Exact Exchange Research Articles

A Look at Real‐World Transition‐Metal Thermochemistry and Kinetics with Local Hybrid Functionals

AbstractLocal hybrid functionals (LHs) use a position‐dependent admixture of exact exchange in real space, which has previously been shown to offer various advantages over global hybrids and the potential to construct functionals with wide applicability. While main‐group thermochemistry and kinetics and other properties have already been studied extensively, no broad and systematic investigation for the energetics of transition‐metal complexes has been reported so far for LHs. To close this gap, we evaluate eight LHs for three previously reported test sets on barrier heights and reaction energies of real‐world transition metal complexes, in comparison with several other rung‐4 hybrid functionals. The recent LH20t‐D4 method emerges as the top‐performing functional for the overall benchmark, comparable to the simpler TPSS0‐D4 and slightly before the more complex range‐separated ωB97M‐V. But LH20t‐D4 and ωB97M‐V perform much better for main‐group energetics, making them overall more reliable tools to study organometallic reaction mechanisms. Given also its previously observed excellent performance for mixed‐valence systems, LH20t‐D4 is thus a widely applicable functional in both main‐group and transition‐metal chemistry, while also providing convincing accuracy for many spectroscopic properties. The earlier LH14t‐calPBE‐D4 local hybrid also performs well, while some first‐generation LHs fall behind.

Crystal Structure Evolution of Fluorine under High Pressure

Fluorinated compounds in the last decade were applied as photo-thermo-refractive glasses, high-stress lubricants, and pharmaceutical drugs due to their good mechanical properties and biocompatibility. Although fluorinated materials are largely employed, the possibility of predicting new structures was limited by the impossibility to use density functional theory (DFT) to describe interatomic and intermolecular interactions correctly. This is seen linearly to increase with fluorine concentration. In crystal structure prediction, modern algorithms are usually combined with first-principles methods employed for global solution, which sometimes fail to describe systems as in the case of strongly correlated materials. Fluorine is one of the tricky elements, which is characterized by relativistic effects and no overlap between the DFT exchange hole and the exact exchange hole. Thus, no relativistic exchange–correlation functional was seen to adequately describe fluorine. In this work, we have found an excellent compromise to investigate fluorinated materials using a combination of SCAN (exchange) and rVV10 (correlation) functionals. This was found through the fundamental study of α- and β-fluorine phases, showing α-fluorine as the most stable structure at temperatures lower than 35 K and 0 GPa with respect to β-fluorine. Further, we have computed crystal structure evolution under pressure looking for new stable fluorine allotropes using the USPEX evolutionary algorithm coupled with the SCAN-rVV10 exchange–correlation functional discovering two phase transitions: one from C2/c (i.e., α-fluorine) to Cmca at ∼5.5 GPa and from Cmca to the P4̅21c phase at 220 GPa; all these structures possess metallic behavior. The achievements of this work lie far beyond the thermodynamic of fluorine crystals under pressure. It will give the right instrument to understand the chemical behavior of fluorinated materials under pressure with consequent great speed up to the crystal structure prediction of fluorinated and fluorine-based materials.

Excited-State Properties for Extended Systems: Efficient Hybrid Density Functional Methods.

