Time-domain Density Functional Theory Research Articles

Suppressed nonradiative electron–hole recombination in bismuth halide perovskite Cs3Bi2Cl9: Time domain ab initio analysis

Time-domain density functional theory, coupled with non-adiabatic molecular dynamics simulations, was employed to explore the defect characteristics and the associated nonradiative recombination processes in the bismuth halide perovskite Cs3Bi2Cl9. Our findings indicate that Cs3Bi2Cl9 inherently exhibits p-type semiconductor behavior, with vacancies at the Cs and Bi sites acting as predominant shallow acceptor defects. Although Cl vacancy and interstitial Cl defects introduce trap states within the bandgap of Cs3Bi2Cl9, the by-defect electron–hole (e-h) recombination is substantially impeded, which is attributed to the remarkable local structural deformations associated with the BiCl63− octahedral compression around the defects, which further results in decoupling between the defect state and the band edge state. As a result, the enhanced delocalization of defect states leads to a notably small wave function overlap between defect states and band edge states, as well as weak nonadiabatic couplings dominated by low-frequency phonons. Our study offers crucial insights into the mechanism of defect-mediated e-h recombination in bismuth-based perovskites and provides guidelines for designing efficient optoelectronic devices based on these materials.

Ligand Controls Excited Charge Carrier Dynamics in Metal-Rich CdSe Quantum Dots: Computational Insights.

Small metal-rich semiconducting quantum dots (QDs) are promising for solid-state lighting and single-photon emission due to their highly tunable yet narrow emission line widths. Nonetheless, the anionic ligands commonly employed to passivate these QDs exert a substantial influence on the optoelectronic characteristics, primarily owing to strong electron-phonon interactions. In this work, we combine time-domain density functional theory and nonadiabatic molecular dynamics to investigate the excited charge carrier dynamics of Cd28Se17X22 QDs (X = HCOO-, OH-, Cl-, and SH-) at ambient conditions. These chemically distinct but regularly used molecular groups influence the dynamic surface-ligand interfacial interactions in Cd-rich QDs, drastically modifying their vibrational characteristics. The strong electron-phonon coupling leads to substantial transient variations at the band edge states. The strength of these interactions closely depends on the physicochemical characteristics of passivating ligands. Consequently, the ligands largely control the nonradiative recombination rates and emission characteristics in these QDs. Our simulations indicate that Cd28Se17(OH)22 has the fastest nonradiative recombination rate due to the strongest electron-phonon interactions. Conversely, QDs passivated with thiolate or chloride exhibit considerably longer carrier lifetimes and suppressed nonradiative processes. The ligand-controlled electron-phonon interactions further give rise to the broadest and narrowest intrinsic optical line widths for OH and Cl-passivated single QDs, respectively. Obtained computational insights lay the groundwork for designing appropriate passivating ligands on metal-rich QDs, making them suitable for a wide range of applications, from blue LEDs to quantum emitters.

Data-Driven Design of Electroactive Spacer Molecules to Tune Charge Carrier Dynamics in Layered Halide Perovskite Heterostructures.

Crafting rational heterojunctions with nanostructured materials is instrumental in fostering effective interfacial charge separation and transport for optoelectronics. Layered halide perovskites (LHPs) that form heterojunctions between organic spacer molecules and inorganic metal halide layers exhibit tunable photophysics owing to their customizable band alignment. However, controlling photogenerated carrier dynamics by strategically designing layered perovskite heterojunctions remains largely unexplored. We combine a data-driven approach with time-domain density functional theory (TD-DFT) and non-adiabatic molecular dynamics (NAMD) to screen and select electronically active spacer dications (A') that introduce a type-II heterojunction in the lead iodide-based Dion-Jacobson phase LHPs. The composition-structure-electronic property correlations reveal that the number of nitrogens in aromatic heterocycles is the key factor in designing electron-accepting spacers in these perovskites. The detailed atomistic simulations validate the design strategy further by modeling (A')PbI4 perovskites, which incorporate three different screened electroactive A' spacers. The computed excited charge carrier dynamics illustrate the phonon-mediated ultrafast interfacial electron transfer from the inorganic conduction band edge to the lower-lying unoccupied orbitals of spacers, exhibiting photoluminescence quenching in these (A')PbI4 perovskites. The spatially separated electrons and holes at the type-II heterojunction interface prolong the excited charge carrier lifetime, boosting the carrier transport and exciton dynamics. Our work illustrates a robust in silico approach for designing LHPs with exciting optoelectronic properties originating from their fine-tuned heterojunctions.

