Many-body Perturbation Calculations Research Articles

Optical spectra and exciton radiative lifetimes in bulk transition metal dichalcogenides.

The optical response of layered transition metal dichalcogenides (TMDCs) exhibits remarkable excitonic properties which are important from both fundamental and device application viewpoints. One of these phenomena is the observation of intralayer/interlayer excitons. While much effort has been done to characterize excitons in monolayer TMDCs and their heterostructures, a quite limited number of works have addressed the exciton spectra of their bulk counterparts. In this work, we employ ab initio many-body perturbation calculations to investigate the exciton dynamics and spectra of bulk 2H-MX2 (M = Mo, W, and X = S, Se). For molybdenum-based systems, we find the presence of interlayer excitons at energies higher than the first bright exciton (XA), with non-negligible strength intensity. Our results also show that interlayer excitons in tungsten-based systems are almost degenerate in energy with XA and possess very small oscillator strengths when compared with molybdenum-based systems. At room temperature, and considering the thermal exciton fine-structure population for the XA-exciton, we estimate effective radiative lifetimes in the range of ∼4-14 ns. For higher energy excitons we predict longer effective lifetimes of tens of nanoseconds.

Excitonic insulator to superconductor phase transition in ultra-compressed helium

Helium, the second most abundant element in the universe, exhibits an extremely large electronic band gap of about 20 eV at ambient pressures. While the metallization pressure of helium has been accurately determined, thus far little attention has been paid to the specific mechanisms driving the band-gap closure and electronic properties of this quantum crystal in the terapascal regime (1 TPa = 10 Mbar). Here, we employ density functional theory and many-body perturbation calculations to fill up this knowledge gap. It is found that prior to reaching metallicity helium becomes an excitonic insulator (EI), an exotic state of matter in which electrostatically bound electron-hole pairs may form spontaneously. Furthermore, we predict metallic helium to be a superconductor with a critical temperature of ≈ 20 K just above its metallization pressure and of ≈ 70 K at 100 TPa. These unforeseen phenomena may be critical for improving our fundamental understanding and modeling of celestial bodies.

Quasiparticle band structure of SrTiO3 and BaTiO3 : A combined LDA+U and G0W0 approach

We present the quasiparticle band structures of prototypical oxide perovskites ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{BaTiO}}_{3}$, two seemingly simple oxides for which accurate calculations of the electronic structure have been met with significant (and somewhat unexpected) challenges. Previous ${G}^{0}{W}^{0}$ calculations predicted a band gap ranging from 3.36 to 3.82 eV for ${\mathrm{SrTiO}}_{3}$, with a majority of the studies giving a band gap around 3.7 $\ensuremath{\sim}$ 3.8 eV, to be compared with the experimental value of 3.25 eV. A similar discrepancy between theory and experiment is also observed for ${\mathrm{BaTiO}}_{3}$. We show that the ${G}^{0}{W}^{0}$ approach can predict reasonably accurate band gaps of ${\mathrm{SrTiO}}_{3}$ and ${\mathrm{BaTiO}}_{3}$, provided that the calculations are carried out on top of the local density approximation (LDA) plus $U$ ($\mathrm{LDA}+U$) solutions and are fully converged. The deficiency of the LDA in describing the localized $3d$ states, although not particularly critical in this case, still results in a poor mean-field starting point for subsequent many-body perturbation calculations. ${G}^{0}{W}^{0}$ calculations starting from the $\mathrm{LDA}+U$ solutions, on the other hand, give significantly improved results for both systems. Our work demonstrates the accuracy and applicability of the combined ${G}^{0}{W}^{0}$ and $\mathrm{LDA}+U$ approach in calculating the quasiparticle band structures for materials involving localized $3d$ states, not only for systems with fully occupied $3d$ semicore states as has been shown before, but also for systems in which the $3d$ states are nominally unoccupied.

RESPACK: An ab initio tool for derivation of effective low-energy model of material

