INDEX computer representation

J.R.M. Smits, W.J. Meissen, G.J. Daalmans and G. Kateman, Using molecular representations in combination with neural networks. A case study prediction of the HPLC retention index. Computers Chem., 18 (1994) 157-172. 

GORE. The CORE Electronic Chemistry Library is a joint project of Cornell University, OCLC (On-line Computer Library Center), Bell Communications Research (Bellcore), and the American Chemical Society. The CORE database will contain the full text of American Chemical Society Journals from 1980, associated information from Chemical Abstracts Service, and selected reference texts. It will provide machine-readable text that can be searched and displayed, graphical representations of equations and figures, and full-page document images. The project will examine the performance obtained by the use of a traditional printed index as compared with a hypertext system (SUPERBOOK) and a document retrieval system (Pixlook) (6,116). 

The main computational attraction of the SCF method is that it reduces to a one-electron matrix problem the manipulations are those of matrices of the size of the number of basis functions. This means, for example, that any orbital transformations which may have to be done involve transformations of matrix representations of one-electron operators no time-consuming transformations of the four-index electron-repulsion integrals have to be done explicitly. The electron-repulsion terms are all contained in the Hartree-Fock matrix via G or,... 

Fig. 7 Comparative representation of the progress curves for the CIPAH ligands of Fig. 6 bound to human breast cancer MCF-7 cells, employing the recorded EROD/human-QRAR reactivity-activity information from Table 10 into logistic chemical-biological interactions modeled by Eq. (89), on the mapped unitary time scale of Eq. (15), for each index/quantum chemical method considered and for an EROD EC50 = 34.696 pM norm parameter as computed with algebraic definition (12b) and the EROD/human data of Table 5...

Now turn to computational aspects. For matrices / and pp, a block representation is easy to find by simple algebra (see Appendix B). As a result, we get charge density matrix of the QCTB model, Eq. (B4), and the respective NOON spectrum, Eq. (B5). It comes to a suitable working formula for the main EUE index ... 

Full four-component electronic structure methods do not need to be considered as unavoidably expensive, as it was believed in the early days of relativistic quantum chemistry. Four-component correlation methods are hardly more expensive in computational terms once the four-index transformation from four-component atomic basis functions to molecular spinors has been efficiently accomplished. And even the SCF step can be performed very efficiently with a fairly small prefactor in the scaling expression compared with the nonrelativistic situation. Nevertheless, one may wonder what might be the most appropriate representation of a Fock-type operator in such one-electron equations for computational purposes. 

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