Session J28: Focus Session: New Frontiers in Electronic Structure Theory II

Semi-empirical density functionals

Two aspects of the development of functionals for practical density functional theory calculations will be discussed. First I will report on the current status of range-separated functionals based on Becke's 1997 generalized gradient approximation, augmented with a range-separation that gives 100\% exact exchange at long electron-electron distances. A family of 4 functionals, wB97, wB97X, wB97X-D and wB97X-2 have been developed based on physical arguments followed by parameter fitting with a diverse training set. Their performance is assessed on a yet-more diverse range of independent test data. The prospects for improving range-separated functionals by additional refinement of the form of the separator will be discussed and illustrated with comparative calculations. Second, if time and progress permit, I will discuss the development of functionals that correct a multi-configurational reference wave function, as opposed to the Kohn-Sham single configuration. In these cases, the reference system has partially interacting electrons, and the correlation functional provides the residual electron-electron interactions. An approach that naturally addresses the challenge of potentially double-counting electron interactions will be presented.   

Van der Waals forces in solids: Challenges for density functionals

While the importance of van der Waals (vdW) forces for binding between molecules is well established, their influence on the cohesive properties of solids remains to be quantified from first-principles. In particular, most state-of-the-art density functionals yield systematic deviations for the lattice constants, cohesive energies, bulk moduli and transition pressures for a range of solid-state systems. We evaluate the long-range $C_6$ dispersion coefficients for ions in solids and use them to assess the effect of the long-range vdW forces on the abovementioned cohesive properties of ionic (NaCl, AgCl, MgO) and semiconductor (Si, GaAs) solids. For all of these systems, we obtain consistently accurate results by coupling the long-range $C_6R^{-6}$ dispersion energy with the Perdew-Burke-Ernzerhof functional for the short range. We compare our results for the cohesive properties with recently developed functionals for solids.   

A first-principles study of weakly bound molecules using exact exchange and the Random Phase Approximation

We present a study of the binding energy (BE) curves of rare gas and alkaline-earth dimers using an energy functional that includes exact exchange (EXX), and correlation energies within RPA. Our results for the equilibrium positions, and long range behavior of the potential energy curves show great improvements over those obtained at the standard LDA/GGA DFT levels. For Ar and Kr, our BE results are improved as well and are comparable to that of so-called vdW-DF functional, although EXX/RPA yields BE curves that agree better with experiment for large separation distances, as expected. We also discuss shortcoming of the EXX/RPA perturbative approach and analyze possible sources of error in the description of the BE curve of alkaline-earth dimers, in particular Be$_2$, exhibiting an unphysical maximum at large separation. We suggest that the lack of self-consistency in current EXX/RPA approaches might be largely responsible for most of the observed shortcomings. Finally we present a tight binding approach to obtain the eigenvalues of the dielectric matrix entering the calculation of the RPA correlation energy, that greatly improves the efficiency of EXX/RPA calculations.   

Spectrum slicing methods to solve the Kohn-Sham problem

Very large first-principles electronic structure calculations present a challenge as the number of atoms increases owing to the scaling of the eigenvalue problem. We present a spectrum slicing method by which the eigenvalue problem is solved in a divide and conquer fashion. This reduces the cost of quadratic scaling tasks such as orthogonalization in exchange for an increase in the number matrix-vector products. The algorithm is demonstrated on a large system of aluminum atoms in the liquid state.   

Van der Waals Interactions in Density Functional Theory: Intermolecular Complexes

Conventional density functional theory (GGA and hybrid functionals) fails to account for dispersion interactions and is therefore not applicable to systems where van der Waals interactions play a dominant role, such as intermolecular complexes and biomolecules. The exchange-hole dipole moment (XDM) dispersion model of Becke and Johnson [A. D. Becke and E. R. Johnson, \textit{J. Chem. Phys.} \textbf{127}, 154108 (2007)] corrects for this deficiency. We have previously shown that the XDM dispersion model can be combined with standard GGA functionals (PW86 for exchange and PBE for correlation) to give accurate binding energy curves for rare-gas diatomics [F. O. Kannemann and A. D. Becke, \textit{J. Chem. Theory Comput.} \textbf{5}, 719 (2009)]. Here we present further tests of the GGA-XDM method using benchmark sets including hydrogen bonding, electrostatic, dispersion and stacking interactions, and systems ranging from rare-gas diatomics to biomolecular complexes.   

Chemical accuracy for the van der Waals density functional

Dispersion interactions are ubiquitous in nature and contribute to the binding in biomolecules and molecules on surfaces. However, due to their non-locality and small magnitude, they are difficult to describe accurately by electronic structure methods. For example, density functional theory (DFT) with standard functionals can give misleading results for systems where dispersion is important. Therefore, many schemes have been developed that try to improve the description of dispersion in DFT. Here we show that the accuracy of one scheme, the van der Waals density functional proposed by Dion et al. [Phys. Rev. Lett. 92, 246401 (2004)], can be dramatically improved through the judicious choice of exchange functional. This is demonstrated on various benchmark sets for weak interactions and for surface adsorption energies. Since at least similar accuracy for other important properties of matter such as bulk lattice constants is achieved compared to standard semi-local functionals, this opens a way to even more realistic simulations on the nanoscale.   

