Quantum Chemical Topology

Exploring the influence of metal cations on individual hydrogen bonds in Watson-Crick guanine-cytosine DNA base pair: An interacting quantum atoms analysis

This study delves into the nature of individual hydrogen bonds and the relationship between metal cations and hydrogen bonding in the Watson-Crick guanine-cytosine (GC) base pair and its alkali and alkaline earth cation-containing complexes (Mn+-GC). The findings reveal how metal cations affect the nature and strength of individual hydrogen bonds. The study employs interacting quantum atoms (IQA) analysis to comprehensively understand three individual hydrogen bonds within the GC base pair and its cationic derivatives. These analyses unveil the nature and strength of hydrogen bonds and serve as a valuable reference for exploring the impact of cations (and other factors) on each hydrogen bond. All the H ⋯ D interactions (H is hydrogen and D is oxygen or nitrogen) in the GC base pair are primarily electrostatic in nature, with the charge transfer component playing a substantial role. Introducing a metal cation perturbs all H ⋯ D interatomic interactions in the system, weakening the nearest hydrogen bond to the cation (indicated by a) and reinforcing the other (b and c) interactions. Notably, the interaction a, the strongest H ⋯ D interaction in the GC base pair, becomes the weakest in the Mn+-GC complexes. A broader perspective on the stability of GC and Mn+-GC complexes is provided through interacting quantum fragments (IQF) analysis. This approach considers all pairwise interactions between fragments and intra-fragment components, offering a complete view of the factors that stabilize and destabilize GC and Mn+-GC complexes. The IQF analysis underscores the importance of electron sharing, with the dominant contribution arising from the inter-fragment exchange-correlation term, in shaping and sustaining GC and Mn+-GC complexes. From this point of view, alkaline and alkaline earth cations have distinct effects, with alkaline cations generally weakening inter-fragment interactions and alkaline earth cations strengthening them. In addition, IQA and IQF calculations demonstrate that the hydration of cations led to small changes in the hydrogen bonding network. Finally, the IQA interatomic energies associated with the hydrogen bonds and also inter-fragment interaction energies provide robust indicators for characterizing hydrogen bonds and complex stability, showing a strong correlation with total interaction energies.

Transfer learning of hyperparameters for fast construction of anisotropic GPR models: design and application to the machine-learned force field FFLUX

The polarisable machine-learned force field FFLUX requires pre-trained anisotropic Gaussian process regression (GPR) models of atomic energies and multipole moments to propagate unbiased molecular dynamics simulations. The outcome of FFLUX simulations is highly dependent on the predictive accuracy of the underlying models whose training entails determining the optimal set of model hyperparameters. Unfortunately, traditional direct learning (DL) procedures do not scale well on this task, especially when the hyperparameter search is initiated from a (set of) random guess solution(s). Additionally, the complexity of the hyperparameter space (HS) increases with the number of geometrical input features, at least for anisotropic kernels, making the optimization of hyperparameters even more challenging. In this study, we propose a transfer learning (TL) protocol that accelerates the training process of anisotropic GPR models by facilitating access to promising regions of the HS. The protocol is based on a seeding-relaxation mechanism in which an excellent guess solution is identified by rapidly building one or several small source models over a subset of the target training set before readjusting the previous guess over the entire set. We demonstrate the performance of this protocol by building and assessing the performance of DL and TL models of atomic energies and charges in various conformations of benzene, ethanol, formic acid dimer and the drug fomepizole. Our experiments suggest that TL models can be built one order of magnitude faster while preserving the quality of their DL analogs. Most importantly, when deployed in FFLUX simulations, TL models compete with or even outperform their DL analogs when it comes to performing FFLUX geometry optimization and computing harmonic vibrational modes.

C5 Pentacle Structures: A Localization-Delocalization Matrices Approach

This article explores the possible presence of a pentacle valence bond structure in C5 ${_5 }$ cyclic molecules. At this end, we have used quantum chemistry tools to elucidate the possible arrangement and the nature of chemical bonds within linear, cyclic, and three-dimensional structures only formed by five carbon atoms. While the linear structure is clearly the most stable one, local minima were obtained for both bi- and three-dimensional structures. Using the localization-delocalization matrices approach, we characterize both the minimum linear structure and the cyclic ones. Interestingly, the linear structure is a combination of ionic and covalent bonds, albeit the four distances are almost identical, when using Density Functional Theory. For cyclic C5 ${_5 }$ , the pentacle bonding arrangement emerges as a significant Lewis structure, indicative of an unusual formal configuration characterized by five intersecting C-C bonds. Our calculations show that this pentacle arrangement in cyclic C5 ${_5 }$ scheme is also present in the more known cyclo-pentadienyl molecule.

