Random Phase Approximation Research Articles

Modeling of High-Harmonic Generation in the C60 Fullerene Using Ab Initio, DFT-Based, and Semiempirical Methods.

We report calculations of the high-harmonic generation spectra of the C60 fullerene molecule carried out by employing a diverse set of real-time time-dependent quantum chemical methods. All methodologies involve expanding the propagated electronic wave function in bases consisting of the ground and singly excited time-independent eigenstates obtained through the solution of the corresponding linear-response equations. We identify the correlation and exchange effect in the spectra by comparing the results from methods relying on the Hartree-Fock reference determinant with those obtained using approaches based on the density functional theory with different exchange-correlation functionals. The effect of the full random-phase approximation treatment of the excited electronic states is also analyzed and compared with the configuration interaction singles and the Tamm-Dancoff approximation. We also showcase the fact that the real-time extension of the semiempirical method INDO/S can be effectively applied for an approximate description of laser-driven dynamics in large systems.

Isoscalar giant quadrupole resonance of even-even 112-124Sn isotopes using BCS-QRPA

Using self-consistent Bardeen - Cooper - Schriffer + Hartree - Fock and quasiparticle random phase approximation, the isoscalar giant quadrupole resonance in the isotopes of 112,114,116,118,120,122,124Sn has been studied in this work. Five sets of Skyrme-type interactions of different values of the nuclear matter incompressibility coefficient KNM and effective mass m*/m are used in the calculations. Additionally, the impact of different types of pairing forces (i.e., volume, surface, and mixed) is examined. Comparisons are made between the computed strength distributions, centroid energies Ecen, scaled energies Es, and constrained energies Econ of the isoscalar giant quadrupole resonance and the available experimental data. Analysis is done on the relationships between KNM and m*/m, and the estimated properties.

Modulation Instability and Convergence of the Random-Phase Approximation for Stochastic Sea States

The nonlinear Schrödinger equation is widely used as an approximate model for the evolution in time of the water wave envelope. In the context of simulating ocean waves, initial conditions are typically generated from a measured power spectrum using the random-phase approximation, and periodized on an interval of length L. It is known that most realistic ocean waves power spectra do not exhibit modulation instability, but the most severe ones do; it is thus a natural question to ask whether the periodized random-phase approximation has the correct stability properties. In this work, we specify a random-phase approximation scaling, so that, in the limit of L→∞,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$L\\rightarrow \\infty ,$$\\end{document} the stability properties of the periodized problem are identical to those of the continuous power spectrum on the infinite line. Moreover, it is seen through concrete examples that using a too short computational domain can completely suppress the modulation instability.

Dynamic polarization, quantum spectral function and effective mass for black phosphorous: Random phase approximation approach at finite temperature

In this work, the finite-temperature dynamic polarization function of black phosphorus is obtained using the random phase approximation (RPA) for the lower band of the corresponding effective Hamiltonian. The maximum temperature-dependent polarization of the orthorhombic honeycomb structure of black phosphorus is observed at ω=0.54eV for wavectors at the Fermi level. Several peaks are thus observed indicating that an overall Fermi-liquid behavior is present but with different kinds of quasiparticles. These quasiparticles appear due to the highly anisotropic energy dispersion. Experiments conducted on black phosphorous at a temperature of 10 K have a tremendous effect on the scattering mechanism. Subsequently, the quasiparticle behavior is studied through the spectral function and the effective mass, each resolved on the three components of the wave number. The resulting effective mass anisotropy causes the plasmon to disperse completely, leading to a lower resonant frequency when there is a larger mass along one of the axes. At large wavelengths, the RPA result is almost identical to that obtained from the classical plasmon dispersion.

Correlated ion stopping in dense plasmas with a temperature‐dependent plasmon pole approximation

AbstractThe plasmon pole approximation used for the stopping function in a dense electron plasma is given a temperature‐dependent cutoff wavenumber via the ion projectile thermal wavelength. Excepted for projectile inter‐ion distance smaller than the target electron screening length and small ion fragment velocities, featuring a attosecond interaction time with a maximum correlated ion stopping (CIS) in inertial confinement fusion and warm dense matter (WDM), the given procedure is shown to yield back accurately the CIS estimated within the standard random phase approximation framework at any temperature, provided the ion fragment distribution is taken Gaussian.

