Kohn-Sham Density Functional Methods Research Articles

Influence of First and Second Coordination Environment on Structural Fe(II) Sites in MIL-101 for C–H Bond Activation in Methane

Divalent iron sites in tri-iron oxo-centered metal nodes in metal–organic frameworks (MOFs) catalyze light alkane oxidation. The first two steps of the reaction sequence, which are also the most energetically demanding ones, are the formation of the active species, Fe(IV)═O, by N2O decomposition and subsequent C–H bond cleavage. We have employed Kohn–Sham density functional methods to explore how modification of the microenvironment around the Fe(II) center can modulate its catalytic activity, akin to what noted in metalloenzymes. We have varied the substituents on the organic linker of the MIL-101(Fe) MOF, as a way to modulate the energy barriers associated with the first two steps of the methane to methanol reaction. The calculations show that varying substituents has a minimal electronic effect on the iron center and its first coordination shell. However, their proximity to the active site can modify the barriers by 20%. Hydrogen bond donors can lower both barriers, such that the resulting Fe(IV)═O species are simultaneously more stable and more reactive than those of the parent MOF. The screening of a large set of systems allowed us to establish rules for the selection of second coordination shell elements to improve the reactivity of oxoferryl-based catalysts: (i) functionality with a low pKa or large positive electrostatic potential, (ii) a distance around 1.5 Å between the oxoferryl and any atom of the ring substituent, and (iii) low conformational flexibility of the added substituent.

Effects of exchange-correlation functionals on the structure and the photoionization dynamics of Na40 versus Na92 cluster

SynopsisWe study the photoionization properties of the Nan (n=40 and 92) clusters in a spherical jellium frame using the Kohn-Sham density functional method. Two well known form of exchange-correlation (xc) functional in the framework of local density approximation (LDA) with Gunnarsson-Lundqvist parametrization[1] are employed: i) the electron self-interaction correction (LDA-SIC) [1] and ii) the van Leeuwen and Baerends model potential (LDA-LB94) [1].

Topological Phase Transitions in Zinc-Blende Semimetals Driven Exclusively by Electronic Temperature.

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.

Investigation of Multiconfigurational Short-Range Density Functional Theory for Electronic Excitations in Organic Molecules.

Computational methods that can accurately and effectively predict all types of electronic excitations for any molecular system are missing in the toolbox of the computational chemist. Although various Kohn-Sham density-functional methods (KS-DFT) fulfill this aim in some cases, they become inadequate when the molecule has near-degeneracies and/or low-lying double-excited states. To address these issues we have recently proposed multiconfiguration short-range density-functional theory-MC-srDFT-as a new tool in the toolbox. While initial applications for systems with multireference character and double excitations have been promising, it is nevertheless important that the accuracy of MC-srDFT is at least comparable to the best KS-DFT methods also for organic molecules that are typically of single-reference character. In this paper we therefore systematically investigate the performance of MC-srDFT for a selected benchmark set of electronic excitations of organic molecules, covering the most common types of organic chromophores. This investigation confirms the expectation that the MC-srDFT method is accurate for a broad range of excitations and comparable to accurate wave function methods such as CASPT2, NEVPT2, and the coupled cluster based CC2 and CC3.

Increasing the applicability of density functional theory. III. Do consistent Kohn-Sham density functional methods exist?

The concept of a "consistent," Kohn-Sham (KS) density functional theory (DFT) is discussed, where the functional is able to provide good total energies and its self-consistent potential is such that the KS eigenvalues correspond to accurate approximations to the principal ionization potentials for the molecule. Today, none of the vast number of DFT approximations show this property. The one exception is the ab initio dft method built upon the optimized effective potential strategy for exchange and correlation. This qualifies as a DFT method because it represents the correlated density as a single determinant and by imposing that condition, generates local exchange and correlation operators which are used in self-consistent solutions of the orbitals and eigenvalues. Such a "consistent" DFT shares many of the properties of the Dyson equation, but without its frequency dependence and associated complications. The relationship between ab initio dft based on MBPT2 functional and GW method is discussed. Ab initio dft provides a self-consistent, frequency independent, effective independent particle alternative with a local correlation potential.