Two-electron Reduced-Density-Matrix Mechanics: With Application to Many-electron Atoms and Molecules

In 1959 Charles Coulson popularized the challenge of computing the ground-state energy as a functional of the two-electron reduced density matrix (2-RDM) without the many-electron wavefunction. Recently, theoretical and computational advances have led to two classes of 2-RDM methods [1]: (i) the variational calculation of the 2-RDM subject to approximate $N$-representability conditions and (ii) the non-variational calculation of the 2-RDM from the anti-Hermitian contracted Schr\"{o}dinger equation. I will develop the background for the 2-RDM methods, discuss recent theoretical and computational advances, and present some applications, including the detection of poly-radical correlation in polyaromatic acene and aryne chains, the study of protonated acetylene and malonaldehyde beyond the Born-Oppenheimer approximation, and the computation of activation energies in pericyclic reactions of open- and closed-shell molecular species. \\[4pt] [1] ``Two-electron Reduced-Density-Matrix Mechanics with Application to Many-electron Atoms and Molecules,'' edited by D. A. Mazziotti, Advances in Chemical Physics Vol. 134 (Wiley, New York, 2007).   

First principles EPR spectra of organic transition metal complexes

We present first principles, density functional theory calculations of the EPR spectrum of mononuclear and binuclear organic transition metal complexes, that constitute building block of more complicated catalysts for the water splitting reaction. We apply here the modern theory of orbital magnetization and we obtain the EPR g-tensor by computing the derivative of the orbital magnetization with respect to the electronic spin flip. This method allowed us to incorporate self-interaction corrections in the Hamiltonian, at the level of DFT+U. We found that the DFT+U method improves the agreement with respect to experiment, of the EPR g-tensor and hyperfine couplings parameters for high spin complexes. We also discuss the success and failures of DFT+U as an energy functional, and the importance of benchmarking improved- or post-DFT methods (such as hybrid functionals) against the EPR spectra of transition metals complexes.   

Hartree-Fock and Kohn-Sham method for open systems

The source-sink potential (SSP) method [1,2] provides a simple description of electron transport through molecules. Starting from the tight-binding approach, the infinite contacts are replaced by complex potentials. Extending SSP, we describe how to introduce complex potentials into the Hartree-Fock and the Kohn-Sham method. Doing so enables us to model open systems with a current passing through, while accounting for exchange and correlation effects. The implementation of these methods and initial results will be discussed. \\ \\ $[1]$ F. Goyer, M. Ernzerhof, M. Zhuang, J. Chem. Phys. 126, 144104 (2007).\\ $[2]$ M. Ernzerhof, J. Chem. Phys. 127, 204709 (2007).   

A Converse Approach to NMR Chemical Shifts for Norm-Conserving Pseudopotentials

Building on the recently developed converse approach for the ab-initio calculation of NMR chemical shifts [1], we present a corresponding framework that is suitable in connection with norm-conserving pseudopotentials. Our approach uses the GIPAW transformation [2] to set up a formalism where the derivative of the orbital magnetization [3] is taken with respect to a microscopic, localized magnetic dipole in the presence of pseudopotentials. The advantages of our method are that it is conceptually simple, the need for a linear-response framework is avoided, and it is applicable to large systems. We present results for calculations of several well-studied systems, including the carbon, hydrogen, fluorine, and phosphorus shifts in various molecules and solids. Our results are in very good agreement with both linear-response calculations and experimental results.\\[4pt] [1] T. Thonhauser et al., J. Chem. Phys. {\bf 131}, 101101 (2009).\newline [2] C. J. Pickard and F. Mauri, Phys. Rev. B {\bf 63}, 245101 (2001).\newline [3] T. Thonhauser et al., Phys. Rev. Lett. {\bf 95}, 137205 (2005).   

Beyond a single solvated electron: Hybrid quantum Monte Carlo and molecular mechanics approach

A hybrid computational approach combining quantum Monte Carlo and molecular mechanics (QMC/MM) has been recently developed for an accurate treatment of electron correlation in systems that require a large number of explicit solvent molecules. Here, QMC/MM is utilized to address the issue of binding of two excess electrons to water clusters of medium-to-large size. Such systems are relevant to the studies of interaction of excess electrons with solvent molecules during electron-energy transfer in medium. A modeling strategy is proposed that combines polarizable force field simulations and density functional theoretical calculations for geometries and binding energies of dianionic clusters, and QMC/MM calculations for refined binding energies. The possibility of stable doubly charged anionic water clusters is demonstrated. The study explores binding properties of various structural motifs and how stability towards spontaneous electron detachment depends on cluster size. Applicability of QMC/MM to the studies of metastable systems is discussed.