Showing papers on "Random phase approximation published in 2018"
TL;DR: For the first time, thorough benchmarks of important approximation schemes regarding various quantities such as different energies, in particular the exchange-correlation free energy, and the static structure factor are possible.
202 citations
TL;DR: In this article, a fully non-local Bohm potential for the QHD model is presented, which is linked to the electron polarization function in the random phase approximation, and the dynamic QHD exchange correlation potential is introduced in the framework of local field corrections.
Abstract: Quantum hydrodynamics (QHD) theory for finite temperature plasmas is consistently derived in the framework of the local density approximation of the free energy with first order density gradient correction. Previously known results are revised and improved with a clear description of the underlying approximations. A fully non-local Bohm potential, which goes beyond all previous results and is linked to the electron polarization function in the random phase approximation, for the QHD model is presented. The dynamic QHD exchange correlation potential is introduced in the framework of local field corrections and considered for the case of the relaxation time approximation. Finally, the range of applicability of the QHD is discussed.
126 citations
17 Dec 2018
TL;DR: In this paper, the authors show that large magnetic anisotropy gives rise to strong magnon-magnon interactions that leads to a drastic failure of the random phase approximation (RPA) and demonstrate that classical Monte Carlo (MC) simulations correctly describe the critical temperatures in the large MA limit and agree with RPA when the MA becomes small.
Abstract: Magnetic order in two-dimensional (2D) materials is intimately coupled to magnetic anisotropy (MA) since the Mermin–Wagner theorem implies that rotational symmetry cannot be spontaneously broken at finite temperatures in 2D. Large MA thus comprises a key ingredient in the search for magnetic 2D materials that retains the magnetic order above room temperature. Magnetic interactions are typically modeled in terms of Heisenberg models and the temperature dependence on magnetic properties can be obtained with the random phase approximation (RPA), which treats magnon interactions at the mean-field level. In the present work we show that large MA gives rise to strong magnon–magnon interactions that leads to a drastic failure of the RPA. We then demonstrate that classical Monte Carlo (MC) simulations correctly describe the critical temperatures in the large MA limit and agree with RPA when the MA becomes small. A fit of the MC results leads to a simple expression for the critical temperatures as a function of MA and exchange coupling constants, which significantly simplifies the theoretical search for new 2D magnetic materials with high critical temperatures. The expression is tested on a monolayer of CrI, which were recently observed to exhibit ferromagnetic order below 45 K and we find excellent agreement with the experimental value.
80 citations
TL;DR: The structural properties of strongly coupled ions in dense plasmas with moderately to strongly degenerate electrons are investigated in the framework of the one-component plasma model of ions interacting through a screened pair interaction potential and it is demonstrated that at r_{s}>1, where r is the ratio of the mean interelectronic distance to the Bohr radius, electronic correlations beyond RPA have a nonnegligible effect on the structural properties.
Abstract: The structural properties of strongly coupled ions in dense plasmas with moderately to strongly degenerate electrons are investigated in the framework of the one-component plasma model of ions interacting through a screened pair interaction potential. Special focus is put on the description of the electronic screening in the Singwi-Tosi-Land-Sjolander (STLS) approximation. Different cross-checks and analyses using ion potentials obtained from ground-state quantum Monte Carlo data, the random phase approximation (RPA), and existing analytical models are presented for the computation of the structural properties, such as the pair distribution and the static structure factor, of strongly coupled ions. The results are highly sensitive to the features of the screened pair interaction potential. This effect is particularly visible in the static structure factor. The applicability range of the screened potential computed from STLS is identified in terms of density and temperature of the electrons. It is demonstrated that at r_{s}>1, where r_{s} is the ratio of the mean interelectronic distance to the Bohr radius, electronic correlations beyond RPA have a nonnegligible effect on the structural properties. Additionally, the applicability of the hypernetted chain approximation for the calculation of the structural properties using the screened pair interaction potential is analyzed employing the effective coupling parameter approach.
67 citations
TL;DR: In this article, the authors show that large magnetic anisotropy gives rise to strong magnon-magnon interactions that leads to a drastic failure of the Random Phase Approximation (RPA).
