Theory Calculations Research Articles

Stability, Electronic, and Piezoelectric Properties of H‐ and F‐Functionalized BP Sheets

Herein, the electronic and piezoelectric properties of different types of (chair form and boat form) H/F‐functionalized boron phosphide (BP) sheets are examined by density‐functional theory calculations. After H/F atoms adsorb on both sides of pristine hexagonal boron phosphide (h‐BP) cell, the functionalized BP structure undergoes significant flatness distortion. The H/F‐functionalized BP sheets are predicted to be thermodynamically and dynamically stable. According to the calculations, it is demonstrated that chemical functionalization is an effective method to modulate the bandgap of h‐BP in a wide range (0.80–3.63 eV). The chair form F–BP–H shows large e31 (−0.7 × 10−10 C m−1) and d31 (−0.68 pm V−1). The d11 of boat form F–BP–H is 4.32 pm V−1, which is 95.5% higher than the pristine h‐BP monolayer (2.21 pm V−1). The study provides a possible way to modulate the intrinsic characteristics of the pristine h‐BP sheet, which would broaden its potential applications in the future for wider range of applications.

Cd(II)-based fish-bone-like 1D coordination polymer: structural elucidation and computational study

{[Cd(L)2(PBT)2]}n (1) [H2L = 5-nitro-isophthalic acid; PBT = 2-pyridin-4-ylbenzothiazole], 1D Coordination Polymer (1D-CP), is characterized by single crystal X-ray diffraction. The structure of 1 contains carboxylate bridges of L2- to Cd(II), where one carboxylate chelates to Cd(II) and the other -COO bridges to two neighboring Cd(II) centers that then form eight-membered dinuclear metallacycles (Cd2C2O4). The 1D chains self-assemble via H-bonding and π⋅⋅⋅π interactions to form a supramolecular aggregate that resembles a fish-bone pattern. These interactions are further explored by Hirshfeld Surface Analysis. Density Functional Theory (DFT) computations using the crystallographic parameters of 1 predicted an energy gap, ΔE (EHOMO – ELUMO) of 3.67 eV, which is comparable to the experimental band gap obtained from a Tauc’s plot, 3.73 eV. The band gap value demonstrates the semiconducting character and may be used for device fabrication. Furthermore, molecular electrostatic potential (MEP) shows strong electrophilic reaction potential and predicts reactive sites. The PBT ligand is emissive (370 nm) while H2L is non-emissive. DMF suspensions of 1 emit at 525 nm with a long lifetime, 0.715 ns compared to the lifetime of PBT (0.05 ns). This supports that extended conjugation occurs upon formation of the 1D-CP, altering the photophysics.

Solvent-Mediated Rate Deceleration of Diels–Alder Reactions for Enhanced Selectivity: Quantum Mechanical Insights

Solvents can have a tremendous influence on the rate and selectivity of chemical reactions, but their effects are not always well accounted for. In the present work, density functional theory computations are used to investigate the influence of solvent on the Diels–Alder reactions of 9-methylanthracene with (5-oxo-2H-furan-2-yl) acetate and different anhydrides considering the overall reaction rates as well as selectivity between possible isomeric products. Crucially, we find that overall reaction rates are higher in non-polar toluene, whereas selectivity is enhanced in the polar solvent acetone. In the case of (5-oxo-2H-furan-2-yl) acetate, the difference in the reaction barriers is enhanced by 2.4 kJ/mol in acetone as compared to the gas phase, halving the yield of the side product. Similar results are found for the reaction of 9-methylanthracene with chloro-maleic anhydride and cyano-maleic anhydride, highlighting the generality of the trends observed. After presenting the energetics, a detailed discussion of the reactivity is given using electrostatic potentials, frontier orbitals, reactivity indices and Fukui functions. In summary, this study highlights the importance of solvent in influencing reaction rates and illustrates the possibility of studying its effects computationally.

Simulation of Spin Chains with Off-Diagonal Coupling Using the Inchworm Method.

