Session P35: Focus Session: DFT V: Partitioning and Embedding Theories; Finite-Temperature

Exactly Embedded Density Functional Theory for Modeling Chemical Reactions

We will describe embedded density functional theory methods for performing accurate and scalable electronic structure theory calculations in large molecular systems [1,2], with application to clusters, liquids, and electrode interfaces. \\[4pt] [1] Goodpaster JD, Ananth N, Manby FR, and Miller TF, J. Chem. Phys., 133 (2010) 084103. \\[0pt] [2] Goodpaster JD, Barnes TA, and Miller TF, J. Chem. Phys., 134 (2011) 164108.   

Exactly embedded DFT for the efficient simulation of large systems

Although standard wavefunction-based approaches to electronic structure problems have experienced great success in the study of small systems, their poor size scaling prohibits their application to larger systems. One promising technique for overcoming this scaling problem is embedded Density Functional Theory (e-DFT), in which a large system is divided into many smaller subsystems, with individual wavefunction-based calculations being performed on each subsystem. Using our newly developed Exactly Embedded (EE) technique, we demonstrate highly accurate e-DFT calculations on aqueous systems consisting of hundreds of atoms. Furthermore, these calculations are shown to exhibit excellent size scaling and to be massively parallelizable, allowing for efficient calculations of condensed-phase systems.   

A unified quantum mechanics embedding theory for materials and molecules

It is essentially impossible to apply highly accurate quantum mechanics methods to large material samples, creating a need for a sophisticated embedding theory that can locally refine the accuracy of predicted properties. Here, we present a new ab-initio embedding theory that can treat different regions in the material with quantum mechanics methods of appropriately varying levels of accuracy in a seamless way. We first remove the non-uniqueness of embedding potential definitions that exists in most previous embedding theories by introducing a physical constraint that all regions share a common embedding (interaction) potential. We then introduce a key step to achieve seamless embedding: reformulating the system's total energy solely in terms of the embedding potential, i.e., we construct a potential-functional embedding theory (PFET). We demonstrate how to efficiently solve PFET for molecules and materials and give an outlook for how to perform seamless ``multi-physics'' material simulations with PFET.   

Multi-level partitioning using embedded density functional theory

Embedded density functional theory (e-DFT) methods are typically limited to the description of weakly interacting systems, because an exact form of the kinetic energy (KE) density functional is unknown. We have developed a method that avoids approximations to the KE functional and provides a formally exact approach to performing electronic structure calculations in the e-DFT framework. This framework allows systems to be divided into smaller subsystems which can be treated at different levels of theory with the inter-subsystem potential calculated using our e-DFT protocol. Therefore, in regions of large systems where DFT is known to perform poorly, such as van der Waals interactions and strongly correlated electrons, wavefunction calculations can be used. We discuss density partitioning strategies for embedded density functional theory and the accuracy of this multi-level method.   

Partition Density Functional Theory

Partition Density Functional Theory (PDFT) is a formally exact method for obtaining molecular properties from self-consistent calculations on isolated fragments [1,2]. For a given choice of fragmentation, PDFT outputs the (in principle exact) molecular energy and density, as well as fragment densities that sum to the correct molecular density. I describe our progress understanding the behavior of the fragment energies as a function of fragment occupations, derivative discontinuities, practical implementation, and applications of PDFT to small molecules. I also discuss implications for ground-state Density Functional Theory, such as the promise of PDFT to circumvent the delocalization error of approximate density functionals. \\[4pt] [1] M.H. Cohen and A. Wasserman, J. Phys. Chem. A, 111, 2229(2007).\\[0pt] [2] P. Elliott, K. Burke, M.H. Cohen, and A. Wasserman, Phys. Rev. A 82, 024501 (2010).   

Finding Partition Potentials

Partition Density Functional Theory is a formally exact approach to partitioning molecules into fragments via functional minimization and constraints on fragment densities. Cohen and Car proposed a Dynamical Optimization Algorithm for Partition Theory inspired by the Car-Parrinello Method of electronic structure [1]. We modify this algorithm to incorporate a reference HOMO wave-function calculation as a guide to obtain the partition potential, a global quantity arising as the Lagrange multiplier that guarantees satisfaction of the density constraint. We report on the implementation of this procedure for one-dimensional systems, and possible implications for linear-scaling electronic-structure calculations.\\[4pt] [1] M. H. Cohen, and R. Car, J. Phys. Chem. A 2008, 112, 571-575   

Temperature dependence of Thomas-Fermi errors

Finite temperature Thomas-Fermi theory, in addition to its success in systems dominated by classical behavior, can also form the basis for development of a finite temperature local density approximation and its leading corrections. It is therefore imperative that we fully understand its limitations and strengths. To this end, the temperature dependence of Thomas-Fermi errors in densities and integrated quantities for simple models is explored. Behavior of finite-temperature Thomas-Fermi theory in limiting cases will be discussed in the contexts of traditional DFT and its semiclassical foundations. Analysis of finite temperature Thomas-Fermi as a potential functional will be presented.   

Exact Conditions in Finite-Temperature Density-Functional Theory

Density-Functional Theory (DFT) for electrons at finite-temperature is increasingly important in condensed matter and chemistry. The exact conditions that have proven crucial in constraining and constructing accurate approximations for ground-state DFT are generalized to finite-temperature, including the adiabatic connection formula [1]. We discuss consequences for functional construction. \\[4pt] [1] S. Pittalis, C. R. Proetto, A. Floris, A. Sanna, C. Bersier, K. Burke, and E. K. U. Gross, Phys. Rev. Lett, 107, 163001 (2011)   

Systematic Results in Finite Temperature DFT

An exact representation for the non-interacting free energy density functional is identified from the thermodynamics of a non-uniform, finite temperature system of particles in an external potential. A formally exact functional density expansion whose leading term is the Thomas-Fermi approximation is described to second order in the density non-uniformity. The familiar Perrot form [Phys. Rev. A 20, 586 (1979)] is recovered from a subsequent smooth gradient expansion. A related formal expansion about the Thomas-Fermi plus von Weizsacker functional to second order is also described and discussed.   

Finite Temperature Scaling of the Free Energy Density Functional

Recently, we reported exact scaling relations and related bounds and inequalities for the non-interacting (``Kohn-Sham'') free-energy density functional [Phys. Rev. B \textbf{84}, 125118 (2011)]. Here we extend the analysis to obtain similar results for the full,interacting functional. The extension is obtained by dimensionless analysis for the case of $v$-representable densities. Connection with the corresponding ground-state scaling is made.   

Construction of Generalized Gradient Approximation Free Energy Density Functionals

By analyis of the second-order gradient approximation (SGA) for the non-interacting electron free energy density, we propose a finite-temperature generalized gradient approximation (ftGGA) for the noninteracting free energy density (both kinetic and entropic contributions). By analogy we also introduce a ftGGA for the exchange free energy density functional. We have implemented the finite-temperature Thomas-Fermi (ftTF), SGA, and a new finite-temperature GGA free-energy functional in the orbital-free density functional theory (OFDFT) code PROFESS. We compare self-consistent OFDFT results with standard Kohn-Sham data. The local pseudopotentials used in the OFDFT calculations are validated by comparison between Kohn-Sham results obtained with standard non-local pseudopotentials and with the same local pseudopotentials.