The Use of Isotopic Molecules for the Complete Determination of Force Constants. I. Linear Molecules

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Abstract
Equations are developed which show the maximum amount of information which can be obtained concerning the force constants with isotopic linear molecules. It is demonstrated that a unique solution can be found in terms of the expressions Σkλk, Σkλk2, and Σkλk3, where λk=4π2νk2, provided the νk are known for the ``unsubstituted'' molecule and for certain isotopic molecules involving respectively single, double, and triple substitutions; i.e., if ABCD··· is the unsubstituted molecule, isotopic molecules of the types A*BCD···, AB*CD···, etc., A*B*CD···, etc., and A*B*C*D···, etc., are required. More than two isotopic forms (such as A and A*) of any given atom are not required. For the triatomic molecule, only the singly substituted forms are required (this is also true for the perpendicular vibrations of the tetratomic molecule). It is also found that the force constants of the symmetrical linear molecule may be found using only symmetrical isotopic molecules; the number of these required is naturally less than the number required for an unsymmetrical molecule having the same number of atoms.

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