Valley-Related Multipiezo Effect and Noncollinear Spin Current in an Altermagnet Fe2Se2O Monolayer.

An altermagnet exhibits many novel physical phenomena because of its intrinsic antiferromagnetic coupling and natural band spin splitting, which are expected to give rise to new types of magnetic electronic components. In this study, an Fe2Se2O monolayer is proven to be an altermagnet with out-of-plane magnetic anisotropy, and its Néel temperature is determined to be 319 K. The spin splitting of the Fe2Se2O monolayer reaches 860 meV. Moreover, an Fe2Se2O monolayer presents a pair of energy valleys, which can be polarized and reversed by applying uniaxial strains along different directions, resulting in a piezovalley effect. Under the strain, the net magnetization can be induced in the Fe2Se2O monolayer by doping with holes, thereby realizing a piezomagnetic property. Interestingly, noncollinear spin current can be generated by applying an in-plane electric field on an unstrained Fe2Se2O monolayer doped with 0.2 hole/formula unit. These excellent physical properties make the Fe2Se2O monolayer a promising candidate for multifunctional spintronic and valleytronic devices.

Twinning Engineering of Platinum/Iridium Nanonets as Turing-Type Catalysts for Efficient Water Splitting.

The twin boundary, a common lattice plane of mirror-symmetric crystals, may have high reactivity due to special atomic coordination. However, twinning platinum and iridium nanocatalysts are grand challenges due to the high stacking fault energies that are nearly 1 order of magnitude larger than those of easy-twinning gold and silver. Here, we demonstrate that Turing structuring, realized by selective etching of superthin metal film, provides 14.3 and 18.9 times increases in twin-boundary densities for platinum and iridium nanonets, comparable to the highly twinned silver nanocatalysts. The Turing configurations with abundant low-coordination atoms contribute to the formation of nanotwins and create a large active surface area. Theoretical calculations reveal that the specific atom arrangement on the twin boundary changes the electronic structure and reduces the energy barrier of water dissociation. The optimal Turing-type platinum nanonets demonstrated excellent hydrogen-evolution-reaction performance with a 25.6 mV overpotential at 10.0 mA·cm-2 and a 14.8-fold increase in mass activity. And the bifunctional Turing iridium catalysts integrated in the water electrolyzer had a mass activity 23.0 times that of commercial iridium catalysts. This work opens a new avenue for nanocrystal twinning as a facile paradigm for designing high-performance nanocatalysts.

Influence of electronic correlation on the valley and topological properties of VSiGeP4 monolayer.

Valley is used as a new degree of freedom for information encoding and storage. In this work, the valley and topological properties of the VSiGeP4 monolayer were studied by adjusting the U value based on first-principles calculations. The VSiGeP4 monolayer remains in a ferromagnetic ground state regardless of the change in the U value. The magnetic anisotropy of the VSiGeP4 monolayer is initially in-plane, and then turns out-of-plane with the increase in the U value. Moreover, a topological phase transition is observed in the present VSiGeP4 monolayer with the increase in U value from 0 to 3 eV, i.e., the VSiGeP4 monolayer behaves as a bipolar magnetic semiconductor, a ferrovalley semiconductor, a half-valley metal characteristic, and a quantum anomalous Hall state. The mechanism of the topological phase transition behavior of the VSiGeP4 monolayer was analyzed. It was found that the variation in U values would change the strength of the electronic correlation effect, resulting in the valley and topological properties. In addition, carrier doping was studied to design a valleytronic device using this VSiGeP4 monolayer. By doping 0.05 electrons per f.u., the VSiGeP4 monolayer with a U value of 3 eV exhibits 100% spin polarization. This study indicates that the VSiGeP4 monolayer has potential applications in spintronic, valleytronic, and topological electronic nanodevices.

Anharmonic and quantum effects in Pm3̄ AlM(M = Hf, Zr)H6 under high pressure: A first-principles study.

