Application of various population methods to some oxygenated compounds

The charge on oxygen for a series of compounds was obtained using Mulliken population, natural population analysis (NPA), integrated projected electron population (IPP) analysis, and Bader's topological density analysis, “integrated Bader populations” (IBP). The orbital-based methods (Mulliken and NPA) predict oxygen charges of about –0.6 whereas the spatial-based methods (IPP and IBP) predict charges of about – 1.2 to – 1.3. The differences are ascribed primarily to the nuclear-centered basis sets used in the orbital methods that minimize local atomic polarization effects. Accordingly, such population analyses should be used for electronic structure considerations only with due circumspection. The IPP method as an approximation to IBP shows gross similarities; small but significant differences vary in a nonsystematic manner and IPP values must also be used with care.     

A test of the Hirshfeld definition of atomic charges and moments

Summary The Hirshfeld population analysis scheme which carves the molecular density into atomic density contributions is tested. This method does not require a reference to basis sets or their respective locations, but is based on a different physical and mathematical footing. The advantage of this method is that, when the molecular deformation density converges to the true solution, the computed net charges will necessarily converge. This method also allows a straightforward definition for local moments. About 36 molecules have been used to compute the conventional Mulliken and Löwdin population analyses with STO3G, 6311G** and Dunning-Hay split valence basis sets. These results have been compared to the estimates provided by the Hirshfeld model. The charges found in the Hirshfeld method are smaller than those from the other methods.     

Optimized Atomic Partial Charges and Radii Defined by Radical Voronoi Tessellation of Bulk Phase Simulations

We present a novel method for the computation of well-defined optimized atomic partial charges and radii from the total electron density. Our method is based on a two-step radical Voronoi tessellation of the (possibly periodic) system and subsequent integration of the total electron density within each Voronoi cell. First, the total electron density is partitioned into the contributions of each molecule, and subsequently the electron density within each molecule is assigned to the individual atoms using a second set of atomic radii for the radical Voronoi tessellation. The radii are optimized on-the-fly to minimize the fluctuation (variance) of molecular and atomic charges. Therefore, our method is completely free of empirical parameters. As a by-product, two sets of optimized atomic radii are produced in each run, which take into account many specific properties of the system investigated. The application of an on-the-fly interpolation scheme reduces discretization noise in the Voronoi integration. The approach is particularly well suited for the calculation of partial charges in periodic bulk phase systems. We apply the method to five exemplary liquid phase simulations and show how the optimized charges can help to understand the interactions in the systems. Well-known effects such as reduced ion charges below unity in ionic liquid systems are correctly predicted without any tuning, empiricism, or rescaling. We show that the basis set dependence of our method is very small. Only the total electron density is evaluated, and thus, the approach can be combined with any electronic structure method that provides volumetric total electron densities—it is not limited to Hartree–Fock or density functional theory (DFT). We have implemented the method into our open-source software tool TRAVIS.     

A quantitative analysis of light‐driven charge transfer processes using voronoi partitioning of time dependent DFT‐derived electron densities

An analytical method is presented that provides quantitative insight into light‐driven electron density rearrangement using the output of standard time‐dependent density functional theory (TD‐DFT) computations on molecular compounds. Using final and initial electron densities for photochemical processes, the subtraction of summed electron density in each atom‐centered Voronoi polyhedron yields the electronic charge difference, Q ^VECD. This subtractive method can also be used with Bader, Mulliken and Hirshfeld charges. A validation study shows Q ^VECD to have the most consistent performance across basis sets and good conservation of charge between electronic states. Besides vertical transitions, relaxation processes can be investigated as well. Significant electron transfer is computed for isomerization on the excited state energy surface of azobenzene. A number of linear anilinepyridinium donor‐bridge‐acceptor chromophores was examined using Q ^VECD to unravel the influence of its pi‐conjugated bridge on charge separation. Finally, the usefulness of the presented method as a tool in optimizing charge transfer is shown for a homologous series of organometallic pigments. The presented work allows facile calculation of a novel, relevant quantity describing charge transfer processes at the atomic level. © 2017 The Authors Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

DNA碱基的电子相关效应

分别在Hartree-Fock和二级Moller-Plesset微扰理论MP2的电子相关校正水平, 用6-31G^*^*基函数对四种DNA碱基胞嘧啶、胸腺嘧啶、鸟嘌呤和腺嘌呤的能量、偶极矩、电荷分布和分子静电势等性质进行了系统的从头计算研究。其中, 采用Z矢量方法在波函数中加入MP2级别的电子相关校正; 分别用Mulliken布居分析、静电势导出电荷CHELPG以及自然布居分析NPA方法计算分子中原子电荷。在上述计算结果的基础上, 系统地分析了DNA碱基的电子相关效应。     

原子电荷计算方法的对比

原子电荷是对化学体系中电荷分布最简单、最直观的描述形式之一,在理论和实际应用中都有重要意义.本文介绍了12种重要的原子电荷计算方法的原理和特点,通过大量实例从不同角度比较了它们的优缺点.这些方法包括Mulliken、分子环境中的原子轨道(AOIM)、Hirshfeld、原子偶极矩校正的Hirshfeld布居(ADCH)、自然布居分析(NPA)、Merz-Kollmann(MK)、分子中的原子(AIM)、Merck分子力场94(MMFF94)、AM1-BCC、Gasteiger、电荷模型2(CM2)以及电荷均衡(QEq)方法.最后本文对如何在实际应用中选择合适的计算方法给出了建议.     

