.034	−5.793	−5.735	−1.862	−1.539	−1.535	3.873
C3	−5.705	−5.639	−5.617	−1.532	−1.509	−1.488	4.085
C4	−6.266	−6.259	−5.969	−2.691	−1.954	−1.691	3.278
C5	−6.354	−6.350	−6.045	−2.723	−2.719	−1.752	3.322
C6	−6.136	−5.883	−5.804	−2.649	−1.638	−1.573	3.155
D1	−6.026	−6.025	−5.717	−1.868	−1.866	−1.674	3.850
D2	−5.885	−5.646	−5.622	−1.846	−1.626	−1.532	3.776
D3	−5.541	−5.526	−5.507	−1.567	−1.512	−1.481	3.941
D4	−6.141	−6.137	−5.854	−2.678	−1.936	−1.794	3.176
D5	−6.248	−6.246	−5.946	−2.712	−2.710	−1.861	3.234
D6	−6.004	−5.755	−5.727	−2.639	−1.744	−1.550	3.088
E1	−6.155	−5.744	−5.635	−1.924	−1.879	−1.593	3.711
E2	−6.036	−5.539	−5.512	−1.867	−1.742	−1.511	3.645
E3	−5.909	−5.441	−5.342	−1.712	−1.700	−1.325	3.630
E4	−6.255	−5.834	−5.723	−2.645	−1.923	−1.748	3.078
E5	−6.346	−5.917	−5.801	−2.731	−2.587	−1.782	3.069
E6	−6.086	−5.634	−5.589	−2.615	−1.768	−1.713	2.975
F1	−5.882	−5.490	−5.335	−1.762	−1.612	−1.114	3.574
F2	−5.773	−5.306	−5.242	−1.666	−1.312	−1.100	3.576
F3	−5.657	−5.149	−5.140	−1.318	−1.228	−1.085	3.822
F4	−6.003	−5.598	−5.440	−2.564	−1.714	−1.368	2.876
F5	−6.100	−5.683	−5.523	−2.683	−2.526	−1.405	2.840
F6	−5.895	−5.399	−5.349	−2.573	−1.337	−1.240	2.776
G1	−5.842	−5.406	−5.357	−1.724	−1.677	−1.185	3.632
G2	−5.736	−5.284	−5.233	−1.663	−1.307	−1.159	3.570
G3	−5.636	−5.152	−5.136	−1.306	−1.259	−1.148	3.829
G4	−5.942	−5.491	−5.443	−2.602	−1.731	−1.319	2.842
G5	−6.034	−5.570	−5.524	−2.631	−2.620	−1.402	2.893
G6	−5.845	−5.373	−5.322	−2.574	−1.333	−1.277	2.748

and visualized in Figure 4, Figure 5 and Figure 6, reveal a series of consistent trends that provide clear insight into how donor and acceptor modification modulates the electronic properties of these complexes.

Across all frameworks, donor substitution (configurations 2, 3, and 6) exerts a predictable destabilizing influence on the HOMO. Introducing a diarylamino group at the four-position of the pyridine ring increases electron density in the vicinity of the metal center, raising the HOMO energy relative to the unfunctionalized complex (configuration 1). This upward shift is modest, typically a few tenths of an electron volt, but remarkably systematic, appearing in every framework from A through G. The trend matches what is generally observed for electron-rich para substituents in Fe(II) polypyridyl and Fe–NHC systems, where increased $\pi$-donation perturbs the metal-centered $t_{2g}$ manifold and narrows the energetic gap between the highest occupied orbitals. In some complexes (e.g., A1, A2, and A5), LUMO and LUMO+1 are (near-)degenerate and therefore appear identical, reflecting the symmetry and ligand-centered $\pi$ character of these orbitals.

On the other hand, acceptor substitution (configurations 4, 5, and 6) exerts its influence almost exclusively on the LUMO. The presence of a carboxylic acid group consistently lowers the LUMO energy, with reductions often exceeding 0.3–0.5 eV relative to the parent complex. This stabilization is large, robust with respect to ligand framework, and dominates the electronic behavior of configurations containing an acceptor. The combined donor–acceptor effect in configuration 6, therefore, acts from both sides: The donor raises the HOMO while the acceptor lowers the LUMO, producing the smallest HOMO–LUMO gaps in each framework. This push–pull contraction of the MLCT energy gap is conceptually identical to the behavior described in D–$\pi$–A photosensitizers and aligns with the electronic-tuning strategies previously outlined for Fe–NHC complexes [79].

The magnitude of the HOMO–LUMO gap varies significantly across substitution patterns. The parent structures (1) exhibit the widest gaps, typically around 3.6–4.0 eV, indicative of relatively high MLCT excitation energies. Donor-only modifications (configurations 2 and 3) produce only small decreases in the HOMO–LUMO gap, and the magnitude of this effect varies depending on the framework. Acceptors alone (configurations 4 and 5) produce substantially smaller gaps across the board, with decreases of 0.4–0.7 eV common for all frameworks. The most striking effect appears in configuration 6, where donor and acceptor substituents operate cooperatively. These dyes consistently display the narrowest HOMO–LUMO gaps in their respective ligand families. For example, B6, F6, and G6 show gaps near 2.75–2.80 eV, values more than 1 eV smaller than those of their unsubstituted counterparts. Such dramatic reductions in gap energy suggest substantial redshifts in the MLCT transitions, marking configuration 6 as the most electronically responsive design motif within the entire set of theoretical models.

