Bond orders analysis

Natural bond order analysis (NBO) is the name of a whole set of analysis techniques. One of these is the natural population analysis (NPA) for obtaining... 

Nalewajski, R. F. and A. Michalak. 1996. Charge sensitivity and bond-order analysis of reactivity trends in allyl-IMoOd Systems Two-reactant approach. J. Phys. Chem. 100 20076-20088. 

Lapid H., Agmon N., Petersen M. K. and Voth G. A. (2005) A bond-order analysis of the mechanism for hydrated proton mobility in liquid water, J. Chem. Phys. 122, 014606. 

Several alternatives to the Mulliken population have been presented that attempt to provide more rigorous estimates of the charges on atoms in molecules or clusters although not all have been applied in chemisorption and catalysis. We quote the Natural Bond Order analysis, and the elegant topological analysis of the electron density or of the electron localization function, ELF, introduced by Becke and Edgecombe. " ELF analysis has... 

Let us now evaluate exo-endo selectivity in cyclopropene addition to benzo[c]heterocycles. On the basis of bond order analysis, the exo addition of cyclopropene to benzo[c]furan was selected over the endo addition while in the case of benzo[c]pyrrole and benzo[c]thiophene, it was suggested that SOI might be responsible for formation of an exo cycloadduct product. The computed activation energies for cyclopropene addition to the benzo[c]-fused heterocycle clearly favors formation of the exo cycloadduct. The activation barrier with benzo[c]furan was... 

Beryllium-silicon bonds are a recent development. They are likewise prepared by the reaction of the metal halide with alkali metal silyls, but unlike the Mg analogues, both of the well-characterized Be examples are base-free. While [(te/T-Bu3Si)BeCl] is oligomeric, the molecular structure of (tert-Bu3Si)2Be features a perfectly linear Si-Be-Si unit. CpBe(SiMe3), prepared from CpBeCl and trimethylsilyllithium in pentane, exhibits an intriguing thermal chemistry. The identity of the primary thermolysis products, Scheme 14, implies the participation of silylene intermediates, a contention supported by DFT/NBO (density functional theory/natural bond order) analysis. ... 

This follows well from a bond order analysis (Eq. (10.7)) of the changing interactions when the molecule moves form its initial state through transition state to final state. This is illustrated in Table 10.7. 

Table 19. Mulliken Charge and Mayer Bond Order Analysis of V10O31H12 Clusters...

Consideration of both the Mayer bond order analysis and the molecular orbital analysis indicates that the Mo-Mo bond order predicted by the p,-LX half-arrow method for [CpMo(p,-02CH)]2(p,-PH2)(p,-H) is much more in accord with the theoretical calculations than is the bond order of two predicted by the half-electron method. A variety of other studies support the use of the p,-LX half-arrow electron-counting method for predicting M-M bond orders in dinuclear compounds [52-59]. In particular, Hoffmann and Albright have used MO theory to analyze the... 

Bond-order analysis of heteronuclear covalent interactions is considerably more complicated, but feasible in principle. An obvious assumption, Rq = y ro(l) ro(2), predicts correct values for d = d Ra and suggests D = pKRlx". The parameter P = x( )/xO) is taken as the ratio of electronegativities x(0 r (i) [19] to compensate for polarization effects. Hence,... 

Scheme 4.34) [108]. According to the experimentally determined bond lengths, a natural bond orbital (NBO) bond order analysis and the calculated nucleus-independent chemical shifts (NICSs), the bowl-shaped circulene 158 can be considered as a fourfold benzoannulated [4] radialene, not a fourfold napthoannulated cyclobutadiene. 

Before we can calculate Nn in a Monte Carlo simulation we need to have a numerical technique that enables us to distinguish between particles in a liquid and solid environment. To this end, we use local bond-order analysis introduced by Steinhardt et al. [11] and applied to study nucleation by Frenkel and coworkers [8, 12, 13]. The advantage of this analysis is that it is only sensitive to the overall degree of crystallinity in the system, but independent of any specific crystal structure. This requirement is important as otherwise we would apply an external biasing potential, that could force the system to crystallize in a specific structure. A second advantage is that these bond-order parameters can be constructed so as to be independent of the reference frame. 

Using this local bond-order analysis we can sample the equilibrium distribution function for the probability P(n) in a Monte Carlo simulation. In all cases we performed Monte Carlo simulations in the isobaric-isothermal (NPT) ensemble. In this ensemble the average of a microscopic quantity A is given by... 

Fig. 27. Structure analysis of two independent crystal nuclei of size n = 100 and 200 from the simulations with parameters = 8 and k = 10. The figure shows the results for the fit parameters for the local bond-order analysis as a function of the distance from the center of mass of the nuclei. The core of the cluster of size n = 100 has a clear bcc signature, where the cluster of size n = 200 shows a clear fee structure...

---