Zero-flux surfaces of the electrostatic potential: the border of influence zones of nucleophilic and electrophilic sites in crystalline environment

Electronic Force Density Fields: Insights into Partial Bonds, Transition States, and Chemical Structure Evolution

This paper presents the quantum-topological binding approach, in which the electrostatic and total static force density fields, Fes(r) and F ( r ) , together with the electron density gradient field ∇ρ(r), are simultaneously analyzed to elucidate the chemical structure of transition states and the nature of interatomic interactions for semibroken semiformed partial chemical bonds. The approach attributes the discrepancies between the force fields F ( r ) and Fes(r) to the nonclassical electron-electron interaction effects. The internuclear gap between the zero-flux boundaries of Fes(r) and ∇ρ(r) indicates the interatomic charge transfer phenomenon (ICT) that occurs upon the formation of a system from free atoms. Concomitantly, the mismatch of the zero-flux surfaces defined in - F ( r ) and ∇ρ(r) can be interpreted as a phenomenon of the electron-transfer-induced quantum chemical response (QCR), which originates from the electron exchange correlation. Our study permits the assertion of parallels between partial bonds and noncovalent interactions, as both typically exhibit incomplete QCRs, indicating the partial electron sharing of the transferred density. The changes in atomic and pseudoatomic charges are employed to describe the evolution of the chemical structure upon the substitution reaction. It is observed that the acquired difference in the actual atomic electronegativity causes polarization upon the heterolytic breaking of virtually nonpolar bonds. It is further proposed that the proximity of closely related stationary states along the reaction path on a potential energy hypersurface implies their similarity in the manifestation of the ICT and sympathetic QCR. Furthermore, the involvement of an electron pair in a partial bond facilitates its delocalization through the attraction by the static forces F ( r ) and Fes(r) to a neighboring nucleus and through the smearing by the Pauli kinetic force FP(r).

Toward the Chemical Structure of Diborane: Electronic Force Density Fields, Effective Electronegativity, and Internuclear Turning Surface Properties

The chemical structure of diborane was elucidated through the superposition of the vector fields of the electron density gradient ∇ρ(r), the electrostatic force Fes(r), and the kinetic force Fk(r), together with the analysis of the cumulative charges of the atoms and pseudoatoms delimited in the aforementioned fields. It was proposed that the Fk-pseudoatomic charge could be employed as a metric for quantifying the ionic component of a related atomic charge. The electron permeability across an internuclear turning surface─specifically, the zero-flux surface in Fk(r)─was characterized by probing it through mapping the total static potential φem(r). The conceptualization of post hoc electronegativity was presented for consideration. Our analysis revealed that the ordinary B-H and bent B-μ-H bonds in diborane demonstrate the polar covalent character with minor contributions of the ionic component. The former bond exhibits a greater electron permeability through the internuclear turning surface, indicating a stronger tendency for electron sharing between the corresponding nucleus-dominated regions. The electron density accumulation along the bent B-μ-H bond path diverges from the minimum action trajectories of the forces Fes(r) and Fk(r). This phenomenon can be associated with the structural strain within the angled, three-center two-electron bonding B-μ-H-B. The internuclear B···B paths were identified in Fes(r) and Fk(r), in contrast to ∇ρ(r). This fact, in conjunction with a pronounced electron permeability through the mutual turning surface between the two boron nuclei, implies a certain degree of electron exchange between the boron-dominated pseudoatomic regions. Furthermore, the anomalous [B-]H···μ-H intermolecular polar interactions were described between the strongly negatively charged hydrogen atoms in the monoclinic crystalline β-phase of diborane. In fact, the ionic contributions to the charges of the hydrogen atoms are shown to be relatively small.

Applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. Chemical bonding and binding features in the crystal and dimer of 1,3-bis(2-hydroxyethyl)-6-methyluracil