Abstract: Magnetic order in two-dimensional (2D) materials is intimately coupled to magnetic anisotropy (MA) since the Mermin-Wagner theorem implies that rotational symmetry cannot be spontaneously broken at finite temperatures in 2D. Large MA thus comprises a key ingredient in the search for magnetic 2D materials that retains the magnetic order above room temperature. Magnetic interactions are typically modeled in terms of Heisenberg models and the temperature dependence on magnetic properties can be obtained with the Random Phase Approximation (RPA), which treats magnon interactions at the mean-field level. In the present work we show that large MA gives rise to strong magnon-magnon interactions that leads to a drastic failure of the RPA. We then demonstrate that classical Monte Carlo (MC) simulations correctly describe the critical temperatures in the large MA limit and agree with RPA when the MA becomes small. A fit of the MC results leads to a simple expression for the critical temperatures as a function of MA and exchange coupling constants, which significantly simplifies the theoretical search for new 2D magnetic materials with high critical temperatures. The expression is tested on a monolayer of CrI$_3$, which were recently observed to exhibit ferromagnetic order below 45 K and we find excellent agreement with the experimental value.
66 citations
TL;DR: Two previously discussed regimes are identified: a Gross-Neveu transition to a strongly correlated Mott insulator and a semimetallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation.
Abstract: The role of electron-electron interactions in two-dimensional Dirac fermion systems remains enigmatic. Using a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction, we identify the two previously discussed regimes: a Gross-Neveu transition to a strongly correlated Mott insulator and a semimetallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation. We predict that experimental realizations of Dirac fermions span this crossover and that this determines whether the Fermi velocity is increased or decreased by interactions. We explain several long-standing mysteries, including why the observed Fermi velocity in graphene is consistently about 20% larger than values obtained from ab initio calculations and why graphene on different substrates shows different behaviors.
63 citations
TL;DR: An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions and is one of the most efficient multireFER approaches accounting for dynamic electron correlation also for the strongly correlated systems.
Abstract: An adiabatic connection (AC) formula for the electron correlation energy is derived for a broad class of multireference wave functions. The AC expression recovers dynamic correlation energy and assures a balanced treatment of the correlation energy. Coupling the AC formalism with the extended random phase approximation allows one to find the correlation energy only from reference one- and two-electron reduced density matrices. If the generalized valence bond perfect pairing model is employed a simple closed-form expression for the approximate AC formula is obtained. This results in the overall M^{5} scaling of the computation cost making the method one of the most efficient multireference approaches accounting for dynamic electron correlation also for the strongly correlated systems.
48 citations
TL;DR: In this paper, the structural phase transitions of different materials, including metal to metal, metal to semiconductor, and semiconductor-to-semiconductor transitions, were explored using methods based on the random phase approximation.
Abstract: The structural phase transitions of different materials, including metal to metal, metal to semiconductor, and semiconductor to semiconductor transitions, were explored using methods based on the random phase approximation. Transition pressures for Si, Ge, SiC, GaAs, ${\mathrm{SiO}}_{2}$, Pb, C, and BN from their stable low-pressure phases to certain high-pressure phases were computed with several semilocal density functionals and from the adiabatic connection fluctuation-dissipation formulation of density functional theory at zero temperature. In addition to the random phase approximation (RPA), three approximate beyond-RPA methods were also investigated to determine the impact of exchange-correlation kernel corrections. Results at finite temperature were obtained with the inclusion of zero-point energy contributions from the phonon spectra. We find that including temperature effects is most important for systems with nearly degenerate phases such as for boron nitride and carbon. In combination with thermal corrections, the kernel-corrected correlation methods deliver high accuracy compared to experimental data and can serve as a useful benchmark method in place of more expensive correlated calculations.
47 citations
TL;DR: The predicted melting point is correlated with the energy difference between cubic diamond and the beta-tin phase of silicon, establishing that this energy difference is an important benchmark for the development of approximate functionals.
Abstract: The melting point of silicon in the cubic diamond phase is calculated using the random phase approximation (RPA). The RPA includes exact exchange as well as an approximate treatment of local as well as nonlocal many body correlation effects of the electrons. We predict a melting temperature of about 1735 and 1640 K without and with core polarization effects, respectively. Both values are within 3% of the experimental melting temperature of 1687 K. In comparison, the commonly used gradient approximation to density functional theory predicts a melting point that is 200 K too low, and hybrid functionals overestimate the melting point by 150 K. We correlate the predicted melting point with the energy difference between cubic diamond and the beta-tin phase of silicon, establishing that this energy difference is an important benchmark for the development of approximate functionals. The current results demonstrate that the RPA can be used to predict accurate finite temperature properties and underlines the excellent predictive properties of the RPA for condensed matter.
