materials Article First-Principles Simulation of Dielectric Function in Biomolecules Puja Adhikari 1 , Rudolf Podgornik 2,3,4,5, * , Bahaa Jawad 1 and Wai-Yim Ching 1, *   Citation: Adhikari, P.; Podgornik, R.; Jawad, B.; Ching, W.-Y. First-Principles Simulation of Dielectric Function in Biomolecules. Materials 2021, 14, 5774. https:// doi.org/10.3390/ma14195774 Academic Editor: Claudio Canale Received: 3 September 2021 Accepted: 28 September 2021 Published: 2 October 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1 Department of Physics and Astronomy, University of Missouri-Kansas City, Kansas City, MO 64110, USA; paz67@umkc.edu (P.A.); bajrmd@mail.umkc.edu (B.J.) 2 School of Physical Sciences, Kavli Institute of Theoretical Science, University of Chinese Academy of Sciences, Beijing 100049, China 3 CAS Key Laboratory of Soft Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100090, China 4 Wenzhou Institute, University of Chinese Academy of Sciences, Wenzhou 325000, China 5 Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000 Ljubljana, Slovenia * Correspondence: rudipod@gmail.com (R.P.); Chingw@umkc.edu (W.-Y.C.) Abstract: The dielectric spectra of complex biomolecules reflect the molecular heterogeneity of the proteins and are particularly important for the calculations of electrostatic (Coulomb) and electrodynamic (van der Waals) interactions in protein physics. The dielectric response of the proteins can be decomposed into different components depending on the size, structure, composition, locality, and environment of the protein in general. We present a new robust simulation method anchored in rigorous ab initio quantum mechanical calculations of explicit atomistic models, without any indeterminate parameters to compute and gain insight into the dielectric spectra of small proteins under different conditions. We implement this methodology to a polypeptide RGD-4C (1FUV) in different environments, and the SD1 domain in the spike protein of SARS-COV-2. Two peaks at 5.2–5.7 eV and 14.4–15.2 eV in the dielectric absorption spectra are observed for 1FUV and SD1 in vacuum as well as in their solvated and salted models. Keywords: electrostatic interaction; dielectric function; biomolecules; ab initio simulation; random phase approximation 1. Introduction The dielectric properties of proteins in aqueous solutions have been studied for several decades [1] and play a crucial role in the calculations of protein electrostatic Coulomb interactions [2] as well as electrodynamic dispersion van der Waals interactions [3,4], specif- ically to calculate the protein–protein and protein–nucleic acid interactions, characterize the folding pathways, and investigate solution behavior and stability. In fact, quite recently electrostatic contributions have been invoked as a possible source of the differences be- tween the binding free energy of the spike proteins of SARS-CoV-2 and SARS-CoV to the ACE2 human receptor [5], as well as being the principal interaction component between the spike proteins of SARS-CoV-2 virus and the charged electret fibers in personal protective gear [6]. The problem of the macroscopic protein dielectric “constant” is exacerbated by the fact that, as in other biomolecular systems such as lipid membrane bilayers composed of differ- ent segregated molecular components, the underlying microscopic dielectric properties are heterogeneous [7] and the continuum assumptions become—to say the least—problematic on a molecular level [8]. Consequently, the protein dielectric constant appears rather as a phenomenological parameter, or even a phenomenological function of the position inside the protein core [9], that depends on the model used to describe the heterogeneous molecu- lar structure of proteins, then a single universal constant grounded in some fundamental theory [10]. These are important issues as many continuum computational approaches [11] Materials 2021, 14, 5774. https://doi.org/10.3390/ma14195774 https://www.mdpi.com/journal/materials