Structural phase transition, s±-wave pairing, and magnetic stripe order in bilayered superconductor La3Ni2O7 under pressure

Motivated by the recently discovered high-Tc superconductor La3Ni2O7, we comprehensively study this system using density functional theory and random phase approximation calculations. At low pressures, the Amam phase is stable, containing the Y2− mode distortion from the Fmmm phase, while the Fmmm phase is unstable. Because of small differences in enthalpy and a considerable Y2− mode amplitude, the two phases may coexist in the range between 10.6 and 14 GPa, beyond which the Fmmm phase dominates. In addition, the magnetic stripe-type spin order with wavevector (π, 0) was stable at the intermediate region. Pairing is induced in the s±-wave channel due to partial nesting between the M = (π, π) centered pockets and portions of the Fermi surface centered at the X = (π, 0) and Y = (0, π) points. This resembles results for iron-based superconductors but has a fundamental difference with iron pnictides and selenides. Moreover, our present efforts also suggest La3Ni2O7 is qualitatively different from infinite-layer nickelates and cuprate superconductors.

Revisiting the Vashishta-Singwi dielectric scheme for the warm dense uniform electron fluid

The finite temperature version of the Vashishta-Singwi (VS) dielectric scheme for the paramagnetic warm dense uniform electron fluid is revisited correcting for an earlier thermodynamic derivative error. The VS scheme handles quantum mechanical effects at the level of the random phase approximation and treats correlations via the density expansion of a generalized Singwi-Tosi-Land-Sjölander (STLS) closure that inserts a parameter determined by enforcing the compressibility sum rule. Systematic comparison with quasiexact results, based on quantum Monte Carlo simulations, reveals a structural superiority of the VS scheme towards strong coupling and a thermodynamic superiority of the STLS scheme courtesy of a favorable cancellation of errors. Guidelines are provided for the construction of dielectric schemes that are expected to be more accurate but computationally costly. Published by the American Physical Society 2024

Ab-initio DFT＋[formula omitted] study on the electronic correlation in multiferroic XY-antiferromagnetic Ba2CoGe2O7

Ab-initio density functional theory (DFT)＋U has been used to study the spin-resolved electronic band structure and the partial density of states of the multiferroic XY-antiferromagnetic Ba2CoGe2O7. Using the constrained random-phase approximation (cRPA) method, the value of Hubbard U and Hund’s coupling JH has been determined and plugged into the further dynamical mean field theory (DMFT) calculations. The strong metal-ligand hybridization between Co-3d and O-2p orbitals in the CoO4 tetrahedron has been demonstrated via DFT and DFT＋DMFT calculations. The calculated indirect band gap in the antiferromagnetic state without and with U (=5 eV) correction is found to be 0.67 and 2.71 eV, respectively. The highest calculated ordered magnetic moment of 2.7 μB/Co2+ is close to the reported experimental value. The presented DFT calculations based on the different orbital models brings the underlying strong electronic correlation in the Ba2CoGe2O7.

Toward a new approach for the pygmy dipole resonance in even–even nuclei. Application to isotopes 144,148,150,152,154Sm

A many-body Hamiltonian consisting of a spherical shell model mean-field term, a pairing interaction for alike nucleons and a dipole–dipole interaction, with the dipole operator involving a cubic term in the radial coordinate, was studied within a quasiparticle random-phase approximation and applied numerically to five even–even isotopes of Sm. The resulting wavefunctions were further used to calculate the B(E1) values, which at their turn were employed to calculate the photoabsorption cross section, integrated moments of the cross section and energy weighted sum rule (EWSR). The calculated cross section and its integrated moments were compared with the available data, and a good agreement was observed. Two regions were distinguished: one corresponding to the pygmy dipole resonance (PDR) (1–10 MeV) and the other to the giant dipole resonance (GDR) (10–20 MeV), which were studied separately. The peaks belonging to each of the two ranges were analyzed in detail. The PDR states were located around the neutron separation energy and were mainly formed by the collective isoscalar and neutron collective states. The PDR states describe oscillations of the neutron excess against protons from the isospin-saturated core. The character of the states from the GDR region, isoscalar or isovector, is also pointed out. The PDR states carry only 0.8%–2.7% of the total EWSR and 0.4%–5.9% of the total E1 strength. The dependence of the dipole strength on nuclear deformation is evidenced. A comment on the cross section splitting into two branches for deformed isotopes is included. The r-cubic term and nuclear deformation have opposite effects on the dipole strength. In addition, it diminishes the effect of nonconservation of the center of mass momentum. The famous Thomas–Reiche–Kuhn sum rule formula is generalized to the case of the Schiff dipole momentum. The new sum rule is well satisfied. The projected spherical single-particle basis used in our formalism allows for a unified description of spherical transitional and deformed isotopes.

