By Mikhail E Elyashberg
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Additional info for Contemporary Computer-Assisted Approaches to Molecular Structure Elucidation
5a), the presence of the conjunction of frequencies w1(i) 4 w2(i) ... 4wn(i) is a necessary condition for the molecule to contain the structural unit Ai. 4)], shows that a suﬃcient condition for the General Principles of CASE Systems 21 absence of a structural element in the sample under investigation is that the spectrum should not contain at least one of the characteristic features of this group. , Ag(j), Ab(j) A A, then wj ! , Ag(j). 6) takes into account the possibility of a signal overlap in the spectra: the feature wj may appear as a result of overlap of absorption lines associated with any combination of units included into set A.
The disjunction of Ai and Ak corresponds to the non-excluding ‘‘or’’ and is designated by Ai _ Ak (‘‘Either the Ai or the Ak fragment, or both together, are present in the molecule’’). 4. The Boolean function Ai - wj is called an implication. It corresponds to the expression ‘‘if Ai, then wj’’ (‘‘If the molecule contains the Ai fragment, then the spectral feature wj is observed in a spectrum’’). The following identities of Boolean algebra are valid: a ! b ¼ a _ b ¼ b ! 4) are referred to as de Morgan’s laws.
In addition, for any set, the total number of double bonds or rings provided should not exceed that calculated from the empirical formula. The following sets of fragments were found: 1. 2. 3. 4. 5. 6. 7. 8. CN CN CN CN CN CN CN CN O¼CH[AR] O¼CH[AR] O¼CH[AR] O¼CH[AR] O¼CH[AR] O¼CH[AR] O¼CH[AR] O¼CH[AR] N-CH3 1,3,5-AR N-CH3 1,2,4-AR N-CH3 1,2,3,4-AR N-CH3 1,4-AR (C)CH3 1,3,5-AR (C)CH3 1,2,4-AR (C)CH3 1,2,3,4-AR (C)CH3 1,4-AR Two fragments, CN and O¼CH[AR], are included in all sets, whereas other fragments are available in diﬀerent combinations.