We considered it timely to test the applicability of transferable multipole pseudo-atoms for restoring inner-crystal electronic force density fields. The procedure was carried out on the crystal of 1,3-bis(2-hydroxyethyl)-6-methyluracil, and some derived properties of the scalar potential and vector force fields were compared with those obtained from the experimental multipole model and from the aspherical pseudo-atom model with parameters fitted to the calculated structure factors. The procedure was shown to accurately replicate the general vector-field behavior, the peculiarities of the quantum potentials and the characteristics of the force-field pseudoatoms, such as charge, shape and volume, as well as to reproduce the relative arrangement of atomic and pseudoatomic zero-flux surfaces along internuclear regions. It was found that, in addition to the quantum-topological atoms, the force-field pseudoatoms are spatially reproduced within a single structural fragment and similar environment. In addition, the classical and nonclassical hydrogen bonds in the uracil derivative crystal, as well as the H...O, N...O and N...C interactions in the free π-stacked dimer of the uracil derivative molecules, were studied using the potential and force fields within the concepts of interatomic charge transfer and electron lone pair donation-acceptance. Remarkably, the nitrogen atoms in the N...O and N...C interactions behave rather like a Lewis base and an electron contributor. At the same time, the hydrogen atom in the H...O interaction, being a Lewis acid, also participates in the interatomic electron transfer by acting as a contributor. Thus, it has been argued that, when describing polar interatomic interactions within orbital-free considerations, it makes more physical sense to identify electronegative (electron occupier) and electropositive (electron contributor) atoms or subatomic fragments rather than nucleophilic and electrophilic sites.

New Crystal Form of Human Neuropilin-1 b1 Fragment with Six Electrostatic Mutations Complexed with KDKPPR Peptide Ligand

Neuropilin 1 (NRP1), a cell-surface co-receptor of a number of growth factors and other signaling molecules, has long been the focus of attention due to its association with the development and the progression of several types of cancer. For example, the KDKPPR peptide has recently been combined with a photosensitizer and a contrast agent to bind NRP1 for the detection and treatment by photodynamic therapy of glioblastoma, an aggressive brain cancer. The main therapeutic target is a pocket of the fragment b1 of NRP1 (NRP1-b1), in which vascular endothelial growth factors (VEGFs) bind. In the crystal packing of native human NRP1-b1, the VEGF-binding site is obstructed by a crystallographic symmetry neighbor protein, which prevents the binding of ligands. Six charged amino acids located at the protein surface were mutated to allow the protein to form a new crystal packing. The structure of the mutated fragment b1 complexed with the KDKPPR peptide was determined by X-ray crystallography. The variant crystallized in a new crystal form with the VEGF-binding cleft exposed to the solvent and, as expected, filled by the C-terminal moiety of the peptide. The atomic interactions were analyzed using new approaches based on a multipolar electron density model. Among other things, these methods indicated the role played by Asp320 and Glu348 in the electrostatic steering of the ligand in its binding site. Molecular dynamics simulations were carried out to further analyze the peptide binding and motion of the wild-type and mutant proteins. The simulations revealed that specific loops interacting with the peptide exhibited mobility in both the unbound and bound forms.

Real-Space Interpretation of Interatomic Charge Transfer and Electron Exchange Effects by Combining Static and Kinetic Potentials and Associated Vector Fields

Intricate behaviour of one-electron potentials from the Euler equation for electron density and corresponding gradient force fields in crystals was studied. Channels of locally enhanced kinetic potential and corresponding saddle Lagrange points were found between chemically bonded atoms. Superposition of electrostatic ϕ e s r and kinetic ϕ k r potentials and electron density ρ r allowed partitioning any molecules and crystals into atomic ρ - and potential-based ϕ -basins; ϕ k -basins explicitly account for the electron exchange effect, which is missed for ϕ e s -ones. Phenomena of interatomic charge transfer and related electron exchange were explained in terms of space gaps between zero-flux surfaces of ρ - and ϕ -basins. The gap between ϕ e s - and ρ -basins represents the charge transfer, while the gap between ϕ k - and ρ -basins is a real-space manifestation of sharing the transferred electrons caused by the static exchange and kinetic effects as a response against the electron transfer. The regularity describing relative positions of ρ -, ϕ e s -, and ϕ k - basin boundaries between interacting atoms was proposed. The position of ϕ k -boundary between ϕ e s - and ρ -ones within an electron occupier atom determines the extent of transferred electron sharing. The stronger an H⋅⋅⋅O hydrogen bond is, the deeper hydrogen atom's ϕ k -basin penetrates oxygen atom's ρ -basin, while for covalent bonds a ϕ k -boundary closely approaches a ϕ e s -one indicating almost complete sharing of the transferred electrons. In the case of ionic bonds, the same region corresponds to electron pairing within the ρ -basin of an electron occupier atom.