Time-dependent density functional theory has become state-of-the-art for describing photophysical and photochemical processes in extended materials because of its affordable cost. The inclusion of exact exchange was shown to be essential for the correct description of the long-range asymptotics of electronic interactions and thus a well-balanced description of valence, Rydberg, and charge-transfer excitations. Several approaches for an efficient treatment of exact exchange have been established for the ground state, while implementations for excited-state properties are rare. Furthermore, the high computational costs required for excited-state properties in comparison to ground-state computations often hinder large-scale applications on periodic systems with hybrid functional accuracy. We therefore propose two approximate schemes for improving computational efficiency for the treatment of exact exchange. Within the auxiliary density matrix method (ADMM), exact exchange is estimated using a relatively small auxiliary basis and the introduced basis set incompleteness error is compensated by an exchange density functional correction term. Benchmark results for a test set of 35 molecules demonstrate that the mean absolute error introduced by ADMM is smaller than 0.3 pm for excited-state bond lengths and in the range of 0.02-0.04 eV for vertical excitation, adiabatic excitation, and fluorescence energies. Computational timings for a series of covalent-organic frameworks demonstrate that a speed-up of at least 1 order of magnitude can be achieved for excited-state geometry optimizations in comparison to conventional hybrid functionals. The second method is to use a semiempirical tight binding approximation for both Coulomb and exchange contributions to the excited-state kernel. This simplified Tamm-Dancoff approximation (sTDA) achieves an accuracy comparable to approximated hybrid density functional theory when referring to highly accurate coupled-cluster reference data. We find that excited-state bond lengths deviate by 1.1 pm on average and mean absolute errors in vertical excitation, adiabatic excitation, and fluorescence energies are in the range of 0.2-0.5 eV. In comparison to ADMM-approximated hybrid functional theory, sTDA accelerates the computation of broad-band excitation spectra by 1 order of magnitude, suggesting its potential use for large-scale screening purposes.

Electronic structure of intrinsic defects in c -gallium nitride: Density functional theory study without the jellium approximation

We report the first nonjellium, systematic, density functional theory (DFT) study of intrinsic and extrinsic defects and defect levels in zinc-blende (cubic) gallium nitride. We use the local moment counter charge (LMCC) method, the standard Perdew-Becke-Ernzerhoff (PBE) exchange-correlation potential, and two pseudopotentials, where the Ga $3d$ orbitals are either in the core $({d}^{0})$ or explicitly in the valence set $({d}^{10})$. We studied 64, 216, 512, and 1000 atom supercells, and demonstrated convergence to the infinite limit, crucial for delineating deep from shallow states near band edges, and for demonstrating the elimination of finite cell-size errors. Contrary to common claims, we find that exact exchange is not required to obtain defect levels across the experimental band gap. As was true in silicon, silicon carbide, and gallium arsenide, the extremal LMCC defect levels of the aggregate of defects yield an effective LMCC defect band gap that is within 10% of the experimental gap (3.3 eV) for both pseudopotentials. We demonstrate that the gallium vacancy is more complicated than previously reported. There is dramatic metastability--a nearest-neighbor nitrogen atom shifts into the gallium site, forming an antisite, nitrogen vacancy pair, which is more stable than the simple vacancy for positive charge states. Our assessment of the ${d}^{0}$ and ${d}^{10}$ pseudopotentials yields minimal differences in defect structures and defect levels. The better agreement of the ${d}^{0}$ lattice constant with experiment suggests that the more computationally economical ${d}^{0}$ pseudopotentials are sufficient to achieve the fidelity possible within the physical accuracy of DFT, and thereby enable calculations in larger supercells necessary to demonstrate convergence with respect to finite size supercell errors.

Density-functional theory vs density-functional fits.

Kohn-Sham density-functional theory (DFT), the predominant framework for electronic structure computations in chemistry today, has undergone considerable evolution in the past few decades. The earliest DFT approximations were based on uniform electron gas models completely free of empirical parameters. Tremendous improvements were made by incorporating density gradients and a small number of parameters, typically one or two, obtained from fits to atomic data. Incorporation of exact exchange and fitting to molecular data, such as experimental heats of formation, allowed even further improvements. This, however, opened a Pandora's Box of fitting possibilities, given the limitless choices of chemical reactions that can be fit. The result is a recent explosion of DFT approximations empirically fit to hundreds, or thousands, of chemical reference data. These fitted density functionals may contain several dozen empirical parameters. What has been lost in this fitting trend is physical modeling based on theory. In this work, we present a density functional comprising our best efforts to model exchange-correlation in DFT using good theory. We compare its performance to that of heavily fit density functionals using the GMTKN55 chemical reference data of Goerigk and co-workers [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. Our density-functional theory, using only a handful of physically motivated pre-factors, competes with the best heavily fit Kohn-Sham functionals in the literature.

