Improved convergence of the ‘atoms in molecules’ multipole expansion of electrostatic interaction

Carbonyl-Based Redox-Active Compounds as Organic Electrodes for Batteries: Escape from Middle-High Redox Potentials and Further Improvement?

Extracting─from the vast space of organic compounds─the best electrode candidates for achieving energy material breakthrough requires the identification of the microscopic causes and origins of various macroscopic features, including notably electrochemical and conduction properties. As a first guess of their capabilities, molecular DFT calculations and quantum theory of atoms in molecules (QTAIM)-derived indicators were applied to explore the family of pyrano[3,2-b]pyran-2,6-dione (PPD, i.e., A0) compounds, expanded to A0 fused with various kinds of rings (benzene, fluorinated benzene, thiophene, and merged thiophene/benzene). A glimpse of up-to-now elusive key incidences of introducing oxygen in vicinity to the carbonyl redox center within 6MRs─as embedded in the A0 core central unit common to all A-type compounds─has been gained. Furthermore, the main driving force toward achieving modulated low redox potential/band gaps thanks to fusing the aromatic rings for the A compound series was discovered.

Non-covalent interactions from a Quantum Chemical Topology perspective

About half a century after its little-known beginnings, the quantum topological approach called QTAIM has grown into a widespread, but still not mainstream, methodology of interpretational quantum chemistry. Although often confused in textbooks with yet another population analysis, be it perhaps an elegant but somewhat esoteric one, QTAIM has been enriched with about a dozen other research areas sharing its main mathematical language, such as Interacting Quantum Atoms (IQA) or Electron Localisation Function (ELF), to form an overarching approach called Quantum Chemical Topology (QCT). Instead of reviewing the latter's role in understanding non-covalent interactions, we propose a number of ideas emerging from the full consequences of the space-filling nature of topological atoms, and discuss how they (will) impact on interatomic interactions, including non-covalent ones. The architecture of a force field called FFLUX, which is based on these ideas, is outlined. A new method called Relative Energy Gradient (REG) is put forward, which is able, by computation, to detect which fragments of a given molecular assembly govern the energetic behaviour of this whole assembly. This method can offer insight into the typical balance of competing atomic energies both in covalent and non-covalent case studies. A brief discussion on so-called bond critical points is given, highlighting concerns about their meaning, mainly in the arena of non-covalent interactions.

Multipolar electrostatics for hairpin and pseudoknots in RNA: Improving the accuracy of force field potential energy function

Molecular dynamics (MD) simulations that rely on force field methods has been widely used to explore the structure and function of RNAs. However, the current commonly used force fields are limited by the electrostatic description offered by atomic charge, dipole and at most quadrupole moments, failing to capture the anisotropic picture of electronic features. Actually, the distribution of electrons around atomic nuclei is not spherically symmetric but is geometry dependent. A multipolar electrostatic model based on high rank multipole moments is described in this work, which allows us to combine polarizability and anisotropy of electron density. RNA secondary structure was taken as a research system, and its substructures including stem, loops (hairpin loop, bulge loop, internal loop, and multi-branch loop), and pseudoknots (H-type and K-type) were investigated, respectively, as well as the hairpin. First, the atom-atom electrostatic properties derived from one chain of a duplex RNA 2MVY in our previous work (Ref. 58) were measured by the pilot RNA systems of hairpin, hairpin loop, stem, and H-type pseudoknot, respectively. The prediction results were not satisfactory. Consequently, to obtain a general set of electrostatic parameters for RNA force fields, the convergence behavior of the atom-atom electrostatic interactions in the pilot RNA systems was explored using high rank atomic multipole moments. The pilot RNA systems were cut into four types of different-sized molecular fragments, and the single nucleotide fragment and nucleotide-paired fragment proved to be the most reasonable systems for base-unpairing regions and base-pairing regions to investigate the convergence behavior of all types of atom-atom electrostatic interactions, respectively. Transferability of the electrostatic properties drawn from the pilot RNA systems to the corresponding test systems was also investigated. Furthermore, the convergence behavior of atomic electrostatic interactions in other substructures including bulge loop, internal loop, multi-branch loop, and K-type pseudoknot was expected to be modeled via the hairpin.

Multipolar Description of Atom-Atom Electrostatic Interaction Energies in Single/Double-Stranded DNAs

Molecular force field simulation is an effective method to explore the properties of DNA molecules in depth. Almost all current popular force fields calculate atom-atom electrostatic interaction energies for DNAs based on the atomic charge and dipole or quadrupole moments, without considering high-rank atomic multipole moments for more accurate electrostatics. Actually, the distribution of electrons around atomic nuclei is not spherically symmetric but is geometry dependent. In this work, a multipole expansion method that allows us to combine polarizability and anisotropy was applied. One single-stranded DNA and one double-stranded DNA were selected as pilot systems. Deoxynucleotides were cut out from pilot systems and capped by mimicking the original DNA environment. Atomic multipole moments were integrated instead of fixed-point charges to calculate atom-atom electrostatic energies to improve the accuracy of force fields for DNA simulations. Also, the applicability of modeling the behavior of both single-stranded and double-stranded DNAs was investigated. The calculation results indicated that the models can be transferred from pilot systems to test systems, which is of great significance for the development of future DNA force fields.

