A NEW CRITERION FOR THE DETERMINATION OF MOLECULAR STRUCTURES FROM GROUND STATE ROTATIONAL CONSTANTS

1J. Kraitchman, Am. Journal of Phys. 21, 17 (1953).Author Institution: Division of Pure Physics, National Research Council“$Kraitchman^{1}$ has shown that a single isotopic substitution on an atom is sufficient to determine directly the co-ordintates of that atom with respect to the principal axes of the original molecule. Kraitehman’s formulae represent exaet solutions of the equations for the equilibrium moments of inertia. However, the effers of the zero-point vibrations are such that the co-ordinates obtained by substitution from the ground state moments of inertia $I_{o}$ are not the $r_{o}$ values but are systematically less than $r_{o}$. These co-ordinates have been called r (substitution) or $r_{s}$ and it is found that {r}_{o}\simeq \frac{{r}_{o}+{r}_{e}}{2}, { and }{I}_{s}=\sum_{i}{m}_{i}{r}^{2}_{si}\simeq \frac{{I}_{o}+{I}_{e}}{2}. In the usual method of solution, the co-ordinate of one atom is determined from the equation for $I_{o}$ and therefore the difference $I_{o}-I_{s}$ must be made up by this one co-ordinate. This introduces a large error in the struetures normally determined from ground state constants, and results in the variations of $0.01 \AA$ in structures determined from different sets of isotopic speeies. If instead, we obtain the structure only from the $r_{s}$ coordinates and make no attempt to reproduce the $I_{o}$ values, the structure is independent of the isotopic species used in the determination. The variation in the struetures obtained from different sets of isotopic species appears to depend only on the uncertainties in the rotational constants, and in some examples is less than $0.00005 \AA$. In addition, the accuracy is independent of the mass of the substituted atom, and therefore H atoms are located just as accurately as the heavier atoms. The $r_{s}$ structures of $HCN, N_{2}O, OCS, CH_{3}CCH, CH_{3}CN, CH_{3}NC$, and the methyl halides have been determined by the isotopic substitution method. For the first three molecules comparisons can be made with couilibrium data, and it is found that the $r_{s}$ bond lengths are less than $0.002 \AA$ greater than the $r_{e}$. The primary interest in the remainder of the molecules is in the structure of the methyl group. The anomalous separation of the II and D atoms previously found is readily explained and does not appear in the $r_{s}$ structures. The consistency of the results is such that comparisons between molecules can be made with confidence.