Differences between frameworks also contribute to variations in absolute orbital energies. For a fixed substitution pattern, meridional tetracarbene complexes (B–D) generally exhibit higher HOMO energies and moderately lower LUMO energies compared to the tripodal frameworks (E–G), reflecting their stronger ligand fields and greater degree of $\pi$ conjugation. Complexes based on framework C tend to display the highest HOMO energies overall, consistent with the highly donating nature of the pbmbi ligand. Conversely, frameworks F and G exhibit somewhat lower HOMO energies and slightly higher LUMO energies, leading to moderately larger gaps for configurations lacking acceptors. However, once both donor and acceptor groups are added, the differences between frameworks become much less important. The push–pull effect dominates the HOMO–LUMO gap, and the substituents, not the ligand framework, mainly determine the electronic structure.

The molecular-orbital isosurfaces (Supplementary Materials (SM) Figures S1–S14) provide a useful qualitative complement. In every complex studied, the HOMO retains predominantly metal-centered character with significant Fe dπ contribution, whereas the LUMO remains ligand-centered, localized mainly on the pyridine rings. Donor groups contribute electron density to the HOMO when present, while acceptor groups contribute to the LUMO; however, the fundamental MLCT character of the frontier transition, metal-to-pyridine, remains unchanged across all dyes. This robustness is important: even the large geometric differences between the meridional (A–D) and tripodal (E–G) frameworks do not change the fundamental orbital pattern, showing that donor and acceptor groups modify the electronic structure in an additive way without affecting the MLCT character.

The isosurface plots also confirm the electronic rationale underlying the HOMO–LUMO energy trends. Donor-substituted dyes show HOMO density extending onto the diarylamino fragment, consistent with HOMO destabilization. When present, acceptors consistently draw LUMO density toward the carboxyl group, indicating LUMO stabilization. In the push–pull systems (6), the HOMO is polarized toward the donor, while the LUMO is polarized toward the acceptor, enabling the largest spatial and energetic orbital separation within each framework. This type of orbital polarization is a feature of efficient D–$\pi$–A chromophores and explains why configuration 6 yields the most pronounced gap reduction found in all proposed configurations.

2.4. Electronic Transitions & Spectra

The calculated vertical excitation energies ($E^{\mathrm{vert}}$) correspond to the lowest dipole-allowed transition from the singlet ground state to an excited singlet state (${\mathrm{S}}_0\to {\mathrm{S}}_n$). Here, n is not necessarily equal to 1; rather, we identify the first transition that carries the highest oscillator strength as the lowest dipole-allowed transition, which, in turn, dominates the absorption spectrum. In addition to intensity, the nature of the excited state is also taken into account: only transitions exhibiting clear metal-to-ligand charge-transfer (MLCT) character are considered relevant, as MLCT states are the photoactive states responsible for charge injection in DSSC operation. All excitation energies are obtained within the vertical (Franck–Condon) approximation, in which vibronic effects and nuclear relaxation in the excited state are neglected. A fully vibronic treatment would require geometry optimizations and Hessian calculations for the relevant excited states, which are computationally prohibitive for systems of the present size. Under this approximation, the computed ($E^{\mathrm{vert}}$) values are taken as theoretical estimates of the experimental (${\lambda }_{\max }$). Numerous previous studies have demonstrated the reliability of this approach [110,111,112,130,131,132].

In experimental DSSC devices, dye molecules operate typically in solvent-containing media, which also contain the ${\mathrm{I}}^{-}/{\mathrm{I}}_3^{-}$ electrolyte redox couple. To approximate these solution-phase conditions, all ground- and excited-state calculations in this work were performed using the CPCM implicit solvation model with acetonitrile as the solvent. Acetonitrile was chosen as the solvent since it is the most commonly employed medium in experimental spectroscopic and electrochemical studies of Fe(II)–NHC complexes, and is widely used as a reference solvent in DSSC-related computational investigations. The resulting excitation energies [$E^{\mathrm{vert}}\left({\lambda }_{\max }\right)]$, expressed in both nm and eV, together with the corresponding oscillator strengths and molecular-orbital assignments, are summarized in

Table 3. Electronic singlet transitions, in nm and eV, and their assignments, calculated at the CPCM-B3LYP/def2-TZVP level in acetonitrile solvent.