Assessing Force Field Potential Energy Function Accuracy via a Multipolar Description of Atomic Electrostatic Interactions in RNA

Computational investigations of RNA properties often rely on a molecular mechanical approach to define molecular potential energy. Force fields for RNA typically employ a point charge model of electrostatics, which does not provide a realistic quantum-mechanical picture. In reality, electron distributions around nuclei are not spherically symmetric and are geometry dependent. A multipole expansion method which allows for incorporation of polarizability and anisotropy in a force field is described, and its applicability to modeling the behavior of RNA molecules is investigated. Transferability of the model, critical for force field development, is also investigated.

Minimal distributed charges: Multipolar quality at the cost of point charge electrostatics

Most empirical force fields use atom-centered point charges (PCs) to represent the electrostatic potential (ESP) around molecules. While such PC models are computationally efficient, they are unable to capture anisotropic electronic features, such as σ holes or lone pairs. These features are better described using atomic multipole (MTP) moments, which significantly improve the quality of the resulting ESP. However, the improvement comes at the expense of a considerably increased computational complexity and cost for calculating the interaction energies and forces. In the present work, a novel minimal distributed charge model (MDCM) based on off-centered point charges is presented and the quality of the resulting ESP is compared to the performance of MTPs and atom-centered PC models for several test molecules. All three models are fitted using the same algorithm based on differential evolution, which is available as a Fortran90 program from the authors upon request. We show that the MDCM is capable of approximating the reference ab initio ESP with an accuracy as good as, or better than, MTPs without the need for computationally expensive higher order multipoles. Further it is demonstrated that the MDCM is numerically stable in molecular dynamics simulations and is able to reproduce electrostatic interaction energies and thermodynamic quantities with the same accuracy as MTPs at reduced computational cost.

The bonding picture in hypervalent XF3 (X = Cl, Br, I, At) fluorides revisited with quantum chemical topology

Hypervalent XF₃ (X = Cl, Br, I, At) fluorides exhibit T-shaped C_2V equilibrium structures with the heavier of them, AtF₃ , also revealing an almost isoenergetic planar D_3h structure. Factors explaining this behavior based on simple "chemical intuition" are currently missing. In this work, we combine non-relativistic (ClF₃ ), scalar-relativistic and two-component (X = Br - At) density functional theory calculations, and bonding analyses based on the electron localization function and the quantum theory of atoms in molecules. Typical signatures of charge-shift bonding have been identified at the bent T-shaped structures of ClF₃ and BrF₃ , while the bonds of the other structures exhibit a dominant ionic character. With the aim of explaining the D_3h structure of AtF₃ , we extend the multipole expansion analysis to the framework of two-component single-reference calculations. This methodological advance enables us to rationalize the relative stability of the T-shaped C_2v and the planar D_3h structures: the Coulomb repulsions between the two lone-pairs of the central atom and between each lone-pair and each fluorine ligand are found significantly larger at the D_3h structures than at the C_2v ones for X = Cl - I, but not with X = At. This comes with the increasing stabilization, along the XF₃ series, of the planar D_3h structure with respect to the global T-shaped C_2v minima. Hence, we show that the careful use of principles that are at the heart of the valence shell electron pair repulsion model provides reasonable justifications for stable planar D_3h structures in AX₃ E₂ systems. © 2017 Wiley Periodicals, Inc.

