RSC Advances View Article Online PAPER View Journal | View Issue New scaling relations to compute atom-in-material polarizabilities and dispersion coefficients: part 1. Cite this: RSC Adv.,2019,9, 19297 Theory and accuracy† Thomas A. Manz, *a Taoyi Chen, a Daniel J. Cole, b Nidia Gabaldon Limasa and Benjamin Fiszbeina Polarizabilities and London dispersion forces are important to many chemical processes. Force fields for classical atomistic simulations can be constructed using atom-in-material polarizabilities and Cn (n ¼ 6, 8, 9, 10.) dispersion coefficients. This article addresses the key question of how to efficiently assign these parameters to constituent atoms in a material so that properties of the whole material are better reproduced. We develop a new set of scaling laws and computational algorithms (called MCLF) to do this in an accurate and computationally efficient manner across diverse material types. We introduce a conduction limit upper bound and m-scaling to describe the different behaviors of surface and buried atoms. We validate MCLF by comparing Creative Commons Attribution 3.0 Unported Licence. results to high-level benchmarks for isolated neutral and charged atoms, diverse diatomic molecules, various polyatomic molecules (e.g., polyacenes, fullerenes, and small organic and inorganic molecules), and dense solids (including metallic, covalent, and ionic). We also present results for the HIV reverse transcriptase enzyme complexed with an inhibitor molecule. MCLF provides the non-directionally screened polarizabilities required to construct force fields, the directionally-screened static polarizability tensor components and eigenvalues, and environmentally screened C6 coefficients. Overall, MCLF has improved accuracy compared to the TS-SCS Received 23rd April 2019 method.ForTS-SCS,wecomparedchargepartitioning methods and show DDEC6 partitioning yields more Accepted 3rd June 2019 accurate results than Hirshfeld partitioning. MCLF also gives approximations for C8,C9,andC10 dispersion DOI: 10.1039/c9ra03003d coefficients and quantum Drude oscillator parameters. This method should find widespread applications to This article is licensed under a rsc.li/rsc-advances parameterize classical force fields and density functional theory (DFT) + dispersion methods. 3,9–12 ff Open Access Article. Published on 19 June 2019. Downloaded 6/24/2019 3:33:38 PM. 1. Introduction eld design. Polarization e ects are especially important for simulating materials containing ions.13–20 When considered along- When combined with large-scale density functional theory (DFT) side the importance of accurate theoretical methods to study van der calculations, the DDEC method has been shown to be suitable for Waals interactions at the nanoscale,21 it is clear that a crucial feature assigning atom-centered point charges for exible molecular of new methods to compute these important quantities is the ability 1–8 mechanics force-eld design. The assignment of C6 coefficients to scale to large system sizes in reasonable computational time. and atomic polarizabilities is another active area of research in force In this article, we develop new scaling laws and an associated method to compute polarizabilities and dispersion coefficients for atoms-in-materials (AIMs). These new scaling laws and a Department of Chemical & Materials Engineering, New Mexico State University, Las computational method give good results for isolated atoms, Cruces, New Mexico, 88003-8001, USA. E-mail: [email protected] diatomic molecules, polyatomic molecules, nanostructured bSchool of Natural and Environmental Sciences, Newcastle University, Newcastle upon Tyne NE1 7RU, UK materials, solids, and other materials. This new method is † Electronic supplementary information (ESI) available: A pdf le containing: abbreviated MCLF according to the authors' last name initials damping radii denition (S1); def2QZVPPDD basis set denition (S2); m scaling (where the C is both for Chen and Cole). We performed tests on formula for wp (S3); and plot of the smooth cutoff function (S4). A 7-zip format isolated neutral and charged atoms, small molecules, fullerenes, archive containing: isolated atoms reference data and regression results and their polyatomic molecules, solids, and a large biomolecule with extrapolation up to element 109; def2QZVPPDD.gbs and def2QZVPPDD.pseudo les containing the full basis set and RECP parameter tabulations, respectively; MCLF. The results were compared with experimental data, high HIV reverse transcriptase complex geometry, ONETEP input les, and tabulated level CCSD calculations, time-dependent DFT (TD-DFT) calcula- MCLF and TS-SCS results for every atom in the material; MCLF and TS-SCS input tions, or published force-eld parameters. and output les for the CH2Br2 example