Essential correlation

For these reasons, in the MCSCF method the number of CSFs is usually kept to a small to moderate number (e.g. a few to several thousand) chosen to describe essential correlations (i.e. configuration crossings, near degeneracies, proper dissociation, etc, all of which are often tenned non-dynamicaI correlations) and important dynamical correlations (those electron-pair correlations of angular, radial, left-right, etc nature that are important when low-lying virtual orbitals are present). 

The scope of application of the Regular Solution Theory is limited only to estimating solute partitioning in PE/ethanol systems. The Retention Indices system is currently only developed for PE/ethanol and PE/water systems. Their better accuracy is not surprising since they are essentially correlations of this experimental data. 

We have investigated peptides whose structures were known beforehand from NMR or x-ray spectroscopy and related these structures to 2D-IR spectroscopy. Ultimately, one would like to deduce the structure of an unknown sample from a 2D-IR spectrum. In the case of 2D NMR spectroscopy, two different phenomena are actually needed to determine peptide structures. Essentially, correlation spectroscopy (COSY) is utilized in a first step to assign protons that are adjacent in the chemical structure of the peptide so that J coupling gives rise to cross peaks in these 2D spectra. However, this through-bond effect cannot be directly related to the three-dimensional structure of the sample, since that would require quantum chemistry calculations, which presently cannot be performed with sufficient accuracy. The nuclear Overhauser effect (NOE), which is an incoherent population transfer process and has a simple distance dependence, is used as an additional piece of information in order to measure the distance in... 

Knowledge of the impact of the major sources of uncertainty in input data on the estimate of exposure is essential. Correlation coefficients and scatter... 

While in first- and second-row atoms the inclusion of f functions in the AO basis is desirable, as seen so far, this is found to be necessary in heavier atoms such as transition metals, for example. Reliable transition energies (i.e. errors smaller than 0.2 eV) are only found after inclusion of two f functions, where a tight component is necessary for the correlation description of the innermost 3s 3p subshell and the less compact f AO is to account for the essential correlation energy in the outermost 3d4s subshell. A detailed study of correlation effects in the (3s3p) subshell of Sch, TiH and VH has just been made in connection with the electronic spectrum of these compounds, and the reader is referred to this article. 

The successful development of volcano plots is intimately tied both to the identification of appropriate descriptors and to the relation of these descriptors to the catalytic properties of interest. Many approaches, of varying levels of complexity, are available to identify suitable descriptors and to incorporate these into volcano plots. Some classes of volcanoes have been developed in an empirical or semiempirical manner, by essentially correlating experimental reaction rates with experimentally or computationally determined values of catalytic parameters. An early example of a purely empirical volcano, in the field of electrocatalysis, was... 

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