Generalized Gradient Approach Research Articles

A DFT calculation of electronic structures, magnetic, and thermoelectric properties of the new equiatomic quaternary Heusler alloy RuTiCrSi

AbstractThe stabilities, mechanical, electronic, and magnetic properties of the new equiatomic quaternary Heusler alloy (EQHA) RuTiCrSi were investigated using the Kohn‐Sham DFT (KS‐DFT) calculations within the generalized gradient approach (GGA), the modified version of the exchange potential introduced by Becke and Johnson in addition to the GGA (mBJ‐GGA), and Heyd‐Scuseria‐Ernzerhof (HSE06) hybrid functional. The ground‐state equilibrium energy reveals that the ferromagnetic with type 2 structure is the more stable. The RuTiCrSi is energetically, mechanically, and dynamically stable. The calculated self‐consistent total magnetic moment is 2 μB and agrees well with the Slater‐Pauling rule of . The electronic structure results from mBJ‐GGA and HSE06 functionals show a half‐metallic behavior. A high Curie temperature is obtained using the mean‐field approximation. The thermoelectric response was calculated using the semi‐classical Boltzmann transport equation under constant relaxation time. The maximum value of Seebeck coefficient is observed at the ambient temperature of . It was also observed that the power factor increases significantly as temperature rises. Therefore, the new EQHA RuTiCrSi seems to be a potential candidate for spintronic thermoelectric applications.

Probing Mechanical, Thermoelectric, and Magnetic Properties of ACr2O4 (A = Hg, Cd) Spinel Oxides for Energy Storage Applications

DFT calculations are employed to examine the half-metallic, thermoelectric, as well as electronics properties of Cr-based spinels ACr2O4 (A = Hg, Cd). The structural and elastic properties are calculated using the PBEsol-GGA, a modified Perdew–Burke–Ernzerhof plus generalized gradient approach (mBJ + GGA). The modified-Becke Johnson (mBJ) potential is also employed to examine the electronics and thermoelectric properties. In the ferromagnetic (FM) phase, the stability of the structures is validated through energy differences calculations among the ferromagnetic (FM) and non-magnetic (NM) periods. Additionally, the Chopin technique is used to examine in detail the elastic properties. The 2p-states of chalcogenide and the 3d-states of Cr atoms, which result in significant Fermi-level hybridization, provide the total magnetic moments. Furthermore, it is found that the examined spinels may be employed potentially in thermoelectric devices by looking into transport characteristics like the power factor, Seebeck coefficient, and thermal and electrical conductance.

Optoelectronic properties and lattice thermal conductivity of Cs2CuBiX6 (X = F, Cl, Br, I) double perovskites: Thermodynamic and ab initio approaches

In this work, a first-principles method called full potential linearized augmented plane wave (FP-LAPW) within the generalized gradient approach (GGA) is used to investigate potential double free lead halide perovskites applications. The structural and elastic parameters of double perovskites Cs2CuBiX6 (X = F, Cl, Br, I) are investigated, and the results show that these compounds are stable, have a ductile character, and are characterized by a noticeable elastic anisotropy. Lattice thermal conductivity is calculated via Slack's equation for all studied materials, reflecting a good potential for thermoelectric applications. The calculations of the electronic and optical properties are performed using the GGA combined with the modified Becke-Johnson (mBJ) potential with the incorporation of the spin-orbit coupling (SOC). This SO effect allowed us to have correct bandgap behaviour for the Bi states. The studied compounds have large dispersion in their bands and low carrier effective masses. Furthermore, acceptable quality properties such as long diffusion length, tuneable bandgap, high mobility, ambipolar charge transport, and high absorption reinforce these double perovskites and make them even more suitable for photovoltaic applications.