Chemical bonding within AIIIBVI materials under uniaxial compression

The work provides a comprehensive explanation of the nature of chemical bonding through quantum chemical topology for multilayers of AIIIBVI compounds, such as GaSe, InSe, and GaTe, spanning pressures from 0 GPa to 30 GPa. These compounds are subjected to pressure orthogonal to the multilayers. Quantum chemical topological indices indicate that uniaxial pressure induces changes in hybridisation, leading to the disappearance of interlayer van der Waals forces. The distinct nature of the elements within the compounds results in different pressures at which van der Waals interactions disappear, as revealed by non-covalent interaction analysis. The presence or absence of chemical bonding is assessed by quantum topological indices as Espinosa indices, charge density distribution difference, and crystal orbital Hamilton populations. The varying changes in hybridisation, as indicated by topological indices, are corroborated by variations in the population of the electronic projected density of states. Ultimately, the type of chemical bonding is identified through the Espinosa indices in the field of Bader theory. This analysis confirms the existence of shared shell bonds between AIII and BVI atoms in vacuum that goes to an intermediate bond between shared and closed shells called the transition zone with increasing pressure. The implications and importance of this work extend beyond the presented results. It suggests that many other classes of two-dimensional materials may undergo phase transitions under uniaxial stress, leading to the formation of new phases with potentially interesting electronic properties.

Revisiting the bonding evolution theory: a fresh perspective on the ammonia pyramidal inversion and bond dissociations in ethane and borazane

This work offers a comprehensive and fresh perspective on the bonding evolution theory (BET) framework, originally proposed by Silvi and collaborators [X. Krokidis, S. Noury and B. Silvi, Characterization of elementary chemical processes by catastrophe theory, J. Phys. Chem. A, 1997, 101, 7277-7282]. By underscoring Thom's foundational work, we identify the parametric function characterizing bonding events along a reaction pathway through a three-step sequence to establish such association rigorously, namely: (a) computing the determinant of the Hessian matrix at all potentially degenerate critical points, (b) computing the relative distance between these points, and (c) assigning the unfolding based on these computations and considering the maximum number of critical points for each unfolding. In-depth examination of the ammonia inversion and the dissociation of ethane and ammonia borane molecules yields a striking discovery: no elliptic umbilic flag is detected along the reactive coordinate for any of the systems, contradicting previous reports. Our findings indicate that the core mechanisms of these chemical reactions can be understood using only two folds, the simplest polynomial of Thom's theory, leading to considerable simplification. In contrast to previous reports, no signatures of the elliptic umbilic unfolding were detected in any of the systems examined. This finding dramatically simplifies the topological rationalization of electron rearrangements within the BET framework, opening new approaches for investigating complex reactions.

How to Compute Atomistic Insight in DFT Clusters: The REG-IQA Approach

The relative energy gradient (REG) method is paired with the topological energy partitioning method interacting quantum atoms (IQA), as REG-IQA, to provide detailed and unbiased knowledge on the intra- and interatomic interactions. REG operates on a sequence of geometries representing a dynamical change of a system. Its recent application to peptide hydrolysis of the human immunodeficiency virus-1 (HIV-1) protease (PDB code: 4HVP) has demonstrated its full potential in recovering reaction mechanisms and through-space electrostatic and exchange-correlation effects, making it a compelling tool for analyzing enzymatic reactions. In this study, the computational efficiency of the REG-IQA method for the 133-atom HIV-1 protease quantum mechanical system is analyzed in every detail and substantially improved by means of three different approaches. The first approach of smaller integration grids for IQA integrations reduces the computational overhead by about a factor of 3. The second approach uses the line-simplification Ramer-Douglas-Peucker (RDP) algorithm, which outputs the minimal number of geometries necessary for the REG-IQA analysis for a predetermined root mean squared error (RMSE) tolerance. This cuts the computational time of the whole REG analysis by a factor of 2 if an RMSE of 0.5 kJ/mol is considered. The third approach consists of a "biased" or "unbiased" selection of a specific subset of atoms of the whole initial quantum mechanical model wave-function, which results in more than a 10-fold speed-up per geometry for the IQA calculation, without deterioration of the outcome of the REG-IQA analysis. Finally, to show the capability of these approaches, the findings gathered from the HIV-1 protease system are also applied to a different system named haloalcohol dehalogenase (HheC). In summary, this study takes the REG-IQA method to a computationally feasible and highly accurate level, making it viable for the analysis of a multitude of enzymatic systems.

Bonding and antibonding characters of the first order reduced density matrix. A new look at two charge-shift bonds

This article reports a new way of analyzing chemical bonds based on the use of gradient of a first order reduced density matrix (1-RDM) map to partition bonds into atomic core, valence, and dorsal regions that can be further characterized as bonding or antibonding. These classifications are directly related to the familiar language of molecular orbital analysis. Analyses based on these quantities and the critical points of the 1-RDM performed on two charge-shift bonds show that although they share common features, there are fundamental differences in these interactions that are detected neither by density-based analysis nor by valence bond theory. The results suggest the gradient of 1-RDM as a valuable tool in bond analysis.

