Random Phase Approximation Method Research Articles

Benchmarking doubles-corrected random-phase approximation methods for frequency dependent polarizabilities: Aromatic molecules calculated at the RPA, HRPA, RPA(D), HRPA(D), and SOPPA levels.

The performance of different polarization propagator methods, such as RPA, RPA(D), HRPA, HRPA(D), and SOPPA, have been tested against CC3 values for both static and dynamic polarizabilities. The test set consists of 14 (hetero-)aromatic medium-sized organic molecules, mostly with a high degree of symmetry. The benchmark of the methods remarkably reveals that RPA and HRPA(D) yield results comparable with the CC3 values and that they outperform SOPPA for these molecules. For a subset of the molecules, a comparison could be made to experimental values. The comparison for static polarizabilities proves that RPA and HRPA(D) as well as RPA(D) reproduce experimental values to a satisfying precision, whereas the SOPPA method compared to these three methods appears to perform only adequately. An investigation of the performance of Sadlej's polarized triple zeta basis set against Dunning's aug-cc-pVTZ basis set was also carried out. It is found that in contrast to other methods, Sadlej's basis set did not perform sufficiently compared to the larger aug-cc-pVTZ basis set for the RPA based methods.

Gamow-Teller excitations at finite temperature: Competition between pairing and temperature effects

The relativistic and nonrelativistic finite temperature proton-neutron quasiparticle random phase approximation (FT-PNQRPA) methods are developed to study the interplay of the pairing and temperature effects on the Gamow-Teller excitations in open-shell nuclei, as well as to explore the model dependence of the results by using two rather different frameworks for effective nuclear interactions. The Skyrme-type functional SkM* is employed in the nonrelativistic framework, while the density-dependent meson-exchange interaction DD-ME2 is implemented in the relativistic approach. Both the isoscalar and isovector pairing interactions are taken into account within the FT-PNQRPA. Model calculations show that below the critical temperatures the Gamow-Teller excitations display a sensitivity to both the finite temperature and pairing effects, and this demonstrates the necessity for implementing both in the theoretical framework. The established FT-PNQRPA opens perspectives for the future complete and consistent description of astrophysically relevant weak interaction processes in nuclei at finite temperature such as $\beta$-decays, electron capture, and neutrino-nucleus reactions.

Long-range behavior of a nonlocal correlation-energy density functional based on the random-phase approximation

We propose a density-based nonlocal correlation energy functional, corresponding to a revised form of the seamless van der Waals (vdW) density functional developed by Dobson and coauthors in the late nineties. The functional, termed as rDW99 in this work, has the same energy expression as the random phase approximation (RPA), but its key ingredient---the noninteracting density response function---is expressed entirely in terms of the electron density and density gradient. This is enabled by generalizing the Lindhard function from the homogeneous electron gas (HEG) to inhomogeneous electron systems. Compared to the original DW99 functional of Dobson and coauthors, we have introduced two revisions in rDW99: (1) A gap correction is incorporated into the generalized Lindhard function, making the functional more suitable for describing inhomogeneous, and in particular insulating, systems; (2) an approximate, yet fairly accurate, analytical form of the Lindhard function in real space is developed which facilitates the numerical evaluation of the rDW99 functional. In contrast with previously developed vdW density functionals, the nonlocal polarization effect is naturally captured in the rDW99 functional. The functional form, as it stands right now, is computationally still rather involving in a straightforward implementation. However, we anticipate that numerical techniques can be developed to significantly reduce the computational cost. As a first step, we assess the quality of rDW99 for describing the vdW interactions in the nonoverlapping asymptotic regime by computing the ${C}_{6}$ coefficients for a set of 43 atoms and molecules. With only one adjustable parameter, the mean absolute percentage error (MAPE) of the ${C}_{6}$ coefficients is estimated to be $8.7%$. In this work, ${C}_{6}$ coefficients corresponding to the standard RPA method are also computed for the same test set, and the MAPE for the RPA ${C}_{6}$ coefficients is estimated to be $13.2%$.

