EPAW-1.0 code for evolutionary optimization of PAW datasets especially for high-pressure applications

Abstract 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 ( r c ) 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 n p o p 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 n p o p solution vector ( n p o p = 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 n p o p number of solution strings have been optimized, n p o p 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.