showing symmetric (MCLF) and As discussed in several recent reviews and perspectives, the asymmetric (TS-SCS) atom-in-material polarizability tensors; C8,A and C10,A models dispersion interaction is a long-range, non-local interaction for isolated atoms; and detailed MCLF and TS-SCS results for each material in the following test sets: diatomic molecules, small molecules and molecule pairs, caused by uctuating multipoles between atoms in mate- 22–26 solids, polyacenes and fullerenes. See DOI: 10.1039/c9ra03003d rials. It is especially important in (i) condensed phases This journal is © The Royal Society of Chemistry 2019 RSC Adv.,2019,9, 19297–19324 | 19297 View Article Online RSC Advances Paper including liquids, supercritical uids, solids, and colloids, (ii) geometry-based method to calculate C6,C8, and C9 dispersion nanostructure binding such as the graphene layers forming coefficients and dispersion energies, but this method does not graphite, and (iii) the formation of noble gas dimers. The yield polarizability tensors.11 The recently formulated D4 dispersion interaction is closely related to AIM polarizabilities. models are geometry-based methods that extend the D3 The dispersion energy can be described by an expansion series. formalism by including atomic-charge dependence.35–37 The The leading term is inversely proportional to R6, where R is the exchange-dipole model (XDM) is an orbital-dependent distance between two atoms. The coefficient of this term is approach that yields AIM dipole, quadrupole, and octupole 38–42 called the C6 dispersion coefficient, and this term quanties polarizabilities and C6,C8, and C10 dispersion coefficients. uctuating dipole–dipole interactions between two atoms. The Several density-dependent XDM variants have been formu- ffi 43,44 ffl intermolecular C6 coe cient is given by the sum of all inter- lated. In 2009, Tkatchenko and Sche er introduced the TS ffi 12 atomic contributions method for isotropic AIM polarizabilities and C6 coe cients. X X mol Both the XDM and TS methods yielded isotropic AIM polariz- C ¼ C ; (1) 6 6 AB abilities rather than molecular polarizability tensors.12,38–44 In A˛M1B˛M2 both the XDM and TS methods, the AIM unscreened polariz- where M1 and M2 refer to the rst and the second molecules. ability is given by Higher-order terms represent different interactions.27 For AIM hr3i example, the eighth-order (C8) term describes the uctuating TS ¼ ref a a ref (2) dipole–quadrupole interaction between two atoms. The ninth- hr3i order (C ) term describes the uctuating dipole–dipole–dipole 9 where “ref” refers to the reference value for an isolated neutral interaction between three atoms. The tenth-order (C ) term 10 atom of the same chemical element, “AIM” refers to the parti- describes the uctuating quadrupole–quadrupole and dipole– tioned atom-in-material value, and hr3i refers to the r-cubed octupole interaction between two atoms. radial moment. Both the XDM and TS methods originally used ffi Methods for computing polarizabilities and dispersion coe - 45 3 AIM 12,42 Creative Commons Attribution 3.0 Unported Licence. Hirshfeld partitioning to compute the hr i values. cients can be divided into two broad classes: (A) quantum chem- In 2012, Tkatchenko et al. introduced self-consistent istry methods that explicitly compute the system response to an screening (TS-SCS) via the dipole interaction tensor to yield electric eld (e.g., TD-DFT, CCSD perturbation response theory, ffi the molecular polarizability tensor and screened C6 coe - etc.) and (B) AIM models. Class A methods can be highly accurate cients.46 The TS-SCS dipole interaction tensor uses a quantum for computing polarizabilities and dispersion coefficients of harmonic oscillator (QHO) model similar to that used by Mayer a whole molecule, but they do not provide AIM properties. but extended over imaginary frequencies and omitting charge– Therefore, class A methods cannot be regarded as more accurate dipole and charge–charge terms.33,34,46 That same article also versions of class B methods. Parameterizing a molecular used a multibody dispersion (MBD46,47) energy model based on This article is licensed under a mechanics force-eld from quantum mechanics requires an AIM a coupled uctuating dipole model (CFDM47,48). The TS-SCS (i.e., class B) model. Our goal here is not merely to develop screened static polarizability and characteristic frequency for a computationally cheaper method than TD-DFT or CCSD each atom are fed into the CFDM model to obtain the MBD Open Access Article. Published on 19 June 2019. Downloaded 6/24/2019 3:33:38 PM. perturbation response theory to compute accurate system polar- energy.46 The TS-SCS approach has advantages of yielding izabilities and dispersion coefficients, but rather to exceed the a molecular