Construction of an Au/g-C3N4/GO/Au substrate by a layer-by-layer assembly approach for surface-enhanced Raman spectroscopy

In this work, an Au/g-C3N4/GO/Au hybrid nanofilm for surface-enhanced Raman scattering (SERS) substrate application was prepared by a facile layer-by-layer assembly technique using nanosheet-structured graphitic carbon nitride (g-C3N4), graphene oxide (GO) and 40 nm-gold nanoparticles (Au NPs). The effects of composition, assembly sequence and assembly cycles on the SERS performance were optimized to achieve the SERS-active substrate. The detection limit of Au/g-C3N4/GO/Au substrate for crystal violet and rhodamine 6 G probe molecules reached as high as 10−8 M, with good stability and uniformity. Its further application in food colorants detection (erythrosine, carmine and temptation red) had successfully met the national food safety standards and the quantitative detection for erythrosine and temptation red had also been established. Based on finite-difference time-domain element simulation and density functional theory quantum chemical calculation, the mechanism of the SERS effect of the substrate was unveiled, which is attributed to the combination of electromagnetic enhancement effect of Au nanoparticle aggregates and chemical enhancement effect of GO and g-C3N4. Notably, water droplet evaporation induced Raman enhancement was observed on the Au/g-C3N4/GO/Au substrate. This can be ascribed to the inhomogeneous evaporation of the droplet that promotes the enrichment of the probe molecules into the center of the droplet. This novel enhancement strategy provides a new idea for further improving detection sensitivity of SERS substrate materials.

Extending Carrier Lifetime of Antiferromagnetic LaFeO3 Perovskite by Regulating Magnetic Ordering: Time-Domain Ab Initio Analysis.

Focusing on LaFeO3, we investigated the effects of magnetic ordering on carrier relaxation using time-domain density functional theory and nonadiabatic molecular dynamics. The results show that the hot energy and carrier relaxation occur on a sub-2 ps time scale due to the strong intraband nonadiabatic coupling, and the corresponding time scales are distinct depending on the magnetic ordering of LaFeO3. Importantly, the energy relaxation is slower than hot carrier relaxation, guaranteeing photogenerated hot carriers can be effectively relaxed to the band edge before cooling. Following hot carrier relaxation, the charge recombination occurs on the nanosecond scale due to the small interband nonadiabatic coupling and short pure-dephasing times. In addition, the A-AFM system has the longest carrier lifetimes because of its weakest nonadiabatic coupling. Our study suggests that the carrier lifetime can be controlled by changing the magnetic ordering of perovskite oxides and provides valuable principles for the design of high-performance photoelectrodes.

Lattice softness regulates recombination and lifetime of carrier in Germanium doped CsPbI2Br perovskite: First principles DFT and NAMD simulations

Perovskite materials are characterized by high concentration of intrinsic defects. These defects lead to non-radiative recombination of electron and hole pairs, which is one of the major factors leading to the poor performance of the optoelectronic devices fabricated from these materials. Using the first-principles method, we have demonstrated that energy loss due to non-radiative recombination is suppressed in defective CsPbI2Br (D-CsPbI2Br) with the doping of Germanium (Ge) in CsGexPb1-xI2Br (x ​= ​0.15). Bromine vacancy (VBr) in CsPbI2Br introduces localized states as seen in the PDOS, however, doping of Ge eliminates these states. Using nonadiabatic molecular dynamics (NA-MD) and time-domain density functional theory, we show that the lifetime of the charge carriers is extended in Ge-doped CsPbI2Br (D-GeCsPbI2Br) by a factor of 3 and the dephasing time shortens to 6.2 ns. The electron localization function (ELF) plots of bulk CsPbI2Br (B–CsPbI2Br) show that charge localization increases around the Ge atom and it decreases the interaction between Pb atoms. In D-CsPbI2Br, phonons from a wide range of frequencies participate in scattering, and weak non-adiabatic (NA) coupling between electron and phonon in association with phonon modes in the low-frequency spectrum is responsible for extending the lifetime of charge carriers. Strong dynamic disorder in molecular dynamics (MD) simulations points to softening of lattice in D-GeCsPbI2Br. The increase in lattice softness of the Ge-doped is confirmed by the reduced value of bulk modulus (13.2 ​GPa) in D-GeCsPbI2Br as compared to the value in D-CsPbI2Br (13.6 ​GPa). Computing inverse participation ratio (IPR) gives the degree of localization of charge in the valence-band maximum (VBM) and conduction-band minimum (CBM). We have investigated the behavior of IPR and carrier lifetime with temperature, and based on these results, we found that lattice softness and a lifetime of charge carriers increase in D-GeCsPbI2Br.