Quenching factor of Gamow-Teller and spin dipole giant resonances

Gamow-Teller (GT) and spin-dipole (SD) strength distributions of four doubly magic nuclei $^{48}$Ca, $^{90}$Zr, $^{132}$Sn and $^{208}$Pb are studied by the self-consistent Hartree-Fock plus random phase approximation (RPA) method. The Skyrme forces SAMi and SAMi-T without/with tensor interactions are adopted in our calculations. The calculated strengths are compared with available experimental data. The RPA results of GT and SD strengths of all four nuclei show fine agreement with observed GT and SD resonances in energy. A small GT peak below the main GT resonance is better described by the Skyrme interaction SAMi-T with the tensor terms. The quenching factors for GT and SD are extracted from the comparisons between RPA results and experimental strengths. It is pointed out that the quenching effect on experimental SD peaks is somewhat modest compared with that on GT peaks in the four nuclei.

Scattering and absorption characteristics of graphene coated metamaterial cylinder

Terahertz (THz) wave interaction from graphene coated metamaterial cylinder has been investigated analytically and numerically. The analytical formulation of electromagnetic fields is being modeled in the frame work of Mie theory while the modeling of the graphene is done by random phase approximation method. The causality principle based Kramer-Kroing relations are used to simulate the DNG metamaterial, while the DPS metamaterial is modeled by the Drude relations of SiO2. The analytical formulation is developed for both parallel and perpendicular polarized waves. The impedance boundary conditions (IBC) approach is used to model the infinitely thin graphene coating on metamaterial cylinder. Further the IBC at the interface of graphene layer and metamaterial cylinder are applied to compute the unknown scattering coefficients. The efficiency factors i.e., scattering efficiency (Qsca), extinction efficiency (Qexc) & absorption efficiency (Qabs) and bistatic radar cross section (RCS) have been computed analytically as well as numerically for both micro and nano cores. The influence of graphene parameters i.e., chemical potential (μc) & scattering rate (τ1) and size of metamaterial cylinder (R) on the scattering efficiency (Qsca) and extinction efficiency (Qexc) has been analyzed for DPS and DNG cores. It is observed that the in the nano regime, for perpendicularly polarized wave, graphene coated metamaterial cylinder supports the localized surface plasmon resonance (LSPR) modes and LSPR is found sensitive to the change in the graphene parameters and core size. However, it is reported that the parallel polarized wave has same response towards the DPS and DNG cores in the nano regime. It is concluded that under suitable parameters the graphene coating may provide extraordinary degree of freedom to actively control the THz interactions i.e., scattering efficiency, extinction efficiency and bistatic RCS. The present work may have potential applications in designing and manufacturing of Electromagnetic invisibility, cloaking and target protection devices for THz region.

Reducing the Many-Electron Self-Interaction Error in the Second-Order Screened Exchange Method.

Preserving the beneficial properties of the second-order screened exchange (SOSEX) method, such as its freedom from one-body self-correlation error, and its seamless treatment of long-range dispersion interaction, we construct new nonlocal functionals by down-scaling the higher-order terms in the SOSEX series to reduce the many-body self-correlation error in molecular systems. Our down-scaled SOSEX (dsSOSEX) and scaled equation SOSEX (seSOSEX) approaches deliver considerably more accurate noncovalent interaction energies, reaction energies, and barrier heights than the original SOSEX method. The dsSOSEX approach improves on the description of medium- and long-range correlation, for example, in isogyric processes, while the seSOSEX approach improves on the description of processes with short- and medium-range rearrangement in the electronic structure, such as atomization. The He2+ potential energy curve shows that the many-body self-correlation error is slightly smaller in the dsSOSEX method than in the seSOSEX approach. Furthermore, the H2 potential energy curve reveals that the static correlation error can also be reduced at medium range by the dsSOSEX and seSOSEX schemes. As our dsSOSEX method provides a better description of medium- and long-range correlation, it generally leads to more accurate energetics than the seSOSEX method; hence it should be preferred over the latter. We compare our results to other empirical and nonempirical direct random phase approximation (dRPA) and beyond-dRPA methods and also discuss the possibilities for further development.

