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On the total number of atomic assocations of an N ‐atomic molecule
Author(s) -
Schnupp Peter
Publication year - 1968
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560020305
Subject(s) - atomic number , atoms in molecules , atomic physics , value (mathematics) , operator (biology) , coordination number , molecule , effective atomic number , atomic theory , mathematics , physics , chemistry , quantum mechanics , ion , statistics , electron , biochemistry , repressor , transcription factor , gene
The total number of different possible atomic associations of an N ‐atomic molecule lies between a value P N (all N atoms identical) and A N (all atoms different). P N may be obtained reducing the problem to a classical problem in number theory. A N may be given as an operator expression which can be evaluated using the non‐numerical programming language FORMAC. The relation P N ≦ 2 N –1 ≦ A N gives a rough estimate for the orders of magnitude to be expected. The number Z ( G ) Nof all atomic associations of grade (number of “partial unions”) G for N atoms can be computed using a recursive formula.