Session H28: Focus Session: New Frontiers in Electronic Structure Theory I

DFT and beyond: A discussion of exact exchange plus local- and nonlocal-density approximations to the correlation functional

Local- and semilocal-density approximations (LDA/GGA) to density-functional theory, although tremendously successful for describing the properties of many molecules and materials, suffer from, amongst others, self-interaction errors and the absence of long-range van der Waals interactions. One at present most systematic approach for handling the xc functional appears to be exact exchange combined with the random phase approximation for correlation. We show that significant insight can be obtained by this approach, e.g. for studying the interaction between two graphene sheets [1], cohesive and surface energies of transition metals [2], or the adsorption of CO on close-packed transition metal surfaces [3]. For some of these systems the LDA and GGA give an even qualitatively wrong description. --- Despite the success for the mentioned systems we also identify shortcomings of the approach, in particular for molecules. --- A second route discussed in this talk concerns the linkage of LDA+$U$ and many-body perturbation theory: $G_0W_0$@LDA+$U$. We discuss results for the $4f$ lanthanide- oxide series [4] as well as for $3d$ transition metal oxides. -- - 1) A. Sanfilippo, X.G. Ren, P. Rinke, A. Tkatchenko, V. Blum, K. Reuter, and M. Scheffler, in preparation. 2) A.Soon and Matthias Scheffler, in preparation. 2) X. Ren, P. Rinke, and M. Scheffler, Phys. Rev. B {\bf 80}, 045402 (2009). 4) H. Jiang, R.I. G\'omez-Abal, P. Rinke, and M. Scheffler, Phys. Rev. Lett. {\bf 102}, 126403 (2009).   

Accurate binding energies in transition-metal molecules using a position-dependent GGA+U(R) approach

Despite the importance of transition metals in a variety of biological and inorganic systems, density functional theory calculations often fail quantitatively in describing the stable intermediate electronic structures, splittings, and geometries as well as reaction barriers and geometries of transition states. We have shown how augmenting the generalized- gradient approximation (GGA) with a Hubbard U, which is obtained from a self-consistent linear response procedure, can greatly improve energetic and structural descriptions of both small, prototypical systems, such as Fe$_2$, and large systems like Co(II) porphyrin SAMs. However, one major shortcoming of this approach remains: we must use a calculated average of the values of Hubbard U when comparing points along a potential energy surface. We now introduce an improvement to GGA+U that incorporates variations in the value of linear-response U with changes in geometry. We show a few examples where this position-dependent GGA+U(R) approach proves particularly useful by improving binding energies and frequencies. We also present a protocol for predicting the change in U with respect to changes in coordinates, as a tool for deciding whether a standard GGA+U approach is sufficient. This approach may be directly included in structural relaxations, transition-state finding methods, and dynamics calculations.   

Self-consistent Meta-GGA for Solids, with Application to the CO Adsorption Puzzle

A new proposed meta-GGA in density functional theory (DFT), the revTPSS,\footnote{J.P. Perdew, \textit{et al}, Phys. Rev. Lett. \textbf{103}, 026403(2009).} unites the advantages of PBEsol and TPSS, giving good lattice constants, as well as good surface and atomization energies. Perhaps the enthusiasm to implement TPSS self-consistently was hindered by its errors in lattice constants (only slightly smaller than the errors of standard GGA's), which might also cause TPSS not so widely adopted for solid calculations. With the improvement of the lattice constants, revTPSS becomes the potential workhorse for both condensed matter physics and quantum chemistry. We implement the revTPSS self-consistently in the VASP code with application to the CO adsorption puzzle. The preliminary results on the site preference and adsorption energy of CO on metallic surfaces look promising. Some standard benchmarking tests, such as lattice constants, bulk moduli, and atomization energies, will also be presented.   

