No Arabic abstract
Large scale electronic structure calculations require modern high performance computing (HPC) resources and, as important, mature HPC applications that can make efficient use of those. Real-space grid-based applications of Density Functional Theory (DFT) using the Projector Augmented Wave method (PAW) can give the same accuracy as DFT codes relying on a plane wave basis set but exhibit an improved scalability on distributed memory machines. The projection operations of the PAW Hamiltonian are known to be the performance critical part due to their limitation by the available memory bandwidth. We investigate on the utility of a 3D factorizable basis of Hermite functions for the localized PAW projector functions which allows to reduce the bandwidth requirements for the grid representation of the projector functions in projection operations. Additional on-the-fly sampling of the 1D basis functions eliminates the memory transfer almost entirely. For an quantitative assessment of the expected memory bandwidth savings we show performance results of a first implementation on GPUs. Finally, we suggest a PAW generation scheme adjusted to the analytically given projector functions.
In this work, we report for the first time, detailed calculations of elastic and thermodynamic properties of organic poly(3,4-ethylenedioxythiophene), PEDOT, in an undiluted state, using PBE and PBEsol-PAW pseudopotentials within the framework of Generalized Gradient Approximation Density Functional Theory. Contrary to Molecular Dynamic simulations, series of PBE and PBEsol-PAW calculations in the current work revealed the most stable state of monoclinic structured pristine PEDOT. We determined thirteen (13) independent elastic constants with elastic compliance which enables us to establish other elastic properties of pristine PEDOT; the Pughs ratio and the Vickers hardness calculations show small mismatches with PBE and PBEsol-PAW pseudopotentials. The Debye temperature TD is predicted both in the PBE and PBEsol-PAW calculations while the specific heat capacity Cv(T) follows the Dulong-Petit curve having no mismatch with Debye model at low temperature, with PBE predicting a higher Debye sound velocity than PBEsol-PAW. As accuracy tests only, we performed electronic structure calculations of PEDOT and compared with available data in the literature.
We present and motivate an efficient way to include orbital dependent many--body correlations in trial wave function of real--space Quantum Monte Carlo methods for use in electronic structure calculations. We apply our new orbital--dependent backflow wave function to calculate ground state energies of the first row atoms using variational and diffusion Monte Carlo methods. The systematic overall gain of correlation energy with respect to single determinant Jastrow-Slater wave functions is competitive with the best single determinant trial wave functions currently available. The computational cost per Monte Carlo step is comparable to that of simple backflow calculations.
Analytical representations in the time and frequency domains are derived for the most frequently used phenomenological fit functions for non-Debye relaxation processes. In the time domain the relaxation functions corresponding to the complex frequency dependent Cole-Cole, Cole-Davidson and Havriliak-Negami susceptibilities are also represented in terms of $H$-functions. In the frequency domain the complex frequency dependent susceptibility function corresponding to the time dependent stretched exponential relaxation function is given in terms of $H$-functions. The new representations are useful for fitting to experiment.
We introduce a coarse-grained deep neural network model (CG-DNN) for liquid water that utilizes 50 rotational and translational invariant coordinates, and is trained exclusively against energies of ~30,000 bulk water configurations. Our CG-DNN potential accurately predicts both the energies and molecular forces of water; within 0.9 meV/molecule and 54 meV/angstrom of a reference (coarse-grained bond-order potential) model. The CG-DNN water model also provides good prediction of several structural, thermodynamic, and temperature dependent properties of liquid water, with values close to that obtained from the reference model. More importantly, CG-DNN captures the well-known density anomaly of liquid water observed in experiments. Our work lays the groundwork for a scheme where existing empirical water models can be utilized to develop fully flexible neural network framework that can subsequently be trained against sparse data from high-fidelity albeit expensive beyond-DFT calculations.
In silico materials design is hampered by the computational complexity of Kohn-Sham DFT, which scales cubically with the system size. Owing to the development of new-generation kinetic energy density functionals (KEDFs), orbital-free DFT (OFDFT, a linear-scaling method) can now be successfully applied to a large class of semiconductors and such finite systems as quantum dots and metal clusters. In this work, we present DFTpy, an open source software implementing OFDFT written entirely in Python 3 and outsourcing the computationally expensive operations to third-party modules, such as NumPy and SciPy. When fast simulations are in order, DFTpy exploits the fast Fourier transforms (FFTs) from PyFFTW. New-generation, nonlocal and density-dependent-kernel KEDFs are made computationally efficient by employing linear splines and other methods for fast kernel builds. We showcase DFTpy by solving for the electronic structure of a million-atom system of aluminum metal which was computed on a single CPU. The Python 3 implementation is object-oriented, opening the door to easy implementation of new features. As an example, we present a time-dependent OFDFT implementation (hydrodynamic DFT) which we use to compute the spectra of small metal cluster recovering qualitatively the time-dependent Kohn-Sham DFT result. The Python code base allows for easy implementation of APIs. We showcase the combination of DFTpy and ASE for molecular dynamics simulations (NVT) of liquid metals. DFTpy is released under the MIT license.