Electronic, elastic and pressure-induced phase transitions of tetragonal NaBH4 under high pressure

In this study; the structural, electronic and mechanical properties of sodium borohydride (NaBH4) compound were studied under high hydrostatic pressure from 0 to 300 GPa using the generalized gradient approach (GGA) within the framework of density functional theory (DFT). In the study, the NaBH4 compound transformed from the tetragonal structure with the space group P42 /nmc to the triclinic structure with the space group with the effect of gradually increasing pressure. Enthalpy and total energy calculations were performed to observe the agreement of the study with the experimental results. As a result of the calculations, it was concluded that a phase transition of the NaBH4 compound occurred at approximately 22.6 GPa from the tetragonal structure to the triclinic structure. In addition, the electronic properties of the NaBH4 compound were investigated and 6.22 and 4.95 eV band gaps were obtained for the P42 /nmc and phases, respectively.

Theoretical studies of optoelectronic properties of AlP1-xBix ternaries: Promising light sources for fiber optic communications

The aim of this paper is to investigate the optoelectronic properties of the new ternary alloys AlP1-xBix at different concentrations of Bismuth x (0 ≤ x ≤ 1), using super cell 16 atoms special quasi-random structures within the full-potential linearized augmented plane wave method (FP-LAPW) employing Wien2k based on the density functional theory. The generalized gradient approach of Perdew et al. (GGA-PBEsol) was used to study the structural properties. The electronic and optical properties were predicted using the local density (LDA) and Tran–Blaha-modified Becke–Johnson (TB-mBJ) approaches. The lattice parameters (a), bulk modulus (B) and band gap energy (Eg) are calculated and analyzed for ternary alloys and their binaries. It is found that the variation of the lattice constant a(x) exhibits a small bowing parameter equal to (−0.1366Å) according to Vigard's law. Band structure analysis shows that AlP1-xBix ternaries have direct band gaps for concentrations x (0 ≤x ≤ 1). The (TB-mBJ) results show that the band gap values of AlP1-xBix vary from 2.322 eV to 0.426 eV which corresponds to wavelengths from 0.534μm to 2.910μm. Furthermore, we investigated in detail the optical properties of AlP1-xBix ternaries. We can point out that this work represents the first theoretical study on these ternaries. The calculation confirms that the AlP1-xBix ternary alloys are promising candidate for optoelectronics, and in particular for light sources for fiber-optic communications.

Density functional theory investigation on structural, mechanical, electronic and vibrational properties of Heusler alloys AlXIr2 (X = Co, Cr, Cu, Fe and Zn)

This study focuses on the detailed investigation of full-Heusler AlXIr2 (X = Co, Cr, Cu, Fe and Zn) alloys. A first-principal plane-wave pseudopotential method based on density functional theory is adopted. The quantum-espresso package combined with the generalized gradient approach is used to reveal the structural, electronic, magnetic, mechanical and lattice dynamic properties of full-Heusler AlXIr2 (X = Co, Cr, Cu, Fe and Zn) alloys. The elastic constants are used to determine elastic stabilities of alloys based on Born criteria. The analysis showed that all alloys are elastically stable. Further detailed analysis has been carried out to reveal mechanical properties. It is found that all alloys are ductile and anisotropic. The electronic band structures are also obtained. All alloys except for AlCrIr2 are found to be metallic. AlCrIr2 has half-metallic nature. In addition, AlCrIr2, AlFeIr2 and AlCoIr2 has shown magnetic properties. The phonon spectra and density of states are investigated to examine dynamical stability. It is seen that all alloys exhibit dynamical stability due to having positive phonon frequencies.