We study the dynamical simulation of an open quantum spin chain with nearest neighboring coupling, where each spin in the chain is associated with a harmonic bath. This is an extension of our previous work (Wang, G.; Cai, Z. J. Chem. Theory Comput. 2023, 19, 8523-8540) by generalizing the application of the inchworm method and the technique of modular path integrals from diagonally coupled cases to off-diagonally coupled cases. Additionally, to reduce computational and memory cost in long time simulation, we apply tensor-train representation to efficiently represent the reduced density matrix of the spin chains, and employ the transfer tensor method (TTM) to avoid exponential growth of computational cost with respect to time. Abundant numerical experiments are performed to validate our method.

Tuning the electrochemical performance of a biphenylene coated metal as the anode for K+-ion batteries

The researchers employed density functional theory (DFT) computations to assess suitability of BP-biphenylene (b-BP) monolayers for application in potassium-ion battery systems. In their evaluations, the researchers considered various factors, like adsorption energy (Ead) of the b-BP monolayer with adsorbed potassium adatoms, in addition to diffusion energy barrier (Ebar) and storage capacity and of potassium ions on this surface. The results indicated that the b-BP monolayer has significantly higher potassium-ion storage capacities, reaching 1026 mAh/g, compared to typical graphite anodes and other carbon materials. The Ebar for potassium ions on the b-BP monolayer was determined to be 0.22 eV. Furthermore, anticipated open-circuit voltage (OCV) values for this material were found to lie within acceptable range of 0.25–1.2 V, making it suitable for use as an anode. These research findings underscore the potential of the b-BP monolayer as an appropriate anode material for potassium-ion battery (KIBs) applications.

DFT study of electronic and nonlinear optical properties of alkaline earth metals and superalkalis doped all-cis-1, 2, 3, 4, 5, 6-hexafluorocyclohexane as an efficient excess electron system

Continual advancements are being pursued to discover innovative strategies for developing materials with remarkable nonlinear optical (NLO) response. Herein, electronic, geometric, thermodynamic and NLO properties of excess electron systems based on stacked Janus dimer, all-cis-1,2,3,4,5,6-hexafluorocyclohexane (C6H6F6)2 are thoroughly investigated. The excess electron systems are designed by doping alkaline earth metals (AEMs) on fluorine face and superalkalis on hydrogen face of Janus dimer. The higher values of vertical ionization energies (VIE) and interaction energies (Eint), confirm the electronic and thermodynamic stabilities of the designed complexes, respectively. Natural bond orbital (NBO) analysis is performed, and the excess electron character of the complexes is confirmed through frontier molecular orbital (FMO) analysis by highest occupied molecular orbital (HOMO) iso-densities. FMO shows a significant decrease in energy gaps (Egap) of the complexes (i.e., Eg = 1.80–3.12 eV), compared to the stacked Janus dimer (i.e., Eg = 9.41 eV). The transparency of the complexes to UV region is confirmed through UV–vis analyses, revealing their maximum absorption in visible and near-IR regions. The higher NLO response of the designed excess electron systems is further proved by the greater values of first hyperpolarizability (β o ) i.e., up to 1.70 × 106 au. Moreover, the time dependent-density functional theory (TD-DFT) computations and two-level model are employed to investigate the controlling factors of hyperpolarizability, illustrating the contribution of transition energy (∆E3), change in dipole moment (∆μ) and oscillator strength (f o ) in controlling the β o . Ab-initio molecular dynamics (AIMD) simulation further confirm that the designed superalkalide complexes are kinetically and thermally stable. The thorough investigation of these excess electron systems proves them an appropriate candidate for NLO applications.

Complexes of a Frustrated Lewis Pair-Supported P(-1) Ligand.