47 citations
TL;DR: In this paper, an extensive set of surface and chemisorption energies calculated using state-of-the-art many-body perturbation theory is presented. But the RPA is not a universally accurate method for surface science.
Abstract: We present an extensive set of surface and chemisorption energies calculated using state of the art many-body perturbation theory. In the first part of the paper we consider 10 surface reactions in the low coverage regime where experimental data is available. Here the random phase approximation (RPA) is found to yield high accuracy for both adsorption and surface energies. In contrast, all the considered density functionals fail to describe both quantities accurately. This establishes the RPA as a universally accurate method for surface science. In the second part, we use the RPA to construct a database of 200 high quality adsorption energies for reactions involving OH, CH, NO, CO, N2, N, O, and H over a wide range of 3d, 4d, and 5d transition metals. Due to the significant computational demand, these results are obtained in the high coverage regime where adsorbate–adsorbate interactions can be significant. RPA is compared to the more advanced renormalized adiabatic LDA (rALDA) method for a subset of the ...
46 citations
TL;DR: In this article, a vertex correction based on the exact exchange (EXX) potential of time-dependent density functional theory is introduced, which is constrained to be local but is expected to capture similar physics as the Hartree-Fock vertex.
Abstract: With the aim of constructing an electronic structure approach that systematically goes beyond the GW and random phase approximation (RPA) we introduce a vertex correction based on the exact-exchange (EXX) potential of time-dependent density functional theory. The EXX vertex function is constrained to be local but is expected to capture similar physics as the Hartree-Fock vertex. With the EXX vertex we then unify different beyond-RPA approaches such as the various re-summations of RPA with exchange (RPAx) and the second order screened exchange (SOSEX) approximation. The theoretical analysis is supported by numerical studies on the hydrogen dimer and the electron gas, and we discuss the role of including the vertex correction in both the screened interaction and the self energy. Finally, we give details on our implementation within the plane-wave pseudo potential framework and demonstrate the excellent performance of the different RPAx methods in describing the energetics of hydrogen and van der Waals bonds.
TL;DR: In this paper, a quantum-mechanical non-local theory of chiral Fermi arc plasmons in WSMs with broken time-reversal symmetry is presented.
Abstract: The surface of a Weyl semimetal (WSM) displays Fermi arcs, i.e., disjoint segments of a two-dimensional Fermi contour. We present a quantum-mechanical nonlocal theory of chiral Fermi arc plasmons in WSMs with broken time-reversal symmetry. These are collective excitations constructed from topological Fermi arc and bulk electron states and arising from electron-electron interactions, which are treated in the realm of the random phase approximation. Our theory includes quantum effects associated with the penetration of the Fermi arc surface states into the bulk and dissipation, which is intrinsically nonlocal in nature and arises from decay processes mainly involving bulk electron-hole pair excitations.
TL;DR: In this article, the Hartree-Fock plus random phase approximation of the IAS was used to reproduce the excitation energy without compromising other properties of finite nuclei in a heavy nucleus.
Abstract: We analyze and propose a solution to the apparent inconsistency between our current knowledge of the equation of state of asymmetric nuclear matter, the energy of the isobaric analog state (IAS) in a heavy nucleus such as $^{208}\mathrm{Pb}$, and the isospin symmetry breaking forces in the nuclear medium. This is achieved by performing state-of-the-art Hartree-Fock plus random phase approximation calculations of the IAS that include all isospin symmetry breaking contributions. To this aim, we propose a new effective interaction that is successful in reproducing the IAS excitation energy without compromising other properties of finite nuclei.
TL;DR: Low computational cost, compared to AC-CAS or perturbational approaches, makes AC0 the most efficient ab initio approach to capturing electron correlation for the CAS wave functions.
Abstract: Recently, the adiabatic connection (AC) formula for the electron correlation energy has been proposed for a broad class of multireference wave functions (Pernal, K. Electron Correlation from the Adiabatic Connection for Multireference Wave Functions. Phys. Rev. Lett. 2018, 120, 013001). We show that the AC formula used together with the extended random phase approximation (ERPA) can be efficiently applied to complete active space (CAS) wave functions to recover the remaining electron correlation. Unlike most of the perturbation theory approaches, the proposed AC-CAS method does not require construction of higher than two-electron reduced density matrices, which offers an immediate computational saving. In addition, we show that typically the AC-CAS systematically reduces the errors of both the absolute value of energy and of the energy differences (energy barrier) upon enlarging active spaces for electrons and orbitals. AC-CAS consistently gains in accuracy from including more active electrons. We also pr...