Chemical Bonding Perspective on Low-Lying SiC4H2 Isomers: Conceptual Quantum Chemical Views

The nature of the chemical bonding in seven low-lying isomers of SiC₄H₂ is analyzed through quantum chemical concepts. Out of the seven, four isomers, 1-ethynyl-3-silacycloprop-1(2)-en-3-ylidene (1), diethynylsilylidene (2), 1-sila-1,2,3,4-pentatetraenylidene (4), and 1,3-butadiynylsilylidene (5), have already been identified in the laboratory. The other three isomers, 2-methylenesilabicyclo[1.1.0]but-1(3)-en-4-ylidene (3), 4-sila-2-methylenebicyclo[1.1.0]but-1(3)-en-4-ylidene (6), and 3-ethynyl-1-silapropadienylidene (7) remain elusive in the laboratory to date (J. Phys. Chem. A, 2020, 124, 987-1002). Deep insight into the characteristics of chemical bonding is explored with different bonding analysis tools. Quantum theory of atoms in molecules (QTAIM), interaction quantum atoms analysis, natural bond orbital analysis, adaptive natural density partitioning, electron localization function (ELF), Laplacian of electron density, energy decomposition analysis, atomic charge analysis, bond order analysis, and frontier molecular orbital analysis are employed in the present work to gain a better understanding of the chemical bonding perspective in SiC₄H₂ isomers. Different quantum chemical topology approaches (QTAIM, ELF, and Laplacian of electron density) are employed to complement each other. The obtained results dictate that the lone pair of the silicon atom participate in delocalization and influences the structural stability of isomers.

Topological Analysis of Functions on Arbitrary Grids: Applications to Quantum Chemistry

Algorithms are presented for performing a topological analysis of an arbitrary function, evaluated on an arbitrary grid of points. These algorithms work strictly by post-processing the data and require no additional function evaluations. This is achieved by connecting the grid points with a neighborhood graph, allowing the topological analysis to be recast as a problem in the graph theory. The flexibility of the approach is demonstrated for various applications involving analysis of the charge and magnetically induced current densities in molecules, where features of the neighborhood graph are found to correspond to chemically relevant topographical properties, such as Bader charges. These properties converge using orders of magnitude fewer grid points than uniform-grid approaches while exhibiting an appealing O[N log(N)] scaling of the computational cost. The issue of grid bias is discussed in the context of graph-based algorithms and strategies for avoiding this bias are presented. Python implementations of the algorithms are provided.

On the Notation of Catastrophes in the Framework of Bonding Evolution Theory: the Case of Normal and Inverse Electron Demand Diels-Alder Reactions

This paper generalizes very recent and unexpected findings [ J. Phys. Chem. A , 2021 , 125 , 5152-5165] regarding the known "direct- and inverse-electron demand" Diels-Alder mechanisms. Application of bonding evolution theory evidence that the key electron rearrangement associated with significant chemical events (e.g., the breaking/forming processes of bonds) can be characterized via the simplest fold polynomial. To the CC bond formation, neither substituent position nor the type of electronic demand induces a measurable cusp-type signature. On the opposite to the case of [4+2] cycloaddition between 1,3-butadiene and ethylene where the two new CC single bonds occur beyond the transition state (TS), in the activated cases, the first CC bond formation occurs in the domain of structural stability featuring the TS, whereas the second one remains located in the deactivation path connecting the TS with the cycloadduct.

Towards an atomistic understanding of polymorphism in molecular solids

Understanding and controlling polymorphism in molecular solids is a major unsolved problem in crystal engineering. While the ability to calculate accurate lattice energies with atomistic modelling provides valuable insight into the associated energy scales, existing methods cannot connect energy differences to the delicate balances of intra- and intermolecular forces that ultimately determine polymorph stability ordering. We report herein a protocol for applying Quantum Chemical Topology (QCT) to study the key intra- and intermolecular interactions in molecular solids, which we use to compare the three known polymorphs of succinic acid including the recently-discovered γ form. QCT provides a rigorous partitioning of the total energy into contributions associated with topological atoms, and a quantitative and chemically intuitive description of the intra- and intermolecular interactions. The newly-proposed Relative Energy Gradient (REG) method ranks atomistic energy terms (steric, electrostatic and exchange) by their importance in constructing the total energy profile for a chemical process. We find that the conformation of the succinic acid molecule is governed by a balance of large and opposing electrostatic interactions, while the H-bond dimerisation is governed by a combination of electrostatics and sterics. In the solids, an atomistic energy balance emerges that governs the contraction, towards the equilibrium geometry, of a molecular cluster representing the bulk crystal. The protocol we put forward is as general as the capabilities of the underlying quantum-mechanical model and it can provide novel perspectives on polymorphism in a wide range of chemical systems.

Noble-gas compounds: A general procedure of bonding analysis

This paper accounts for a general procedure of bonding analysis that is, expectedly, adequate to describe any type of interaction involving the noble-gas (Ng) atoms. Building on our recently proposed classification of the Ng-X bonds (X = binding partner) [New J. Chem. 44, 15536 (2020)], these contacts are first distinguished into three types, namely, A, B, or C, based on the topology of the electron energy density H(r) and on the shape of its plotted form. Bonds of type B or C are, then, further assigned as B-loose (B^l) or B-tight (B^t) and C-loose (C^l) or C-tight (C^t) depending on the sign that H(r) takes along the Ng-X bond path located from the topological analysis of ρ(r), particularly at around the bond critical point (BCP). Any bond of type A, B^l/B^t, or C^l/C^t is, finally, assayed in terms of contribution of covalency. This is accomplished by studying the maximum, minimum, and average value of H(r) over the volume enclosed by the low-density reduced density gradient (RDG) isosurface associated with the bond (typically, the RDG isosurface including the BCP) and the average ρ(r) over the same volume. The bond assignment is also corroborated by calculating the values of quantitative indices specifically defined for the various types of interactions (A, B, or C). The generality of our taken approach should encourage its wide application to the study of Ng compounds.

