Calculation Of Ground State Energy Research Articles

Prediction of topological Dirac semimetal in Ca-based Zintl layered compounds CaM2X2 (M\u2009=\u2009Zn or Cd; X\u2009=\u2009N, P, As, Sb, or Bi)

Topological Dirac materials are attracting a lot of attention because they offer exotic physical phenomena. An exhaustive search coupled with first-principles calculations was implemented to investigate 10 Zintl compounds with a chemical formula of CaM2X2 (M = Zn or Cd, X = N, P, As, Sb, or Bi) under three crystal structures: CaAl2Si2-, ThCr2Si2-, and BaCu2S2-type crystal phases. All of the materials were found to energetically prefer the CaAl2Si2-type structure based on total ground state energy calculations. Symmetry-based indicators are used to evaluate their topological properties. Interestingly, we found that CaM2Bi2 (M = Zn or Cd) are topological crystalline insulators. Further calculations under the hybrid functional approach and analysis using k · p model reveal that they exhibit topological Dirac semimetal (TDSM) states, where the four-fold degenerate Dirac points are located along the high symmetry line in-between Г to A points. These findings are verified through Green's function surface state calculations under HSE06. Finally, phonon spectra calculations revealed that CaCd2Bi2 is thermodynamically stable. The Zintl phase of AM2X2 compounds have not been identified in any topological material databases, thus can be a new playground in the search for new topological materials.

First-Principles Calculations to Investigate the Mechanical Structure and Optical Properties of Lead Halide Perovskite CH3NH3PbI3

We report the study of the mechanical structure and optical properties of lead halide perovskite CH3NH3PbI3 using ab initio methods. The ground state energy calculations were performed within density functional theory and generalized gradient approximation using the pseudopotential method with plane-wave basis sets. The norm conserving pseudopotential was used. The ground state properties of the electronic structure of the perovskite were used and elastic parameters such as bulk modulus B, Young’s modulus E, shear modulus G, and Poisson’s ratio υ were determined and found to be in good agreement with experimental values. The ratio B / G obtained was found to be greater than 1.75. Poisson’s ratio ( υ ) was obtained as 0.25 implying that CH3NH3PbI3 is a ductile material. The absorption coefficient within the energy range of 0 to 6 eV was found to be 5.76 × 105 cm−1 indicating maximum absorption. The absorption coefficient compares well with the available experimental and computed values.

Calculation of Ground State and Hartree Energies of Mos2/Wse2 Assembled Type Ii Quantum Well

Calculation of Ground State and Hartree Energies of Mos2/Wse2 Assembled Type Ii Quantum Well

Ab initio study of the phase stability of modulated structures in Co-doped Ni-Mn-In (Sn) Heusler alloys

Using ab initio calculations, the phase stability of modulated and tetragonal martensitic structures in Ni43.75Co6.25Mn43.75(In, Sn)6.25 Heusler alloys with different magnetic order is investigated. The stability against the segregation is considered by a method for generating all possible decay reactions assuming the calculated ground state energies of each composition. It is shown that the highest probable stability under equilibrium conditions is demonstrated by alloys with tetragonal martensitic structure in accordance with reactions: Ni35Co5Mn35In5 → 25Mn + 35Ni + 5Mn2InCo and Ni35Co5Mn35Sn5 → 5CoSn + 35Mn + 35Ni.

DFT and TD-DFT Calculations of Orbital Energies and Photovoltaic Properties of Small Molecule Donor and Acceptor Materials Used in Organic Solar Cells