RESPACK is a first-principles calculation software for evaluating the interaction parameters of materials and is able to calculate maximally localized Wannier functions, response functions based on the random phase approximation and related optical properties, and frequency-dependent electronic interaction parameters. RESPACK receives its input data from a band-calculation code using norm-conserving pseudopotentials with plane-wave basis sets. Automatic generation scripts that convert the band-structure results to the RESPACK inputs are prepared for xTAPP and Quantum ESPRESSO. An input file for specifying the RESPACK calculation conditions is designed pursuing simplicity and is given in the Fortran namelist format. RESPACK supports hybrid parallelization using OpenMP and MPI and can treat large systems including a few hundred atoms in the calculation cell. Program summaryProgram Title: RESPACKCPC Library link to program files:https://dx.doi.org/10.17632/3cxb7474nj.1Developer’s repository link:https://sites.google.com/view/kazuma7k6rLicensing provisions: GNU General Public Licence v3.0Programming language:Fortran, PythonExternal routines:LAPACK, BLAS, MPINature of problem: Ab initio calculations for maximally localized Wannier function, response function with random-phase approximation, and matrix-element evaluations of frequency-dependent screened direct and exchange interactions. With this code, an effective low-energy model of materials is derived from first principles.Solution method: Our method is based on ab initio many-body perturbation calculation and the maximally localized Wannier function calculation. The program employs the plane-wave basis set, and evaluations of matrix elements are performed with the fast Fourier transformation. The generalized tetrahedron method is used for the Brillouin Zone integral.Additional comments including restrictions and unusual features: RESPACK supports xTAPP and Quantum ESPRESSO packages, and automatic generation scripts for converting the band-calculation results to the RESPACK inputs are prepared for these software. The current RESPACK only supports band-calculation codes using norm-conserving pseudopotentials with plane-wave basis sets. RESPACK supports hybrid parallelization using OpenMP and MPI to treat large systems in which a few hundred atoms are contained in unit cell.

Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling.

In the Monte Carlo many-body perturbation (MC-MP) method, the conventional correlation-correction formula, which is a long sum of products of low-dimensional integrals, is first recast into a short sum of high-dimensional integrals over electron-pair and imaginary-time coordinates. These high-dimensional integrals are then evaluated by the Monte Carlo method with random coordinates generated by the Metropolis-Hasting algorithm according to a suitable distribution. The latter algorithm, while advantageous in its ability to sample nearly any distribution, introduces autocorrelation in sampled coordinates, which, in turn, increases the statistical uncertainty of the integrals and thus the computational cost. It also involves wasteful rejected moves and an initial "burn-in" step as well as displays hysteresis. Here, an algorithm is proposed that directly produces a random sequence of electron-pair coordinates for the same distribution used in the MC-MP method, which is free from autocorrelation, rejected moves, a burn-in step, or hysteresis. This direct-sampling algorithm is shown to accelerate second- and third-order Monte Carlo many-body perturbation calculations by up to 222% and 38%, respectively.

Convergence acceleration of Monte Carlo many-body perturbation methods by using many control variates.

The use of many control variates is proposed as a method to accelerate the second- and third-order Monte Carlo (MC) many-body perturbation (MC-MP2 and MC-MP3) calculations. A control variate is an exactly integrable function that is strongly correlated or anti-correlated with the target function to be integrated by the MC method. Evaluating both integrals and their covariances in the same MC run, one can effect a mutual cancellation of the statistical uncertainties and biases in the MC integrations, thereby accelerating its convergence considerably. Six and thirty-six control variates, whose integrals are known a priori, are generated for MC-MP2 and MC-MP3, respectively, by systematically replacing one or more two-electron-integral vertices of certain configurations by zero-valued overlap-integral vertices in their Goldstone diagrams. The variances and covariances of these control variates are computed at a marginal cost, enhancing the overall efficiency of the MC-MP2 and MC-MP3 calculations by a factor of up to 14 and 20, respectively.

Pressure effect on structural stability and optical absorption of triclinic NbS3 from DFT and many-body perturbation calculations

In this paper, we investigated the structural stability, mechanical, vibrational, electronic, and optical properties; and the exciton binding energy of the quasi 1D transition metal trichalcogenide NbS3 under pressure. The structural properties are in good agreement with previous computational and experimental studies. Calculated elastic constants satisfy the Born stability criteria and suggest that NbS3 is mechanically stable against distortion under pressure up to 4.84 GPa. Vibrational properties via phonon calculations showed that NbS3 is dynamically stable when submitted to small atomic displacements. The results predict the maximum optical absorption coefficient of the bulk NbS3 at 5.13 × 105 cm−1 and it occurs in the visible range spectrum at 3.09 eV. From G0W0 and BSE calculations, we found that the size of the optical bandgap reduces from 1.01 to 0.48 eV as the pressure increases from 0 to 4 GPa. Our calculations also predicted the existence of bound excitons with binding energy ranges from 130 to 160 meV.

