Random Phase Approximation Research Articles

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.

Linear Scaling Calculations of Excitation Energies with Active-Space Particle-Particle Random-Phase Approximation.

We developed an efficient active-space particle-particle random-phase approximation (ppRPA) approach to calculate accurate charge-neutral excitation energies of molecular systems. The active-space ppRPA approach constrains both indexes in particle and hole pairs in the ppRPA matrix, which only selects frontier orbitals with dominant contributions to low-lying excitation energies. It employs the truncation in both orbital indexes in the particle-particle and the hole-hole spaces. The resulting matrix, whose eigenvalues are excitation energies, has a dimension that is independent of the size of the systems. The computational effort for the excitation energy calculation, therefore, scales linearly with system size and is negligible compared with the ground-state calculation of the (N - 2)-electron system, where N is the electron number of the molecule. With the active space consisting of 30 occupied and 30 virtual orbitals, the active-space ppRPA approach predicts the excitation energies of valence, charge-transfer, Rydberg, double, and diradical excitations with the mean absolute errors (MAEs) smaller than 0.03 eV compared with the full-space ppRPA results. As a side product, we also applied the active-space ppRPA approach in the renormalized singles (RS) T-matrix approach. Combining the non-interacting pair approximation that approximates the contribution to the self-energy outside the active space, the active-space GRSTRS@PBE approach predicts accurate absolute and relative core-level binding energies with the MAEs around 1.58 and 0.3 eV, respectively. The developed linear scaling calculation of excitation energies is promising for applications to large and complex systems.

Microphase versus macrophase separation in the square-well-linear fluid: A theoretical and computational study.

Due to the presence of competing interactions, the square-well-linear fluid can exhibit either liquid-vapor equilibrium (macrophase separation) or clustering (microphase separation). Here we address the issue of determining the boundary between these two regimes, i.e., the Lifshitz point, expressed in terms of a relationship between the parameters of the model. To this aim, we carry out Monte Carlo simulations to compute the structure factor of the fluid, whose behavior at low wave vectors accurately captures the tendency of the fluid to form aggregates or, alternatively, to phase separate. Specifically, for a number of different combinations of attraction and repulsion ranges, we make the system go across the Lifshitz point by increasing the strength of the repulsion. We use simulation results to benchmark the performance of two theories of fluids, namely, the hypernetted chain (HNC) equationand the analytically solvable random phase approximation (RPA); in particular, the RPA theory is applied with two different prescriptions as for the direct correlation function inside the core. Overall, the HNC theory proves to be an appropriate tool to characterize the fluid structure and the low-wave-vector behavior of the structure factor is consistent with the threshold between microphase and macrophase separation established through simulation. The structural predictions of the RPA theory turn out to be less accurate, but this theory offers the advantage of providing an analytical expression of the Lifshitz point. Compared to simulation, both RPA schemes predict a Lifshitz point that falls within the macrophase-separation region of parameters: in the best case, barriers roughly twice higher than predicted are required to attain clustering conditions.

Diblock Copolymer Melt in an Electric Field: Stability of the Homogeneous State in the Random Phase Approximation

The contribution of I.Ya. Erukhimovich (1947–2022) to the creation of the theory of microphase separation in di- and triblock copolymers has been briefly analyzed. His matrix method of calculating correlation functions for multicomponent polymer systems has been applied to find the spinodal of a diblock copolymer melt in a static electric field. It has been strictly shown that for a linear dependence of local dielectric constant of the copolymer on the order parameter the spinodal condition remains the same as in the absence of the electric field. The correction to the critical value of the Flory‒Huggins parameter has been calculated for more general case of the quadratic dependence.