DFT and TD-DFT calculations of HOMO and LUMO energies and photovoltaic properties are carried out on four selected pentathiophene donor and one IDIC-4F acceptor molecules using B3LYP and PBE0 functionals for the ground state energy calculations and CAM-B3LYP functional for the excited state calculations. The discrepancy between the calculated and experimental energies is reduced by correlating them with a linear fit. The fitted energies of HOMO and LUMO are used to calculate the Voc of an OSC based on these donors and acceptor blend and compared with experimental values. Using the Scharber model the calculated PCE of the donor-acceptor molecules agree with the experiment. It has been found that fluorine substitution can be used to improve charge transport by reducing the electron and hole reorganization energies of the molecules. It is also found that the introduction of fluorine onto the donor pentathiophene unit of the donor molecule results in a change of polarity of the distributed charges in the molecule due to the high electronegativity of the fluorine atom. The quantum chemical potential (μ), chemical hardness (η) and electronegativity (χ), and electrostatic potential maps (EPMs) are also calculated to identify different charge distribution regions in all five molecules.

Cis boron hydrogen chains: Theoretical calculations

Ab initio quantum Hartree-Fock and Møller–Plesset approximations used to study cis boron hydrogen cis-(BH)n chains. The ground-state energies, binding energies, Mulliken population and the optimal geometrical configurations of cis-(BH)n are reported in terms of the chain size n. The calculated ground-state energies in terms of chain dimerization un showed two phases cis-transoid and Trans-cisoid. The energies of these two phases at MP2 fitted into the modified Su-Schrieffer-Heeger (SSH) model in order to determine the corresponding parameters. According to this model, the dimerization induces a band gap around 0.12 eV for cis-transoid phase and 0.11 eV for the trans-cisoid one.

Selfconsistent random phase approximation methods.

This Perspective reviews recent efforts toward selfconsistent calculations of ground-state energies within the random phase approximation (RPA) in the (generalized) Kohn-Sham (KS) density functional theory context. Since the RPA correlation energy explicitly depends on the non-interacting KS potential, an additional condition to determine the energy as a functional of the density is necessary. This observation leads to the concept of functional selfconsistency (FSC), which requires that the KS density equals the interacting density defined as the functional derivative of the ground-state energy with respect to the external potential. While all existing selfconsistent RPA schemes violate FSC, the recent generalized KS semicanonical projected RPA (GKS-spRPA) method takes a step toward satisfying it. This leads to systematic improvements in densities, binding energy curves, reference state stability, and molecular properties compared to non-selfconsistent RPA as well as optimized effective potential RPA. GKS-spRPA orbital energies accurately approximate valence and core ionization potentials, and even electron affinities of non-valence bound anions. The computational cost and performance of GKS-spRPA are compared to those of related selfconsistent schemes, including GW and orbital optimization methods, and limitations are discussed. Large differences between KS and interacting densities observed in the absence of FSC and the well-rounded performance of GKS-spRPA suggest that the KS potential as a density functional should be defined via the FSC condition for explicitly potential-dependent density functionals.

First-principles-based high-throughput computation for high entropy alloys with short range order

We extend the small set of ordered structures (SSOS) method to calculate several typical materials properties of high entropy alloys (HEAs) with short range order (SRO). Using both equimolar and non-equimolar quinary CoCuFeNiPd HEAs with SRO as an example, we calculate ground state energy, lattice constant, mass density and elastic moduli, and compare them with those obtained from the special quasi-random structure (SQS) method. The calculated properties are in good agreement with those obtained by SQS. Importantly, the computational cost of the SSOS method for achieving the same accuracy is only a small fraction of the computational cost of the SQS method. We further show that the application of machine learning methods can further reduce the computational cost of the SSOS method and maintain the same level of accuracy, making it especially suitable for high-throughput calculations of HEAs with SRO.

Multicomponent Unitary Coupled Cluster and Equation-of-Motion for Quantum Computation.