Evaluation of density functionals using valence and core excited spectra of Ni(II) tetrahlides

We present a systematic evaluation of the performance of various density functional theories using the series of tetrahalide complexes of nickel(II). We report the accuracy of the ground state electronic structure from calculations employing gradient corrected (GGA), hybrid GGA, and meta-GGA functionals with systematic variation of exchange and correlation functions. Reference data for these calculations included valence and core excitation spectroscopic results and molecular geometry data. The core excitation spectra at the Ni L-edges and Cl K-edges were analyzed for extracting experimental orbital coefficient information of the lowest lying unoccupied frontier orbitals. Both the core and valence excitation spectra were simulated using time dependent density functional theory. In order to probe the basis set saturation effect \textit{ab initio} calculations were also performed. The theoretically converging series of post-SCF methods allowed us for the evaluation of basis set saturation. The calculated atomic spin densities, orbital energies, and excitation data are compared to those from density functional calculations. A new hybrid functional is presented for the most reasonable description of the ground state of nickel(II) complexes.   

Linear-scaling and projector self-consistent DFT+U for electronic correlations in large systems

ONETEP is an \textit{ab initio} total-energy and force code for which the computational effort scales linearly with the number of atoms, recently shown to scale up to 32,000 atoms on 64 cores [1][2]. Conventional exchange-correlation functionals are often unable to describe the electronic structure of biomolecules and metal-oxide nanostructures correctly, tending to under-localise states associated with transition metal sites. We show that non-orthogonal, generalised Wannier functions provide an efficient basis of projectors with which to describe these localised states, thus to construct a Hubbard-model like correction, DFT+U [3], to treat correlations. We demonstrate DFT+U calculations that are self-consistent over the charge density, Wannier projectors and interaction parameters. The tensorial character of the occupancy matrices, accounting for Wannier projector non-orthogonality, is discussed and illuminated numerically. We present a parallelised,linear-scaling implementation of the DFT+U energies and forces in ONETEP, providing for accurate calculations on large organometallic compounds and nanostructures. [1] C.-K.~Skylaris, et. al. \emph{J.}\emph{Chem.}\emph{Phys.} \textbf{122} 084119 (2005). [2] N.~D.~M.~Hine, et. al. \emph{Comp.}\emph{Phys.}\emph{Comm.} \textbf{180} 1041 (2008). [3] M. Cococcioni, S. de Gironcoli, \emph{Phys.}\emph{Rev.}\emph{B.} \textbf{71} 035105 (2005).   

Time-dependent density-matrix functional theory formalism to study biexcitonic phenomena in bulk systems and nanostructures

We formulate a time-dependent density-matrix functional theory (TDDMFT) approach to study higher-order correlation effects like biexcitons in different bulk systems and nanostructures. In particular, we derive the TDDMFT version of the Schroedinger equation for biexcitons in terms of the one-body and two-body reduced density matrices. To test the approach, we calculate the biexcitonic binding energies in the case of different exchange- correlation (XC) potentials for bulk CuCl, CuBr, CdS and ZnO materials with rather large biexcitonic binding energies. We show that the excitonic, biexcitonic and other higher-order correlation effects are more pronounced in the case when the XC kernel contains a $1/q^{2}$ Coulomb singularity. Also, we analyze the role of non-adiabaticity of the XC potential in description of the higher-order correlation effects within the TDDMFT.   

Meta-generalized gradient approximations: What they can and cannot do for you

In the meta-GGA, as first proposed by Becke, the exchange-correlation energy is expressed as a single integral over position space of a function of the electron density, its gradient, and the orbital kinetic energy density of Kohn-Sham density functional theory. Meta-GGA is the highest level of semilocal (hence computationally efficient) approximation. Like the simpler GGA, it can be constructed nonempirically [1,2] by constraint satisfaction. But, unlike the GGA, it is capable of high simultaneous accuracy for atoms and molecules on the one hand and solids on the other, because it provides different GGA descriptions in regions where one orbital shape dominates and where all orbitals overlap strongly. A good meta-GGA may work in all situations where the exact exchange-correlation hole is well-localized around its electron (atoms, slowly-varying densities, many molecules and solids near equilibrium). But it will necessarily fail to the extent that the exact exchange-correlation hole is delocalized, as in many stretched-bond situations or where long-range van der Waals effects are important. While full nonlocality is needed to describe the latter situations, the meta-GGA appears to be otherwise a good compromise between accuracy and efficiency. Further improvements to the meta-GGA may still be possible. Selfconsistent meta-GGA's are increasingly available in standard codes for atoms, molecules, and solids. [1] J. Tao, J.P. Perdew, V.N. Staroverov, and G.E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003). [2] J.P. Perdew, A. Ruzsinszky, G.I. Csonka, L.A. Constantin, and J.Sun, Phys. Rev. Lett. 103, 026403 (2009).   