Dye	Electronic	${\mathit{E}}^{\mathbf{vert}}\left({\mathit{\lambda }}_{\mathbf{max}}\right)$	${\mathit{E}}^{\mathbf{vert}}\left({\mathit{\lambda }}_{\mathbf{max}}\right)$	Oscillator	MO Designation
	Transition	(nm)	(eV)	Strength (f)	Character (Coef)
A1	${\mathrm{S}}_0\to {\mathrm{S}}_{10}$	415.0	2.988	0.074	H-1 → L (0.8598)
A2	${\mathrm{S}}_0\to {\mathrm{S}}_9$	433.6	2.860	0.080	H-2 → L (0.4751)
A3	${\mathrm{S}}_0\to {\mathrm{S}}_9$	446.0	2.780	0.112	H → L+1 (0.6283)
A4	${\mathrm{S}}_0\to {\mathrm{S}}_{11}$	407.3	3.044	0.079	H-2 → L+2 (0.7128)
A5	${\mathrm{S}}_0\to {\mathrm{S}}_8$	450.6	2.751	0.173	H-1 → L+1 (0.3923)
A6	${\mathrm{S}}_0\to {\mathrm{S}}_6$	463.3	2.676	0.085	H-1 → L+1 (0.4363)
B1	${\mathrm{S}}_0\to {\mathrm{S}}_{12}$	356.6	3.477	0.276	H → L+3 (0.7884)
B2	${\mathrm{S}}_0\to {\mathrm{S}}_{12}$	361.9	3.426	0.438	H → L+3 (0.6993)
B3	${\mathrm{S}}_0\to {\mathrm{S}}_{10}$	383.3	3.235	0.592	H-1 → L (0.2415)
B4	${\mathrm{S}}_0\to {\mathrm{S}}_{12}$	436.3	2.841	0.195	H → L+3 (0.6860)
B5	${\mathrm{S}}_0\to {\mathrm{S}}_5$	440.2	2.817	0.398	H-2 → L (0.2933)
B6	${\mathrm{S}}_0\to {\mathrm{S}}_{10}$	392.6	3.158	0.110	H-1 → L+1 (0.5088)
C1	${\mathrm{S}}_0\to {\mathrm{S}}_8$	361.0	3.434	0.169	H-1 → L (0.4603)
C2	${\mathrm{S}}_0\to {\mathrm{S}}_9$	362.2	3.423	0.296	H → L+2 (0.4673)
C3	${\mathrm{S}}_0\to {\mathrm{S}}_{10}$	369.6	3.355	0.675	H-1 → L+1 (0.4863)
C4	${\mathrm{S}}_0\to {\mathrm{S}}_8$	365.5	3.392	0.114	H-1 → L+2 (0.7269)
C5	${\mathrm{S}}_0\to {\mathrm{S}}_5$	424.8	2.919	0.346	H-1 → L (0.4572)
C6	${\mathrm{S}}_0\to {\mathrm{S}}_{10}$	359.4	3.450	0.258	H → L+2 (0.5401)
D1	${\mathrm{S}}_0\to {\mathrm{S}}_{12}$	360.5	3.439	0.180	H → L+3 (0.8355)
D2	${\mathrm{S}}_0\to {\mathrm{S}}_{11}$	376.7	3.291	0.306	H → L+3 (0.5077)
D3	${\mathrm{S}}_0\to {\mathrm{S}}_{11}$	382.1	3.245	0.586	H-1 → L+2 (0.3721)
D4	${\mathrm{S}}_0\to {\mathrm{S}}_6$	434.7	2.852	0.183	H-1 → L (0.7188)
D5	${\mathrm{S}}_0\to {\mathrm{S}}_8$	441.1	2.811	0.343	H-2 → L+1 (0.3884)
D6	${\mathrm{S}}_0\to {\mathrm{S}}_{12}$	375.3	3.304	0.278	H-1 → L+2 (0.5503)
E1	${\mathrm{S}}_0\to {\mathrm{S}}_{11}$	374.6	3.310	0.092	H-1 → L+2 (0.8233)
E2	${\mathrm{S}}_0\to {\mathrm{S}}_{11}$	376.7	3.291	0.116	H → L+2 (0.3394)
E3	${\mathrm{S}}_0\to {\mathrm{S}}_{10}$	374.2	3.314	0.296	H → L+2 (0.8794)
E4	${\mathrm{S}}_0\to {\mathrm{S}}_4$	476.1	2.604	0.140	H-1 → L (0.8201)
E5	${\mathrm{S}}_0\to {\mathrm{S}}_5$	481.8	2.573	0.243	H-1 → L (0.8790)
E6	${\mathrm{S}}_0\to {\mathrm{S}}_4$	499.7	2.481	0.150	H → L (0.7074)
F1	${\mathrm{S}}_0\to {\mathrm{S}}_5$	414.9	2.989	0.190	H-1 → L (0.9901)
F2	${\mathrm{S}}_0\to {\mathrm{S}}_4$	425.1	2.917	0.131	H-1 → L (0.7450)
F3	${\mathrm{S}}_0\to {\mathrm{S}}_6$	393.4	3.151	0.507	H-1 → L (0.7977)
F4	${\mathrm{S}}_0\to {\mathrm{S}}_4$	498.9	2.485	0.145	H-1 → L (0.7179)
F5	${\mathrm{S}}_0\to {\mathrm{S}}_3$	519.4	2.387	0.287	H-1 → L (0.9789)
F6	${\mathrm{S}}_0\to {\mathrm{S}}_2$	531.5	2.333	0.210	H-1 → L (0.8677)
G1	${\mathrm{S}}_0\to {\mathrm{S}}_6$	413.4	2.999	0.075	H-1 → L+1 (0.4235)
G2	${\mathrm{S}}_0\to {\mathrm{S}}_8$	381.1	3.254	0.153	H-1 → L+1 (0.4841)
G3	${\mathrm{S}}_0\to {\mathrm{S}}_7$	387.7	3.198	0.216	H → L+1 (0.8211)
G4	${\mathrm{S}}_0\to {\mathrm{S}}_2$	528.5	2.346	0.155	H-1 → L (0.7123)
G5	${\mathrm{S}}_0\to {\mathrm{S}}_3$	539.3	2.299	0.149	H-1 → L+1 (0.8709)
G6	${\mathrm{S}}_0\to {\mathrm{S}}_2$	540.9	2.292	0.164	H-1 → L (0.8705)

for all 42 proposed dye sensitizers. Moreover, the plots of the calculated absorption UV–vis spectra of iron dyes A1 to G6 using a Gaussian lineshape are shown in Figures S15–S35 in the Supplementary Materials.