Atomic properties of N(2)O(4) based on its experimental charge density

Nitrogen dioxide, being known to exist as a dimer N2O4 in the crystal with a very long N-N bond length of 1.76 A, was crystallized at low-temperature conditions on a diffractometer. High-resolution X-ray data (sin(theta/lambda) = 1.249 A-1) were recorded with a CCD area detector to allow the generation of an experimental charge density distribution. By making use of Bader's AIM theory, zero-flux surfaces were calculated, and we examined atomic volumes and atomic charges obtained from this experiment and various theoretical calculations. Four commonly used methods of computing atomic charges (Mulliken, AIM, NPA, and CHELP) were considered. The AIM charges are rather independent from the used basis set. Interestingly, the evaluated atomic volumes are very similar between experiment and theory, although in theory isolated molecules are considered. For the long N-N bond a bond order n of approximately 0.5 was derived from a comparison with appropriate model compounds.     

Comparison of atomic charges derived via different procedures

Atomic charges were obtained from ab initio molecular orbital calculations using a variety of procedures to compare them and assess their utility. Two procedures based on the molecular orbitals were examined, the Mulliken population analysis and the Weinhold–Reed Natural Population Analysis. Two procedures using the charge density distribution were included; the Hirshfeld procedure and Bader's Atoms in Molecules method. Charges also were derived by fitting the electrostatic potential (CHELPG) and making use of the atomic polar tensors (GAPT). The procedures were first examined for basis set independence, and then applied to a group of hydrocarbons. The dipole moments for these molecules were computed from the various atomic charges and compared to the total SCF dipole moments. This was followed by an examination of a series of substituted methanes, simple hydrides, and a group of typical organic compounds such as carbonyl derivatives, nitriles, and nitro compounds. In some cases, the ability of the charges to reproduce electrostatic potentials was examined. © John Wiley & Sons, Inc.     

Communication: Hilbert-space partitioning of the molecular one-electron density matrix with orthogonal projectors

A double-atom partitioning of the molecular one-electron density matrix is used to describe atoms and bonds. All calculations are performed in Hilbert space. The concept of atomic weight functions (familiar from Hirshfeld analysis of the electron density) is extended to atomic weight matrices. These are constructed to be orthogonal projection operators on atomic subspaces, which has significant advantages in the interpretation of the bond contributions. In close analogy to the iterative Hirshfeld procedure, self-consistency is built in at the level of atomic charges and occupancies. The method is applied to a test set of about 67 molecules, representing various types of chemical binding. A close correlation is observed between the atomic charges and the Hirshfeld-I atomic charges.     

Generalized charge sensitivity analysis

Charge sensitivity analysis was originally introduced in the trivial-atom resolution. Here, we extend this resolution into force-field atoms. The AMBERff99 force-field resolution was employed. The effective electronegativities and hardnesses were derived for five different population analyses (Mulliken, Hirschfeld, AIM, NPA and Voronoi charges) by applying evolutionary algorithms.     

Atomic charges,dipole moments,and Fukui functions using the Hirshfeld partitioning of the electron density

In the Hirshfeld partitioning of the electron density, the molecular electron density is decomposed in atomic contributions, proportional to the weight of the isolated atom density in the promolecule density, constructed by superimposing the isolated atom electron densities placed on the positions the atoms have in the molecule. A maximal conservation of the information of the isolated atoms in the atoms-in-molecules is thereby secured. Atomic charges, atomic dipole moments, and Fukui functions resulting from the Hirshfeld partitioning of the electron density are computed for a large series of molecules. In a representative set of organic and hypervalent molecules, they are compared with other commonly used population analysis methods. The expected bond polarities are recovered, but the charges are much smaller compared to other methods. Condensed Fukui functions for a large number of molecules, undergoing an electrophilic or a nucleophilic attack, are computed and compared with the HOMO and LUMO densities, integrated over the Hirshfeld atoms in molecules.     

Comment on “Extending Hirshfeld‐I to bulk and periodic materials”

In recent years, several methods have been developed that partition the electron density among atoms using spherically symmetric atomic weights. D. E. P. Vanpoucke, P. Bultinck, and I. Van Driessche (J. Comput. Chem. 2012, doi: 10.1002/jcc.23088) recently reported a periodic implementation of the Hirshfeld‐I method that uses a combination of Becke‐style and uniform integration grids and modified atomic reference densities to compute net atomic charges in periodic materials. Herein, this method is discussed in the context of earlier periodic implementations of the Hirshfeld‐I method, the Iterated Stockholder Atoms method, and the density derived electrostatic and chemical method.     

