Accurate Correlation Potentials from the Self-Consistent Random Phase Approximation - Trushin, Egor; Fauser, Steffen; Mölkner, Andreas; Erhard, Jannis; Görling, Andreas (Physical Review Letters, 2025)
Density-functional theory (DFT) within the Kohn-Sham (KS) formalism is the most widely used approach to treat electronic structures of molecules and solids in physics, chemistry, and materials science, and the development of more accurate functionals for the KS exchange and correlation energy has been a major research focus for decades. The corresponding exchange and correlation potentials, on the other hand, have attracted little attention. Those cases for which reference potentials are available showed that in particular correlation potentials from common approximate density functionals are of poor quality and sometimes have little in common with the exact potentials. This hampers the further development of KS-DFT. Here, we show that highly accurate correlation potentials can be obtained within the random phase approximation (RPA). In conjunction with the exact exchange potential, which, like the RPA correlation potential, is accessible within the optimized effective potential method, highly accurate exchange-correlation potentials are available and provide a basis for the further development of DFT. We present a numerically stable approach for efficiently carrying out self-consistent RPA calculations and combine it with a KS inversion method to obtain reference correlation potentials from highly accurate electron densities from coupled cluster calculations. Accurate exchange-correlation potentials have to yield KS eigenvalues for the highest occupied molecular orbital that are close to the negative of the ionization potential. This is indeed the case, the RPA highest occupied molecular orbital eigenvalues yield ionization potentials that can compete with GW ionization potentials.
CRIS-Team Scopus Importer:2025-02-28

Accurate NMR Shieldings with σ-Functionals - Fauser, Steffen; Drontschenko, Viktoria; Ochsenfeld, Christian; Görling, Andreas (Journal of Chemical Theory and Computation, 2024)
In recent years, density-functional methods relying on a new type of fifth-rung correlation functionals called σ-functionals have been introduced. σ-Functionals are technically closely related to the random phase approximation and require the same computational effort but yield distinctively higher accuracies for reaction and transition state energies of main group chemistry and even outperform double-hybrid functionals for these energies. In this work, we systematically investigate how accurate σ-functionals can describe nuclear magnetic resonance (NMR) shieldings. It turns out that σ-functionals yield very accurate NMR shieldings, even though in their optimization, exclusively, energies are employed as reference data and response properties such as NMR shieldings are not involved at all. This shows that σ-functionals combine universal applicability with accuracy. Indeed, the NMR shieldings from a σ-functional using input orbitals and eigenvalues from Kohn-Sham calculations with the exchange-correlation functional of Perdew, Burke and Ernzerhof (PBE) turned out to be the most accurate ones among the NMR shieldings calculated with various density-functional methods including methods using double-hybrid functionals. That σ-functionals can be used for calculating both reliable energies and response properties like NMR shieldings characterizes them as all-purpose functionals, which is appealing from an application point of view.
CRIS-Team Scopus Importer:2024-07-19

Assessment of RPA and σ-functional methods for the calculation of dipole moments and static polarizabilities and hyperpolarizabilities - Mandalia, Raviraj; Fauser, Steffen; Trushin, Egor; Görling, Andreas (Journal of Chemical Physics, 2025)
In the present paper, we assess the performance of methods based on the random phase approximation (RPA) and on σ-functionals for predicting static optical properties, i.e., dipole moment, polarizability, and first and second hyperpolarizability, of small- and medium-sized molecules, including chain-like systems. First, we provide accurate reference data by coupled-cluster singles, doubles, with perturbative triples calculations with sufficiently large basis sets. The RPA and σ-functional calculations are carried out post-self-consistently using input orbitals and eigenvalues from the hybrid density-functional calculation. The optimal fraction of exact non-local exchange in these calculations is found to be quite high, around 0.5-0.6 in RPA and around 0.8-1.0 in σ-functional methods. σ-functional methods, however, proved to be less sensitive than RPA methods with respect to the amount of exact non-local exchange used in the generation of their input data. σ-functional methods are shown to outperform in accuracy RPA methods and various other considered density-functional theory methods for static optical properties and, thus, are well-suited for the calculation of linear and non-linear optical properties.
CRIS-Team Scopus Importer:2025-05-23