Perturbation calculations of nucleon–nucleon effective interactions in the Hartree–Fock basis

We prove that the Hartree–Fock (HF) basis provides good convergences for many-body perturbation calculations with renormalized realistic nuclear forces. Two types of ab initio perturbation calculations of effective interactions have been performed in the HF basis instead of the harmonic oscillator basis. One is called the Brillouin–Wigner (BW) perturbation and another is the Rayleigh–Schrödinger (RS) perturbation. The results show that ab initio perturbation calculations within the HF basis have comparably good convergences as the nonperturbative in-medium similarity renormalization group. In the HF basis some types of perturbation diagrams can be cancelled out, while the cancellation does not happen in the harmonic oscillator basis. We have investigated the sd shell with the chiral N3LO potential softened by . With the low-momentum N3LO potential, we first perform the spherical HF calculation for the 16O core, and use the perturbations to derive the sd-shelleffective two-body interactions in the HF basis. The calculations give simultaneously single-particle energies and excitation spectra of two-valence-particle systems (i.e. 18O, 18F, and 18Ne in the sd shell). Convergences have been analyzed order by order. We find that the HF RS perturbation gives even better results than the HF BW approximation. The HF effective interactions derived by the perturbations can be used for further many-body calculations.

Quasiparticle band structures of CuCl, CuBr, AgCl, and AgBr: The extreme case

We present a systematic study of the quasiparticle band structures of transition-metal halides CuCl, CuBr, AgCl, and AgBr. We show that GW calculations for cuprous halides are significantly more challenging computationally than ZnO, a much-discussed extreme case. The local-density approximation (LDA) within density functional theory severely underestimates the band gaps of CuCl and CuBr due to the inaccurate treatment of the semicore $d$ electrons. As a result, many-body perturbation calculations within the ${\mathrm{G}}^{0}{\mathrm{W}}^{0}$ approach fail to give accurate quasiparticle properties starting from the LDA mean-field solution. The $\mathrm{LDA}+U$ method (with the screened Coulomb and exchange parameters calculated using a constrained random-phase-approximation approach), on the other hand, provides a much better starting point for subsequent ${\mathrm{G}}^{0}{\mathrm{W}}^{0}$ calculations. When properly converged, the ${\mathrm{G}}^{0}{\mathrm{W}}^{0}/\mathrm{LDA}+U$ approach is able to reproduce the experimental minimum band gaps of all four compounds to within 0.1 eV. These results, however, can be achieved only by applying extremely high cutoff parameters, which would be very difficult without using our recently developed accelerated GW approach. Our work demonstrates the applicability and accuracy of the ${\mathrm{G}}^{0}{\mathrm{W}}^{0}/\mathrm{LDA}+U$ method in predicting the quasiparticle band structure of these materials and other systems involving localized semicore states.

Explicit correlation factors

We analyze the performance of 17 different correlation factors in explicitly correlated second-order many-body perturbation calculations for correlation energies. Highly performing correlation factors are found to have near-universal shape and size in the short range of electron-electron distance (0<r12<1.5a.u.). The long-range behavior (r12>1.5a.u.) is insignificant insofar as the factor becomes near constant, leaving an orbital expansion to describe decoupled electrons. An analysis based on a low-rank Taylor expansion of the correlation factor seems limited, except that a negative second derivative with the value of around −1.3a.u. correlates with high performance.

EXTENDED CALCULATIONS WITH SPECTROSCOPIC ACCURACY: ENERGY LEVELS AND TRANSITION PROPERTIES FOR THE FLUORINE-LIKE ISOELECTRONIC SEQUENCE WITH Z = 24–30

ABSTRACT We have performed extensive multiconfiguration Dirac–Hartree–Fock calculations and second-order many-body perturbation calculations for F-like ions with Z = 24–30. Energy levels and transition rates for electric dipole (E1), electric-quadrupole (E2), electric-octupole (E3), magnetic dipole (M1), and magnetic-quadrupole (M2) transitions, as well as radiative lifetimes, are provided for the lowest 200 levels belonging to the , , , , , and configurations of each ion. The results from the two sets of calculations are in excellent agreement. Extensive comparisons are also made with other theoretical results and observed data from the CHIANTI and NIST databases. The present energies and wavelengths are believed to be accurate enough to aid line identifications involving the n = 3 and n = 4 configurations, for which observations are largely missing. The calculated wavelengths and transition data will be useful in the modeling and diagnostics of astrophysical and fusion plasmas.

