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

Assessment of quality and reliability of band structures from exact-exchange-only Kohn-Sham, hybrid, and GW methods - Trushin, Egor; Görling, Andreas (European Physical Journal B, 2018)
Band gaps for a large number of semiconductors obtained with the exact-exchange(EXX)-only Kohn-Sham method are compared to those from various generalized Kohn-Sham methods based on hybrid functionals and with experimental values. EXX band gaps are shown to be of superior quality than the band gaps from most of the considered hybrid methods, band gaps obtained with the hybrid functional HSE06 have a similar quality as EXX ones. The EXX method is found to yield d-electron binding energies that are clearly superior to those determined within the local density approximation and to be comparable to d-electron binding energies from GW approaches. EXX plane-wave pseudopotential calculations and EXX all-electron calculations are shown to yield very similar KS transition energies demonstrating that the plane-wave pseudopotential approach is well-suited for EXX methods. Previous discrepancies between pseudopotential and all-electron calculations, most likely, have to be attributed to technical problems in early all-electron EXX calculations.

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

Assessment of the exact-exchange-only Kohn-Sham method for the calculation of band structures for transition metal oxide and metal halide perovskites - Trushin, Egor; Fromm, Lukas; Görling, Andreas (Physical Review B, 2019)
In the present paper we assess the performance of the exact-exchange-only (EXX) Kohn-Sham method to predict band structures of transition metal oxide and metal halide perovskites with the main emphasis on band gaps. For the considered set of prototypical systems with cubic structure, the performance of the EXX method for the prediction of band gaps is comparable with other popular methods for this purpose like density-functional calculations with the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional and one-shot GW (G(0)W(0)). Comparison with experimental values suggests that in the case of perovskites the EXX method, like HSE and GW methods, should be supplemented by a treatment of electron-phonon effects. The EXX method is computationally more efficient than G(0)W(0) and also provides post-self-consistent access to one-electron wave functions and band structures within the complete Brillouin zone with much lower computational effort than both G(0)W(0) and hybrid DFT methods. We confirm the importance of including the higher-lying semicore shells within the explicitly treated states for halide perovskites which was already noted by earlier studies. Calculations taking into account only the valence space without the semicore states, however, remain still a reasonable option in practice. Spin-orbit coupling effects seem to be slightly underestimated in DFT calculations both with respect to GW and experiment. The source of this underestimation can be of both technical and formal nature, and this point requires more critical consideration. For CH3NH3PbI3, sizable Rashba spin splittings appear for the structure with the C-N bond of the methylammonium ion not lying along the long diagonal of the cubic unit cell.
CRIS-Team WoS Importer:2019-09-10

Band gaps, ionization potentials, and electron affinities of periodic electron systems via the adiabatic-connection fluctuation-dissipation theorem - Trushin, Egor; Betzinger, Markus; Bluegel, Stefan; Görling, Andreas (Physical Review B - Condensed Matter and Materials Physics, 2016)
An approach to calculate fundamental band gaps, ionization energies, and electron affinities of periodic electron systems is explored. Starting from total energies obtained with the help of the adiabatic-connection fluctuation-dissipation (ACFD) theorem, these physical observables are calculated according to their basic definition by differences of the total energies of the N-, (N-1)-, and (N+1)-electron system. The response functions entering the ACFD theorem are approximated here by the direct random phase approximation (dRPA). For a set of prototypical semiconductors and insulators it is shown that even with this quite drastic approximation the resulting band gaps are very close to experiment and of a similar quality to those from the computationally more involved GW approximation. By going beyond the dRPA in the future the accuracy of the calculated band gaps may be significantly improved further.

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

First-Principles Calculation of Triplet Exciton Diffusion in Crystalline Poly(p-phenylene vinylene) - Lyskov, Igor; Trushin, Egor; Baragiola, Ben Q.; Schmidt, Timothy W.; Cole, Jared H.; Russo, Salvy P. (Journal of Physical Chemistry C, 2019)
In this article, we present multiscale modeling of triplet exciton energy migrating through the archetypical poly(p-phenylene vinylene) (PPV) polymer in the crystal phase. We combine electronic structure calculations with coupled exciton-nuclear quantum dynamics in order to parameterize exciton evolution in J-A nd H-aggregate configurations. We then apply this parameterization to a master-equation approach to describe transport at the nanoscale. We find that triplet transport is characterized by two remarkably different components: A fast and coherent intrachain and a slow and incoherent interchain. Energy migration along the polymer backbone is accompanied by coherent superpositions developing between neighboring sites in the first 20 fs; however, no interchain coherence develops. The nonequilibrium exciton density exhibits an initial ultrafast ballistic spread followed by normal diffusive propagation. At room temperature, the diffusion coefficients along the respective interchain axes are found to be Da = 2.48 × 10-2 cm2 s-1, Db = 4.18 × 10-2 cm2 s-1, and Dc = 3.03 cm2 s-1 along the fast axis. ©
CRIS-Team Scopus Importer:2019-11-19