Quantum mechanical simulation of various phases of KVF3 perovskite

The relative stability ΔE of the cubic Pm m (C), of the two tetragonal P bm (T1) and I cm (T2), and of the orthorhombic Pbnm (O) phases of KVF3 has been computed both for the ferromagnetic (FM) and antiferromagnetic (AFM) solutions, by using the B3LYP full range hybrid functional and the Hartree–Fock (HF) Hamiltonian, an all-electron Gaussian type basis set and the CRYSTAL code. The stabilization of the T2 phase with respect to the C one (152 μHa for B3LYP, 180 μHa for HF, per 2 formula units) is due to the rotation of the VF6 octahedra with respect to the c axis, by 4.1–4.6 degrees. The O phase is slightly less stable than the T2 phase (by 6 and 20 μHa for B3LYP and HF); it is, however, a stable structure as the dynamical analysis confirms. The mechanism of the stabilization of the AFM solution with respect to the FM one is discussed through the spin density maps, and is related to the key role of the exact exchange term (20% in B3LYP, 100% in HF). The G-AFM phase (the first six neighbors of the reference V ion with spin reversed) is more stable than the FM one by about 500 (HF) and 1800 (B3LYP) μHa per two formula units. A volume reduction is observed in the C to T passage, and in the FM to AFM one, both being of the order of 0.3–0.5 at the B3LYP level. Atomic charges, magnetic moments and bond populations, evaluated according to a Mulliken partition of the charge a spin density functions, complete the analysis. The IR and Raman spectra of the FM and AFM C, T2 and O cells are discussed; the only noticeable difference between the various space groups appears in the modes with wavenumbers lower than 100 cm−1.

First steps towards achieving both ultranonlocality and a reliable description of electronic binding in a meta-generalized gradient approximation

It has been demonstrated that a meta-generalized gradient approximation (meta-GGA) to the exchange-correlation energy of density functional theory can show a pronounced derivative discontinuity and significant ultranonlocality similar to exact exchange, and can accurately predict the band gaps of many solids. We here investigate whether within the meta-GGA form these properties are compatible with a reasonable accuracy for electronic binding energies. With the help of two transparent and inexpensive correlation functional constructions we demonstrate that this is the case. We report atomization energies, show that reliable bond lengths are obtained for many systems, and find promising results for reaction barrier heights, while keeping the strong derivative discontinuity and ultranonlocality, and thus accuracy for band gaps.

Double Hybrids and Noncovalent Interactions: How Far Can We Go?

The accurate evaluation of weak noncovalent interactions in large, that is those containing up to thousand atoms, molecular systems represents a difficult challenge for any quantum chemical method. Indeed, some approximations are often introduced to render affordable these calculations. Here, we consider the PBE-QIDH/DH-SVPD protocol, combining a nonempirical double hybrid functional (PBE-QIDH) with a small basis set (DH-SVPD) tailored for noncovalent interactions with a double aim: (i) explore the robustness and accuracy of this protocol with respect to other Density Functional Approximations; (ii) illustrate how its performances are affected by the computational parameters underlying the calculation of the exact exchange and the Coulomb contribution, as well as the perturbative term. To this end, we consider three data sets, namely S66, L7, and CiM13, incorporating molecules of increasing size. On the bright side, our results suggest that the PBE-QIDH/DH-SVPD protocol is particularly accurate for large systems such as those contained in the CiM13 set (up to more than 1000 atoms and 14 000 basis functions), for which the DLPNO approximation leads to a significant speed-up for the evaluation of the perturbative correlation term. However, our analysis also points out the limit of this statistical exercise, when the quality of the reference data cannot be easily assessed, due to the size of the molecular complexes involved, and when the number of molecules is limited.

