Adiabatic-connection Fluctuation-dissipation Theorem Research Articles

Reaction barriers at metal surfaces computed using the random phase approximation: Can we beat DFT in the generalized gradient approximation?

Reaction barriers for molecules dissociating on metal surfaces (as relevant to heterogeneous catalysis) are often difficult to predict accurately with density functional theory (DFT). Although the results obtained for several dissociative chemisorption reactions via DFT in the generalized gradient approximation (GGA), in meta-GGA, and for GGA exchange + van der Waals correlation scatter around the true reaction barrier, there is an entire class of dissociative chemisorption reactions for which GGA-type functionals collectively underestimate the reaction barrier. Little is known why GGA-DFT collectively fails in some cases and not in others, and we do not know whether other methods suffer from the same inconsistency. Here, we present barrier heights for dissociative chemisorption reactions obtained from the random phase approximation in the adiabatic-connection fluctuation-dissipation theorem (ACFDT-RPA) and from hybrid functionals with different amounts of exact exchange. By comparing the results obtained for the dissociative chemisorption reaction of H2 on Al(110) (where GGA-DFT collectively underestimates the barrier) and H2 on Cu(111) (where GGA-DFT scatters around the true barrier), we can gauge whether the inconsistent description of the systems persists for hybrid functionals and ACFDT-RPA. We find hybrid functionals to improve the relative description of the two systems, but to fall short of chemical accuracy. ACFDT-RPA improves the results further and leads to chemically accurate barriers for both systems. Together with an analysis of the density of states and the results from selected GGA, meta-GGA, and GGA exchange + van der Waals correlation functionals, these results allow us to discuss possible origins for the inconsistent behavior of GGA-based functionals for molecule-metal reaction barriers.

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

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

Avoiding spin contamination and spatial symmetry breaking by exact-exchange-only optimized-effective-potential methods within the symmetrized Kohn-Sham framework.

For open-shell atoms and molecules, Kohn-Sham (KS) methods typically resort to spin-polarized approaches that exhibit spin-contamination and often break spatial symmetries. As a result, the KS Hamiltonian operator and the KS orbitals do not exhibit the space and spin symmetry of the physical electron system. The KS formalism can be symmetrized in a rigorous way only in real space, only in spin space, or both in real and spin space. Within such symmetrized KS frameworks, we present exact-exchange-only optimized-effective-potential (OEP) methods that are free of spin contamination and/or spatial symmetry breaking. The effect of symmetrizations on the total energy and its parts and on the exchange potential is analyzed. The presented exact-exchange-only OEP methods may serve as a starting point for high-level symmetrized KS methods based, e.g., on the adiabatic-connection fluctuation-dissipation theorem.

First-principles study of electronic and optical properties of novel 2D TiOS monolayer and bilayer—Dimensionality reduction opens up a band gap in TiOS

The finding of advanced functional materials with superior properties to existing ones to develop cutting-edge technologies for societal advancement is indispensable. We identify a new two-dimensional (2D) TiOS, which opens up a band gap due to the lowering of the dimensionality employing first-principles computations within the framework of density functional theory (DFT) and beyond. Electronic structure estimations reveal that bulk TiOS is metal whereas the 2D-TiOS possesses a band gap of ∼4.5 eV within GW approximation, which is higher than the band gap of 2D-InOF and 2D transition metal dichalcogenides. The computed phonon dispersion curves show that the 2D-TiOS is dynamically stable. The 2D-TiOS has a very high absorption coefficient in the 0–50 eV. Third-order elastic constants (TOECs) of this 2D-TiOS are achieved using DFT and within the adiabatic-connection fluctuation–dissipation theorem in the random phase approximation. Surprisingly, we find a band overlap, indicating that TiOS/TiOS bilayer is a metal. If the incident light frequency surpasses the plasma frequency (60.00 eV), and then the bilayer turns out to be transparent. Our findings suggest that this 2D sheet is a promising alternative for nanotechnology and optoelectronic devices.