Broken Symmetry Approach to Density Functional Calculation of Magnetic Anisotropy or Zero Field Splittings for Multinuclear Complexes with Antiferromagnetic Coupling

Antiferromagnetic coupling in multinuclear transition metal complexes usually leads to electronic ground states that cannot be described by a single Slater determinant and that are therefore difficult to describe by Kohn-Sham density functional methods. Density functional calculations in such cases are usually converged to broken symmetry solutions which break spin and, in many cases, also spatial symmetry. While a procedure exists to extract isotropic Heisenberg (exchange) coupling constants from such calculations, no such approach is yet established for the calculation of magnetic anisotropy energies or zero field splitting parameters. This work proposes such a procedure. The broken symmetry solutions are not only used to extract the exchange couplings but also single-ion D tensors which are then used to construct a (phenomenological) spin Hamiltonian, from which the magnetic anisotropy and the zero-field energy levels can be computed. The procedure is demonstrated for a bi- and a trinuclear Mn(III) model compound.

First-principles scattering-state approach for nonlinear electrical transport in nanostructures

We present an ab initio scattering-state method for calculating the electrical transport properties of nanostructures at a finite bias voltage. A typical system of interest consists of two semi-infinite crystalline metal probes and a nanostructure (e.g., an atomic wire or a molecule) placed between the probes. The two metal probes have different chemical potentials at a finite bias voltage. The electronic structure of the system is described by the Kohn-Sham density functional method, with appropriate boundary conditions imposed on the electronic density and potential inside the metal probes. We expand the electronic wave functions with pseudoatomic orbitals and directly solve the self-consistent Kohn-Sham equation to obtain the transmission probabilities of electrons incident from either of the probes. The current through the molecule or nanostructure is then obtained by integrating the transmission between the two chemical potentials. Our scattering-state method provides stable and efficient algorithms for the complex bands, scattering-state wave functions, and the nonequilibrium steady-state electron density. As illustrations of the method, we present the calculated electrical transport properties of a defective carbon nanotube, a four-carbon atomic chain, and a benzene-dithiol molecular junction.

Ab initio DFT: Getting the right answer for the right reason

Some highlights of the WATOC plenary lecture are presented. We discuss what ab initio dft is, and that unlike standard density functional methods (DFT) methods, it has to converge to the right answer in the limit of basis and correlation like ab initio wavefunction methods. We obtain the correct behavior of the exchange and correlation potentials. In the case of correlation in particular, these are vastly different than those obtained by standard methods like LYP and PBE, and sufficiently different for exchange, that the numerical effect of the correct potentials is quite important. With the correct potentials, the orbital energies in Kohn–Sham DFT are shown to approximately satisfy a kind of Koopmans' theorem, while at the same time, the differences between the occupied orbital energies and the unoccupied orbital energies, offers an excellent zeroth-order approximation to the excitation energy. We demonstrate that we can build a local correlation potential using an optimized effective potential (OEP) strategy, that is equally applicable to non-local Hartree–Fock exchange as it is to local exchange. This makes it possible to create consistent ‘hybrid’ dft methods at the level of the potential. Some numerical consequences are discussed.

Linear-scaling density-functional theory with Gaussian orbitals and periodic boundary conditions: Efficient evaluation of energy and forces via the fast multipole method

We report methodological and computational details of our Kohn-Sham density-functional method with Gaussian orbitals for systems with periodic boundary conditions. Our approach for the Coulomb problem is based on the direct space fast multipole method, which achieves not only linear scaling of computational time with system size but also very high accuracy in all infinite summations. The latter is pivotal for avoiding numerical instabilities that have previously plagued calculations with large bases, especially those containing diffuse functions. Our program also makes extensive use of other linear-scaling techniques recently developed for large clusters. Using these theoretical tools, we have implemented computational programs for energy and analytic energy gradients (forces) that make it possible to optimize geometries of periodic systems with great efficiency and accuracy. Vibrational frequencies are then accurately obtained from finite differences of forces. We demonstrate the capabilities of our methods with benchmark calculations on polyacetylene, polyphenylenevinylene, and a (5,0) carbon nanotube, employing basis sets of double zeta plus polarization quality, in conjunction with the generalized gradient approximation and kinetic-energy density-dependent functionals. The largest calculation reported in this paper contains 244 atoms and 1344 contracted Gaussians in the unit cell.

