Comparison of direct and flow integration based charge density population analyses

Different exhaustive and fuzzy partitions of the molecular electron density (rho) into atomic densities (rho(A)) are used to compute the atomic charges (Q(A)) of a representative set of molecules. The Q(A)'s derived from a direct integration of rho(A) are compared to those obtained from integrating the deformation density rho(def) = rho - rho(0) within each atomic domain. Our analysis shows that the latter methods tend to give Q(A)'s similar to those of the (arbitrary) reference atomic densities rho(A)(0) used in the definition of the promolecular density, rho(0) = SigmaArho(A)(0). Moreover, we show that the basis set independence of these charges is a sign not of their intrinsic quality, as commonly stated, but of the practical insensitivity on the basis set of the atomic domains that are employed in this type of methods.     

Generalized electron number distribution functions: real space versus orbital space descriptions

The algebraic expressions previously derived to compute the electron number distribution functions (EDF) for exhaustive partitions of the physical space into sharp-boundary atoms are generalized to allow for the use of fuzzy atoms and orbital-based partitions. In some of the latter, the atomic overlap matrix required to obtain the EDF is analytical. This makes them attractive alternatives to other definitions, as the one based on the atomic basins of the quantum theory of atoms in molecules (QTAIM), which are more physically sound but also much more demanding computationally. We will compute the EDF for a series of test molecules using different fuzzy and orbital-based partitions and compare them to QTAIM EDF. The effects of electron correlation and the use of the core approximation on the EDF will also be explored.     

Building molecular charge distributions from fragments: Application to HIV-1 protease inhibitors

Interaction energies are a function of the molecular charge distribution. In previous work, we found that the set of atomic partial charges giving the best agreement with experimental vacuum dipole moments were from density functional theory calculations using an extended basis set. Extension of such computations to larger molecules requires an atomic partial charge calculation beyond present computational resources. A solution to this problem is the calculation of atomic partial charges for segments of the molecule and reassociation of such fragments to yield partial charges for the entire molecule. Various partitions and reassociation methods for five molecules relevant to HIV-1 protease inhibitors are examined. A useful method of reassociation is introduced in which atomic partial charges for a large molecule are computed by fitting to the combined electrostatic potential calculated from the fragment partial charges. As expected, the best sites for partitions are shown to be carbon—carbon rather than carbon—nitrogen bonds. © 1997 by John Wiley & Sons, Inc.     

Experimental and theoretical charge density distribution of the colossal magnetoresistive transition metal sulfide FeCr2S4

The total charge density distribution rho(r) of the colossal magnetoresistive transition metal sulfide FeCr(2)S(4) was evaluated through a multipole formalism from a set of structure factors obtained both experimentally, by means of single crystal high-quality x-ray diffraction data collected at T=23 K, and theoretically, with an extended-basis unrestricted Hartree-Fock periodic calculation on the experimental geometry. A full topological analysis, followed by the calculation of local energy density values and net atomic charges, was performed using the quantum theory of atoms in molecules. The experimental and theoretical results were compared. Good agreement was found for the topological properties of the system, as well as for the atomic net charges and the nature of the chemical bonds. An analysis of the electron density rho(r), its Laplacian nabla(2)[rho(r)], and the total energy density H(r) at the bond critical points was employed to classify all the interactions that resulted as predominantly closed shell (ionic) in nature. The topological indicators of the bonded interactions for Fe are distinct from those for Cr. The Fe-S bond distances were found to be 0.145 A shorter than the ideal values computed on the basis of Shannon's crystal radii, much shorter than the Cr-S distances with respect to their ideal Shannon lengths. Concomitantly, rho(r) and |H(r)| at the bond critical points are greater for Fe-S interactions, indicating that the local concentration of charge density in the internuclear region is larger for the tetrahedrally coordinated iron than for the octahedrally coordinated chromium. The isosurface in the real space for nabla(2)[rho(r)]=0 was plotted for both iron and chromium, pointing out the local zones of valence shell charge concentration and relating them to the partial d-orbital occupancy of the two transition metal atoms.     

Theory of intermolecular interactions: The long range terms in the dipole–dipole,monopoles–dipole,and monopoles–bond polarizabilities approximations

The problem of evaluating the long range terms (electrostatic, polarization, dispersion) of the interaction energy between molecules at intermediate distances (i.e. distances of the order of magnitude of the molecular dimensions) is considered. Instead of being approximated by its dipole part, the exact interaction Hamiltonian is treated as proposed by Longuet-Higgins [11], i.e. the matrix elements are interpreted as electrostatic interactions between state and transition charge distributions. These charge distributions are approximated in a systematic way by sets of point charges (localized on the atoms) or sets of dipoles (localized on the bonds). The various contributions to the energy may then be expressed in terms of atomic net charges and bond polarizabilities. More refined approximations of the charge distributions could be used and correspondingly improved formulae could be derived: as an example, a formula for the σ-π dispersion energy is derived, where the σ charge distributions are approximated by bond transition dipoles (leading to σ bond polarizabilities in the final formula) while the π charge distributions are approximated by atomic charges.     

