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To assess the results obtained for the Voronoi Deformation Density charge method, let us briefly reconsider the definitions of atomic charges used in this and other work

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

JOURNAL OF COMPUTATIONAL CHEMISTRY, no. 2 (2004): 189-210

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摘要

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 comp...更多

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简介
  • One of the most generally used concepts in chemistry is the atomic charge, which has the following intuitive meaning: when two noninteracting atoms A and B (1) form a chemical bond (2), the atomic charge of A resulting from the formation of the chemical bond is the amount of electronic density gained from (2a) or lost to (2b) atom B (Scheme 1).
  • Most molecules are not ideal cases and chemists[1,2,3,4,5,6,7,8] have tried to develop over the years methods to quantify the atomic charge.
  • In this article the authors address the problem of assigning a value to the atomic charge, and the authors judge various methods for doing so in the light of the usefulness of the resulting atomic charges for the characterization of the nature of the chemical bond
重点内容
  • One of the most generally used concepts in chemistry is the atomic charge, which has the following intuitive meaning: when two noninteracting atoms A and B (1) form a chemical bond (2), the atomic charge of A resulting from the formation of the chemical bond is the amount of electronic density gained from (2a) or lost to (2b) atom B (Scheme 1)
  • The amount of electronic charge density flowing from one compartment of space to the other is defined as the Voronoi Deformation Density (VDD) atomic charge
  • To assess the results obtained for the VDD charge method, let us briefly reconsider the definitions of atomic charges used in this and other work
  • We divide the methods into two major groups: methods based on representation of the molecular wave function with the help of basis functions and methods based on the electron density as a function in space
  • The Mulliken charges[1] and its improvements[2,3] are based on the wave function representation with basis functions and inevitably suffer from the problems of: the spatial extent of the basis functions—they are usually centered on a nucleus but will extend over other atomic domains; and the existence of overlap terms, which have to be partitioned over the atoms
  • When the overlap populations become large, which is the case in large basis sets with diffuse basis functions, the half-half partitioning of the Mulliken population analysis[1] yields totally unphysical charges, which do not properly converge with increasing basis set size
方法
  • VDD Scheme for Calculating Atomic Charges

    To which nucleus do the electrons go when a chemical bond is formed? In general, atomic charge schemes tackle this question by computing the amount of charge contained in an atomic volume.
  • A natural and objective way to answer this question is to stand half-way between two atoms, and, when the chemical interaction is turned on, measure the amount of electronic density that crosses the bond midplane.
  • This means that the space is divided by the bond midplane into two equal parts.
  • This definition of atomic charge is conceptually very simple and at the same time objective in the sense that it is unambiguous, i.e., not dependent on atomic properties with some degree of empiricism or arbitrariness
结果
  • Results and Discussion

    the authors present the atomic charges for the four different methods (Mulliken, Hirshfeld, VDD, and Bader) and subject the computed values to a thorough analysis.
  • The authors' main goal is to evaluate if the charge values in this large variety of molecular systems are well defined and chemically meaningful.
  • “Chemical intuition” denotes expectations based on a large body of experimental data, which are summarized in, for instance, the electronegativities of the atoms.
  • For each molecular system or set of systems, these two criteria are tested, and the authors carefully consider the values of the atomic charges and judge the chemical applicability of the four charge methods
结论
  • Concluding Remarks

    To assess the results obtained for the VDD charge method, let them briefly reconsider the definitions of atomic charges used in this and other work.
  • When the overlap populations become large, which is the case in large basis sets with diffuse basis functions, the half-half partitioning of the Mulliken population analysis[1] yields totally unphysical charges, which do not properly converge with increasing basis set size
  • Attempts to circumvent this problem have not given the desired results.[2,3] The NPA charges[3] employ explicitly orthogonalized atomic orbitals, and solve the overlap population problem.
  • The use of basis set dependent methods as a tool to analyze the atomic charges is questionable
表格
  • Table1: Basis Set Dependence of Atomic Charges (in a.u.) for CH4, CH3Li, and HCN
  • Table2: Atomic Charges (in a.u.) for Fluorine and Chlorine Substituted Methanes, CH3X, CH2X2, CHX3, and CX4. We focus on the atomic charges for the carbon atom in the fluorine substituted methanes. In the order CH4, CH3F, CH2F2, CHF3, and CF4, the Bader carbon charges are 0.081, 0.639, 1.221, 1.844, and 2.511 a.u. and the NPA carbon charges are Ϫ0.880, Ϫ0.095, 0.562, 1.120, and 1.620 a.u. Both methods show the correct trend, however, the absolute values are too large, which makes them both not suitable for interpretation of the nature of the chemical bond. Chemists do not classify the bond between carbon and fluorine as ionic, whereas the Bader method gives an increase of the atomic charge on carbon from ϩ0.081 in CH4 to ϩ0.639 a.u. in CH3F. With each additional F substitution a similar increase of the carbon charge with about ϩ0.6 a.u. occurs. The NPA method also tends to give a too ionic view of the bonds. From a carbon charge of Ϫ0.880 a.u. calculated with NPA for CH4 (which, as mentioned earlier, suggests an extremely ionic COH bond), it apparently has the COF bond too ionic because the total carbon charge drops very much in CH3F, to Ϫ0.095 a.u. Subsequent F substitutions give, each time, an increase of the carbon charge by some ϩ0.5 to ϩ0.6 a.u. The NPA method has reduced the basis set dependency of the Mulliken
  • Table3: Atomic Charges (in a.u.) of A and dipole moments ␮ (in D) for Diatomics AB
  • Table4: Charges (in a.u.) of the Metal Atoms in Metalhydrides and Metalfluorides
  • Table5: Charges (in a.u.) of the Noble Gas Atoms in XHϩ
  • Table6: Methyl Group Charges (in a.u.) for Methyl Derivatives
  • Table7: Comparison of Various Charge Analysis Methods: Atomic Charges (in a.u.) for H2O, CH2O, and NH3
  • Table8: Atomic Charges (in a.u.) of Methane, Methyllithium, and Ni(CO)[<a class="ref-link" id="c4" href="#r4">4</a>] with the Promolecule Calculated with Restricted Spherical Ground-State Atoms at the X␣VWN/TZ2P and BP86/TZ2P Level and with Valence State Atoms at the X␣VWN/TZ2P and BP86/TZ2P Level.a
  • Table9: Atomic Charges (in a.u.) for the Transition Metal Complexes Cr(CO)[<a class="ref-link" id="c6" href="#r6">6</a>] and Fe(CO)5.a
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引用论文
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