Jan-Erik

We present a bio-inspired stochastic optimization strategy that optimizes projector augmented wave (PAW) datasets, for a user-specified pressure range, to realize the highest possible accuracy in high-throughput density functional theory calculations within the framework of PAW method. We named the optimizer “Evolutionary Generator of projector augmented wave datasets” (EPAW-1.0). The self-learning evolutionary algorithms in EPAW-1.0 adaptively tune some of the PAW parameters (such as different radii, and reference energies) to generate evolutionary optimized PAW (EPAW) datasets. In the course of designing EPAW dataset with a specific pseudo partial waves and projectors generation scheme, the code keeps the user-specified electronic configuration unaltered and the augmentation radius (rc) on the verge of the user allowed maximum without resulting in sphere overlap. The EPAW-1.0 algorithm homes on to a soft, transferable and unified EPAW dataset using various measures including the equation of state (EoS) of standard elemental materials within a user-specified pressure range that allows probing ∼50% volume compression with respect to the equilibrium atomic volume (corresponding to the energy minimum). The measures used by the EPAW algorithm also can be used to balance the efficiency and accuracy of the dataset.

Program Title: EPAW-1.0

Program Files doi:http://dx.doi.org/10.17632/ms52ym7vcn.1

Licensing provisions: GNU General Public License 3 (GPLv3)

Programming languages: Fortran90, Fortran77, Python3.0, bash shell, gnuplot5.0.

External routines/libraries: ATOMPAW, Quantum ESPRESSO, related linear algebra package.

Nature of problem: EPAW-1.0 is a hybrid recipe [2] that documents an interdisciplinary research integrating evolutionary computing with density functional theory (DFT). It offers a partially automated and consistent route to generate evolutionary optimized PAW (EPAW) datasets that show uniform performance for simulations up to a predefined high pressure. In particular, EPAW-1.0 makes use of evolutionary algorithms [[3], [4], [5], [6], [7]], PAW dataset generator (ATOMPAW [8], for example) and electronic-structure calculation code (Quantum Espresso [9], for example) to generate efficient and transferable EPAW datasets. EPAW datasets provide optimal accuracy in solid-state ab initio calculations within the favorable PAW computational framework — very close to the precision of targeted all-electron full potential linearized Augmented-plane-wave (AE-FLAPW) approach. We set the EoS from WIEN2k [1] calculations as our target, but any reliable EoS can be in use. The better the target EoS, the better is the performance of the EPAW datasets. Similarly, electronic-structure calculation code and PAW dataset generator code can also be replaced.

Solution Method: The implementation has two parts: a. Generating a diverse random initial population for EPAW-1.0 to start with; b. Generating EPAW dataset using EPAW-1.0.

A hybrid method, combining an in-house evolutionary strategy named Completely Adaptive Random Mutation Hill Climbing [6] (CARMHC) with ATOMPAW [8] program, quickly optimizes a set (population) of npop solutions (PAW dataset descriptors) from which the iterative process of EPAW-1.0 starts. The optimization condition involves superimposing the logarithmic derivative curves of the all-electron and pseudo radial wave functions, simultaneously satisfying necessary constraints on logarithmic derivatives, partial waves, pseudo partial waves and projector basis sets [[2], [8], [10], [11], [12]]. To start with, the method generates a diverse initial population of npop solution vector (npop= cardinality of the GA’s population in EPAW-1.0) randomly in the neighborhood of the initial educated guess based on problem-specific knowledge from the ATOMPAW program and iteratively tunes the population to minimize the area under the logarithmic derivative curves.

Once npop number of solution strings have been optimized, npop individuals are feed into the EPAW-1.0’s initial population. Equilibrium total energies are evaluated using Quantum Espresso distribution [9] and fitted to a finite strain expansion. Pressures are calculated using a 4-parameter Birch–Murnaghan fit [[13], [14]]. EPAW-1.0 employs genetic algorithms (GAs) [[15], [16], [17], [18], [19]] as the evolutionary procedure and iteratively tunes the free parameters of the PAW dataset generator to minimize the difference in equation of states (EoS) with respect to the given target EoS for the specified pressure range.

Additional comments: EPAW-1.0 is an evolutionary procedure blended with external density functional theory (DFT) formalism (as implemented in ATOMPAW and Quantum Espresso, for example). The ATOMPAW code generates dataset by a self-consistent all-electron atomic structure calculation within the framework of DFT. The projector and basis functions are derived from the eigenstates of the all-electron atomic Hamiltonian. They are determined by iteratively solving radial differential equations. Equilibrium total energies at some equidistant volume points for a specific elemental crystal are evaluated using Quantum Espresso distribution [9]. The EPAW-1.0 program conserves different constraints [2] on logarithmic derivatives and basis sets to avoid numerical instability, ghost states, and to promote an excellent transferability. More details about the constraints can be found in the methodology part of reference 1. It also provides a goodness measure of the generated dataset concerning the targeted results.

The adsorption of SO₂ on single crystalline TiO₂(110) has been investigated by means of polarized infrared reflection-absorption spectroscopy (IRRAS) experiments and density functional theory (DFT) calculations. IR absorption bands were detected at 1324 cm−1 and 985 cm−1 with p-polarized light incident along both the [11¯0] and [001] crystallographic directions at 123 K. When the temperature was increased to 153 K, the peak at 1324 cm−1 disappears, while a new, weak band appears at 995 cm−1. Simultaneously, a band at 995 cm−1 also emerges with s-polarized light along the [11¯0] direction. Based on the symmetry properties of the IRRAS spectra and accompanying ab initio simulations of the spectra employing a three layer model (vacuum-adsorbate-substrate), it is shown that the low temperature absorption IRRAS bands can be attributed to an SO₃-like adsorbate structure. This is also the most stable adsorption structure (E_ad = −0.58 eV) on the stoichiometric surface. The combined IRRAS and DFT results show that the band appearing at 995 cm−1 is associated with a surface sulfite specie which is stabilized by residual surface water. The DFT calculations also revealed that a stable adsorption structure exists on a reduced TiO₂ surface, where SO₂ binds strongly to an oxygen vacancy site. It is suggested that this is an intermediate that form surface sulfate upon further reactions with water, although it was not observed on the stoichiometric surface studied in this work.

Analysis of the chemical-organic knowledge represented as a giant network reveals that it contains millions of reaction sequences closing into cycles. Without realizing it, independent chemists working at different times have jointly created examples of cyclic sequences that allow for the recovery of useful reagents and for the autoamplification of synthetically important molecules, those that mimic biological cycles, and those that can be operated one-pot.

NOC-ing on heaven′s door: Big-data analysis of the network of organic chemistry (NOC), reveals that over many decades, chemists have created—unknowingly—millions of cyclic reaction sequences including those that recover valuable substrates, those that amplify useful chemicals, or those that mimic biological cycles. The image shows a special type of a cycle (the so-called clique) in which any member can be made from any other one in one step. Colors correspond to years in which a reaction was first reported.