Structure determination from rotational constants

The effect of low temperatures affecting the ortho para ratio is more important for light molecules, such as F and 2H2, than for heavy ones, such as 19F2 and 14N2. The reason is that the separation of the J= 0 and J= 1 levels is smaller for a heavier molecule and a lower temperature is required before a significant deviation from the normal ortho para ratio is observed. 

5 Rotational Raman spectra of symmetric and asymmetric rotor molecules 

For a symmetric rotor molecule the selection rules for the rotational Raman spectrum are 

For asymmetric rotors the selection rule in. / is A./ = 0, 1, 2, but the fact that K is not a good quantum number results in the additional selection rules being too complex for discussion here. 

Measurement and assignment of the rotational spectrum of a diatomic or other linear molecule result in a value of the rotational constant. In general, this will be B0. which relates 

The effect of low temperatures affecting the ortho para ratio is more important for light 

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Discussion of the answers to questions like these are the mark of careful analysis. There is a wealth of data and a large number of excellent structure determinations from rotational constants in the literature. 

Although gold(I) fluoride has not been isolated, it has been prepared by laser ablation of Au metal in the presence of SFg. From its microwave spectrum, an equilibrium Au—F bond length of 192 pm has been determined from rotational constants. Yellow AuCl, AuBr and Aul can be made by reactions 22.151 and 22.152 overheating AuCl and AuBr results in decomposition to the elements. Crystalline AuCl, AuBr and Aul possess zig-zag chain structures (22.80). The halides disproportionate when treated with H2O disproportionation of Au(I) (equation 22.153) does not parallel that of Cu(I) to Cu and Cu(II). 

The principal application of the Kraitchman equations [Eq. (9)1 is for the determination of the atomic coordinates, at, bSi and cs. From a study of the rotational spectrum of the parent and of a species with single isotopic substitution the coordinates of the substituted atom may be determined. These coordinates are referred to as substitution coordinates or rs coordinates. Each new species yields new coordinates, and since all of the coordinates are in the same coordinate system, the calculation of substitution or rs bond distances and bond angles is a simple process. Costain,s demonstrated that there are definite advantages to the use of the Kraitchman equations to obtain molecular parameters. These advantages are sufficient to make the use of Kraitchman s equations the preferred method of structure determination from ground-state rotational constants. 

The simplest, most direct, and most precise determination of bond distances and bond angles from rotational constants is from equilibrium values of these constants. Equilibrium parameters have a well-defined interpretation and are virtually invariant to isotopic substitution. Unfortunately, the required spectra in the first excited vibrational states are nearly always very difficult to obtain. In addition, the rotational constants must be free of the effects of perturbations and resonances. As a result, equilibrium structures have been obtained only for diatomic molecules and a few small polyatomic molecules. An example is the structure of S02 obtained by Morino et al.19 (Table 1). Also shown in the table is the approximate re structure called the rm structure by Watson.17... 

In the third group of molecules for which complete r, structures have not been obtained are those for which the number of independent rotational constants available is less than the number of independent parameters. In these cases some of the structural parameters must be obtained from other data or assumed. The most logical source of other data is an electron diffraction investigation. Unfortunately, the distance or angle parameters determined by electron diffraction studies are not the same as those obtained from rotational constants. (See Laurie, this volume, Kuchitsu and Cyvin,2 and Kuchitsu.2S) This lends an extra degree of uncertainty to this procedure. 

However, even for a small molecule such as HgCO, determination of the rotational constants in the v = 1 levels of all the vibrations presents considerable difficulties. In larger molecules it may be possible to determine only Aq, Bq and Cq. In such cases the simplest way to determine the structure is to ignore the differences from A, and Cg and make sufficient isotopic substitutions to give a complete, but approximate, structure, called the Tq structure. 

Quadrupole coupling constants for molecules are usually determined from the hyperfine structure of pure rotational spectra or from electric-beam and magnetic-beam resonance spectroscopies. Nuclear magnetic resonance, electron spin resonance and Mossbauer spectroscopies are also routes to the property. There is a large amount of experimental data for and halogen-substituted molecules. Less data is available for deuterium because the nuclear quadrupole is small. 