Several complexes of the intramolecular frustrated Lewis pair (FLP)-supported P(-1) ligand [iPr2P(C6H4)BCy2{P}]- are presented (Cy=cyclohexyl). Chief among these is the first example of a monomeric zinc bis(phosphido) complex, which was synthesized as a potential precursor for the solution-phase deposition of Zn3P2. While this goal was ultimately unsuccessful, the Zn(II) complex acts as a convenient springboard to other metal phosphide species via transmetallation: affording a tellurium bis(phosphido) complex and a formal adduct of the phosphorus subhalide PPCl2. Trapping experiments show that the PPCl2 adduct can also be prepared directly through the in situ reduction of PCl3 in the presence of an intramolecular FLP ligand. Lastly, we report a formal η2-phosphaborene complex of cobalt(-1) which is isoelectronic to olefin complexes, and explore its bonding via density functional theory (DFT) computations.

Highly Tensile Strained Cu(100) Surfaces by Epitaxial Grown Hexagonal Boron Nitride for CO2 Electroreduction to C2+ Products.

Copper (Cu) has been considered as the most promising catalyst for the electrochemical conversion of CO2 to multicarbon (C2+) products. However, insufficient coverage of the *CO intermediate on the C2+ formation Cu(100) facet largely hinders the C-C coupling process and thus the C2+ conversion efficiency. Herein, we developed an epitaxial growth strategy to generate highly tensile-strained Cu(100) facets via the epitaxial growth of hexagonal boron nitride (hBN) on Cu(100) facets to promote *CO coverage for efficient CO2 to C2+ conversion. The highest ∼6% tensile strain on the Cu(100) facets was obtained by lattice mismatch between the Cu(100) and hBN(002) facets. Theory calculations indicated that tensile-strained Cu(100) facets deliver a notable d-band center upshift to enhance *CO adsorption. As a result, the obtained highly tensile-strained Cu(100) facets enabled an 8-fold improvement of *CO coverage and thus a 83.4% C2+ Faradaic efficiency at 1.2 A cm-2 in strongly acidic electrolyte (pH = 1).

Synthesis and DFT investigations of novel 13-(pyrimidin-2-yl)-6H,12H-6,12-epiminodibenzo[b,f][1,5]dioxocine derivatives

Heterocyclic compounds containing nitrogen and oxygen atoms are of great importance and wide applications in the fields of biomedicine and functional materials. In this paper, novel 13-aryl-6H,12H-6,12-epiminodibenzo[b,f][1,5]dioxocines generated from cascade reactions between arylamines and 2-hydroxybenzaldehyde have been explored through both experiments and theoretical calculations. Experimental investigations showed that pyrimidin-2-amine could react with 2-hydroxybenzaldehyde in acetonitrile at 80 °C to afford the desired 13-(pyrimidin-2-yl)-6H,12H-6,12-epiminodibenzo[b,f][1,5]dioxocines with 50 mol % of p-toluenesulfonic acid as catalyst, but aniline reacted with 2-hydroxybenzaldehyde to generate aldimine instead of the target bridged heterocylic compound. Density functional theory (DFT) computations were conducted to investigate the reaction mechanisms of 2-hydroxybenzaldehyde reacting with pyrimidin-2-amine and aniline, respectively. The experimental findings can be reasonably explained by theoretical calculations. Both the experimental explorations and suggested mechanisms indicate that the reactivity of the model reaction is sensitive to the electron density on the amino group of arylamine and the aldehyde group of 2-hydroxybenzaldehyde, which can be finely tuned with the aromatic ring structure and the substituents on it.

Large‐Area Lead Monolayers under Cover: Intercalation, Doping, and Phase Transformation

Intercalation is a promising approach for tailoring the electronic structure of epitaxial graphene on SiC. It enables the formation of otherwise unstable 2D phases of elements and allows the investigation of the interplay between the 2D materials and the substrate. Detailed studies have been conducted on the Pb intercalation process, as well as the structure and electronic properties of the 2D Pb layer using low‐energy electron microscopy and photoelectron spectroscopy. The low‐energy bands of Pb show good agreement with density‐functional theory calculations. A uniform Pb intercalation layer with (1 × 1) periodicity with respect to the SiC substrate is found. The quasifreestanding graphene is effectively screened from the doping influence of the substrate, leading to charge neutrality. Instead, the 2D Pb layer compensates for the spontaneous polarization of the substrate, allowing for the doping of a metal layer under cover. A phase transformation from the (1 × 1) intercalation phase into a bubble phase with quasi‐tenfold periodicity with respect to graphene occurs if the system is provided with sufficient energy. These results experimentally quantify the interaction between the 2D Pb layer, the substrate, and the graphene layer, demonstrating a first step toward controlling the diversity of 2D Pb phases.