Raman intensities from Kohn–Sham calculations

Raman intensity calculations have been performed for nine small main-group molecules using the Kohn–Sham density functional method. A combination of numerical and analytic derivation techniques was used as implemented in the program package DEMON. The effect of the applied functional, the basis set augmentation, and the numerical fitting of the exchange-correlation potential have been investigated along with other aspects of the computations. The results obtained at the local level using valence triple-zeta plus 2 polarization functions (VTZP+) basis sets compare well with experiment and with the results obtained from the Hartree–Fock and correlation methods using large basis sets, whereas nonlocal corrections did not yield improvements in the predicted local Raman intensities. Systematic analysis proved the sensitivity of the results obtained with the gradient corrected nonlocal functional to the numerical fitting applied in the calculations of the exchange-correlation terms. We demonstrated that omitting the fitting procedure from nonlocal calculations improves the quality of the Raman intensities while the grid used for fitting does not have an influence on the Raman intensities. Effects of the reference geometry, step size for evaluating the numerical derivatives and the threshold of energy convergence were also tested.

Tautomerism in uracil, cytosine and guanine: a comparison of electron correlation predicted by ab initio and density functional theory methods

The structures and relative energies of the tautomers of uracil, cytosine and guanine are predicted using high level ab initio methods and a Kohn-Sham density functional method employing a B-LYP functional. The structures calculated at the MP2 level are in better accord with available microwave data than are those at either the SCF or the B-LYP level. For both uracil and guanine highly correlated ab initio wavefunctions (MP4) and the density functional treatment (B-LYP) give relative energies of the tautomers to within 4 kJ mol −1, whilst for cytosine the corresponding value is somewhat larger. In the case of uracil and guanine, this difference is not sufficient to alter the ordering of the tautomers. For cytosine, where three tautomers are within about 5 kJ mol −1, the ordering given by the two approaches is different, with that from the ab initio method being in agreement with experiment. These results indicate that density functional theory methods, as presently used, may not be as accurate as traditional ab initio methods in describing tautomeric equilibria.

Anisotropic electron-impurity scattering in diluteAlLi: (Small) corrections to the local-density approximation

We have examined several improvements to a previously reported calculation of Dingle temperatures [L. Cole et al., Phys. Rev. Lett. 42, 1174 (1979)] for dilute $\mathrm{Al}\mathrm{Li}$, including self-interaction corrections and other nonlocal effects in the exchange and correlation potential. The scattering rates (or Dingle temperatures) are changed only slightly from the values obtained previously using the Kohn-Sham density-functional method with the local-density approximation. In particular, the calculated anisotropy remains strong, and the discrepancy with observed isotropy is unresolved.

Impurity Scattering on the Fermi Surfaces: A (More) Realistic Calculation

The electron-impurity scattering rate and resulting Dingle temperatures ${X}_{\mathrm{D}}$ are calculated for dilute $\mathrm{Al}\mathrm{Li}$. The multiple-plane-wave model of Sorbello is used, but unlike previous approaches the scattering of individual plane waves is treated self-consistently, using the Kohn-Sham density-functional method (and including the main effect of the lattice potential). Electron-phonon renormalization of ${X}_{\mathrm{D}}$ is included. We discuss the implications of the local approximation for the exchange and correlation.

Screening of light impurities in simple metals

The Kohn-Sham density functional method is used to calculate self-consistent electron densities around H, He and Li impurities in jellium host corresponding to Li, Al and Mg metals. The differences in the density profiles for interstitial and substitutional impurities are investigated. Residual resistivities, relaxation energies and charge transfer in dilute alloys are evaluated.