Bond order calculation

Bond orders calculated from experimental bond lengths (122i. 

In Table 1-9 we have collected only the 7r-bond orders calculated by allvalence-electrons methods and compared their values with those deduced from experimental bond lengths. Both data are indicative of an aromatic molecule with a large dienic character. The 2-3 and 4-5 bonds especially present a large double-bond character, whereas both C-S bonds are relatively simple. 

The indazole molecular structure (Figure 11) shows the tautomeric proton bonded to N-1 (1//-indazole. Section 4.04.1.5.1). A linear correlation between the bond lengths and the bond orders calculated by the CNDO/2 method was observed (74T2903). 

The spectrochemical data on 1,2- and 2,1-benzisoxazoles were reviewed in 1962 and reported on in greater detail in 1967 62HC(l7)l,p. 159, 62HC(17)l, p. 213, 67AHC(8)277). These reviews discuss tt-electron densities, bond order calculations and dipole moment studies for these ring systems. 

Typical coupling constants for isothiazoles are given in Table 5. The electronegative nitrogen atom reduces 3,4 and V3.5 from the values of 3.50 Hz and 0.27 Hz, respectively, in thiophene. The V values correlate quite well with rr-bond orders calculated by MO methods (74CJC833). 

The tables below give some examples of atomic charges and bond orders calculated by various methods as a function of the basis set at the HF level of theory. It is evident that the Mulliken and Ldwdin methods do not converge as the basis set is increased, and the values in general behave unpredictably. Especially the presence of diffuse functions lead to absurd behaviours, as the aug-cc-pVXZ basis sets illustrate for CH4. Note also that... 

The i.r. and Raman spectra of the cyclic phosphate (104) and its SbCls complex have been assigned and force constants and bond orders calculated. The high frequency of vp o (1308 cm ) may be due to a strong... 

Table 4 Correlation of the number of classical structures with calculated bond lengths for Ceo and Cn. The bond environment column describes the arrangements of the carbon atoms which have the bond in common. The column labelled with a f is the bond order calculated using resonance theory as described in the text.

Bond orders calculated on this basis for the various types of two-center link in anions BgHg (100), BgHg " (99), and BjoHio (57) are... 

Table III compares the bond orders calculated both by the HMO and by the semiempirical methods. The geometry of a molecule may be crucial to quantum chemical calculations it is not known for 4. Whereas Dewar et used an iterative procedure (correlation between bond lengths and bond orders), other workers preferred standard geometry or a combination of naphthalene and furan values. ...

Figure 6.9 shows charges and bond orders calculated for an enolate (the conjugate base of ethenol or vinyl alcohol) and for a protonated enone system (protonated... 

Fig. 6.9 Atom charges and bond orders calculated using the AMI, PM3 and HF/3-21G( ) methods. In a and b the charges and bond orders are all from the Mulliken approach. In c and d the charges are all electrostatic potential charges, and the bond orders are Mulliken for AMI and PM3, and Lowdin for HF/3-21G< ) (Lowdin bond orders were not available for AMI and PM3 from the Spartan program used). Note that charges and bond orders involving hydrogens have been omitted...

Figure 7.8 shows charges and bond orders calculated for an enolate and a protonated enone system (the same as in Fig. 6.9), using B3LYP/6-31G and HF/ 3-21G. The results are qualitatively similar regardless of whether one uses B3LYP or HF, or Mulliken versus electrostatic potential/Lowdin. This is in contrast to the... 

Fig. 7.8 Atom charges and bond orders calculated using B3LYP/6-31G and FLF/3-21G methods. Note that charges and bond orders involving hydrogens have been omitted...

If one wants information on bonding that is based on more than the proximity of nuclei, this can be extracted from the wavefunction by requesting that after a calculation of, say, energy or optimized geometry, a bond order calculation be performed, or the wavefunction can be used for an AIM calculation (possibly by a specialized program). 

Indiscriminate application of the ndc shows it to be in fairly good agreement with most of the high nuclearity clusters (Table VI). Furthermore, the metal-metal bond orders calculated in this way compare much more reasonably with that expected in the pure metals. 

Reacting bond orders, calculated and experimental isotope effects in proton transfer reactions... 

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