Polarization of Electron Density Databases of Transferable Multipolar Atoms Theo Leduc, Emmanuel Aubert, Enrique Espinosa, Christian Jelsch, Cristian Iordache, Benoît Guillot To cite this version: Theo Leduc, Emmanuel Aubert, Enrique Espinosa, Christian Jelsch, Cristian Iordache, et al.. Polar- ization of Electron Density Databases of Transferable Multipolar Atoms. Journal of Physical Chem- istry A, American Chemical Society, 2019, 123 (32), pp.7156-7170. 10.1021/acs.jpca.9b05051. hal- 02355909 HAL Id: hal-02355909 https://hal.archives-ouvertes.fr/hal-02355909 Submitted on 8 Nov 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. This is an open access article published under an ACS AuthorChoice License, which permits copying and redistribution of the article or any adaptations for non-commercial purposes. Article Cite This: J. Phys. Chem. A 2019, 123, 7156−7170 pubs.acs.org/JPCA Polarization of Electron Density Databases of Transferable Multipolar Atoms Theó Leduc, Emmanuel Aubert, Enrique Espinosa, Christian Jelsch, Cristian Iordache, and Benoît Guillot* Universitéde Lorraine, CNRS, CRM2, F-54000 Nancy, France *S Supporting Information ABSTRACT: Polarizability is a key molecular property involved in either macroscopic (i.e., dielectric constant) and microscopic properties (i.e., interaction energies). In rigid molecules, this property only depends on the ability of the electron density (ED) to acquire electrostatic moments in response to applied electric fields. Databases of transferable electron density fragments are a cheap and efficient way to access molecular EDs. This approach is rooted in the relative conservation of the atomic ED between different molecules, termed transferability principle. The present work discusses the application of this transferability principle to the polarizability, an electron density-derived property, partitioned in atomic contributions using the Quantum Theory of Atoms In Molecules topology. The energetic consequences of accounting for in situ deformation (polarization) of database multipolar atoms are investigated in detail by using a high-quality quantum chemical benchmark. 1. INTRODUCTION subatomic resolution X-ray diffraction data. HCMM allows to fi Electrostatic interactions play a major role in noncovalent describe and quantify ne details in the molecular ED, such as intermolecular interactions occurring in crystal packings and bonding and lone pair electrons. It also allows the modeling of between ligands and biological macromolecules. These ED in intermolecular regions, giving access to the quantitative interactions are often a main driving force in intermolecular characterization of intermolecular interactions such as hydro- binding. At equilibrium distances, the usual order of magnitude gen bonds. Globally, all ED deformation features, such as the of electrostatic interactions makes them an important electron redistribution upon covalent bond formation in a 1 molecule or intermolecular polarization effects when a contribution to the total interaction energy. Moreover, fl binding sites in proteins usually show electrostatic comple- molecular ED is under the in uence of neighboring molecules Downloaded via 193.48.208.41 on November 8, 2019 at 13:39:34 (UTC). mentarity with their ligand. Molecular dynamics force fields in in a crystal, are within the scope of the HCMM modeling. biomolecular modeling include calculations of electrostatic Consequently, HCMM modeling gives access to a wealth of ED descriptors [source function,5 quantum theory of atoms in interaction energies with, for instance, the use of partial atomic 6 charges to describe the Coulombic term. However, molecular molecules (QTAIM) topology. ..] used to characterize intra- See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. electrostatic properties originate from the total charge and intermolecular interactions. Finally, an experimental ED, distribution of the molecule under examination, that is, from once modeled in the HCMM approach, allows derivation of the atom nuclei and from the electron distribution in the important molecular properties such as electrostatic potential molecule. The latter property, the molecular electron density (ESP), electric moments, or atomic charges. (ED), can actually be obtained by first-principle calculations or The literature describing various applications of charge be measured by ultrahigh-resolution X-ray diffraction experi- density research is extremely vast and goes to organic small ments. The molecular ED can be represented as a summation molecules with biological activities to inorganic or organo- metallic compounds, with applications toward crystal engineer- of appropriately modeled atomic ED. Such approach is 7,8 9,10 11 commonly followed in charge density research, which recently ing, medicinal chemistry, catalysis, etc. The exper- evolved into a new field termed “Quantum Crystallography”.2 imental approach of charge density modeling, however, ff ED modeling relies, in a vast majority of experimental cases, on strongly relies on the accuracy and resolution of the di raction fi the multipolar atom model of Hansen and Coppens data used for the re nement of the ED model. Indeed, in the (HCMM).3,4 This model provides not only reliable atomic case of an experimental determination of a molecular ED, it is coordinates and thermal displacement parameters but also allows for accounting most of the aspherical features of atomic Received: May 28, 2019 EDs. HCMM describes the molecular ED using multipolar Revised: July 5, 2019 parameters (see Methods section) that can be fitted against Published: July 11, 2019 © 2019 American Chemical Society 7156 DOI: 10.1021/acs.jpca.9b05051 J. Phys. Chem. A 2019, 123, 7156−7170 The Journal of Physical Chemistry A Article commonly admitted within the charge density science degree) but neglecting the noncovalent environment, such as community that an X-ray data resolution of about 0.5 Å is crystal field effect, ionic bridges, van der Waals contacts, or compulsory to obtain reliable results. This obviously hinders hydrogen bonds. Hence, the averaging process on which the the application of a charge density refinement to biological construction of the ELMAM2 library relies includes similar macromolecules whose crystals, besides very few exceptional atomic multipolar EDs extracted from various noncovalent cases,12,13 cannot give access to such high quality and high- environments. In addition to the averaging procedure, the resolution diffraction data. However, scientists of the charge spherical harmonic functions used in the multipolar expansion density community have observed that multipolar parameters of ELMAM2 atoms are constrained to follow the local of atoms characterized by similar chemical environments in symmetry of the atom. This leads to a reduction in the different crystals are very similar and could reliably be number of multipole populations needed to model a given 14 transferred from a molecule to another. This, termed as atom type.29 As a consequence, the transferable ED fragments the transferability principle, has led to the construction of lack noncovalent context-sensitive features such as intermo- libraries of multipolar pseudoatoms, (i.e., sets of atomic lecular polarization effects, limiting possible interpretations of multipolar parameters), allowing quasi-instantaneous recon- fine, local, electrostatic details that could be induced by a struction of ED distributions of very large molecular systems molecular environment. This averaging process is believed to such as biological macromolecules, without the need of cause some partial loss of atomic polarization that this work fi performing a full multipole re nement against experimental aims to reconstruct. data. The seminal paper for the creation of pseudoatom fi 15 It must be noted that some molecular mechanics force elds databanks dates back to 1995 when Pichon-Pesme et al. have already include explicit computation of inducible electrostatics, reconstructed the charge distribution of a peptide backbone such as AMOEBA30 or SIBFA.31 In these force fields, iterative using multipolar parameters previously obtained from the fi algorithms apply polarization on each atom, until convergence, experimental ED re nements of small peptides and isolated using a tensor formalism to symbolize the electrostatic amino acids. This has led the Nancy group to the construction induction up to the quadrupolar level. In the field of charge of the experimental library of multipolar atom model density research, noteworthy efforts to obtain polarization (ELMAM), which contains all the possible chemically unique fi energies based on the ED encompass up to now the PIXEL pseudoatoms (i.e., atoms as de ned in the multipolar method from Gavezzotti32,33 and the CrystalExplorer software formalism) found in the 20 proteinogenic natural amino 1,34 16 from Spackman. acids. The database has been improved afterward The present article, however, describes and tests a new (ELMAM2) so that it covers now most