Direct inversions

Remade F and Levine R D 1993 Time domain information from resonant Raman excitation profiles a direct inversion by maximum entropy J. Chem. Phys. 99 4908-25... 

Cable J R and Albrecht A C 1986 A direct inverse transform for resonance Raman scattering J. Chem. Phys. 84 4745-54... 

Csaszar P and Pulay P 1984 Geometry optimization by direct inversion in the iterative subspace J. Moi. Struct. (Theochem) 114 31... 

Ionova I V and Carter E A 1995 Crbital-based direct inversion in the iterative subspace for the generalized valence bond method J. Chem. Phys. 102 1251... 

Hamilton T P and Pulay P 1986 Direct Inversion In the Iterative subspace (DNS) optimization of open-shell, excited-state and small multiconfiguratlonal SCF wavefunctlons J. Chem. Phys. 84 5728... 

DIIS (direct inversion of the iterative subspace) algorithm used to improve SCF convergence... 

When three-point interpolation fails to yield a convergent calculation, you can request a second accelerator for any SCFcalculation via the Semi-empirical Options dialog box and the Ab Initio Options dialog box. This alternative method. Direct Inversion in the Iterative Subspace (DIIS), was developed by Peter Pulay [P. Pulay, Chem. Phys. Lett., 73, 393 (1980) J. Comp. Chem., 3, 556(1982)]. DIIS relies on the fact that the eigenvectors of the density and Fock matrices are identical at self-consistency. At SCF convergence, the following condition exists... 

Photolytic epimerizations of this type would represent a potentially useful method of direct inversion of chiral centers. However, competition by numerous other intramolecular processes vide infra) frequently renders its more general utilization less practical. 

Direct inversions of the concentration distribution profiles to obtain molecular weight distribution information are generally impossible because of comphcations involving non-ideality. Successful attempts have been given but only for simple discrete forms of polydispersity (two to three macromolecular species [93]). 

Considering the diagonalized form (5) of the image formation equation, a very tempting solution is to perform straightforward direct inversion in the Fourier space and then Fourier transform back to get the deconvolved image. 

Figure 2b and Eq. (10) show that the Wiener inverse-filter is close to the direct inverse-hlter for frequencies of high signal-to-noise ratio (SNR), but is strongly attenuated where the SNR is poor ... 

When plotted as a function of drop size (Fig. 9), the contact angle was found to decrease with increasing drop height. A different analysis of these data was performed in the original paper. In that case the maximum slope near the drop edge was used, as well as a direct inversion of the droplet shape. The data could be fit to an empirical 1/z function. In the present analysis we use the method of the effective contact angles defined earlier, together with Eq. (18). For the Flamaker constant A, we calculated a value of approximately -2 X 10 ° J. However, the best fit to Eq. (18) is for a pure exponential decay of the form ... 

Determination of a Flexible (12D) Water Dimer Potential via Direct Inversion of Spectroscopic Data. 

The conversion of light to electric current in photovoltaic devices is the direct inversion of the electroluminescent process in OLEDs, thus it is not surprising that the same molecular glasses as described above have also been used for the realization of solar cells. There are at least two different types of approaches, however, that shall be described now. 

The fluorinase enzyme mediates a substitution reaction whereby fluoride ion displaces L-methionine with formation of a C-F bond and cleavage of a C-S bond. In order to explore the mechanism in detail, the process has been explored both experimentally and theoretically. The stereochemical course of the reaction was of immediate interest, particularly to delineate between direct inversion or double inversion during the substitution process. A direct substitution will proceed with inversion of configuration at the C5 carbon, whereas a double inversion process will proceed with an overall retention of configuration at the C-5 carbon. To explore this, it was important to prepare SAM 8 carrying a stereospecifically... 

Perhaps the most intriguing observation of helicenes is the unexpected ease with which these compounds racemize thermally. According to Martin 1031 three pathways for the thermal racemization can be considered 1) via bond breaking 2) via an internal double Diels-Alder adduct, and 3) via a direct inversion. Martin rejected the first possibility because it is not in accordance with kinetic data for the racemization. He could exclude the second possibility in an elegant way by using appropriately substituted derivativesl03>. 

---