The variational quantum eigensolver (VQE) algorithm combined with the unitary coupled cluster (UCC) ansatz has been developed for the quantum computation of molecular energies and wave functions within the Born-Oppenheimer approximation. Herein, this approach is extended to multicomponent systems to enable the quantum mechanical treatment of more than one type of particle, such as electrons and positrons or electrons and nuclei, without invoking the Born-Oppenheimer approximation. Specifically, we introduce the multicomponent unitary coupled cluster (mcUCC) method combined with the VQE algorithm for the calculation of ground-state energies and wave functions as well as the multicomponent equation-of-motion (mcEOM) method for the calculation of excitation energies. These methods are developed within the nuclear-electronic orbital (NEO) framework and are formulated in the qubit basis to enable implementations on quantum computers. Moreover, these methods are used to calculate the ground-state energy and excitation energies of positronium hydride, where both electrons and the positron are treated quantum mechanically, as well as the H2 molecule, where both electrons and one proton are treated quantum mechanically. These applications validate the implementation and provide benchmark data for future calculations. The errors due to Trotterization of the mcUCC ansatz are also analyzed. This formalism, as well as the accompanying computer code, will serve as the basis for applications to more complex multicomponent systems, such as simulations of photoinduced nonadiabatic molecular processes, on both classical and quantum computers.

High-resolution time of flight neutron diffraction and magnetization studies of spin reorientation and polar transitions in SmCrO3

Rare-earth chromates have always been of interest due to temperature-induced magnetization reversal and spin-reorientation phase transitions (SRPTs). In orthochromates containing magnetic rare earths, the spin configuration is supposed to undergo a characteristic changeover across the SRPT followed by an independent ordering of rare-earth moments leading to polar order. However, due to the presence of nearly 14% of highly neutron-absorbing isotope $^{149}\mathrm{Sm}$ in natural Sm based compounds, correct magnetic structure determination of ${\mathrm{SmCrO}}_{3}$ through neutron diffraction measurements has been a challenge. In the present study we investigate the pre- and post-SRPT spin configurations in well characterized ${\mathrm{SmCrO}}_{3}$ through time of flight neutron diffraction measurements carried out in zero field at the high-resolution high-flux WISH beam line of ISIS, in the United Kingdom. Magnetization measurement shows a canted antiferromagnetic phase transition at ${T}_{N1}=192\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, giving rise to a weak ferromagnetism, which undergoes a SRPT at 37 K. Rietveld analysis of the neutron powder diffraction data shows that below ${T}_{N1}=192\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ the ${\mathrm{Cr}}^{3+}$ and ${\mathrm{Sm}}^{3+}$ moments order in a $P{b}^{\ensuremath{'}}{n}^{\ensuremath{'}}m$:${\mathrm{\ensuremath{\Gamma}}}_{4}$(${\mathbit{G}}_{\mathbit{x}},{A}_{y},{F}_{Z};{F}_{Z}^{R}$) spin configuration with their tiny ferromagnetic components ${F}_{Z}$ and $\phantom{\rule{0.28em}{0ex}}{F}_{Z}^{R},$ giving rise to weak ferromagnetism. Below 37 K the $P{b}^{\ensuremath{'}}{n}^{\ensuremath{'}}m$:${\mathrm{\ensuremath{\Gamma}}}_{4}$(${\mathbit{G}}_{\mathbit{x}},{A}_{y},{F}_{Z};{F}_{Z}^{R}$) configuration transforms to $Pb{n}^{\ensuremath{'}}{m}^{\ensuremath{'}}:{\mathrm{\ensuremath{\Gamma}}}_{2}$(${F}_{x},{C}_{y},{\mathbit{G}}_{\mathbit{Z}};{F}_{x}^{R},\phantom{\rule{0.16em}{0ex}}{\mathbit{C}}_{\mathbit{y}}^{\mathbit{R}}$) as a result of continuous rotation of ${\mathrm{Cr}}^{3+}$ moments, while approaching SRPT below ${T}_{N1}$. At still lower temperatures the $Pb{n}^{\ensuremath{'}}{m}^{\ensuremath{'}}:{\mathrm{\ensuremath{\Gamma}}}_{2}$(${F}_{x},{C}_{y},{\mathbit{G}}_{\mathbit{Z}};{F}_{x}^{R},\phantom{\rule{0.16em}{0ex}}{\mathbit{C}}_{\mathbit{y}}^{\mathbit{R}}$) phase transforms to polar phases, either the $P{2}_{1}^{\ensuremath{'}}{2}_{1}^{\ensuremath{'}}{2}_{1}:{\mathrm{\ensuremath{\Gamma}}}_{26}$(${C}_{x},{\mathbit{G}}_{\mathbit{y}},{F}_{z};{\mathbit{C}}_{\mathbit{x}}^{\mathbit{R}},\phantom{\rule{0.16em}{0ex}}{A}_{y}^{R},\phantom{\rule{0.16em}{0ex}}{F}_{z}^{R}$) or the $P{n}^{\ensuremath{'}}a{2}_{1}^{\ensuremath{'}}:{\mathrm{\ensuremath{\Gamma}}}_{27}$(${F}_{x},{C}_{y},{\mathbit{G}}_{\mathbit{z}};{F}_{x}^{R},\phantom{\rule{0.16em}{0ex}}{\mathbit{C}}_{\mathbit{y}}^{\mathbit{R}},{G}_{z}^{R}$) phase, as a result of independent antiferromagnetic ordering of ${\mathrm{Sm}}^{3+}$ moments at ${T}_{N2}l4\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ through ${\mathrm{Sm}}^{3+}\text{\ensuremath{-}}{\mathrm{Sm}}^{3+}$ direct interaction. Our result of the transformation of ${\mathrm{SmCrO}}_{3}$ from ${\mathrm{\ensuremath{\Gamma}}}_{4}$ to ${\mathrm{\ensuremath{\Gamma}}}_{2}$ below SRPT is in contradiction with the ${\mathrm{\ensuremath{\Gamma}}}_{1}$(${A}_{x},{\mathbit{G}}_{\mathbit{y}},{C}_{Z};{C}_{z}^{R}$) spin configuration as reported in Tripathi et al. [Phys. Rev. B 96, 174421 (2017)]. This issue has been independently settled through ground-state energy calculation using spin-dependent density functional theory confirming the ${\mathrm{\ensuremath{\Gamma}}}_{2}$ spin configuration to be of lower energy as compared to that of the ${\mathrm{\ensuremath{\Gamma}}}_{1}$. The role of magnetocrystalline anisotropy in the occurrence of SRPT has been discussed.