Robust and accurate hybrid random-phase-approximation methods.

A fully self-consistent hybrid dRPA (direct random phase approximation) method, named sc-H[γ]dRPA, is presented with γ = 1/3. The exchange potential of the new method contains a fraction γ of nonlocal Hartree-Fock-like exchange besides the exact local Kohn-Sham (KS) exchange potential. The sc-H[γ]dRPA method, in contrast to a straightforward self-consistent dRPA method within the KS formalism, does not suffer from convergence problems for systems with small eigenvalue gaps. Moreover, the sc-H[γ]dRPA method yields distinctively more accurate reaction, isomerization, and transition state energies than other dRPA approaches, e.g., the frequently used non-self-consistent dRPA method using orbitals and eigenvalues from a KS calculation with the exchange-correlation potential of Perdew, Burke, and Ernzerhof (PBE). The sc-H[γ]dRPA method outperforms second-order Møller-Plesset perturbation theory and coupled cluster singles doubles methods while exhibiting a more favorable scaling of computational costs with system size. A value of γ = 1/3 is shown to be a good choice also for a dRPA@PBE[γ] method, which is a non-self-consistent dRPA method using orbitals and eigenvalues from the hybrid PBE0 method with an admixture of γ = 1/3 of exact exchange instead of the 25% of the PBE0 functional. The dRPA@PBE[γ] method yields reaction, isomerization, and transition state energies that are as good as the sc-H[γ]dRPA ones but is computationally simpler and more efficient because it does not require the self-consistent construction of the dRPA correlation potential. The direct sc-H[γ]dRPA, on the other hand, in contrast to all standard density-functional methods, yields qualitatively correct correlation potentials.

Noniterative Doubles Corrections to the Random Phase and Higher Random Phase Approximations: Singlet and Triplet Excitation Energies.

The second‐order noniterative doubles‐corrected random phase approximation (RPA) method has been extended to triplet excitation energies and the doubles‐corrected higher RPA method as well as a shifted version for calculating singlet and triplet excitation energies are presented here for the first time. A benchmark set consisting of 20 molecules with a total of 117 singlet and 71 triplet excited states has been used to test the performance of the new methods by comparison with previous results obtained with the second‐order polarization propagator approximation (SOPPA) and the third order approximate coupled cluster singles, doubles and triples model CC3. In general, the second‐order doubles corrections to RPA and HRPA significantly reduce both the mean deviation as well as the standard deviation of the errors compared to the CC3 results. The accuracy of the new methods approaches the accuracy of the SOPPA method while using only 10–60% of the calculation time. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

Isoscalar and isovector giant resonances in 92,94,96,98,100Mo and 90,92,94Zr

The response functions, S(E), and centroid energies, ECEN, of the isoscalar and isovector giant resonances of multipolarity L = 0–3 in 92,94,96,98,100Mo and 90,92,94Zr have been calculated employing the spherical Hartree-Fock (HF) based random phase approximation (RPA) method, using the Skyrme-type effective nucleon-nucleon interaction. In particular, we investigate the recent experimental results of the uncharacteristic behavior of ECEN for the isoscalar giant resonances, by extending our HF-based RPA calculations with only the KDE0v1 interaction to 32 additional Skyrme interactions. The main result of our investigation is that we find significant disagreements between the theoretical and the experimental values of ECEN for isoscalar giant monopole and dipole resonance of some nuclei. For the isoscalar giant octupole resonance we find the theoretical values of the ECEN to be well above the experimental results. We also study the sensitivity of ECEN to nuclear matter (NM) properties, including the effective mass, the incompressibility coefficient and the symmetry energy at saturation density, by determining the Pearson linear correlation coefficient between the calculated values of ECEN and the various nuclear matter properties of each Skyrme parametrization. For the isovector giant dipole resonance we find good agreement between the experimental and theoretical values of ECEN for Skyrme interactions with values of the enhancement coefficient of the energy weighted sum rule, κ, in the range between 0.25–0.70.