Third-Order Elastic Constants of Germanium and Silicon using Adiabatic-Connection Fluctuation-Dissipation Theorem in Random Phase Approximation

Third-Order Elastic Constants of Germanium and Silicon using Adiabatic-Connection Fluctuation-Dissipation Theorem in Random Phase Approximation

Simple Exchange-Correlation Energy Functionals for Strongly Coupled Light-Matter Systems Based on the Fluctuation-Dissipation Theorem.

Recent experimental advances in strongly coupled light-matter systems have sparked the development of general abinitio methods capable of describing interacting light-matter systems from first principles. One of these methods, quantum-electrodynamical density-functional theory (QEDFT), promises computationally efficient calculations for large correlated light-matter systems with the quality of the calculation depending on the underlying approximation for the exchange-correlation functional. So far no true density-functional approximation has been introduced limiting the efficient application of the theory. In this Letter, we introduce the first gradient-based density functional for the QEDFT exchange-correlation energy derived from the adiabatic-connection fluctuation-dissipation theorem. We benchmark this simple-to-implement approximation on small systems in optical cavities and demonstrate its relatively low computational costs for fullerene molecules up to C_{180} coupled to 400 000 photon modes in a dissipative optical cavity. This Letter now makes first principle calculations of much larger systems possible within the QEDFT framework effectively combining quantum optics with large-scale electronic structure theory.

Scaled σ-functionals for the Kohn-Sham correlation energy with scaling functions from the homogeneous electron gas.

The recently introduced σ-functionals constitute a new type of functionals for the Kohn-Sham (KS) correlation energy. σ-Functionals are based on the adiabatic-connection fluctuation-dissipation theorem, are computationally closely related to the well-known direct random phase approximation (dRPA), and are formally rooted in many-body perturbation theory along the adiabatic connection. In σ-functionals, the function of the eigenvalues σ of the Kohn-Sham response matrix that enters the coupling constant and frequency integration in the dRPA is replaced by another function optimized with the help of reference sets of atomization, reaction, transition state, and non-covalent interaction energies. σ-Functionals are highly accurate and yield chemical accuracy of 1 kcal/mol in reaction or transition state energies, in main group chemistry. A shortcoming of σ-functionals is their inability to accurately describe processes involving a change of the electron number, such as ionizations or electron attachments. This problem is attributed to unphysical self-interactions caused by the neglect of the exchange kernel in the dRPA and σ-functionals. Here, we tackle this problem by introducing a frequency- and σ-dependent scaling of the eigenvalues σ of the KS response function that models the effect of the exchange kernel. The scaling factors are determined with the help of the homogeneous electron gas. The resulting scaled σ-functionals retain the accuracy of their unscaled parent functionals but in addition yield very accurate ionization potentials and electron affinities. Moreover, atomization and total energies are found to be exceptionally accurate. Scaled σ-functionals are computationally highly efficient like their unscaled counterparts.

Improving the Accuracy of Modelling CO2 Electroreduction on Copper Using Many-Body Perturbation Theory.

Copper (Cu) remains the most important metal catalyst for the carbon dioxide reduction reaction (CO2 RR) into C2 products. Due to limited evidence from in situ experiments, mechanistic studies are often performed in the framework of density functional theory (DFT), using functionals at the generalized gradient approximation (GGA) level, which have fundamental difficulties to correctly describe CO adsorption and surface stability. We employ the adiabatic connection fluctuation dissipation theorem within the random phase approximation (RPA), in combination with the linearized Poisson-Boltzmann equation to describe solvation effects, to investigate the mechanism of CO2 RR on the Cu(100) facet. Qualitatively different from the DFT-GGA results, RPA results propose the formation of *OCCHO as the potential determining step towards C2 products. The results suggest that it is important to use more accurate methods like RPA when modeling reactions involving multiple CO-related species like CO2 RR.

