Session F46: Real Space Methods for the Electronic Structure Problem

Stochastic Density Functional Theory: Real- and Energy-Space Fragmentation for Noise Reduction

Real-space/plane-wave based density function theory (DFT) is an important approach to understand electronic, optical, and magnetic properties of semiconductor and metallic materials. However, the computational scaling of conventional DFT methods is relatively high. Such a high scaling limits DFT applications in modeling complex materials such as semiconductor/metallic devices and nanomaterials. Therefore, developing linear scaling DFT methods is necessary for studying complex materials. While most linear scaling DFT assumes a localized density matrix, this assumption is not required for stochastic DFT method which utilizes stochastic orbitals instead of deterministic Kohn-Sham orbitals. However, noise in stochastic DFT limits the efficiency of this approach. Various noise reduction techniques that use fragmentations in  real space and/or energy space have been developed. These techniques can significantly reduce the noise level in stochastic DFT to enhance the computational efficiency. These noise-reduction stochastic DFT methods have been applied to geometry optimization of semiconductor materials which is a challenging problem for stochastic DFT with noisy atomic forces.    

DFT-FE — a massively parallel real-space density functional theory code using higher-order adaptive spectral finite-element discretization, and its large-scale application to study dislocation core energetics in crystalline materials

Kohn-Sham density functional theory (DFT) calculations have been instrumental in providing many crucial insights into materials behavior and occupy a sizable fraction of world's computational resources today. However, the stringent accuracy requirements in DFT needed to compute meaningful material properties, in conjunction with the asymptotic cubic-scaling computational complexity with number of electrons, demand huge computational resources. Thus, these calculations are routinely limited to material systems with at most few thousands of electrons. In this talk, we present a massively parallel real-space DFT framework (DFT-FE), which is based on a local real-space variational formulation of the Kohn-Sham DFT energy functional discretized with higher-order adaptive spectral finite-element, and handles pseudopotential and all-electron calculations in the same framework. We will present the efficient and scalable numerical algorithms in conjunction with mixed precision strategies for the solution of Kohn-Sham equations, that has enabled computationally efficient, fast and accurate DFT calculations on generic material systems reaching ~100,000 electrons, on both many-core and hybrid CPU-GPU architectures. DFT-FE achieves an order of magnitude performance advantage over widely used plane-wave codes both in CPU-times and wall-times. Further, we will present our recent work on developing a robust and efficient preconditioner for self-consistent field iterations in Kohn-Sham DFT. Finally, we demonstrate the successful application of DFT-FE to accurately study the core energtics of pyramidal dislocations in magnesium, which have so far been out of reach as large system sizes containing thousands of atoms are required to accurately resolve the relevant physics in the dislocation core.    

Exploring Ion Dynamics in Charged Systems using Real-Space Pseudopotential Density Functional Theory

Ions are prevalent in Nature. Their dynamics is key to understanding various physical processes and chemical reactions. Proton hopping, for instance, is an important mechanism to explain the exceptionally high diffusivity of protons in water. Studies have demonstrated such proton transfer mechanisms may be vital to biochemical systems. To study proton hopping by first-principles approaches, it is common to use a supercell. These boundary conditions can add artificial correlated motion. Moreover, charged systems in supercells often adopt a uniform compensating background charge to avoid the computation of divergent electrostatic energies. However, it is not clear how well this approach reproduces the physical boundary conditions felt by the proton. We will compare supercell methods with a confined domain method where there is no need of a compensating charge within the same framework of real-space pseudopotential density functional theory.   

The Power of TDDFT in Real-Time and Real-Space: From Light Harvesting to Photoemission

Solving the time-dependent equations of Kohn-Sham or generalized Kohn-Sham theory by propagation in real time on a grid in real space is a powerful approach for calculating electronic excitations. The technique is ideally suited for studying large systems and long-range charge-transfer phenomena due to its excellent parallelization. We here discuss two example of electron dynamics that can excellently be described with the real-time and real-space technique. First, we discuss how to simulate photoemission as a process in real time. When a system is excited by an electromagnetic field of sufficient frequency, it can emit electrons. We simulate the emission of the outgoing wave packet in real time and calculate the corresponding kinetic energy spectrum. In this way, angular resolved photoemission signals can be calculated. Challenging phenomena, like pump-probe photoemission mapping excited states and circular dichroism in the angular distribution of the emitted electrons are thus obtained in close agreement with experiments. Second, we discuss how the energy-transfer processes that occur in natural light-harvesting systems can be studied via real-space and real-time techniques. We demonstrate in calculations for the antenna complexes of photosynthetic bacteria how one can extract just from the time-dependent density information about how energy is transported between the chromophores and thus efficiently collected.   

