Atomic Charges In Molecules Research Articles

Atomic charges in molecules defined by molecular real space partition into atomic subspaces.

Atomic charge (AC), which is the charge distribution of a molecule, is an important property that is closely associated with structures, reactivities, and intra- and inter-molecular interactions among molecules. Several theoretical models or methods can be used to obtain the magnitudes of AC with different characteristics. These models can be classified into fuzzy-atoms models and models partitioning a molecule into individual atoms with sharp boundaries. The first category includes Mulliken, natural population analysis (NPA), Hirshfeld, Merz-Kollman-Singh (MK), CHELPG, the electronegativity equalization method (EEM), the atom-bond electronegativity equalization method (ABEEM), and atomic polar tensor (APT). The second category is derived from quantum chemical topology (QCT) and includes the quantum theory of atoms in molecules (QTAIM) and QCT analysis based on the potential acting on one electron in a molecule (PAEMQCT). Herein, after giving a bird's-eye view of the population methods of the first category, we specifically describe some features of the second category. We only present the basic framework of QCT for obtaining ACs from QTAIM and PAEMQCT and show their important characteristics. QCT establishes the basis of the following chemical concept: a molecule is spatially partitioned into individual atoms with sharp boundaries. The ACs from QTAIM are close to the atomic valence in chemistry, and ACs from PAEMQCT may be practically suitable for modeling intra- and inter-molecular interactions.

Energy Electronegativity and Chemical Bonding

Historical development of the concept of electronegativity (EN) and its significance and prospects for physical and structural chemistry are discussed. The current cutting-edge results are reviewed: new methods of determining the ENs of atoms in solid metals and of bond polarities and effective atomic charges in molecules and crystals. The ENs of nanosized elements are calculated for the first time, enabling us to understand their unusual reactivity, particularly the fixation of N2 by nanodiamond. Bond polarities in fluorides are also determined for the first time, taking into account the peculiarities of the fluorine atom's electronic structure and its electron affinity.

Apples to apples comparison of standardized to unstandardized principal component analysis of methods that assign partial atomic charges in molecules.

Articles by Cho et al. (ChemPhysChem, 2020, 21, 688-696) and Manz (RSC Adv., 2020, 10, 44121-44148) performed unstandardized and standardized, respectively, principal component analysis (PCA) to study atomic charge assignment methods for molecular systems. Both articles used subsets of atomic charges computed by Cho et al.; however, the data subsets employed were not strictly identical. Herein, an element by element analysis of this dataset is first performed to compare the spread of charge values across individual chemical elements and charge assignment methods. This reveals an underlying problem with the reported Becke partial atomic charges in this dataset. Due to their unphysical values, these Becke charges were not included in the subsequent PCA. Standardized and unstandardized PCA are performed across two datasets: (i) 19 charge assignment methods having a complete basis set limit and (ii) all 25 charge assignment methods (excluding Becke) for which Cho et al. computed atomic charges. The dataset contained ∼2000 molecules having a total of 29 907 atoms in materials. The following five methods (listed here in alphabetical order) showed the greatest correlation to the first principal component in standardized and unstandardized PCA: DDEC6, Hirshfeld-I, ISA, MBIS, and MBSBickelhaupt (note: MBSBickelhaupt does not appear in the 19 methods dataset). For standardized PCA, the DDEC6 method ranked first followed closely by MBIS. For unstandardized PCA, Hirshfeld-I (19 methods) or MBSBickelhaupt (25 methods) ranked first followed by DDEC6 in second place (both 19 and 25 methods).

Solvated State of Ethylenediamine in Nonaqueous Solvents, According to Quantum Chemical Data

Quantum chemical modeling is used to study the equilibrium geometric parameters and atomic charges in molecules of ethylenediamine (En) in the free state, methanol (MeOH), acetonitrile (AN), N,N‑dimethylformamide (DMF) and dimethylsulfoxide (DMSO), along with the Gibbs energies and enthalpies of amine solvation in the considered solvents. It is found that the conformational state of En is approximately the same in each solvent. In aprotic solvents, the solvation of En proceeds mainly because of the universal type of interactions between amine molecules and solvent molecules; in methanol, solvation energy of En and the solvate’s stability are determined by both universal and specific types of solute–solvent interactions with the contribution from the universal type of interactions predominating.

Seven confluence principles: a case study of standardized statistical analysis for 26 methods that assign net atomic charges in molecules.

