6. MÉTODO
7.4 Registro visual
We reanalyzed the earlier electron diffraction experimental data on CrCl2 [3]. We did not
feel comfortable with the conclusions of that publication after learning that the vapors of chromium dichloride might have contained trimeric species as well besides the monomers and dimers that were taken into account in that analysis [2]. Therefore, taking into consideration the computed structures of the dimer and trimer, we introduced certain constraints into the electron diffraction analysis about the bond length differences of these species and the monomer. Similarly, we also accepted some of the bond lengths of the oligomers from computation, in order to decrease the number of refineable parameters in the ED analysis.
2.14.1
Experimental Details
A sample of CrCl2 was provided by Professor Herald Sch¨afer from the University of
M¨unster [100]. CrCl2 is a rather involatile solid; hence, high-temperature experimental
conditions were needed for the ED analysis. The diffractometer used was the ’Budapest Apparatus’ [101, 102] with a high-temperature molybdenum nozzle used to inject the sample [103] into the diffraction chamber. The nozzle temperature was set to 1170±50 K. Because the CrCl2 vapor may be complex, the combined electron diffraction/quadrupole
mass spectrometric technique was utilized [102,104]. The wavelength of the electron beam was 0.04911 ˚A, and the two nozzle-to-plate distances were 189.29 mm and 497.66 mm. The ranges of intensity data used at 50 cm and 19 cm were 2.00 ≤ s ≤ 14.00 ˚A−1 and
9.25 ≤ s ≤ 29.00 ˚A−1 (s = 4πλ−1sin1
2θ, where λ is the electron wavelength and θ is
the scattering angle), respectively. The data intervals were ∆s = 0.125 and 0.250 ˚A−1,
respectively.
2.14.2
Least-Squares Refinement
We first needed the mean amplitudes of vibration from our monomer, dimer, and trimer global minima before any least-squares treatment of our system began. To accomplish this, we first performed harmonic vibrational calculations on the global minima to obtain the Hessian in Cartesian coordinates. This force-field along with the respective atomic motions were used to carry out a normal coordinate analysis and calculate the mean amplitudes of vibration through the use of the ASYM20 software package [105].
The least-squares method was applied to the molecular intensities in the form of the corresponding equation: sM(s) = X i X j6=i |fi(s)||fj(s)| B(s) cos[ηi(s)−ηj(s)] exp(− 1 2l 2 ijs2) sin[s(rij −κijs2)] (2.86)
where|f(s)|andη(s) are the absolute values and phases of the complex electron scattering angles [106,107],rij are the internuclear distances, lij andκij are the corresponding mean
amplitudes of vibration and asymmetry constants, andB(s) is the background scattering. The least-squares refinement was done through the use of a modified version of the KCED software package [108].
Our strategy for the least-squares treatment was the following: we accepted as con- straints, at least at the initial stages of the refinement, all the differences of the different
cluster bond lengths from that of the monomer. It is well known that the physical mean- ing of bond lengths coming from different techniques is different [109] and simply taking over bond lengths from the computation (equilibrium bond length, rM
e ) to the analysis
of electron diffraction data (where we determine thermal average bond lengths, rg) would
be erroneous. However, taking the differences of bond lengths approximately cancels the difference between their physical meaning, and therefore, their use as constraints is an accepted procedure. The stretching vibrations of metal halides are usually anharmonic, and this influences the molecular intensities. The so-called asymmetry parameter, κ, de- scribing the stretching anharmonicity, can usually be refined. However, with so many closely spaced bond lengths this was impossible; therefore, we assumed the asymmetry parameter based on other transition metal dihalides [110].
Furthermore, we also accepted the bond angles of the dimer and trimer from the computation. We also carried out normal coordinate analyses based on the computed frequencies and force fields of all three species, in order to calculate vibrational amplitudes. These amplitudes were used as starting parameters, and many of them were later refined during the analysis. The parameters that were refined at the first stages of the analysis were the bond length and the vibrational amplitudes of the monomer molecule, the vapor composition, and the vibrational amplitudes of the other chromium-chlorine bond lengths grouped together with the monomer amplitude. We also refined the amplitudes of the most important nonbonded distances. The analysis was performed with the so-called static analysis, meaning that a thermally averaged structure was refined. Such a structure suffers from the shrinkage effect and usually has a lower symmetry than the equilibrium structure. Therefore, we introduced and refined the parameters describing the puckering and bending motions of the dimers and trimers.
We found that with the above constraints, the agreement between the experimental and theoretical distributions was not satisfactory, especially in the region of the bond length, indicating that the constrained bond length differences did not quite correspond to the measured structures. Therefore, we tried to carefully refine them, and they usually refined to somewhat smaller values than the computed ones. Since the computed bond length differences were not exactly the same from different levels of computations, we decided that allowing to refine these values was justified. Further, we let the bond angle of the monomer and those of the dimer also refine. They stayed close to the computed values.