A mutant T1 lipase homology modeling, and its molecular docking and molecular dynamics simulation with fatty acids

A thermostable T1 lipase from Geobacillus zalihae exhibits broad substrate specificity and good potential application in fats and oils. However, structural insight into the enzyme against substrates is poorly understood at the molecular level. Herein, the study aimed to examine interactions between a mutant T1 lipase (Mut-T1 lipase) and selected fatty acids (caprylic, myristic, stearic, oleic, linoleic and linolenic acids) by performing molecular docking and molecular dynamics (MD) simulation. The structure of Mut-T1 lipase obtained by homology modeling was reliable for molecular docking and MD simulation. Molecular docking revealed that Mut-T1 lipase showed low binding affinity for caprylic acid (-4.97 kcal/mol) compared to the other fatty acids (-5.65 to -6.88 kcal/mol). However, the conformation of Mut-T1 lipase-caprylic acid complex was comparably stable during the simulation, in terms of less root-mean square fluctuation. Besides, solvent accessible surface area value of Mut-T1 lipase-fatty acid complexes decreased with increasing chain length of fatty acid. van der Waals interactions were requisite in maintaining complex stability during the binding process. This work provides structural insight into interactions between the lipase and the fatty acids, which will facilitate design and applications of new mutants of T1 lipase in modifying fats and oils.

Electrostatic Potential Topology for Probing Molecular Structure, Bonding and Reactivity

Following the pioneering investigations of Bader on the topology of molecular electron density, the topology analysis of its sister field viz. molecular electrostatic potential (MESP) was taken up by the authors’ groups. Through these studies, MESP topology emerged as a powerful tool for exploring molecular bonding and reactivity patterns. The MESP topology features are mapped in terms of its critical points (CPs), such as bond critical points (BCPs), while the minima identify electron-rich locations, such as lone pairs and π-bonds. The gradient paths of MESP vividly bring out the atoms-in-molecule picture of neutral molecules and anions. The MESP-based characterization of a molecule in terms of electron-rich and -deficient regions provides a robust prediction about its interaction with other molecules. This leads to a clear picture of molecular aggregation, hydrogen bonding, lone pair–π interactions, π-conjugation, aromaticity and reaction mechanisms. This review summarizes the contributions of the authors’ groups over the last three decades and those of the other active groups towards understanding chemical bonding, molecular recognition, and reactivity through topology analysis of MESP.

Role Differences in Healthcare: Overcoming Borders through Semiotic Skin is the Basis for Communication

Role differences in healthcare systems are the very foundation of communication in this specific field of environment. It has to be understood as a collective corporation between collective individuals and thus connect through intertwined border zones. These border zones between collective communicators holds the notions of individuality, which is represented in the ability to decipher and negotiate the multiple layers in the communicative border zone. These processes in border zones of persons - in relation with others - are dealt with by the Semiotic Skin Theory. In addition, the biological skin is central for human lives and the Semiotic Skin is conceptualized as a socio-somatic-semiotic, layered and dynamic membrane that operates as a semi-permeable, communicative boundary. A constant interpretation between a self-reflecting system and an unending spiral of semiosis is the emergent of the semiotic skin. It creates a semi-permeable barrier that holds the very notions of the multi-layered skin-on-the-skin that is reflected in an embodied communication between humans and environment. In this theoretical understanding of an embodied aspect of not only meaning-making but also the regulative aspect of embodied interaction with others, the very idea of borders of individuality becomes the notion of interpretation. Any communication in a medical setting involves actions on the border of mutual understanding - e.g. communication between a pediatrician and a child. The concepts of a collective patient and a collective doctor are introduced as to understand the aspects of the multiple dynamics of the semiotic skin as the holder of an individual's personal ideas/interpretations in the interaction with one other person, holding multiple aspects from others as well. Examples of the interaction between patients and the healthcare system in Denmark illustrate how a new theoretical and practical performance of mastering the communicative partnership in the cross field between the healthcare system and psychology is born.

Electronic criterion for categorizing the chalcogen and halogen bonds: sulfur–iodine interactions in crystals

Diversity of mutual orientations of Y–S and I–X and covalent bonds in molecular crystals complicate categorizing noncovalent chalcogen and halogen bonds. Here, the different types of S...I interactions with short interatomic distances are analysed. The selection of S...I interactions for the categorization of the chalcogen and halogen bonds has been made using angles that determine the mutual orientation of electron lone pairs and σ-holes interacted S and I atoms. In complicated cases of noncovalent interactions with `hole-to-hole' of S and I orientations, distinguishing the chalcogen and halogen bonds is only possible if the atom is uniquely determined, which also provides the electrophilic site. The electronic criterion for chalcogen/halogen bonds categorizing that is based on analysis of dispositions of electron density and electrostatic potential minima along the interatomic lines has been suggested and its effectiveness has been demonstrated.