Low-Scaling Self-Consistent Minimization of a Density Matrix Based Random Phase Approximation Method in the Atomic Orbital Space.

An efficient minimization of the random phase approximation (RPA) energy with respect to the one-particle density matrix in the atomic orbital space is presented. The problem of imposing full self-consistency on functionals depending on the potential itself is bypassed by approximating the RPA Hamiltonian on the basis of the well-known Hartree-Fock Hamiltonian making our self-consistent RPA method completely parameter-free. It is shown that the new method not only outperforms post-Kohn-Sham RPA in describing noncovalent interactions but also gives accurate dipole moments demonstrating the high quality of the calculated densities. Furthermore, the main drawback of atomic orbital based methods, in increasing the prefactor as compared to their canonical counterparts, is overcome by introducing Cholesky decomposed projectors allowing the use of large basis sets. Exploiting the locality of atomic and/or Cholesky orbitals enables us to present a self-consistent RPA method which shows asymptotically quadratic scaling opening the door for calculations on large molecular systems.

Description of noncovalent interactions involving π-system with high precision: An assessment of RPA, MP2, and DFT-D methods.

Efficient approaches with high precision are essential for understanding the formation and stability of noncovalent interaction complexes. Here, 21 noncovalent interaction complexes involving π-system are selected and grouped in three subsets according to ETS-NOCV method: dispersion-dominated, electrostatic-dominated, and mixed. We mainly focus on examining the performance of random-phase approximation (RPA) on these π systems. The tested RPA-based method includes standard RPA and its variants including the related single excitations (SEs), renormalized single excitations (rSEs), second-order screened exchange (SOSEX), and the renormalized second-order perturbation theory (rPT2). The routine second-order Møller-Plesset perturbation theory (MP2) and three popular DFT-D functionals (M06-2X-D3, ωB97XD, and PBE-D3(BJ)) are also assessed for comparison. In this work, besides the calculation of interaction energies at Dunning-type aug-cc-pVDZ and aug-cc-pVTZ basis set, we also present a larger database of interaction energies calculated using MP2 and RPA methods with Dunning-type aug-cc-pVQZ basis set. An accurate CCSD(T)/CBS scheme is used to provide benchmark database. In addition to the high-level results, we also provide potential energy surfaces (PES) of different interaction type. Among all the tested methods, MP2 has a satisfactory performance on electrostatic-dominated and mixed-type systems, except for dispersion-dominated systems. DFT-D functionals, especially ωB97XD functional, has a balanced performance across all the tested systems. Importantly, for RPA-based methods, the calculation accuracy can be dramatically improved by taking into account SE or exchange effects, especially in the mixed complexes. We conclude that rPT2 among all the test RPA-based methods gives an overall satisfactory performance across different interaction types. © 2019 Wiley Periodicals, Inc.

Investigation of the rhodium-catalyzed hydroboration of NHC-boranes: the role of alkene coordination and the origin of enantioselectivity.

The mechanism of the intramolecular enantioselective rhodium(i)-catalyzed hydroboration of NHC-boranes is investigated by experimental reactivity measurements and molecular electronic structure calculations, within the framework of the Density Functional Theory and the Random Phase Approximation methods. The crucial role of alkene coordination and the origin of enantioselectivity are discussed. Two possible mechanisms are considered, via either prior hydride migratory insertion or boron migratory insertion. The minimum energy computed pathway leads to the enantiomer experimentally observed, therefore supporting the hydride migratory insertion mechanism. Calculations of the final steps of the catalytic cycle, i.e. regeneration of the catalyst and release of the product, give us further insights into the mechanism and rationalize the experimental results.