Rare-earth ferrobismuthites: ferromagnetic ceramic semiconductors with applicability in spintronic devices

We report here the synthesis process of the perovskite-like complex material Bi0.5R0.5FeO3 (R=Eu, Sm, Dy) using the ceramic method, as well as its structural, optical, magnetic, and electrical characterizations. Refined X-ray diffraction data revealed that this material crystallizes in an orthorhombic structure (space group Pnma number 62). The band gap value in the optical response shown in the diffuse reflectance spectroscopy curve was typical of semiconductor materials. The magnetization exhibited a very low coercive field hysteretic behavior, which is characteristic of weak ferromagnetism, for all temperatures examined below 300 K and the various magnetic fields applied. The real and complex electric permittivity curves showed the occurrence of dielectric relaxation processes at 113 K in agreement with reports of pyroelectric and thermo-stimulated currents as a function of temperature revealing the appearance of ferroelectric polarization below 113 K with possible magnetoelectric coupling. On the other hand, we made a theoretical study of the electronic structure with and without the inclusion of a Berry distortional phase and ab-initio calculations following the density functional theory formalism and the pseudopotential plane wave method. In this formalism, the exchange and correlation mechanisms are described by the generalized gradient approach (GGA + U) considering spin polarization. The Berry phase analysis suggested the occurrence of ferroelectricity at temperatures below 113 K consistent with the experimental analysis evidencing a biferroic behavior at low temperatures given that the distortional phase introduces hybridizations between the 3d-Fe and 2p-O states favoring the appearance of Dzyaloshinskii-Moriya interactions, which, in turn, facilitate the appearance of ferroelectricity coexisting with a weak ferromagnetism. The thermodynamic properties in the presence or absence of the Berry phase by means of the Debye quasiharmonic model revealed the appearance of a ferroelectric transition at 113 K, which corroborates their magnetoelectric nature at low temperatures. The ferromagnetic semiconducting character found at room temperature enhances this material for applications in spintronics technology.

Electronic transport properties of compressed and stretched helicene-graphene nanostructures, a theoretical study

We present our ab initio simulations of strained helicene molecular junction. First, we present ab-initio models of [n]helicenes up to [100]helicene done by two different recent reactive force field molecular geometry optimization methods (ReaxFF CHOCsKNaClIFLi, 2019 and CHONSMgPNaCuCl, 2018). We used the [4]helicene and [10]helicene models for Density Functional Theory (DFT) electronic transport calculations of various graphene-helicene-graphene molecular junction configurations on Local Density Approximation (LDA) or Generalized Gradient Approach (GGA) level of exchange and correlation energy with Perdew-Zinger (PZ) or Perdew–Burke–Ernzerhof (PBE) functionals and Grimme DFT-D3 van der Waals correction. The electronic transport properties are studied by using of the Green's functions formalism. The electron transmissions and densities of states of [4]helicene (and [10]helicene) attached as a molecular junction in three different configurations to zigzag graphene nanoribbon (ZGNR) electrodes of three different widths were obtained. The structures are analyzed while relaxed, compressed or stretched. The current-voltage and current-strain characteristics are presented and results are compared and discussed. The work is supported by a short review summarizing some of the recent studies related to graphene, helicene, and molecular junctions under strain.

Thermodynamic evidence of the ferroelectric Berry phase in europium-based ferrobismuthite Eu2Bi2Fe4O12

The possible low temperature biferroic feature of Eu2Bi2Fe4O12 complex perovskites was recently reported. The aim of this work is to present a theoretical study of the structural, magnetic, electronic and ferroelectric properties of this material. Several energy minimization processes were performed for three types of cationic distributions, different angles of rotation, octahedral inclination, and some kinds of magnetic ordering. The results reveal that the most stable crystallographic arrangement corresponds to an intercalated distribution of the Eu3+ and Bi3+ cations between the FeO6 octahedra. Similarly, energy is minimized for rotations and octahedral inclinations corresponding to angles θe = 12.86° and ϕe= 13.32°, respectively. With respect to the distribution of magnetic moments, the results reveal that a G-type antiferromagnetic configuration is the most energetically favorable. The electronic structure is studied from ab initio calculations following the formalism of density functional theory and the pseudopotential plane wave method. In this formalism, the exchange and correlation mechanisms are described by means of the generalized gradient approach (GGA + U), considering spin polarization. The ferroelectric characteristic is analysed by determining ferroelectric polarization based on the calculation of the Berry phase. The theoretical results obtained are consistent with the experimental reports, which is why the Eu2Bi2Fe4O12 material is expected to exhibit biferroic behavior at low temperatures, because the Berry phase introduces hybridizations between the 3d-Fe and 2p-O states that favor the occurrence of Dzyaloshinskii-Moriya interactions, which facilitate the occurrence of ferroelectricity coexisting with weak ferromagnetism. An extensive study of the thermodynamic properties in the presence and absence of the Berry phase is undertaken by means of the Debye quasi harmonic model. The specific heat difference with and without the Berry phase reveals the occurrence of a ferroelectric transition at T = 113 K without the application of external pressure. When the applied pressure is incremented, a systematic increase in the transition temperature is observed due to the reduction of overlap between the 3d-Fe orbitals and the 2p-O orbitals in the compressed octahedra of perovskite.