The structure of low-lying 1− states in 90,94Zr from (α,α′γ) and (p,p′γ) reactions

The low-lying dipole strength was investigated in 90,94 Zr via the (p,p′γ) reaction at 80 MeV and via the (α,α′γ) reaction at 130 MeV. These experiments were performed at the Research Center for Nuclear Physics (Osaka University) and made combined use of the high-resolution magnetic spectrometer Grand Raiden and the CAGRA HPGe gamma array. The comparison of our results with existing (γ,γ′) reaction data shows differences in the excitation patterns. In the present experimental conditions, in fact, both α and p probes are exciting the investigated 1− states mainly through the short-range nuclear force, expected to favour the population of surface excitations. Distorted Wave Born Approximation (DWBA) calculations were made using form factors built assuming specific transition densities, characterized by a strong neutron component at the nuclear surface and based on Random Phase Approximation (RPA). A combined analysis of the (α,α′γ) and (p,p′γ) data was performed to investigate the isoscalar character of the 1− states in 90,94Zr. Although an overall general consistency was obtained in the studied energy intervals, not all (p,p′γ) cross sections were well reproduced using the isoscalar strength deduced from (α,α′γ) data. This might suggest that the mixing of isoscalar and isovector components and the degree of collectivity are not the same for all the 1− states studied.

Fluctuations, structure, and size inside coacervates.

Aqueous solutions of oppositely charged macromolecules exhibit the ubiquitous phenomenon of coacervation. This subject is of considerable current interest due to numerous biotechnological applications of coacervates and the general premise of biomolecular condensates. Towards a theoretical foundation of structural features of coacervates, we present a field-theoretic treatment of coacervates formed by uniformly charged flexible polycations and polyanions in an electrolyte solution. We delineate different regimes of polymer concentration fluctuations and structural features of coacervates based on the concentrations of polycation and polyanion, salt concentration, and experimentally observable length scales. We present closed-form formulas for correlation length of polymer concentration fluctuations, scattering structure factor, and radius of gyration of a labelled polyelectrolyte chain inside a concentrated coacervate. Using random phase approximation suitable for concentrated polymer systems, we show that the inter-monomer electrostatic interaction is screened by interpenetration of all charged polymer chains and that the screening length depends on the individual concentrations of the polycation and the polyanion, as well as the salt concentration. Our calculations show that the scattering intensity decreases monotonically with scattering wave vector at higher salt concentrations, while it exhibits a peak at intermediate scattering wave vector at lower salt concentrations. Furthermore, we predict that the dependence of the radius of gyration of a labelled chain on its degree of polymerization generally obeys the Gaussian chain statistics. However, the chain is modestly swollen, the extent of which depending on polyelectrolyte composition, salt concentration, and the electrostatic features of the polycation and polyanion such as the degree of ionization.

Dual nature of low-energy isoscalar monopole and dipole states in light nuclei

Isoscalar monopole (IS0) and dipole (IS1) states located below and around the alpha-particle threshold Sα in prolate 24Mg are investigated within fully self-consistent Skyrme Quasiparticle Random-Phase Approximation (QRPA) approach. It is shown that these states demonstrate strong mean-field (MF) effects: dipole vorticity, deformation-induced monopole-quadrupole (IS0/IS2) and dipole-octupole (IS1/IS3) coupling. At the same time, the density distributions show precursors of a cluster structure. So we get a cluster/MF duality with a strong dominance of MF impact. IS0 QRPA results are compared with iThemba Lab and RCNP (α, α′) data.

Bulk plasmon-limited mobility in semiconductors: from bulk to nanowires

Analytical expressions are obtained for the low-field mobility in semiconductors for scattering of three-dimensional (3D), two-dimensional (2D), and one-dimensional (1D) charged carriers by bulk plasmons. The consideration is based on the quantum kinetic equation and model distribution function in form of a shifted Fermi distribution and includes calculations of the dielectric function of 3D, 2D and 1D carriers in the random phase approximation. The resulting analytical expressions give dependences of the plasmon limited mobility on the dimensionality of charge carrier system, their density, effective mass, temperature and confining dimensions. The plasmon limited mobility decreases as the dimensionality of the electron gas D decreases. The physical reason for this is an increase in the absolute value of the cutoff vector with a decrease in D. Comparison of our calculations with known experimental data shows that relative contribution of the electron–plasmon scattering to total mobility reaches a maximum in the temperature range 10–100 K and can be a few percent in bulk crystals, ten of percent in quantum wells, and is close to the experimental values in nanowires. A noticeable effect of the scattering 3D, 2D and 1D electrons by bulk plasmons on mobility is expected in semiconductors with a sufficiently high mobility of more than 105 cm2 V−1 s.

