Standard Kohn-Sham Density Functional Theory Research Articles

Variational Pair-Density Functional Theory: Dealing with Strong Correlation at the Protein Scale.

Multiconfigurational pair-density functional theory (MC-PDFT) offers a promising solution to the challenges faced by traditional density functional theory (DFT) in addressing molecular systems containing transition metals, open-shells, or strong correlations in general. By utilizing both the density and on-top pair-density, MC-PDFT can make use of a more flexible multiconfigurational wave function to capture the necessary static correlation, while the pair-density functional also includes the effect of dynamic correlation. So far, MC-PDFT has been used after a multiconfigurational self-consistent field (MCSCF) step, using the orbitals and configuration interaction coefficients from the converged MCSCF wave function to compute PDFT energies and properties. Here, instead, we propose to perform a direct optimization of the wave function using the pair-density functionals, resulting in a variational formulation of MC-PDFT. We derive the expressions for the wave function gradient and illustrate their similarity to standard MCSCF equations. Furthermore, we illustrate the accuracy on a set of singlet-triplet gaps as well as dissociation curves. Our findings highlight one of MC-PDFT's standout features: a reduced dependency on the active space size compared to conventional multiconfigurational wave function methodologies. Additionally, we show that the computational cost of MC-PDFT is potentially lower than MCSCF and often on-par with standard Kohn-Sham DFT, which is demonstrated by performing a MC-PDFT calculation of the entire ferredoxin protein with 1447 atoms and nearly 12000 basis functions.

Computational Investigation of the Spin-Density Asymmetry in Photosynthetic Reaction Center Models from First Principles.

We present a computational analysis of the spin-density asymmetry in cation radical states of reaction center models from photosystem I, photosystem II, and bacteria from Synechococcus elongatus, Thermococcus vulcanus, and Rhodobacter sphaeroides, respectively. The recently developed frozen-density embedding (FDE)-diab methodology [J. Chem. Phys., 2018, 148, 214104] allowed us to effectively avoid the spin-density overdelocalization error characteristic for the standard Kohn-Sham density functional theory and to reliably calculate spin-density distributions and electronic couplings for a number of molecular systems ranging from inner pairs of (bacterio)chlorophyll a molecules in vacuum to large proteins including up to about 2000 atoms. The calculated spin densities show a good agreement with available experimental results and were used to validate reaction center models reported in the literature. Here, we demonstrate that the applied theoretical approach is very sensitive to changes in molecular structures and the relative orientation of molecules. This makes FDE-diab a valuable tool for electronic structure calculations of large photosynthetic models effectively complementing the existing experimental techniques.

Communication: Becke's virial exciton model gives accurate charge-transfer excitation energies.

First singlet (S1) excitations are of primary importance in the photoluminescence spectra of organic chromophores. However, due to the multi-determinantal nature of the singlet excited states, standard Kohn-Sham density-functional theory (DFT) is not applicable. While linear-response time-dependent DFT is the method of choice for the computation of excitation energies, it fails severely for excitations with charge-transfer character. Becke's recent virial exciton model [A. D. Becke, J. Chem. Phys. 148, 044112 (2018)] offers a promising solution to employ standard DFT for calculation of the S1 excitation energy in molecular systems. Here, it is shown that the virial exciton model is free of charge-transfer error. It is equally reliable for S1 excitations with significant charge-transfer character as for other classes of transitions.

Towards the blackbox computation of magnetic exchange coupling parameters in polynuclear transition-metal complexes: Theory, implementation, and application

We present a method for calculating magnetic coupling parameters from a single spin-configuration via analytic derivatives of the electronic energy with respect to the local spin direction. This method does not introduce new approximations beyond those found in the Heisenberg-Dirac Hamiltonian and a standard Kohn-Sham Density Functional Theory calculation, and in the limit of an ideal Heisenberg system it reproduces the coupling as determined from spin-projected energy-differences. Our method employs a generalized perturbative approach to constrained density functional theory, where exact expressions for the energy to second order in the constraints are obtained by analytic derivatives from coupled-perturbed theory. When the relative angle between magnetization vectors of metal atoms enters as a constraint, this allows us to calculate all the magnetic exchange couplings of a system from derivatives with respect to local spin directions from the high-spin configuration. Because of the favorable computational scaling of our method with respect to the number of spin-centers, as compared to the broken-symmetry energy-differences approach, this opens the possibility for the blackbox exploration of magnetic properties in large polynuclear transition-metal complexes. In this work we outline the motivation, theory, and implementation of this method, and present results for several model systems and transition-metal complexes with a variety of density functional approximations and Hartree-Fock.

Molecular binding energies from partition density functional theory

Approximate molecular calculations via standard Kohn-Sham density functional theory are exactly reproduced by performing self-consistent calculations on isolated fragments via partition density functional theory [P. Elliott, K. Burke, M. H. Cohen, and A. Wasserman, Phys. Rev. A 82, 024501 (2010)]. We illustrate this with the binding curves of small diatomic molecules. We find that partition energies are in all cases qualitatively similar and numerically close to actual binding energies. We discuss qualitative features of the associated partition potentials.

First-principles study of the band structure and optical absorption of CuGaS2

CuGaS${}_{2}$ is the most promising chalcopyrite host for intermediate-band thin-film solar cells. Standard Kohn-Sham density functional theory fails in describing the band structure of chalcopyrite materials, due to the strong underestimation of the band gap and the poor description of $p$-$d$ hybridization, which makes it inadvisable to use this approach to study the states in the gap induced by doping. We used a state-of-the-art restricted self-consistent $GW$ approach to determine the electronic states of CuGaS${}_{2}$: in the energy range of interest for optical absorption, the $GW$ corrections shift the Kohn-Sham bands almost rigidly, as we proved through analysis of the effective masses, bandwidths, and relative position of the conduction energy valleys. Furthermore, starting from the $GW$ quasiparticle bands, we calculated optical absorption spectra using different approximations. We show that the time-dependent density functional theory can be an efficient alternative to the solution of the Bethe-Salpeter equation when the exchange-correlation kernels derived from the Bethe-Salpeter equation are employed. This conclusion is important for further studies of optical properties of supercells including dopants.

Density functional theory with London dispersion corrections

AbstractDispersion corrections to standard Kohn–Sham density functional theory (DFT) are reviewed. The focus is on computationally efficient methods for large systems that do not depend on virtual orbitals or rely on separated fragments. The recommended approaches (van der Waals density functional and DFT‐D) are asymptotically correct and can be used in combination with standard or slightly modified (short‐range) exchange–correlation functionals. The importance of the dispersion energy in intramolecular cases (conformational problems and thermochemistry) is highlighted. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 211‐228 DOI: 10.1002/wcms.30This article is categorized under: Electronic Structure Theory > Density Functional Theory

A consistent and accurateab initioparametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu

The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C(6) coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.

Two avenues to self-interaction correction within Kohn—Sham theory: unitary invariance is the shortcut

The most widely used density functionals for the exchange-correlation energy are inexact for one-electron systems. Their self-interaction errors can be severe in some applications. The problem is not only to correct the self-interaction error, but to do so in a way that will not violate size-consistency and will not go outside the standard Kohn-Sham density functional theory. The solution via the optimized effective potential (OEP) method will be discussed, first for the Perdew-Zunger self-interaction correction (whose performance for molecules is briefly summarized) and then for the more modern self-interaction corrections based upon unitarily invariant indicators of iso-orbital regions. For the latter approaches, the OEP construction is greatly simplified. The kinetic-energy-based iso-orbital indicator TW σ(r)/Tσ(r) will be discussed and plotted, along with an alternative exchange-based indicator.