The binding of atomic hydrogen on graphene from density functional theory and diffusion Monte Carlo calculations.

In this work, density functional theory (DFT) and diffusion Monte Carlo (DMC) methods are used to calculate the binding energy of a H atom chemisorbed on the graphene surface. The DMC value of the binding energy is about 16% smaller in magnitude than the Perdew-Burke-Ernzerhof (PBE) result. The inclusion of exact exchange through the use of the Heyd-Scuseria-Ernzerhof functional brings the DFT value of the binding energy closer in line with the DMC result. It is also found that there are significant differences in the charge distributions determined using PBE and DMC approaches.

Fast All-Electron Hybrid Functionals and Their Application to Rare-Earth Iron Garnets

Virtual materials design requires not only the simulation of a huge number of systems, but also of systems with ever larger sizes and through increasingly accurate models of the electronic structure. These can be provided by density functional theory (DFT) using not only simple local approximations to the unknown exchange and correlation functional, but also more complex approaches such as hybrid functionals, which include some part of Hartree–Fock exact exchange. While hybrid functionals allow many properties such as lattice constants, bond lengths, magnetic moments and band gaps, to be calculated with improved accuracy, they require the calculation of a nonlocal potential, resulting in high computational costs, that scale rapidly with the system size. This limits their wide application. Here, we present a new highly-scalable implementation of the nonlocal Hartree-Fock-type potential into FLEUR—an all-electron electronic structure code that implements the full-potential linearized augmented plane-wave (FLAPW) method. This implementation enables the use of hybrid functionals for systems with several hundred atoms. By porting this algorithm to GPU accelerators, we can leverage future exascale supercomputers which we demonstrate by reporting scaling results for up to 64 GPUs and up to 12,000 CPU cores for a single k-point. As proof of principle, we apply the algorithm to large and complex iron garnet materials (YIG, GdIG, TmIG) that are used in several spintronic applications.

Hybrid functionals with local range separation: Accurate atomization energies and reaction barrier heights.

Range-separated hybrid approximations to the exchange-correlation density functional mix exact and semi-local exchange in a position-dependent manner. In their conventional form, the range separation is controlled by a constant parameter. Turning this constant into a density functional leads to a locally space-dependent range-separation function and thus a more powerful and flexible range-separation approach. In this work, we explore the self-consistent implementation of a local range-separated hybrid, taking into account a one-electron self-interaction correction and the behavior under uniform density scaling. We discuss different forms of the local range-separation function that depend on the electron density, its gradient, and the kinetic energy density. For test sets of atomization energies, reaction barrier heights, and total energies of atoms, we demonstrate that our best model is a clear improvement over common global range-separated hybrid functionals and can compete with density functionals that contain multiple empirical parameters. Promising results for equilibrium bond lengths, harmonic vibrational frequencies, and vertical ionization potentials further underline the potential and flexibility of our approach.

Single Excitation Energies Obtained from the Ensemble “HOMO–LUMO Gap”: Exact Results and Approximations

In calculations based on density functional theory, the "HOMO-LUMO gap" (difference between the highest occupied and lowest unoccupied molecular orbital energies) is often used as a low-cost, ad hoc approximation for the lowest excitation energy. Here we show that a simple correction based on rigorous ensemble density functional theory makes the HOMO-LUMO gap exact in principle and significantly more accurate in practice. The introduced perturbative ensemble density functional theory approach predicts different and useful values for singlet-singlet and singlet-triplet excitations, using semilocal and hybrid approximations. Excitation energies are similar in quality to time-dependent density functional theory, especially at high fractions of exact exchange. The approach therefore offers an easy-to-implement and low-cost route to robust prediction of molecular excitation energies.

Benchmarking of Density Functionals for the Description of Optical Properties of Newly Synthesized π-Conjugated TADF Blue Emitters.