TL;DR: Experimental investigation of deep-inelastic and fusion-fission outcomes in the Ni+^{60}Ni reaction has been carried out, indicating that microscopic models incorporating one-body dissipation and fluctuations provide a potential tool for exploring dissipation in low-energy heavy ion collisions.
Abstract: Energy dissipative processes play a key role in how quantum many-body systems dynamically evolve toward equilibrium. In closed quantum systems, such processes are attributed to the transfer of energy from collective motion to single-particle degrees of freedom; however, the quantum many-body dynamics of this evolutionary process is poorly understood. To explore energy dissipative phenomena and equilibration dynamics in one such system, an experimental investigation of deep-inelastic and fusion-fission outcomes in the ^{58}Ni+^{60}Ni reaction has been carried out. Experimental outcomes have been compared to theoretical predictions using time dependent Hartree-Fock and time dependent random phase approximation approaches, which, respectively, incorporate one-body energy dissipation and fluctuations. Excellent quantitative agreement has been found between experiment and calculations, indicating that microscopic models incorporating one-body dissipation and fluctuations provide a potential tool for exploring dissipation in low-energy heavy ion collisions.
TL;DR: In this article, the authors check the accuracy of constrained random phase approximation (cRPA) downfolding scheme by considering one-dimensional two-and three-orbital Hubbard models with a target band at the Fermi level and one or two screening bands away from the Fermani level.
Abstract: We check the accuracy of the constrained random phase approximation (cRPA) downfolding scheme by considering one-dimensional two- and three-orbital Hubbard models with a target band at the Fermi level and one or two screening bands away from the Fermi level. Using numerically exact quantum Monte Carlo simulations of the full and downfolded model, we demonstrate that depending on filling, the effective interaction in the low-energy theory is either barely screened or antiscreened, in contrast to the cRPA prediction. This observation is explained by a functional renormalization group analysis, which shows that the cRPA contribution to the screening is to a large extent canceled by other diagrams in the direct particle-hole channel. We comment on the implications of this finding for the ab initio estimation of interaction parameters in low-energy descriptions of solids.
TL;DR: In this paper, a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction was used to identify the two previously discussed regimes: a Gross-Neveu transition to a strongly correlated Mott insulator, and a semi-metallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation.
Abstract: The role of electron-electron interactions on two-dimensional Dirac fermions remains enigmatic. Using a combination of nonperturbative numerical and analytical techniques that incorporate both the contact and long-range parts of the Coulomb interaction, we identify the two previously discussed regimes: a Gross-Neveu transition to a strongly correlated Mott insulator, and a semi-metallic state with a logarithmically diverging Fermi velocity accurately described by the random phase approximation. Most interestingly, experimental realizations of Dirac fermions span the crossover between these two regimes providing the physical mechanism that masks this velocity divergence. We explain several long-standing mysteries including why the observed Fermi velocity in graphene is consistently about 20 percent larger than the best values calculated using ab initio and why graphene on different substrates show different behavior.
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TL;DR: In this paper, a weak coupling approach to superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime, was developed, and it was shown that inter-valley electron pairing with either chiral ($d+i d$ mixed with $p-i p$) or helical form factor is the dominant instability.
Abstract: We develop a weak coupling approach to superconductivity in twisted bilayer graphene, starting from the Fermi liquid regime. A key observation is that near half filling, the fermiology consists of well nested Fermi pockets derived from opposite valleys, leading to enhanced valley fluctuation, which in turn can mediate superconductivity. This scenario is studied within the random phase approximation. We find that inter-valley electron pairing with either chiral ($d+i d$ mixed with $p-i p$) or helical form factor is the dominant instability. An approximate SO(4) spin-valley symmetry implies a near degeneracy of spin-singlet and triplet pairing. On increasing interactions, commensurate inter-valley coherence wave (IVCW) order can arise, with simultaneous condensation at the three M points in the Brillouin Zone, and a $2\times2$ pattern in real space. In simple treatments though, this leads to a full gap at fillings $\pm (1/2+1/8)$, slightly away from half-filling. An SO(4) symmetry breaking "anti-Hunds" coupling favors the spin-singlet order both for the IVCW and the superconductor, consistent with observations. Mott insulators derived from phase fluctuating superconductors are also discussed, which exhibit both symmetry protected and intrinsic topological orders.
