Full spectrum optical constant interface to the Materials Project J. J. Kasa,b, F. D. Vilaa,b, C. D. Pemmarajub, M. P. Prangec, K. A. Perssond, R. X. Yangd, J. J. Rehra,b,∗ aDepartment of Physics, University of Washington, Seattle, WA 98195, USA bStanford Institute for Materials and Energies Sciences, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA cPhysical and Computational Sciences Directorate, Pacific Northwest National Laboratory: Richland, WA 99352 dMaterials Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA Abstract Optical constants characterize the interaction of materials with light and are important properties in material design. Here we present a Python-based Corvus workflow for simulations of full spectrum optical constants from the UV- VIS to hard x-ray wavelengths based on the real-space Green's function code FEFF10 and structural data from the Materials Project (MP). The Corvus workflow manager and its associated tools provide an interface to FEFF10 and the MP database. The workflow parallelizes the FEFF computations of optical constants over all absorption edges for each material in the MP database specified by a unique MP-ID. The workflow tools determine the distribution of computational resources needed for that case. Similarly, the optical constants for selected sets of materials can be computed in a single-shot. To illustrate the approach, we present results for nearly all elemental solids in the periodic table, as well as a sample compound, and compared with experimental results. As in x-ray absorption spectra, these results are interpreted in terms of an atomic-like background and fine-structure contributions. Keywords: Optical constants, Materials Project, FEFF, Corvus 1. Introduction quantitative.[8{17] Also limited tables of theoretical op- tical constants of materials have been compiled over the Optical constants characterize the frequency depen- optical range.[18, 19] However, such calculations involve dent interaction between light and matter in the long- many-body calculations of optical response, and become wavelength limit. Thus they are often important char- computationally intractable for many materials over broad acteristics in materials design. These properties include spectral ranges. In contrast, the real-space Green's func- the complex dielectric constant and index of refraction, tion (RSGF) approach in FEFF10 includes the key many- as well as the energy-loss function, photoabsorption co- body effects, is highly automated and has proved to be efficient, and optical reflectivity.[1{4] Many other physi- quite accurate for general materials in the x-ray regime. cal properties can be derived from the optical constants, Moreover the code can be semi-quantitative in the UV-VIS including electron energy loss spectra (EELS), inelastic to soft-x-ray regime.[20] Thus the code provides an effi- mean-free paths, the atomic scattering amplitudes, and cient platform for calculations of dielectric properties over Hamaker constants for the van der Waals interaction. For a broad spectral range. Consequently, theoretical calcula- these purposes, tabulations of experimentally determined tions based on FEFF10 provide an attractive alternative to optical constants are widely used.[1{4] For practical rea- available theoretical and experimental tabulations of op- sons, however, such tabulations are limited to a rela- tical constants for many purposes. Nevertheless, selected tively small number of well characterized materials over experimental measurements are important to validate the limited spectral ranges and limited environmental condi- theory. tions. Thus here we focus on broad spectrum theoreti- cal treatments for the systems defined in the Materials Recently K- and L-shell XAS calculations based on the Project(MP) database. FEFF code have been added for a very large number of Significant progress has been made in the fundamen- materials in the Materials Project (MP) database.[21, 22] arXiv:2108.10981v2 [cond-mat.mtrl-sci] 26 Aug 2021 tal theory of optical properties since the pioneering These data have been exploited, e.g., in machine-learning works of Nozieres and Pines,[5] Adler,[6] and Wiser.[7] models for the interpretation of XAS data.