Silicene-2DEG heterostructures: Collective excitations investigations

This paper investigates collective excitations in a heterostructure consisting of a silicene sheet and a parallel GaAs quantum well by employing the random-phase approximation within exchange-correlation effects. We find that two plasmonic modes exist in the systems, corresponding to in-phase (optical) and out-of-phase (acoustical) oscillations of charged particles in two layers. Calculations show that interactions between electrons in two layers decrease the energy of both two plasmon modes, completely differing from other double-layer structures. The increase in inter-layer separation significantly decreases both optical and acoustical modes’ frequencies. We observe that taking into account local field correction and increasing quantum well width pronouncedly decrease acoustical mode frequency. However, the increase in the bandgap, caused by an external electric field, decreases only the frequency of the optical collective mode. Finally, as carrier density in quantum well decreases, the acoustical mode energy noticeably declines while that of the optical one seems extremely stable.

Low-Scaling Algorithm for the Random Phase Approximation Using Tensor Hypercontraction with k-point Sampling.

We present a low-scaling algorithm for the random phase approximation (RPA) with k-point sampling in the framework of tensor hypercontraction (THC) for electron repulsion integrals (ERIs). The THC factorization is obtained via a revised interpolative separable density fitting (ISDF) procedure with a momentum-dependent auxiliary basis for generic single-particle Bloch orbitals. Our formulation does not require preoptimized interpolating points or auxiliary bases, and the accuracy is systematically controlled by the number of interpolating points. The resulting RPA algorithm scales linearly with the number of k-points and cubically with the system size without any assumption on sparsity or locality of orbitals. The errors of ERIs and RPA energy show rapid convergence with respect to the size of the THC auxiliary basis, suggesting a promising and robust direction to construct efficient algorithms of higher order many-body perturbation theories for large-scale systems.

Particle-Particle Collective Excitations of Sn isotopes

In this paper, energy-level schemes and reduced electric transition strengths of neutron-rich Tin isotopes 102, 110, 116, 120, 122Sn (Z=50) are studied using collective models, that is, particle-particle Tamm-Dancoff Approximation and particle-particle Random Phase Approximation. According to these models, the excited states of closed-core A+2 systems with multipolarity J and isospin T can be described as a linear combination of particle-particle pairs. In our investigation, the low-lying states of the investigated isotopes 102, 110, 116, 120, 122Sn are described by acting two-particle operators on a correlated core 100Sn, 108Sn, 114Sn, 118Sn, and 120Sn, respectively. The Hamiltonian is diagonalized within the model space include {1g7/2, 2d5/2, 2d3/2, 3s1/2 and 1h11/2} orbits, using the matrix elements of neutron-neutron interaction and modified surface delta interaction. The calculated values are checked by using the resultant eigenvalues and eigenvectors to calculate the excitation energies and reduced electric transition strengths. Our calculated results are compared to the available experimental data, and these comparisons led to reasonable agreements. Effective charges are also used to account for the core polarization effect.

Complex Linear Response Functions for a Multiconfigurational Self-Consistent Field Wave Function in a High Performance Computing Environment.

We present novel developments for the highly efficient evaluation of complex linear response functions of a multiconfigurational self-consistent field (MCSCF) wave function as implemented in MultiPsi. Specifically, expressions for the direct evaluation of linear response properties at given frequencies using the complex polarization propagator (CPP) approach have been implemented, within both the Tamm-Dancoff approximation (TDA) and the random phase approximation (RPA). Purely real algebra with symmetric and antisymmetric trial vectors in a shared subspace is used wherein the linear response equations are solved. Two bottlenecks of large scale MC-CPP calculations, namely, the memory footprint and computational time, are addressed. The former is addressed by limiting the size of the subspace of trial vectors by using singular value decomposition (SVD) on either orbital or CI subspaces. The latter is addressed using an efficient parallel implementation as well as the strategy of dynamically adding linear response equations at near-convergence to neighboring roots. Furthermore, a novel methodology for decomposing MC-CPP spectra in terms of intuitive orbital excitations in an approximate fashion is presented. The performance of the code is illustrated with several numerical examples, including the X-ray spectrum of a molecule with nearly one hundred atoms. Additionally, for X-ray spectroscopy, the effect of including or excluding the core orbital in the active space on small covalent metal complexes is discussed.