Ternary halide perovskites for possible optoelectronic applications revealed by Artificial Intelligence and DFT calculations

In this article, we present 134 AMX3 compounds as potential candidates to adopt the perovskite structure. These compounds, where X = F, Cl, Br or I, and M = an alkali or earth-alkali element, were found as feasible by a previously informed Artificial Neural Network (ANN). None of these compounds have been reported as synthesized up to now. The ANN assesses the probability of a set of atoms to crystallize with the perovskite structure using structural factors as input data. In addition, we implemented geometry optimization calculations with periodic boundary conditions to test the stability of the perovskite compounds predicted by the ANN. These calculations were performed within the Generalized Gradient Approach using the functional PBEsol. After these calculations, 96 of the 134 compounds preserved the most symmetric form of the perovskite structure. The rest of the compounds had a distortion within the octahedral framework. As a consequence of the DFT calculations, we found that the 134 AMX3 perovskite compounds spanned band-gap energies up to 7.88 eV. In this manner, the here reported compounds may find an application as new solar cells or transparent semiconductors, for instance.

Experimental and theoretical investigations of the structural, magnetic and electronic characteristics of copper ferrite nanostructures as potential spin-filtering candidates

Employing both experimental and first-principle techniques, the structural, dielectric, magnetic, and electronic characteristics of spinel-structured copper ferrite (CuFe2O4) nanoparticles (NPs) are examined. The CuFe2O4 NPs are synthesized by a co-precipitation technique (CPT) and characterized by transmission electron microscopy (TEM), scanning electron microscopy (SEM), vibrating sample magnetometer (VSM), and X-ray photoelectron spectroscopy (XPS). The SEM results display that the CuFe2O4 NPs possess mixed spinel phases. The composition of NP elements is determined via Energy-dispersive X-ray (EDX) spectroscopy. The magnetization and coercivity are evaluated by VSM measurements. The principal peaks of the O 1s, Cu 2p, and Fe 2p states are appeared at peculiar binding energies in XPS spectra. The magnetic features and electronic structures of the CuFe2O4 NPs are examined via density functional theory (DFT) together with on-site correction for Coulomb interaction using the generalized gradient approach (GGA + U) technique for exchange and correlation term. The CuFe2O4 NPs derived from the bulk spinel structure possess a magnetic semiconducting character. The results of density of states (DOSs) reveal an insulating character having an energy band gap of ~1.75 eV for both spin channels. The local magnetic moments display a ferrimagnetic spin arrangement in the CuFe2O4 nanostructure, manifesting through the hybridized d states of Fe/Cu and the p orbitals of O atoms. The K-edge X-ray absorption spectra (XAS) of Cu, Fe, and O ions in the CuFe2O4 nanostructure are also modeled with GGA + U technique and compared with the XPS results. The structural features of the local environment of Cu2+, Fe3+, and O2- ions are scrutinized theoretically to discern the ion sites centered at octahedral or tetrahedral lattice voids. The alternating current (AC) conductivity diminishes with the augmentation in frequency, yielding a semiconductive nature. The characterization of CuFe2O4 NPs can provide insights into their preferential magnetic and dielectric behaviors applicable in miniature magnetoelectronic and energy-storage devices.