The lowest intense singlet transitions span roughly 2.30–3.50 eV (≈540–355 nm), placing all dyes in the visible region (Table 3). For each framework A–G, the effect of substitution on the excitation energy follows the same qualitative pattern observed for the frontier-orbital gaps. The parent complexes (1) consistently exhibit the highest excited-state energies (shortest wavelengths), while donor or acceptor substitution lowers the transition energy to varying degrees. Donor-only substitution (2 and 3) produces only modest redshifts relative to the unsubstituted dyes, typically on the order of 0.1–0.3 eV. In contrast, introducing carboxylic acid acceptors (4 and 5) leads to a much more pronounced redshift, with excitation energies often reduced by ≈0.4–0.7 eV compared to the corresponding 1 dye in the same framework. The donor–acceptor push–pull systems (6) generally maintain similarly low or slightly lower excitation energies than the acceptor-only analogues, especially in frameworks E–G where the lowest values of the whole series are found (e.g., 2.48 eV for E6, 2.33 eV for F6, 2.29 eV for G6).

When comparing different complex frameworks at a fixed substitution pattern, clear trends also emerge. For the unsubstituted complexes (1), the meridional tetracarbene systems B–D give the most blue-shifted transitions (≈3.43–3.48 eV), whereas A, F, and G absorb around 3.0 eV. Once carboxylate acceptors are introduced (4 and 5), the tripodal frameworks E–G become particularly effective at lowering the excitation energy: E4–E5, F4–F5, and G4–G5 lie between ≈2.60 and 2.30 eV, significantly redshifted relative to the corresponding B–D derivatives. The same tendency is observed for the push–pull series (6), where E6–G6 exhibit the lowest transition energies within each configuration, while the meridional NHC-rich complexes C6 and D6 remain comparatively blue-shifted. These trends mirror the HOMO–LUMO gaps discussed in the previous section, confirming that donor–acceptor engineering is a more decisive handle on the MLCT energy than the underlying framework, once a strong-field NHC environment is in place.

Oscillator strengths further refine this picture. All lowest-intensity transitions have non-zero oscillator strength, confirming that they are optically accessible and will contribute to the main absorption bands. On average, double-donor systems (3) exhibit the largest oscillator strengths across frameworks, with several cases exceeding ($f\approx 0.5$) (e.g., B3, C3, D3, F3), indicating very bright MLCT bands. Double-acceptor dyes (5) also show relatively strong transitions ($f\approx$ 0.25–0.40), while parent (1), single-donor (2), single-acceptor (4), and push–pull (6) complexes tend to display moderate intensities ($\mathbf{f}\approx$ 0.1–0.3). Thus, there is a trade-off: donor-rich systems often deliver the most intense absorption, whereas acceptor and push–pull designs give the largest redshifts. From a DSSC perspective, the best candidates are those that combine substantial redshift with still-significant oscillator strengths, such as B5, C5, D5, E5, F5, and G5, as well as the tripodal push–pull complexes E6–G6.

The orbital assignments in Table 3 show that all lowest intense transitions are dominated by a single configuration involving frontier orbitals, typically HOMO or HOMO − 1 to LUMO or LUMO + 1, with significant coefficients (≈0.4–0.9). This indicates that the transitions retain a clean MLCT character across the entire series rather than being strongly mixed. Donor substitution enhances the contribution of donor-localized orbitals to the HOMO/HOMO − 1, while acceptor substitution draws the LUMO (or LUMO + 1) toward the carboxylate arm. Consequently, the bright states in the push–pull dyes (6) can be viewed as strongly polarized MLCT transitions from donor-enhanced metal/aryl orbitals to acceptor-anchored ligand orbitals. Together with the frontier-orbital analysis, these results confirm that substitution primarily tunes the energy, intensity, and directionality of MLCT transitions.

2.5. Solar Cell Efficiency Variables

To evaluate the photovoltaic performance of the 42 Fe–NHC dyes, several key descriptors relevant to DSSC operation were examined: the free energies of electron injection ($\Delta G_{\mathrm{inj}}$) and dye regeneration ($\Delta G_{\mathrm{reg}}$), the light-harvesting efficiency (LHE), the excited-state lifetime ($\tau$), and the hole-transport reorganization energy (${\lambda }_{\mathrm{hole}}$). The computed values are summarized in

Table 4. DSSC efficiency variables: GSOP, ESOP, $\Delta G_{\mathrm{inj}}$, $\Delta G_{\mathrm{reg}}$, LHE, and $\tau$.

