Statistical analysis atomization energies

In these models, the potential energy function is based on the molecular mechanics all-atom force field and includes the bond, angle, dihedral and non-bonded energy terms. The parameterization is based on the statistical analysis of sets of experimental structures. If a variable q describes a degree of freedom in the system (e.g., bond distances, angles, dihedrals) then, P(q), the probability distribution associated with this degree of freedom, is related to the potential of mean force, W(q), by the following equation... 

Fig. 4. The CoMFA process consists of individual steps (adapted from Cramer et al. 1988). First, interaction energies are computed between all molecules in alignment and a probe atom on a regular grid. This information is stored in a particular format in order to allow for multivariate statistical analysis. The PLS method then produces a statistical model which can be interpreted and used for prediction.

The calculation of the energy or the fitting of the test sequence in the fold of the template is no easy matter. The utilization of a full force field with complete atom representation does not properly discriminate between the different folds [31]. This seems to be related to an energy surface that is too fine and the presence of numerous local minima. In its place a potential function based on a statistical analysis of known protein structures has been developed [34], The pair-wise penalty function provides a pseudo-energy based on the number of times the specific interaction has been observed in known protein structures. This function provides amino acid-amino acid interactions as well as a measure for the solvent exposure of each amino acid [34],... 

D Rodbard, DM Hutt. Statistical analysis of radioimmunoassays and immunoradio-metric (labelled antibody) assays A generalized weighted, iterative, least-squares method for logistic curve fitting. In Radioimmunoassay and Related Procedures in Medicine, Vol I. Vienna International Atomic Energy Agency, 1974, p 165. 

The notion that methods of statistical analysis should be applied to reactor safety standards was first put forward by Siddall of Atomic Energy of Canada Ltd., Chalk River, Ontario in 1959 (57). This early paper is of interest because it invokes the notion of a balance between increased wealth of the community that may be expected to accrue from the advent of nuclear power on the credit side, and risks of injuries and deaths because of the hazards of the nuclear process on the other it goes on to suggest money costs (economic criteria) as the avenue through which to achieve such a balance. The details given in the paper are only generally relevant today, but some of the introductory sentences have a modern sound to them and are worth quoting as an introduction to the basic philosophy of the probability approach to reactor safety. The study of nuclear-reactor safety (i.e., in 1959, some 15 years ago in the life of an industry now only 20 years of age) is in an unsatisfactory state. Some aspects of the problem have received... 

For our statistical analysis, we exclude those molecules for which either the experimental atomization energy or the vibrational correction is unknown H202> N2H2 and HNC. In addition, we have excluded HOF, which has the largest experimental uncertainty and for which we shall later see that the experimental value must be in error. Except for O3 (1.7 kJ/mol), C2H2 (1 kJ/mol), CH2 (2.2 kJ/moI) and HCN (2.6 kJ/moI), the uncertainty in De for the other molecules is smaller than... 

Our final statistical sample for the atomization energy thus consists of the 16 molecules ticked in Table 15.1. These molecules should be well suited for testing the performance of the standard electronic-structure models for the four molecules omitted from the statistical analysis, the calculations presented here should serve as accurate predictions of the equilibrium atomization energies. 

For our statistical analysis, we have excluded all reactions involving HNC, N2H2 and H2O2, for which no experimental equilibrium atomization energies exist, and HOF, for which the experimental equilibrium atomization energy is probably in error. This leaves us with a set of 13 reactions (shown in bold in Table 15.29) on which our statistical analysis of the performance of the Hartree-Fock, MP2, CCSD and CCSD(T) models is based. 

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