Effect of AFM ordering on thermoelectric responses of Mg3X2 (X: C, Si, Ge) monolayers : a DFT insight

Two-dimensional materials have gained a lot of attention in the last few decades due to their potential applications in thermoelectric and nano-electronic devices. This study systematically presents the mechanical, electronic and thermoelectric characteristics of two-dimensional honeycomb-kagomeMg3X2(X:C,Si,Ge) structures in the framework of density functional theory computations and by solving semiclassical Boltzmann transport equation. The geometrical stability of these structures is validated by phonon spectrum and molecular dynamics simulations. Following the elastic constants, we have inferred that all the systems are mechanically stable and brittle in nature. Lower values of Debye temperature of all structures suggest thatMg3X2monolayers should have lower values of lattice thermal conductivity compared to graphene. Electronic structure calculations indicate that these materials are semimetallic in their nonmagnetic phase. All the structures display remarkably low lattice thermal conductivity (0.9-1.5 W (mK)-1) due to a large scattering factor and higher anharmonicity. The presence of sharp density of states peaks close to the Fermi level, arising from nearly flat and dispersionless band in the antiferromagnetic (AFM) arrangement, is poised to enhance the Seebeck coefficient, thereby potentially boosting the thermoelectric performance. The estimated values of thermoelectric figure of merit (ZT) are around 0.78 and 0.67 forMg3Si2andMg3Ge2structure respectively in AFM phase atT= 700 K. These outcomes of our findings suggest thatMg3X2monolayers exhibit substantial promise for thermoelectric device application.

On Scheduling Mechanisms Beyond the Worst Case

AbstractThe problem of scheduling unrelated machines has been studied since the inception of algorithmic mechanism design (Nisan and Ronen, Algorithmic mechanism design(extended abstract). In: Proceedings of the Thirty First Annual ACM Symposium on Theory of Computing (STOC), pp. 129–140, 1999. It is a resource allocation problem that entails assigning m tasks to n machines for execution. Machines are regarded as strategic agents who may lie about their execution costs so as to minimize their time cost. To address the situation when monetary payment is not an option to compensate the machines’ costs, Koutsoupias (Theory Comput Syst 54:375–387, 2014) devised two truthful mechanisms, K and P respectively, that achieves an approximation ratio of $$\frac{n+1}{2}$$ n + 1 2 and n, for social cost minimization. In addition, no truthful mechanism can achieve an approximation ratio better than $$\frac{n+1}{2}$$ n + 1 2 . Hence, mechanism K is optimal. While the approximation ratio provides a strong worst-case guarantee, it also limits us to a comprehensive understanding of mechanism performance on various inputs. This paper investigates these two scheduling mechanisms beyond the worst case. We first show that mechanism K achieves a smaller social cost than mechanism P on every input. That is, mechanism K is pointwise better than mechanism P. Next, for each task, when machines’ execution costs are independent and identically drawn from a task-specific distribution, we show that the average-case approximation ratio of mechanism K converges to a constant determined by the task-specific distribution. This bound is tight for mechanism K. For a better understanding of this distribution-dependent constant, on the one hand, we estimate its value by plugging in a few common distributions; on the other, we show that this converging bound improves a known bound (Zhang in Algorithmica 83(6):1638–1652, 2021)) which only captures the single-task setting. Last, we find that the average-case approximation ratio of mechanism P converges to the same constant.