Computational modeling of the optical characteristics of organic molecules with potential for thermally activated delayed fluorescence (TADF) may assist markedly the development of more efficient emitting materials for organic light-emitting diodes. Recent theoretical studies in this area employ mostly methods from density functional theory (DFT). In order to obtain accurate predictions within this approach, the choice of a proper functional is crucial. In the current study, we focus on testing the performance of a set of DFT functionals for estimation of the excitation and emission energy and the excited singlet-triplet energy gap of three newly synthesized compounds with capacity for TADF. The emitters are designed specifically to enable charge transfer by π-electron conjugation, at the same time possessing high-energy excited triplet states. The functionals chosen for testing are from various groups ranging from gradient-corrected through global hybrids to range-separated ones. The results show that the monitored optical properties are especially sensitive to how the long-range part of the exchange energy is treated within the functional. The accurate functional should also be able to provide well balanced distribution of the π-electrons among the molecular fragments. Global hybrids with moderate (less than 0.4) share of exact exchange (B3LYP, PBE0) and the meta-GGA HSE06 are outlined as the best performing methods for the systems under study. They can predict all important optical parameters correctly, both qualitatively and quantitatively.

Analysis of the Geometric and Electronic Structure of Spin-Coupled Iron-Sulfur Dimers with Broken-Symmetry DFT: Implications for FeMoco.

The open-shell electronic structure of iron–sulfur clusters presents considerable challenges to quantum chemistry, with the complex iron–molybdenum cofactor (FeMoco) of nitrogenase representing perhaps the ultimate challenge for either wavefunction or density functional theory. While broken-symmetry density functional theory has seen some success in describing the electronic structure of such cofactors, there is a large exchange–correlation functional dependence in calculations that is not fully understood. In this work, we present a geometric benchmarking test set, FeMoD11, of synthetic spin-coupled Fe–Fe and Mo–Fe dimers, with relevance to the molecular and electronic structure of the Mo-nitrogenase FeMo cofactor. The reference data consists of high-resolution crystal structures of metal dimer compounds in different oxidation states. Multiple density functionals are tested on their ability to reproduce the local geometry, specifically the Fe–Fe/Mo–Fe distance, for both antiferromagnetically coupled and ferromagnetically coupled dimers via the broken-symmetry approach. The metal–metal distance is revealed not only to be highly sensitive to the amount of exact exchange in the functional but also to the specific exchange and correlation functionals. For the antiferromagnetically coupled dimers, the calculated metal–metal distance correlates well with the covalency of the bridging metal–ligand bonds, as revealed via the corresponding orbital analysis, Hirshfeld S/Fe charges, and Fe–S Mayer bond order. Superexchange via bridging ligands is expected to be the dominant interaction in these dimers, and our results suggest that functionals that predict accurate Fe–Fe and Mo–Fe distances describe the overall metal–ligand covalency more accurately and in turn the superexchange of these systems. The best performing density functionals of the 16 tested for the FeMoD11 test set are revealed to be either the nonhybrid functionals r2SCAN and B97-D3 or hybrid functionals with 10–15% exact exchange: TPSSh and B3LYP*. These same four functionals are furthermore found to reproduce the high-resolution X-ray structure of FeMoco well according to quantum mechanics/molecular mechanics (QM/MM) calculations. Almost all nonhybrid functionals systematically underestimate Fe–Fe and Mo–Fe distances (with r2SCAN and B97-D3 being the sole exceptions), while hybrid functionals with >15% exact exchange (including range-separated hybrid functionals) overestimate them. The results overall suggest r2SCAN, B97-D3, TPSSh, and B3LYP* as accurate density functionals for describing the electronic structure of iron–sulfur clusters in general, including the complex FeMoco cluster of nitrogenase.

On the Sensitivity to Density-Functional Approximations for CO Binding Energies of Single-Atom Catalysts in Nitrogen-Doped Graphene.