The mechanism insight for improved photocatalysis and interfacial charges transfer of surface-dispersed Ag0 modified layered graphite-phase carbon nitride nanosheets

A series of surface-dispersed Ag0 modified lamellar-graphite-phase carbon nitride nanosheets (Ag/LGCNs) are synthesized by a straightforward method to construct the noble metal/semiconductor heterojunction. The localized surface plasmon resonance (LSPR) effect results in an optimum degradation rate (Kapp) for rhodamine B ∼ 5.53 × 10−2∙min−1 (9 times higher than that of pure LGCNs), and the sample exhibited outstanding stability. The experiments with sacrificial reagents showed that the h+ and ∙O2– are primary active photocatalytic species in the present samples. The optical and photo-electro-chemical studies of the samples, confirm enhanced photo-responsiveness and photogenerated carriers' separation and transport with an appropriate amount of Ag0. The corresponding mechanism is formulated using photocurrent analysis, impedance analysis, finite-difference time-domain (FDTD) simulation and density functional theory (DFT). FDTD simulation evidenced an intense electromagnetic field at the Ag/LGCN’s interface under visible radiation attributable to the LSPR effect of Ag0 nanoparticles and an increased field intensity with the size of Ag0 nanoparticles. The DFT computations show that the difference in Fermi energy level and the work function contributes to an interfacial built-in electric field between Ag0 nanoparticles and LGCNs. Furthermore, the mechanism for reduced band gap and improved photocatalytic performance for Ag/LGCNs is explained by the energy band studies.

Enhancing the photoelectrochemical activity of monoclinic BiVO4 by discretizing oxygen vacancies: insights from DFT calculations.

Monoclinic bismuth vanadate (BiVO4) has emerged as an excellent optically active photoanode material due to its unique physical and chemical properties. Experiments reported that the low concentration of oxygen vacancies enhances the photoelectrochemical (PEC) activity of BiVO4, but the high concentration of oxygen vacancies decreases the charge carrier lifetime. Using time-domain density functional theory and molecular dynamics, we have demonstrated that the distribution of oxygen vacancies has strong effects on the static electronic structure and nonadiabatic (NA) coupling of the BiVO4 photoanode. The localized oxygen vacancies create charge recombination centers within the band gap and enhance the NA coupling between the VBM and the CBM, resulting in fast charge and energy losses. By contrast, the discrete oxygen vacancies can eliminate the charge recombination centers and decrease the NA coupling between the VBM and the CBM, enhancing the PEC activity of monoclinic BiVO4. Our study suggests that the PEC performance of a photoanode can be improved by changing the distribution of oxygen vacancies.

Anion Doping Delays Nonradiative Electron-Hole Recombination in Cs-Based All-Inorganic Perovskites: Time Domain ab Initio Analysis.

Using time-domain density functional theory combined with nonadiabatic (NA) molecular dynamics, we demonstrate that composition engineering of the X-site anions has a strong influence on the nonradiative electron-hole recombination and thermodynamic stability of cesium-based all-inorganic perovskites. Partial substitution of iodine(I) with bromine (Br) and acetate (Ac) anions reduces the NA electron-vibrational coupling by minimizing the overlap between the electron and hole wave functions and suppressing atomic fluctuations. The doping also widens the energy gap to further reduce the NA coupling and to enhance the open-circuit voltage of perovskite solar cells. These factors increase the charge carrier lifetime by an order of magnitude and improve structural stability in the series CsPbI1.88BrAc0.12 > CsPbI2Br > CsPbI3. The fundamental atomistic insights into the influence of anion doping on the photophysical properties of the all-inorganic lead halide perovskites guide the design of efficient optoelectronic materials.