Electrostatics Explains the Reverse Lewis Acidity of BH3 and Boron Trihalides: Infrared Intensities and a Relative Energy Gradient (REG) Analysis of IQA Energies

The reaction path for the formation of BX₃–NH₃ (X = H, F, Cl, Br) complexes was divided into two processes: (i) rehybridization of the acid while adopting a pyramidal geometry, and (ii) the complex formation from the pyramidal geometries of the acid and base. The interacting quantum atom (IQA) method was used to investigate the Lewis acidity trend of these compounds. This topological analysis suggests that the boron–halogen bond exhibits a considerable degree of ionicity. A relative energy gradient (REG) analysis on IQA energies indicates that the acid–base complex formation is highly dependent on electrostatic energy. With increasing halogen electronegativity, a higher degree of ionicity of the B–X is observed, causing an increase in the absolute value of X and B charges. This increases not only the attractive electrostatic energy between the acid and base but also enhances the repulsive energy. The latter is the main factor behind the acidity trend exhibited by trihalides. Changes in geometry are relevant only for complexes where BH₃ acts as an acid, where lower steric hindrance facilitates the adoption of the pyramidal geometry observed in the complex. The CCTDP analysis shows that infrared intensities of BX₃–NH₃ are determined mostly by the atomic charges and not by the charge transfer or polarization. The opposite is observed in covalent analogues.

On the nature of bonding in the photochemical addition of two ethylenes: C-C bond formation in the excited state?

In this work, the 2s + 2s (face-to-face) prototypical example of a photochemical reaction has been re-examined to characterize the evolution of chemical bonding. The analysis of the electron localization function (as an indirect measure of the Pauli principle) along the minimum energy path provides strong evidence supporting that CC bond formation occurs not in the excited state but in the ground electronic state after crossing the rhombohedral S₁/S₀ conical intersection.

Structural insights into SARS-CoV-2 spike protein and its natural mutants found in Mexican population

The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a newly emerged coronavirus responsible for coronavirus disease 2019 (COVID-19); it become a pandemic since March 2020. To date, there have been described three lineages of SARS-CoV-2 circulating worldwide, two of them are found among Mexican population, within these, we observed three mutations of spike (S) protein located at amino acids H49Y, D614G, and T573I. To understand if these mutations could affect the structural behavior of S protein of SARS-CoV-2, as well as the binding with S protein inhibitors (cepharanthine, nelfinavir, and hydroxychloroquine), molecular dynamic simulations and molecular docking were employed. It was found that these punctual mutations affect considerably the structural behavior of the S protein compared to wild type, which also affect the binding of its inhibitors into their respective binding site. Thus, further experimental studies are needed to explore if these affectations have an impact on drug-S protein binding and its possible clinical effect.

Topological population analysis and pairing/unpairing electron distribution evolution: Atomic B3+ cluster bending mode, a case study

Local and non-local topological treatment of electronic distributions are applied to a simple out of equilibrium case of an electron-deficient three-atom cluster, B3⁺. The bending movement is described in detail through the onset and disappearance of critical points defining two kinds of molecular structures, characterizing a transition state (TS) and predicting two stable equilibrium geometries. All points in this rich evolution and the structural change in the out of equilibrium conformations has been featured and distinguished by the behavior of the population magnitudes and of the paired and unpaired electron densities within the non-local and local points of view of the topological formalism. The unpaired or electron hole density appears as relevant in both versions, the non-local or integrated one, in which it is sometimes called free-valence and also for its complementary counterpart, the local one, to describe and to quantify the interatomic interactions. The stability of the cluster B₃⁺ is characterized in terms of a topologically defined ring structure and the highest total two- and three-center populations, thus showing the role of the geometry, the covalence, and the complex patterns. Consideration of the electron correlation effects constitutes the basement of the results gathered, thus displaying their influence in the formation and breaking of boron bonding interactions.

Partitioning a Molecule into the Atomic Basins and the Resultant Atomic Charges from Quantum Chemical Topology Analysis of the Kohn-Sham Potential

Quantum chemical topology (QCT) solidifies the chemical basic concepts demonstrating how a molecular system is intrinsically partitioned into its components and what the interaction lines between them are. Here, QCT analysis using a Kohn-Sham one-electron potential (KSpot) in KS equation as a scalar function is initiated and explored, showing KSpot and its resultant electron force lines have novel spatial features which reveal that an atom in a molecule is a spatial basin governed by its nucleus as a 3D-attractor that terminates all the electron force lines defined by the negative gradient of KSpot and that a chemical bond line is just a minimum path of KSpot for the electron motion. Particularly, the atomic charges from this KSpot QCT analysis are moderate and good, having much lower dependence on basis sets chosen for computation. This may provide a platform for the study of molecular structures and properties, intra- and intermolecular electrostatic interaction, energy decomposition, and construction of force field.

