Systematic Comparison of Experimental, Quantum Mechanical, and Molecular Mechanical Bond Lengths for Organic Molecules

Abstract

Ab initio calculations give, with an accuracy depending on the sophistication of the method, a bond length as an equilibrium value, r e. The experimental bond lengths are always vibrationally averaged and may be expressed in different ways (r g, r z, r a, etc.). Since high-quality ab initio calculations now are capable of giving bond lengths that are approximately of experimental accuracy, it is important to be able to interconvert these values. We find that the bond lengths optimized at the TZ2P+f CCSD level may be considered as the converged r e values and that the MM3 and MM4 force fields successfully convert r g to r e values. We also evaluated the performance of quantum mechanics at the 6-31G* MP2 and the 6-31G* B3LYP levels and found that the bond lengths (r e) at the 6-31G* B3LYP level are better than these at the 6-31G* MP2 level for molecules with only first-row atoms. However, the bond lengths for the bonds involving second-row atoms are too long at the 6-31G* B3LYP level, and for these, the 6-31G* MP2 level is recommended. An empirical formula is given for the conversion of the theoretical r e values calculated at these levels to the r g values.

Theoretical investigation of unimolecular decomposition channels of furan4

“…This accuracy is SCHEME 6 typical of B3LYP for equilibrium structures of compounds consisting of first-row atoms. 11 We hope that the method is equally reliable for transition states.…”

“…10 This method has been shown to give reliable structures for molecules consisting of the first-row atoms. 11 Vibrational analyses were carried out, at the same level of theory, to characterize the optimized structures as equilibrium or transition states. Intrinsic reaction coordinate Ž .…”

Ab initio and molecular mechanics (MM3) calculations on alkyl- and arylboronic acids

“…The difference is very large in the case of hydrogen, which has a very small mass and lies high up in the potential well, so the r g value will be larger than r e by about 0.02-0.03 Å . 21 For atoms heavier than hydrogen, the differences are very small in most cases. Both MM3 r g and MM3 r e values are listed in Tables 2-6.…”

Molecular mechanics (MM4) study of amines

“…Ab initio calculations were used to determine molecular mechanics parameters as long ago as 1972, 13 and subsequently they have been used more frequently as computer power increased enough to allow better results to be obtained more easily. [13][14][15][16] From our previous experience, if we can fit the experimental moments of inertia accurately for a group structures, we will also fit the MP2/6-311þþG(2d,2p) calculated structures [which we will hereafter refer to as MP2/B (for big basis)], allowing for the truncation errors 17 in the later [which we then refer to as MP2/ BC or BC (for big basis and corrected)], and for the interconversion of r z and r e structures. In this study, the MP2/BC calculations were used to provide some of the required information when the necessary experimental data were not available or were uncertain.…”