Influence of non-metals doping on the structural, electronic, optical, and photocatalytic properties of rutile TiO2 based on density functional theory computations

This study investigates the influence of non-metal doping (C, F, N, and S) on the structural, electronic, and optical properties of rutile TiO2 using Hubbard-corrected density functional theory (DFT) within the Quantum ESPRESSO code. Rutile TiO2 is a promising material for environmental remediation and renewable energy applications. However, it has a large bandgap of 3.03 eV, which confines its use to UV light. By substituting oxygen atoms with a single dopant atom, we aim to shift the absorption edge toward the visible spectrum. Our findings reveal that doping with C, N, and S results in a redshift of the bandgap, while F doping does not exhibit this effect. The imaginary part of the dielectric function indicates shifted absorption edges for C, N, and S-doped TiO2, making them suitable for photocatalytic applications. Additionally, an increased refractive index after doping suggests the presence of excess charge carriers that affect light propagation. This work provides valuable insights for experimentalists exploring non-metal doping influences on rutile TiO2 for photocatalysis.

Electrolyte-triggered in-situ polymerization of multi-site organic cathodes for superior-longevity cation-anion co-storage secondary batteries

Organic electrodes are promising as next-generation energy storage materials owing to their diverse structures, low mass, and environmental friendliness. Nevertheless, the dissolution and degradation of organic active species in electrolytes are remaining obstacles to their authentic commercialization. Herein, we report an instantaneous in-situ upgrading strategy to convert multi-site organic cathode materials, e.g., 1-aminoanthraquinone (1-AAQ) and 1,5-diaminoanthraquinone (1,5-DAAQ), into poly(1-aminoanthraquinone) (PAAQ) and poly(1,5-diaminoanthraquinone) (PDAAQ) simply by dropping the electrolyte during battery assembly without extra operations. The remarkable chemistry is essentially a chemical polymerization process of redox-active organic monomers triggered by the electrolyte containing magnesium bis(hexamethyldisilazide) (Mg(HMDS)2) as an initiator. Notably, due to the π-conjugated polymer chain with inhibited dissolution, high conductivity, and improved stability, the as-obtained PDAAQ cathode delivered a high specific capacity (254 mAh/g at 100 mA/g), superior rate performance (83 mAh/g at 2000 mA/g), and excellent cycling stability for over 8000 cycles accompanied by an average capacity decay of only 0.0026 % per cycle. Detailed characterizations further explore the kinetic behaviors and verify a reversible hybrid cation–anion co-redox mechanism of PDDAQ cathode, which involves reversible Mg2+ cation insertion/extraction on AQ units and anion doping/de-doping reactions on the PANI backbones. Density functional theory (DFT) computations demonstrate the optimized structure of the discharged products and indicate that Mg2+ preferably interact with two carbonyls oxygen atoms and nitrogen atom for both PAAQ and PDAAQ. This study demonstrates an intriguing in-situ chemical-polymerization synthetic approach for preparing multi-site organic electrode materials that compromise structure optimization and synthetic efforts, offering great promise for high-performance and sustainable secondary batteries.

Experimental and theoretical studies of carbacylamidophosphate-La (III) complexes: Synthesis, crystal structure, antibacterial activity, electronic and morphology properties