First-principles calculations were employed to investigate the impact of quantum ionic fluctuations and lattice anharmonicity on the crystal structure and superconductivity of Pm3̄ AlM(M = Hf, Zr)H6 at pressures of 0.3-21.2 GPa (AlHfH6) and 4.7-39.5 GPa (AlZrH6) within the stochastic self-consistent harmonic approximation. A correction is predicted for the crystal lattice parameters, phonon spectra, and superconducting critical temperatures, previously estimated without considering ionic fluctuations on the crystal structure and assuming the harmonic approximation for lattice dynamics. The findings suggest that quantum ionic fluctuations have a significant impact on the crystal lattice parameters, phonon spectra, and superconducting critical temperatures. Based on our anharmonic phonon spectra, the structures will be dynamically stable at 0.3 GPa for AlHfH6 and 6.2 GPa for AlZrH6, ∼6 and 7 GPa lower than pressures given by the harmonic approximation, respectively. Due to the anharmonic correction of their frequencies, the electron-phonon coupling constants (λ) are suppressed by 28% at 11 GPa for AlHfH6 and 22% at 30 GPa for AlZrH6, respectively. The decrease in λ causes Tc to be overestimated by ∼12 K at 11 GPa for AlHfH6 and 30 GPa for AlZrH6. Even if the anharmonic and quantum effects are not as strong as those of Pm3̄n-AlH3, our results also indicate that metal hydrides with hydrogen atoms in interstitial sites are subject to anharmonic effects. Our results will inevitably stimulate future high-pressure experiments on synthesis, structural, and conductivity measurements.

First-principles study of high-pressure structural phase transition and superconductivity of YBeH8.

The theory-led prediction of LaBeH8, which has a high superconducting critical temperature (Tc) above liquid nitrogen under a pressure level below 1 Mbar, has been experimentally confirmed. YBeH8, which has a structural configuration similar to that of LaBeH8, has also been predicted to be a high-temperature superconductor at high pressure. In this study, we focus on the structural phase transition and superconductivity of YBeH8 under pressure by using first-principles calculations. Except for the known face-centered cubic phase of Fm3̄m, we found a monoclinic phase with P1̄ symmetry. Moreover, the P1̄ phase transforms to the Fm3̄m phase at ∼200 GPa with zero-point energy corrections. Interestingly, the P1̄ phase undergoes a complex electronic phase transition from semiconductor to metal and then to superconducting states with a low Tc of 40 K at 200 GPa. The Fm3̄m phase exhibits a high Tc of 201 K at 200 GPa, and its Tc does not change significantly with pressure. When we combine the method using two coupling constants, λopt and λac, with first-principles calculations, λopt is mainly supplied by the Be-H alloy backbone, which accounts for about 85% of total λ and makes the greatest contribution to the high Tc. These insights not only contribute to a deeper understanding of the superconducting behavior of this ternary hydride but may also guide the experimental synthesis of hydrogen-rich compounds.

Superconductivity of cubic MB6 (M = Na, K, Rb, Cs).

Previous studies have shown that NaB6, KB6, and RbB6 adopting Pm3̄m are superconductors with a relatively high Tc under ambient conditions. In this paper, we conducted systematic structural and related properties research on CsB6 through a genetic evolution algorithm and total energy calculations based on density functional theory between 0 and 20 GPa. Our results reveal a cubic Pm3̄m CsB6, which is dynamically stable under the pressures we studied. We systematically calculated the formation enthalpies, electronic properties, and superconducting properties of Pm3̄m MB6 (M = Na, K, Rb, Cs). They all exhibit metallic features, and boron has high contributions to band structures, density of states, and electron-phonon coupling (EPC). The calculated results about the Helmholtz free energy difference of Pm3̄m CsB6 at 0, 10, and 20 GPa indicate that it is stable upon chemical decomposition (decomposition to simple substances Cs and B) from 0 to 400 K. The phonon density of states indicates that boron atoms occupy the high frequency area. The EPC results show that Pm3̄m CsB6 is a superconductor with Tc = 11.7 K at 0 GPa, close to NaB6 (13.1 K), KB6 (11.7 K), and RbB6 (11.3 K) at 0 GPa in our work, which indicates that boron atoms play an essential role in superconductivity: vibrations of B6 regular octagons lead to the high Tc of Pm3̄m MB6. Our work about Pm3̄m hexaborides provides a supplementary study on the borides of the group IA elements (without Fr and Li) and has an important guiding significance for the experimental synthesis of CsB6.

Coexisting Ferroelectric and Ferrovalley Polarizations in Bilayer Stacked Magnetic Semiconductors.