TL;DR: In this paper, the authors give a pedagogical introduction to possible approaches for describing electron correlation energy based on the McLachlan and Ball formula, which provides a common umbrella for RPA approximations proposed for uncorrelated (Hartree-Fock or Kohn-Sham), partially correlated (strongly orthogonal geminals) references.
Abstract: Random phase approximation (RPA) electron correlation methods have gained in popularity in the recent years. A number of RPA correlation energy variants emerged in the Kohn–Sham DFT framework and in the theory of strongly orthogonal geminals. Foundations of most RPA approaches trace back to an exact expression for two-electron reduced density matrix written in terms of one-electron density matrix and dynamic one-electron response functions, originally presented in the seminal paper of McLachlan and Ball (Rev. Mod. Phys. 1964, 36, 844). The aim of this article is to give a pedagogical introduction to possible approaches for describing electron correlation energy based on the McLachlan and Ball formula. The focus of the presentation is to formulate electron-interaction energy expressions as functions of reduced density matrices. On one hand, it provides a common umbrella for RPA approximations proposed for uncorrelated (Hartree–Fock or Kohn–Sham) as well as partially correlated (strongly orthogonal geminals) references. On the other hand, such presentation may stimulate new developments in density matrix functional theory.
TL;DR: P perturbation theory can systematically correct RPA but only for systems and properties qualitatively well captured by RPA, as indicated by small α̅ values.
Abstract: It has been suspected since the early days of the random-phase approximation (RPA) that corrections to RPA correlation energies result mostly from short-range correlation effects and are thus amenable to perturbation theory Here we test this hypothesis by analyzing formal and numerical results for the most common beyond-RPA perturbative corrections, including the bare second-order exchange (SOX), second-order screened exchange (SOSEX), and approximate exchange kernel (AXK) methods Our analysis is facilitated by efficient and robust algorithms based on the resolution-of-the-identity (RI) approximation and numerical frequency integration, which enable benchmark beyond-RPA calculations on medium- and large-size molecules with size-independent accuracy The AXK method systematically improves upon RPA, SOX, and SOSEX for reaction barrier heights, reaction energies, and noncovalent interaction energies of main-group compounds The improved accuracy of AXK compared with SOX and SOSEX is attributed to stronger screening of bare SOX in AXK For reactions involving transition-metal compounds, particularly 3d transition-metal dimers, the AXK correction is too small and can even have the wrong sign These observations are rationalized by a measure α of the effective coupling strength for beyond-RPA correlation When the effective coupling strength increases beyond a critical α value of approximately 05, the RPA errors increase rapidly and perturbative corrections become unreliable Thus, perturbation theory can systematically correct RPA but only for systems and properties qualitatively well captured by RPA, as indicated by small α values
TL;DR: A parallel implementation of the method is presented, 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.
Abstract: 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 NbasisNocc. Furthermore, we present a parallel im...
TL;DR: Efficient methods to calculate beyond random phase approximation (RPA) correlation energies for molecular systems with up to 500 atoms are presented, using the resolution-of-the-identity and a double-Laplace transform of the non-interacting polarization propagator in conjunction with an atomic orbital formalism.
Abstract: We present efficient methods to calculate beyond random phase approximation (RPA) correlation energies for molecular systems with up to 500 atoms. To reduce the computational cost, we employ the resolution-of-the-identity and a double-Laplace transform of the non-interacting polarization propagator in conjunction with an atomic orbital formalism. Further improvements are achieved using integral screening and the introduction of Cholesky decomposed densities. Our methods are applicable to the dielectric matrix formalism of RPA including second-order screened exchange (RPA-SOSEX), the RPA electron-hole time-dependent Hartree-Fock (RPA-eh-TDHF) approximation, and RPA renormalized perturbation theory using an approximate exchange kernel (RPA-AXK). We give an application of our methodology by presenting RPA-SOSEX benchmark results for the L7 test set of large, dispersion dominated molecules, yielding a mean absolute error below 1 kcal/mol. The present work enables calculating beyond RPA correlation energies for significantly larger molecules than possible to date, thereby extending the applicability of these methods to a wider range of chemical systems.
TL;DR: In this article, the second random-phase approximation model corrected by a subtraction procedure designed to cure double counting, instabilities, and ultraviolet divergences, is employed for the first time to analyze the dipole strength and polarizability in 48Ca.