The present study tries to contribute to the body of knowledge concerning the effects of O-donor ligands based on carbacylamidophosphate on the topology, geometry, and dimensions of relevant metal complexes. Accordingly, the octa-coordinated lanthanum (III) complex with formula, [La(L1)4Cl2]Cl (C1) (L1 = 4-NC5H4C(O)NHP(O)(NC6H12)2), has been synthesized and its crystal structure has been determined. In the crystal structure, C1 is C2-symmetrical, and there are separate [La(L1)4Cl2]+ cations and Cl- anions. In the complex molecule, the four L1 ligands adopt two anti- and two syn-chelating conformations. Moreover, two other carbacylamidophosphate-based lanthanide complexes La(L2)2(NO3)3 (C2) (L2 = PhC(O)NHP(O)(NH(tert‑C4H9))2)2(NO3) and La(L3)2(NO3)3(H2O)[(CH3)2CO] (C3) (L3 = (4-NO2C6H4CONHPO(NC4H8O)2) were considered and density functional theory computations, at the B3PW91 level, were performed to gain a deeper understanding of the structural and electronic properties in complexes (C1 - C3). Nano and micro-structures of (C’1 - C’3) were prepared by means of a sonochemical process to study how the reaction condition and non-covalent forces function in terms of the form as well as the size of the particles in these complexes. Thermal gravimetric analysis (TGA) and differential thermal analysis (DTA) were performed on compounds C’1- C’3. The Hirshfeld surface analysis and NCI method were used to show the effects of non-covalent interactions on the compounds’ morphologies. The antimicrobial activity of all selected compounds has been screened against two Gram-positive (Bacillus subtilis, Staphylococcus aureus) and one Gram-negative (Escherichia coli) bacteria by well diffusion method. The results indicated that all selected compounds did not show any antibacterial activity against bacteria as compared to standard drugs.

Improved Gaussian basis sets for norm-conserving 4f-in-core pseudopotentials of trivalent lanthanides (Ln = Ce-Lu).

The first-principles quantum chemical computations often scale as Nk (N = basis sets; k = 1-4 for linear scaling, Hartree-Fock or density functional theory methods), which makes the development of accurate pseudopotentials and efficient basis sets necessary ingredients in modeling of heavy elements such as lanthanides and actinides. Recently, we have developed 4f-in-core norm-conserving pseudopotentials and associated basis sets for the trivalent lanthanides [Lu et al., J. Chem. Theory Comput. 19, 82-96 (2023)]. In the present paper, we present a unified approach to optimize high-quality Gaussian basis sets for modeling and simulations of condensed-phase systems. The newly generated basis sets not only capture the low total energy and fairly reasonable condition number of overlap matrix of lanthanide-containing systems, but also exhibit good transferability and reproducibility. These advantages ensure the accuracy of the basis sets while avoiding linear dependency concern of atom-centered basis sets. The performance of the basis sets is further illustrated in lanthanide molecular and condensed-phase systems by using Gaussian-plane wave density functional approach of CP2K. These new basis sets can be of particular interest to model structurally complicated lanthanide molecules, clusters, solutions, and solid systems.

Tandem Methanolysis and Catalytic Transfer Hydrogenolysis of Polyethylene Terephthalate to p‐Xylene over Cu/ZnZrOx Catalysts

We demonstrate a novel approach of utilizing methanol (CH3OH) in a dual role for (1) the methanolysis of polyethylene terephthalate (PET) to form dimethyl terephthalate (DMT) at near‐quantitative yields (~97%) and (2) serving as an in‐situ H2 source for the catalytic transfer hydrogenolysis (CTH) of DMT to p‐xylene (PX, ~63% at 240 °C and 16 h) on a reducible ZnZrOx supported Cu catalyst (i.e., Cu/ZnZrOx). Pre‐ and post‐reaction surface and bulk characterization, along with density functional theory (DFT) computations, explicate the dual role of the metal‐support interface of Cu/ZnZrOx in activating both CH3OH and DMT and facilitating a lower free‐energy pathway for both CH3OH dehydrogenation and DMT hydrogenolysis, compared to Cu supported on a redox‐neutral SiO2 support. Loading studies and thermodynamic calculations showed that, under reaction conditions, CH3OH in the gas phase, rather than in the liquid phase, is critical for CTH of DMT. Interestingly, the Cu/ZnZrOx catalyst was also effective for the methanolysis and hydrogenolysis of C‐C bonds (compared to C‐O bonds for PET) of waste polycarbonate (PC), largely forming xylenol (~38%) and methyl isopropyl anisole (~42%) demonstrating the versatility of this approach toward valorizing a wide range of condensation polymers.

Tandem Methanolysis and Catalytic Transfer Hydrogenolysis of Polyethylene Terephthalate to p-Xylene Over Cu/ZnZrOx Catalysts.