Density functional theory (DFT) methods are the working horse in screening new catalytic materials. They are widely used to predict trends in binding energies, which are then used to compare the activity of different materials. The binding strength of CO is an important descriptor to the CO2 reduction catalytic activity of the single transition metal atoms embedded on nitrogen-doped graphene (TM/NG). In this work, however, we show that CO binding strengths in different TM/NG has very different sensitivity to DFT methods. Specifically, Fe/NG CO binding energy changes dramatically with the percentage of exact exchange in the functional; Co/NG does less so, while Ni/NG nearly has no change. Such varying behaviors is a direct result of different local spin configurations, similar to the performance of DFT methods for metal porphyrin complexes. Therefore, caution should be exercised when using DFT binding energies for quantitative predictions in TM/NG single atom catalysis.

All-Electron BSE@GW Method for K-Edge Core Electron Excitation Energies.

We present an accurate computational approach to calculate absolute K-edge core electron excitation energies as measured by X-ray absorption spectroscopy. Our approach employs an all-electron Bethe-Salpeter equation (BSE) formalism based on GW quasiparticle energies (BSE@GW) using numeric atom-centered orbitals (NAOs). The BSE@GW method has become an increasingly popular method for the computation of neutral valence excitation energies of molecules. However, it was so far not applied to molecular K-edge excitation energies. We discuss the influence of different numerical approximations on the BSE@GW calculation and employ in our final setup (i) exact numeric algorithms for the frequency integration of the GW self-energy, (ii) G0W0 and BSE starting points with ∼50% of exact exchange, (iii) the Tamm-Dancoff approximation and (iv) relativistic corrections. We study the basis set dependence and convergence with common Gaussian-type orbital and NAO basis sets. We identify the importance of additional spatially confined basis functions as well as of diffuse augmenting basis functions. The accuracy of our BSE@GW method is assessed for a benchmark set of small organic molecules, previously used for benchmarking the equation-of-motion coupled cluster method [Peng et al., J. Chem. Theory Comput., 2015, 11, 4146], as well as the medium-sized dibenzothiophene (DBT) molecule. Our BSE@GW results for absolute excitation energies are in excellent agreement with the experiment, with a mean average error of only 0.63 eV for the benchmark set and with errors <1 eV for the DBT molecule.

Length-Gauge Optical Matrix Elements in WIEN2k

Hybrid exchange-correlation functionals provide superior electronic structure and optical properties of semiconductors or insulators as compared to semilocal exchange-correlation potentials due to admixing a portion of the non-local exact exchange potential from a Hartree–Fock theory. Since the non-local potential does not commute with the position operator, the momentum matrix elements do not fully capture the oscillator strength, while the length-gauge velocity matrix elements do. So far, length-gauge velocity matrix elements were not accessible in the all-electron full-potential WIEN2k package. We demonstrate the feasibility of computing length-gauge matrix elements in WIEN2k for a hybrid exchange-correlation functional based on a finite difference approach. To illustrate the implementation we determined matrix elements for optical transitions between the conduction and valence bands in GaAs, GaN, (CH3NH3)PbI3 and a monolayer MoS2. The non-locality of the Hartree–Fock exact exchange potential leads to a strong enhancement of the oscillator strength as noticed recently in calculations employing pseudopotentials (Laurien and Rubel: arXiv:2111.14772 (2021)). We obtained an analytical expression for the enhancement factor for the difference in eigenvalues not captured by the kinetic energy. It is expected that these results can also be extended to other non-local potentials, e.g., a many-body GW approximation.