Hydrogen bonding in ionic liquids

Ionic liquids (IL) and hydrogen bonding (H-bonding) are two diverse fields for which there is a developing recognition of significant overlap. Doubly ionic H-bonds occur when a H-bond forms between a cation and anion, and are a key feature of ILs. Doubly ionic H-bonds represent a wide area of H-bonding which has yet to be fully recognised, characterised or explored. H-bonds in ILs (both protic and aprotic) are bifurcated and chelating, and unlike many molecular liquids a significant variety of distinct H-bonds are formed between different types and numbers of donor and acceptor sites within a given IL. Traditional more neutral H-bonds can also be formed in functionalised ILs, adding a further level of complexity. Ab initio computed parameters; association energies, partial charges, density descriptors as encompassed by the QTAIM methodology (ρBCP), qualitative molecular orbital theory and NBO analysis provide established and robust mechanisms for understanding and interpreting traditional neutral and ionic H-bonds. In this review the applicability and extension of these parameters to describe and quantify the doubly ionic H-bond has been explored. Estimating the H-bonding energy is difficult because at a fundamental level the H-bond and ionic interaction are coupled. The NBO and QTAIM methodologies, unlike the total energy, are local descriptors and therefore can be used to directly compare neutral, ionic and doubly ionic H-bonds. The charged nature of the ions influences the ionic characteristics of the H-bond and vice versa, in addition the close association of the ions leads to enhanced orbital overlap and covalent contributions. The charge on the ions raises the energy of the Ylp and lowers the energy of the X-H σ* NBOs resulting in greater charge transfer, strengthening the H-bond. Using this range of parameters and comparing doubly ionic H-bonds to more traditional neutral and ionic H-bonds it is clear that doubly ionic H-bonds cover the full range of weak through to very strong H-bonds.

Charge Anisotropy: Where Atomic Multipoles Matter Most

Specific intermolecular interactions are largely guided by electrostatics. However, the most common model for electrostatic interactions-atomic point charges-fails to reproduce anisotropic charge distributions, such as lone pairs and sigma holes. Although this has long been known, point charges are still widely used in chemical modeling and reasoning. In this contribution, we analyze the deficiency of atomic point charges in reproducing the electrostatic potential (ESP) around molecules and find that multipole moments up to quadrupoles can, with a much lower error than point charges, reproduce the relevant ESP for all cases. Mapping the surface to the closest atom allows to compare ESP errors between atom types and to identify cases with the most urgent need for atomic multipoles. Our analysis shows that almost all heteroatoms require multipoles to correctly describe their charge distribution, with the most serious cases being nitrogen, sulfur, and halogens. Comparison with small molecule crystallography data studies supports our findings and emphasizes the need for incorporating anisotropic charge descriptions in chemical models. The scheme introduced here can be used to identify anisotropic binding preferences for atom types where there is too little coverage in crystal structure databases.

Accuracy and tractability of a kriging model of intramolecular polarizable multipolar electrostatics and its application to histidine

We propose a generic method to model polarization in the context of high-rank multipolar electrostatics. This method involves the machine learning technique kriging, here used to capture the response of an atomic multipole moment of a given atom to a change in the positions of the atoms surrounding this atom. The atoms are malleable boxes with sharp boundaries, they do not overlap and exhaust space. The method is applied to histidine where it is able to predict atomic multipole moments (up to hexadecapole) for unseen configurations, after training on 600 geometries distorted using normal modes of each of its 24 local energy minima at B3LYP/apc-1 level. The quality of the predictions is assessed by calculating the Coulomb energy between an atom for which the moments have been predicted and the surrounding atoms (having exact moments). Only interactions between atoms separated by three or more bonds ("1, 4 and higher" interactions) are included in this energy error. This energy is compared with that of a central atom with exact multipole moments interacting with the same environment. The resulting energy discrepancies are summed for 328 atom-atom interactions, for each of the 29 atoms of histidine being a central atom in turn. For 80% of the 539 test configurations (outside the training set), this summed energy deviates by less than 1 kcal mol(-1).

Biomolecular electrostatics and solvation: a computational perspective

An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of the basic elements of biomolecular solvation (e.g. solvent structure, polarization, ion binding, and non-polar behavior) in order to provide a background to understand the different types of solvation models.

Properties of liquid water from a systematic refinement of a high-rank multipolar electrostatic potential

We build on previous work [S. Y. Liem and P. L. A. Popelier, J. Chem. Theory Comput. 4, 353 (2008)], where for the first time, a high-rank multipolar electrostatic potential was used in molecular dynamics simulations of liquid water at a wide range of pressures and temperatures, and using a multipolar Ewald summation. Water is represented as a rigid body, with atomic multipole moments defined by quantum chemical topology partitioning its gas phase electron density. The effect of the level of theory on the local structure of liquid water is systematically addressed. Values for Lennard-Jones (LJ) parameters are optimized, for both oxygen and hydrogen atoms, against bulk properties. The best LJ parameters were then used in a set of simulations at 30 different temperatures (1 atm) and another set at 11 different pressures (at 298 K). Inclusion of the hydrogen LJ parameters significantly increases the self-diffusion coefficient. The behavior of bulk properties was studied and the local water structure analyzed by both radial and spatial distribution functions. Comparisons with familiar point-charge potentials, such as TIP3P, TIP4P, TIP5P, and simple point charge, show the benefits of multipole moments.

