Density LOGIC method

LOGIC Method The local-to-global-information-construction (LOGIC) method [32] has been applied to the estimation of the density of alkanes at 25°C. In this method the groups are atom-centered substructures, FRELB (fragment reduced to an... 

Application of the LOGIC method is demonstrated in Figure 3.4.1 with 3,8-diethyldecane. The estimated density is 0.7740gem-3. Experimental values of 0.7770 and 0.7340gem-3 are known at 20 and 80°C, respectively [34], Interpolation yields a value of 0.7732gem-3 at 25°C, which compares favorably with the estimated value. 

As discussed in the introduction, a major motivation for the development of methods to controllably functionalize silicon surfaces is the opportunity to create novel hybrid organic/silicon devices. By integrating organic molecules with silicon substrates it should be possible to expand the functionality of conventional microelectronic devices. Possibilities include high-density molecular memory and logic as well as chemical and biochemical sensors. Realization of these opportunities requires not only the development of the attachment chemistries, as discussed in the previous sections, but also detailed studies of the electronic properties of the resulting surfaces. 

Several approximations that allow simple estimates of bond parameters are presented as a demonstration that predictions based on quantum potentials are of correct order, and not as an alternative to well-established methods of quantum chemistry. In the same spirit it is demonstrated that the fundamental thermodynamic definition of chemical equilibrium can be derived directly from known quantum potentials. The main advantage of the quantum potential route is that it offers a logical scheme in terms of which to understand the physics of chemical binding. It is only with respect to electron-density distributions in bonds that its predictions deviate from conventional interpretations in a way that can be tested experimentally. 

For the more restrictive CSF expansion spaces, such as PPMC and RCI expansions, it occurs that entire transition density vectors will vanish for particular combinations of orbital indices. It is most convenient if a logical flag is set during the construction of the three vectors, one flag for each vector, to indicate that it contains non-zero elements. This avoids the eflbrt required to check each element individually for these zero vectors. The updates of the elements of the matrix C that result from a particular transition density vector involve two DO loops one over the CSF index, which determines the second subscript of the matrix C, and the other over an orbital index, which, combined with a density matrix orbital index, is used to determine the first subscript of C. Either choice of the ordering of these two loops results in an outer product matrix assembly method. 

The logical extension of GGA methods is to allow the exchange and correlation functionals to depend on higher order derivatives of the electron density, with the Laplacian (V ) being the second-order term. Alternatively, the functional can be taken to depend on the orbital kinetic energy density t, which for a single orbital is identical to the von Weizsacker kinetic energy Tw (eq. (6.3)). 

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