Polar bonds lengths

Figure B3.1.9 [83] displays the errors (in pieometres eompared to experimental findings) in the equilibrium bond lengths for a series of 28 moleeules obtained at the FIF, MP2-4, CCSD, CCSD(T), and CISD levels of theory using three polarized eorrelation-eonsistent basis sets (valenee DZ tlu-ough to QZ).

The experimental bond length is 1.476. Both the triple zeta basis set and multiple polarization functions are needed to produce a very accurate structure for this molecule. 

The experimental value for the dipole moment of CO is 0.122 D, with the polarity C 0+, for a bond length of 1.1281 A. Calculated values with the aug-cc-pVXZ basis sets are given in Table 11.21. Some other results using other basis sets are shown in Table 11.22. 

Nitrones are a rather polarized 1,3-dipoles so that the transition structure of their cydoaddition reactions to alkenes activated by an electron-withdrawing substituent would involve some asynchronous nature with respect to the newly forming bonds, especially so in the Lewis acid-catalyzed reactions. Therefore, the transition structures for the catalyzed nitrone cydoaddition reactions were estimated on the basis of ab-initio calculations using the 3-21G basis set. A model reaction indudes the interaction between CH2=NH(0) and acrolein in the presence or absence of BH3 as an acid catalyst (Scheme 7.30). Both the catalyzed and uncatalyzed reactions have only one transition state in each case, indicating that the reactions are both concerted. However, the synchronous nature between the newly forming 01-C5 and C3-C4 bonds in the transition structure TS-J of the catalyzed reaction is rather different from that in the uncatalyzed reaction TS-K. For example, the bond lengths and bond orders in the uncatalyzed reaction are 1.93 A and 0.37 for the 01-C5 bond and 2.47 A and 0.19 for the C3-C4 bond, while those in... 

The choice of basis set in ab initio calculations has been the subject of numerous theoretical studies. Early SCF calculations utilized mainly spht-va-lence basis sets such as 3-21G and 4-31G. The importance of inclusion of d polarization functions on sulfur atoms has been stressed by several authors. For instance, Suleimenov and Ha found that the omission of d polarization functions leads to a substantially lower barrier for the internal rotation ( 16 kj mol for the central bond of H2S4) and produces an unreahstically large S-S bond length for the most stable rotamer [4]. In general, the use of... 

Bond polarity also contributes to bond length because partial charges generate electrical attraction that pulls the atoms closer together. For example, notice in Table 9 that C—O bonds are slightly shorter than either C—C or O—O bonds. This is a result of the polarity of the C—O bond. 

Figure 18. Contour plots of the potential energy surfaces of the first three electronic states of H2O. The polar plots depict the movement of one H atom around OH with an OH bond length fixed at 1.07 A. Energies are in electron volts relative to the ground electronic state. The X and B states are degenerate at the conical intersection (denoted by (g)) in the (a) H—OH geometry and (b) H—HO geometry. Reprinted fix)m [75] with permission from the American Association for the Advancement of Science.

Final detennination of the structure was made by proposing a structural model with Cu sitting in threefold hollow sites and O atoms on atop sites with respect to the Cu atoms (Fig. 27.16). A program, FEFFIT, was used to analyze the data (Stem et al., 1995). This calculates the phase and amplitude parameters for the various backscatters. The EXAFS for the parallel polarization could be fitted six Cu-Cu interactions at a bond distance of 2.67 A and three Cu-Pt interactions at 2.6 A. For the perpendicular polarization, the data could be fitted one Cu-0 interaction at 1.96 A and three Cu-Pt interactions at 2.6 A. The Cu-Pt bond length is shorter than the sum of the metallic radii of Cu and Pt, which is 2.66 A. This indicates a Cu oxidation state different from zero, which agrees with the XANES results. 

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