Application of multipolar charge models and molecular dynamics simulations to study stark shifts in inhomogeneous electric fields

Atomic multipole moments are used to investigate vibrational frequency shifts of CO and H(2) in uniform and inhomogeneous electric fields using ab initio calculations and Molecular Dynamics (MD) simulations. The importance of using atomic multipole moments that can accurately represent both molecular electrostatics and the vibrational response of the molecule to changes in the local electric field is highlighted. The vibrational response of CO to applied uniform and inhomogeneous electric fields is examined using Density Functional Theory calculations for a range of test fields, and the results are used to assess the performance of different atomic multipole models. In uniform fields, the calculated Stark tuning rates of Deltamu = 0.52 cm(-1)/(MV/cm) (DFT), Deltamu = 0.55 cm(-1)/(MV/cm) (fluctuating three-point charge model), and Deltamu = 0.64 cm(-1)/(MV/cm) (Multipole model up to octupole), compare favorably with the experimentally measured value of 0.67 cm(-1)/(MV/cm). For H(2), which has no permanent dipole moment, CCSD(T) calculations demonstrate the importance of bond-weakening effects in force fields in response to the applied inhomogeneous electric field. Finally, CO in hexagonal ice is considered as a test system to highlight the performance of selected multipolar models in MD simulations. The approach discussed here can be applied to calibrate a range of multipolar charge models for diatomic probes, with applications to interpret Stark spectroscopy measurements in protein active sites.

An analysis of the electrostatic interaction between nucleic acid bases

Results from several commonly used approximate methods of evaluating electrostatic interactions have been compared to the rigorous, nonexpanded electrostatic energies at both uncorrelated and correlated levels of theory. We examined a number of energy profiles for both hydrogen bonded and stacked configurations of the nucleic acid base pairs. We found that the penetration effects play an extremely important role and the expanded electrostatic energies are significantly underestimated with respect to the ab initio values. Apart from the inability to reproduce the magnitudes of the ab initio electrostatic energy, there are other problems with the available approximate electrostatic models. For example, the distributed multipole analysis, one of the most advanced methods, is extremely sensitive to the basis set and level of theory used to evaluate the multipole moments. Detailed ab initio results are provided that other researchers could use to test their approximate models.

A convergent multipole expansion for 1,3 and 1,4 Coulomb interactions

Traditionally force fields express 1,3 and 1,4 interactions as bonded terms via potentials that involve valence and torsion angles, respectively. These interactions are not modeled by point charge terms, which are confined to electrostatic interactions between more distant atoms (1,n where n>4). Here we show that both 1,3 and 1,4 interactions can be described on the same footing as 1,n (n>4) interactions by a convergent multipole expansion of the Coulomb energy of the participating atom pairs. The atomic multipole moments are generated by the theory of quantum chemical topology. The procedure to make the multipole expansion convergent is based on a "shift procedure" described in earlier work [L. Joubert and P. L. A. Popelier, Molec. Phys. 100, 3357 (2002)].

Calculation of electrostatic interaction energies in molecular dimers from atomic multipole moments obtained by different methods of electron density partitioning

Accurate and fast evaluation of electrostatic interactions in molecular systems is still one of the most challenging tasks in the rapidly advancing field of macromolecular chemistry, including molecular recognition, protein modeling and drug design. One of the most convenient and accurate approaches is based on a Buckingham-type approximation that uses the multipole moment expansion of molecular/atomic charge distributions. In the mid-1980s it was shown that the pseudoatom model commonly used in experimental X-ray charge density studies can be easily combined with the Buckingham-type approach for calculation of electrostatic interactions, plus atom-atom potentials for evaluation of the total interaction energies in molecular systems. While many such studies have been reported, little attention has been paid to the accuracy of evaluation of the purely electrostatic interactions as errors may be absorbed in the semiempirical atom-atom potentials that have to be used to account for exchange repulsion and dispersion forces. This study is aimed at the evaluation of the accuracy of the calculation of electrostatic interaction energies with the Buckingham approach. To eliminate experimental uncertainties, the atomic moments are based on theoretical single-molecule electron densities calculated at various levels of theory. The electrostatic interaction energies for a total of 11 dimers of alpha-glycine, N-acetylglycine and L-(+)-lactic acid structures calculated according to Buckingham with pseudoatom, stockholder and atoms-in-molecules moments are compared with those evaluated with the Morokuma-Ziegler energy decomposition scheme. For alpha-glycine a comparison with direct "pixel-by-pixel" integration method, recently developed Gavezzotti, is also made. It is found that the theoretical pseudoatom moments combined with the Buckingham model do predict the correct relative electrostatic interactions energies, although the absolute interaction energies are underestimated in some cases. The good agreement between electrostatic interaction energies computed with Morokuma-Ziegler partitioning, Gavezzotti's method, and the Buckingham approach with atoms-in-molecules moments demonstrates that reliable and accurate evaluation of electrostatic interactions in molecular systems of considerable complexity is now feasible.