This article studies two kinds of information extracted from statistical correlations between methods for assigning net atomic charges (NACs) in molecules. First, relative charge transfer magnitudes are quantified by performing instant least squares fitting (ILSF) on the NACs reported by Cho et al. (ChemPhysChem, 2020, 21, 688–696) across 26 methods applied to ∼2000 molecules. The Hirshfeld and Voronoi deformation density (VDD) methods had the smallest charge transfer magnitudes, while the quantum theory of atoms in molecules (QTAIM) method had the largest charge transfer magnitude. Methods optimized to reproduce the molecular dipole moment (e.g., ACP, ADCH, CM5) have smaller charge transfer magnitudes than methods optimized to reproduce the molecular electrostatic potential (e.g., CHELPG, HLY, MK, RESP). Several methods had charge transfer magnitudes even larger than the electrostatic potential fitting group. Second, confluence between different charge assignment methods is quantified to identify which charge assignment method produces the best NAC values for predicting via linear correlations the results of 20 charge assignment methods having a complete basis set limit across the dataset of ∼2000 molecules. The DDEC6 NACs were the best such predictor of the entire dataset. Seven confluence principles are introduced explaining why confluent quantitative descriptors offer predictive advantages for modeling a broad range of physical properties and target applications. These confluence principles can be applied in various fields of scientific inquiry. A theory is derived showing confluence is better revealed by standardized statistical analysis (e.g., principal components analysis of the correlation matrix and standardized reversible linear regression) than by unstandardized statistical analysis. These confluence principles were used together with other key principles and the scientific method to make assigning atom-in-material properties non-arbitrary. The N@C60 system provides an unambiguous and non-arbitrary falsifiable test of atomic population analysis methods. The HLY, ISA, MK, and RESP methods failed for this material.

A simple model for calculating atomic charges in molecules.

We propose a new atomic-charge analysis, termed adjusted charge partitioning (ACP) scheme. To partition the molecular electronic density into atomic components, weighting factors cAr2n-2exp(-αAr) with atomic parameters cA and αA are used. Extensive numerical tests were performed for 540 molecules containing 17 main-group elements H, Li to F, Na to Cl, Br, and I. The estimated dipole moments and atomic charges are compared with the data provided by a large number of alternative atomic-charge schemes including the Mulliken, Löwdin, Hirshfeld, Hirshfeld Iterative, CM5, ESP, NPA, and QTAIM population analyses. These tests show that the resulting atomic charges are insensitive to basis sets used, chemically consistent and accurately reproduce experimental dipole moments.

Review of Experimental GAPT and Infrared Atomic Charges in Molecules

This review contains experimental values of polar tensors and generalized atomic polar tensor (GAPT) charges determined since the publication of the polar tensor formulism for infrared intensity interpretation in 1961. GAPT charges, also called mean dipole moment derivatives, for 167 atoms of 67 molecules are discussed and compared with infrared charges also determined completely from experimental intensities. The importance of the charge transfer and polarization dynamic contributions to the GAPT charge are emphasized as they differentiate this charge from most theoretically calculated charges. The inclusion of these dynamic contributions is shown to be necessary to provide adequate numerical descriptions of core electron ionization energy processes. These contributions are expected to be important in studies of chemical reactivity.

Atomic Charges in Molecules: A Classical Concept in Modern Computational Chemistry

Atomic Charges in Molecules: A Classical Concept in Modern Computational Chemistry

Divalent pseudoatoms for modeling Si(100) surfaces

An accurate first-principles treatment of complex systems, such as surfaces, continues to be a major challenge in computational chemistry. A popular approach to treat such systems is the use of cluster models, where a moderately sized model system is constructed by excising a cluster from the extended surface. This requires cutting chemical bonds, creating dangling bonds on the cluster boundary atoms that can introduce unphysical errors. Pseudobond, pseudoatom, and quantum capping potential approaches have been developed to treat such systems using a boundary "design-atom" subject to an appropriately fitted effective potential. However, previous approaches have been developed only for truncation of a single covalent bond. They may not be adequate for many important problems involving surface chemistry or materials chemistry, where multiple covalent bonds are severed between layers. In this paper, we have extended the pseudoatom formulation for divalent silicon, which can be employed to describe accurate Si(100) surface chemistry. The effective core potential parameters of our pseudoatom are obtained by fitting to geometrical parameters and atomic charges of molecules containing Si-Si and Si-O bonds, making our pseudoatom robust for applicability in different bonding environments. We calibrate the performance of our pseudoatom approach in small molecules and surface models, and also discuss its ability to describe heteroatomic bonds using multiple theoretical methods.

