Absolute empirical methods

MINDO/3 methods clearly have severe problems with some of the conjugated systems. The MNDO/AM1/PM3 family perform somewhat better, although none of them can predict the correct ordering. The SAMI method is not an improvement for this case. The mean absolute deviation (MAD) for the predicted stabilities is 10kcal/mol, which is a typical accuracy for semi-empirical methods. 

Empirical Methods. The empirical methods use calibration standards to derive sensitivity factors that can be used to determine the unknown concentration of given elements in similar matrices [3. The sensitivity factors are derived from calibration curves that plot measured secondary ion intensities versus the known concentration of standards. Three types of sensitivity factors have been used the absolute sensitivity factor, the relative sensitivity factor, and the indexed relative elemental sensitivity factor. 

A Antisymmetrizing operator A Vector potential P First hyperpolarizability P Resonance parameter in semi-empirical theory B Magnetic field (magnetic induction) X, /r, A, cr Basis functions (atomic orbitals), ab initio or semi-empirical methods rraiipp inrliiflinp basis fiinrHon 7] An infinitesimal scalar rj Absolute hardness h Planck s constant H hjl K h Core or other effective one-electron operator hap Matrix element of a one-electron operator in AO basis Matrix element of a one-electron operator in semi-empirical theory... 

If we are asked to determine the amount of nickel in a sample of a metal alloy, we would expect that nickel is a specific component of the alloy and that the absolute amount of it could be measured. In many fields of analysis the names of some parameters that we measure refer only to a part of a component entity in the sample. Such a name does not precisely identify a specific part of the sample, but is related to the particular method used. These are empirical methods - they have been arrived at by a large number of experiments to provide results that are useful in certain practical applications. The results can be interpreted to formulate diagnoses, treatments or management decisions. The justification and basis for such methods is that they can give results that have been found to correlate with some important performance characteristics. Unfortunately though, they seldom increase our understanding of the mechanisms of action or processes involved. 

In fact, none of these points is really so important in a semi-empirical method, because such methods are not designed for performing absolute calculations on single molecules, but rather for studying the trends of physical properties in a series of related compounds. Computational experience shows that the general picture of the electronic structure is not significantly altered whatever method may be chosen, as long as the parameters or the coordinate axes of orbitals are varied within reasonable limits. 

Relative and/or Empirical Methods for Determining Absolute Configuration... 

Thiel (1998) lists mean absolute deviations between calculated AfH29S and experimental AfH29S for two ab initio methods, a density functional variant of the ab inito method and three semi-empirical methods. They are G2 1.58, G2(MP2) 2.04, B3LYP 3.11, MNDO 9.32, AMI 7.81, and PM3 7.01 kcal mol 1 respectively. See below for comments on ab initio calculations. 

This does not mean that the methods available today are too inaccurate to be useful. The relative accuracy for a series of related species is often much higher than the absolute accuracy attainable for any one molecule. Moreover, empirical methods can be designed to be very accurate indeed albeit with respect to a restricted set of molecular types and/or properties. Provided that the system of interest is representative of the types of molecules used for the original para-meterisation, good results can be obtained. However, we always need to be cautious of placing too much faith in computed results alone and should always cross-check theory and experiment. Together, calculation and observation make powerful complementary tools for the study of chemical systems. 

The rates and mechanisms of chemical reactions can be predicted, in principle, by the standard methods of statistical thermodynamics, in terms of the partition functions of reactants and the transition-state complex. However, the range of applicability of this transition-state (absolute rate) theory is severely limited by the fact, that an evaluation of the vibrational partition function for the transition state requires a detailed consideration of the whole PES for the reaction. Thus, a calculation of the absolute rate constants is possible only for relatively simple systems. This indicates a need for more approximate, empirical methods of treating chemical reactions and formulating the reactivity theory, which would allow... 

As an alternative to ab initio methods, the semi-empirical quantum-chemical methods are fast and applicable for the calculation of molecular descriptors of long series of structurally complex and large molecules. Most of these methods have been developed within the mathematical framework of the molecular orbital theory (SCF MO), but use a number of simplifications and approximations in the computational procedure that reduce dramatically the computer time [6]. The most popular semi-empirical methods are Austin Model 1 (AMI) [7] and Parametric Model 3 (PM3) [8]. The results produced by different semi-empirical methods are generally not comparable, but they often do reproduce similar trends. For example, the electronic net charges calculated by the AMI, MNDO (modified neglect of diatomic overlap), and INDO (intermediate neglect of diatomic overlap) methods were found to be quite different in their absolute values, but were consistent in their trends. Intermediate between the ab initio and semi-empirical methods in terms of the demand in computational resources are algorithms based on density functional theory (DFT) [9]. 

A convenient empirical method [6] for determining the absolute configurations of the biphenyl moieties in ellagitannins without chemical degradation was exploited based on the accumulated CD spectra of the compounds whose atropisomerism of the chiral HHDP group in each... 

By means of analytical-mathematical or empirical methods, results which provide absolute data on the risks of a technical installation or a technical system can be obtained. The statement of absolute risk data could, however, under some circumstances represent an insufficient indication. The data, for example, on accidental death risk per person and per working hour in mining, namely 0.0000003, represent accurate but not very helpful knowledge. If, however, it is known that the risk of death while working in a mine is 30 times greater than in the case of professional activity with the health service [9-27], then on the basis of this relationship meaningful decisions on the social or industrial level can be made. 

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