Contributions in this section are important because they provide structural information (geometries, dipole moments, and rotational constants) of individual tautomers in the gas phase. The molecular structure and tautomer equilibrium of 1,2,3-triazole (20) has been determined by MW spectroscopy [88ACSA(A)500].This case is paradigmatic since it illustrates one of the limitations of this technique the sensitivity depends on the dipole moment and compounds without a permanent dipole are invisible for MW. In the case of 1,2,3-triazole, the dipole moments are 4.38 and 0.218 D for 20b and 20a, respectively. Hence the signals for 20a are very weak. Nevertheless, the relative abundance of the tautomers, estimated from intensity measurements, is 20b/20a 1 1000 at room temperature. The structural refinement of 20a was carried out based upon the electron diffraction data (Section V,D,4). 

Most of the force fields described in the literature and of interest for us involve potential constants derived more or less by trial-and-error techniques. Starting values for the constants were taken from various sources vibrational spectra, structural data of strain-free compounds (for reference parameters), microwave spectra (32) (rotational barriers), thermodynamic measurements (rotational barriers (33), nonbonded interactions (1)). As a consequence of the incomplete adjustment of force field parameters by trial-and-error methods, a multitude of force fields has emerged whose virtues and shortcomings are difficult to assess, and which depend on the demands of the various authors. In view of this, we shall not discuss numerical values of potential constants derived by trial-and-error methods but rather describe in some detail a least-squares procedure for the systematic optimisation of potential constants which has been developed by Lifson and Warshel some time ago (7 7). Other authors (34, 35) have used least-squares techniques for the optimisation of the parameters of nonbonded interactions from crystal data. Overend and Scherer had previously applied procedures of this kind for determining optimal force constants from vibrational spectroscopic data (36). 

The purpose of this report is to demonstrate the ease with which highly accurate equilibrium structures can be determined by combining laboratory microwave data with the results of ab initio calculations. In this procedure, the effects of vibration-rotation interaction are calculated and removed from the observed rotational constants, Aq, Bq and Cq. The resulting values correspond to approximate rigid-rotor constants and and are thus inversely... 

Five isotopomers of Sia were studied in Ref (20), and are labeled as follows Si- Si- Si (I) Si- Si- Si (II) Si- Si- Si (III) Si- "Si- Si (IV) Si- Si- °Si (V). Rotational constants for each (both corrected and uncorrected for vibration-rotation interaction) can be found towards the bottom of Table I. Structures obtained by various refinement procedures are collected in Table II. Two distinct fitting procedures were used. In the first, the structures were refined against all three rotational constants A, B and C while only A and C were used in the second procedure. Since truly planar nuclear configurations have only two independent moments of inertia (A = / - 4 - 7. = 0), use of B (or C) involves a redundancy if the other is included. In practice, however, vibration-rotation effects spoil the exact proportionality between rotational constants and reciprocal moments of inertia and values of A calculated from effective moments of inertia determined from the Aq, Bq and Co constants do not vanish. Hence refining effective (ro) structures against all three is not without merit. Ao is called the inertial defect and amounts to ca. 0.4 amu for all five isotopomers. After correcting by the calculated vibration-rotation interactions, the inertial defect is reduced by an order of magnitude in all cases. 

In a previous study of cyclic SiCs, a residual inertial defect of only slightly smaller magnitude was found, despite the fact that an extremely high level of calculation (surpassing that in the present study) was used to determine the vibration-rotation interaction contributions to the rotational constants. This was subsequently traced to the so-called electronic contribution, which arises from a breakdown of the assumption that the atoms can be treated as point masses at the nuclear positions. Corrections for this somewhat exotic effect were carried out in that work and reduced the inertial defect from about 0.20 to less than 0.003 amu A. However, the associated change in the rotational constants had an entirely negligible effect on the inferred structural parameters. Hence, this issue is not considered further in this work. 

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