Partial Atomic Charges and Screened Charge Models of the Electrostatic Potential.

We propose a new screened charge method for calculating partial atomic charges in molecules by electrostatic potential (ESP) fitting. The model, called full density screening (FDS), is used to approximate the screening effect of full charge densities of atoms in molecules. The results are compared to the conventional ESP fitting method based on point charges and to our previously proposed outer density screening (ODS) method, in which the parameters are reoptimized for the present purpose. In ODS, the charge density of an atom is represented by the sum of a point charge and a smeared negative charge distributed in a Slater-type orbital (STO). In FDS, the charge density of an atom is taken to be the sum of the charge density of the neutral atom and a partial atomic charge (of either sign) distributed in an STO. The ζ values of the STOs used in these two models are optimized in the present study to best reproduce the electrostatic potentials. The quality of the fit to the electrostatics is improved in the screened charge methods, especially for the regions that are within one van der Waals radius of the centers of atoms. It is also found that the charges derived by fitting electrostatic potentials with screened charges are less sensitive to the positions of the fitting points than are those derived with conventional electrostatic fitting. Moreover, we found that the electrostatic-potential-fitted (ESP) charges from the screened charge methods are similar to those from the point-charge method except for molecules containing the methyl group, where we have explored the use of restraints on nonpolar H atoms. We recommend the FDS model if the only goal is ESP fitting to obtain partial atomic charges or a fit to the ESP field. However, the ODS model is more accurate for electronic embedding in combined quantum mechanical and molecular mechanical (QM/MM) modeling and is more accurate than point-charge models for ESP fitting, and it is recommended for applications involving QM/MM methods. Since the screened charges describe the electrostatic potentials more accurately than point charges, since they asymptotically act as point charges at long distances, and since the electrostatic potential in terms of the screened charges is still a sum of functions centered at the atoms, the screened-charge representation of the electrostatic potential can be used in the same way as the conventional point-charge representation to model the electrostatic interactions, but it is more realistic. For the H atom and p block elements, the error in the fit to the electrostatic potential is reduced by about a factor of 3, and the sensitivity of the derived partial atomic charges to the choice of fitting points is reduced by about a factor of 2. For s and d block elements, there are also improvements in the inner regions but not necessarily in the outer regions.

Calculating atomic charges in molecules and crystals by a new electronegativity equalization method

The new method of the electronegativity equalization of atoms in molecules and crystals based on Mulliken’ scale is proposed. Calculating the atomic charges by this method gives results which are in accordance with the chemical intuition and empirical estimations.

The Significance of Parameters in Charge Equilibration Models.

Charge equilibration models such as the electronegativity equalization method (EEM) and the split charge equilibration (SQE) are extensively used in the literature for the efficient computation of accurate atomic charges in molecules. However, there is no consensus on a generic set of optimal parameters, even when one only considers parameters calibrated against atomic charges in organic molecules. In this work, the origin of the disagreement in the parameters is investigated by comparing and analyzing six sets of parameters based on two sets of molecules and three calibration procedures. The resulting statistical analysis clearly indicates that the conventional least-squares cost function based solely on atomic charges is in general ill-conditioned and not capable of fixing all parameters in a charge-equilibration model. Methodological guidelines are formulated to improve the stability of the parameters. Although in this case a simple interpretation of individual parameters is not possible, charge equilibration models remain of great practical use for the computation of atomic charges.

Design of Non-aqueous Liquid Electrolytes for Rechargeable Li-O2 Batteries

Liquid electrolytes for rechargeable Li-air batteries were chosen from viewpoints of the electrochemical stability against O2 radical, O2−. Mulliken atomic charges of electrolyte solvents and their reversibility of O2/O2− redox couple were first examined. In the carbonate-based electrolytes, the localization of positive charge in the molecules was confirmed, resulting in low reversibility of O2 radical. The electrolytes must be decomposed by the nucleophilic O2 radical. On the other hand, the nitrile-based and piperidinium-based electrolytes provided high O2 radical reversibility because all of the atomic charges in molecules and cations were either negative or almost zero. It was found that the electronic distribution of electrolyte solvents affected their electrochemical stability against O2 radical. Considering the electrochemical and chemical stability against Li metal, the piperidiniumbased ionic liquid was adopted as an electrolyte solvent in this study. The cell with piperidinium-based electrolyte achieved considerably low charging voltage of around 3.2 V and low voltage gap of about 0.75 V in the discharge-charge profiles, compared to conventional cells with carbonate-based electrolyte. It was, thus, concluded that the charging performances strongly influenced on the O2 radical stability of electrolyte solvent.

