Bond lengths accuracy

All these calculations require a set of atomic orbitals from which MOs can be calculated (the basis set). The earliest to be used were Slater-type orbitals (STOs) but these are mathematically inconvenient, and the STO-3G minimal basis set, which uses gaussian functions to mimic Slater orbitals, is commonly used. More sophisticated gaussian basis sets, which lead to improved accuracy, carry labels such as 6-31G(d) and 6-31++G(dp). Successive increases in basis set size (STO-3G—>3-21G—>3-31G(d)—>6-311G(3df)) give improved bond-length accuracy. 

Figure 5.17 shows the rotational Raman spectrum of N2 obtained with 476.5 nm radiation from an argon ion laser. From this spectrum a very accurate value for Bq of 1.857 672 0.000 027 cm has been obtained from which a value for the bond length tq of 1.099 985 0.000 010 A results. Such accuracy is typical of high-resolution rotational Raman spectroscopy. 

These difficulties have led to a revival of work on internal coordinate approaches, and to date several such techniques have been reported based on methods of rigid-body dynamics [8,19,34-37] and the Lagrange-Hamilton formalism [38-42]. These methods often have little in common in their analytical formulations, but they all may be reasonably referred to as internal coordinate molecular dynamics (ICMD) to underline their main distinction from conventional MD They all consider molecular motion in the space of generalized internal coordinates rather than in the usual Cartesian coordinate space. Their main goal is to compute long-duration macromolecular trajectories with acceptable accuracy but at a lower cost than Cartesian coordinate MD with bond length constraints. This task mrned out to be more complicated than it seemed initially. 

Fig. 60. Configuration and relevant coordinates of the planar HF dimer in stable and transition configurations. The angles and intermolecular distance are = 9°, 6 = 116°, R = 2.673 A in the stable configuration 0, = 02 = 54.9°, R = 2.S61 k in the transition configuration. The HF bond lengths are constant within an accuracy of 0.003 A.

The usefulness of quantum-chemical methods varies considerably depending on what sort of force field parameter is to be calculated (for a detailed discussion, see [46]). There are relatively few molecular properties which quantum chemistry can provide in such a way that they can be used directly and profitably in the construction of a force field. Quantum chemistry does very well for molecular bond lengths and bond angles. Even semiempirical methods can do a good job for standard organic molecules. However, in many cases, these are known with sufficient accuracy a C-C single bond is 1.53 A except under exotic circumstances. Similarly, vibrational force constants can often be transferred from similar molecules and need not be recalculated. 

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