Quantifying individual (anti)bonding molecular orbitals' contributions to chemical bonding

The shapes of molecular orbitals (MOs) in polyatomic molecules are often difficult for meaningful chemical interpretations. We report protocols to quantify contributions made by individual orbitals (molecular canonical and natural) of classical bonding, non-bonding or anti-bonding nature to (i) electron density into the inter-nuclear region and (ii) diatomic electron delocalization, DI(A,B). In other words, these protocols universally explain orbital's inputs to two fundamental and energy-lowering mechanisms of chemical bonding (interactions) and ease the chemical interpretation of their character in polyatomic molecules. They reveal that the MO and real-space density descriptions of the interactions are equivalent and, importantly, equally apply to all atom-pairs regardless if they are involved in a highly attractive or repulsive interaction. Hence, they not only remove ambiguity in chemical bonding interpretations (based on either MO or electron density approaches) but also demonstrate complementarity between the two such seemingly different techniques. Finally, our approach challenges some classical assumptions about MOs, such as the role of core electrons, the degree of bonding in antibonding MOs and the relative importance of frontier orbitals. Just as an example, we show that orthodox antibonding orbitals can make a significant contribution of a bonding nature to a classical covalent bond or major contribution to DI(A,B) of an intramolecular and highly repulsive HH interaction.

Interacting Quantum Atoms Approach and Electrostatic Solvation Energy: Assessing Atomic and Group Solvation Contributions

The interacting quantum atoms (IQA) method decomposes the total energy of a molecular system in terms of one- and two-center (atomic) contributions within the context of the quantum theory of atoms in molecules. Here we incorporate electrostatic continuum solvent effects into the IQA energy decomposition. To this end, the interaction between the solute electrostatic potential and the solvent screening charges as defined within the COSMO solvation model is now included in a new version of the PROMOLDEN code, allowing thus to apply IQA in combination with COSMO-quantum chemical methods as well as to partition the electrostatic solvation energy into effective atomic and group contributions. To test the robustness of this approach, we carry out COSMO-HF/aug-cc-pVTZ calculations followed by IQA calculations on more than 400 neutral and ionic solutes extracted from the MNSol database. The computational results reveal a detailed atomic mapping of the electrostatic solvation energy that is useful to assess to what extent the solvation energy can be decomposed into atomic and group contributions of various parts of a solute molecule, as generally assumed by empirical methodologies that estimate solvation energy and/or logP values.

A relative energy gradient (REG) study of the planar and perpendicular torsional energy barriers in biphenyl

Biphenyl is a prototype molecule, the study of which is important for a proper understanding of stereo-electronic effects. In the gas phase it has an equilibrium central torsion angle of ~ 45° and shows both a planar (0°) and a perpendicular (90°) torsional energy barrier. The latter is analysed for the first time. We use the newly proposed REG method, which is an exhaustive procedure that automatically ranks atomic energy contributions according to their importance in explaining the energy profile of a total system. Here, the REG method operates on energy contributions computed by the interacting quantum atoms method. This method is minimal in architecture and provides a crisp picture of well-defined and well-separated electrostatic, steric and exchange (covalent) energies at atomistic level. It is shown that the bond critical point occurring between the ortho-hydrogens in the planar geometry has been wrongly interpreted as a sign of repulsive interaction. A convenient metaphor of analysing football matches is introduced to clarify the role of a REG analysis.

FALDI-based criterion for and the origin of an electron density bridge with an associated (3,-1) critical point on Bader's molecular graph

The total electron density (ED) along the λ₂ -eigenvector is decomposed into contributions which either facilitate or hinder the presence of an electron density bridge (DB, often called an atomic interaction line or a bond path). Our FALDI-based approach explains a DB presence as a result of a dominating rate of change of facilitating factors relative to the rate of change of hindering factors; a novel and universal criterion for a DB presence is, thus, proposed. Importantly, facilitating factors show, in absolute terms, a concentration of ED in the internuclear region as commonly observed for most chemical bonds, whereas hindering factors show a depletion of ED in the internuclear region. We test our approach on four intramolecular interactions, namely (i) an attractive classical H-bond, (ii) a repulsive O⋅⋅⋅O interaction, (iii) an attractive Cl⋅⋅⋅Cl interaction, and (iv) an attractive CH⋅⋅⋅HC interaction. (Dis)appearance of a DB is (i) shown to be due to a "small" change in molecular environment and (ii) qualitatively and quantitatively linked with specific atoms and atom-pairs. The protocol described is equally applicable (a) to any internuclear region, (b) regardless of what kind of interaction (attractive/repulsive) atoms are involved in, (c) at any level of theory used to compute the molecular structure and corresponding wavefunction, and (d) equilibrium or nonequilibrium structures. Finally, we argue for a paradigm shift in the description of chemical interactions, from the ED perspective, in favor of a multicenter rather than diatomic approach in interpreting ED distributions in internuclear regions. © 2018 Wiley Periodicals, Inc.