A simple variational quantum Monte Carlo-effective mass approach for excitons and trions in quantum dots

A computational model is presented to calculate the ground state energy of neutral and charged excitons confined in semiconductor quantum dots. The model is based on the variational Quantum Monte Carlo method and effective mass Hamiltonians. Through an iterative Newton–Raphson process, minimizing the local energy, and (optional) parallelization of random walkers, fast and accurate estimates of both confinement and Coulomb binding energies can be obtained in standard desktop computers. To illustrate the reach of the model, we provide Fortran programs and illustrative calculations for colloidal CdSe nanoplatelets with large lateral dimensions and dielectric confinement, where electronic correlations are strong. The results compare well with exact variational calculations and largely outperform configuration interaction calculations in computational efficiency. Program summaryProgram title: vqmc-emaCPC Library link to program files:https://doi.org/10.17632/dtpyc2pffg.1Licensing provisions: GPLv3Programming language: Fortran 90Nature of problem: Calculation of either exciton or trion ground state energy and wave function in a cuboidal semiconductor nanoplatelet. Hard wall quantum confinement coexists with dielectric confinement (self-energy and Coulomb polarization terms).Solution method: Variational quantum Monte Carlo with effective mass Hamiltonians, integrated into a Newton–Raphson solver. OMP parallelization library can be (optionally) linked.

