Determination of Molecular Structures from Ground State Rotational Constants

Abstract

Kraitchman has shown that a single isotopic substitution on an atom is sufficient to determine directly the coordinates of that atom with respect to the principal axes of the original molecule. Kraitchman's formulas represent exact solutions of the equations for the equilibrium moments of inertia. However, the effects of the zero-point vibrations are such that the coordinates obtained by substitution from the ground state moments of inertia I0 are systematically less than r0. These coordinates have here been called r (substitution) or rs, and it is found that rs≃(r0+re)/2, and Is= ∑ imirsi2≃(I0+Ie)/2. In the usual method of solution, the coordinate of one atom is determined from the equation for I0, and therefore the difference I0—Is must be made up by this one coordinate. This introduces a large error in the structures normally determined from ground state constants, and results in variations of 0.01 A in structures determined from different sets of isotopic species. If instead, we obtain the structure only from the rs coordinates and make no attempt to reproduce the I0 values, the structure is virtually independent of the isotopic species used in the determination. The variation in the structures obtained from different sets of isotopic species appears to depend only on the uncertainties in the rotational constants. 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 rs structures of HCN, N2O, OCS, CH3CCH, CH3CN, CH3NC, and the methyl halides have been determined by the isotopic substitution method. For the first three molecules comparisons can be made with equilibrium data, and it is found that the rs bond lengths are no more than 0.002 A greater than the re. The primary interest in the other molecules studied is in the structure of the methyl group. The anomalous separation of the H and D coordinates previously found is readily explained and does not appear in the rs structures. The consistency of the results is such that comparisons between molecules can be made with confidence.

The Structure of the Other Rotamer of Formic Acid, cis-HCOOH1,2

“…From Kraitchman's equations the a-coordinate of Hi, am (see Fig. 2 for numbering of the atoms), was found to be imaginary, and the a-coordinate of C, ac, was found to be 0.0788 Ä, which is less than the minimum value (0.15 Ä) that Costain [15] has suggested can be reliably determined from Kraitchman's equations. Accordingly these two coordinates were determined as follows: am was fixed using the double substitution method of Krisher and Pierce [16] on the isotope pairs (DCOOH, HCOOH) and (DCOOD, HCOOD).…”

Thioamide spectroscopy: long path length absorption and quantum chemical studies of thioformamide vapour, CHSNH2/CHSND2

“…Table 1 presents the results of the structural calculations for the x ' A ' state along with the bond lengths and bond angles derived from microwave analyses (3). The calculated values are strictly re quantities where each of the nuclei are at the bottoms of their potential wells while the results of the microwave analyses are r , substitution quantities (20) and usually re < r , . The agreement is satisfactory with the largest difference in a bond length being 0.027 A for C-N. At this level of computation, thioformamide was found to be strictly planar at the nitrogen centre.…”

Microwave Spectrum, Geometry, and Hyperfine Constants of PdCO

“…Fitted Substitution (r I ) Structure. The contribution of vibrational effects to the measured moments of inertia is partially accounted for by the inclusion of a vibration-rotation parameter ( ), which is taken to be independent of isotopomer: 31 The same assumption is made in the conventional substitution method (r s ), 32 and where principal moments of several isotopic species have been obtained (as in PdCO), the resulting structures should be the same. Such a fit was carried out, and the resulting r I geometry is also in Table 3.…”