Implementation of Ensemble Density Functional Theory for excited states in the real-space Octopus code

Ensemble Density Functional Theory is a method to calculate excitation energies from an ensemble of ground and excited states, which can resolve some shortcomings – like multiplet splittings and double excitations – of Time-Dependent Density Functional Theory (TDDFT) approximations. Whereas many EDFT formulations require self-consistent ensemble calculations, the computationally efficient Direct Ensemble Correction (DEC) takes the form of a correction to the Kohn-Sham energy differences, as in linear-response TDDFT [Yang et al., Phys. Rev. Lett. 119, 033003 (2017)]. This theory, in the symmetry-eigenstate Hartree-exchange approximation, has already been applied to model systems and atoms, but now we implement DEC in the real-space Octopus code to be able to apply it to larger real systems. Octopus is well-suited for this study because it can handle model systems as well as real systems, and both finite and periodic boundary conditions. We compare the results from DEC to other standard excited-state approaches like Configuration Interaction Singles, and both linear-response and time-propagation Time-Dependent Hartree-Fock and TDDFT. We also analyze the computational cost and accuracy of DEC compared to these different approaches.   

DFT Embedding in Python for Realistically-sized Systems

With modern hardware advances, the exascale computing era has begun. Thus, for computational chemistry and physics, multiscale models of materials and biological systems are arguably the most important platforms for tackling the challenges ahead. Nowadays, density functional theory (DFT) is the method of choice. However, DFT's computational scaling hampers its applicability to realistically sized systems. In an effort to retain the predictivity of DFT while at the same time reducing the computational cost, we present eDFTpy, a density embedding Python code. In eDFTpy, the system is split into weakly interacting subsystems treated either at the Kohn-Sham DFT level or at the orbital-free DFT level. Inter-subsystem interactions are evaluated with orbital-free DFT. This leads to a linear-scaling, low prefactor algorithm having essentially KS-DFT accuracy that can be used for realistically-sized systems. The parallelization scheme of eDFTpy is state-of-the-art: it has low memory cost and small communication time, thus strong parallel scaling to thousands of cores is achieved.   

Magnons from real-space real-time time-dependent density functional theory

In the last couple of years, the first studies investigating magnetization dynamics from first principles in real time have emerged. We recently developed an efficient and non-perturbative scheme to compute magnetic excitations for extended systems employing the framework of real-time time-dependent density functional theory, which is an alternative to the linear-response TDDFT formulation.

To investigate magnons, we drive the system out of equilibrium using an ultrashort magnetic kick perpendicular to the ground-state magnetization of the material. The dynamical properties of the system are obtained by propagating the time-dependent Kohn-Sham equations in real time, and the analysis of the time-dependent magnetization reveals the transverse magnetic excitation spectrum of the magnet.

In the limit of weak magnetic kicks, we recover the results obtained using the linear-response formulation of time-dependent density functional theory.

Interestingly, our approach does not rely on the assumptions of small perturbations and can be used to investigate nonlinear phenomena induced by a strong magnetic field as well as out-of-equilibrium situations where the system is kicked from an excited state. In this talk, we will present results for nonlinear magnetic excitations from first principles in iron and nickel oxide.

Using the real-space method, we benefit from a favorable scaling for large systems, such as supercells needed for describing small momenta. Moreover, using the flexibility of choosing boundary conditions that are employed, we also implemented a method using "twisted boundary conditions" employing the generalized Bloch theorem, allowing for studying magnons employing only primitive cells instead of supercells.   

Atomic fingerprinting of heteroatoms using noncontact atomic force microscopy

Richard P. Feynman said the following during his talk at the APS annual meeting in 1959: “If you have a strange substance and you want to know what it is, you go through a long and complicated process of chemical analysis.… It would be very easy to make an analysis of any complicated chemical substance; all one would have to do would be to look at it and see where the atoms are. The only trouble is that the electron microscope is one hundred times too poor.” Feynman’s idea has been, partially, realized through the use of noncontact atomic force microscope (nc-AFM). Nc-AFM with a functionalized CO tip made visualization of molecules and atoms possible. This atomic resolution dazzles the scientific world and opens new avenues of science. However, the measured nc-AFM images are sometimes hard to interpret. To be specific, using the common CO tip can barely distinguish heteroatoms (such as N, S, etc.) from C atoms.

We employ real-space pseudopotentials constructed within density functional theory code, PARSEC (http://real-space.org/), to simulate nc-AFM images using various functionalized tips at different tip heights. Our simulation work has demonstrated that using nc-AFM with a chemically inert tip (CO tip) followed by a metallic tip (Cu tip) is a promising method to discriminate heteroatoms from C atoms within molecules.   

A first principles investigation of electronic charge distribution in random alloys

In this presentation, we investigate, from the first principles, the electronic charge distribution in random alloys by applying super cell calculations with a linear scaling real space ab initio method, namely the LSMS method. We revisit the so-called qV relation, a phenomenon observed by previous super cell calculations that the excess charge at each atomic site depends linearly on the long range electrostatic potential, or Madelung potential, at the site. We reveal the underlying mechanism that drives the establishment of the qV relation. We show that this relation can be used to improve the conventional KKR-CPA method, or other CPA based ab initio k-space methods, in the self-consistent field calculations.