Calculated properties to improve CASE

As was seen in the previous section, substructure classifiers are only one step in reducing the number of structures generated during CASE. Eigure 9.3 demonstrates that mass spectral match value and partitioning behavior reduced candidate numbers further, although many cases with more than 10 possible structures remained even within this small subset of 71 spectra. In terms of positive identification, even 10 possible structures is too many and would mean the purchase (or synthesis) of these reference compounds before a complete identification could be made. This is obviously 

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Another way to improve the error in a simulation, at least for properties such as the energy and the heat capacity that depend on the size of the system (the extensive properties), is to increase the number of atoms or molecules in the calculation. The standard deviation of the average of such a property is proportional to l/ /N. Thus, more accurate values can be obtained by running longer simulations on larger systems. In computer simulation it is unfortunately the case that the more effort that is expended the better the results that are obtained. Such is life ... 

Theoreticians did little to improve their case by proposing yet more complicated and obviously unreUable parameter schemes. For example, it is usual to call the C2 axis of the water molecule the z-axis. The molecule doesn t care, it must have the same energy, electric dipole moment and enthalpy of formation no matter how we label the axes. I have to tell you that some of the more esoteric versions of extended Hiickel theory did not satisfy this simple criterion. It proved possible to calculate different physical properties depending on the arbitrary choice of coordinate system. 

As for basis-set convergence, triple- calculations at the MP2 and CCSD levels are provided for comparison to die double- results. For this particular property, the results for p-benzyne are not terribly sensitive to improvements in the Ilexibility of the basis set. In the pyridynium ion case, die CCSD results are also not very sensitive, but a large effect is seen at the MP2 level. This has more to do with the instability of the perturbation expansion than any intrinsic difference between the isoelectronic aryiies. 

The properties are most useful when there are several closely overlapping peaks, and higher order derivatives are commonly employed, for example in electron spin resonance and electronic absorption spectroscopy, to improve resolution. Figure 3.11 illustrates the first and second derivatives of two closely overlapping peaks. The second derivative clearly indicates two peaks and fairly accurately pinpoints their positions. The appearance of the first derivative would suggest that the peak is not pure but, in this case, probably does not provide definitive evidence. It is, of course, possible to continue and calculate the third, fourth, etc., derivatives. 

To understand this discrepancy, we need to remember that there is a second source of error in any experiment systematic error that causes a shift in the measured values from the true value and reduces the accuracy of the result. By making more measurements, we can reduce the uncertainty due to random errors and improve the precision of our result however, if systematic errors are present, the average value will continue to deviate from the true value. Such systematic errors may result from a miscalibration of the experimental apparatus or from a fundamental inadequacy in the technique for measuring a property. In the case of Millikan s experiment, the then-accepted value for the viscosity of air (used in calculating the charge e) was subsequently found to be wrong. This caused his results to be systematically too high. 

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