It has long been expected that the coexistence of ferroelectric and ferrovalley polarizations in one magnetic semiconductor could offer the possibility to revolutionize electronic devices. In this study, monolayer and bilayer YI2 are studied. Monolayer YI2 is a ferromagnetic semiconductor and exhibits a valley polarization up to 105 meV. All of the present bilayer YI2 regardless of stacking orders show antiferromagnetic states. Interestingly, the bilayer YI2 with 3R-type stackings shows not only valley polarization but also unexpected ferroelectric polarization, proving the concurrent ferrovalley and multiferroics behaviors. Moreover, the valley polarization of 3R-type bilayer YI2 can be reversed by controlling the direction of ferroelectric polarization through an electric field or manipulating the magnetization direction using an external magnetic field. The amazing phenomenon is also demonstrated in 2D van der Waals LaI2 and GdBr2 bilayers. A design idea of multifunctional devices is proposed based on the concurrent ferrovalley and multiferroics characteristics.

Structural diversity and hydrogen storage properties in the system K-Si-H.

KSiH3 exhibits 4.1 wt% experimental hydrogen storage capacity and shows reversibility under moderate conditions, which provides fresh impetus to the search for other complex hydrides in the K-Si-H system. Here, we reproduce the stable Fm3̄m phase of K2SiH6 and uncover two denser phases, space groups P3̄m1 and P63mc at ambient pressure, by means of first-principles structure searches. We note that P3̄m1-K2SiH6 has a high hydrogen content of 5.4 wt% and a volumetric density of 88.3 g L-1. Further calculations suggest a favorable dehydrogenation temperature Tdes of -20.1/55.8 °C with decomposition into KSi + K + H2. The higher hydrogen density and appropriate dehydrogenation temperature indicate that K2SiH6 is a promising hydrogen storage material, and our results provide helpful and clear guidance for further experimental studies. We found three further potential hydrogen storage materials stable at high pressure: K2SiH8, KSiH7 and KSiH8. These results suggest the need for further investigations into hydrogen storage materials among such ternary hydrides at high pressure.

Proposed Superconducting Electride Li_{6}C by sp-Hybridized Cage States at Moderate Pressures.

The combination of electride state and superconductivity within the same compound, e.g., [Ca_{24}Al_{28}O_{6}]^{4+}(4e^{-}), opens up a new category of conventional superconductors. However, neither the underlying causations to explain superconducting behaviors nor effects of interstitial quasiatoms (ISQs) on superconductivity remain unclear. Here we have designed an efficient and resource-saving method to identify superconducting electrides only by chemical compositions and bonding characteristics. A representative superconducting electride Li_{6}C with a noteworthy T_{c} of 10 K below 1 Mbar among the known binary electrides has been revealed. Our first-principles studies unveil that the anomalous sp-hybridized cage-state ISQs, as a guest in Li_{6}C, exhibit unexpected ionic and covalent bonds, which act as a chemical precompression to lower dynamically stable pressure. More importantly, we uncover that, contrary to common expectations, the high T_{c} is attributed to the strong electron-phonon coupling derived from the synergy of interatomic coupling effect, phonon softening caused by Fermi surface nesting, and phonon-coupled bands, which are mainly dominated by host sp-hybridized electrons, rather than the ISQs. Our present results elucidate a new superconducting mechanism of electrides and shed light on the way for seeking a high-T_{c} superconductor at lower pressures in cage-state electrides.

Enhanced resistive switching performance in yttrium-doped CH3NH3PbI3 perovskite devices.

In this study, yttrium-doped CH3NH3PbI3 (Y-MAPbI3) and pure CH3NH3PbI3 (MAPbI3) perovskite films have been fabricated using a one-step solution spin coating method in a glove box. X-ray diffractometry and field-emission scanning electron microscopy were used to characterize the crystal structures and morphologies of perovskite films, respectively. It was found that the orientation of the crystal changed and the grains became more uniform in Y-MAPbI3 film, compared with the pure MAPbI3 perovskite film. The films were used to prepare the resistive switching memory devices with the device structure of Al/Y-MAPbI3 (MAPbI3)/ITO-glass. The memory performance of both devices was studied and showed a bipolar resistive switching behavior. The Al/MAPbI3/ITO device had an endurance of about 328 cycles. In contrast, the Al/Y-MAPbI3/ITO device exhibited an enhanced performance with a long endurance up to 3000 cycles. Moreover, the Al/Y-MAPbI3/ITO device also showed a higher ON/OFF ratio of over 103, long retention time (≥104 s), lower operation voltage (±0.5 V) and outstanding reproducibility. Additionally, the conduction mechanism of the high resistance state transformed from space-charge limited current for a Y free device to the Schottky emission after Y doping. The present results indicate that the Al/Y-MAPbI3/ITO device has a great potential to be used in high-performance memory devices.