Energetic, Topological and Electric Field Analyses of Cation-Cation Nucleic Acid Interactions in Watson-Crick Disposition

A theoretical study of the effect of the diprotonation on the nucleic acid bases (A : U, A : T and G : C) in Watson-Crick conformation has been carried out by means of DFT computational methods in vacuum. In addition, the corresponding neutral and monoprotonated binary complexes have been considered. Most of the diprotonated species studied are stable, even though the binding energy is positive due to the overall repulsive electrostatic term. Local electrostatic attractive forces in the regions of hydrogen bonds (HBs) are responsible for equilibrium geometries, as shown by the electric field lines connecting the electrophilic and nucleophilic sites involved in the HB interactions. Secondary electrostatic effects also affect the assembling of the nucleic acid complexes in either neutral or cationic form. In particular, the electric field lines flowing from electrophilic sites in one base to nucleophilic sites in the other reinforce the linking between them. Hence, when the nucleophilic site concerns the free lone pair of the heteroatom involved in the HB interaction as acceptor, the HB distance shortens. However, if the free lone pair of the HB acceptor interacts with an electrophilic site in the same molecule, the HB distance elongates, weakening the HB interaction. The topological analysis of the electron density distribution in HB regions indicates that neutral, monoprotonated and diprotonated complexes show no differences in the nature of their HB's.

Quantum Crystallography: Current Developments and Future Perspectives

Crystallography and quantum mechanics have always been tightly connected because reliable quantum mechanical models are needed to determine crystal structures. Due to this natural synergy, nowadays accurate distributions of electrons in space can be obtained from diffraction and scattering experiments. In the original definition of quantum crystallography (QCr) given by Massa, Karle and Huang, direct extraction of wavefunctions or density matrices from measured intensities of reflections or, conversely, ad hoc quantum mechanical calculations to enhance the accuracy of the crystallographic refinement are implicated. Nevertheless, many other active and emerging research areas involving quantum mechanics and scattering experiments are not covered by the original definition although they enable to observe and explain quantum phenomena as accurately and successfully as the original strategies. Therefore, we give an overview over current research that is related to a broader notion of QCr, and discuss options how QCr can evolve to become a complete and independent domain of natural sciences. The goal of this paper is to initiate discussions around QCr, but not to find a final definition of the field.

Structural analysis of adsorption processes of 5FU and imiquimodon hydrogels using AMBER/PM3 hybrid model

El modelo hibrido AMBER/PM3permitió determinar las propiedades estructurales del 5FU e imiquimod individualmente y después de la adsorción en hidrogeles de quitosano entrecruzados con genipina, respectivamente. Se observó que la energía libre de Gibbs (ΔG) disminuye con la adsorción, sin embargo, en ambos procesos se encontró estabilidad termodinámica y espontaneidad; ΔG fue verificado mediante el incremento en los momentos dipolares. Por otro lado, el coeficiente de partición estableció el carácter hidrofìlico con respecto al agua presente en el hidrogel, el cual aumenta con la adsorción. El FTIR evidenció que existen desplazamientos en las señales. Se observaron las bandas de puente de hidrógeno, atribuidas a la formación de enlaces, para realizar la adsorción de los fármacos. La adsorción fue verificada mediante los MESP y los análisis de superficie, en donde se apreció la distribución de zonas nucleofílicas y electrofílicas.

Reversibility of imido-based ionic liquids: a theoretical and experimental study

Theoretical and experimental methods were used to study the reversibility of a series of imido-based ionic liquids.

Charged versus Neutral Hydrogen-Bonded Complexes: Is There a Difference in the Nature of the Hydrogen Bonds?

A theoretical study on some carboxylic acid dimers formed by positively or negatively charged molecules has been carried out by using DFT methods. The resulting dimers possess either a charge of +2 or -2. In addition, the corresponding neutral complexes have also been considered. The electron density distribution described by the atoms in molecules and the natural bond orbital methods, as well as the electric field maps of the systems, have been analyzed and compared without finding significant differences between the neutral and ionic complexes. The interaction energy along the dissociation path of the charged dimers shows both a local minimum and a local maximum, defining a stability region between them. When this energetic profile is recalculated by removing the repulsion between the charged groups, it resembles to those of the neutral molecules. Hence, the characteristics of the charged dimers are similar to those of the neutral ones: the addition of a repulsion term for the charged groups permits to retrieve the energetic profiles dependence with the distance in the charged system. The interacting quantum atom (IQA) method has been used to calculate the interaction energy terms, including the classic Coulombic term between the whole molecules and the corresponding of the carboxylic acid groups. The IQA results show repulsive electrostatic interactions when the whole molecules are considered in the ionic complexes, but attractive ones between the carboxylic groups in both neutral and ionic complexes.

