Session U13: Focus Session: Frontiers in Electronic Structure Theory II

Self-consistent van der Waals density functional: Development and Applications

The inability of density functional theory (DFT), with standard exchange-correlation functionals, to correctly describe van der Waals/dispersion (vdW) interactions has severely limited its applicability to sparsely packed systems, such as organic and biological molecules.  Numerous attempts have been made to correct these deficiencies; however, many of them either require extensive reparameterization for each new situation or scale poorly with system size.  In this paper, I will discuss the development and implementation of an exchange-correlation functional which correctly incorporates non-local vdW interactions within DFT (vdW-DF)\footnote{M. Dion, H. Rydberg, E. Schr\"{o}der, B. I. Lundqvist and D. C. Langreth, Phys. Rev. Lett., {\bf 92}, 246401 (2004)}.  In addition, I will present our recent development of the corresponding exchange- correlation potential ($V_{\rm xc}$)\footnote{T. Thonhauser, V. R. Cooper, S. Li, A. Puzder, P. Hyldgaard, and David C. Langreth, Phys. Rev. B, {\bf 76}, 125112 (2007)}. The $V_{\rm xc}$ gives us the ability to compute Hellmann-Feynman forces, allowing for structural relaxations and molecular dynamics simulation. Using the $V_{\rm xc}$ I will examine the nature of the van der Waals bond between molecules. Finally, to demonstrate the power of the vdW-DF, I will discuss our relatively large scale application of the functional to study the influence of stacking interactions on the structure and stability of DNA. Here, I will show how these interactions are crucial for defining the twist and base pair separation in DNA and how methyl-nucleobase and methyl-methyl interactions give additional stability to DNA.   

Stochastic Time-Dependent Current-Density Functional Theory

Static and dynamical density functional methods have been applied with a certain degree of success to a variety of closed quantum mechanical systems, i.e., systems that can be described via a Hamiltonian dynamics. However, the relevance of open quantum systems - those coupled to external environments, e.g., baths or reservoirs - cannot be overestimated. To investigate open quantum systems with DFT methods we have introduced a new theory, we have named Stochastic Time-Dependent Current Density Functional theory (S-TDCDFT) $[1]$: starting from a suitable description of the system dynamics via a {\it stochastic} Schr\"odinger equation $[2]$, we have proven that given an initial quantum state and the coupling between the system and the environment, there is a one-to-one correspondence between the ensemble-averaged current density and the external vector potential applied to the system.\\ In this talk, I will introduce the stochastic formalism needed for the description of open quantum systems, discuss in details the theorem of Stochastic TD-CDFT, and provide few examples of its applicability like the dissipative dynamics of excited systems, quantum-measurement theory and other applications relevant to charge and energy transport in nanoscale systems.\\ $[1]$ M. Di Ventra and R. D'Agosta, Physical Review Letters {\bf 98}, 226403 (2007)\\ $[2]$ N.G. van Kampen, {\it Stochastic processes in Physics and Chemistry}, (North Holland, 2001), 2nd ed.   

Investigating interaction-induced chaos using time-dependent density functional theory

Systems whose underlying classical dynamics are chaotic exhibit signatures of the chaos in their quantum mechanics. In this talk I will discuss the possibility of using time-dependent density functional theory (TDDFT) to study the case when chaos is induced by electron interaction alone. Nearest-neighbor level- spacing statistics are in principle exactly and directly accessible from time-dependent density functional theory (TDDFT). Can the linear response formalism of TDDFT reveal the mechanism of chaos induced by electron-interaction alone? A simple model of a few-electron quantum dot highlights the necessity to go beyond the adiabatic approximation in TDDFT.   

Time-dependent NEGF calculations of extended systems

A non-equilibrium GF (NEGF) model based on time dependent perturbation theory is developed to propagate electronic structure and molecular conductance of extended electrode-molecule-electrode nanostructures. In this model, we take advantage of the two time variable nature of the KB equations in order to formulate a mixed time-frequency representation for the lesser GF. This allows us to include bulk affected electrodes with non-trivial energy representations in our propagation. It also allows us to express dynamical observables such as current with highly informative Wigner distributions that shed light on the physical causes for certain dynamic features. Preliminary calculations, performed on simple systems, reveal that the dynamic current has both a direct and an alternating contribution. The direct current is due to a bulk affected state and the alternating component is due to a superposition of states. The amplitude of the alternating current can be changed dramatically by adjusting the bias pulse.   