Describing transition metal homogeneous catalysis using the random phase approximation

The performance of the direct random phase approximation (RPA) method based on a Kohn–Sham reference for transition metal chemistry is studied by making comparison to (dispersion-corrected) density functional theory (DFT) and (spin-scaled) Moller–Plesset theory. The recently developed local-pair coupled-cluster method DLPNO-CCSD(T) is used as a benchmark. Emphasis is placed on the study of complete realistic mechanisms and reactions involving large systems. Electronic energies for the mechanism of C–H and C–C bond activation by rhodium fragments are presented as well as for ruthenium-catalyzed olefin metathesis. In addition, the WCCR10 test set, which comprises ten reactions, is revisited, and reaction energies for the reaction of a $$\mu $$ -chloride-bridged palladacyclic dimer with phosphane ligands are presented. RPA yields results that are on average within 2–3 kcal/mol of the theoretical benchmark with a maximum deviation of 5 kcal/mol. Of the methods studied, RPA behaves most systematically and is able to provide results of similar accuracy to dispersion-corrected functionals. RPA can thus serve as a complementary method to DFT to obtain insight into transition metal chemistry. Attention is paid to the basis set convergence behavior of RPA as well.

Single, Double Electronic Excitations and Exciton Effective Conjugation Lengths in π-Conjugated Systems.

The 21Ag and 11Bu excited states of two prototypical π-conjugated compounds, polyacetylene and polydiacetylene, are investigated with the recently developed particle-particle random phase approximation (pp-RPA) method combined with the B3LYP functional. The polymer-limit transition energies are estimated as 1.38 and 1.72 eV for the 21Ag and 11Bu states, respectively, from an extrapolation of the computed excitation energies of model oligomers. These values increase to 1.95 and 2.24 eV for the same transitions when ground-state structures with ∼33% larger bond length alternation are adopted. Applying the pp-RPA to the vertical excitation energies in oligodiacetylene, the polymer-limit transition energies of the 21Ag and 11Bu states are computed to be 2.06 and 2.28 eV, respectively. These results are in good agreement with experimental values or theoretical best estimates, indicating that the pp-RPA method shows great promise for understanding many photophysical phenomena involving both single and double excitations.

Giant Monopole Resonance and Nuclear Incompressibility of Hypernuclei**Supported by the National Natural Science Foundation of China under Grant Nos 11575060, 11775014, 11505058 and 11435014.

The isoscalar giant monopole resonances (ISGMRs) of hypernuclei , , and are investigated using a fully self-consistent Skyrme–Hartree–Fock plus random phase approximation method. The Skyrme-type forces, SGII, No.5 and SΛΛ1, are adopted to describe the nucleon–nucleon, Λ hyperon–nucleon and Λ hyperon–Λ hyperon (ΛΛ) interactions, respectively. For a given hyperon fraction, we find that effects of ΛΛ interaction on the properties of infinite symmetric nuclear matter and finite hypernuclei are very small. The ISGMR strengths are shifted to the high energy region when two Λ are added into normal nuclei. The changes are from two parts, one is due to the mean field calculations, and the other is from the residual interaction associated with Λ hyperons. The constrained energies are increased by about 0.5–0.7 MeV, which consequently enhances the effective incompressibility modulus of hypernuclei.

Accurate and Efficient Parallel Implementation of an Effective Linear-Scaling Direct Random Phase Approximation Method.

An efficient algorithm for calculating the random phase approximation (RPA) correlation energy is presented that is as accurate as the canonical molecular orbital resolution-of-the-identity RPA (RI-RPA) with the important advantage of an effective linear-scaling behavior (instead of quartic) for large systems due to a formulation in the local atomic orbital space. The high accuracy is achieved by utilizing optimized minimax integration schemes and the local Coulomb metric attenuated by the complementary error function for the RI approximation. The memory bottleneck of former atomic orbital (AO)-RI-RPA implementations ( Schurkus, H. F.; Ochsenfeld, C. J. Chem. Phys. 2016 , 144 , 031101 and Luenser, A.; Schurkus, H. F.; Ochsenfeld, C. J. Chem. Theory Comput. 2017 , 13 , 1647 - 1655 ) is addressed by precontraction of the large 3-center integral matrix with the Cholesky factors of the ground state density reducing the memory requirements of that matrix by a factor of [Formula: see text]. Furthermore, we present a parallel implementation of our method, which not only leads to faster RPA correlation energy calculations but also to a scalable decrease in memory requirements, opening the door for investigations of large molecules even on small- to medium-sized computing clusters. Although it is known that AO methods are highly efficient for extended systems, where sparsity allows for reaching the linear-scaling regime, we show that our work also extends the applicability when considering highly delocalized systems for which no linear scaling can be achieved. As an example, the interlayer distance of two covalent organic framework pore fragments (comprising 384 atoms in total) is analyzed.