Density Functional Theory Estimate of Halide Perovskite Band Gap: When Spin Orbit Coupling Helps

The description of the band gap of halide perovskites at the level of density functional theory (DFT) has been subject of several studies but still presents significant problems and deviations from experimental values. Various approaches have been proposed, including the use of system-specific hybrid functionals with a variable amount of exact exchange or the explicit inclusion of spin–orbit coupling (SOC) effects. In this work, we present a pragmatic recipe to compute the band gap of halide perovskites with a minimum average error. The recipe is tested on a set of 36 halide perovskites of the type ABX3 [A = Cs, methyl-ammonium (MA), and formamidinium (FA); B = Ge, Sn, and Pb; and X = Cl, Br, and I] for which experimental estimates of the band gap have been reported in the literature. Upon assessment of the accuracy of commonly used DFT functionals and the analysis of their performances based on error and statistical analysis, we suggest a strategy to compute band gaps in halide perovskites with a single functional. This is based on the use of the hybrid HSE06 functional where SOC is included exclusively for Pb-containing compounds. The results are rationalized in terms of the materials’ chemical nature and are corroborated by the prediction of their expected efficiencies in solar cells. The calculated efficiencies from band gaps obtained with the proposed approach closely follow the experimental trend, demonstrating the importance of adopting a reliable but material-independent computational strategy to screen new halide perovskite materials for solar energy conversion.

DFT Calculations for Structural, Electronic, and Magnetic Properties of ZnFe2O4 Spinel Oxide: The Role of Exchange-Correlation Functional

In this study, quantum-mechanical calculations in the framework of the Density Functional Theory (DFT) were performed to investigate the role of exchange-correlation functional in describing structural, electronic, and magnetic properties of ZnFe2O4. Herein B3LYP, PBE0, B1WC, and WC1LYP functionals implemented in the CRYSTAL17 code were considered due to the different amounts of the exact Hartree-Fock exchange fraction. In particular, the role of HF fraction on ZnFe2O4 properties was addressed for the first time. Indeed, structural, electronic, and magnetic properties indicate the dependence upon the exchange fraction, where WC1LYP with a 16% exact HF exchange exhibits the best performance compared to the other hybrid functionals. The obtained results reveal an excellent agreement for bandgap, local magnetic moment, long-range magnetic ordering, and unit-cell lattice parameters, overcoming previous theoretical studies based on local/semilocal exchange-correlation treatments. These results confirm the importance of hybrid HF/DFT with controlled HF term contribution to describe the essential features of strongly correlated materials.

Evaluating the impact of Hartree-Fock exact exchange on the performance of global hybrid functionals for the vertical excited-state energies of fused-ring electron acceptors using TD-DFT.

The acceptor-donor-acceptor structured fused-ring electron acceptors (FREAs) have piqued interest for organic solar cells. We herein employ time-dependent density functional theory to evaluate the effect of Hartree-Fock exact exchange (HFX) on the performance of 16 global hybrid functionals for computing the maximum absorption wavelengths (λver-theo) and the vertical excitation energies (Ever-theo) of 34 molecules. We customize the HFX ratio in the functionals used to perform an in-depth analysis of its impact on the Ever-theo values. The computed λver-theo values strictly follow an inverse proportionality to the HFX percentage. The performance of the methods with the same ratio of HFX is almost identical, such as B3LYP, B3PW91, and mPW3PBE containing 20% HFX. The performance enhances with a relatively higher HFX ratio of 21% in X3LYP, B971, B972, and 22% in B98 giving smaller deviations. APF and APFD containing 23% HFX provide the smallest deviations for all compounds, with a mean signed error limited to 0.02 eV and a mean absolute error (MAE) of 0.06 eV. The performance drops using M06 and M05 with comparatively higher HFX ratios providing MAE values of 0.07 eV and 0.1 eV, respectively. M06-2X with 54% HFX provides the largest MAE value of 0.35 eV. The lowest obtained MAE is 0.06 eV at 23 to 25% HFX in most of the functionals considered in this study, suggesting that these are the optimal values for the prediction of excitation energies of FREAs. It has also been found that global hybrids seem to be more efficient for larger-sized molecules with a smaller bandgap.