Many-Body Density Matrix Perturbation Theory

One fundamental limitation of quantum chemical methods is the accuracy of the approximate many-body theoretical framework that is utilized. Accurate many- body formalisms for quantum chemical methods do exist, but these methods are computationally very expensive. Methods also exist that are much less computationally expensive such as Hatree-Fock, Density Functional and the Hybrid Functional theories, but at a reduced representation of the exact many-body ground state. This severely limits either the system size that can be addressed accurately, or the accuracy of the representation of the many-body ground state. What is essential is a method which represents the many-body ground state accurately, but with a low computational cost. Recently, a method for determining the response, to any order of the perturbation, within the density matrix formalism has been discovered. This method is very simple and computationally efficient, and it immediately opens up the possibility of computing the variational many- body ground state to unprecedented accuracy within a simplified computational approach. Within this article, we report on the theoretical development of this methodology, which we refer to as Many Body Density Matrix Perturbation Theory. This theory has many significant advantages over existing methods. One, its computational cost is equivalent to Hartree-Fock. Two it is a variational upper bound to the exact energy. And three, it has no self-interaction.   

Conformational hierarchies of weakly bonded systems: Accuracy of dispersion corrected DFT

It is well known that long-range dispersion interactions, important for stabilization of, e.g., molecular crystals, biomolecules and physisorption, are badly described by state-of-the-art \textit{xc} functionals in DFT, but naturally included in post-HF methods or empirically in force field simulations. We have implemented a semi-empirical $C_6/R^6$ correction [1,2] in the numeric atom-centered orbital based code FHI-aims [3] and obtained correction parameters by fitting to a database of high quality \textit{ab initio} calculations [2], improving on previous results due to the more accurate basis set (0.5 kcal/mol average error for binding energies using PBE+$C_6$). We assess the accuracy and impact of the correction on conformational energy \emph{hierarchies} of (i) (H$_2$O)$_n$ clusters ($n$=2-6), (ii) Ala$_2$ and Ala$_4$, and (iii) infinite polyalanine conformers, comparing to published post-HF results for (i) and (ii). Even though the relative energies are not changed for small H$_2$O clusters and Ala$_2$ compared to \textsc{DFT-GGA}, the impact of dispersion on the conformation hierarchy of larger systems is surprisingly large, reaching $\sim$1-4 kcal/mol for different polyalanine conformers. [1] S. Grimme, J. Comput. Chem. 25, 1463 (2004) [2] P. Jurecka et al., J. Comput. Chem. 28, 555 (2007) [3] V. Blum et al., FHI ab initio molecular simulations (FHI-aims) project.   

Iterative computation of dielectric eigenmodes

We present an iterative method for the calculation of the eigenvectors of dielectric matrices of materials and nanostructures, based on Density Functional Theory, within a linear response framework. We show that by computing a relatively small number of eigenvectors via iterative dielectric response calculations, one may reconstruct the full dielectric matrix of a given system to high accuracy. The proposed method bypasses the need for the calculation of a large number of excited states required by earlier dielectric matrix computations based on the Random Phase Approximation. The scaling of the algorithm and the efficiency of the approach will be demonstrated by the calculation of the static dielectric properties of a variety of nanostructures, including silicon rods and slabs.   

Comparison of vibrational and electronic contributions to van der Waals interactions

The van der Waals interaction can be caused by either ionic vibrations or instantaneous electronic motion relative to the atomic center. In this study, the vibrational contribution to the van der Waals interaction is formulated by considering the interaction between induced dipoles caused by the infrared-active normal modes of a neutral molecule. Using the derived formula, the contribution is quantified, within the density-functional theory formalism, using a screened, i.e., self-consistent, vibrational polarizability. Applications for several neutral nonpolar dimers are presented. It is found that the vibrational contributions for the dimers are substantially smaller than their electronic contributions. The ratio of the vibrational to electronic contributions depends strongly on the ratio of the screened vibrational to electronic polarizabilities and on the ratio of the frequency of the strongest infrared-active mode to an ionization energy.   

Recent progress in ab initio density matrix renormalization group methodology

We present some recent developments in the \textit{ab initio} density matrix renormalization group (DMRG) method for quantum chemical problems, in particular our local, quadratic scaling algorithm [1] for low dimensional systems. This method is particularly suited for the description of strong nondynamic correlation, and allows us to compute numerically exact (FCI) correlated energies for large active spaces, up to one order of magnitude larger then can be done by conventional CASCI techniques. Other features of this method are its inherent multireference nature, compactness, variational results, size-consistency and size-extensivity. In addition we will review the problems (predominantly organic electronic materials) on which we applied the \textit{ab initio} DMRG: \qquad 1) metal-insulator transition in hydrogen chains [1] \qquad 2) all-trans polyacetylene [1] \qquad 3) acenes [2] \qquad 4) polydiacetylenes [3]. \bigskip References [1] Hachmann, Cardoen, Chan, \textit{JCP} 125 (\textbf{2006}), 144101. [2] Hachmann, Dorando, Avil\'{e}s, Chan, \textit{JCP} 127 (\textbf{2007}), 134309. [3] \textit{unpublished}.