NUMERICAL STABILITIES IN FITTING ATOMIC CHARGES TO ELECTRIC FIELD AND ELECTROSTATIC POTENTIAL

It is known that electrostatic potential (ESP) derived atomic charges for molecular systems suffer from rank deficiency in least-square fitting. In this paper, we studied numerical properties of atomic charges by fitting to ESP and electric field (EF) for a series of molecular systems, ranging from small molecules to peptides. Our study shows that although atomic charges of certain atoms in a molecule may differ a lot resulting from different fitting schemes, the effect on some observed physical properties of the molecules, such as solvation free energy and radial distributions of the solvent, are negligible. For all the molecules studied in this paper, it is shown that by incorporating EF terms in the least-square fitting, the rank of the least-squares matrix is increased, and the full rank is achieved when only EF terms are included. The current study demonstrates that by using EF, instead of the widely used ESP, in least-square fitting of atomic charges, one can obtain numerically more stable and better defined atomic charges in molecules. Such derived atomic charges may have more desirable properties and better numerical stabilities in studying detailed molecular processes such as in molecular dynamics simulation of macromolecules.

Investigation of influence of electrical induction on electrostatic interaction of atoms and molecules in solution. 1. Dependence of atomic charges in molecule from environment based on the model of FQ theory

AbstractA new scheme to predict the behavior of atomic charges in molecules that depend on the environment is described. This method combines some advantages of earlier techniques (i.e., partial equalization of orbital electronegativities; fluctuating charge) and new approaches (i.e., two systems of σ and π electrons considered separately, with the use of new parameters). This method has avoided mistakes in the concept of dot charges on atoms. The new technique makes it possible to apply Thole's polarizabilities and van der Waals steric radii of atoms in molecules obtained from natural bond orbital (NBO) steric analysis. The new parameters demonstrate the degree of capability of the polarizabilities of atoms and bonds show the degree of mobility of electrons at creating the bond. The validity of our approximations is proved at a qualitative level. This new method can produce results showing good agreement with the results of ab initio calculations. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007

Accurate partial atomic charges for high-energy molecules using class IV charge models with the MIDI! basis set

We have recently developed a new class IV charge model for calculating partial atomic charges in molecules. The new model, called charge model 3 (CM3), was parameterized for calculations on molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br by Hartree–Fock theory and by hybrid density functional theory (HDFT) based on the modified Perdew–Wang density functional with several basis sets. In the present article, we extend CM3 for calculating partial atomic charges by Hartree–Fock theory with the economical but well balanced MIDI! basis set. Then, using a test set of accurate dipole moments for molecules containing nitramine functional groups (which include many high-energy materials), we demonstrate the utility of several parameters designed to improve the charges in molecules containing both N and O atoms. We also show that one of our most recently developed CM3 models that is designed for use with wave functions calculated at the mPWXPW91/MIDI! level of theory (where X denotes a variable percentage of Hartree–Fock exchange) gives accurate charge distributions in nitramines without additional parameters for N and O. To demonstrate the reliability of partial atomic charges calculated with CM3, we use these atomic charges to calculate polarization free energies for several nitramines, including the commonly used explosives 1,3,5-trinitro-s-triazine (RDX) and 2,4,6,8,10,12-hexanitrohexaazaisowurtzitane (HNIW), in nitromethane. These polarization energies are large and negative, indicating that electrostatic interactions between the charge distribution of the molecule and the solvent make a large contribution to the free energy of solvation of nitramines. By extension, the same conclusion should apply to solid-state condensation. Also, in contrast to some other charge models, CM3 yields atomic charges that are relatively insensitive to the presence of buried atoms and small conformational changes in the molecule, as well as to the level of treatment of electron correlation. This type of charge model should be useful in the future development of solvation models and force fields designed to estimate intramolecular interactions of nitramines in the condensed phase.

Parameterization of charge model 3 for AM1, PM3, BLYP, and B3LYP.