TL;DR: In this article, constrained random phase approximation calculations for prototypical oxides with a different occupation of the d shell, LaTiO3, LaVO3, and LaCrO3 (d3) were performed to study the evolution of the effective Coulomb interactions when applying epitaxial strain.
Abstract: Epitaxial strain offers an effective route to tune the physical parameters in transition metal oxides. So far, most studies have focused on the effects of strain on the bandwidths and crystal field splitting, but recent experimental and theoretical works have shown that also the effective Coulomb interaction changes upon structural modifications. This effect is expected to be of paramount importance in current material engineering studies based on epitaxy-based material synthesization. Here, we perform constrained random phase approximation calculations for prototypical oxides with a different occupation of the d shell, LaTiO3 (d1), LaVO3 (d2), and LaCrO3 (d3), and systematically study the evolution of the effective Coulomb interactions (Hubbard U and Hund's J) when applying epitaxial strain. Surprisingly, we find that the response upon strain is strongly dependent on the material. For LaTiO3, the interaction parameters are determined by the degree of localization of the orbitals, and grow with increasing tensile strain. In contrast, LaCrO3 shows the opposite trends: the interactions parameters shrink upon tensile strain. This is caused by the enhanced screening due to the larger electron filling. LaVO3 shows an intermediate behavior.
TL;DR: In this article, the relative stability of two polymorphs is correctly predicted, and a significantly improved agreement with experiment compared to that from local, semi-local and hybrid functionals is obtained in terms of the enthalpy of transformation, regardless of the density functional approximations used in producing the input wave functions for RPA calculations.
Abstract: Iron disulfide (FeS2) has attracted a lot of interest for photovoltaic and photoelectrochemical applications due to its favorable electronic and optical properties. The theoretical description of FeS2 has been confronted with the problem of common density functional approximations failing to correctly account for the relative stability of pyrite and marcasite polymorphs of FeS2. We address this issue by using the adiabatic-connection fluctuation-dissipation theorem (ACFDT) in the random phase approximation (RPA). The relative stability of the two polymorphs is correctly predicted, and a significantly improved agreement with experiment compared to that from local, semi-local and hybrid functionals is obtained in terms of the enthalpy of transformation, regardless of the density functional approximations used in producing the input wave functions for RPA calculations. We attribute the stability of the pyrite phase to the electron correlation related to the low energy excitation from Fe d states to the S–S state. Equilibrium volumes very close to the experimental values are predicted for both phases as well. The contributions of zero-point energy corrections and finite temperature effects are considered and found to be insignificant compared to dynamical correlation included in the ACFDT-RPA approach. This study highlights the importance of considering the difference in high-order dynamical correlation as described by ACFDT-RPA due to the distinction in the Kohn–Sham band structure for a correct description of the relative stability of competing phases that are energetically very close to each other.
TL;DR: It is shown that in the limit of a small permanent dipole moment, the functional in integrand exponent takes the well known form of the Poisson-Boltzmann-Langevin (PBL) functional.
Abstract: We present a nonlocal statistical field theory of a dilute electrolyte solution with a small additive of dipolar particles. We postulate that every dipolar particle is associated with an arbitrary probability distribution function (PDF) of distance between its charge centers. Using the standard Hubbard–Stratonovich transformation, we represent the configuration integral of the system in the functional integral form. We show that in the limit of a small permanent dipole moment, the functional in integrand exponent takes the well known form of the Poisson–Boltzmann–Langevin (PBL) functional. In the mean-field approximation we obtain a non-linear integro-differential equation with respect to the mean-field electrostatic potential, generalizing the PBL equation for the point-like dipoles obtained first by Abrashkin et al. We apply the obtained equation in its linearized form to derivation of the expressions for the mean-field electrostatic potential of the point-like test ion and its solvation free energy in salt-free solution, as well as in solution with salt ions. For the 'Yukawa'-type PDF we obtain analytic relations for both the electrostatic potential and the solvation free energy of the point-like test ion. We obtain a general expression for the bulk electrostatic free energy of the solution within the Random phase approximation (RPA). For the salt-free solution of the dipolar particles for the Yukawa-type PDF we obtain an analytic relation for the electrostatic free energy, resulting in two limiting regimes. Finally, we analyze the limiting laws, following from the general relation for the electrostatic free energy of solution in presence of both the ions and the dipolar particles for the case of Yukawa-type PDF.