MP2-IQA: upscaling the analysis of topologically partitioned electron correlation

When electronic correlation energy is partitioned topologically, a detailed picture of its distribution emerges, both within atoms and between any two atoms. This methodology allows one to study dispersion beyond its more narrow definition in long-range Rayleigh-Schrödinger perturbation theory. The interacting quantum atoms (IQA) method was applied to MP2/6-31G(d,p) (uncontracted) wave functions of a wide variety of systems: glycine…water (hydration), the ethene dimer (π-π interactions), benzene (aromaticity), cyclobutadiene (antiaromaticity), and NH₃BH₃ (dative bond). Through the study of molecular complexes it turns out that dispersion energy is either important to a system's stabilization (for the C₂H₄ dimer) or not important (for Gly…H₂O). We have also discovered that the delocalization in benzene lowers the strength of Coulomb repulsion in the bonds, which has been quantified for the first time through IQA. Finally, we showed that the nature of the dative bond is much different from that of a regular covalent bond as it is not destabilized by electronic correlation. Finally, the conclusions obtained for these archetypical systems have implications for the future of the quantum topological force field FFLUX in the simulation of larger systems. Graphical abstract Atomic and bond dynamic correlation energies are now available thanks to IQA. Larger molecules can now be accessed to include resonance and solvation of FFLUX force field.

TopoMS: Comprehensive topological exploration for molecular and condensed-matter systems

We introduce TopoMS, a computational tool enabling detailed topological analysis of molecular and condensed-matter systems, including the computation of atomic volumes and charges through the quantum theory of atoms in molecules, as well as the complete molecular graph. With roots in techniques from computational topology, and using a shared-memory parallel approach, TopoMS provides scalable, numerically robust, and topologically consistent analysis. TopoMS can be used as a command-line tool or with a GUI (graphical user interface), where the latter also enables an interactive exploration of the molecular graph. This paper presents algorithmic details of TopoMS and compares it with state-of-the-art tools: Bader charge analysis v1.0 (Arnaldsson et al., 01/11/17) and molecular graph extraction using Critic2 (Otero-de-la-Roza et al., Comput. Phys. Commun. 2014, 185, 1007). TopoMS not only combines the functionality of these individual codes but also demonstrates up to 4× performance gain on a standard laptop, faster convergence to fine-grid solution, robustness against lattice bias, and topological consistency. TopoMS is released publicly under BSD License. © 2018 Wiley Periodicals, Inc.

An Electron Density Source-Function Study of DNA Base Pairs in Their Neutral and Ionized Ground States†

The source function (SF) decomposes the electron density at any point into contributions from all other points in the molecule, complex, or crystal. The SF "illuminates" those regions in a molecule that most contribute to the electron density at a point of reference. When this point of reference is the bond critical point (BCP), a commonly used surrogate of chemical bonding, then the SF analysis at an atomic resolution within the framework of Bader's Quantum Theory of Atoms in Molecules returns the contribution of each atom in the system to the electron density at that BCP. The SF is used to locate the important regions that control the hydrogen bonds in both Watson-Crick (WC) DNA dimers (adenine:thymine (AT) and guanine:cytosine (GC)) which are studied in their neutral and their singly ionized (radical cationic and anionic) ground states. The atomic contributions to the electron density at the BCPs of the hydrogen bonds in the two dimers are found to be delocalized to various extents. Surprisingly, gaining or loosing an electron has similar net effects on some hydrogen bonds concealing subtle compensations traced to atomic sources contributions. Coarser levels of resolutions (groups, rings, and/or monomers-in-dimers) reveal that distant groups and rings often have non-negligible effects especially on the weaker hydrogen bonds such as the third weak CH⋅⋅⋅O hydrogen bond in AT. Interestingly, neither the purine nor the pyrimidine in the neutral or ionized forms dominate any given hydrogen bond despite that the former has more atoms that can act as source or sink for the density at its BCP. © 2018 Wiley Periodicals, Inc.

A fully analytical integration of properties over the 3D volume of the β sphere in topological atoms

Atomic multipole moments associated with a spherical volume fully residing within a topological atom (i.e., the β sphere) can be obtained analytically. Such an integration is thus free of quadrature grids. A general formula for an arbitrary rank spherical harmonic multipole moment is derived, for an electron density comprising Gaussian primitives of arbitrary angular momentum. The closed expressions derived here are also sufficient to calculate the electrostatic potential, the two types of kinetic energy, as well as the potential energy between atoms. Some integrals have not been solved explicitly before but through recursion and substitution are broken down to more elementary listed integrals. The proposed method is based on a central formula that shifts Gaussian primitives from one center to another, which can be derived from the well-known plane-wave expansion (or Rayleigh equation). © 2018 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

An interacting quantum atom study of model SN 2 reactions (X- ···CH3 X, X = F, Cl, Br, and I)

The quantum chemical topology method has been used to analyze the energetic profiles in the X-  + CH3 X → XCH3  + X- SN 2 reactions, with X = F, Cl, Br, and I. The evolution of the electron density properties at the BCPs along the reaction coordinate has been analysed. The interacting quantum atoms (IQA) method has been used to evaluate the intra-atomic and interatomic energy variations along the reaction path. The different energetic terms have been examined by the relative energy gradient method and the ANANKE program, which enables automatic and unbiased IQA analysis. Four of the six most important IQA energy contributions were needed to reproduce the reaction barrier common to all reactions. The four reactions considered share many common characteristics but when X = F a number of particularities occur. © 2017 Wiley Periodicals, Inc.

