The n 1 Rule

More complicated splitting patterns conform to an extension of the n + 1 rule and will be discussed in Section 13 11... 

It turns out that fully filled or half-filled subshells have added stability compared with subshells having some other numbers of electrons. One effect of this added stability is the fact that some elements do not follow the n +1 rule exactly. For example, copper would be expected to have a configuration... 

To get the electron configuration of ions, a new rule is followed. We first write the electron configuration of the neutral atom. Then, for positive ions, we remove the electrons in the subshell with highest principal quantum number first. Note that these electrons might not have been added last, because of the n + / rule. Nevertheless, the electrons from the shell with highest principal quantum number are removed first. For negative ions, we add electrons to the shell of highest principal quantum number. (That shell has the electrons added last by the n +1 rule.)... 

A given peak will be split into a number of peaks equal to the number of equivalent hydrogens on the adjacent carbons plus 1 (the n + 1 rule). This represents a clue about the structure that can help lead to identification of the compound. 

The additional detail provided by a high resolution spectrum allows more information to be determined about the structure of the compound. Analysing the multiplets allows the neighbouring proton environment to be identified. This can be done using the n + 1 rule, where n is the number of carbon atoms attached to the next-door carbon atom and n + 1 is the number of peaks that will be seen in the cluster. 

One particularly interesting category of metallocarborane is that in which a single metal atom is shared between two polyhedra that have a vertex in eommon. In effect, the metal is sandwiched between two nido-carborane residues. Examples are shown in Fig. 17. For such commo compounds, the metal can be assumed to contribute three AO s to the skeletal bonding of each polyhedron, when the (n + 1) rule for closo clusters is found to be obeyed. For example, the isoelectronic... 

Coupling follows the n + 1 rule. According to this rule, a peak splits into n + 1 peaks due to neighboring hydrogen atoms, where n is the number of equivalent hydrogen atoms. The amount of splitting is expressed by the coupling constant (J). 

A French group of writers and mathematicians called the Oulipo still discuss and create literary works involving constrained writing, which provides them with a means of triggering ideas, inspiration, and mind expansion. The Oulipo (Ouvrior de Utterature P tentielle) have experimented with such constraints as the N+1 rule in which every noun in a story is replaced with the word that falls 7 words ahead of it in the dictionary. Thus, Call me Ishmael from might become Call me... 

The n + 1 rule should be amended to read When a proton H is coupled to Hfo, Hc, H(i, etc., and Jab Jac, Jad, etc., the original signal for Ha is split into n + 1 peaks by n H, protons, each of these lines is further split into n + 1 peaks by n Hc protons, and each of these into n + 1 lines by n H(i protons, and so on. Bear in mind that because of overlapping peaks, the number of lines actually observed can be less than that expected on the basis of the splitting rule. 

If immunogenicity studies demonstrate that a similar immune response is obtained at intervals shorter than the proposed clinical dosing interval (e.g., 4-6 weeks), then a truncated dosing interval (2-3 weeks) can be used in the repeat dose safety studies. The FDA recommends that one more dose than the clinical dosing regimen (N) be used in animal studies. This is termed the N + 1 rule [61].The number of animals used per group should be sufficient to detect... 

The preceding analysis for the splitting of 1,1,2-tribromoethane can be extended to more complicated systems. In general, the multiplicity (number of peaks) of an NMR signal is given by the N +1 rule ... 

Hb has three Ha protons on each side. Because the six H. protons are equivalent to each other, the n + 1 rule can be used to determine splitting 6+1=7 peaks, a septet... 

The (n + 1) rule only applies in systems where the coupling constant (J) between the protons is the same. Fortunately this is common in aliphatic systems. 

The energy derivatives can be found from each equation by multiplying on the left with Cj. This corresponds to the n +1 rule as illustrated with the first-derivative equation... 

Yet another complication in NMR spectroscopy arises when a signal is split by two or more nonequivaJent kinds of protons, as is the case with trans-cinnamaldehyde, isolated from oil of cinnamon (Figure 13.22). Although the n + 1 rule correctly predicts splitting caused by equivalent protons, splittings caused by nonequivalent protons are more complex. 

Second-order spectra are characterized by peak spacings that do not correspond to coupling constants, by nonbinomial intensities, by chemical shifts that are not at the midpoints of resonance multiplets, and by multiplicities that do not follow the n + 1 rules. (See Figures 4-1, 4-2, and 4-3.) Even when the spectrum has the appearance of being first order, it may not be. Lines can coincide in such a way that the spectrum assumes a simpler appearance than seems consistent with the actual spectral parameters (a situation called deceptive simplicity). For example, in the ABX spectrum, the X nucleus is coupled to two nuclei (A and B) that are themselves closely coupled. When is extremely small, the A and B... 

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