Bonding distance, definition

Given the above definition of a bond distance, we can analyze species lifetimes. The lifetime of all species is less than 12 fs above 2.6g/cc, which is roughly the period of an O-H bond vibration (ca. 10 fs). Hence, water does not contain any molecular states above 75 GPa and at 2000 K but instead forms a collection of short-lived transient states. The L simulations at 2.6g/cc (77 GPa) and 2000 K yield lifetimes nearly identical to that found in the S simulations (within 0.5 fs), which indicates that the amorphous states formed from the L simulations are closely related to the superionic bcc crystal states found in the S simulations. 

Compounds 39, 42 and 44 exist as discrete monomeric molecules. The Zn—C bond distances are close to the values of simple diafkylzinc compounds obtained from gas-phase electron diffraction studies and are also close to the values predicted by DFT computational studies . Because the zinc atoms in 39, 42 and 44 are located at special positions in the crystallographic unit ceU (at 0.25, 0.25, 0.5 in 39, and at 0, 0, 0 in both 42 and 44) the C—Zn—C bond angles are by definition 180° as a consequence of space-group symmetry. Compound 43 forms dimers in the solid state via hydrogen bridges between... 

This is the inner boundary condition. It has two serious flaws. The reaction between A and B may not occur at a rate very much faster than the reactants can approach one another. As was discussed in Sect. 3.1, this can lead to an appreciable probability of formation of the species (AB), which can be better described as an encounter pair. This difficulty was neatly handled by Collins and Kimball [4] and is discussed in Sect. 4 and Chap. 8 Sect. 2.4. The other flaw is the specification of one definite distance at which reaction occurs, the encounter distance. Even if the reaction proceeds with similar rates when the separation distance varies by 0.1nm (the largest likely variation of bond distance), this will be a small variation compared with the encounter distance, which is typically >0.5nm. Means to circumvent this difficulty are discussed in Chap. 8 Sect. 2.4 and Chap. 9 Sect. 4. 

The structures of some square planar and tetrahedral complexes (314) have been definitely ascertained by means of X-ray analysis.2259-2266 Ni—N and Ni—O bond distances in these four-coordinate complexes are in the range 190-200 and 184-190 pm respectively, and do not differ substantially on going from one complex to another. The structures of two dinuclear complexes were reported to contain both bridging and terminal salicylaldimines (315).2269,2270... 

In contrast to outer-sphere reactions, the simple observation that a reaction occurs by an inner-sphere mechanism necessarily introduces an element of structural definition. The relative dispositions of the oxidizing and reducing agents are immediately established and, except for structurally flexible bridging ligands such as NC5H4(CH2) C5H4N, the internuclear separation between redox sites can be inferred from known bond distances. Even so, bimolecular inner-sphere reactions necessarily occur by a sequence of elementary steps (Scheme 2) and the observed rate constant may include contributions from any of the series of steps. 

There is evidence from Raman studies that oxalate coordinates in a bidentate manner without elimination of a peroxo group [6], Possibly here, as for the picolinate complex, the question of the coordination could be more definitively answered by observation of 13C coordination-induced NMR chemical shifts. The x-ray structure for the oxalate complex shows that the two V0ox bond distances are very different. The VO distance to the equatorial oxalato oxygen is 2.060(4) A compared to 2.251(4) A to the apical oxygen [15], Similarly long distances are found in the picolinato complex (VOpic 2.290 A [16]) and other complexes [20], These distances are indicative of relatively weak bonds to the apical oxygens, and dissociation of that bond... 

One can dissociate the NO dimer simply by increasing the N-N bond distance to infinity. One can also require that during that process the molecule remain on the singlet surface, which by definition has a wavefunction and thus density that has equal spin-up and spin-down components everywhere in space. We are not interested in spin-restricted dynamics. We are interested in the much more balanced chemical dynamics that treats each half of the dissociated dimer correctly in DFT via a spin-polarized calculation. This decision must be made independent of whether or not one wants to use spatial symmetry to reduce the cost of the calculation. Spin-unrestricted DFT chemical dynamics will be called balanced in the following. 

All monochlorinated saturated cyclic hydrocarbons from propane to hexane have been studied in the gas phase. The data in Table 25 demonstrate a definite correlation between the ring size and the C—Cl bond distances. The exocyclic bonds lengthen steadily from 174.0(11) pm in the three-membered ring to 181.0(4) pm in the five-membered ring and... 

The BOs may be useful to evaluate the structural stability comprehensively, because the BO parameter depends on both the bonding distances and the number of the bonding pair. The total BOs for each structure shown in Figure 13.10 are calculated by using the following definition ... 

Bond distances in A, bond angles in deg. From Reference 80. Bond angle for definition see Figure 3. 

Crystals of 5 so far have always been twinned, so accurate bond lengths could not be determined, but the X-ray analysis showed definitely that the compound is monomeric. The structure was confirmed by an electron-diffraction study, carried out at the University of Oslo. A representation is shown in Fig. 2 the molecule is planar, with bond distance Si-N 175.3, N-C 140.0, C=C 134.2 pm. The Si NMR spectrum shows that the silicon atom is deshielded (5 = 78.3 ppm) consistent with low coordination at Si. 

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