Exploring the Gradient Paths and Zero Flux Surfaces of Molecular Electrostatic Potential

The gradient vector field of molecular electrostatic potential, ∇V(r), has remained relatively unexplored in molecular quantum mechanics. The present article explores the conceptual as well as practical aspects of this vector field. A three-dimensional atomic partition of molecular space has been achieved on the basis of zero flux surfaces (ZFSs) of ∇V(r). Such ZFSs may completely enclose some of the atoms in the molecule, unlike what is observed in density-based atomic partitioning. The demonstration of this phenomenon is elucidated through typical examples, e.g., N2, CO, H2O, H2CO, OF(•), :CH2, and NH3BF3, where the electronegative atoms or group of atoms (group electronegativity) exhibits a closed ZFS of ∇V(r) around them. The present article determines an explicit reason for this phenomenon and also provides a necessary and sufficient condition for such a closed ZFS of ∇V(r) to exist. It also describes how the potential-based picture of atoms in molecules differs from its electron density-based analogue. This work further illustrates the manifestation of anisotropy in the gradient paths of MESP of some molecular systems, with respect to CO, (•)OH, H2O, and H2CO, and points to its potential in understanding the reactivity patterns of the interacting molecules.

Molecular Electrostatic Potential-Based Atoms in Molecules: Shielding Effects and Reactivity Patterns

The Atoms in Molecules (AIM) concept based on the zero-flux surface (ZFS) of the gradient of molecular electrostatic potential (MESP) has been recently proposed by the present authors. The nature of MESP-based atomic basins brings out the asymmetric electronic distribution in a molecule. An electron-rich atom among the two bonded atoms is seen to possess a completely closed MESP-based atomic basin. The present article illustrates the nature of atomic basins for a variety of molecules such as BF, BH3, AlCl3, B2H6, and Al2Cl6, and a Lewis acid–base pair, viz. NH3BH3 wherein the electronic distribution is not merely guided by difference in the electronegativity of the atoms. The study also explores some transition metal complexes, viz. Ni(CO)4, Fe(CO)5, Cr(CO)6, Mn2(CO)10, Co2(CO)8, Fe(η5-C5H5)2, Co(η3-C3H5), and Co(η3-C3H5)(CO)3, which show a similar phenomenon of intricate charge transfer among the ligands and the metal centre. The present article employs MESP-based AIM for a qualitative explanation of the shielding or deshielding effects revealed by NMR data as well as susceptibility of an atomic region towards an electrophilic or nucleophilic attack. Because the topographical features of MESP and thus the nature of atomic basins are not very sensitive to the level of theory and basis set, the present article demonstrates the capability of MESP as a consistent and simple tool for the portrayal of asymmetry in molecular charge distribution.

The paradox of hydrogen-bonded anion-anion aggregates in oxoanions: a fundamental electrostatic problem explained in terms of electrophilic···nucleophilic interactions

A theoretical study of anionic complexes formed by two partly deprotonated oxoacids joined by hydrogen bonds has been carried out at the MP2 computational level. In spite of the ionic repulsion, local energy minima are found both in the gas phase and in aqueous solution. Electrostatic potential and electron density topologies, and the comparison with neutral complexes formed by oxoacids, reveal that the ionization has no significant effect on the properties of the hydrogen bonds. The stability of the complexes in the gas phase is explained by attractive forces localized in a volume situated in the hydrogen bond and defined as the electrostatic attraction region (EAR) and determined by the topological analyses of the electron density and the electrostatic potential, and by the electric field lines. In solution, the strong anionic repulsion is mostly screened by the effect of the surrounding polar solvent, which only leads to a weak destabilizing interaction in the hydrogen bond region and finally favors the overall stability of the complexes. The anion-anion complexes have been compared with the corresponding neutral ones (as salts or protonated forms), showing that EAR remains unchanged along the series.

Implementation of a protein reduced point charge model toward molecular dynamics applications

A reduced point charge model was developed in a previous work from the study of extrema in smoothed charge density distribution functions generated from the Amber99 molecular electrostatic potential. In the present work, such a point charge distribution is coupled with the Amber99 force field and implemented in the program TINKER to allow molecular dynamics (MD) simulations of proteins. First applications to two polypeptides that involve α-helix and β-sheet motifs are analyzed and compared to all-atom MD simulations. Two types of coarse-grained (CG)-based trajectories are generated using, on one hand, harmonic bond stretching terms and, on the other hand, distance restraints. Results show that the use of the unrestrained CG conditions are sufficient to preserve most of the secondary structure characteristics but restraints lead to a better agreement between CG and all-atom simulation results such as rmsd, dipole moment, and time-dependent mean square deviation functions.