Integrated topological properties

The above argument stresses the importance of adapting the Koch-Popelier criteria [40] in experimental studies, since they include not only local but also integrated topological properties to characterize HBs. New density-based... 

Therefore, selected spectroscopic and microscopic techniques are applied to the characterization of chemical structure formation and morphology in thin polyurethane (PU) layers on Au, Al, and Cu Infrared spectroscopy offers convenient access to the integral chemical properties of thin-fihn and bulk-like polymer samples, while optical (OM) and scanning force microscopy (SFM) allow detailed insights into homogeneity and topology. 

Fomenko, A. T., and Zieschang, H. On typical topological properties of integrable Hamiltonian systems. Izvestiya Akad. Nauk SSSR (1987) (in print). 

In this arena, energetic properties are usually derived by integrating densities over real space domains, and not by examining appropriate scalar or vector fields. Exceptions to this rule exist the localized orbital locator (LOL) focuses on the topological properties of a kinetic energy density [34], and the QTAIM virial (t ) and energy density (J ) fields are commonly examined at critical points (CPs) of the density. The latter are however computed from the density and its derivatives through the QTAIM s local virial theorem [1], that depends on an arbitrary choice of the kinetic stress tensor [9]. 

Many of the rigorous definitions of atomic and bond properties that are described in this article invoke the concepts of the quantum-mechanical theory of atoms in molecules (AIMs) (see Atoms in Molecules). The AIMs consist of nuclei and disjoint portions of Cartesian space called atomic basins. Direct integration of property densities over those basins yields the first-order properties of AIMs, whereas the calculations of the second-order properties and quantities such as atomic electronegativities and similarities are somewhat more involved. Topological analysis of the electron density p r) that accompanies the construction of AIMs yields a wealth of other information, including the location of major interactions within molecules. ... 

An alternative method that can be used to characterize the topology of PES is the line integral technique developed by Baer [53,54], which uses properties of the non-adiabatic coupling between states to identify and locate different types of intersections. The method has been applied to study the complex PES topologies in a number of small molecules such as H3 [55,56] and C2H [57]. 

Correspondingly, the values of nF characterize the connectivity of the lattice of particles or skeleton of a PS and the values of Zc characterize the interconnectivity of the lattice of pores of the same PS. Connectivity of PS is the major topological attribute, which in the general case does not depend on the shape and size of the PS s individual supramolecular elements, although the latter characterize the major geometrical properties of PS [8], Appropriately, the classification of PSs by the degree of interconnectivity with allocation of various types of integrity is possible. 

Fortunately, over the past several years, the problems associated with each of the above requirements have been overcome and now integrated opto-chips are now relatively routinely fabricated [2, 3, 5, 63, 64, 271-278, 290-297]. The problem of irregular VLSI surface topology has been overcome by use of planarizing polymers such as Futerrex PC3-6000. The reflow properties of this polymer reduce the 1-6 micron semiconductor circuit features to surface variations of 0.2 microns after planarization. The optical quality of planarized surfac-... 

The inherent valne of the topological method is that these atomic basins are defined by the electron density distribution of the molecule. No arbitrary assumptions are required. The atomic basins are quantum mechanically well-defined spaces, individnally satisfying the virial theorem. Properties of an atom defined by its atomic basin can be obtained by integration of the appropriate operator within the atomic basin. The molecular property is then simply the sum of the atomic properties. 

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