Random Phase Approximation Method Research Articles

Enhancement of electron–phonon coupling due to increased magnetism and applied hydrostatic pressure in FeSe

Inspired by the parabolic trend of the superconducting transition temperature (Tc ) of bulk FeSe under hydrostatic pressure, we investigated the effect of magnetism and hydrostatic pressure on the electron–phonon coupling (EPC) in FeSe using density-functional perturbation theory. We found that both magnetism and hydrostatic pressure enhanced EPC. The enhancement of the EPC is mainly attributed to phonon softening and deformation potential induced by magnetism, rather than Fermi surface nesting. Furthermore, we investigated the effect of spin fluctuations on superconductivity by applying the random phase approximation method. A possible application of our results to the phase diagram of FeSe under hydrostatic pressure was discussed, and we demonstrated that when EPC and spin fluctuations are both considered, a parabolic superconducting Tc may be obtained, providing a plausible explanation for the phase of FeSe under hydrostatic pressure.

Effect of non-metal doping on the optoelectronic properties of ZrS2/ZrSe2 heterostructure under strain: a first-principles study.

In this paper, we systematically studied the effects of non-metallic element (B, C, N, O, F) doping and biaxial stretching on the photoelectric properties of ZrS2/ZrSe2 heterostructures by using the first-principles calculation method based on density functional theory. The results show that the p-type doping is realized by B, C, and N atom doping, and the n-type doping is realized by O and F atom doping. The doping of B and C atoms produces impurity energy levels in the band gap, which affects the conductivity of the heterostructure. The band gap of N and O atom-doped heterostructures increases under tensile strain, but it is still a direct band gap. The analysis of the optical properties of the heterostructures shows that the doping of non-metallic atoms can adjust the optical absorption rate and reflectivity of the heterostructures. Under the action of tensile strain, the optical properties of the doped heterostructures have changed significantly in the low-energy region. This article provides a theoretical basis for the future application of ZrS2/ZrSe2 heterostructures. This paper uses the first-principles calculation method based on density functional theory. The PBE exchange-correlation functional based on generalized gradient approximation (GGA) is selected for the specific calculation, and the crystal structure is geometrically optimized by the ultrasoft pseudopotential method. It is verified that when the cutoff energy of the ZrS2/ZrSe2 heterostructure is 500 eV, the K-point grid is selected to be 10 × 10 × 2 with the lowest energy, so the cutoff energy is selected to be 500 eV. The K-point grid is selected to be 10 × 10 × 2. The convergence limits for structural optimization are as follows: the maximum force between atoms is 0.01 eV/Å, the convergence threshold of the maximum energy change is set to 10-9 eV/atom, and the convergence threshold of the maximum displacement is 0.001 Å. In order to avoid the influence of atomic periodic motion between different atomic layers, a vacuum layer of 20 Å is added in the vertical direction. Considering the interaction of vdW between the interfaces, the DFT-D2 method is used to verify. The optical properties were calculated by the random phase approximation method, and the K-point grid was selected as 12 × 12 × 2.

Refractory and thermoelectric properties of stabilized Tricalcium aluminate allotrope: A first-principles calculation approach

Tricalcium aluminate (Ca3Al2O6) is an indispensable component of Portland cement due to its high strength and reactivity. This study investigates the equilibrium lattice structure as well as the electronic and refractory properties of a newly discovered allotrope of Ca3Al2O6 using density functional theory and random phase approximation methods. Using density functional perturbation theory, we investigate the phonon dispersion of the refined structure’s experimental stability. In addition, the lattice thermal conductivity and thermoelectric figure of merit are computed by solving the Boltzmann Transport Equation with the modified Debye Callaway model and the Relaxation time Approximation methods. The computed Figure of merit, determined by the carrier concentration, indicates a substantial enhancement of 40 to 100-fold, leading to a superior figure of merit of 0.25 and 0.6 when appropriately doped. As a result, we anticipate that stable allotropes of Ca3Al2O6 in the Pm3̄m phase will be useful as energy-harvesting, convective cooling and infrared radiation shield-based cement materials in the cement and concrete industries.

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).

Generalized perturbative singles corrections to the random phase approximation method: Impact on noncovalent interaction energies of closed- and open-shell dimers.