Application of relativistic continuum random phase approximation to giant dipole resonance of $$^{208}$$Pb and $$^{132}$$Sn

Application of relativistic continuum random phase approximation to giant dipole resonance of $$^{208}$$Pb and $$^{132}$$Sn

Basis Set Requirements of σ-Functionals for Gaussian- and Slater-Type Basis Functions and Comparison with Range-Separated Hybrid and Double Hybrid Functionals.

σ-Functionals belong to the class of Kohn-Sham (KS) correlation functionals based on the adiabatic-connection fluctuation-dissipation theorem and are technically closely related to the random phase approximation (RPA). They have the same computational demand as the latter, with the computational effort of an energy evaluation for both methods being lower than that of a preceding hybrid DFT calculation for typical systems but yield much higher accuracy, reaching chemical accuracy of 1 kcal/mol for quantities such as reactions and transition energies in main group chemistry. In previous work on σ-functionals, rather large Gaussian basis sets have been used. Here, we investigate the actual basis set requirements of σ-functionals and present three setups that employ smaller Gaussian basis sets ranging from quadruple-ζ (QZ) to triple-ζ (TZ) quality and represent a good compromise between accuracy and computational efficiency. Furthermore, we introduce an implementation of σ-functionals based on Slater-type basis sets and present two setups of QZ and TZ quality for this implementation. We test the accuracy of these setups on a large database of various physical properties and types of reactions, as well as equilibrium geometries and vibrational frequencies. As expected, the accuracy of σ-functional calculations becomes somewhat lower with a decreasing basis set size. However, for all setups considered here, calculations with σ-functionals are clearly more accurate than those within the RPA and even more so than those of the conventional KS methods. For the smallest setup using Gaussian-type basis functions and Slater-type basis functions, we introduce a reparametrization that reduces the loss in accuracy due to the basis set error to some extent. A comparison with the range-separated hybrid ωB97X-V and the double hybrid DSD-BLYP-D3 shows that σ functionals outperform in accuracy both of these accurate and, for their class, representative functionals.

Translational eigenstates of He@C60 from four-dimensional abinitio potential energy surfaces interpolated using Gaussian process regression.

We investigate the endofullerene system 3He@C60 with a four-dimensional potential energy surface (PES) to include the three He translational degrees of freedom and C60 cage radius. We compare second order Møller-Plesset perturbation theory (MP2), spin component scaled-MP2, scaled opposite spin-MP2, random phase approximation (RPA)@Perdew, Burke, and Ernzerhof (PBE), and corrected Hartree-Fock-RPA to calibrate and gain confidence in the choice of electronic structure method. Due to the high cost of these calculations, the PES is interpolated using Gaussian Process Regression (GPR), owing to its effectiveness with sparse training data. The PES is split into a two-dimensional radial surface, to which corrections are applied to achieve an overall four-dimensional surface. The nuclear Hamiltonian is diagonalized to generate the in-cage translational/vibrational eigenstates. The degeneracy of the three-dimensional harmonic oscillator energies with principal quantum number n is lifted due to the anharmonicity in the radial potential. The (2l + 1)-fold degeneracy of the angular momentum states is also weakly lifted, due to the angular dependence in the potential. We calculate the fundamental frequency to range between 96 and 110 cm-1 depending on the electronic structure method used. Error bars of the eigenstate energies were calculated from the GPR and are on the order of ∼±1.5 cm-1. Wavefunctions are also compared by considering their overlap and Hellinger distance to the one-dimensional empirical potential. As with the energies, the two abinitio methods MP2 and RPA@PBE show the best agreement. While MP2 has better agreement than RPA@PBE, due to its higher computational efficiency and comparable performance, we recommend RPA as an alternative electronic structure method of choice to MP2 for these systems.