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

Improving Exchange-Correlation Potentials of Standard Density Functionals with the Optimized-Effective-Potential Method for Higher Accuracy of Excitation Energies - Trushin, Egor; Görling, Andreas (Journal of Chemical Theory and Computation, 2025)
We present a general scheme to improve the exchange-correlation potential of standard Kohn-Sham methods, like the PBE (Perdew, Burke, Ernzerhof) or PBE0 method, by enforcing exact conditions the exchange-correlation potential has to obey during their calculation. The required modifications of the potentials are enabled by generating the potentials within the optimized-effective-potential (OEP) framework instead of directly taking the functional derivative with respect to the electron density on a real-space grid as usual. We generalize a condition for the exact exchange potential that involves the eigenvalues of the highest occupied molecular orbital such that it is applicable to arbitrary approximate exchange potentials. The new approach yields strongly improved exchange-correlation potentials which lead to qualitatively and quantitatively improved KS orbital and eigenvalue spectra containing a Rydberg series as required and obeying much better the Kohn-Sham ionization energy theorem. If the resulting orbitals and eigenvalues are used as input quantities in time-dependent density-functional theory (TDDFT) to calculate excitation energies then the accuracy of the latter is drastically improved, e.g., for TDDFT with the PBE functional the accuracy of excitation energies is improved by a factor of roughly three. This make the introduced approach highly attractive for generating input orbitals and eigenvalues for TDDFT but potentially also for high-rung correlation functionals that are typically evaluated in a post-SCF (post self-consistent-field) manner. We apply the new approach to calculate exchange-correlation potentials to the PBE and PBE0 functionals but the approach is generally applicable to any functional.
CRIS-Team Scopus Importer:2025-02-14

Kohn-Sham inversion for open-shell systems - Erhard, Jannis; Trushin, Egor; Görling, Andreas (Journal of Chemical Physics, 2025)
Methods based on density-functional theory usually treat open-shell atoms and molecules within the spin-unrestricted Kohn-Sham (KS) formalism, which breaks symmetries in real and spin space. Symmetry breaking is possible because the KS Hamiltonian operator does not need to exhibit the full symmetry of the physical Hamiltonian operator, but only the symmetry of the spin density, which is generally lower. Symmetry breaking leads to spin contamination and prevents a proper classification of the KS wave function with respect to the symmetries of the physical electron system. Formally well-justified variants of the KS formalism that restore symmetries in real space, in spin space, or in both have been introduced long ago, but have rarely been used in practice. Here, we introduce numerically stable KS inversion methods to construct reference KS potentials from reference spin-densities for all four possibilities to treat open shell systems, non-symmetrized, spin-symmetrized, space-symmetrized, and fully-symmetrized. The reference spin-densities are obtained by full configuration interaction and high-level coupled cluster methods for the considered atoms and diatomic molecules. The decomposition of the total energy in contributions such as the non-interacting kinetic, the exchange, and the correlation energy is different in the four KS formalisms. Reference values for these differences are provided for the considered atoms and molecules. All KS inversions, except the fully symmetrized one, lead in some cases to solutions violating the Aufbau principle. In the purely spin-symmetrized KS formalism, this represents a violation of the KS v-representability condition, i.e., no proper KS wave functions exist in those cases.
CRIS-Team Scopus Importer:2025-01-31

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.

Numerically stable inversion approach to construct Kohn-Sham potentials for given electron densities within a Gaussian basis set framework - Erhard, Jannis; Trushin, Egor; Görling, Andreas (Journal of Chemical Physics, 2022)
We present a Kohn-Sham (KS) inversion approach to construct KS exchange-correlation potentials corresponding to given electron densities. This method is based on an iterative procedure using linear response to update potentials. All involved quantities, i.e., orbitals, potentials, and response functions, are represented by Gaussian basis functions. In contrast to previous KS inversion methods relying on Gaussian basis sets, the method presented here is numerically stable even for standard basis sets from basis set libraries due to a preprocessing of the auxiliary basis used to represent an exchange-correlation charge density that generates the exchange-correlation potential. The new KS inversion method is applied to reference densities of various atoms and molecules obtained by full configuration interaction or CCSD(T) (coupled cluster singles doubles perturbative triples). The considered examples encompass cases known to be difficult, such as stretched hydrogen or lithium hydride molecules or the beryllium isoelectronic series. For the stretched hydrogen molecule, potentials of benchmark quality are obtained by employing large basis sets. For the carbon monoxide molecule, we show that the correlation potential from the random phase approximation (RPA) is in excellent qualitative and quantitative agreement with the correlation potential from the KS inversion of a CCSD(T) reference density. This indicates that RPA correlation potentials, in contrast to those from semi-local density-functionals, resemble the exact correlation potential. Besides providing exchange-correlation potentials for benchmark purposes, the proposed KS inversion method may be used in density-partition-based quantum embedding and in subsystem density-functional methods because it combines numerical stability with computational efficiency.
CRIS-Team Scopus Importer:2022-06-10