Dye	HOMO	${\mathit{E}}^{\mathbf{vert}}\left({\mathit{\lambda }}_{\mathbf{max}}\right)$	GSOP	ESOP	$\mathbf{\Delta }{\mathit{G}}_{\mathbf{inj}}$	$\mathbf{\Delta }{\mathit{G}}_{\mathbf{reg}}$	LHE	$\mathit{\tau }$
	(eV)	(eV)	(eV)	(eV)	(eV)	(eV)	(%)	(ns)
A1	−6.195	2.988	6.195	3.207	−0.793	−1.395	15.7	33.6
A2	−5.808	2.860	5.808	2.948	−1.052	−1.008	16.8	34.1
A3	−5.728	2.780	5.728	2.948	−1.052	−0.928	22.8	25.7
A4	−6.321	3.044	6.321	3.277	−0.723	−1.521	16.7	30.4
A5	−6.403	2.751	6.403	3.652	−0.348	−1.603	32.8	17.0
A6	−5.842	2.676	5.842	3.166	−0.834	−1.042	17.8	36.6
B1	−5.584	3.477	5.584	2.107	−1.893	−0.784	47.1	6.7
B2	−5.482	3.426	5.482	2.056	−1.944	−0.682	63.5	4.3
B3	−5.391	3.235	5.391	2.156	−1.844	−0.591	74.4	3.6
B4	−5.688	2.841	5.688	2.847	−1.153	−0.888	36.2	14.2
B5	−5.781	2.817	5.781	2.964	−1.036	−0.981	60.0	7.1
B6	−5.531	3.158	5.531	2.373	−1.627	−0.731	22.4	20.3
C1	−5.880	3.434	5.880	2.446	−1.554	−1.080	32.2	11.2
C2	−5.735	3.423	5.735	2.312	−1.688	−0.935	49.4	6.4
C3	−5.617	3.355	5.617	2.262	−1.738	−0.817	78.9	2.9
C4	−5.969	3.727	5.969	2.577	−1.423	−1.169	23.1	14.1
C5	−6.045	2.919	6.045	3.126	−0.874	−1.245	54.9	7.6
C6	−5.804	3.450	5.804	2.354	−1.646	−1.004	44.7	7.3
D1	−5.717	3.439	5.717	2.278	−1.722	−0.917	33.9	10.5
D2	−5.622	3.291	5.622	2.331	−1.669	−0.822	50.6	6.7
D3	−5.507	3.245	5.507	2.262	−1.738	−0.707	74.1	3.6
D4	−5.854	2.852	5.854	3.002	−0.998	−1.054	34.4	14.9
D5	−5.946	2.811	5.946	3.135	−0.865	−1.146	54.6	8.2
D6	−5.727	3.304	5.727	2.423	−1.577	−0.927	47.3	7.3
E1	−5.635	3.310	5.635	2.325	−1.675	−0.835	19.1	22.1
E2	−5.512	3.291	5.512	2.221	−1.779	−0.712	23.4	17.8
E3	−5.342	3.314	5.342	2.028	−1.972	−0.542	49.4	6.9
E4	−5.723	2.604	5.723	3.119	−0.881	−0.923	27.6	23.4
E5	−5.801	2.573	5.801	3.228	−0.772	−1.001	42.9	13.8
E6	−5.589	2.481	5.589	3.108	−0.892	−0.789	29.2	24.1
F1	−5.335	2.989	5.335	2.346	−1.654	−0.535	35.5	13.1
F2	−5.242	2.917	5.242	2.325	−1.675	−0.442	26.0	20.0
F3	−5.140	3.151	5.140	1.989	−2.011	−0.340	68.9	4.4
F4	−5.440	2.485	5.440	2.955	−1.045	−0.640	28.4	24.9
F5	−5.523	2.387	5.523	3.136	−0.864	−0.723	48.4	13.6
F6	−5.349	2.333	5.349	3.016	−0.984	−0.549	38.3	19.5
G1	−5.357	2.999	5.357	2.358	−1.642	−0.557	15.8	33.2
G2	−5.233	3.254	5.233	1.979	−2.021	−0.433	29.7	13.8
G3	−5.136	3.198	5.136	1.938	−2.062	−0.336	39.2	10.1
G4	−5.443	2.346	5.443	3.097	−0.903	−0.643	30.0	26.1
G5	−5.524	2.299	5.524	3.225	−0.775	−0.724	29.0	28.3
G6	−5.322	2.292	5.322	3.030	−0.970	−0.522	31.5	25.8

and

Table 5. Hole transport reorganization energy.

