Session P02: Developments of DFT from Quantum to Statistical Mechanics (IV)

Efficient molecular density functional theory using generalized spherical harmonics expansions

We show that generalized spherical harmonics are well suited a basis set for representing the space and orientation molecular density for the resolution of the (classical) molecular density functional theory. We consider the common system made of a rigid molecule of arbitrary complexity immersed in a molecular solvent, both represented by molecules with interacting atomic sites and classical force fields. The molecular solvent density ρ(r,Ω) around the solute is a function of the position r and of the three Euler angles Ω describing the solvent orientation. The standard density functional, equivalent to the HNC closure for the solute-solvent correlations in the liquid theory, is minimized with respect to ρ(r,Ω). The up-to-now very expensive angular convolution products are advantageously replaced by simple products between projections onto generalized spherical harmonics. The dramatic gain in speed of resolution enables to explore in a systematic way molecular solutes of up to nanometric sizes in arbitrary solvents and to calculate their solvation free energy and associated microscopic solvent structure in at most a few minutes. We show how this theory must be completed to fulfil thermodynamic consistency, at least in terms of pressure and surface tension. We finaly illustrate the formalism by tackling the solvation of molecules of various complexity in water.   

Connecting Quantum and Classical DFT

Because particles are distinguishable in classical DFT, one can relate the pair correlation function of a uniform system to the density response of an inhomogeneous system, in which one of the particles is considered an external impurity. We apply the same reasoning as an uncontrolled approximation to estimate the pair correlation function of a uniform quantum electron gas, assuming one of the electrons can be distinguished from all others (a ``blue" electron). The errors in this approximation should shrink with increasing temperature. We report the accuracy and limitations of this approach.   

Steps in the Exact Kohn-Sham Potential of Ensemble Density-functional Theory for Excited States and Their Relation to the Derivative Discontinuity

An accurate approximation to the exchange-correlation (xc) part of the Kohn-Sham (KS) potential is essential for any density-functional calculation. Density-functional theory (DFT) is widely used in condensed matter physics, quantum chemistry and many other fields. Therefore, understanding the behaviour of the exact xc potential and developing improved approximations to it are of the utmost importance. The focus of calculations within DFT is usually on the ground state. However, knowledge of how the system responds to an excitation is important. In this talk we present the exact KS potential of an ensemble of the ground state and the first excited state of a 1D diatomic molecule. For this system, upon excitation, a small amount of charge transfers from one atom to the other. In the corresponding exact ensemble xc potential we find two plateaus: one that forms around the nucleus of the acceptor atom, associated with the derivative discontinuity of that atom (Δ), and another that forms around the donor atom and corresponds to a new phenomenon which we term the 'charge-transfer derivative discontinuity'. The relevance of the aforementioned features to an accurate prediction of the excitation spectrum is discussed.   

Time-Dependent Multi-Component Density Functional Theory for Coupled Electron-Positron-Nuclear Dynamics

Positrons have been studied and utilized in various fields of molecular physics and surface science. We are particularly interested in dynamics of positron-atom compound systems under laser fields, which has been actively conducted mainly by experiments, because the microscopic mechanism of correlated dynamics of positrons with electrons and nuclei in these experiments is far from understanding. Here we propose and develop time-dependent multi-component density functional theory (TDMCDFT) for coupled electron-positron dynamics to explore the dynamics of positron-molecular compound systems. This TDMCDFT is a first-principles approach that can simulate formally exact excited state quantum dynamics of coupled electron-positron systems. In the present work we propose an adiabatic local density approximation for time-dependent electron-positron correlation. We apply this TDMCDFT approach to the dynamics of positron detachment from polar and non-polar molecules under various laser fields. Furthermore we derive the TDMCDFT-Ehrenfest molecular dynamics scheme to account for the coupling to nuclear motion. We elucidate the difference in the dynamics between polar and non-polar molecules and how laser intensity and frequency and nuclear motion play a role for efficient positron detachment.   

Validating Molecular Dynamics and Joint DFT Predictions of Interfacial Water Using X-Ray Reflectivity

Capturing the structure and properties of water next to a solid surface presents a unique challenge for both Kohn-Sham and classical density-functional theories due to a complex interplay between chemical binding, electrostatic interactions, steric effects, and dispersion. X-ray reflectivity measurements determine the electron density of aqueous interfaces with high precision, but rely on model-dependent fitting to obtain the corresponding structural model. We present a validation protocol which enables calculation of interfacial X-ray structure factors from theory for direct comparison to experimental measurements. We apply this protocol to benchmark first principles molecular dynamics, classical molecular dynamics, and joint DFT simulations of the Al₂O₃/water interface, probing the effect of pressure, temperature, and finite size upon the predicted structural model. We explore the relative strengths and weaknesses of each class of theory, gaining insights into the bonding and structural properties of interfacial water which will aid future development of more accurate electronic and classical density-functionals.   