Atoms-in-molecules in momentum space: a Hirshfeld partitioning of electron momentum densities

A direct application of the Hirshfeld atomic partitioning (HAP) scheme is implemented for molecular electron momentum densities (EMDs). The momentum density contributions of individual atoms in diverse molecular systems are analyzed along with their topographical features and the kinetic energies of the atomic partitions. The proposed p-space HAP-based charge scheme does seem to possess the desirable attributes expected of any atoms in molecules partitioning. In addition to this, the main strength of the p-space HAP is the exact knowledge of the kinetic energy functional and the inherent ease in computing the kinetic energy. The charges derived from HAP in momentum space are found to match chemical intuition and the generally known chemical characteristics such as electronegativity, etc.     

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.     

Fractionally charged ions in crystal lattices of organic ion-radical salts

The energy of an atom in a molecule is discussed on the basis of the definition of the chemical potential of electrons in a quantum system. An expression for the energy of the fractionally charged atom is proposed, and a master equation for the charge-dependent cohesive energy of a crystal is developed. Calculated net atomic charges in solid alkali halides are close to unity and their calculated cohesive energies indicate few percent of covalent bonding. The charge transfer at the energy minimum calculated for several organic, conducting ion-radical salts agree perfectly with the values determined experimentally. The lattice is found to be stabilized by the charge transfer, although the ionic interactions reproduce only part of the crystal cohesive energy.     

A density functional theory study on boundary of “superreduced” transition metal carbonyl anions [M(CO)n] (M=Cr, n=5, 4, 3, z=2, 4, 6; M=Mn, n=5, 4, 3, z=1, 3, 5; M=Fe, n=4, 3, 2, z=2, 4, 6; M=Co, n=4, 3, 2, z=1, 3, 5)

A nonlocal density functional theory (DFT) method has been applied to the calculations on optimized geometry, Mulliken atomic net charges and interatomic Mulliken bond orders as well as total bonding energies (E) in the binary transition metal carbonyl anions with different reduced states [M(CO)_n]^z− (M=Cr, n=5, 4, 3, z=2, 4, 6; M=Mn, n=5, 4, 3, z=1, 3, 5; M=Fe, n=4, 3, 2, z=2, 4, 6; M=Co, n=4, 3, 2, z=1, 3, 5). For comparison of relative stability, a relative stabilization energy D is defined as D=E([M(CO)_n]^z− )-nE(CO). The calculated C-O distances are lengthened monotonously with the increase of the anionic charge, but the M-C distances are significantly lengthened only in the higher reduced states. The relative stabilization energy calculated is a considerable negative value in the lower reduced states, but a larger positive value in the higher reduced states. The DFT calculations show that with the increase of the anionic charge, the Mulliken net charges on the M, C, and O atoms all increase, however, an excess of the anionic charge is mainly located at the central metal atom. The calculated C-O Mulliken bond orders decrease consistently with the increase of the anionic charge, but the M-C bond orders exhibit an irregular behavior. However, the total bond orders calculated clearly explain the higher reduced states to be considerably unstable. From analysis of the calculated results, it is deduced that the stability of the binary transition metal carbonyl anions [M(CO)_n]^z− studied are associated with the coordination number n and the anionic charge z, further, it is possible for the anions studied to be stable if n≥z, conversely, it is impossible when n<z.     

Experimental electron density distribution of dopamine hydrochloride

Careful high-resolution x-ray diffraction measurements at 90 K have been used to map the electron density distribution in a single crystal of dopamine hydrochloride, a neurotransmitter. A least-squares refinement procedure has been used in which multipole parameters are added to describe the distortions of the atomic electron distributions from spherical symmetry. The refinement also yields improved estimates of the x-ray phases, which have been used to plot maps of the electron distribution. The most electron-rich areas of the molecule are the hydroxyl groups that show large buildups of electron density at the position of the nonbonded lone pairs. The sum of the net atomic charges for the ammonium group is +0.2(2). The net atomic charge for the chloride ion is –0.1(1).     