Geometry-independent superfluid weight in multiorbital lattices from the generalized random phase approximation

The superfluid weight of a generic lattice model with attractive Hubbard interaction is computed analytically in the isolated band limit within the generalized random phase approximation. Time-reversal symmetry, spin rotational symmetry, and the uniform pairing condition are assumed. It is found that the relation obtained in Huhtinen [] between the superfluid weight in the flat band limit and the so-called minimal quantum metric is valid even at the level of the generalized random phase approximation. For an isolated, but not necessarily flat, band it is found that the correction to the superfluid weight obtained from the generalized random phase approximation Ds(1)=Ds,c(1)+Ds,g(1) is also the sum of a conventional contribution Ds,c(1) and a geometric contribution Ds,g(1), as in the case of the known mean-field result Ds(0)=Ds,c(0)+Ds,g(0), in which the geometric term Ds,g(0) is a weighted average of the quantum metric. The conventional contribution is geometry independent, that is, independent of the orbital positions, while it is possible to find a preferred, or natural, set of orbital positions such that Ds,g(1)=0. Useful analytic expressions are derived for both the natural orbital positions and the minimal quantum metric, including its extension to bands that are not necessarily flat. Finally, using some simple examples, it is argued that the natural orbital positions may lead to a more refined classification of the topological properties of the band structure. Published by the American Physical Society 2024

Re-Examination of the Effect of Pairing Gaps on Gamow–Teller Strength Distributions and β-Decay Rates

β-decay is one of the key factors for understanding the r-process and evolution of massive stars. The Gamow–Teller (GT) transitions drive the β-decay process. We employ the proton–neutron quasiparticle random phase approximation (pn-QRPA) model to calculate terrestrial and stellar β-decay rates for 50 top-ranked nuclei possessing astrophysical significance according to a recent survey. The model parameters of the pn-QRPA model affect the predicted results of β-decay. The current study investigates the effect of nucleon–nucleon pairing gaps on charge-changing transitions and the associated β decay rates. Three different values of pairing gaps, namely TF, 3TF, and 5TF, were used in our investigation. It was concluded that both GT strength distributions and half-lives are sensitive to pairing gap values. The 3TF pairing gap scheme, in our chosen nuclear model, resulted in the best prediction with around 80% of the calculated half-lives within a factor 10 of the measured ones. The 3TF pairing scheme also led to the calculation of the biggest β-decay rates in stellar matter.

Accurate Excitation Energies of Point Defects from Fast Particle-Particle Random Phase Approximation Calculations.

We present an efficient particle-particle random phase approximation (ppRPA) approach that predicts accurate excitation energies of point defects, including the nitrogen-vacancy (NV-) and silicon-vacancy (SiV0) centers in diamond and the divacancy center (VV0) in 4H silicon carbide, with errors of ±0.2 eV compared with experimental values. Starting from the (N + 2)-electron ground state calculated with density functional theory (DFT), the ppRPA excitation energies of the N-electron system are calculated as the differences between the two-electron removal energies of the (N + 2)-electron system. We demonstrate that the ppRPA excitation energies converge rapidly with a few hundred canonical active-space orbitals. We also show that active-space ppRPA has weak DFT starting-point dependence and is significantly cheaper than the corresponding ground-state DFT calculation. This work establishes ppRPA as an accurate and low-cost tool for investigating excited-state properties of point defects and opens up new opportunities for applications of ppRPA to periodic bulk materials.

Calculation of screened Coulomb interaction parameters for the charge-disproportionated insulator CaFeO3

We calculate the screened electron-electron interaction for the charge-disproportionated insulator CaFeO3 using the constrained random-phase approximation (cRPA). While in many correlated materials the formation of a Mott-insulating state is driven by a large local Coulomb repulsion, represented by the Hubbard U, several cases have been identified more recently in which U is strongly screened and instead the Hund's interaction J dominates the physics. Our results confirm a strong screening of the local Coulomb repulsion U in CaFeO3, whereas J is much less screened and can thus stabilize a charge-disproportionated insulating state. This is consistent with the case of the rare-earth nickelates, where similar behavior has been demonstrated. In addition, we validate some common assumptions used for parametrizing the local electron-electron interaction in first-principles calculations based on density-functional theory (DFT), we assess the dependence of the interaction on the choice of correlated orbitals, and we discuss the use of the calculated interaction parameters in DFT+U calculations of CaFeO3. Our work also highlights certain limitations for the direct use of cRPA results in DFT-based first-principles calculations, in particular for systems with strong entanglement between the correlated and uncorrelated bands. Published by the American Physical Society 2024

