Buried volume

In the following years, the percent buried volume, % has emerged as a standard and intuitive parameter able to describe reasonably well the steric properties of NHCs [75]. The is the fraction of the volume of the fust coordination sphere around the metal occupied by a given ligand, see Fig. 1.17 [75]. 

Figure 76 Schematic depiction of percent buried volume f%...

Figure 3 Percent buried volume (%VgJ, steric parameter of some common NHC ligands computed from the DFT-optimized geometries of [(NHC)lr(CO)fl] complexes in which d=2. iO A and R = 3.5 For comparison purposes, the values of two...

To address this difficulty, Nolan, Cavallo, and co-workers introduced the percent buried volume a steric parameter specifically tailored to the steric topology of... 

Table 1 Comparison of the percent buried volume (%V J values in [Pd(NHC)(cin)CI] complexes...

The third dimension in the analysis (depth) is significant because the synchrotron X-rays penetrate deeply in most materials. This has several ramifications. First, buried volumes, such as fluid inclusions, can be analyzed. Second, one needs to know the sample thickness to correct for absorption effects (see quantification discussion below). Third, it is important to minimize the mounting substrate because this material is a source of scattered radiation that contributes to the spectral background. Fourth, the sampling depth depends on the energy of the fluorescence X-ray and therefore is element dependent. This fact can be used to advantage by selecting a sample thickness to achieve optimum sensitivity for the suite of elements of interest. 

FIGURE 14.1 (a) Cone angle and (b) Percent Buried Volume. In both cases, the M—P distance is defined as 228 pm. 

This reference also provides percent buried volumes for a variety of N-heterocyclic carbenes. 28. 

Cavallo and coworkers have shown that the stability of a singlet carbene (with respect to dimerization) can be ascertained via calculation of two key properties of a carbene [23]. The steric bulk is quantified using percent of buried volume, %Vbur (shown later) [24], while the electronic nature is quantified using the singlet-triplet energy gap (Es-x)- It was shown that a linear correlation = 0.93 or... 

Figure 1.17 Percent of buried volume for characterizing the steric properties of NHC ligands [24].

The initial intuition that steric properties of NHCs could be modulated and could impact catalytic behavior stimulated the development of steric descriptors to quantify the steric requirement of different NHCs and, possibly, to compare them with tertiary phosphines. For obvious reasons, the Tolman cone angle [23] and related descriptors [24-36], largely used to measure the steric property of phosphines, could not be used for NHCs since they are not cone shaped. After some initial attempts such as the fence model [37], work in the field mostly converged on the percent buried volume, %14mr> 21s a standard and intuitive descriptor (in line with the main philosophy used by Tolman to develop the cone angle) able to describe reasonably well the steric bulkiness of NHCs [9,22,38-40]. 

While the Al angle and the percent of buried volume do not correlate with the P-( )/a ratio, the Ah angle proves to be nicely related to the regioselectivity of the process (Figure 5.17) [32]. To the best of our knowledge, it is the first time that this structural descriptor is correlated successfully to an observed reactivity... 

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