EXTENDED RELATIVISTIC CONFIGURATION INTERACTION AND MANY-BODY PERTURBATION CALCULATIONS OF SPECTROSCOPIC DATA FOR THE N ≤ 6 CONFIGURATIONS IN Ne-LIKE IONS BETWEEN Cr xv AND Kr xxvii

ABSTRACT Level energies, wavelengths, electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transition rates, oscillator strengths, and line strengths from combined relativistic configuration interaction and many-body perturbation calculations are reported for the 201 fine-structure states of the , , , , , , and configurations in all Ne-like ions between Cr xv and Kr xxvii. Calculated level energies and transition data are compared with experiments from the National Institute of Standards and Technology (NIST) and CHIANTI databases, and other recent benchmark calculations. The mean energy difference with the NIST experiments is only 0.05%. The present calculations significantly increase the amount of accurate spectroscopic data for the n &gt; 3 states in a number of Ne-like ions of astrophysical interest. A complete data set should be helpful for analyzing new observations from solar and other astrophysical sources, and is also likely to be useful for modeling and diagnosing a variety of plasmas, including astronomical and fusion plasma.

Spontaneous Charge Carrier Localization in Extended One-Dimensional Systems.

Charge carrier localization in extended atomic systems has been described previously as being driven by disorder, point defects, or distortions of the ionic lattice. Here we show for the first time by means of first-principles computations that charge carriers can spontaneously localize due to a purely electronic effect in otherwise perfectly ordered structures. Optimally tuned range-separated density functional theory and many-body perturbation calculations within the GW approximation reveal that in trans-polyacetylene and polythiophene the hole density localizes on a length scale of several nanometers. This is due to exchange-induced translational symmetry breaking of the charge density. Ionization potentials, optical absorption peaks, excitonic binding energies, and the optimally tuned range parameter itself all become independent of polymer length as it exceeds the critical localization length. Moreover, we find that lattice disorder and the formation of a polaron result from the charge localization in contrast to the traditional view that lattice distortions precede charge localization. Our results can explain experimental findings that polarons in conjugated polymers form instantaneously after exposure to ultrafast light pulses.

CALCULATIONS WITH SPECTROSCOPIC ACCURACY: ENERGIES AND TRANSITION RATES IN THE NITROGEN ISOELECTRONIC SEQUENCE FROM Ar XII TO Zn XXIV

ABSTRACT Combined relativistic configuration interaction and many-body perturbation calculations are performed for the 359 fine-structure levels of the 2s 2 2p 3, 2 s2p 4, 2p 5, 2s 2 2p 2 3l, 2 s2p 3 3l, 2p 4 3l, and 2s 2 2p 2 4l configurations in N-like ions from Ar xii to Zn xxiv. Complete and consistent data sets of energies, wavelengths, radiative rates, oscillator strengths, and line strengths for all possible electric dipole, magnetic dipole, electric quadrupole, and magnetic quadrupole transitions among the 359 levels are given for each ion. The present work significantly increases the amount of accurate data for ions in the nitrogen-like sequence, and the accuracy of the energy levels is high enough to enable the identification and interpretation of observed spectra involving the n = 3, 4 levels, for which experimental values are largely scarce. Meanwhile, the results should be of great help for modeling and diagnosing astrophysical and fusion plasmas.

Why Is MP2-Water "Cooler" and "Denser" than DFT-Water?

Density functional theory (DFT) with a dispersionless generalized gradient approximation (GGA) needs much higher temperature and pressure than the ambient conditions to maintain water in the liquid phase at the correct (1 g/cm(3)) density during first-principles simulations. Conversely, ab initio second-order many-body perturbation (MP2) calculations of liquid water require lower temperature and pressure than DFT/GGA to keep water liquid. Here we present a unifying explanation of these trends derived from classical water simulations using a polarizable force field with different sets of parameters. We show that the different temperatures and pressures between DFT/GGA and MP2 at which the simulated water displays the experimentally observed liquid structure under the ambient conditions can be largely explained by their differences in polarizability and dispersion interaction, respectively. In DFT/GGA, the polarizability and thus the induced dipole moments and the hydrogen-bond strength are all overestimated. This hinders the rotational motion of molecules and requires a higher temperature for DFT-water to be liquid. MP2 gives a stronger dispersion interaction and thus shorter intermolecular distances than dispersionless DFT/GGA, which is why MP2-water is denser than DFT-water under the same external pressure.

First-Principles Structural and Electronic Characterization of Ordered SiO2Nanowires

Density functional theory and molecular dynamics simulations have been used to optimize the structure of nanowires of SiO2. The starting structures were based on β-cristobalite, ortho-tridymite, β-tridymite, and rutile crystals. The analysis of the electronic structure has been validated by many-body perturbation calculations using the G0W0 and GW + Bethe-Salpeter equation approximations, to account for quasiparticle and excitonic effects. The calculations indicate that many of these nanowires have semiconducting character, while the corresponding bulk solids are insulators. In the case of thick rutilelike nanowires, we found the gap congested with surface states. Electronic charge is transferred from silicon atoms to oxygen atoms, and the bonding in the nanowires is partly ionic and partly covalent. The magnitude of the band gap can be engineered by changing the structure and the thickness of the nanowires.