We demonstrate a novel approach of utilizing methanol (CH3OH) in a dual role for (1) the methanolysis of polyethylene terephthalate (PET) to form dimethyl terephthalate (DMT) at near-quantitative yields (~97 %) and (2) serving as an in situ H2 source for the catalytic transfer hydrogenolysis (CTH) of DMT to p-xylene (PX, ~63 % at 240 °C and 16 h) on a reducible ZnZrOx supported Cu catalyst (i.e., Cu/ZnZrOx). Pre- and post-reaction surface and bulk characterization, along with density functional theory (DFT) computations, explicate the dual role of the metal-support interface of Cu/ZnZrOx in activating both CH3OH and DMT and facilitating a lower free-energy pathway for both CH3OH dehydrogenation and DMT hydrogenolysis, compared to Cu supported on a redox-neutral SiO2 support. Loading studies and thermodynamic calculations showed that, under reaction conditions, CH3OH in the gas phase, rather than in the liquid phase, is critical for CTH of DMT. Interestingly, the Cu/ZnZrOx catalyst was also effective for the methanolysis and hydrogenolysis of C-C bonds (compared to C-O bonds for PET) of waste polycarbonate (PC), largely forming xylenol (~38 %) and methyl isopropyl anisole (~42 %) demonstrating the versatility of this approach toward valorizing a wide range of condensation polymers.

Optimised structural, electronic, optical and mechanical properties of SrTiO3-xHx for photovoltaic applications: a DFT insight

Density Functional Theory (DFT) computations, by CASTEP code with GGA-PBE correlation functional, for SrTiO3-xHx have been carried out to compute elastic, mechanical, structural, electronic, and optical characteristics of SrTiO3-xHx perovskite hydride material at varied levels of replacements (x = 0, 0.3, 0.6, 0.9, 1.2, 1.5, 1.8, 2.1, 2.4, 2.7, and 3.0). With the doping of hydrogen, the structure changed from cubic to orthorhombic and then tetragonal. Elastic parameters and negative value of formation energies demonstrate the durability and formability of these materials. It is established that these compounds are brittle by examining the B/G ratio and Poisson ratio. A bandgap is increased from 1.791 eV to 2.441 eV as dopant concentration rises, changing the semiconductor's nature from indirect to direct. Additionally, a detailed explanation of the optical properties for photons in the energy spectrum of 0–10 eV was provided dielectric functions, refractive indices, extinction coefficients, and 0–50 eV were provided including reflectance, absorbance, and energy loss. By increasing hydrogen doping, the highest absorption peak in the visible region is observed for x = 2.1, which shows that SrTiO3-xHx perovskite hydride has revealed stronger potential for photovoltaic applications.

Unified Implementation of Relativistic Wave Function Methods: 4C-iCIPT2 as a Showcase.

In parallel to the unified construction of relativistic Hamiltonians based solely on physical arguments (J. Chem. Phys. 2024, 160, 084111), a unified implementation of relativistic wave function methods is achieved here via programming techniques (e.g., template metaprogramming and polymorphism in C++). That is, once the code for constructing the Hamiltonian matrix is made ready, all the rest can be generated automatically from existing templates used for the nonrelativistic counterparts. This is facilitated by decomposing a second-quantized relativistic Hamiltonian into diagrams that are topologically the same as those required for computing the basic coupling coefficients between spin-free configuration state functions (CSF). Moreover, both time reversal and binary double point group symmetries can readily be incorporated into molecular integrals and Hamiltonian matrix elements. The latter can first be evaluated in the space of (randomly selected) spin-dependent determinants and then transformed to that of spin-dependent CSFs, thanks to simple relations in between. As a showcase, we consider here the no-pair four-component relativistic iterative configuration interaction with selection and perturbation correction (4C-iCIPT2), which is a natural extension of the spin-free iCIPT2 (J. Chem. Theory Comput. 2021, 17, 949), and can provide near-exact numerical results within the manifold of positive energy states (PES), as demonstrated by numerical examples.