Rocksalt or cesium chloride: Investigating the relative stability of the cesium halide structures with random phase approximation based methods

The ground state structural and energetic properties for rocksalt and cesium chloride phases of the cesium halides were explored using the random phase approximation (RPA) and beyond-RPA methods to benchmark the nonempirical SCAN meta-GGA and its empirical dispersion corrections. The importance of nonadditivity and higher-order multipole moments of dispersion in these systems is discussed. RPA generally predicts the equilibrium volume for these halides within 2.4% of the experimental value, while beyond-RPA methods utilizing the renormalized adiabatic LDA (rALDA) exchange-correlation kernel are typically within 1.8%. The zero-point vibrational energy is small and shows that the stability of these halides is purely due to electronic correlation effects. The rAPBE kernel as a correction to RPA overestimates the equilibrium volume and could not predict the correct phase ordering in the case of cesium chloride, while the rALDA kernel consistently predicted results in agreement with the experiment for all of the halides. However, due to its reasonable accuracy with lower computational cost, SCAN+rVV10 proved to be a good alternative to the RPA-like methods for describing the properties of these ionic solids.

Molybdenum disulfide and water interaction parameters.

Understanding the interaction between water and molybdenum disulfide (MoS2) is of crucial importance to investigate the physics of various applications involving MoS2 and water interfaces. An accurate force field is required to describe water and MoS2 interactions. In this work, water-MoS2 force field parameters are derived using the high-accuracy random phase approximation (RPA) method and validated by comparing to experiments. The parameters obtained from the RPA method result in water-MoS2 interface properties (solid-liquid work of adhesion) in good comparison to the experimental measurements. An accurate description of MoS2-water interaction will facilitate the study of MoS2 in applications such as DNA sequencing, sea water desalination, and power generation.

Pygmy and Giant Dipole Resonances in Proton-Rich Nuclei 17,18Ne**Supported by the National Natural Science Foundation of China under Grant Nos 11375022, 11575060, 11505058 and 11435014.

The pygmy and giant dipole resonances in proton-rich nuclei 17,18Ne are investigated with a fully self-consistent approach. The properties of ground states are calculated in the Skyrme Hartree–Fock with the Bardeen–Cooper–Schrieffer approximation to take into account the pairing correlation. The quasiparticle random phase approximation (QRPA) method is used to explore the properties of excited dipole states. In the calculations the SLy5 Skyrme interaction is employed. In addition to the giant dipole resonances, pygmy dipole resonances (PDR) are found to be located in the energy region below 10 MeV in both 17,18Ne. The strength and transition density show that the low-lying states are typical PDR states. However, analyzing the QRPA amplitudes of proton and neutron 2 quasiparticle (2qp) configurations for a given low-lying state in 17,18Ne, we find that the PDR state is less collective, more like a single 2qp excitation.

Robust d -wave pairing symmetry in multiorbital cobalt high-temperature superconductors

The pairing symmetry of the newly proposed cobalt high temperature (high-$T_c$) superconductors formed by vertex shared cation-anion tetrahedral complexes is studied by the methods of mean field, random phase approximation (RPA) and functional renormalization group (FRG) analysis. The results of all these methods show that the $d_{x^2-y^2}$ pairing symmetry is robustly favored near half filling. The RPA and FRG methods, which are valid in weak interaction regions, predict that the superconducting state is also strongly orbital selective, namely the $d_{x^2-y^2}$ orbital that has the largest density near half filling among the three $t_{2g}$ orbitals dominates superconducting pairing. These results suggest that the new materials, if synthesized, can provide indisputable test to high-$T_c$ pairing mechanism and the validity of different theoretical methods.