Frequency evaluation

Guidance on performing a quantitative frequency evaluation is beyond the scope of this book. Reference 4 provides detailed guidance on frequency evaluation. 

Qualitative frequency evaluation can be used to screen out events that are extremely unlikely to occur (i.e., have such a remote chance of occurring that further evaluation is unnecessary). This method is particularly appropriate for use in conjunction with qualitative consequence evaluation as a means of ranking risks. 

Qualitative frequency evaluation involves defining broad categories of event frequency, which can be used to assess the likelihood of occurrence of a specific incident outcome (consequence). These categories cover a full spectmm of frequencies, from those representing events that are likely to those that are highly unlikely. Definitions of likelihood categories vary, but Table 5.4 presents a typical list and definitions. 

The response to the second question is in terms of relative computation times for energy calculations, geometry optimizations and frequency evaluations on different size molecules. This is addressed in the final chapter of this section. Overview and Cost. 

This chapter addresses the relative cost of molecular mechanics and quantum chemical models for energy and equilibrium geometry calculations as well as for frequency evaluations. Taken together with performance issues addressed in previous chapters, this allows broad recommendations to be made regarding selection of an appropriate model. 

Relative times for the MMFF molecular mechanics model, the AMI semi-empirical model, Hartree-Fock models with 3-2IG, 6-3IG and 6-311+G basis sets, EDFl and B3LYP density functional models and the MP2 model with 6-3IG and 6-311+G basis sets, for energy calculations, geometry optimizations and frequency evaluations, and the localized MP2 (LMP2) model with 6-3 IG and... 

In 50 the author presents a further investigation of the frequency evaluation techniques which are recently proposed by Ixaru et al. for exponentially fitted multistep algorithms for the solution of first-order ordinary differential equations (ODEs). These studies have a scope which is to maximize the benefits of the exponentially-fitted methods via the evaluation of the frequency of the problem. The proposed by Ixaru and co-workers method for frequency... 

Stable configurations of ionic clusters (M X-)n and (M +X 2)n have been calculated for a number of species on the basis of a simple Born-Mayer approach by minimizing the total energy. (42-44) The vibrational frequencies evaluated for small clusters of alkali halides compare well with the FIR data of matrix isolated species. (43)... 

Probability of undesired event The probability of pipeline crack creation is evaluated from pipeline incidents statistics (database EGIG), which collected incident data since year 1970 on more than 122 000 km of pipelines. The overall incident frequency evaluated from database is equal to 0.41 incidents per year per 1 000 km. The incidents can have many causes, e most frequent cause is external interference (47%) Fig. 2. 

The frequency evaluated at one of the particle sizes equated to zero need not always exist For example, the Brownian aggregation frequency is unbounded when one of the particle sizes approaches zero. This is a reflection of the fact that aggregation is virtually certain between two particles when one of them is much smaller than the other and consequently capable of very rapid diffusional motion relative to the other much larger particle. In this case a(0, /y)/ cannot be expected to exist. 

On the other hand the values of the vibrational frequencies evaluated near the minimum of the potential energy surface may not be appropriate for large excess energy. In particular, potential models seem to show that the VdW bending motions must correlate with the overall rotation of the Ar atom around the aromatic plane for energies of about 250 cm above the minimum. This effect must produce a sudden increase in the density of... 

In essence, two of these three electrons form a n bond, on top of the existing (j bond, and the remaining electron is place into an antibonding n orbital. The sulfur-sulfur bond thus assumes a partial 7c-character 1112,113]. As a direct consequence, the rotation becomes restricted and, particularly in cyclic disulfides, molecular structures may flatten. Even the possible formation of cis- and rran -isomers of (MeSSMe) could recently be verified through identification of two distinct vibrational stretching frequencies evaluated from time-resolved resonance Raman spectroscopy measurements. These findings were also supported by corresponding calculations [118, 119, 146]. 

Muramatsu, T., Intensity and Frequency Evaluation of Sodium Temperature Fluctuation Related to Thermal Striping Phenomena Based on Numerical Methods, Proceeding of the 5th International Symposium on Refined Flow Modelling and Turbulence Measurements - Paris, France, 1993. 

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