Term-value method

Of the four methods discussed above, the two-state fit method is the most accurate if satisfactory expressions are available for the energy levels of the two states and there are no earlier precise constants available for either state (e.g., from microwave studies). This method is equivalent to the term value method with correlation included. The rotational constants in the two states are highly correlated, and it is frequently possible to change the molecular constants in a correlated manner by an order of magnitude times the standard deviations without seriously impairing the quality of the fit. If the molecular constants of one state... 

At least three classes of spectrum-fitting programs exist that are suitable for reducing line spectra to molecular constants the term-value method (Aslund, 1974), the direct approach (Zare, et al., 1973), and merging of separate band-by-band fits (Albritton, et al., 1977 Coxon, 1978 Tellinghuisen, 1996). 

The term-value method (Aslund, 1974) has the effect of focusing on a single electronic state. Transitions from many bands are converted, in a model-independent manner, to a set of term values. Many of the term values are multiply determined from several branches of many bands. The term-value approach reduces an enormous number of observed transitions to a much smaller number of preaveraged energy levels. In many cases, especially when one state is perturbed, the term-value approach can aid the assignment process and vastly simplify part of the least-squares parameter optimization process. The term value approach has been criticized by Zare, et al., (1973) and Albritton, et al., (1977). 

Section 6.13.2 and illustrated in Figure 6.5. The possible inaccuracies of the method were made clear and it was stressed that these are reduced by obtaining term values near to the dissociation limit. Whether this can be done depends very much on the relative dispositions of the various potential curves in a particular molecule and whether electronic transitions between them are allowed. How many ground state vibrational term values can be obtained from an emission spectrum is determined by the Franck-Condon principle. If r c r" then progressions in emission are very short and few term values result but if r is very different from r", as in the A U — system of carbon monoxide discussed in Section 7.2.5.4, long progressions are observed in emission and a more accurate value of Dq can be obtained. 

The term gradient method is often applied to algorithms that make use of a gradient to find stationary points. It is always possible to estimate the gradient numerically, for example by calculating the function value at points that are close together in space... 

Lobo et al. [47] proposed the packing factor, F, and experimentally determined that it better represented the data than the calculated a/e term. Values calculated using surface area per cubic foot and percent free gas space from manufacturer s tables can be as much as 40% off. The ralues are dependent upon the method of packing the tower, i.e., dry dumped, wet dumped, or wet dumped and shaken. The latter condition may approximate the situation after a tower has been running a while and the packing settled. 

Boundary value methods provide a description of the solution either by providing values at specific locations or by an expansion in a series of functions. Thus, the key issues are the method of representing the solution, the number of points or terms in the series, and how the approximation converges to the exact answer, i.e., how the error changes with the number of points or number of terms in the series. These issues are discussed for each of the methods finite difference, orthogonal collocation, and Galerkin finite element methods. 

The methods considered in the rest of this chapter are generally termed descent methods for minimization because a given step is pursued only if it yields an improved value for the objective function. First we cover methods that use function values or first or second derivatives in Section 5.3, followed by a review of several methods that use only function values in Section 5.4. 

It has been demonstrated in several benchmark calculations that the CR-CCSD(T) (completely renormalized CCSD(T)) and CR-CCSD(TQ) (completely renormalized CCSD(TQ)) methods provide an excellent description of entire PESs involving single and double bond dissociation (P, 13, 15, 17-19, 21, 111), highly-excited vibrational term values near dissociation 17, 18, 21, 111), and... 

Attachments or Appendices Miscellaneous back-up information such as discussion of rejected or less-probable scenarios, documents of special interest or value, method and conduct of the investigation and team membership, photographs, diagrams, calculations, lab reports, references, noncontributory factors, terms of reference. 

Here, Vo is the potential energy, which, however, does not affect the RFR term. This method is first checked for its self-consistency using a real-valued potential... 

AB2 Systems. Since layered structures are important variants in AB2 systems (e.g. the Cdl2 and CdCb families of structures), it was deemed necessary to always use a Coulomb potential without a damping term. The method chosen to perform the full Coulomb sum was the one suggested by de Leeuw66. Again, the resulting structure candidates in general did not depend on the exact values of the effective potential. The most common structure types found are summarized in table 3. We note that these include many commonly found structures like anatas,... 

Linnett o gives a discussion of the use of valence force fieid with the addition ol selected cross terms. One method of reducing the number of constants to Tdc determined from the frequencies is to carry over from molecule to molecule certain force constants for squared terms and even for cross terms. Linnett mentions in this connection the work of Crawford and Brinkley who studied acetylene, ethane, methylacetylene, dimethylacetylene, hydrogen cyanide, methyl cyanide and the methyl halides in this way, and were able, for all the molecules, to account for 84 frequencies with 31 constants. Linnetttreated some of these compounds using a different force field. He was able to account satisfactorily for 25 frequencies using 11 force constants. From our point of view the trouble with these results is that Linnett obtained a value for the C - C force constant in these acetylene derivatives which was different from that obtained by Crawford and Brinkley. For C - C in methyl cyanide for example, Linnett obtained... 

A suitable validated analytical method for the total dissolved metal analysis is essential to the study. The analytical detection limit should be lower than the appropriate chronic or long term value from the exotoxicity tests. 

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