The post-Kohn-Sham (KS) random phase approximation (RPA) method may provide a poor description of interaction energies of weakly bonded molecules due to inherent density errors in approximate KS functionals. To overcome these errors, we develop a generalized formalism to incorporate perturbative singles (pS) corrections to the RPA method using orbital rotations as a perturbation parameter. The pS schemes differ in the choice of orbital-rotation gradient and Hessian. We propose a pS scheme termed RPA singles (RPAS)[Hartree-Fock (HF)] that uses the RPA orbital-rotation gradient and time-dependent HF Hessian. This correction reduces the errors in noncovalent interaction energies of closed- and open-shell dimers. For the open-shell dimers, the RPAS(HF) method leads to a consistent error reduction by 50% or more compared to the RPA method for the cases of hydrogen-bonding, metal-solvent, carbene-solvent, and dispersion interactions. We also find that the pS corrections are more important in error reduction compared to higher-order exchange corrections to the RPA method. Overall, for open shells, the RPAS(HF)-corrected RPA method provides chemical accuracy for noncovalent interactions and is more reliable than other perturbative schemes and dispersion-corrected density functional approximations, highlighting its importance as a reliable beyond-RPA correction.

Corrected density functional theory and the random phase approximation: Improved accuracy at little extra cost.

We recently introduced an efficient methodology to perform density-corrected Hartree-Fock density functional theory [DC(HF)-DFT] calculations and an extension to it we called "corrected" HF DFT [C(HF)-DFT] [Graf and Thom, J. Chem. Theory Comput. 19 5427-5438 (2023)]. In this work, we take a further step and combine C(HF)-DFT, augmented with a straightforward orbital energy correction, with the random phase approximation (RPA). We refer to the resulting methodology as corrected HF RPA [C(HF)-RPA]. We evaluate the proposed methodology across various RPA methods: direct RPA (dRPA), RPA with an approximate exchange kernel, and RPA with second-order screened exchange. C(HF)-dRPA demonstrates very promising performance; for RPA with exchange methods, on the other hand, we often find over-corrections.

RPA, an Accurate and Fast Method for the Computation of Static Nonlinear Optical Properties.

The accurate computation of static nonlinear optical properties (SNLOPs) in large polymers requires accounting for electronic correlation effects with a reasonable computational cost. The Random Phase Approximation (RPA) used in the adiabatic connection fluctuation theorem is known to be a reliable and cost-effective method to render electronic correlation effects when combined with density-fitting techniques and integration over imaginary frequencies. We explore the ability of the RPA energy expression to predict SNLOPs by evaluating RPA electronic energies in the presence of finite electric fields to obtain (using the finite difference method) static polarizabilities and hyperpolarizabilities. We show that the RPA based on hybrid functional self-consistent field calculations yields accurate SNLOPs as the best-tuned double-hybrid functionals developed today, with the additional advantage that the RPA avoids any system-specific adjustment.

Nuclear ground state correlations

The paper discusses ground state correlations (GSC) in nuclei, which are especially clearly manifested when using the formalism of quantum Green’s functions (FG) and Feynman diagrams. In addition to one-particleone-hole GSC, which appear in the well known random phase approximation method (RPA), there exist and give a noticeable quantitative contribution THE GSCs resulting from the use of configurations that are more complex than in RPA. Namely, configurations containing phonons and configurations containing only three quasiparticles, respectively, the GSC-phon and GSC3. This last case of GSC3 is considered in detail in the present paper. It is shown that GSC3 make a significant quantitative contribution IN THE problems related to the explanation of some characteristics of low-lying excited states (phonons) and transitions between them in even-even nuclei.

Uncertainty quantification for neutrino opacities in core-collapse supernovae and neutron star mergers

We perform an extensive study of the correlations between the neutrino-nucleon inverse mean free paths (IMFPs) and the underlying equation of states (EoSs). Strong interaction uncertainties in the neutrino mean free path are investigated in different density regimes. The nucleon effective mass, the nucleon chemical potentials, and the residual interactions in the medium play an important role in determining neutrino-nucleon interactions in a density-dependent manner. We study how the above quantities are constrained by an EoS consistent with (i) nuclear mass measurements, (ii) proton-proton scattering phase shifts, and (iii) neutron star observations. We then study the uncertainties of both the charged current and the neutral current neutrino-nucleon inverse mean free paths due to the variation of these quantities, using Hartree-Fock+random phase approximation method. Finally, we calculate the Pearson correlation coefficients between (i) the EoS-based quantities and the EoS-based quantities; (ii) the EoS-based quantities and the IMFPs; (iii) the IMFPs and the IMFPs. We find a strong impact of residual interactions on neutrino opacity in the spin and spin-isospin channels, which are not well constrained by current nuclear modelings.