Improving the Accuracy of Modelling CO2 Electroreduction on Copper Using Many‐Body Perturbation Theory

AbstractCopper (Cu) remains the most important metal catalyst for the carbon dioxide reduction reaction (CO2RR) into C2 products. Due to limited evidence from in situ experiments, mechanistic studies are often performed in the framework of density functional theory (DFT), using functionals at the generalized gradient approximation (GGA) level, which have fundamental difficulties to correctly describe CO adsorption and surface stability. We employ the adiabatic connection fluctuation dissipation theorem within the random phase approximation (RPA), in combination with the linearized Poisson–Boltzmann equation to describe solvation effects, to investigate the mechanism of CO2RR on the Cu(100) facet. Qualitatively different from the DFT‐GGA results, RPA results propose the formation of *OCCHO as the potential determining step towards C2 products. The results suggest that it is important to use more accurate methods like RPA when modeling reactions involving multiple CO‐related species like CO2RR.

Tension between predicting accurate ground state correlation energies and excitation energies from adiabatic approximations in TDDFT.

The connection between the adiabatic excitation energy of time-dependent density functional theory and the ground state correlation energy from the adiabatic connection fluctuation-dissipation theorem (ACFDT) is explored in the limiting case of one excited state. An exact expression is derived for any adiabatic Hartree-exchange-correlation kernel that connects the excitation energy and the potential contribution to correlation. The resulting formula is applied to the asymmetric Hubbard dimer, a system where this limit is exact. Results from a hierarchy of approximations to the kernel, including the random phase approximation (RPA) with and without exchange and the adiabatically exact (AE) approximation, are compared to the exact ones. At full coupling, the numerical results indicate a tension between predicting an accurate excitation energy and an accurate potential contribution to correlation. The AE approximation is capable of making accurate predictions of both quantities, but only in parts of the parameter space that classify as weakly correlated, while RPA tends to be unable to accurately predict these properties simultaneously anywhere. For a strongly correlated dimer, the AE approximation greatly overestimates the excitation energy yet continues to yield an accurate ground state correlation energy due to its accurate prediction of the adiabatic connection integrand. If similar trends hold for real systems, the development of correlation kernels will be important for applications of the ACFDT in systems with large potential contributions to correlation.

Scrutinizing GW-Based Methods Using the Hubbard Dimer.

Using the simple (symmetric) Hubbard dimer, we analyze some important features of the GW approximation. We show that the problem of the existence of multiple quasiparticle solutions in the (perturbative) one-shot GW method and its partially self-consistent version is solved by full self-consistency. We also analyze the neutral excitation spectrum using the Bethe-Salpeter equation (BSE) formalism within the standard GW approximation and find, in particular, that 1) some neutral excitation energies become complex when the electron-electron interaction U increases, which can be traced back to the approximate nature of the GW quasiparticle energies; 2) the BSE formalism yields accurate correlation energies over a wide range of U when the trace (or plasmon) formula is employed; 3) the trace formula is sensitive to the occurrence of complex excitation energies (especially singlet), while the expression obtained from the adiabatic-connection fluctuation-dissipation theorem (ACFDT) is more stable (yet less accurate); 4) the trace formula has the correct behavior for weak (i.e., small U) interaction, unlike the ACFDT expression.

Accurate total energies from the adiabatic-connection fluctuation-dissipation theorem

In the context of inhomogeneous one-dimensional finite systems, recent numerical advances [Phys. Rev. B 103, 125155 (2021)] allow us to compute the exact coupling-constant dependent exchange-correlation kernel $f^\lambda_\text{xc}(x,x',\omega)$ within linear response time-dependent density functional theory. This permits an improved understanding of ground-state total energies derived from the adiabatic-connection fluctuation-dissipation theorem (ACFDT). We consider both `one-shot' and `self-consistent' ACFDT calculations, and demonstrate that chemical accuracy is reliably preserved when the frequency dependence in the exact functional $f_\text{xc}[n](\omega=0)$ is neglected. This performance is understood on the grounds that the exact $f_\text{xc}[n]$ varies slowly over the most relevant $\omega$ range (but not in general), and hence the spatial structure in $f_\text{xc}[n](\omega=0)$ is able to largely remedy the principal issue in the present context: self-interaction (examined from the perspective of the exchange-correlation hole). Moreover, we find that the implicit orbitals contained within a self-consistent ACFDT calculation utilizing the adiabatic exact kernel $f_\text{xc}[n](\omega=0)$ are remarkably similar to the exact Kohn-Sham orbitals, thus further establishing that the majority of the physics required to capture the ground-state total energy resides in the spatial dependence of $f_\text{xc}[n]$ at $\omega = 0$.