Moderate Pressure Stabilized Pentazolate Cyclo-N5- Anion in Zn(N5)2 Salt.

Stabilization of the pentazole anion only by acidic circumstances entrapment impedes the realization of a full-nitrogen substance; however, compression of nitrogen-rich nitrides has been recommend as an alternative way that has more controllable advantages to acquire the atomic nitrogen states. Through the structure searches are in conjunction with first-principle calculations, moderate pressure stabilized nitrogen-rich zinc nitrides with abundant extended nitrogen structures, e.g., cyclo-N5, infinite -(N4)n- chains, three-point stars N(N3), and N2 dumbbells, are predicted. The resonance between alternating σ bonds and π bonds in poly nitrogen sublattices takes charge of the coexistence of single and double bonds. The Zn(N5)2 salt has a noteworthy energy density (6.57 kJ/g) among the reported binary metal nitrides and synthesized pentazolate hydrates. An excellent Vicker's hardness (34 GPa) and detonation performance is unraveled. Although Zn(N5)2 salt is not expected to be recoverable at ambient conditions, it is worth noting that Zn(N5)2 is found to be stable at a very low pressure of ∼30 GPa, which is only half of those pressures required to synthesize CsN5. We clarified that the metal-centering octahedral pentazolate framework was entrapped by dual ionic-covalent bonds. More importantly, the covalent bonding can effectively enhance the chemical insensitivity and thermal stability, further preventing the autodecomposition of monatomic solid N5- anions into dinitrogen. Meanwhile, a unique topological pseudogap that attached to a metastable phase of ZnN4 salt is exposed for the first time, due to the dual effects of strong covalent sp2 hybridization interaction and the origin of ionic states.

Hydrogen-bond enhancement triggered structural evolution and band gap engineering of hybrid perovskite (C6H5CH2NH3)2PbI4 under high pressure.

Hybrid organic-inorganic perovskites (HOIPs) have gained substantial attention due to their excellent photovoltaic and optoelectronic properties. Herein, we comprehensively investigate a typical two-dimensional (2D) hybrid perovskite (C6H5CH2NH3)2PbI4 to track its structural and band gap evolution applied by the maximum pressure of 27.2 GPa. Remarkably, an unprecedented band gap narrowing down to the Shockley-Queisser limit is observed upon compression to 20.1 GPa. Two phase transitions have been observed during this process: the ambient Pbca phase converts into the Pccn phase at 4.6 GPa and then undergoes an isostructural phase transition at 7.7 GPa. The Fourier Transform Infrared (FTIR) spectroscopy reveals that pressure-enhanced hydrogen bonding plays an important role in structural modifications and band gap variations. This work not only enables high pressure as a clean tool to tune the structure and band gap of hybrid perovskite, but also maps a pioneering route towards realizing ideal photovoltaic materials-by-design.

Interface hybridization and spin filter effect in metal-free phthalocyanine spin valves.

Spin-orbit coupling (SOC) has long been regarded as the core interaction to determine the efficiency of spin conserved transport in semiconductor spintronics. In this report, a spin-valve device with a Co/metal-free phthalocyanine (H2Pc)/Co stacking structure is fabricated. The magnetoresistance effect was successfully obtained in the device. It is also found that the magnetoresistance response is relatively smaller than that of metallic phthalocyanines, clearly implying that SOC is not the key factor to affect the magnetoresistance in phthalocyanine spin-valves. The dominant mechanism that determines the spin transport efficiency in the present H2Pc devices was systemically explored by combining both experimental measurements and first-principles calculation analysis. It was noticed that both the crystalline structure and molecular orientation of the H2Pc layer could be modified by the contact under-layer materials, which changes the magnetization intensity of the ferromagnetic metallic electrode due to the strong interface hybridization of Co/H2Pc. Meanwhile, the theoretical calculations clearly demonstrated that the spin filter effect from the second H2Pc layer should be responsible for the decrease of the magnetoresistance response in the present spin-valves compared to those using metallic phthalocyanine layers. This investigation may trigger new insights into the role of SOC strength and interface hybridization in organic spintronics.