Basis Set Requirements of σ-Functionals for Gaussian- and Slater-Type Basis Functions and Comparison with Range-Separated Hybrid and Double Hybrid Functionals - Fauser, Steffen; Förster, Arno; Redeker, Leon; Neiß, Christian; Erhard, Jannis; Trushin, Egor; Görling, Andreas (Journal of Chemical Theory and Computation, 2024)
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.
CRIS-Team Scopus Importer:2024-04-05
Keywords: Basis sets; Chemical calculations; Electrical energy; Energy; Quality management

Chemical accuracy with σ-functionals for the Kohn-Sham correlation energy optimized for different input orbitals and eigenvalues - Fauser, Steffen; Trushin, Egor; Neiß, Christian; Görling, Andreas (Journal of Chemical Physics, 2021)
Recently, a new type of orbital-dependent functional for the Kohn-Sham (KS) correlation energy, σ-functionals, was introduced. Technically, σ-functionals are closely related to the well-known direct random phase approximation (dRPA). Within the dRPA, a function of the eigenvalues σ of the frequency-dependent KS response function is integrated over purely imaginary frequencies. In σ-functionals, this function is replaced by one that is optimized with respect to reference sets of atomization, reaction, transition state, and non-covalent interaction energies. The previously introduced σ-functional uses input orbitals and eigenvalues from KS calculations with the generalized gradient approximation (GGA) exchange-correlation functional of Perdew, Burke, and Ernzerhof (PBE). Here, σ-functionals using input orbitals and eigenvalues from the meta-GGA TPSS and the hybrid-functionals PBE0 and B3LYP are presented and tested. The number of reference sets taken into account in the optimization of the σ-functionals is larger than in the first PBE based σ-functional and includes sets with 3d-transition metal compounds. Therefore, also a reparameterized PBE based σ-functional is introduced. The σ-functionals based on PBE0 and B3LYP orbitals and eigenvalues reach chemical accuracy for main group chemistry. For the 10 966 reactions from the highly accurate W4-11RE reference set, the B3LYP based σ-functional exhibits a mean average deviation of 1.03 kcal/mol compared to 1.08 kcal/mol for the coupled cluster singles doubles perturbative triples method if the same valence quadruple zeta basis set is used. For 3d-transition metal chemistry, accuracies of about 2 kcal/mol are reached. The computational effort for the post-self-consistent evaluation of the σ-functional is lower than that of a preceding PBE0 or B3LYP calculation for typical systems.
CRIS-Team Scopus Importer:2021-10-22

Effects of isotope and chemical incoherence on self-diffusion of atoms in liquid alloys of gallium with isotopes of nickel: Experiments based on quasielastic neutron scattering versus molecular dynamics simulations - Goychuk, Igor; Panchenko, Artem; Shahzad, Anjum; Fauser, Steffen; Neiß, Christian; Götz, Klaus; Vogel, Carola; Weißer, Matthias; Hakim, Bishoy; Embs, Jan Peter; Englhard, Jonas; Bachmann, Julien; et al. (Physical Review B, 2025)
Quasielastic neutron scattering (QENS) is a powerful experimental technique to investigate the diffusion of atoms in liquids. It relies on the fact that at low 𝑄 values essentially only incoherent scattering is observed from the diffusing atoms. In the case of alloys composed of two chemical elements, it is commonly believed that at low 𝑄 QENS mainly probes the self-diffusion of the element with a nonzero incoherent scattering cross-section, while the element with a zero incoherent scattering cross-section does not contribute. However, the findings of this study challenge this belief. The study examines alloys of natural gallium (which has a nonzero incoherent scattering cross-section) and isotopes 58 Ni and 60 Ni (both of which have a zero incoherent scattering cross-section). A crucial factor to consider here is chemical incoherence, which typically leads to the renormalization of the incoherent cross-sections of different chemical elements within a mixture. Unfortunately, this renormalization is often disregarded in an ad hoc manner. Significantly, the alloy containing 58 Ni shows a notable renormalization, scattering incoherently to a similar degree as natural nickel in a comparable alloy with equivalent concentrations of chemical elements. Similarly perplexing, natural nickel scatters with great intensity despite being predominantly composed of 58 Ni and 60 Ni (around 94% of the total). This behavior can be attributed to the accepted phenomenon of isotope incoherence. We calculate the integral diffusion coefficients of Ga and Ni atoms in various liquid alloys from QENS experiments. These values are then compared to the results obtained from corresponding molecular dynamics simulations conducted at various temperatures, taking into account chemical incoherence. The comparison shows good agreement within the range of errors for the Ga1−𝑥⁢ 58Ni𝑥 alloy at two concentrations (𝑥=0.02 and 𝑥=0.1). The agreement also partially holds for the Ga1−𝑥⁢Ni𝑥 alloy with natural nickel and for the Ga1−𝑥⁢ 60Ni𝑥 alloy, despite certain difficulties discusse
CRIS-Team Scopus Importer:2025-02-17
Keywords: Diffusion; Alloys; Liquid metals; Ab initio molecular dynamics; Molecular dynamics; Neutron scattering