Elastic and mechanical properties of aluminium and silicon carbide using density functional theory and beyond

For a long time and until now, there is still a lack of theoretical and experimental data on the third-order elastic constants, which limits the chance of producing new materials with targeted mechanical responses. For this purpose, we went back to the sixties (i.e., the year 1960 and after) to understand and improve these constants because they play a highly significant role in engineering. Applying density functional theory and for the first time with the adiabatic-connection fluctuation–dissipation theorem in the random phase approximation, we study the electronic, elastic, and mechanical properties of aluminium and silicon carbide. Our second-order elastic constants predictions give an extraordinary agreement with experimental data. In this framework, we investigate the mechanical properties such as Young’s modulus, Poisson’s ratio, bulk modulus, and shear modulus of diamond and silicon structures. Also, we visualize the three-dimensional plot, as well as two-dimensional for Young’s modulus, and others. For the third-order elastic constants, we show that we can be used our random phase approximation results as a reference to the place of experimental values.

Toward chemical accuracy at low computational cost: Density-functional theory with σ-functionals for the correlation energy.

We introduce new functionals for the Kohn-Sham correlation energy that are based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem and are named σ-functionals. Like in the well-established direct random phase approximation (dRPA), σ-functionals require as input exclusively eigenvalues σ of the frequency-dependent KS response function. In the new functionals, functions of σ replace the σ-dependent dRPA expression in the coupling-constant and frequency integrations contained in the ACFD theorem. We optimize σ-functionals with the help of reference sets for atomization, reaction, transition state, and non-covalent interaction energies. The optimized functionals are to be used in a post-self-consistent way using orbitals and eigenvalues from conventional Kohn-Sham calculations employing the exchange-correlation functional of Perdew, Burke, and Ernzerhof. The accuracy of the presented approach is much higher than that of dRPA methods and is comparable to that of high-level wave function methods. Reaction and transition state energies from σ-functionals exhibit accuracies close to 1 kcal/mol and thus approach chemical accuracy. For the 10 966 reactions of the W4-11RE reference set, the mean absolute deviation is 1.25 kcal/mol compared to 3.21 kcal/mol in the dRPA case. Non-covalent binding energies are accurate to a few tenths of a kcal/mol. The presented approach is highly efficient, and the post-self-consistent calculation of the total energy requires less computational time than a density-functional calculation with a hybrid functional and thus can be easily carried out routinely. σ-Functionals can be implemented in any existing dRPA code with negligible programming effort.

Potential Energy Surfaces without Unphysical Discontinuities: The Coulomb Hole Plus Screened Exchange Approach.

In this work, we show the advantages of using the Coulomb hole plus screened exchange (COHSEX) approach in the calculation of potential energy surfaces (PES). In particular, we demonstrate that, unlike perturbative GW and partial self-consistent GW approaches, such as eigenvalue self-consistent GW and quasi-particle (QP) self-consistent GW, the COHSEX approach yields smooth PES without irregularities and discontinuities. Moreover, we show that the ground-state PES obtained from the Bethe-Salpeter equation (BSE), within the adiabatic connection fluctuation dissipation theorem, built with QP energies obtained from perturbative COHSEX on top of Hartree-Fock (BSE@COHSEX@HF) yield very accurate results for diatomic molecules close to their equilibrium distance. When self-consistent COHSEX QP energies and orbitals are used to build the BSE equation, the results become independent of the starting point. We show that self-consistency worsens the total energies but improves the equilibrium distances with respect to BSE@COHSEX@HF. This is mainly due to the changes in the screening inside the BSE.