High-Pressure Bonding Mechanism of Selenium Nitrides.

The high-pressure phase diagrams of binary Se-N system have been constructed using the CALYPSO method and first-principles calculations. Four stable compounds ( Cmc21-SeN2, P21 /m-SeN3, P1̅-SeN4, and P1̅-SeN5) were identified at high pressures. Various peculiar nitrogen polymerization forms composed of single/double nitrogen-nitrogen bonds were found at the nitrogen-rich condition, such as N∞-chains in P21/ m-SeN3, oligomeric N8-chains in P1̅-SeN4, and distorted N63- anion rings in P1̅-SeN5. Peculiar nitrogen polymerization forms make these compounds potential high-energy-density materials (HEDMs). Especially, P1̅-SeN5 has the highest energy density of 4.08 kJ g-1 among the selenium nitrides. The polymerization mechanism of nitrogen in the Se-N system has been explored using the "Lewis-like" two-center-two-electron and three-center-two-electron bonding analysis. Using the nitrogen-rich P1̅-SeN5 as a prototype, it is found that the famous N6 distortion in the polymerized nitrogen HEDM can be explained by the interatomic mechanical unbalance which is induced by the three-center two-electron bonding between the metal atom and the two neighboring nitrogen atoms.

Unique Phase Diagram and Superconductivity of Calcium Hydrides at High Pressures.

Structure prediction studies on Ca-H binary systems under high pressures were carried out, and the structures of calcium hydrides in earlier works were reproduced. The previously unreported composition of CaH9 was found to be stable and experienced the phase transition series Cm → P21/ m → C2/ m from 100 to 400 GPa. To the best of our knowledge, CaH9 may be the only alkaline earth hydride with an odd H content. At 400 GPa, the metastable R3̅ m-CaH10 phase shares the same space group with the R3̅ m-SrH10 phase with puckered honeycomb H layers. The C2/ m phase of CaH9 and the R3̅ m phase of CaH10 are excellent superconductors with Tc values of about 240-266 and 157-175 K at 300 and 400 GPa, respectively. The high contributions of H-derived states at the Fermi level play an important role in the superconductivity of calcium hydrides.

Metallic and anti-metallic properties of strongly covalently bonded energetic AlN5 nitrides.

High pressure can stimulate numerous novel physical effects which are not observed under ambient conditions, such as the electronic redistribution and delocalization phenomenon in strongly covalently bonded nitrides. Through first principles simulations, we report a new N-rich aluminum nitride AlN5, which crystallizes with the space group P1[combining macron] at 20 GPa and then transforms into the I4[combining macron]2d phase at 60 GPa. We have identified and proved the delocalization effects of π electrons in the strongly covalent Lewis poly-nitrogen structure via the one-dimensional particle in a box mechanism, which contributes to the metallization and stability of the system. This implies that not all strongly covalently bonded systems with highly localized electrons exhibit nonmetallic properties in III-V main group nitrides. Furthermore, pressure results in the hybridization configuration mutation from sp2 in the P1[combining macron] phase to a mixture of sp2 and sp3 hybridization in the I4[combining macron]2d phase, which leads to phase transition from metal to insulator. With increasing pressure, the band gap increases abnormally, exhibiting anti-metallization induced by the strong hybridization. Interestingly, the P1[combining macron] and I4[combining macron]2d structures are simultaneously accompanied by a high energy density and hardness, which enable them to have a greater ability to resist elasticity, plastic deformation and external force destruction in potential applications. Their energy density and hardness are up to 3.29 kJ g-1 and 15.2 GPa in the P1[combining macron] phase but especially 6.14 kJ g-1 and 31.7 GPa in the I4[combining macron]2d phase.

Unusual interfacial magnetic interactions for τ-MnAl with Fe(Co) atomic layers.