Generalized small set of ordered structures method for the solid-solution phase of high-entropy alloys

We present a generalization of the small set of ordered structures (SSOS) method that is especially suitable for high-throughput density-functional theory (DFT) calculations of high-entropy alloys in solid-solution phase. Using equiatomic quinary high-entropy alloys with fcc lattice structure, we show that the solution of the existing SSOS method is not unique. In fact, there are six solutions each containing three special ordered structures (SOS) when the range of atomistic pair correlations is up to second-nearest neighbors (NN). We also demonstrate that the SSOS method can be extended to consider atomic pair correlations up to the third NN. In this case, there are 24 solutions each containing six SOS and a negative weight. By increasing the number of SOS to seven to get rid of the negative weight, we show that there are 444 solutions. We further propose an averaging scheme to deal with the nonuniqueness of the generalized SSOS method. The generalized SSOS method allows fast, accurate calculations of ground-state energies of equiatomic high-entropy alloys, thus ideally suitable for high-throughput DFT calculations.

First Principle Study of the Mechanical Properties and Phonon Dispersion of the Iron Pnictide Compound EuFe2As2.

We present results on the first principle study of the elastic constants and the phonon dispersion of EuFe2As2 at zero pressure. The ground-state energy calculations were performed within Density Functional Theory (DFT) and the generalized gradient approximation using the pseudopotential method with plane-wave basis sets. The projector augmented-wave (PAW) pseudopotentials were used in our calculation. The open source code QUANTUM ESPRESSSO was used with its pseudopotential database. The study on the elastic constants at zero pressure was a clear indication that the compound is mechanically stable, and the phonon dispersion study also indicated that the compound is dynamically stable. The elastic constants and mechanical properties also led to the conclusion that the compound is ductile and anisotropic.

Variational Model for Low-Dimensional Magnets

The method of nonlocal trial variation function for quantum one-dimensional systems is developed on an example of a spin-1/2 XXZ chain with an alternating magnetic field. A four-site trial wave function for a fermionic representation of the model is constructed. The results obtained using the model with the extended trial wave function show a considerable improvement of accuracy of the ground state energy calculation in the field of critical behavior in comparison with the solutions obtained earlier. The methods for calculating the experimentally observed spin correlation function are considered.

Hybrid Quantum-Classical Neural Network for Calculating Ground State Energies of Molecules.

We present a hybrid quantum-classical neural network that can be trained to perform electronic structure calculation and generate potential energy curves of simple molecules. The method is based on the combination of parameterized quantum circuits and measurements. With unsupervised training, the neural network can generate electronic potential energy curves based on training at certain bond lengths. To demonstrate the power of the proposed new method, we present the results of using the quantum-classical hybrid neural network to calculate ground state potential energy curves of simple molecules such as H, LiH, and BeH. The results are very accurate and the approach could potentially be used to generate complex molecular potential energy surfaces.

Ab-initio Calculations of the Structural, Electronic and Optical Properties of (Cdse)2 Clusters

The distinctive properties of cadmium selenide (CdSe) semiconductor situated it in a multitudinous number of applications. Although (CdSe)2 cluster has more than one isomer, the previous studies concentrated merely on one isomer. The goal of this study was to determine the various stable geometric structure isomers of (CdSe)2 clusters; also, structural, electronic, and optical properties of the stable isomers are investigated using density functional theory (DFT). First, geometry optimization calculations of the possible geometric isomers were carried out using the BroydenFletcher-Goldfarb-Shanno minimization (BFGS) algorithm. Total ground-state energy calculations showed that all the converged isomers have a high probability of existing in any experiment, relying on the implemented experimental technique. Twenty initial possible geometric structures were investigated, in which eleven isomers were converged. However, all of them are relaxed in the 2D planar geometry. The results showed that eleven possible stable isomers were disclosed, where the final structures of the converged isomers produced six different structures; three of them were not detected before. The rhombus structure was ascertained to be the most stable isomer followed by the trapezoidal structure of (CdSe)2. The isomers’ Cd-Se bond length are 2.50-2.74 A, and the average Cd-Se-Cd, Se-Cd-Se angles were 64.5o-123o and 56.3o-114.2o, respectively. Furthermore, the bond angles show that the selenium atom lone-pairs electrons are responsible for shifting the isomers’ structure from the linearity. The total ground-state energy differences were 0.00-1.82 eV. The calculated highest occupied molecular orbital (HOMO), and the lowest unoccupied molecular orbital (LUMO) gap of the isomers implied that the gap depends on the symmetrical geometry of the isomer. Furthermore, it was evident that the most stable isomers are accompanied with larger gaps. The HOMO-LUMO graphs demonstrated that HOMO orbitals were localized around the selenium atom, while LUMO orbitals were distributed around both cadmium and selenium atoms. The calculated absorption spectrum was unique for each isomer. The absorption edges for the isomers are ranging from 2.53 to 3.73 eV. The results show that the obtained absorption spectra peaks’ values (nm) are smaller compared to CdSe experimental results. (CdSe)2 clusters are very active that they straightforwardly react to produce larger clusters. Finally, the results of this study corroborate with previous computational studies.