Geometries and vibrational frequencies with Kohn-Sham methods using σ-functionals for the correlation energy.

Recently, Kohn-Sham (KS) methods with new correlation functionals, called σ-functionals, have been introduced. Technically, σ-functionals are closely related to the well-known random phase approximation (RPA); formally, σ-functionals are rooted in perturbation theory along the adiabatic connection. If employed in a post-self-consistent field manner in a Gaussian basis set framework, then, σ-functional methods are computationally very efficient. Moreover, for main group chemistry, σ-functionals are highly accurate and can compete with high-level wave-function methods. For reaction and transition state energies, e.g., chemical accuracy of 1 kcal/mol is reached. Here, we show how to calculate first derivatives of the total energy with respect to nuclear coordinates for methods using σ-functionals and then carry out geometry optimizations for test sets of main group molecules, transition metal compounds, and non-covalently bonded systems. For main group molecules, we additionally calculate vibrational frequencies. σ-Functional methods are found to yield very accurate geometries and vibrational frequencies for main group molecules superior not only to those from conventional KS methods but also to those from RPA methods. For geometries of transition metal compounds, not surprisingly, best geometries are found for RPA methods, while σ-functional methods yield somewhat less good results. This is attributed to the fact that in the optimization of σ-functionals, transition metal compounds could not be represented well due to the lack of reliable reference data. For non-covalently bonded systems, σ-functionals yield geometries of the same quality as the RPA or as conventional KS schemes combined with dispersion corrections.

0νββ decay to the first 2+ state with a two-nucleon mechanism for a L−R symmetric model

We develop the formalism for calculating the decay rate of neutrinoless double $\ensuremath{\beta}$ decay to the ${2}^{+}$ excited states within the L-R symmetric model. We consider the effects from induced hadronic currents up to next to leading order. The quasiparticle random phase approximation method in a spherical basis is adopted for the nuclear many-body calculation and the corresponding nuclear matrix elements are given. Also, the phase space factors are obtained with numerical electron wave functions. Our results suggest that the nuclear matrix elements are nucleus dependent and they are generally smaller than that of the decay to the ground states. And finally, we give a naive analysis of how current experiment data constrains the L-R symmetric model.

Dipole responses in γ−soft 124–134Xe in the spectroscopic energy region

This study aimed to systematically investigate the low-lying dipole states of even–even 124–134Xe isotopes using the quasiparticle random phase approximation method. Where in all the studied xenon isotopes, electric and magnetic dipole responses were clearly predicted. The calculations predict mainly a scissors mode, while the strength of weakly deformed 132, 134Xe was small compared to moderately deformed 124–130Xe isotopes, where electric dipole excitations make their own contributions as well. The obtained results are consistent with the available experimental data. Since it was not possible to experimentally determine the parity of dipole states here through a comparison of our results with the experiment, we investigated the role of electric and magnetic dipole excitations in forming the spectrum. After comparing the obtained results with the experimentally derived ones, the natures of several observed spin- and parity-unknown excitations were determined.

Study of the Nuclear Structure for Some Nuclei Using Self-Consistent RPA Calculations with Skyrme-Type Interaction

In the present research, some static and dynamic nuclear properties of the closed-shell nuclei; 58Ni, 90Zr, 116Sn, and 144Sm nuclei have been studied using the Random Phase Approximation (RPA) method framework and different Skyrme parameterizations, particularly SyO-, Sk255, SyO+, SLy4, BSk17, and SLy5. In particular, in studies of static properties such as nuclear densities for neutrons, protons, mass, and charge densities with their corresponding rms radii, the single-particle nuclear density distributions All the obtained results agreed well with the relevant experimental data. Concerning the dynamic properties, the excitation energy, transition density, and giant resonance modes for the excitation to the low-lying negative partite excited states 1–, 3–, 5–, and 7– have also been studied. The findings indicate that estimates of RPA with Skyrme-type interactions are a good way to describe the properties of the structure of even-even, closed-shell nuclei.