Chemical Pressure Maps of Molecules and Materials: Merging the Visual and Physical in Bonding Analysis

The characterization of bonding interactions in molecules and materials is one of the major applications of quantum mechanical calculations. Numerous schemes have been devised to identify and visualize chemical bonds, including the electron localization function, quantum theory of atoms in molecules, and natural bond orbital analysis, whereas the energetics of bond formation are generally analyzed in qualitative terms through various forms of energy partitioning schemes. In this Article, we illustrate how the chemical pressure (CP) approach recently developed for analyzing atomic size effects in solid state compounds provides a basis for merging these two approaches, in which bonds are revealed through the forces of attraction and repulsion acting between the atoms. Using a series of model systems that include simple molecules (H₂, CO₂, and S₈), extended structures (graphene and diamond), and systems exhibiting intermolecular interactions (ice and graphite), as well as simple representatives of metallic and ionic bonding (Na and NaH, respectively), we show how CP maps can differentiate a range of bonding phenomena. The approach also allows for the partitioning of the potential and kinetic contributions to the interatomic interactions, yielding schemes that capture the physical model for the chemical bond offered by Ruedenberg and co-workers.

Unfavorable regions in the ramachandran plot: Is it really steric hindrance? The interacting quantum atoms perspective

Accurate description of the intrinsic preferences of amino acids is important to consider when developing a biomolecular force field. In this study, we use a modern energy partitioning approach called Interacting Quantum Atoms to inspect the cause of the φ and ψ torsional preferences of three dipeptides (Gly, Val, and Ile). Repeating energy trends at each of the molecular, functional group, and atomic levels are observed across both (1) the three amino acids and (2) the φ/ψ scans in Ramachandran plots. At the molecular level, it is surprisingly electrostatic destabilization that causes the high-energy regions in the Ramachandran plot, not molecular steric hindrance (related to the intra-atomic energy). At the functional group and atomic levels, the importance of key peptide atoms (Oi-1 , Ci , Ni , Ni+1 ) and some sidechain hydrogen atoms (Hγ ) are identified as responsible for the destabilization seen in the energetically disfavored Ramachandran regions. Consistently, the Oi-1 atoms are particularly important for the explanation of dipeptide intrinsic behavior, where electrostatic and steric destabilization unusually complement one another. The findings suggest that, at least for these dipeptides, it is the peptide group atoms that dominate the intrinsic behavior, more so than the sidechain atoms. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Rhorix: An interface between quantum chemical topology and the 3D graphics program blender

Chemical research is assisted by the creation of visual representations that map concepts (such as atoms and bonds) to 3D objects. These concepts are rooted in chemical theory that predates routine solution of the Schrödinger equation for systems of interesting size. The method of Quantum Chemical Topology (QCT) provides an alternative, parameter-free means to understand chemical phenomena directly from quantum mechanical principles. Representation of the topological elements of QCT has lagged behind the best tools available. Here, we describe a general abstraction (and corresponding file format) that permits the definition of mappings between topological objects and their 3D representations. Possible mappings are discussed and a canonical example is suggested, which has been implemented as a Python "Add-On" named Rhorix for the state-of-the-art 3D modeling program Blender. This allows chemists to use modern drawing tools and artists to access QCT data in a familiar context. A number of examples are discussed. © 2017 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

The Transferability of Topologically Partitioned Electron Correlation Energies in Water Clusters

The electronic effects that govern the cohesion of water clusters are complex, demanding the inclusion of N-body, Coulomb, exchange and correlation effects. Here we present a much needed quantitative study of the effect of correlation (and hence dispersion) energy on the stabilization of water clusters. For this purpose we used a topological energy partitioning method called Interacting Quantum Atoms (IQA) to partition water clusters into topological atoms, based on a MP2/6-31G(d,p) wave function, and modified versions of GAUSSIAN09 and the Quantum Chemical Topology (QCT) program MORFI. Most of the cohesion in the water clusters provided by electron correlation comes from intramolecular energy stabilization. Hydrogen bond-related interactions tend to largely cancel each other. Electron correlation energies are transferable in almost all instances within 1 kcal mol^-1 . This observed transferability is very important to the further development of the QCT force field FFLUX, especially to the future modelling of liquid water.

Geometry Optimization with Machine Trained Topological Atoms

The geometry optimization of a water molecule with a novel type of energy function called FFLUX is presented, which bypasses the traditional bonded potentials. Instead, topologically-partitioned atomic energies are trained by the machine learning method kriging to predict their IQA atomic energies for a previously unseen molecular geometry. Proof-of-concept that FFLUX’s architecture is suitable for geometry optimization is rigorously demonstrated. It is found that accurate kriging models can optimize 2000 distorted geometries to within 0.28 kJ mol⁻¹ of the corresponding ab initio energy, and 50% of those to within 0.05 kJ mol⁻¹. Kriging models are robust enough to optimize the molecular geometry to sub-noise accuracy, when two thirds of the geometric inputs are outside the training range of that model. Finally, the individual components of the potential energy are analyzed, and chemical intuition is reflected in the independent behavior of the three energy terms \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{{\rm{intra}}}^{{\rm{A}}}$$\end{document}EintraA(intra-atomic), \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{{\rm{cl}}}^{\text{AA}\text{'}}$$\end{document}VclAA' (electrostatic) and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${V}_{{\rm{x}}}^{\text{AA}\text{'}}$$\end{document}VxAA' (exchange), in contrast to standard force fields.

