Computational geometry

Minsky, M., and Papert, S., Perceptions An Introduction to Computational Geometry. MIT Press, Cambridge, MA, 1969. 

Ab initio calculations reproduce the experimentally observed geometrical changes. Ethylene is planar (absolute true minimum global minimum) at all theoretical levels. The computed geometry of disilene depends strongly on the basis functions and on electron... 

F.F. Preparate and M.L. Shamos, Computational Geometry, An Introduction, Springer, Heidelberg, 1958. 

To close on a more positive note, we observe that the computed geometry of the enzyme-dienolate complex in the vicinity of the 3-carbonyl is insensitive to the assumed dielectric constant and is in close agreement with X-ray structures of enzyme-inhibitor complexes (see Table 4.11 and Fig. 4.15). It is really quite remarkable that 4 billion years of random walk by mother nature and a few hours of optimization with a quantum chemistry program such as Gaussian (starting with the correct functional groups) lead to the same structure for the active... 

As expected from the valence-bond descriptions of Fig. 3, the computed geometries of the lowest A singlet and triplet states of 16 have quinonoid geometries displaying bond localization (Fig. 5). On the other hand, the quintet A -16... 

J., Zheng, W. (2008) Novel approach to structure-based pharmacophore search using computational geometry and shape matching techniques. / Chem Inf Model 48, 889-901. 

It is, however, for the transition metals themselves that DFT has proven to be a tremendous improvement over HF and post-HF methods, particularly for cases where tlie metal atom is coordinatively unsaturated. The narrow separation between filled and empty d-block orbitals typically leads to enormous non-dynamical correlation problems with an HF treatment, and DFT is much less prone to analogous problems. Even in cases of a saturated coordination sphere, DFT methods typically significantly ouqierform HF or MP2. Jonas and Thiel (1995) used the BP86 functional to compute geometries for the neutral hexacarbonyl complexes of Cr, Mo, and W, the pentacarbonyl complexes of Fe, Ru, and Os, and the tetracarbonyl... 

In terms of computing adiabatic energy differences, if the Bom-Oppenheimer PES for the excited state can be computed, geometry optimization of that state may be carried out using standard techniques. But, as we have been discussing above, we have not yet devised a scheme for computing the excited-state surface, since ground-state orbitals are not appropriate for minimum-determinantal excited-state wave functions. How then to obtain a better excited-state wave function ... 

Grii03] B. Griinbaum, Are your polyhedra the same as my polyhedra , Discrete and Computational Geometry The Goodman-Pollack Festschrift, ed. by B. Aronov, S. Basu, J. Pach, and M. Sharir, Springer Verlag, 2003, 461-488. 

HaS196] R. H. Hardin and N. J. A. Sloane, McLaren s improved snub cube and other new spherical designs in three dimensions, Discrete and Computational Geometry 15 (1996) 429-441. 

Table 2 Computed geometry, energies, and dipole moments (p) of phosphalkenes with ST0-3G and STO 43-1G basis sets...

Finn, P.W., Karraki, L. E., Latombe, J.-C., Motwani, R., Shelton, C., Venkatasubra-manian, S., Yao, A., RAPID randomized pharmacophore identification for drug design, in Proc of the 3rd annual symposium on computational geometry, Nice, France, ACM Press, p. 324-333. 

O R 98] O Rourke, Joseph, Computational Geometry in C, Cambridge University Press,... 

Fig. 12 Example polyacetylenes with pendant radical groups, with a computed geometry example of pendant twisting that severely limits exchange along the main chain.

Select Computer-Geometry optimization to open Molecular mechanics optimization dialog box (Figure 14.9). 

Table 8 Computed geometries and force constants for NHa (experimental values in parentheses)458...

Aarons, Hillier, and Guest have also reported calculations on SiHs and various other species,590 with the computed geometry in reasonable agreement with that found by Wirsam. 

The results from the nonlocal and hybrid DFT calculations show trends similar to those observed for the MO calculations. The computed geometries are very similar to each other the calculated bond lengths for the breaking bond range from 2.14 A, calculated by the hybrid adiabatic connection method (ACM) [24], to 2.16 A, calculated by the nonlocal BLYP [25, 26] functional. A comparison of the results from the nonlocal Becke-Perdew [27] calculations using DZVP and a TZVP basis sets shows that the geometries are influenced to a very small extent by basis set effects [12]. The activation energies calculated by the different nonlocal methods are too low by 1-3 kcal/mol, whereas the hybrid DFT methods overestimate Ea by approximately the same amount. Both the nonlocal and the hybrid DFT methods tend to overestimate the heat of reaction by up to 7 kcal/mol, calculated by the ACM/6-31G method. 

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