The investigation of electronic nature and mechanical properties under spin effects for new half-metallic ferromagnetic chalcogenides Ag3CrX4 (X = S, Se, and Te)

This study presents the electronic and mechanical characteristics of ternary silver-based Ag3CrX4 (X = S, Se, and Te) chalcogenides having simple cubic crystalline structure (SC), conforming P4-3m (space group: 215) that are studied under the spin-polarized Generalized Gradient Approach (GGA) within the framework of the Density Functional Theory (DFT). The stable magnetic phase has been determined as the ferromagnetic (FM) phase for all studied systems. Then, phase stability, mechanical, thermal and electronic characteristics of Ag3CrX4 chalcogenides have been reported. In the calculated spin polarized electronic band structures for Ag3CrX4 chalcogenides, as an indicator of half-metallic behavior, metallicity has been observed in the majority spin channel, while indirect band gaps (1.04 eV for Ag3CrS4, 1.10 eV for Ag3CrSe4, and 1.25 eV for Ag3CrTe4) have been determined in the minority spin channel. Moreover, Ag3CrX4 chalcogenides have been found as thermodynamically stable and structurally synthesizable considering the calculated negative formation enthalpies. Elastic constants of studied chalcogenides satisfying Born-Huang criteria's pointed out the mechanical stability of materials. The predicted mechanical properties determined with elastic constants revealed that Ag3CrX4 chalcogenides belong to soft and ductile material family.

Hypothetical P63/mmc-Type CsCrCl3 Ferromagnet: Half-Metallic Property and Nodal Surface State

This work is focusing on the electronic, magnetic, half-metallic behaviors, and interesting surface state of hypothetical CsCrCl3 ferromagnet with P63/mmc space group that are investigated under the spin-polarized Generalized Gradient Approach (GGA) and spin-polarized GGA plus Hubbard U correction within the framework of the Density Functional Theory (DFT). The calculated total magnetic moment of P63/mmc CsCrCl3 is ~7.397 µB, and the mainly contribution to the total magnetism is coming from the Cr atoms. Based on obtained spin-polarized band structures, we confirmed that this hypothetical CsCrCl3 is a half-metal with 100% spin-polarization. Without spin-orbit coupling, i.e., the spin and the orbit degrees of freedom are dependents, we found that there should be a interesting nodal surface state at kz = plane due to P63/mmc type lattice structure enjoys a two-fold screw axis S2z. Our study can be seen as a strong evidence to exhibit that the protected nodal surface state can be achieved in magnetic materials.

Comprehensive analysis of the influence of dispersion on group-14 rutile-type solids

Weak van der Waals interactions have a notorious influence on the stability of molecular solids and layered materials. In light of this fact, accurate models have been designed to account for such long-range interactions. Here, we explore the influence of the dispersion on the structural properties of dense rutile-type ${\mathrm{SiO}}_{2}$, ${\mathrm{GeO}}_{2}$, ${\mathrm{SnO}}_{2}$, and ${\mathrm{PbO}}_{2}$ structures. Several dispersion methods are discussed including pairwise force field and more physically grounded methods such as the so-called many body dispersion and nonlocal correlation functionals. The results clearly show that such methods and functionals have influence on the predicted crystal structure of the investigated solids, usually improving the structural properties with a reduction of the errors with respect to experiment. In particular, Perdew-Burke-Ernzerhof (PBE) coupled with many body dispersion (MBD)@rsSCS emerges as the most suitable method showing the lowest relative errors. Interestingly, this method reproduces similar results to those obtained by the PBEsol generalized gradient approach (GGA) functional designed to reproduce crystal structures without considering dispersion terms. Finally, we want to point out that the present study suggests that the proper inclusion of dispersion allows one to improve the description of the crystal structure and, consequently, due to the sensibility of either electronic and magnetic properties to it, methods coupling a suitable description of dispersion to a standard PBE GGA functional would lead to an improved description of crystalline solids.

