493 research outputs found

    Degree of atomicity in the chemical bonding: Why to return to the H2 molecule?

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    We analyze two-particle binding factors for the case of \ch{H2} molecule with the help of our original Exact Diagonalization \textit{Ab Intio} (EDABI) approach. Explicitly, we redefine the many-particle covalency and ionicity factors as a function of interatomic distance. Insufficiency of those basic characteristics is stressed and the concept of \textit{atomicity} is introduced and corresponds to the Mott and Hubbard criteria concerning the localization in many-particle systems. This additional characteristic introduces atomic ingredient into the essentially molecular states and thus eliminates a spurious behavior of the standard covalency factor with the increasing interatomic distance, as well as provides a physical reinterpretation of the chemical bond's nature

    Toward complementary characterization of the chemical bond

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    A precise discussion of a single bond requires consideration of two-particle wave function for the particles involved. Here we define and determine rigorously the intrinsic covalency and connected characteristics of the canonical example of the H2 molecule. This is achieved by starting from an analytic form for the two-particle wave function for electrons forming the bond, in which we single out the atomic contribution (atomicity) in an unequivocal manner. The presence of the atomicity and ionicity factors complements the existing attributes of the bond. In this way, a gradual evolution of the molecular state to its two-atom correspondent is traced systematically with increasing interatomic distance. In effect, a direct relation to the onset of incipient Mott-Hubbard atomicity (Mottness) to the intrinsic covalency and ionicity is established. This goal is achieved formally by combining the single-particle wave function readjustment in the entangled state with a simultaneous determination of two-particle states in the particle (second quantization) representation

    Many-particle covalency, ionicity, and atomicity revisited for a few simple example molecules

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    We analyze two-particle binding factors of H2H_{2}, LiHLiH, and HEH+HEH^{+} molecules/ions with the help of our original exact diagonalization ab initio approach. The interelectronic correlations are taken into account rigorously within the second quantization scheme for restricted basis of renormalized single-particle wave functions, i.e., with their size readjusted in the correlated state. This allows us to determine the many-particle covalency and ionicity factors in a natural and intuitive manner in terms of the microscopic single-particle and interaction parameters, also determined within our method. We discuss the limitations of those basic characteristics and introduce the concept of atomicity, corresponding to the Mott and Hubbard criterion concerning localization threshold in many-particle systems. This addition introduces an atomic ingredient into the electron states and thus removes a spurious behavior of covalency with the increasing interatomic distance, as well as provides a more complete physical interpretation of bonding

    Symmetry, Structure and the Constitution of Objects

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    In this paper I focus on the impact on structuralism of the quantum treatment of objects in terms of symmetry groups and, in particular, on the question as to how we might eliminate, or better, reconceptualise such objects in structural terms. With regard to the former, both Cassirer and Eddington not only explicitly and famously tied their structuralism to the development of group theory but also drew on the quantum treatment in order to further their structuralist aims and here I sketch the relevant history with an eye on what lessons might be drawn. With regard to the latter, Ladyman has explicitly cited Castellani's work on the group-theoretical constitution of quantum objects and I indicate both how such an approach needs to be understood if it is to mesh with Ladyman's 'ontic' form of structural realism and how it might accommodate permutation symmetry through a consideration of Huggett's recent account
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