Elastic and mechanical properties of cubic diamond and silicon using density functional theory and the random phase approximation

The elastic constants play a central role in the regulation of the thermo-mechanical and anisotropic response of materials. Nevertheless, there is still a lack of theoretical and experimental data on these constants which limits the possibility of developing new materials with targeted mechanical responses. The elastic constants of diamond and silicon as second and third-order are obtained using density functional theory (LDA, GGA, and HSE) and for the first time with the adiabatic-connection fluctuation–dissipation theorem in the random phase approximation. Our SOECs calculations show an excellent agreement with experimental data. In this framework, we study the mechanical properties such as Young’s modulus, Poisson’s ratio, bulk modulus, and shear modulus of diamond and silicon structures. Also, we visualize the 3D plot, as well as 2D for Young’s modulus, Poisson’s ratio, and others. For the TOECs, we show that can be taken our RPA results as a reference, since there is still a lack of reliable previous theoretical and experimental data of these materials.

Pros and Cons of the Bethe-Salpeter Formalism for Ground-State Energies.

The combination of the many-body Green's function GW approximation and the Bethe-Salpeter equation (BSE) formalism has shown to be a promising alternative to time-dependent density functional theory (TD-DFT) for computing vertical transition energies and oscillator strengths in molecular systems. The BSE formalism can also be employed to compute ground-state correlation energies thanks to the adiabatic-connection fluctuation-dissipation theorem (ACFDT). Here, we study the topology of the ground-state potential energy surfaces (PESs) of several diatomic molecules near their equilibrium bond length. Using comparisons with state-of-art computational approaches (CC3), we show that ACFDT@BSE is surprisingly accurate and can even compete with lower-order coupled cluster methods (CC2 and CCSD) in terms of total energies and equilibrium bond distances for the considered systems. However, we sometimes observe unphysical irregularities on the ground-state PES in relation with difficulties in the identification of a few GW quasiparticle energies.

Analytic energy gradients for the exact exchange Kohn-Sham method.

Analytic energy gradients with respect to nuclear coordinates for an exact exchange-only (EXX) Kohn-Sham method are presented. In the underlying EXX method, the exact exchange potential is obtained as the electrostatic potential of an exchange charge density, which is determined via the optimized effective potential method. Parts of the presented calculation of analytic EXX energy gradients can be reused for analytic energy gradients in self-consistent Kohn-Sham methods treating correlation via the adiabatic-connection fluctuation-dissipation theorem, e.g., methods relying on the random phase approximation. A version of the analytic EXX energy gradients that uses density-fitting is shown to be highly efficient. The accuracy of the analytic energy gradients is tested by comparison with numerically calculated gradients.

Semiempirical van der Waals method for two-dimensional materials with incorporated dielectric functions

A density functional theory based semiempirical van der Waals (vdW) method with dielectric functions being incorporated is developed for two-dimensional materials. The coefficients of interatomic pairwise potentials are derived from atomic polarizabilities obtained via a Clausius-Mossotti relation dedicated for layered crystals. The method not only can efficiently describe the dispersion energy for a range of planar graphene-like materials at nearly the same accuracy as the adiabatic connection fluctuation-dissipation theorem, but also rationalizes experimentally measured relative interfacial strengths of heterostructures and interlayer registry of hexagonal boron nitride that have plagued other vdW methods.

Lieb-Oxford bound and pair correlation functions for density-functional methods based on the adiabatic-connection fluctuation-dissipation theorem.

Compliance with the Lieb-Oxford bound for the indirect Coulomb energy and for the exchange-correlation energy is investigated for a number of density-functional methods based on the adiabatic-connection fluctuation-dissipation (ACFD) theorem to treat correlation. Furthermore, the correlation contribution to the pair density resulting from these methods is compared with highly accurate reference values for the helium atom and for the hydrogen molecule at several bond distances. For molecules, the Lieb-Oxford bound is obeyed by all considered methods. For the homogeneous electron gas, it is violated by all methods for low electron densities. The simplest considered ACFD method, the direct random phase approximation (dRPA), violates the Lieb-Oxford bound much earlier than more advanced ACFD methods that, in addition to the simple Hartree kernel, take into account the exchange kernel and an approximate correlation kernel in the calculation of the correlation energy. While the dRPA yields quite poor correlation contributions to the pair density, those from more advanced ACFD methods are physically reasonable but still leave room for improvements, particularly in the case of the stretched hydrogen molecule.