Modeling Nonresonant X-ray Emission of Second- and Third-Period Elements without Core-Hole Reference States and Empirical Parameters.

Nonresonant X-ray emission (XE) energies and oscillator strengths are obtained using the effective potential of the generalized Kohn-Sham semi-canonical projected random phase approximation (GKS-spRPA) method. XE energies are estimated as a difference between the valence and core ionization eigenvalues, while the oscillator strengths are obtained within a frozen orbital approximation. This straightforward approach provides accurate XE energies without any need for core-hole reference states, empirical shifting parameters, or tuning of density functionals. To account for relativistic corrections to the core orbitals, we have formulated a scalar relativistic (sr) GKS-spRPA approach based on the spin-free X2C one-electron Hamiltonian. The sr-GKS-spRPA method provides highly reliable XE energies using uncontracted basis-sets on atoms where the core-hole is created prior to emission. For the largest basis-sets used in our study, using completely uncontracted polarized core-valence Dunning basis-sets, the mean absolute errors (MAEs) are within 0.7 eV compared to experimental reference values for a test-set consisting of 27 valence-to-core XE energies of molecules with second- and third-period elements. Considering a balance of accuracy and computational effort, we recommend the use of s-uncontracted def2-TZVP for second-period and all-uncontracted def2-TZVP for third-period elements. For this recommended basis-set, the MAE is 0.2 eV. The analytically continued sr-GKS-spRPA approach, with an computational cost, enables efficient computation of XE spectra of molecules such as S8 and C60 with several core-hole states.

Superconductivity, generalized random phase approximation and linear scaling methods

The superfluid weight is an important observable of superconducting materials since it is related to the London penetration depth of the Meissner effect. It can be computed from the change in the grand potential (or free energy) in response to twisted boundary conditions in a torus geometry. Here we review the Bardeen–Cooper–Schrieffer mean-field theory emphasizing its origin as a variational approximation for the grand potential. The variational parameters are the effective fields that enter in the mean-field Hamiltonian, namely the Hartree–Fock potential and the pairing potential. The superfluid weight is usually computed by ignoring the dependence of the effective fields on the twisted boundary conditions. However, it has been pointed out in recent works that this can lead to unphysical results, particularly in the case of lattice models with flat bands. As a first result, we show that taking into account the dependence of the effective fields on the twisted boundary conditions leads in fact to the generalized random phase approximation. Our second result is providing the mean-field grand potential as an explicit function of the one-particle density matrix. This allows us to derive the expression for the superfluid weight within the generalized random phase approximation in a transparent manner. Moreover, reformulating mean-field theory as a well-posed minimization problem in terms of the one-particle density matrix is a first step towards the application to superconducting systems of the linear scaling methods developed in the context of electronic structure theory.

Static polarizabilities within the generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA).

An analytical implementation of static dipole polarizabilities within the generalized Kohn-Sham semicanonical projected random phase approximation (GKS-spRPA) method for spin-restricted closed-shell and spin-unrestricted open-shell references is presented. General second-order analytical derivatives of the GKS-spRPA energy functional are derived using a Lagrangian approach. By resolution-of-the-identity and complex frequency integration methods, an asymptotic O(N4⁡log(N)) scaling of operation count and O(N3) scaling of storage is realized, i.e., the computational requirements are comparable to those for GKS-spRPA ground state energies. GKS-spRPA polarizabilities are assessed for small molecules, conjugated long-chain hydrocarbons, metallocenes, and metal clusters, by comparison against Hartree-Fock (HF), semilocal density functional approximations (DFAs), second-order Møller-Plesset perturbation theory, range-separated hybrids, and experimental data. For conjugated polydiacetylene and polybutatriene oligomers, GKS-spRPA effectively addresses the "overpolarization" problem of semilocal DFAs and the somewhat erratic behavior of post-PBE RPA polarizabilities without empirical adjustments. The ensemble averaged GKS-spRPA polarizabilities of sodium clusters (Nan for n = 2, 3, …, 10) exhibit a mean absolute deviation comparable to PBE with significantly fewer outliers than HF. In conclusion, analytical second-order derivatives of GKS-spRPA energies provide a computationally viable and consistent approach to molecular polarizabilities, including systems prohibitive for other methods due to their size and/or electronic structure.

