Session C9: Invited Session: Recent Developments in Density Functional Theory I

Aneesur Rahman Prize for Computational Physics Lecture: Addressing Dirac's Challenge

After the invention of quantum mechanics, P. A. M. Dirac made the following observation: ``The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that {\it approximate practical methods} of applying quantum mechanics should be developed, which can lead to an explanation of the main features of complex atomic systems...'' The creation of ``approximate practical methods" in response to Dirac's challenge has included the one electron picture, density functional theory and the pseudopotential concept. The combination of such methods in conjunction with contemporary computational platforms and new algorithms offer the possibility of predicting properties of materials solely from knowledge of the atomic species present. I will give an overview of progress in this field with an emphasis on materials at the nanoscale.   

Recent Progress in Linear Scaling DFT

Linear scaling or O(N) electronic structure codes have been under development for around fifteen years. After an initial explosion of interest, the practical difficulties of implementation and efficiency have led to a slow down in development and applications. In this talk I will present details of recent developments in the massively parallel CONQUEST linear scaling DFT code, and make some comments on the linear scaling field in general. The CONQUEST code is one of the leading O(N) codes, and has demonstrated not only excellent scaling to over two million atoms and many thousands of cores but also practical applications to nanostructures on semiconductor surfaces, and recently to biological systems. I will describe the details of the CONQUEST code, including recent developments in basis functions and parallelisation. I will also discuss recent improvements including constrained DFT, exact exchange and TDDFT, all of which have been implemented with linear scaling.\\[4pt] D. R. Bowler and T. Miyazaki, Rep. Prog. Phys. \textbf{75} 036503 (2012).   

Electron response in van der Waals density functionals

There is significant interest in density functional theory (DFT) of dispersive or van der Waals (vdW) interactions and in DFT studies of sparse systems where vdW forces contribute to the cohesion and behavior. The Rutgers-Chalmers van der Waals density functional (vdW-DF) method [PRL \textbf{92}, 246401 (2004); PRB \textbf{76}, 125112 (2007)] is a nonempirical approach to calculate vdW bonding and for DFT characterizations of sparse matter. The vdW-DF framework is defined by a single exchange-correlation density functional that rests on a plasmon-type description for both semilocal components and for a parameter-free evaluation of nonlocal correlation. My talk summarizes a set of vdW-DF studies that seeks to map and analyze details in the vdW-DF electron-response nature. The purpose is in part to extract consequences that can facilitate an experiment-theory comparison that goes beyond binding geometries and energies. The aim is also to seek implications that can help develop the vdW-DF framework. I present an analysis of the relative importance of morphology, screening (image-plane formation), and collective effects in the vdW-DF description of molecular systems. In addition, I compare vdW-DF results with Cu(111) experiments that tests the electron-response behavior in terms of adsorption-induced band shifts, the form of the overall light-molecule physisorption potential, and the corrugation in the kinetic-energy repulsion of molecules at surfaces. Overall, the vdW-DF studies suggest the importance of benchmarking vdW methods across different length scales and by exploring the variation that arise when related structures have a different balance between exchange repulsion and vdW attraction.   

Time-Resolved Dynamics in Time-Dependent Density Functional Theory: Significance of Non-locality in Space and Time

The usual approximations in Time-Dependent Density Functional Theory (TDDFT) have achieved an unprecedented balance between accuracy and efficiency for calculating excitation spectra and response. We show however that these approximations are less successful for time-resolved dynamics beyond the linear response regime. Step and peak structures develop in the exact exchange-correlation potential that have a density-dependence that is non-local both in time and in space, missed by all approximations in use today. The lack of these structures leads to their incorrect predictions of dynamics, such as faster time-scales, and incomplete charge-transfer. [P. Elliott, J.I. Fuks, A. Rubio, N.T. Maitra arXiv:1211.2012; J. I. Fuks, P. Elliott, A. Rubio, N. T. Maitra, arXiv:1211.2849]   

Improving Density Functionals with Quantum Harmonic Oscillators

Density functional theory (DFT) is the most widely used and successful approach for electronic structure calculations. However, one of the pressing challenges for DFT is developing efficient functionals that can accurately capture the omnipresent long-range electron correlations, which determine the structure and stability of many molecules and materials. Here we show that, under certain conditions, the problem of computing the long-range correlation energy of interacting electrons can be mapped to a system of coupled quantum harmonic oscillators (QHOs). The proposed model allows us to synergistically combine concepts from DFT, quantum chemistry, and the widely discussed random-phase approximation for the correlation energy. In the dipole limit, the interaction energy for a system of coupled QHOs can be calculated exactly, thereby leading to an efficient and accurate model for the many-body dispersion energy of complex molecules and materials. The studied examples include intermolecular binding energies, the conformational hierarchy of DNA structures, the geometry and stability of molecular crystals, and supramolecular host--guest complexes (A. Tkatchenko, R. A. DiStasio Jr., R. Car, M. Scheffler, Phys. Rev. Lett. 108, 236402 (2012); R. A. DiStasio Jr., A. von Lilienfeld, A. Tkatchenko, PNAS 109, 14791 (2012); A. Tkatchenko, D. Alfe, K. S. Kim, J. Chem. Theory and Comp. (2012), doi: 10.1021/ct300711r; A. Tkatchenko, A. Ambrosetti, R. A. DiStasio Jr., arXiv:1210.8343v1).