Quantum chemical study of self-doping PPV oligomers: spin distribution of the radical forms

The variational procedure of the Hartree–Fock and Kohn–Sham methods can be modified by adding one or more constraints that fix the number of electrons in a given number of molecular fragments. The corresponding Euler–Lagrange equations lead to a modified Fock matrix, where the contribution from the constraints only depends on the overlap matrix, when using the Mulliken or Hirshfeld atoms-in-molecules method. For all compounds in the test set, the energy shows a quadratic dependence on the fixed charges. This behavior provides a procedure to obtain the atomic electronegativity and hardness parameters in the electronegativity equalization method.     

Theoretical Study of Electron Transfer in Bimolecular System of NH3 and H2O

1 INTRODUCTION Electron transfer is one of the most important reactions in chemistry. This fundamental reaction plays a crucial role in a myriad of processes including acid-base neutralization, electrophilic addition, and a score of enzymatic reactions. Ab initio molecular orbital methods are capable of providing information that can complement experimental data and circumvent solvent effects. The bimolecular system of NH_3 and H_2O has been extensively studied. Kollman et al.[1] report…     

What is the "best" atomic charge model to describe through-space charge-transfer excitations?

We investigate the efficiency of several partial atomic charge models (Mulliken, Hirshfeld, Bader, Natural, Merz-Kollman and ChelpG) for investigating the through-space charge-transfer in push-pull organic compounds with Time-Dependent Density Functional Theory approaches. The results of these models are compared to benchmark values obtained by determining the difference of total densities between the ground and excited states. Both model push-pull oligomers and two classes of "real-life" organic dyes (indoline and diketopyrrolopyrrole) used as sensitisers in solar cell applications have been considered. Though the difference of dipole moments between the ground and excited states is reproduced by most approaches, no atomic charge model is fully satisfactory for reproducing the distance and amount of charge transferred that are provided by the density picture. Overall, the partitioning schemes fitting the electrostatic potential (e.g. Merz-Kollman) stand as the most consistent compromises in the framework of simulating through-space charge-transfer, whereas the other models tend to yield qualitatively inconsistent values.     

取代苯甲酸羧基上H和O原子的部分电荷与Hammett常数之间的线性关系

采用密度泛函分析了取代苯甲酸中羧基上的H1原子和2个氧原子O2和O3的电荷与取代基的Hammett常数之间的线性关系. 比较了不同密度泛函和电荷计算方法B3LYP/6-311G*/(NBO, Mulliken), (BLYP, BP, PWC)/DNP/(Hirshfeld, Mulliken)对上述线性相关系数的影响. 结果表明, BLYP/DNP/Hirshfeld方法的计算精度高且计算速度快. 使用BLYP/DNP/Hirshfeld方法计算了70个取代苯甲酸的部分电荷, 发现H1, O2和O3原子的电荷与取代基Hammett常数σ_p和σ_m之间的线性相关系数可达到0.98以上, 其中O2的电荷和Hammett常数的线性相关性最好. O2的电荷值可以作为Hammett常数的替代, 用于结构性能定量分析, 也可以用于预测取代基的Hammett常数.     

Electron density distribution in molecules of 4-aryl-substituted [2.2]paracyclophanes and regioselectivity of their complexation with Cr(CO)3

Charges on carbon atoms in the molecules of 4-aryl-substituted [2.2]paracyclophanes were estimated and the role of charge control as a kinetic factor in regioselectivity of their complexation with (NH₃)₃Cr(CO)₃ was investigated using electron density distribution analysis by the Bader, Weinhold-Reed (NPA), and Mulliken methods. The most plausible picture of the electron density distribution in substituted [2.2]paracyclophanes was obtained by the Bader method and compared with experimental data on the yields of reaction products. Topological analysis of the electron density distribution in the [2.2]paracyclophane molecule by the Bader method confirmed the existence of a weak antibonding interaction between the stacked benzene rings. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 3, pp. 441–444, March, 1999.     

Electrostatic and covalent contributions in the coordination bonds of transition metal complexes

To develop a molecular mechanics force field for modeling complexes of transition metals and organic ligands, the electrostatic and covalent contributions in the coordination bonds were investigated using quantum mechanical density functional theory and model complexes of glyoxal diimine and the 2+ cations of the first row transition metals. The VDD and Hirshfeld charges are found to be closely correlated with the extent of the electron transfer between the ligands and the cations. Assuming the electrostatic contribution can be represented by the atomic partial charges, the covalent contributions in the coordination bonds are estimated to be in a range of 54-92% for the systems calculated. A simple force field was parametrized to validate the partial charge representation.     

Charge distribution in the water molecule--a comparison of methods

The charge distribution in the water molecule has been analyzed using a broad variety of basis sets, four different quantum mechanical methods (Hartree-Fock, Becke3LYP, MP2, and QCISD), and six population analysis methods (Mulliken, NPA, AIM, CHELPG, Merz-Kollman, and Resp). The influence of the molecular structure on the calculated atomic charges has been studied using small perturbations of the experimentally determined structure.