Theoretical investigations of asymmetric functionalized Y2C-based MXene monolayers

In this research work, the structural, electronic, optical characteristics, and the work function of the asymmetric functionalized Y2CTT’ (T, T’ = F, Cl, Br) MXene monolayers have been investigated using the density functional approach. Herein, bare Y2C MXene monolayer is metallic which is functionalized with two different halide atoms. The upper surface of Y2C monolayer is terminated with T halide atom and the lower surface is terminated with T′ halide atom. For the computation of electronic band structure, generalized gradient approximation with PBE functional as well as hybrid functional (HSE06) is employed, which ensures that the Y2CClBr, Y2CFBr and Y2CFCl monolayers are semiconductor with the indirect bandgap of 1.66 eV, 1.81 eV and 1.82 eV. The evaluation of optical properties using the random phase approximation suggests that the Y2CTT’ monolayers start absorption in IR region, exhibits a small absorption in the visible part and a significant absorption in ultraviolet part of the electromagnetic spectrum. Hence, Y2CTT’ monolayers are the promising candidates in photonic devices specifically ultraviolet detectors, ultraviolet radiation absorbers, etc.

Diblock Copolymer Melt in an Electric Field: Stability of the Homogeneous State in the Random Phase Approximation

Diblock Copolymer Melt in an Electric Field: Stability of the Homogeneous State in the Random Phase Approximation

Toward more accurate surface properties of ceria using many-body perturbation theory.

Despite the wide applications, the abinitio modeling of the ceria based catalyst is challenging. The partial occupation in the 4f orbitals creates a fundamental challenge for commonly used density functional theory (DFT) methods, including semilocal functionals with Hubbard U correction to force localization and hybrid functionals. In this work, we benchmark the random phase approximation (RPA) for ceria surface properties, including surface energy and hydrogenation energy, compared to the results utilizing the DFT + U approach or hybrid functionals. We show that, for the latter approaches, different surface properties require opposite directions of parameter tuning. This forms a dilemma for the parameter based DFT methods, as the improvement of a certain property by tuning parameters will inevitably lead to the worsening of other properties. Our results suggest that the parameter-free many-body perturbation theory methods exemplified by RPA are a promising strategy to escape the dilemma and provide highly accurate descriptions, which will allow us to better understand the catalytic reactions in ceria related systems.

Homogeneous electron liquid in arbitrary dimensions beyond the random phase approximation

Abstract The homogeneous electron liquid is a cornerstone in quantum physics and chemistry. It is an archetypal system in the regime of slowly varying densities in which the exchange-correlation energy can be estimated with many methods. For high densities, the behavior of the ground-state energy is well-known for 1, 2, and 3 dimensions. Here, we extend this model to arbitrary integer dimensions and compute its correlation energy beyond the random phase approximation (RPA). We employ the approach developed by Singwi, Tosi, Land, and Sjölander (STLS), whose description of the electronic density response for 2D and 3D for metallic densities is known to be comparable to Quantum Monte-Carlo. For higher dimensions, we compare the results obtained for the correlation energy with the values previously obtained using RPA. We find that in agreement with what is known for 2 and 3 dimensions, the RPA tends to over-correlate the liquid also at higher dimensions. We furthermore provide new analytical formulae for the unconventional-dimensional case both for the real and imaginary parts of the Lindhard polarizability and for the local field correction of the STLS theory, and illustrate the importance of the plasmon contribution at those high dimensions.