Accurately Determining the Phase Transition Temperature of CsPbI3 via Random-Phase Approximation Calculations and Phase-Transferable Machine Learning Potentials

While metal halide perovskites (MHPs) have shown great potential for various optoelectronic applications, their widespread adoption in commercial photovoltaic cells or photosensors is currently restricted, given that MHPs such as CsPbI3 and FAPbI3 spontaneously transition to an optically inactive nonperovskite phase at ambient conditions. Herein, we put forward an accurate first-principles procedure to obtain fundamental insight into this phase stability conundrum. To this end, we computationally predict the Helmholtz free energy, composed of the electronic ground state energy and thermal corrections, as this is the fundamental quantity describing the phase stability in polymorphic materials. By adopting the random phase approximation method as a wave function-based method that intrinsically accounts for many-body electron correlation effects as a benchmark for the ground state energy, we validate the performance of different exchange-correlation functionals and dispersion methods. The thermal corrections, accessed through the vibrational density of states, are accessed through molecular dynamics simulations, using a phase-transferable machine learning potential to accurately account for the MHPs’ anharmonicity and mitigate size effects. The here proposed procedure is critically validated on CsPbI3, which is a challenging material as its phase stability changes slowly with varying temperature. We demonstrate that our procedure is essential to reproduce the experimental transition temperature, as choosing an inadequate functional can easily miss the transition temperature by more than 100 K. These results demonstrate that the here validated methodology is ideally suited to understand how factors such as strain engineering, surface functionalization, or compositional engineering could help to phase-stabilize MHPs for targeted applications.

Perturbation calculation of the uniform electron gas with a transcorrelated Hamiltonian.

With a transcorrelated Hamiltonian, we perform a many body perturbation calculation on the uniform electron gas in the high density regime. By using a correlation factor optimized for a single determinant Jastrow ansatz, the second order correlation energy is calculated as 1-ln⁡2π2ln(rs)-0.05075. This already reproduces the exact logarithmic term of the random phase approximation (RPA) result, while the constant term is roughly 7% larger than the RPA one. The close agreement with the RPA method demonstrates that the transcorrelated method offers a viable and potentially efficient method for treating metallic systems.

Multiplet effects in the electronic correlation of one-dimensional magnetic transition metal oxides on metals

We use the constrained random phase approximation (cRPA) method to calculate the Hubbard $U$ parameter in four one-dimensional magnetic transition metal atom oxides of composition XO$_2$ (X = Mn, Fe, Co, Ni) on Ir(100). In addition to the expected screening of the oxide, i.e., a significant reduction of the $U$ value by the presence of the metal substrate, we find a strong dependence on the electronic configuration (multiplet) of the X($d$) orbital. Each particular electronic configuration attained by atom X is dictated by the O ligands, as well as by the charge transfer and hybridization with the Ir(100) substrate. We find that MnO$_2$ and NiO$_2$ chains exhibit two different screening regimes, while the case of CoO$_2$ is somewhere in between. The electronic structure of the MnO$_2$ chain remains almost unchanged upon adsorption. Therefore, in this regime, the additional screening is predominantly generated by the electrons of the neighboring metal surface atoms. The screening strength for NiO$_2$/Ir(100) is found to depend on the Ni($d$) configuration in the adsorbed state. The case of FeO$_2$ shows an exceptional behavior, as it is the only insulating system in the absence of metallic substrate and, thus, it has the largest $U$ value. However, this value is significantly reduced by the two mentioned screening effects after adsorption.

Role of the quadrupole deformation in γ-soft nuclei: The case of 124−134Xe

Observation of the scissors mode in the γ-soft and transition nuclei provides the reasoning for investigating the possibility of quadrupole deformation in such nuclei. Using a deformed-based model for an investigation of the scissors mode, the goal of this work was to analyze the effects associated with quadrupole deformation for the so-called “γ-soft” nuclei in the example of even-even 124−134Xe isotopes. Here, the well-known properties of the scissors mode were investigated using just the quadrupole deformed-based rotational, invariant quasiparticle random phase approximation (QRPA) method. The properties of the scissors mode were clearly seen for all the investigated xenon isotopes, demonstrating that quadrupole deformed-based models can easily explain the nature of the low-lying M1 strength for γ-soft nuclei and indicating that quadrupole deformation plays a non-negligible role in the formation of the low-lying dipole strength for such nuclei.