[21, 23] Our In particular modern first-principles calculations based aim here is to complement these properties with a more on time-dependent density functional theory (TDDFT) complete set of optical constants for all edges from the and the Bethe-SalpeterEquation (BSE) are now highly UV-VIS to hard-x-ray energies. Consequently, the results presented here provide significant extension, both in the ∗Corresponding author variety of optical-constant spectra, spectral range, and ma- Email address: [email protected] (J. J. Rehr) terial properties. Our approach is based on the the devel- Preprint submitted to Computational Materials Science August 27, 2021 1e4 opment of the Corvus [opcons] workflow, where Corvus is Expt. (DESY) the workflow engine,[24] and opcons is the target property. FEFF (Opcons) 2 atomic In particular, the approach imports the structural and 1e property data from the MP, and then parallelizes and au- 1e0 tomates the calculations permitting high-throughput cal- culations of optical constants for materials throughout the 1e−2 MP database. Our procedure for theoretical calculations (E) 2 ε of optical constants over all edges essentially follows that 1e−4 Cu described in detail by Prange et al.,[20] but has been up- dated for the FEFF10 code. In addition, refinements for 1e−6 including vibrational disorder via the correlated Debye −8 model using MP data have been added and the calcula- 1e tions for the UV-VIS range have been simplified. To il- 1e−10 lustrate the approach calculations have been carried out 0.1 1 10 100 1000 10000 100000 for nearly all elemental solids throughout the periodic ta- Energy (eV) ble and explicit examples are given for Cu, Ag, and Au, 0.7 full together with comparisons to experimental data. In ad- L−edges 0.6 K−edge dition we show results for a sample compound Al2O3 to validate our approximation in the UV-VIS range. The 0.5 Corvus workflow described here is applicable to [opcons] 0.4 any material available in the MP database as defined by a given MP identificatoin label (MP-ID), thus making pos- 0.3 (E) 5 χ sible routine calculations of optical constants for over 10 0.2 structures. By default, the calculations are carried out with lattice vibration effects included at room tempera- 0.1 ture, while electronic temperature and thermal expansion 0 effects are neglected. However, corrections for thermal ex- pansion, finite temperature, and pressures other than 1 −0.1 atm can be added using subsequent calculations that reuse 2 4 6 8 10 12 14 some of the previously computed data. The workflow is k(E) (Å) naturally parallelized and, for typical settings, requires as little as minutes of wall-clock time per material on mas- Figure 1: Top: Calculated imaginary part of the dielectric function sively parallel systems. 2 for Cu (blue) along with the atomic background χ (see text) (red). Bottom: Approximate opticalp fine structure of the imaginary (blue) part of for Cu vs k = 2E, along with the same fine-structure defined with energies E relative to the K- and L-edges. Note the similarities between the fine structure found in the optical and that of the K-edge. Note also that the fine structure becomes negligible for large k above any edges or outside the optical range. terms of 2(!), 2. Optical constants with Corvus and FEFF10 Z 1 0 0 2 0 ! 2(! ) 1(!) = 1 + P d! 2 02 (1) π 0 ! − ! −1 2(!) L(!) = −Im[ (!)] = 2 2 (2) 1(!) + 2(!) n(!) = n(!) + iκ(!) = (!)1=2 (3) ! µ(!) = 2 κ(!) (4) In general, the optical constants are related to the com- c plex dielectric constant (!) = 1(!) + i2(!) in the long [n(!) − 1]2 + κ(!)2 wave-length limit, where ! is the frequency of the electro- R(!) = ; (5) [n(!) + 1]2 + κ(!)2 magnetic field. Since their real and imaginary parts are re- lated by Kramers-Kronig (KK) transformations, they can where P denotes the principal part of the integral. Note all be calculated from the imaginary part 2(!) (e.g. Fig. that at high energies dielectric response is weak, and 1). In this work the, the Corvus [opcons] workflow yields 2(!) ≈ L(!) ≈ 2κ(!) ≈ µ(!)(c=!). Sum-rules the complex dielectric function (!), energy loss function for the dielectric properties provide a qualitative check L(!), complex index of refraction n(!), absorption coef- on the reliability of the results.[25] Related properties, ficient µ(!), and reflectivity R(!) defined as follows, in such as the local atomic polarizability α(!) = ((!) − 2 1)=(4πn), the Rayleigh forward scattering amplitudes 1.8 2 2 2 f(!) = !α(!)=r0c (where r0 = e =mc is the classi- 1.6 Cu cal radius of the electron, c is the speed of light and 1.4 n = N=V is the atomic number density), electron energy loss spectra (EELS), inelastic mean-free paths, Hamaker 1.2 constants (i!), etc., can also be determined, [20] but 1 are not yet implemented in the present Corvus [opcons] 0.8 workflow. For simplicity here and below we use atomic 0.6 units e = ¯h = m = 1 throughout this paper unless other- FMS wise needed for clarity. XANES (arb. units) 0.4 Stitched MSP The treatment of excitations from the core- and valence- 0.2 FMS-MSP levels generally requires different considerations, so it is 0 convenient to separate the calculations as -0.2 8980 9000 9020 9040 9060 core val 2 = 2 + 2 ; (6) Energy (eV) core where 2 includes the contribution from all levels below a Figure 2: Cu K-edge spectrum obtained using the stitching algorithm fixed core-valence separation energy Ecv, which in FEFF10 (black). For comparison, the curves calculated using FMS (red) and is set to -40 eV.