Complex	${\mathit{E}}^0\left({\mathit{Q}}^0\right)$	${\mathit{E}}^{+}\left({\mathit{Q}}^0\right)$	${\mathit{E}}^0\left({\mathit{Q}}^{+}\right)$	${\mathit{E}}^{+}\left({\mathit{Q}}^{+}\right)$	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_2$	${\mathit{\lambda }}_{\mathbf{hole}}$
	(eV)	(eV)	(eV)	(eV)	(eV)	(eV)	(eV)
A1	−74,813.107	−74,807.804	−74,812.678	−74,807.856	0.428	0.052	0.481
A2	−91,029.039	−91,023.871	−91,028.977	−91,023.939	0.062	0.067	0.130
A3	−107,244.960	−107,239.927	−107,244.891	−107,240.001	0.070	0.074	0.143
A4	−79,944.520	−79,939.143	−79,944.472	−79,939.195	0.048	0.052	0.100
A5	−85,075.939	−85,070.490	−85,075.891	−85,070.541	0.048	0.051	0.099
A6	−96,160.461	−96,155.219	−96,160.396	−96,155.289	0.065	0.069	0.134
B1	−76,654.866	−76,650.072	−76,654.831	−76,650.147	0.036	0.075	0.110
B2	−92,870.742	−92,866.058	−92,870.655	−92,866.155	0.086	0.097	0.184
B3	−109,086.602	−109,082.013	−109,086.507	−109,082.116	0.095	0.103	0.198
B4	−81,786.295	−81,781.413	−81,786.249	−81,781.476	0.045	0.063	0.108
B5	−86,917.716	−86,912.753	−86,917.666	−86,912.805	0.050	0.052	0.102
B6	−97,999.456	−97,994.953	−97,999.385	−97,995.029	0.071	0.076	0.147
C1	−93,374.231	−93,368.976	−93,374.144	−93,369.171	0.087	0.195	0.282
C2	−109,590.117	−109,585.120	−109,589.994	−109,585.242	0.124	0.121	0.245
C3	−125,805.995	−125,801.138	−125,805.890	−125,801.252	0.105	0.113	0.218
C4	−98,505.642	−98,500.437	−98,505.558	−98,500.505	0.084	0.068	0.152
C5	−103,637.047	−103,631.774	−103,636.973	−103,631.836	0.074	0.062	0.136
C6	−114,721.538	−114,716.453	−114,721.406	−114,716.577	0.131	0.124	0.255
D1	−89,485.959	−89,481.081	−89,485.909	−89,481.133	0.051	0.052	0.103
D2	−105,701.858	−105,697.090	−105,701.780	−105,697.167	0.078	0.077	0.154
D3	−121,917.741	−121,913.098	−121,917.650	−121,913.178	0.091	0.079	0.170
D4	−94,617.376	−94,612.414	−94,617.324	−94,612.467	0.052	0.052	0.104
D5	−99,748.785	−99,743.744	−99,748.734	−99,743.796	0.051	0.052	0.102
D6	−110,833.283	−110,828.432	−110,833.208	−110,828.502	0.075	0.071	0.146
E1	−77,855.785	−77,850.962	−77,855.739	−77,851.008	0.046	0.046	0.092
E2	−94,071.710	−94,067.009	−94,071.647	−94,067.073	0.062	0.064	0.126
E3	−110,287.626	−110,283.076	−110,287.551	−110,283.156	0.074	0.081	0.155
E4	−82,987.221	−82,982.328	−82,987.174	−82,982.374	0.047	0.046	0.093
E5	−88,118.651	−88,113.692	−88,118.604	−88,113.737	0.047	0.045	0.092
E6	−99,203.149	−99,198.363	−99,203.084	−99,198.429	0.065	0.066	0.131
F1	−78,792.618	−78,788.096	−78,792.569	−78,788.148	0.049	0.052	0.100
F2	−95,008.534	−95,004.108	−95,008.464	−95,004.186	0.070	0.079	0.149
F3	−111,224.439	−111,220.159	−111,224.354	−111,220.247	0.085	0.088	0.174
F4	−83,924.069	−83,919.477	−83,924.019	−83,919.528	0.050	0.051	0.101
F5	−89,055.512	−89,050.853	−89,055.464	−89,050.902	0.050	0.048	0.098
F6	−100,139.988	−100,135.480	−100,139.932	−100,135.548	0.055	0.068	0.123
G1	−78,792.717	−78,788.202	−78,792.663	−78,788.257	0.054	0.055	0.109
G2	−95,008.635	−95,004.240	−95,008.561	−95,004.313	0.075	0.073	0.147
G3	−111,224.547	−111,220.250	−111,224.463	−111,220.335	0.084	0.086	0.170
G4	−83,924.161	−83,919.580	−83,924.108	−83,919.634	0.053	0.055	0.108
G5	−89,055.602	−89,050.951	−89,055.549	−89,051.004	0.053	0.053	0.106
G6	−100,140.081	−100,134.146	−100,140.007	−100,135.690	0.074	1.544	1.619

.

All complexes exhibit negative $\Delta G_{\mathrm{inj}}$ values, confirming that electron injection from the excited dye into the ${\mathrm{TiO}}_2$ conduction band is thermodynamically favorable for the entire set. Donor-substituted dyes (2 and 3) generally display the largest injection driving forces, reflecting their elevated excited-state oxidation potentials, while acceptor-substituted dyes (4 and 5) provide less negative but still strongly favorable values due to LUMO stabilization. The push–pull systems (6) fall between these two extremes and maintain sufficiently exergonic injection across all frameworks.

Dye regeneration by the ${\mathrm{I}}^{-}/{\mathrm{I}}_3^{-}$ redox couple is also favorable for all complexes, as indicated by negative $\Delta G_{\mathrm{reg}}$ values. The magnitude of $\Delta G_{\mathrm{reg}}$ follows the expected donor–acceptor logic: donor-rich dyes, which possess higher HOMO energies, regenerate more easily but with less negative driving force, whereas acceptor-rich dyes exhibit more exergonic regeneration. The balanced thermodynamics observed for the push–pull designs (typically $-0.5$ to $-1.0$ eV) places them in an acceptable range.

The light-harvesting efficiency mirrors the oscillator strengths of the lowest intense transitions. Double-donor dyes (3) consistently display the highest LHE values, while double-acceptor dyes (5) also show substantial efficiencies. Unsubstituted and singly substituted dyes exhibit moderate LHE, and the push–pull systems (6), although not as bright as donor-rich dyes, combine respectable oscillator strengths with markedly redshifted transitions. From a DSSC perspective, dyes that balance strong absorption with favorable spectral positioning, such as B5, C5, D5, E5, F5, and G5, as well as the push–pull E6–G6 series, appear particularly promising.

Excited-state lifetimes also follow clear trends. Donor-rich dyes, which show the largest oscillator strengths, yield the shortest lifetimes ($\tau \approx$ 3–5 ns), whereas acceptor-only and especially push–pull dyes exhibit longer excited state lifetime values ($\tau \approx$ 20–35 ns). In principle, dye sensitizers with longer excited-state lifetimes are more favorable for efficient charge transfer. Thus, acceptor-only and push–pull dyes (configurations 4, 5, and 6) are expected to exhibit more effective charge separation and, consequently, more favorable electron-injection behavior than the other configurations. While these excited-state lifetime values do not represent full MLCT lifetimes, which require explicit treatment of nonradiative channels, they nonetheless highlight relative differences in radiative behavior across the series.