Electronic structures and optical properties of TiO2: Improved density-functional-theory investigation

TiO2 has been recently used to realize high-temperature ferromagnetic semiconductors. In fact, it has been widely used for a long time as white pigment and sunscreen because of its whiteness, high refractive index, and excellent optical properties. However, its electronic structures and the related properties have not been satisfactorily understood. Here, we use Tran and Blaha's modified Becke-Johnson (TB-mBJ) exchange potential (plus a local density approximation correlation potential) within the density functional theory to investigate electronic structures and optical properties of rutile and anatase TiO2. Our comparative calculations show that the energy gaps obtained from mBJ method agree better with the experimental results than that obtained from local density approximation (LDA) and generalized gradient approximation (GGA), in contrast with substantially overestimated values from many-body perturbation (GW) calculations. As for optical dielectric functions (both real and imaginary parts), refractive index, and extinction coefficients as functions of photon energy, our mBJ calculated results are in excellent agreement with the experimental curves. Our further analysis reveals that these excellent improvements are achieved because mBJ potential describes accurately the energy levels of Ti 3d states. These results should be helpful to understand the high temperature ferromagnetism in doped TiO2. This approach can be used as a standard to understand electronic structures and the related properties of such materials as TiO2.

Relativistic multireference many-body perturbation theory for open-shell ions with multiple valence shell electrons: the transition rates and lifetimes of the excited levels in chlorinelike Fe X

A recently developed relativistic multireference many-body perturbation theory based on multireference configuration-interaction wavefunctions as zeroth-order wavefunctions is outlined. The perturbation theory employs a general class of configuration-interaction wavefunctions as reference functions, and thus is applicable to multiple open valence shell systems with near degeneracy of a manifold of strongly interacting configurations. Multireference many-body perturbation calculations are reported for the ground and excited states of chlorinelike Fe X in which the near degeneracy of a manifold of strongly interacting configurations mandates a multireference treatment. Term energies of a total of 83 excited levels arising from the 3s23p5, 3s3p6, 3s23p43d, 3s3p53d, and 3s23p33d2 configurations of the ion are evaluated to high accuracy. Transition rates associated with E1/M1/E2/M2/E3 radiative decays and lifetimes of a number of excited levels are calculated and compared with laboratory measurements to critically evaluate recent experiments.

Fast second-order many-body perturbation method for extended systems

An application of second-order many-body perturbation theory to energies and energy bands of polymers is often hindered by the steep polynomial dependence of its computational cost on the number of wave vector sampling points $(K)$ in the Brillouin zone (BZ). It is shown that a Hartree-Fock (HF) calculation with a large value of $K$ (120 in the first BZ) followed by a second-order many-body perturbation calculation with a much smaller value $(K=6)$ can lead to reliable, interpolated correlated energy bands and density of states of a polymer at less than 1% of the computational cost of the conventional approach. Quantitative simulations on photoelectron spectra of trans- and cis-polyacetylenes and polyethylene show that the correlated energy bands and densities of states thus obtained agree quantitatively with the observed and are significant (sometimes qualitative) improvements over the HF results. The energy bands and photoelectron spectra of polydiacetylene are predicted by this method to assist in the interpretation of future high-resolution measurements.

B-spline methods for radial Dirac equations

Although B-spline techniques have been used to solve two-point boundary value problems with Dirac Hamiltonians for more than 20 years, the treatment of boundary conditions is still a matter of controversy. Spurious, non-physical, solutions are endemic when boundary conditions are not handled correctly. These pathological problems are absent when traditional finite difference methods are used as in computer packages such as GRASP. Accurate approximation using both finite differences and B-splines depends on controlling local approximation errors, and this common property suggests no a priori reason to suppose that B-spline algorithms should be more prone to generate spurious solutions. The relativistic Bloch operators of [24], when added to the Dirac differential operator, permit the construction of a self-adjoint differential operator for the two-point boundary value problem on a finite interval. Approximate solution of this problem exploiting the properties of B-splines in variational or Galerkin schemes is then straightforward. Although the analysis is presented primarily in terms of the Dirac R-matrix method for electron–atom scattering, it is also relevant to other applications such as relativistic atomic and molecular structure calculations, many-body perturbation calculations of structure and properties and relativistic dynamics.