Recurrent neural network wave functions

A core technology that has emerged from the artificial intelligence revolution is the recurrent neural network (RNN). Its unique sequence-based architecture provides a tractable likelihood estimate with stable training paradigms, a combination that has precipitated many spectacular advances in natural language processing and neural machine translation. This architecture also makes a good candidate for a variational wave function, where the RNN parameters are tuned to learn the approximate ground state of a quantum Hamiltonian. In this paper, we demonstrate the ability of RNNs to represent several many-body wave functions, optimizing the variational parameters using a stochastic approach. Among other attractive features of these variational wave functions, their autoregressive nature allows for the efficient calculation of physical estimators by providing independent samples. We demonstrate the effectiveness of RNN wave functions by calculating ground state energies, correlation functions, and entanglement entropies for several quantum spin models of interest to condensed matter physicists in one and two spatial dimensions.

A benchmark of Gutzwiller conjugate gradient minimization method in ground state energy calculations of dimers

We present numerical results of ground-state energies of 9 molecules in the well-established G2 molecule set given by the Gutzwiller conjugate gradient minimization (GCGM) method. The method, beyond the commonly used Gutzwiller approximation, was recently developed based on Gutzwiller variational wave functions. We find that compared to benchmark data given by full configuration interaction, GCGM total energies are reasonably well reproduced with the minimum basis set. To include the dynamical correlation beyond the minimal basis calculations, we adopt the local density approximation for the dynamical correlation energy Ec. By comparing the results with benchmark data given by experiments and large-basis configuration interaction, the GCGM total energies with Ec are in general better reproduced, but discrepancies are still observed for some dimers.

Ab Initio High-Pressure Study of Semiconductor-Metal Phase Transition of the Chalcogenide Compound KPSe6

We report the results of pressure-induced semiconductor-metal phase transition of the semiconducting chalcogenide compound KPSe6 under high pressure using the ab initio methods. The ground-state energy calculations were performed within density functional theory and the generalized gradient approximation using the pseudopotential method with plane-wave basis sets. The projector augmented-wave (PAW) pseudopotentials were used in our calculation. The optimized lattice parameters were found from total energy calculations as 13 Bohr, 1.6 Bohr, and 1.8 Bohr for cell dimensions one, two, and three, respectively, which are in good agreement with experimental calculations. At zero pressure, the material portrayed a semiconducting property with a direct bandgap of ≈1.7 eV. As we subjected the material to pressure, the band gap was observed to reduce until it disappeared. The phase transition from the semiconductor to metal was found to occur at ∼45 GPa, implying that the material underwent metallization as pressure was increased further.

The Energy Spectrum and Wave Functions of Electrons in Tunnel-Coupled Spherical InAs/GaAs Quantum Dots

Some results of the numerical calculation of the electron ground state energy and electron density in tunnel-coupled InAs/GaAs quantum dots composing a simple cubic superlattice are presented. The calculation is performed within the modified effective mass method taking into account the microscopic (atomic) structure of individual quantum dots without taking spin-orbit coupling and strain effects into account. The dependence of the electron binding energy on radius R of quantum dots is studied. The electron binding energy is demonstrated to be proportional to R3 in the region of R < 27 A.