Geometries and vibrational frequencies with Kohn-Sham methods using σ -functionals for the correlation energy - Neiß, Christian; Fauser, Steffen; Görling, Andreas (Journal of Chemical Physics, 2023)
Recently, Kohn-Sham (KS) methods with new correlation functionals, called σ-functionals, have been introduced. Technically, σ-functionals are closely related to the well-known random phase approximation (RPA); formally, σ-functionals are rooted in perturbation theory along the adiabatic connection. If employed in a post-self-consistent field manner in a Gaussian basis set framework, then, σ-functional methods are computationally very efficient. Moreover, for main group chemistry, σ-functionals are highly accurate and can compete with high-level wave-function methods. For reaction and transition state energies, e.g., chemical accuracy of 1 kcal/mol is reached. Here, we show how to calculate first derivatives of the total energy with respect to nuclear coordinates for methods using σ-functionals and then carry out geometry optimizations for test sets of main group molecules, transition metal compounds, and non-covalently bonded systems. For main group molecules, we additionally calculate vibrational frequencies. σ-Functional methods are found to yield very accurate geometries and vibrational frequencies for main group molecules superior not only to those from conventional KS methods but also to those from RPA methods. For geometries of transition metal compounds, not surprisingly, best geometries are found for RPA methods, while σ-functional methods yield somewhat less good results. This is attributed to the fact that in the optimization of σ-functionals, transition metal compounds could not be represented well due to the lack of reliable reference data. For non-covalently bonded systems, σ-functionals yield geometries of the same quality as the RPA or as conventional KS schemes combined with dispersion corrections.
CRIS-Team Scopus Importer:2023-02-10

Highly precise values for the energy ratios underlying the Lieb-Oxford bound and the convexity conjecture for the adiabatic connection - Fauser, Steffen; Trushin, Egor; Görling, Andreas (Journal of Chemical Physics, 2025)
The response function Kohn-Sham (KS) inversion method is employed to a set of 67 atoms and molecules to access the kinetic and potential energy contributions to the correlation energy, as well as the correlation energy itself. We use these energy contributions to compute highly reliable and accurate reference values for the energy ratios underlying the Lieb-Oxford bound and the convexity conjecture for the adiabatic connection. Commonly used approximate exchange-correlation functionals that go beyond the local density approximation lead to values for the energy ratios that agree surprisingly well with the calculated reference data. The largest value for the energy ratio corresponding to the Lieb-Oxford bound observed for the considered systems is 1.4024, which is well below the estimate of 1.9554 ≤ λ L O ≤ 2.1346 for the Lieb-Oxford bound. The convexity conjecture for the adiabatic connection is not violated for any of the considered systems. We show that the numerical errors of the employed response function KS inversion method using Gaussian basis sets can be kept almost negligibly small by choosing an appropriate computational setup. The KS inversion method, furthermore, requires only moderate computational effort and, therefore, is well-suited to calculate reference data for various quantities of interest in Kohn-Sham density-functional theory for large numbers of molecules.
CRIS-Team Scopus Importer:2025-05-09

Lieb-Oxford bound and pair correlation functions for density-functional methods based on the adiabatic-connection fluctuation-dissipation theorem - Erhard, Jannis; Fauser, Steffen; Moerman, Evgeny; Kalaß, Simon; Trushin, Egor; Görling, Andreas (Faraday Discussions, 2020)
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.

Scaled σ -functionals for the Kohn-Sham correlation energy with scaling functions from the homogeneous electron gas - Erhard, Jannis; Fauser, Steffen; Trushin, Egor; Görling, Andreas (Journal of Chemical Physics, 2022)
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.
CRIS-Team Scopus Importer:2022-09-30