Drag Resistivity of Hole-Hole Static Interactions with the Effect of Non- Homogeneous Dielectric Medium

BACKGROUND: We have study the Coulomb drag phenomena for hole-hole static potentials theoretically and measured numerically using the random phase approximation (RPA) method OBJECTIVE: The drag resistivity is evaluated at low temperature, large interlayer separation limit and weakly screening regime, with the geometry of two atomically thin materials, such as, BLG/GaAs based multilayer system, is a promising systems in nanomaterials and technology METHOD: Static local field corrections (LFC) are considered to take into account the Exchange-correlations (XC) and mutual interaction effects with varying concentrations of active and passive layer RESULT: It is found that the drag resistivity is found enhanced on using the LFC effects and increases on increasing the effective mass. In Fermi-Liquid regime, drag resistivity is directly proportional to T^2, n^(-3), d^(-4) and ϵ^2 with respect to temperature (T), density (n), interlayer separation (d~nm) and dielectric constant (ϵ_2), respectively. CONCLUSION: Dependency of drag resistivity is measured and compared to 2D e-e and e-h coupled-layer systems with and without the effect of non-homogeneous dielectric medium.

Scattering evidence of positional charge correlations in polyelectrolyte complexes

Polyelectrolyte complexation plays an important role in materials science and biology. The internal structure of the resultant polyelectrolyte complex (PEC) phase dictates properties such as physical state, response to external stimuli, and dynamics. Small-angle scattering experiments with X-rays and neutrons have revealed structural similarities between PECs and semidilute solutions of neutral polymers, where the total scattering function exhibits an Ornstein-Zernike form. In spite of consensus among different theoretical predictions, the existence of positional correlations between polyanion and polycation charges has not been confirmed experimentally. Here, we present small-angle neutron scattering profiles where the polycation scattering length density is matched to that of the solvent to extract positional correlations among anionic monomers. The polyanion scattering functions exhibit a peak at the inverse polymer screening radius of Coulomb interactions, q* ≈ 0.2 Å-1. This peak, attributed to Coulomb repulsions between the fragments of polyanions and their attractions to polycations, is even more pronounced in the calculated charge scattering function that quantifies positional correlations of all polymer charges within the PEC. Screening of electrostatic interactions by adding salt leads to the gradual disappearance of this correlation peak, and the scattering functions regain an Ornstein-Zernike form. Experimental scattering results are consistent with those calculated from the random phase approximation, a scaling analysis, and molecular simulations.

Study of collective excitations in monolayer-bilayer graphene heterostructures: Temperature effects

In this paper, we study collective excitations in an M-BLG heterostructure, consisting of one BLG and one parallel MLG sheet on an inhomogeneous background dielectric. Theoretical calculations are carried out within the random-phase approximation, taking into account temperature effects. The results illustrate that two solutions, corresponding to optical and acoustical modes, admit the zero equation of the temperature-dependent dynamical dielectric function of the structure. The energy of these collective modes is significantly larger (smaller) than that in DBLG (DLG) systems with similar parameters. As temperature increases, the frequency of the acoustical mode steadily increases while that of the optical mode only increases in large wave vector regions, found differently with different interlayer separations. Interestingly, we explore that the effects of carrier density in graphene on plasmon properties of M-BLG heterostructures sharply differ from those in both BLG and DLG systems.

Electron energy loss spectra of ZnSe using linear response theory

Beginning from the density functional theory, the linear response theory within the framework of time dependent density functional theory has been applied to study the electron energy loss spectra of ZnSe. The ground state is obtained using first-principles Full-Potential Linearized Augmented Plane Wave method. After settling the crystal structure, the electronic properties such as band structure and density of states are calculated. The electron energy loss spectra are found considering exchange-correlation kernels namely adiabatic local density approximation, long range contribution and the bootstrap. For the sake of completeness and comparison, results using random phase approximation are also incorporated. The inclusion of local field effects in all the kernels improve the agreement of optical and electron energy loss spectra with experimental data. Moreover, agreement in the plasmon peak positions, found using different kernels considering local field effects, with experimental data has also improved.