Theoretical investigation of atomic dynamics of molten metals at melting points

In molten metals, the atomic dynamics have been studied in the present study with the help of equations of motion in terms of the velocity autocorrelation function (VACF), power spectrum G ( ω ) , and mean square displacement r 2 ( t ) . The pair correlation function g ( r ) is used to produce VACF for molten metals in the current study with the help of three different types of structure factor methods i.e. hard sphere Yukawa (HSY) method, optimised random phase approximation (ORPA) method and charged hard sphere (CHS) method. The presently obtained results for molten metals of different groups like Na (Z = 1), Mg (Z = 2), Al (Z = 3), Sn (Z = 4), and Sb (Z = 5) are compared with the molecular dynamic (MD) study and also with the other theoretical data available in the literature. For the present study, our own developed pseudopotential has been used for the calculations of the above-mentioned properties. The screening effect is also been observed over and beyond the bare ion potential with Hartree (H) and the effects of exchanges and correlation were computed using procedures given by Taylor (T) and Nagy (N).

Confinement Effects in Droplet Formation on a Solid Particle.

Formation of a droplet around a spherical solid particle in supersaturated vapor is considered. The number and stability of equilibrium solutions in a closed small system are studied in the canonical ensemble in comparison to an open system in the grand canonical ensemble. Depending on the system's parameters, two modes exist in the canonical ensemble: the first one with only one solution and the second one with three solutions; the presence of the third solution is due to confinement. The analysis is conducted first on a macroscopic thermodynamic level of description, and then the results are supported by studies within two versions of classical density functional theory: the square-gradient approximation with the Carnahan-Starling equation of state for hard spheres on a completely wettable particle and the random-phase approximation with the fundamental measure theory on a poorly wettable particle. In the latter case, a solution breaking the spherical symmetry is observed at a small total number of molecules.

Machine Learning K-Means Clustering of Interpolative Separable Density Fitting Algorithm for Accurate and Efficient Cubic-Scaling Exact Exchange Plus Random Phase Approximation within Plane Waves.

The exact-exchange plus random-phase approximation (EXX+RPA) method has emerged as a crucial tool for precisely characterizing electronic structures in molecular and solid systems. We present an accurate and efficient implementation of EXX+RPA calculations that scale cubically and are conducted within plane waves. Our approach incorporates the interpolative separable density fitting (ISDF) algorithm, effectively mitigating the computational challenges associated with the plane wave basis set. To overcome the constraints of the conventional ISDF algorithm, characterized by the exceptionally high prefactor in QR factorization for interpolation point selection, we introduce an enhanced machine learning K-means method. This method incorporates a novel empirical weight function called "SSM+" for more precise interpolation point selection, capturing physical information more accurately across diverse systems. Our machine learning approach offers a quasiquadratic scaling alternative, effectively replacing the computationally demanding cubic-scaling QRCP algorithm in plane-wave-based EXX+RPA calculations. Furthermore, we enhance the method's capabilities by optimizing GPU acceleration using MATLAB's integrated GPU toolkit. In particular, our approach reduces the computational scaling of χ0 from 3.80 to 2.13 and the overall computational scaling of EXX from 2.74 to 2.10. We achieve a remarkable GPU acceleration speedup of up to 35×. Regarding CPU computation time, the standard quartic-scaling method requires 22 h to compute Si128, while QRCP completes the calculation in only around 1 h, achieving a speedup up to 20×. However, the utilization of the K-means algorithm reduces the time to 800 s, a substantial improvement of 100× compared to the standard algorithm. By employing the K-means algorithm, the computational time for interpolative point calculation using QRCP decreases from 1 h to 1 min, resulting in a 55× speed increase. With this improved algorithm, we successfully computed the dissociation curve of H2 and the equilibrium polyynic geometry of C18 molecules.

Rigorous Screened Interactions for Realistic Correlated Electron Systems.

We derive a widely applicable first-principles approach for determining two-body, static effective interactions for low-energy Hamiltonians with quantitative accuracy. The algebraic construction rigorously conserves all instantaneous two-point correlation functions in a chosen model space at the level of the random phase approximation, improving upon the traditional uncontrolled static approximations. Applied to screened interactions within a quantum embedding framework, we demonstrate these faithfully describe the relaxation of local subspaces via downfolding high-energy physics in molecular systems, as well as enabling a systematically improvable description of the long-range plasmonic contributions in extended graphene.