Session A35: Focus Session: DFT I: Strongly Correlated Systems; GW and Many-Body Perturbation Theory

Real-Space DFT Models for Strong Correlation

Accurate treatment of strongly-correlated electrons remains an important challenge for density-functional theory. Most functionals underestimate the energy lowering arising from non-dynamical electron correlation, as in stretched covalent bonds, open-shell singlet states, and many transition-metal compounds, including semiconductors. We develop a new density-functional approach combining physical insight from chemical structure with real-space modeling of the exchange-correlation hole, based on the Becke-Roussel exchange functional. The method is capable of predicting correct dissociation limits and describing strong correlation in many-electron systems.   

DFT+DMFT versus DFT+U description of Mott insulators: DMFT restores spin and orbital symmetry and removes metastables states

In the last twenty years, the developpement of methods based on the coupling of Density Functional Theory in the Local Density Approximation and Hubbard-like terms has led to a successfull description of many strongly correlated systems. These methods include DFT+U which contains a static description of interaction and the combination of DFT with Dynamical Mean Field Theory (DFT+DMFT) which adds fluctutations to the description of interactions. We present implementations of DFT+U and DFT+DMFT in the same framework, and with the same approximations. We show, in agreement with previous results in the litterature, and even in the simple Hubbard I approximation to DMFT,that DFT+DMFT is able to describe Mott insulator without any breaking of spin and orbital symmetry. We show that this improvement simply remove the appearance of metastable states, and thus solve a practical and physical problem encountered in particular in the description of actinides oxydes in DFT+U calculations.   

Renormalized second-oder perturbation theory for the electron correlation energy: concepts and benchmarks

We present a renormalized second-oder perturbation theory (R2PT) for the electron correlation energy that combines the random-phase approximation (RPA), second-order screened exchange (SOSEX) [1], and renormalized single excitations (rSE) [2]. These three terms all involve a summation of certain types of diagrams to infinite order, and can be viewed as a ``renormalization" of the direct, the exchange and the single excitation (SE) term of 2nd-order Rayleigh-Schr{\"o}rdinger perturbation theory based on an (approximate) Kohn-Sham reference state. A preliminary version of R2PT has been benchmarked for covalently-bonded molecular systems and chemical reaction barrier heights [3] and shows an overall well balanced performance. We have extended this, by including ``off-diagonal'' diagrams into the rSE term and expect this refined version of R2PT to be more generally applicable to electronic systems of different bonding characteristics. Extended benchmarks of van-der-Waals-bonded molecules and crystalline solids will be presented. [1] A. Gr\"uneis {\it et al.}, J. Chem. Phys. \textbf{131}, 154115 (2009). [2] X. Ren {\it et al.}, Phys. Rev. Lett. \textbf{106}, 153003 (2011). [3] J. Paier {\it et al.}, arXiv:cond-mat/1111.0173.   

Efficient GW methods implemented in molecular orbital space: Ionization energy and electron affinity of conjugated molecules

An efficient all-electron non-selfconsistent GW (G$^0$W$^0$) method is proposed, which is based on the full random-phase approximation and implemented in the molecular-orbital space with algorithms for reducing the error coming from the incompleteness of the basis set. The convergence of its result with regard to the size of the basis set is examined. Based on this, we further implement a quasiparticle self-consistent GW (QSGW) approach with Gaussian basis functions. The high computational efficiency allows us to deal with larger molecules from the first principles, and we applied our methods to calculate the ionization energy (IE) and electron affinity (EA) of ten conjugated molecules with up to 32 atoms. The G$^0$W$^0$ result improves the Hartree-Fock result significantly, especially for EA, and, furthermore, the QSGW improves the G$^0$W$^0$ and gives results of both IE and EA in very good agreement with the available experimental data and also with the results from the $\Delta$SCF calculation using the B3LYP functional. This indicates that our all-electron {\it ab initio} GW calculation can describe very well molecular electronic structures, making the QSGW approach a good candidate for investigating electronic and transport properties of molecular systems.   

Exact DFT with the density matrix renormalization group

The density matrix renormalization group (DMRG) is a powerful, controlled numerical method traditionally applied to lattice models of strongly correlated electrons in 1D and 2D. By extending DMRG to simulate electronic structure models on a 1D quasi-continuum grid, we can compute exact Kohn-Sham (KS) potentials and even perform exact full KS calculations.\footnote{E.M. Stoudenmire, Lucas O. Wagner, Steven R. White, Kieron Burke, arXiv:1107.2394} On their own, the continuum DMRG calculations provide significant insight into the structure of strongly correlated many-body wavefunctions both for smaller molecules and chains exceeding one hundred atoms. Combining DMRG with the machinery of density functional theory allows us to explore the reasons for the success or failure of standard DFT approximations and to better understand which many-body effects are faithfully reproduced by the KS system.   