Half-metallic ferromagnetic behavior of cubic lanthanide based on perovskite-type oxide NdCrO3: first-principles calculations

In this study, theoretical investigation on structural, electronic and magnetic properties of the cubic perovskite oxide NdCrO3 has been performed within density functional theory. The exchange and correlation potential is treated by three approximations: generalized gradient approach of Perdew, Burke and Ernzerhof (GGA–PBE), GGA plus band correlated Hubbard parameter (GGA + U) scheme and GGA plus Tran–Blaha-modified Becke–Johnson (TB-mBJ–GGA) approximation which has been used to describe the energy band gap more accurately. Structural results found in the course of this study are in perfect agreement with experimental measurements and show that the ground state of the studied compound is ferromagnetic. The electronic band structures and density of states display a half-metallic behavior of the cubic perovskite NdCrO3 with an indirect band gap in minority spin. The magnetic study shows that the total magnetic moment of 6 μB mainly originates from the both atoms Nd and Cr. The integer value confirms a half-metallic nature of the studied material. Consequently, the NdCrO3 is a promising candidate for the useful spintronic applications.

Elastic and thermophysical properties of BAs under high pressure and temperature

The pseudopotential plane-wave approach in the framework of the density functional theory, and the density functional perturbation theory with the generalized gradient approach for the exchange-correlation functional has been used to calculate the structural phase stability, elastic constants and thermodynamic properties of boron-arsenide (BAs) compound. The BAs compound transforms from the zincblende phase to rock-salt structure; the phase transition pressure was found to be 141.2 GPa with a volume contraction of around 8.2%. The thermodynamic properties under high pressure and temperature up to 125 GPa and 1200 K respectively were also determined, analyzed and discussed in comparison with other data of the literature. The systematic errors in the static energy were corrected using the bpscal EEC method. Our results agree well with those reported in the literature, where for example, our calculated melting temperature (2116 K) deviates from the theoretical one (2132.83 K) with only 0.8%, and the deviation between our result (1.86) of the Grüneisen parameter and the theoretical one (1.921) is only around 3.2%.

Theoretical Modeling of Electronic Excitations of Gas-Phase and Solvated TiO2 Nanoclusters and Nanoparticles of Interest in Photocatalysis.

The optical absorption spectra of (TiO2) n, nanoclusters ( n = 1-20) and nanoparticles ( n = 35, 84) have been calculated from the frequency-dependent dielectric function in the independent particle approximation under the framework of density functional theory. The PBE generalized gradient approach based functional, the so-called PBE+ U method and the PBE0 and PBEx hybrid functionals-containing 25% and 12.5% of nonlocal Fock exchange, respectively-have been used. The simulated spectra have been obtained in the gas phase and in water on previously PBE0 optimized atomic structures. The effect of the solvent has been accounted for by using an implicit water solvation model. For the smallest nanoclusters, the spectra show discrete peaks, whereas for the largest nanoclusters and for the nanoparticles they resemble a continuum absorption band. In the gas phase and for a given density functional, the onset of the absorption (optical gap, Ogap) remains relatively constant for all nanoparticle sizes although it increases with the percentage of nonlocal Fock exchange, as expected. For all tested functionals, the tendency of Ogap in water is very similar to that observed in the gas phase with an almost constant upshift. For comparison, the optical gap has also been calculated at the TD-DFT level with the PBEx functional in the gas phase and in water. Both approaches agree reasonably well although the TD-DFT gap values are lower than those derived from the dielectric-function. Overall, the position of the spectral maxima and the width of the spectra are relatively constant and independent of particle size which may have implications in the understanding of photocatalysis by TiO2.