The ANANKE relative energy gradient (REG) method to automate IQA analysis over configurational change

Much chemical insight ultimately comes down to finding out which fragment of a total system behaves like the total system, in terms of an energy profile. A simple example is that of the water dimer, where this system is regarded as held together by a hydrogen bond. The hydrogen bond consists of two atoms (H···O), which energetically behave similarly to the total system (H₂O)₂. However, from a quantum mechanical point of view, each atom in the total system interacts with any other atom. Thus, the view that the hydrogen bond by itself governs the energetic stability of the water dimer needs rigorous justification. In this work, we propose a method that provides such a justification, in general, but only illustrated on the water dimer here. This method is based on the topological energy partitioning method called interacting quantum atoms (IQA). The method is implemented in the program ANANKE, which calculates correlations between the energy profile of the total system and those of subsystems (or fragments). ANANKE acts on the IQA energy contributions obtained for a sequence of full-system geometries controlled by a coordinate of interest (e.g. the O···H distance in the water dimer). Although applied only for the water dimer in this work, the method is general and able to explain the gauche effect, the torsional barrier in biphenyl, the arrow-pushing scheme of an enzymatic reaction (peptide hydrolysis in the HIV-1 Protease active site), and halogen-alkane nucleophilic substitution (S_N2) reactions. Those applications will appear elsewhere as separate and elaborated case studies; here we focus on the details of the ANANKE method and its justification, using the water dimer as a concrete case.

Quantifying Electron Correlation of the Chemical Bond

The Interacting Quantum Atoms (IQA) method is used to analyze the correlated part of the Møller-Plesset (MP) perturbation theory two-particle density matrix. Such an analysis determines the effects of electron correlation within atoms and between atoms, which covers both bonds and nonbonded through-space atom-atom interactions within a molecule or molecular complex. Electron correlation lowers the energy of the atoms at either end of a bond, but for the bond itself, it can be stabilizing or destabilizing. Bonds are described in a two-dimensional world of exchange and charge transfer, where covalency is not the opposite of ionicity.

Toward amino acid typing for proteins in FFLUX

Continuing the development of the FFLUX, a multipolar polarizable force field driven by machine learning, we present a modern approach to atom-typing and building transferable models for predicting atomic properties in proteins. Amino acid atomic charges in a peptide chain respond to the substitution of a neighboring residue and this response can be categorized in a manner similar to atom-typing. Using a machine learning method called kriging, we are able to build predictive models for an atom that is defined, not only by its local environment, but also by its neighboring residues, for a minimal additional computational cost. We found that prediction errors were up to 11 times lower when using a model specific to the correct group of neighboring residues, with a mean prediction of ∼0.0015 au. This finding suggests that atoms in a force field should be defined by more than just their immediate atomic neighbors. When comparing an atom in a single alanine to an analogous atom in a deca-alanine helix, the mean difference in charge is 0.026 au. Meanwhile, the same difference between a trialanine and a deca-alanine helix is only 0.012 au. When compared to deca-alanine models, the transferable models are up to 20 times faster to train, and require significantly less ab initio calculation, providing a practical route to modeling large biological systems. © 2016 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.

Extending the Domain-Averaged Exchange-Correlation Energies Within the Context of the MC-QTAIM: Tracing Subtle Variations Induced by Isotope Substitution

Recently, it has been demonstrated that the domain-averaged exchange-correlation energies, V^xc , are capable of tracing the covalent character of atom-atom interactions unequivocally and thus pave the way for detailed bonding analysis within the context of the quantum theory of atoms in molecules (QTAIM) [M. García-Revilla, E. Francisco, P. L. Popelier, A. Martín Pendás, ChemPhysChem 2013, 14, 1211-1218]. Herein, the concept of V^xc is extended within the context of the newly developed multicomponent QTAIM (MC-QTAIM). The extended version, Veexc , is capable of analyzing nonadiabatic wavefunctions and thus is sensitive to the mass of nuclei and can trace "locally" the subtle electronic variations induced by isotope substitution. To demonstrate this capability in practice, ab initio nonadiabatic wavefunctions for three isotopically substituted hydrogen cyanide molecules, in which the hydrogen nucleus was assumed to be a proton, deuterium, or tritium, were derived. The resulting wavefunctions were then used to compute Veexc and it emerged that for the hydrogen-carbon bond, the Veexc was distinct for each isotopic composition and varied in line with chemical expectations. Indeed, the introduction of Veexc paves the way for the investigation of vast numbers of structural and kinetic isotope effects within the context of the MC-QTAIM.

Feynman force components: basis for a solution to the covalent vs. ionic dilemma

Feynman force components give fundamentals for distinction between covalent and ionic bonds without referring to the electronegativity concept.