The interfacial magnetic interaction and coupling mechanism for τ-MnAl with Fe(Co) atomic layers have been studied using first principles calculations. The stable surface and interface were firstly determined by the surface energy of τ-MnAl and interface energy of τ-MnAl/Fe(Co) films, respectively. Their magnetic coupling interactions were investigated by varying the Fe(Co) atomic layer numbers. It is noted that both Fe and Co exhibited ferromagnetic coupling with τ-MnAl. Interestingly, an unusual oscillation phenomenon of magnetic coupling for τ-MnAl with Fe(Co) atomic layers was observed depending on the layer thickness of Fe(Co). Moreover, Fe and Co showed different oscillation modes. The energy difference between antiferromagnetic and ferromagnetic states is larger for τ-MnAl/Fe and τ-MnAl/Co when the Fe(Co) layer numbers are even and odd, respectively. Their mechanisms were analyzed based on the band structures and the confinement of electrons in quantum wells. It is found that the magnetic coupling oscillation in τ-MnAl/Fe originated from both the spin up Δ1 band and spin down Δ5 band at the [capital Gamma, Greek, macron] points. Comparatively, the oscillation of τ-MnAl/Co is due to the spin up band at the X[combining macron] point. The present results could provide insight to further understand interfacial exchange interactions among magnetic layers.

High-Pressure Formation of Cobalt Polyhydrides: A First-Principle Study.

The high-pressure phase diagram, crystal structures, and electronic properties of cobalt hydrides are systematically investigated in the pressure range of 1 atm to 300 GPa by first-principle calculations. Except for the experimentally found CoH, two new cobalt polyhydrides CoH2 and CoH3 are discovered at 10 and 30 GPa, respectively. The crystal structure of CoH2 is determined to have cubic symmetry with the space group Fm3̅m and then transforms into the I4/mmm phase above 42 GPa. In addition, CoH3 with Pm3̅m is stable between 30 and 300 GPa, which can be used as a potential hydrogen storage material with a high volumetric hydrogen density of 425 g H2/L. All the cobalt polyhydrides exhibit metallic and ionic characteristics at high pressure. Furthermore, application of the Allen-Dynes-modified McMillan equation estimated no superconductivity for cobalt polyhydrides.

Insights into Antibonding Induced Energy Density Enhancement and Exotic Electronic Properties for Germanium Nitrides at Modest Pressures.

Here, the electronic and bonding features in ground-state structures of germanium nitrides under different components that not accessible at ambient conditions have been systematically studied. The forming essence of weak covalent bonds between the Ge and N atom in high-pressure ionic crystal Fd-3 m-Ge3N4 is induced by the binding effect of electronic clouds originated from the Ge_ p orbitals. Hence, it helps us to understand the essence of covalent bond under high pressure, profoundly. As an excellent reducing agent, germanium transfer electrons to the antibonding state of the N2 dimer in Pa-3-GeN2 phase at 20 GPa, abnormally, weakening the bonding strength considerably than nitrogen gap (N≡N) at ambient pressure. Furthermore, the common cognition that the atomic distance will be shortened under the high pressures has been broken. Amazingly, with a lower range of synthetic pressure (∼15 GPa) and nitrogen contents (28%), its energy density is up to 2.32 kJ·g-1, with a similar order of magnitude than polymeric LiN5 (nonmolecular compound, 2.72 kJ·g-1). It breaks the universal recognition once again that nitrides just containing polymeric nitrogen were regarded as high energy density materials. Hence, antibonding induced energy density enhancement mechanism for low nitrogen content and pressure has been exposed in view of electrons. Both the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) are usually the separated orbitals of N_π* and N_σ*, which are the key to stabilization. Besides, the sp2 hybridizations that exist in N4 units are responsible for the stability of the R-3 c-GeN4 structure and restrict the delocalization of electrons, exhibiting nonmetallic properties.

Charge-patching method for the calculation of electronic structure of polypeptides.

Theoretical study of the electronic structures of protein is a fundamental challenge in computational biochemistry due to the large size of the systems. The electronic structure of a protein is important for some of the important protein functionalities, such as photosynthesis. In this study, we explored the charge-patching method to calculate the electronic structure of polypeptides. This method generates the charge densities of the systems by patching the charge motifs calculated from small prototype systems. The method was tested on a range of polypeptides, including the glycine polypeptide in 27-ribbon, α-helix, 310-helix, and ß-strand structures. After the charge density profiles of these systems were obtained, the electronic structures of these glycine polypeptides were further calculated based on density functional theory (DFT) using a folded-spectrum method. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) were analyzed and compared with conventional direct DFT calculations. The charge-patching method results were found to be in good agreement with the directed DFT results.