TL;DR: In this paper, the ground-state double-excitation amplitudes are obtained from the ring-CCD equations, and the EOM eigenvalue problem is truncated to the singleexcitation (one particle + one hole) subspace.
Abstract: The ground-state correlation energy calculated in the random-phase approximation (RPA) is known to be identical to that calculated using a subset of terms appearing in coupled-cluster theory with double excitations. In particular, this equivalence requires keeping only those terms that generate time-independent ring diagrams, in the Goldstone sense. Here I show that this equivalence extends to neutral excitation energies, for which those calculated in the RPA are identical to those calculated using an approximation to equation-of-motion coupled-cluster theory with double excitations (EOM-CCD). The equivalence requires three approximations to EOM-CCD: first, the ground-state double-excitation amplitudes are obtained from the ring-CCD equations (the same as for the correlation energy); second, the EOM eigenvalue problem is truncated to the single-excitation (one particle + one hole) subspace; third, the similarity transformation of the Fock operator must be neglected, as it corresponds to a dressing of the single-particle propagator, which is not present in the conventional RPA.
TL;DR: In this paper, the collective modes of doped two-dimensional crystalline materials, namely graphene, MoS$_2$ and phosphorene, both monolayer and bilayer structures, are explored using the density functional theory simulations together with the random phase approximation.
Abstract: Collective modes of doped two-dimensional crystalline materials, namely graphene, MoS$_2$ and phosphorene, both monolayer and bilayer structures, are explored using the density functional theory simulations together with the random phase approximation. The many-body dielectric functions of the materials are calculated using an {\it ab initio} based model involving material-realistic physical properties. Having calculated the electron energy-loss, we calculate the collective modes of each material considering the in-phase and out-of-phase modes for bilayer structures. Furthermore, owing to many band structures and intreband transitions, we also find high-energy excitations in the systems. We explain that the material-specific dielectric function considering the polarizability of the crystalline material such as MoS$_2$ are needed to obtain realistic plasmon dispersions. For each material studied here, we find different collective modes and describe their physical origins.
TL;DR: It is shown that these identities extend to excitation energies, for which those calculated in each RPA are identical to those calculated using approximations to equation-of-motion coupled-cluster theory with double excitations (EOM-CCD).
Abstract: The ground-state correlation energy calculated in the random-phase approximation (RPA) is known to be identical to that calculated using a subset of terms appearing in coupled-cluster theory with double excitations (CCD). In particular, for particle-hole (ph) RPA this equivalence requires keeping only those terms that generate time-independent ring diagrams, and for particle-particle (pp) RPA it requires keeping only those terms that generate ladder diagrams. Here I show that these identities extend to excitation energies, for which those calculated in each RPA are identical to those calculated using approximations to equation-of-motion coupled-cluster theory with double excitations (EOM-CCD). The equivalence requires three approximations to EOM-CCD: first, the ground-state CCD amplitudes are obtained from the ring-CCD or ladder-CCD equations (the same as for the correlation energy); second, the EOM eigenvalue problem is truncated to the minimal subspace, which is one particle + one hole for ph-RPA and two particles or two holes for pp-RPA; third, the similarity transformation of the Fock operator must be neglected, as it corresponds to a Brueckner-like dressing of the single-particle propagator, which is not present in the conventional RPA.
TL;DR: In this paper, the electronic properties of a monolayer MoS2 were investigated with the all-electron first principle calculations based on the density functional theory and the spin-orbital couplings (SOCs).
Abstract: The electronic structures of a MoS2 monolayer are investigated with the all-electron first principle calculations based on the density functional theory (DFT) and the spin-orbital couplings (SOCs). Our results show that the monolayer MoS2 is a direct band gap semiconductor with a band gap of 1.8 eV. The SOCs and d-electrons in Mo play a very significant role in deciding its electronic and optical properties. Moreover, electronic elementary excitations are studied theoretically within the diagrammatic self-consistent field theory. Under random phase approximation, it shows that two branches of plasmon modes can be achieved via the conduction-band transitions due to the SOCs, which are different from the plasmons in a two-dimensional electron gas and graphene owing to the quasi-linear energy dispersion in single-layer MoS2. Moreover, the strong optical absorption up to 105 cm-1 and two optical absorption edges I and II can be observed. This study is relevant to the applications of monolayer MoS2 as an advanced photoelectronic device.