Vacancy-Regulated Charge Carrier Dynamics and Suppressed Nonradiative Recombination in Two-Dimensional ReX2 (X = S, Se).

Point defects in semiconductors usually act as nonradiative charge carrier recombination centers, which severely limit the performance of optoelectronic devices. In this work, by combining time-domain density functional theory with nonadiabatic molecular dynamics simulations, we demonstrate suppressed nonradiative charge carrier recombination and prolonged carrier lifetime in two-dimensional (2D) ReX2 (X = S, Se) with S/Se vacancies. In particular, a S vacancy introduces a shallow hole trap state in ReS2, while a Se vacancy introduces both hole and electron trap states in ReSe2. Photoexcited electrons and holes can be rapidly captured by these defect states, while the release process is slow, which contributes to an elongated photocarrier lifetime. The suppressed charge carrier recombination lies in the vacancy-induced low-frequency phonon modes that weaken electron-phonon coupling, as well as the reduced overlap between electron and hole wave functions that decreases nonadiabatic coupling. This work provides physical insights into the charge carrier dynamics of 2D ReX2, which may stimulate considerable interest in using defect engineering for future optoelectronic nanodevices.

Strong Influence of the Anion Radius on the Passivation of Selenium Vacancy in Monolayer InSe: Insights from Time-Domain Ab Initio Analysis

Using nonadiabatic molecular dynamics combined with the time-domain density functional theory, we have explored the influence of selenide vacancy and passivation of anions with different radii on the nonradiative charge trapping and recombination in monolayer InSe. Our results reveal that electron–hole recombination for pristine InSe occurs within several nanoseconds due to the weak nonadiabatic (NA) coupling. Selenide vacancy generates three trap states within the band gap, enhances the NA coupling, and provides new channels for charge carrier relaxation, resulting in the significantly decreased charge carrier recombination time. Passivating the selenide vacancy with anions (O2–, S2–, and Te2–) can eliminate the trap states within the band gap and extend the charge carrier lifetimes because of the decreased NA coupling. Meanwhile, the passivation effect of anions is dramatically dependent on the type of anions, and S2– is more suitable for repairing selenide vacancy than O2– and Te2– because S2– and Se2– have much closer radii. This study provides an atomistic mechanism of the effects of selenide vacancy and anion passivation on the performance of InSe thin-film solar cells and suggests that the choice of anions with a suitable radius is valuable for prolonging the excited-state lifetime.

Terahertz time-domain spectroscopy, imaging and density functional theory based studies of 3, 4, 5 Trinitro 1 H Pyrazole

The paper reports the terahertz time-domain spectroscopy (THz-TDS) and imaging on 3, 4, 5 -Trinitro 1-H Pyrazole (explosive) in solid form between 0.1 and 3.5 THz range, including Density Functional Theory was implemented in this study. We have employed a commercially available fiber-coupled THz reflection mode system. We have experimentally ascertained the optical and dielectric properties such as refractive index, absorption coefficients, and dielectric constants in the THz domain. The refractive index values varies between 1.5 and 2.0 range, and absorption coefficients varies between 10 and 400 cm−1 in the stated THz range. In addition, Density Functional Theory was used to assign some important vibrational modes obtained experimentally. In the next step, the Dimer and Trimer configurations of the molecule were also incorporated in the existing theoretical model for developing a clear-cut understanding the role of the intermolecular vibrational modes in the molecule. The simulated results were compared in the IR region (4000–400 cm−1) and the THz region (0.1–3.5 THz). Finally, an improvised version of the imaging system was used to record the THz time and frequency domain images of pure pyrazole and mixed in a teflon matrix with different concentrations. The spatial distributions of pyrazole in the pure and teflon matrix at different absorption frequencies have been analysed.

The combination of terahertz spectroscopy and density functional theory for vibrational modes and weak interactions analysis of vanillin derivatives

Three vanillin derivatives, including methyl vanillin, ethyl vanillin, and vanillyl alcohol were investigated in the range of 0.4–2.0 THz by terahertz time-domain spectroscopy (THz-TDS) and density functional theory (DFT). Vibrational mode automatic relevance determination (VMARD) method was introduced to assign the absorption peaks to the contribution ratio of corresponding vibrational modes, and VMARD revealed the dihedral angle torsion was the primary vibrational mode. Simultaneously, through independent gradient model based on Hirshfeld partition of molecular density (IGMH) method, van der Waals interaction was ascertained to be dominant weak noncovalent intermolecular interaction. This research, combining THz-TDS and the above-mentioned methods, elucidates the principle of material performance differences with structural analogs in the terahertz frequency band.