We have recently developed a new Class IV charge model for calculating partial atomic charges in molecules. The new model, called Charge Model 3 (CM3), was parameterized for calculations on molecules containing H, Li, C, N, O, F, Si, S, P, Cl, and Br by Hartree-Fock theory and by hybrid density functional theory (DFT) based on the modified Perdew-Wang density functional with several basis sets. In the present article we extend CM3 to semiempirical molecular orbital theory, in particular Austin Model 1 (AM1) and Parameterized Model 3 (PM3), and to the popular BLYP and B3LYP DFT and hybrid DFT methods, respectively. For the BLYP extension, we consider the 6-31G(d) basis set, and for the B3LYP extension, we consider three basis sets: 6-31G(d), 6-31+G(d), and MIDI!6D. We begin with the previous CM3 strategy, which involves 34 parameters for 30 pairs of elements. We then refine the model to improve the charges in compounds that contain N and O. This modification, involving two new parameters, leads to improved dipole moments for amides, bifunctional H, C, N, O compounds, aldehydes, ketones, esters, and carboxylic acids; the improvement for compounds not containing N results from obtaining more physical parameters for carbonyl groups when the O=C-N conjugation of amides is addressed in the parameterization. In addition, for the PM3 method, we added an additional parameter to improve dipole moments of compounds that contain bonds between C and N. This additional parameter leads to improved accuracy in the dipole moments of aromatic nitrogen heterocycles with five-membered rings.

Core Ionization Energies, Mean Dipole Moment Derivatives, and Simple Potential Models for B, N, O, F, P, Cl, and Br Atoms in Molecules

Simple potential models relating experimental 1s electron ionization energies for B, N (sp and sp3 hybrids), O, and F atoms; 1s and 2p ionization energies for P atoms; and 2s and 2p ionization energies for Cl atoms as a function of their atomic mean dipole moment derivatives determined from experimental gas phase infrared fundamental band intensities are reported. Potential models using theoretical Koopmans' energies and generalized atomic polar tensor (GAPT) charges are found to form even more precise models than those using experimental data. This is expected because the potential models depend only on the electronic structures of molecules before ionization takes place and do not take into account relaxation effects. If the experimental ionization energies are adjusted by their relaxation energies, models similar to those obtained using Koopmans' energies are determined. The models permit a simple understanding of substituent effects on core ionization energies in terms of atomic charges in molecules. Most of the potential model slopes investigated are shown to be approximately proportional to the inverse atomic radii of the atom being ionized. Core-valence electron repulsion values inferred from the potential models obtained from experimental data are somewhat smaller than those calculated using Slater orbitals of isolated atoms. The potential model intercepts for 1s and 2p electrons are shown to be proportional to the square of the nuclear charge, consistent with their interpretation as core electron ionization energies of neutral atoms. 1s He, Ne, and Ar and 2p Ar, Kr, and Xe core ionization energies obey the linear relationships obtained for the model intercepts. The results suggest that mean dipole moment derivatives obtained from infrared intensities can be interpreted as atomic charges.

Determination of C 1s Core Level Chemical Shifts in Some Langmuir−Blodgett Films Using a Modified Sanderson Formalism

The modified Sanderson (MS) formalism for calculation of partial charge on atoms has been shown to yield extremely good correlation between the atomic partial charge in organic molecules and core level binding energies determined using X-ray photoelectron spectroscopy (XPS). The MS approach is used to determine partial charges on the carbons in Langmuir-Blodgett (LB) films of lead arachidate and chloroplatinic acid−octadecylamine complexes and from the atomic charges, expected C 1s chemical shifts. Fits to the C 1s core level spectra from the different LB films agree within experimental error with those predicted by the MS calculation. Identification of additional C 1s spectral components that arise from carbons directly coordinated to the carboxylate carbon/amine group highlights the importance of induction effects on partial atomic charges in molecules, an aspect hitherto not taken into account in XPS studies of LB films. Inclusion of the additional C 1s component in the core level fits is shown to lead to solution of a long standing problem regarding quantitative analysis based on the C 1s peak intensities. Applicability of the MS approach to such practical problems in XPS together with its simplicity and intuitiveness make this approach particularly attractive for the experimental chemist.

Charge displacement analysis: A new general method to estimate atomic charges in molecules and clusters

A new method, termed CDA, for charge distribution analysis, to estimate net charges of atoms in molecules or clusters is proposed. The method is based on well defined physical quantities and avoids many of the shortcomings of the Mulliken population analysis while keeping the idea that charge or electronic density on atoms is defined through their basis functions. Several examples, including the CH 4 molecule, bulk MnO and chemisorption of O and CN on Cu(100), are presented.