Finally, the hole-transport reorganization energies, ${\lambda }_{\mathrm{hole}}$ (Table 5), provide insight into the structural changes accompanying oxidation. Many dyes across frameworks A–G exhibit low values of reorganization energies (0.10–0.15 eV), indicative of rigid coordination environments and favorable hole mobility. Particularly low values are observed for configurations 4 and 5 in nearly all frameworks, reinforcing the beneficial role of acceptor substitution. In contrast, a few systems, most notably A1, C1, C2, and C6, display significantly higher ${\lambda }_{\mathrm{hole}}$ (>0.25 eV), suggesting larger geometric rearrangements upon oxidation and potentially less efficient charge-transport performance. With the exception of isolated outliers such as G6, the push–pull systems generally retain low reorganization energies, confirming that strong electronic tuning does not compromise structural rigidity. An outlier is observed for G6, which exhibits a markedly larger ${\lambda }_{\mathrm{hole}}$, mainly due to an increased ${\lambda }_2$ component. This behavior reflects stronger structural relaxation upon oxidation (larger mismatch between the optimized neutral and cationic geometries), consistent with enhanced charge redistribution in the push–pull tripodal architecture. All calculations used to compute ${\lambda }_{\mathrm{hole}}$ were verified to be SCF-converged under identical settings, suggesting that the large value is intrinsic rather than a convergence artifact.

Taken together, these descriptors point to clear design principles for optimizing Fe–NHC sensitizers in DSSCs. Donor substitution enhances injection driving force and oscillator strength, acceptor substitution produces the largest redshifts and lowers reorganization energy, and the combined push–pull effect yields dyes with balanced injection, regeneration, absorption strength, and structural stability. Among the 42 candidates, the double-acceptor configurations (5) in frameworks B–D and push–pull derivatives (6) in frameworks E–G, emerge as particularly attractive, offering notable improvements across multiple performance variables.

3. Materials and Methods

All quantum chemical calculations have been performed with ORCA v5.0.2 code [133,134]. Cube files were generated using the ORCA program orca_plot. Molecular orbital isosurface densities have been visualized using Gabedit v2.5.1 [135]. The ground state equilibrium geometries of all species have been optimized without any symmetry restriction using DFT employing B3LYP functional and the Ahlrichs def2-TZVP [136] basis set. Frequency calculations were performed at the same level of theory as the geometry optimizations to confirm that all optimized structures correspond to true minima, as evidenced by the absence of imaginary frequencies. In addition, single-point energy calculations were performed for both neutral and cationic species at the same B3LYP/def2-TZVP level of theory.

The lowest 50 singlet excited states at the optimized geometries were calculated using TD-DFT with the def2-TZVP basis set and the B3LYP functional. All TD-DFT calculations were performed with the Tamm–Dancoff approximation (TDA) [137], which is set as the default in ORCA. The linear-response conductor-like polarizable continuum model (LR-CPCM) [138] and acetonitrile were used as solvents in all calculations. DFT and TD-DFT calculations were sped up with the resolution-of-the-identity (RI) approximation through the RIJCOSX procedure in ORCA [139,140]. The def2/J auxiliary basis set [141] was used with RIJCOSX. Converged SCF orbitals were obtained using the TightSCF setting in ORCA (energy change $={10}^{-8}{E}_{\mathrm{h}}$).

To assess whether a single-reference treatment is reasonable for the representative Fe–NHC dye A1, we carried out a DLPNO-CCSD/def2-SVP single-point calculation. The resulting T1 diagnostic is found to be 0.01499, consistent with a predominantly single-reference wavefunction. Moreover, the coupled-cluster amplitudes are also found to be well-behaved (largest amplitudes ∼0.05), and the calculation converges smoothly from a closed-shell RHF reference. These diagnostics support the use of single-reference DFT for comparative trend analysis across the dye series.

The B3LYP functional was selected for its well-established performance with Fe(II) N-heterocyclic carbene complexes. Previous benchmark and experimental-computational studies have shown that B3LYP reliably reproduces ground-state geometries, Fe–ligand bond lengths, and ligand-field trends in Fe–NHC systems, while providing a physically meaningful description of MLCT-dominated excited electronic states [61,63,64,70,74,142]. For time-dependent calculations, TD-B3LYP has been demonstrated to capture MLCT excitation energies and substituent-dependent trends with reasonable accuracy, particularly when the focus is on relative comparisons rather than absolute excitation energies. Range-separated hybrids, such as CAM-B3LYP and LC-BLYP, typically increase long-range exact exchange and often lead to systematic blue shifts of MLCT transitions in transition-metal complexes [143,144,145]. Since the present work focuses on comparative substituent-induced trends rather than absolute excitation energies, B3LYP was retained to ensure internal consistency across the dye series. Furthermore, the def2-TZVP basis set was selected as a balanced polarized triple-zeta basis that provides an accurate description of both the Fe(II) center and the ligand $\pi$-system [142]. The lowest excited states examined in this work are predominantly MLCT in character and remain spatially localized on the metal center and conjugated ligand framework. As a result, the absence of diffuse functions is not expected to significantly influence their energies or oscillator strengths. Given the emphasis of the present study on comparative photophysical trends across a large series of dyes, def2-TZVP offers an appropriate balance between accuracy and computational efficiency. Empirical dispersion corrections were not included, as the systems under investigation are dominated by strong metal–ligand coordination and intramolecular covalent interactions. Dispersion effects are therefore expected to have a negligible influence on the electronic structure and MLCT excitation trends. Accordingly, the present work does not aim to establish absolute excitation energies or variationally optimal electronic gaps, but rather to extract reliable relative trends across a chemically consistent set of Fe–NHC sensitizers.