How Hole Injection Accelerates Both Ion Migration and Nonradiative Recombination in Metal Halide Perovskites

Ion migration, hole trapping, and electron-hole recombination are common processes in metal halide perovskites. We demonstrate using ab initio non-adiabatic molecular dynamics and time-domain density functional theory that they are intricately related and strongly influence each other. The hole injection accelerates ion migration by decreasing the diffusion barrier and shortening the migration length. The injected hole also promotes the nonradiative charge recombination by strengthening electron-phonon interactions in the low-frequency region and prolonging the quantum coherence time. The synergy stems from the soft perovskite lattice and response of the valence band maximum to the Pb-I lattice distortion induced by the hole. This work provides important insights into the influence of ion mobility and hole injection on the performance of perovskite solar cells and suggests that high concentration of holes should be avoided.

Charge carrier nonadiabatic dynamics in non-metal doped graphitic carbon nitride.

Graphitic carbon nitride (GCN) has attracted significant attention due to its excellent performance in photocatalytic applications. Non-metal doping of GCN has been widely used to improve the efficiency of the material as a photocatalyst. Using a combination of time-domain density functional theory with nonadiabatic molecular dynamics, we study the charge carrier dynamics in oxygen and boron doped GCN systems. The reported simulations provide a detailed time-domain mechanistic description of the charge separation and recombination processes that are of fundamental importance while evaluating the photovoltaic and photocatalytic performance of the material. The appearance of smaller energy gaps due to the presence of dopant states improves the visible light absorption range of the doped systems. At the same time, the nonradiative lifetimes are shortened in the doped systems as compared to the pristine GCN. In the case of boron doped at a carbon (B-C-GCN), the charge recombination time is very long as compared to the other two doped systems owing to the smaller electron-phonon coupling strength between the valence band maximum and the trap state. The results suggest B-C-GCN as the most suitable candidate among three doped systems studied in this work for applications in photocatalysis. This work sheds light into the influence of dopants on quantum dynamics processes that govern GCN performance and, thus, guides toward building high-performance devices in photocatalysis.

Out-of-plane dipole-modulated photogenerated carrier separation and recombination at Janus-MoSSe/MoS2 van der Waals heterostructure interfaces: an ab initio time-domain study.

Out-of-plane mirror symmetry-breaking provides a powerful tool for engineering the electronic properties and the exciton behavior of two-dimensional materials. Here, by combining time-domain density functional theory with nonadiabatic dynamics, we investigate the underlying mechanism of how the vertical dipole moment modulates the photoexcited carrier transport and the electron-hole recombination dynamics in polar Janus MoSSe/MoS2 stacked heterostructures. It is shown that the stronger nonadiabatic coupling, interlayer-state delocalization and the built-in electric field caused by charge redistribution facilitate a more rapid photocarrier separation across the interface in the S/S stacked bilayer compared with the S/Se bilayer, explaining the experimentally observed stronger photoluminescence quenching effect in the S/S heterostructure. We also found that the photocarrier recombination of the heterostructure with the S/Se interface has a timescale up to nanoseconds, which is ∼4 times longer than that of the S/S bilayer. Such a prolonged recombination time originates from the dipole-weakened nonadiabatic coupling between occupied and unoccupied states instead of quantum coherence and the band gap effect. Overall, Janus MoSSe/MoS2 heterostructures exhibit superior photocatalytic activity, reflecting the ultrafast photocarrier separation triggered by the built-in electric field, suppressed carrier recombination, high solar-to-hydrogen conversion efficiency and the strong absorption coefficient expanding from visible-light to near-infrared-light. The above atomistic and time-domain findings reveal the intrinsic dipole as an effective freedom to regulate the nonadiabatic photocarrier dynamics in Janus-based 2D heterostructures for efficient energy harvesting and optoelectronic applications.

CO Adsorbate Promotes Polaron Photoactivity on the Reduced Rutile TiO2(110) Surface.