Numerically stable optimized effective potential method with standard Gaussian basis sets - Trushin, Egor; Görling, Andreas (Journal of Chemical Physics, 2021)
We present a numerically stable optimized effective potential (OEP) method based on Gaussian basis sets. The key point of the approach is a sequence of preprocessing steps of the auxiliary basis set used to represent exchange or correlation potentials, the Kohn-Sham (KS) response function, and the right-hand side of the OEP equation in conjunction with a representation of exchange or correlation potentials via exchange or correlation charge densities whose electrostatic potentials generate the potentials. Due to the preprocessing, standard Gaussian basis sets from basis set libraries can be used in OEP calculations. As examples, we present numerical stable computational setups based on aux-cc-pwCVXZ basis sets with X = T, Q, 5 for the orbitals and aux-cc-pVDZ/mp2fit and aux-cc-pVTZ/mp2fit auxiliary basis sets and use them to calculate KS exchange potentials with the exact exchange-only KS method for various atoms and molecules. The resulting exchange potentials not only are numerically stable and physically reasonable but also show convergence with increasing quality of the orbital basis sets. The effect of incorporating exact conditions that the KS exchange potential has to obey is discussed. Moreover, it is briefly demonstrated that the presented approach not only works for KS exchange potentials but equally well for correlation potentials within the direct random phase approximation. Besides for OEP methods, the introduced preprocessing of auxiliary basis sets should also be beneficial in procedures to calculate back effective KS potentials from given electron densities.
CRIS-Team Scopus Importer:2021-08-13

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

Spin-current density-functional theory for a correct treatment of spin-orbit interactions and its application to topological phase transitions - Trushin, Egor; Görling, Andreas (Physical Review B, 2018)
Spin-orbit interactions often are taken into account via pseudopotentials or related treatments of core electrons. In this case, the commonly employed Kohn-Sham methods with noncollinear spin are not applicable from a formal point of view. Instead, more general methods in the framework of spin-current density-functional theory (SCDFT) have to be employed. Here, we first review the derivation of SCDFT as a unifying theory that encompasses density-functional theory (DFT) with noncollinear spin, current DFT, and a DFT treatment of currents of the spin. We discuss which parts of SCDFT necessarily have to be taken into account in which physical situation and which parts can be considered on an optional basis. Then, an exact-exchange-only (EXX) SCDFT method (SCEXX) is used to investigate pressure-driven topological phase transition in SnTe and AlBi as representative systems. An estimate of the effect of correlation is obtained by a screening of exchange in the EXX methods. SnTe undergoes a transition from a trivial to a topological insulator, while AlBi is transformed from a topological metal with inverted band edges to a trivial insulator. We show that there is a sizable range of lattice parameters for which electronic structures obtained with noncollinear spin EXX (NCSEXX) and SCEXX belong to different topological classes. Thus, differences between results obtained with NCSEXX and SCEXX, which are due to the consideration of spin currents in SCEXX, are of practical importance in situations when a material simultaneously is characterized by strong spin-orbit interactions and a band ordering governed by small energy differences, e.g., narrow band gaps in semiconductors or small negative gaps in metals with inverted band edges. This is a typical situation for topological materials suggesting to use SCDFT methods for such materials.

The Nature of One-Dimensional Carbon: Polyynic versus Cumulenic - Neiß, Christian; Trushin, Egor; Görling, Andreas (ChemPhysChem, 2014)
A question of both fundamental as well as practical importance is the nature of one-dimensional carbon, in particular whether a one-dimensional carbon allotrope is polyynic or cumulenic, that is, whether bond-length alternation occurs or not. By combining the concept of aromaticity and antiaromaticity with the rule of Peierls distortion, the occurrence and magnitude of bond-length alternation in carbon chains with periodic boundary conditions and corresponding carbon rings as a function of the chain or ring length can be explained. The electronic properties of one-dimensional carbon depend crucially on the bond-length alternation. Whereas it is generally accepted that carbon chains in the limit of infinite length have a polyynic structure at the minimum of the potential energy surface with bond-length alternation, we show here that zero-point vibrations lead to an effective equalization of all carboncarbon bond lengths and thus to a cumulenic structure.
Keywords: bond-length alternation; carbynes; cumulenes; density functional calculations; polyynes