Acceleration of the transcorrelated method for solids

To calculate the electronic structures of solids including electron correlation effects, we have developed the transcorrelated (TC) method. In the TC method, a many-body wave function is represented by a correlated wave function $F \Phi$, where $\Phi$ is a single Slater determinant and $F$ is a Jastrow function, $F=\exp[-\sum_{i [Preview Abstract]

Dispersion Interactions in Molecular Assemblies from First-Principles Calculations

We have investigated inter-molecular interactions in weakly bonded molecular assemblies from first principles, by combining exact exchange energies (EXX) with correlation energies defined by the adiabatic connection fluctuation-dissipation theorem, within the random phase approximation (RPA)[1,2]. We present results for three different types of molecular systems: the benzene crystal, the methane crystal and self-assembled monolayers of phenylenediisocyanide. We describe in detail how computed equilibrium lattice constants and cohesive energies may be affected by input ground state wave functions and orbital energies, by the geometries of the molecular monomers in the assemblies, and by the inclusion of zero point energy contribution to the total energy. We find that the EXX/RPA perturbative approach provides an overall satisfactory, first principle description of dispersion forces, in good agreement with experiments and advanced quantum chemistry results. However, binding energies tend to be underestimated and possible reasons for this discrepancy are discussed. This work was funded by DOE/BES DE-FG02-06ER46262 and DOE/SciDAC DE-FC02-06ER25794.[1] Y. Li, D. Lu, H-V. Nguyen and G. Galli, J. Phys. Chem.(submitted). [2]D. Lu, Y. Li, D. Rocca and G. Galli, Phys. Rev. Lett. 102, 206411(2009).   

Two and three-body interatomic dispersion energy contributions to binding in molecules and solids

Numerical estimates of the leading two and three body dispersion energy terms in van der Waals (vdW) interactions are presented for a broad variety of molecules and solids. The calculations employ London and Axilrod-Teller-Muto expressions damped at short interatomic distances, where the required interatomic dispersion energy coefficients, C6 and C9, are computed from first-principles. The investigated systems include the S22 database of non-covalent interactions, benzene and ice crystals, bilayer graphene, fullerene dimer, a poly peptide (Ala10), an intercalated drug-DNA model (Ellipticine-d(CG)2), 42 DNA base pairs, a protein (DHFR, 2616 atoms), double stranded DNA (1905 atoms), and molecular crystals from a crystal structure blind test. We find that the 2 and 3-body interatomic dispersion energies contribute significantly to binding and cohesive energies, for some systems they can reach up to 50\% of experimental estimates of absolute binding. Our results suggest that interatomic 3-body dispersion potentials should be accounted for in atomistic simulations when modeling bulky molecules or condensed phase systems.   

Excited-state properties of organic photovoltaic materials from a many-body Lanczos-GW approach and time-dependent density functional theory

Many-body GW and time-dependent DFT (TDDFT) are two approaches that in principle allow us to access electronic and optical excited-state properties, which are critical to characterize and engineer organic photovoltaic materials. Recently we have implemented a novel approach to GW that constructs an optimal polarizability basis without using conduction states and avoids plasmon-pole approximation and sum-over-states bottlenecks using a modified Lanczos algorithm. We have also developed a real-time propagation scheme to TDDFT, able to treat large systems efficiently. We apply these two approaches to study the electronic and optical excitations in the electron acceptors often used in bulk heterojunction organic photovoltaics such as fullerene and its derivative PCBM. Our Lanczos-GW approach significantly improves upon ionization potentials and electron affinities. Optical absorption spectra for both fullerenes and PCBM from real-time TDDFT calculations are also in reasonable agreement with experimental data.