First order rules

The first order approximation of ln(s/s )f through Eq.(26), j = 1, gives values of ln(s/s )f within 10% of the exact solution, Eq. (13), even for D/H Isotope effects at 300 K. Eq.(26) is an even better approximation to ln(s/s )f of heavier elements. Within this limitation, we can now derive the first order rules of Isotope chemistry by substitution of Equations (31) and (31a) into Eq. (26). They are  

2) Isotope effects between different compounds occur only 

4)Isotope effects are cumulative (first rule of the geometric mean) 

5)Equivalent Isomers have the same Isotope chemistry. 

For the complete calculation of ln(s/s )f directly from atomic masses and molecular structure, G matrices, and molecular forces, F matrices. It is necessary to relate the modulating co- 

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If catalyst decay over the reaction time can be seen as a decreasing number of active sites, then often a first-order rule holds true... 

Nitropropane As mentioned in Section 3.9, most open-chain compounds—barring severe steric hindrance—are conformationally mobile at room temperature coupling constants in each set average out and become essentially chemically shift equivalent. Thus a 300 MHz, room-temperature spectrum of 1-nitropropane is described as A3M2X2 rather than A,MM XX, and first-order rules apply (see Figure 3.51). 

The proton decoupled 29Si spectrum of tetram-ethylsilane (TMS) is shown at the top of Figure 6.9 with the proton coupled spectrum for comparison as an inset. TMS is the obvious choice for a 29Si reference compound and we set it at zero ppm. The proton-coupled spectrum is quite interesting because the 29Si nucleus is coupled to 12 equivalent protons in TMS. First order rules predict a multiplet with 13 peaks. There are 9 peaks clearly visible and 11 with a little imagination we do not see the full 13 peaks because the outer ones are too weak and are lost in the noise. 

When two or more couplings are present that may be treated by the first-order rules, a repetitive procedure can be used. For example, Fig. 6.6 gives an illustration of the repetitive application of first-order analysis. Usually it is convenient to consider the largest coupling first, but it is immaterial to the final result. 

A system of three sets of protons, each set separated by a large chemical shift, can be designated AaMmXx. If two sets are separated from each other by a small chemical shift, and the third set is widely separated from the other two, we use an AaBbXx designation. If all shift positions are close, the system is AaBbCc. Both end sets are coupled to the middle set with different coupling constants, whereas the end sets may or may not be coupled to one another. The AMX systems are first-order ABX systems can be approximated by using first-order rules, but ABC systems cannot be analyzed by inspection. These more complex patterns are treated in Section 4.12. 

Obviously, the analysis is more complex when two different substituents are present, but it is workable if the absorptions are separated enough so that first-order rules apply. 

The physical basis of the first-order rules is quite clear. Consider a system of two protons, Ha and Hx, and let the two allowed spin-states be a (high energy) and )8 (low energy). Then for upward transitions of the nucleus Ha we can have ... 

By first-order rules, the AjX system gives rise to a doublet of two-proton intensity and a triplet of one-proton intensity. The AgB spectrum may have up to 9 lines and can be highly asymmetrical. 

The obvious effects associated with second-order spectra (for instance, extra lines, distorted intensity patterns, and unequal spacings) generally preclude any injudicious attempts to analyze such systems by first-order rules. However, in some cases second-order spectra have features that are qualitatively indistinguishable from some features of first-order spectra, and so are often misinterpreted. It must be understood that the three cases discussed below are not physical phenomena—they are simply the result of certain combinations of the chemical-shift and spin-coupling parameters. 

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