Herein, we have considered the following approximations: The negative of the highest occupied molecular orbital (HOMO) energy, which is an estimate of the vertical ground state oxidation potential (GSOP): $\mathrm{GSOP}=-{\epsilon }_{\mathrm{HOMO}}$. Excited state oxidation potential (ESOP) is evaluated as [146]

$$\mathrm{ESOP}=\mathrm{GSOP}-E^{\mathrm{vert}}\left({\lambda }_{\max }\right)$$

(1)

where $E^{\mathrm{vert}}$ is the vertical excitation energy $E^{\mathrm{vert}}$ associated with the ${\lambda }_{\max }$ at the ground state geometry. Free energy of electron injection ($\Delta G_{\mathrm{inj}}$) is calculated as [146]

$$\Delta G_{\mathrm{inj}}=\mathrm{ESOP}-E_{\mathrm{CB}}=\mathrm{GSOP}-E^{\mathrm{vert}}\left({\lambda }_{\max }\right)-E_{\mathrm{CB}}$$

(2)

where $E_{\mathrm{CB}}$ is the reduction potential of the conduction band (CB) of the semiconductor. $E_{\mathrm{CB}}=4.0$ eV for ${\mathrm{TiO}}_2$ [147]. The oxidation potential of the dyes must be more positive than the ${\mathrm{I}}^{-}/{\mathrm{I}}_3^{-}$ redox couple, ensuring that there is enough driving force for a fast and efficient regeneration of the dye cation radical. Free energy of dye regeneration ($\Delta G_{\mathrm{reg}}$) is calculated as

$$\Delta G_{\mathrm{reg}}=E_{\mathrm{electrolyte}}^{\mathrm{redox}}-\mathrm{GSOP}$$

(3)

where $E_{\mathrm{electrolyte}}^{\mathrm{redox}}$ is the redox potential of the electrolyte. $E_{\mathrm{electrolyte}}^{\mathrm{redox}}=4.8$ eV for ${\mathrm{I}}^{-}/{\mathrm{I}}_3^{-}$ redox couple [148]. Light-harvesting efficiencies (LHE) are found using the oscillator strengths f obtained by TD-DFT calculations as [149]

$$\mathrm{LHE}=1-{10}^{-f}$$

(4)

Reorganization energy for hole transfer (${\lambda }_{\mathrm{hole}}$) is calculated as [150]

$${\lambda }_{\mathrm{hole}}={\lambda }_1+{\lambda }_2=E^0\left(Q^{+}\right)-E^0\left(Q^0\right)+E^{+}\left(Q^0\right)-E^{+}\left(Q^{+}\right)$$

(5)

The excited state lifetime $\tau$ in nanoseconds (ns) is approximated as [151]

$$\tau ={\displaystyle \frac{1.499}{f{E}^2}}$$

(6)

where E is the TD-DFT excitation energy, in ${\mathrm{cm}}^{-1}$, and f is the oscillator strength of the corresponding excited electronic state. The calculated excited-state lifetimes ($\tau$) correspond to purely radiative lifetimes estimated from TD-DFT oscillator strengths and excitation energies. Nonradiative decay pathways, which dominate experimentally observed MLCT lifetimes in Fe(II) complexes, are not explicitly included, and therefore, $\tau$ values are intended for relative comparison only. Moreover, all calculated GSOP, ESOP, ${\mathrm{TiO}}_2$ conduction-band, and the electrolyte redox potential discussed below are relative to the vacuum (i.e., absolute potentials) and not referred to a reference electrode.

It should be noted that the computational approach adopted in this work is intended to yield consistent, physically meaningful trends rather than exact absolute values for gap energies or absorption onsets. Although alternative approximations or higher levels of theory may improve the accuracy of absolute excitation energies, the modeling of the present work is designed to ensure meaningful analysis of relative trends in absorption properties and charge-transfer energetics.

4. Conclusions

In this work, a systematic computational investigation of 42 Fe–NHC sensitizers was performed to elucidate how donor, acceptor, and donor–acceptor substitution patterns modulate their structural, electronic, and photophysical properties relevant to dye-sensitized solar cells. Several clear and transferable design principles emerge from this study.

• First, donor substitution primarily destabilizes the HOMO and enhances oscillator strength, leading to more intense absorption but only modest redshifts in MLCT transition energies. In contrast, acceptor substitution significantly stabilizes the LUMO and produces the largest redshifts, effectively extending absorption toward lower energies.
• Second, the combined donor–acceptor (push–pull) configuration provides the most balanced photophysical profile, simultaneously achieving reduced MLCT excitation energies, preserved oscillator strengths, favorable electron-injection and dye-regeneration driving forces, and relatively long radiative excited-state lifetimes.
• Among the investigated systems, double-acceptor dyes (configuration 5) in frameworks B–D and push–pull dyes (configuration 6) in the tripodal frameworks E–G emerge as the most promising candidates. In particular, complexes such as B5, C5, D5, E6, F6, and G6 combine substantial absorption redshifts with favorable charge-transfer energetics, making them attractive targets for further experimental exploration.

Overall, this study demonstrates that systematic donor–acceptor engineering within strong-field Fe–NHC coordination environments may provide a powerful strategy for overcoming traditional limitations of iron-based sensitizers. The trends and insights reported here offer clear guidance for the rational design of next-generation, earth-abundant DSSC dyes with improved light-harvesting and charge-transfer performance.