Ground state properties of 3d metals from self-consistent GW approach

The self consistent GW approach (scGW) has been applied to calculate the ground state properties (equilibrium Wigner–Seitz radius SWZ and bulk modulus B) of 3d transition metals Sc, Ti, V, Fe, Co, Ni, and Cu. The approach systematically underestimates SWZ with average relative deviation from the experimental data of about 1% and it overestimates the calculated bulk modulus with relative error of about 25%. It is shown that scGW is superior in accuracy as compared to the local density approximation but it is less accurate than the generalized gradient approach for the materials studied. If compared to the random phase approximation, scGW is slightly less accurate, but its error for 3d metals looks more systematic. The systematic nature of the deviation from the experimental data suggests that the next order of the perturbation theory should allow one to reduce the error.

Improved description of the structural and optoelectronic properties of DNA/RNA nucleobase anhydrous crystals: Experiment and dispersion-corrected density functional theory calculations

The development of low cost and environmentally friendly organic electronic/optoelectronic devices has attracted a lot of interest. The integration of DNA and RNA nucleobases to improve the performance of organic light-emitting diodes has been proposed recently [Gomez et al., Sci. Rep. 4, 7105 (2014)], notwithstanding limited experimental and theoretical information on the optoelectronic properties of DNA/RNA thin films. As a contribution to an improved understanding of DNA/RNA-based devices in the solid state, we have performed in this paper dispersion corrected density functional theory (DFT) and time-dependent DFT (TDDFT) calculations to obtain the optimized geometries, Kohn-Sham band structures and orbitals, charge distribution, optical absorption, Frenkel exciton binding energies, and complex dielectric functions of the five DNA/RNA nucleobase anhydrous crystals, namely cytosine, guanine, adenine, thymine, and uracil. Optical absorption measurements on DNA/RNA nucleobase powders were also performed for comparison with the simulations. An improvement on the local density approximation (LDA) description of the lattice parameter estimates was achieved considering the generalized gradient approach (GGA) with a semiempirical dispersion correction scheme in comparison with structural x-ray data found in the literature. Energy gap correction using the \ensuremath{\Delta}-sol methodology provided a good agreement between theory and experimental estimates from our optical absorption data, greatly surpassing the quality of previous simulations. Effective masses for the carriers were also found, indicating that the guanine crystal as well as the cytosine one (although with some drawbacks) has potential applications in optoelectronics as a direct gap semiconductor, with the other nucleobases presenting either a semiconductor or an insulator character depending on the carrier type. The complex dielectric function exhibits a high degree of anisotropy for different states of light polarization relative to the molecular stacking planes, while the Frenkel exciton binding energy estimation for the adenine crystal is very close to the optical absorption experimental data.

First Principle Calculation of Li<sub>2</sub>Fe<sub>0.5</sub>Cr<sub>0.5</sub>SiO<sub>4</sub> for Li-Ion Battery Cathode

First principle calculation based on Density Functional Theory and U correction (DFT+U) is used to investigate structural change while losing Li atom, average voltage for couple reaction, phase stability, and electronic structure of Li2Fe0.5Cr0.5SiO4. In this calculation, generalized gradient approach (GGA) of Perdew-Burke-Ernzerhof (PBE) is used for exchange-correlation functional. The initial structure of Li2Fe0.5Cr0.5SiO4 is obtained from the pmn21 structure of Li2FeSiO4 and then the Fe site is substituted by 50 % of Cr. The results of calculation show that the optimized Li2Fe0.5Cr0.5SiO4 has a monoclinic structure, which has little different with Li2FeSiO4 structure. Although the delithiated system (LiFe0.5Cr0.5SiO4) is taken into consideration, the structural geometry does not change significantly. It is indicated that the presence of Cr does not affect to the property of structural change. From the density of states (DOS) analysis, the presence of Cr causes the width of band gap become decrease. Therefore, the electronic properties change from insulator to semiconductor-like behavior. Average voltage for couple reaction M+2/ M+3 of Li2Fe0.5Cr0.5SiO4 is about 3.05 V which is lower than Li2FeSiO4. Furthermore, the formation energy for Li2Fe0.5Cr0.5SiO4 and all delithiation have a relatively positive sign compared with Li2FeSiO4 that mean that they have poor phase stability than Li2FeSiO4.