DFT-based embedding theories: Wavefunction-embedding, dynamics, excited states, and applications

The simulation of chemical dynamics in complex systems demands the development of methods with improved accuracy and computational scaling. Density functional theory (DFT) provides a rigorous and flexible framework for achieving this aim, by enabling the embedding of either (i) a subsystem described at the accurate wavefunction level in a DFT environment or (ii) a subsystem described at the DFT level in a tight-binding environment. My talk will focus on recent developments along these lines, including the use of such methods to describe ground- and excited-state chemical dynamics and surface reactions in condensed-phase systems.
  

Applying Exact Conditions to Machine Learned Density Functionals

Historical methods of functional development in density functional theory have been largely guided by analytic conditions that constrain the exact functional one is trying to approximate. Recently, machine learning functionals, which are formed by extrapolating the results from a small number of exactly solved systems to unsolved systems that are similar in nature, have turned away from utilizing constraints on the exact functional. In this work, we show that imposing these exact conditions onto machine learning functionals can improve the ability of the machine learning functionals to extrapolate to unsolved systems.

In particular, we machine learn the non-interacting kinetic energy of a set of densities in two ways. First, we train on the densities without any applied scaling. Second, we train on the densities scaled so that the root mean square of the density is unity, which relates to the unscaled non-interacting kinetic energy through exact conditions. We compare the performance of these machine learning functionals, showing that the latter tends to produce lower errors given an equal number of training data.   

Generating Generalized K-point Grids on the fly

Traditionally, Brillouin zone integration has been done using Monkhorst-Pack K-point grids. Recently, Wisesa et. al. [1] were able to build a database of more general grids that have better folding than traditional Monkhorst-Pack grids. The better folding allows for increased performance in Density Functional Codes. Leveraging concepts from group theory we have developed an on-the-fly-algorithm that generates general K-point grids that have optimal K-point folding.

[1] Wisesa et. al. Efficient generation of generalized Monkhorst-Pack grids through the use of informatics. Phys. Rev. B, 93:155109, Apr 2016   

Inclusion of the ionic zero-point motion in the density functional theory-beyond the Born-Oppenheimer approximation

We introduce a novel method to carry out a zero temperature density functional theory (DFT) calculation for systems in which the ionic motion is treated fully quantum mechanically and the electronic degrees of freedom are treated within imaginary-time dependent DFT. The approach is based on the finite-temperature many-body path-integral formulation of quantum mechanics by taking the zero-temperature limit and treating the imaginary-time propagation of the electronic variables ``exactly'' within the DFT. Our approach goes beyond the familiar Born-Oppenheimer approximation and is limited from being exact only by the approximations involved in the DFT approach and it includes the effects of the electronic charge correlations in imaginary time. The method is tested in simple molecules which contain light atoms, such as hydrogen, where the fluctuations of the distance from its equilibrium position, due to the zero-point-motion, is comparable to the interatomic distances.   

Utilizing Advanced Kinetic Energy Density Based Ingredients for Novel Local Hybrid Mixing Functions

Density functional theory (DFT) has become an invaluable tool across many domains of chemistry and materials science, a success made possible by the high accuracy and efficiency of modern density functional approximations (DFA). Despite continued progress in functional design, conventional DFAs suffer a poor description of the strong many-electron interaction (SMEI) and self-interaction error (SIE). Such deficiencies degrade accuracy in predictions of many properties important for energy applications, including band gaps, stretched bonds, catalysis, charge transfer processes, and reaction barriers¹.

Despite efforts to solve SIE and SMEI within DFT, there is no efficient functional applicable to both molecules and solids that solves the SIE and SMEI and maintains standard DFA accuracy at equilibrium². We investigate the local hybrid functional form, including a space dependent admixture of exact-exchange energy³, to address this absence. A recent local hybrid framework in the QUEST rapid development platform is used to develop local mixing functions from kinetic energy densities².

¹P. Mori-Sánchez, A. J. Cohen, and W. Yang, PRL 100, 146401 (2008)
²J. Sun, A. Ruzsinszky, and J. P. Perdew, PRL 115, 036402 (2015)
³Burke, K., Cruz, F. G., & Lam, K. C., JCP, 109(19), 8161–8167 (1998)