Oxidation states, atomic charges and orbital populations in transition metal complexes

The differences and similarities between calculated atomic charge and formal oxidation state in transition metal complexes are discussed in the light of density functional theory calculations on a variety of four-coordinate complexes. It is shown that the oxidation state formalism provides a framework for the classification of families of compounds related by ligand substitution or redox processes, and can neither be replaced by nor deduced from net atomic charges.     

Pauling resonant structures in real space through electron number probability distributions

A general hierarchy of the coarsed-grained electron probability distributions induced by exhaustive partitions of the physical space is presented. It is argued that when the space is partitioned into atomic regions the consideration of these distributions may provide a first step toward an orbital invariant treatment of resonant structures. We also show that, in this case, the total molecular energy and its components may be partitioned into structure contributions, providing a fruitful extension of the recently developed interacting quantum atoms approach (J. Chem. Theory Comput. 2005, 1, 1096). The above ideas are explored in the hydrogen molecule, where a complete statistical and energetic decomposition into covalent and ionic terms is presented.     

Continuum treatment of electronic polarization effect

A continuum treatment of electronic polarization has been explored for in molecular mechanics simulations in implicit solvents. The dielectric constant for molecule interior is the only parameter in the continuum polarizable model. A value of 4 is found to yield optimal agreement with high-level ab initio quantum mechanical calculations for the tested molecular systems. Interestingly, its performance is not sensitive to the definition of molecular volume, in which the continuum electronic polarization is defined. In this model, quantum mechanical electrostatic field in different dielectric environments from vacuum, low-dielectric organic solvent, and water can be used simultaneously in atomic charge fitting to achieve consistent treatment of electrostatic interactions. The tests show that a single set of atomic charges can be used consistently in different dielectric environments and different molecular conformations, and the atomic charges transfer well from training monomers to tested dimers. The preliminary study gives us the hope of developing a continuum polarizable force field for more consistent simulations of proteins and nucleic acids in implicit solvents.     

A comparative study of some lithium and hydrogen‐bonded complexes: Ab initio and QTAIM studies

The nature of the interactions of cyanide with lithium and hydrogen halides was investigated using ab initio calculations and topological analysis of electron density. The computed properties of the lithium‐bonded complexes RCN···LiX (R = H, F, Cl, Br, C?CH, CH?CH₂, CH₃, C₂H₅; X = Cl, Br) were compared with those of corresponding hydrogen‐bonded complexes RCN···HX. The results show that both types of intermolecular interactions are “closed‐shell” noncovalent interactions. The effect of substitution on the interaction energy and electron density at the bond critical points of the lithium and hydrogen bonding interactions is similar. In comparison, the interaction energies of lithium‐bonded complexes are more negative than those of hydrogen‐bonded counterparts. The electrostatic interaction plays a more important role in the lithium bond than in the hydrogen bond. On complex formation, the net charge and energy of the Li atom decrease and the atomic volume increases, while the net charge and energy of the H atom increase and the atomic volume decreases. © 2013 Wiley Periodicals, Inc.     

Voronoi deformation density (VDD) charges: Assessment of the Mulliken, Bader, Hirshfeld, Weinhold, and VDD methods for charge analysis

We present the Voronoi Deformation Density (VDD) method for computing atomic charges. The VDD method does not explicitly use the basis functions but calculates the amount of electronic density that flows to or from a certain atom due to bond formation by spatial integration of the deformation density over the atomic Voronoi cell. We compare our method to the well-known Mulliken, Hirshfeld, Bader, and Weinhold [Natural Population Analysis (NPA)] charges for a variety of biological, organic, and inorganic molecules. The Mulliken charges are (again) shown to be useless due to heavy basis set dependency, and the Bader charges (and often also the NPA charges) are not realistic, yielding too extreme values that suggest much ionic character even in the case of covalent bonds. The Hirshfeld and VDD charges, which prove to be numerically very similar, are to be recommended because they yield chemically meaningful charges. We stress the need to use spatial integration over an atomic domain to get rid of basis set dependency, and the need to integrate the deformation density in order to obtain a realistic picture of the charge rearrangement upon bonding. An asset of the VDD charges is the transparency of the approach owing to the simple geometric partitioning of space. The deformation density based charges prove to conform to chemical experience.     

计算分子中原子净电荷的新方法及芳烃亲电取代反应定位效应的定量处理

本文提出一种简捷计算分子中原子净电荷的新方法。用这种方法计算了２３种一元取代苯的原子净电荷。计算所得苯环上碳原子净电荷与其￣（１３）Ｃ－ＮＭＲ化学位移有良好的线性关系。利用苯环上碳原子净电荷及立体参数作为输入参数，应用人工神经网络方法预报２４种一元取代苯硝化反应的邻、间、对位产物产率，结果良好。