Exact density functionals for 1d systems

The success of modern density functional theory (DFT) can be attributed to the Kohn-Sham (KS) scheme, for which density functional approximations are both practical and rather simple. We are often left in the dark, however, when trying to understand why certain approximations fail, or how well they approximate the true functional. To study such questions, an exact implementation of KS-DFT is required. Though exact KS-DFT is as difficult as solving the original many-body problem, the density matrix renormalization group (DMRG) gives us a powerful tool to do this. DMRG is a highly efficient wavefunction solver in 1d, which we use to solve model continuum systems with a long-range soft-Coulomb interaction between particles. Using DMRG, we implement exact KS-DFT and investigate its inner workings. Results for some atom chains are discussed and compared to HF and LDA calculations. Preprint at arXiv:1107.2394.   

Exact Kohn-Sham eigenstates versus quasi-particles in simple models of strongly correlated electrons

We present analytic expressions for the exact density functional and Kohn-Sham Hamiltonian of simple tight-binding models of correlated electrons. These are the single- and double-site versions of the Anderson, Hubbard and spinless fermion models. The exact exchange and correlation potentials are fully non-local. The analytic expressions allow to compare the Kohn-Sham eigenstates of exact density functional theory with the many-body quasi-particle states of these correlated-electron systems. The exact Kohn-Sham spectrum describes correctly many of the non-trivial features of the many-body quasi-particle spectrum, as for example the precursors of the Kondo peak. However, we find that some pieces of the quasi-particle spectrum are missing because the many-body phase-space for electron and hole excitations is richer.   

Spectroscopic Fingerprinting of Small Molecules via Many-Body Perturbation Theory

Quantitative understanding of the photophysics of small organic molecules is an important challenge and relevant to a range of energy conversion applications. Existing first-principles methods, such as time-dependent density functional theory, coupled cluster, and other quantum chemistry-based approaches can sometimes provide onset energies with good accuracy, but agreement at higher energies - a more complete spectral fingerprint - is frequently less adequate. Here we use DFT and many-body perturbation theory, within the GW approximation and the Bethe-Salpeter Equation approach, to compute the UV-Vis absorption spectra for a range of small molecules, comparing closely to room-temperature, solution-phase measurements of onsets and spectra. First-principles molecular dynamics is used to prepare snapshots of finite temperature conformations. The effects of continuum and explicit solvation models are considered. The importance of dynamic disorder, delocalized unoccupied states, and solvation are thoroughly discussed in the context of experiments. Support: DOE via the Molecular Foundry and Helios SERC, and NSF via NCN. Computational support provided by NERSC.   

Going beyond DFT for Organic/Titanium Dioxide interfaces

There is increasing interest in organic/oxide interfaces, particularly for light harvesting and light-emitting devices, and it is important to obtain theoretical information for basic quantities such as the energy-level alignment across the interface. Accurate descriptions of the electronic structure of the composite system, as e.g. [1], are however scarce. The method used should give reliable results for both organic and oxide materials, to guarantee a good description of the hybrid system. In this work we have explored different DFT functionals (PZ-LDA, and those that include a fraction of Exact-Exchange as PBE0, HSE and B3LYP [2]) and compared the results with those obtained by Many-Body Perturbation theory with the GW approximation[3]. We have chosen as prototype systems TiO2, both bulk crystal and model surface, and Thiophene. We have found that none of the used DFT schemes give optimal results for both organic and inorganic systems at the same time, so moving beyond DFT is mandatory.\\[4pt] [1] C.D. Valentin et.al., Phys. Rev. Lett. 97, 166803 (2006)\\[0pt] [2] J.P. Perdew et.al., J. Chem. Phys. 105, 9982 (1996); J. Heyd et.al., J. Chem. Phys. 118, 8207 (2003); P.J. Stephens et.al., J. Phys. Chem. 98, 11623 (1994)\\[0pt] [3] A. Marini et.al., Comp. Phys. Comm. 180, 1392 (2009)   

Accurate potential energy surfaces for transition-metal complexes with DFT+U(R)

We introduce an improvement to the Hubbard U augmented density functional approach known as DFT+$U$ that incorporates variations in the value of self-consistently calculated, linear-response $U$ with changes in geometry. This approach overcomes the one major shortcoming of previous DFT+$U$ studies, i.e. the use of an averaged Hubbard U when comparing energies for different points along a potential energy surface is no longer required. While DFT+$U$ is quite successful at providing accurate descriptions of localized electrons (e.g. $d$ or $f$) by correcting self-interaction errors of standard exchange correlation functionals, we show several examples from diatomic molecules to porphyrins to surface science applications where this position-dependent DFT+$U(\mathbf{R})$ provides a significant two- to four-fold improvement over DFT+$U$ predictions. DFT+$U(\mathbf{R})$ reduces errors in binding energies, frequencies, and equilibrium bond lengths by applying the linear-response, position-dependent $U(\mathbf{R})$ at each point. We also propose a metric for whether a standard DFT+$U$ approach is sufficient by determining the strength of the dependence of $U$ on changes in coordinates.