Polarons play a major role in determining the chemical properties of transition-metal oxides. Recent experiments show that adsorbates can attract inner polarons to surface sites. These findings require an atomistic understanding of the adsorbate influence on polaron dynamics and lifetime. We consider reduced rutile TiO2(110) with an oxygen vacancy as a prototypical surface and a CO molecule as a classic probe and perform ab initio adiabatic molecular dynamics, time-domain density functional theory, and nonadiabatic molecular dynamics simulations. The simulations show that subsurface polarons have little influence on CO adsorption and CO can desorb easily. On the contrary, surface polarons strongly enhance CO adsorption. At the same time, the adsorbed CO attracts polarons to the surface, allowing them to participate in catalytic processes with CO. The CO interaction with polarons changes their orbital origin, suppresses polaron hopping, and stabilizes them at surface sites. Partial delocalization of polarons onto CO decouples them from free holes, decreasing the nonadiabatic coupling and shortening the quantum coherence time, thereby reducing charge recombination. The calculations demonstrate that CO prefers to adsorb at the next-nearest-neighbor five-coordinated Ti3+ surface electron polaron sites. The reported results provide a fundamental understanding of the influence of electron polarons on the initial stage of reactant adsorption and the effect of the adsorbate–polaron interaction on the polaron dynamics and lifetime. The study demonstrates how charge and polaron properties can be controlled by adsorbed species, allowing one to design high-performance transition-metal oxide catalysts.

Examination of proline, hydroxyproline and pyroglutamic acid with different polar groups by terahertz spectroscopy

Hydroxyproline (HYP) and pyroglutamic acid (PGA), as amino acid derivatives, are highly similar in structure to proline (Pro). However, their low-frequency vibrations show significant differences in the range of 0.25–2.6 THz. Therefore, this study investigated the reasons for the differences combined with terahertz time domain spectroscopy (THz-TDS) and density functional theory (DFT). The results show that HYP and PGA have stronger absorption of terahertz waves due to the existence of polar substituents. Furthermore, the absorption peaks of HYP and PGA are significant red shifted and blue shifted, respectively. We believe that this is caused by the change in the strength of intermolecular hydrogen bonds. Our findings demonstrate that dipole and hydrogen bond effects play a significant role in low-frequency vibrations.

Temperature Dependence of Spin-Phonon Coupling in [VO(acac)2]: A Computational and Spectroscopic Study.

Molecular electronic spins are good candidates as qubits since they are characterized by a large tunability of their electronic and magnetic properties through a rational chemical design. Coordination compounds of light transition metals are promising systems for spin-based quantum information technologies, thanks to their long spin coherence times up to room temperature. Our work aims at presenting an in-depth study on how the spin–phonon coupling in vanadyl-acetylacetonate, [VO(acac)2], can change as a function of temperature using terahertz time-domain spectroscopy and density functional theory (DFT) calculations. Powder THz spectra were recorded between 10 and 300 K. The temperature dependence of vibrational frequencies was then accounted for in the periodic DFT calculations using unit-cell parameters measured at two different temperatures and the optimized ones, as usually reported in the literature. In this way, it was possible to calculate the observed THz anharmonic frequency shift with high accuracy. The overall differences in the spin–phonon coupling magnitudes as a function of temperature were also highlighted showing that the computed trends have to be ascribed to the anisotropic variation of cell parameters.

Thermal-Driven Dynamic Shape Change of Bimetallic Nanoparticles Extends Hot Electron Lifetime of Pt/MoS2 Catalysts.

Using a combination of time-domain density functional theory and nonadiabatic (NA) molecular dynamics, we demonstrate that the replacement of noble Pt with cheap Sn in the Pt nanoparticles sensitized MoS2 greatly retards the photoexcited "hot" electron relaxation. The simulations show that Sn substitution causes significant geometry distortion associated with the Sn dopant detaching from the Pt nanoparticle base, which decreases the NA coupling and creates an isolated trap state distant from the electron donor state. Generally, smaller NA coupling delays "hot" electron relaxation. At the same time, the photoexcited electron on MoS2 first populates the nanoparticles state and then slowly goes to the trap state, following relaxation to the nanoparticle acceptor state over 1 ps. As a result, the "hot" electron lives over 3.5 times longer than that in pristine Pt/MoS2 system. The long-lived "hot" electron associated with the reduced cost establishes a novel concept for developing high-efficient and cost-effective photocatalysts and photovoltaics.