Topological Phase Transitions in Zinc-Blende Semimetals Driven Exclusively by Electronic Temperature - Trushin, Egor; Görling, Andreas (Physical Review Letters, 2018)
We show that electronic phase transitions in zinc-blende semimetals with quadratic band touching (QBT) at the center of the Brillouin zone, like GaBi, InBi, or HgTe, can occur exclusively due to a change of the electronic temperature without the need to involve structural transformations or electron-phonon coupling. The commonly used Kohn-Sham density-functional methods based on local and semilocal density functionals employing the local density approximation (LDA) or generalized gradient approximations (GGAs), however, are not capable of describing such phenomena because they lack an intrinsic temperature dependence and account for temperature only via the occupation of bands, which essentially leads only to a shift of the Fermi level without changing the shape or topology of bands. Kohn-Sham methods using the exact temperature-dependent exchange potential, not to be confused with the Hartree-Fock exchange potential, on the other hand, describe such phase transitions. A simple modeling of correlation effects can be achieved by screening of the exchange. In the considered zinc-blende compounds the QBT is unstable at low temperatures and a transition to electronic states without QBT takes place. In the case of HgTe and GaBi Weyl points of type I and type II, respectively, emerge during the transitions. This demonstrates that Kohn-Sham methods can describe such topological phase transitions provided they are based on functionals more accurate than those within the LDA or GGA. Moreover, the electronic temperature is identified as a handle to tune topological materials.

Toward chemical accuracy at low computational cost: Density-functional theory with σ-functionals for the correlation energy - Trushin, Egor; Thierbach, Adrian; Görling, Andreas (Journal of Chemical Physics, 2021)
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.
CRIS-Team Scopus Importer:2021-01-22

Understanding band gaps of solids in generalized Kohn-Sham theory - Perdew, John P.; Yang, Weitao; Burke, Kieron; Yang, Zenghui; Gross, Eberhard K. U.; Scheffler, Matthias; Scuseria, Gustavo E.; Henderson, Thomas M.; Zhang, Igor Ying; Ruzsinszky, Adrienn; Peng, Haowei; Sun, Jianwei; et al. (Proceedings of the National Academy of Sciences of the United States of America, 2017)
The fundamental energy gap of a periodic solid distinguishes insulators from metals and characterizes low-energy single-electron excitations. However, the gap in the band structure of the exact multiplicative Kohn-Sham (KS) potential substantially underestimates the fundamental gap, a major limitation of KS densityfunctional theory. Here, we give a simple proof of a theorem: In generalized KS theory (GKS), the band gap of an extended system equals the fundamental gap for the approximate functional if the GKS potential operator is continuous and the density change is delocalized when an electron or hole is added. Our theorem explains how GKS band gaps from metageneralized gradient approximations (meta-GGAs) and hybrid functionals can be more realistic than those from GGAs or even from the exact KS potential. The theorem also follows from earlier work. The band edges in the GKS one-electron spectrum are also related to measurable energies. A linear chain of hydrogen molecules, solid aluminum arsenide, and solid argon provide numerical illustrations.
Keywords: Band gaps; Density-functional theory; Generalized Kohn-Sham theory; Kohn-Sham theory; Solids

Violations of the v -representability condition underlying Kohn-Sham density-functional theory - Trushin, Egor; Erhard, Jannis; Görling, Andreas (Physical Review A, 2024)
Electronic structure methods based on the Kohn-Sham (KS) formalism of density-functional theory are ubiquitously and highly successfully used in physics, chemistry, and materials science. Whether the KS formalism is universally applicable is, however, an open question because it is not known whether a KS model system exists for all physical electron systems. This is the question of whether electron densities of real physical systems are always noninteracting v-representable. Here we give indications that this is not always the case. To that end, we calculated highly accurate electron densities of first and second row atoms with a partially filled p shell by high-level quantum chemistry methods and by full configuration interaction and then tried to determine the effective KS potential by KS inversion. Except for nitrogen and phosphorus this was only possible for an occupation pattern violating the Aufbau principle. This means that the resulting wave function is not a ground state of the KS Hamiltonian operator and therefore not a valid KS wave function, which indicates that the KS formalism is not always applicable. Strategies to avoid the presented v-representability problem are discussed.
CRIS-Team Scopus Importer:2024-08-16