Bond-distance calculation

Geometries Calculated bond distances are typically within 0.02A of experimental values and bond angles within 2°. Geometries for transition states are not available from experiment. Here it must be assumed that the calculations provide descriptions of similar quality to those for equilibrium geometries. 

Table 4.5 Calculated bond distances (in A) and dissociation energies (in eV) for linear AuCN and Au(CN)2 (from unpublished results).

Figure 3. Calculated bond distance (A) in anilinyl and methyl-substituted anilinyl...

Figure 4. Calculated bond distances and spin densities of phenoxyl. Data (from left to right) are from (36, 40a and b).

From Table 13.10 we see that the bond distances are reproduced better in this case than with the ST03G basis. We see that the break in the trend between CH and CH2 again appears, and we continue to attribute it to the change in the important atomic configuration at this juncture in the list. The calculated bond distances are about 4.2% high. The success in calculating bond energies is more difficult to assess, since there is considerably more imcertainty in the experimental results. 

TABLE 2.12. CALCULATED BOND DISTANCES AND ANGLES FOR NITRONATES... 

The Hartree-Fock STO-3G model provides a generally reasonable account of equilibrium geometry in main-group hydrides. The worst results are for alkali metal compounds where, with the exception of NaH, calculated bond distances are significantly shorter than experimental values. Significant errors also appear for systems with two highly electronegative elements, e.g., for F2, where calculated bond distances are shorter than experimental values. 

As with calculated bond distances, Hartree-Fock bond angles show significant improvement in going from STO-3G to 3-2IG basis sets, and lesser improvement in moving on to 6-3 IG. Either of the latter two Hartree-Fock models appears to be suitable for bond angle calculations on moderate size organic molecules. 

The 6-3IG model turns in a poor performance. With a single exception, all bonds are longer than the experimental distances, sometimes by as much as 0.1 to 0.2A. STO-3G and 3-2IG models do not exhibit such consistency, and calculated bond distances for both are often quite far from their respective experimental values. Hartree-Fock models cannot be trusted to account for the geometries of organometallic compounds. 

The default criteria in Spartan have been chosen in an attempt to assure that calculated bond distances, bond angles and dihedral angles are within O.OOSA, 0.5° and 1° of their respective exact values. This will normally be sufRcient, but these criteria can be tightened to more closely approach the exact equilibrium geometry. Alternatively, convergence criteria can be loosened to save computation time. 

Table 1 Experimental and Calculated Bond Distances and Experimental Bond Angles in Tris(4-methoxyphenyl)-l,2,3-triazine3...

Calculated bond distances (pm according to Schomaker/Stevenson), Ref. 

TABLE 5. Calculated bond distances Re(A), total bond dissociation energies Do (kcalmol-1) which include ZPE corrections and force constants of the totally symmetric mode ke (Ncm-1) of the molecules EH4 and ECI4, using relativistic gradient-corrected DFT ... 

Calculated Bond Distances r, Binding Energy to the Support Surface, Et, and Frequencies of Re(CO)3/MgO Bonded to MgO at Various Assumed Defect Sites Comparison of Predictions of Density Functional Theory (Hu et al, 1999) and Experimental Results (Triantafillou etal, 1994)a... 

TABLE 23. Calculated bond distances (pm) in M H cage compounds"... 

We may also employ eqn. (29) to estimate the bond numbers in tetragonal boron. Prom Table 3, we have D(l) = 1.672 A, leading to a normalized icosahedral bond number of 0.4776 and an interstitial bond number of 1.0170. Therefore, the average bond number per atom for the icosahedral B atoms, n, 0j, is 0.5068, and the average number of unsynchronized resonance structures for the icosahedral B atoms, is 6.0702. A check of the internal consistency of these numbers is provided by eqn. (28) D(n) = 1.7932 A. This compares with the experimental average icosahedral bond distance of 1.7874 A, which differs from the calculated bond distance by only 0.3 %. 

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