Superposition method, potential energy

Basis set superposition error (BSSE) is a particular problem for supermolecule treatments of intermolecular forces. As two moieties with incomplete basis sets are brought together, there is an unavoidable improvement in the overall quality of the supermolecule basis set, and thus an artificial energy lowering. Various approximate corrections to BSSE are available, with the most widely used being those based on the counterpoise method (CP) proposed by Boys and Bemardi [3]. There are indications that potential energy surfaces corrected via the CP method may not describe correctly the anisotropy of the molecular interactions, and there have been some suggestions of a bias in the description of the electrostatic properties of the monomers (secondary basis set superposition errors). 

Considerable use continues to be made of classical trajectory calculations in relating the experimentally determined attributes of electronically adiabatic reactions to the features in the potential energy surface that determine these properties. However, over the past 3 or 4 years, considerable progress has been made with semiclassical and quantum mechanical calculations with the result that it is now possible to predict with some degree of confidence the situations in which a purely classical approach to the collision dynamics will give acceptable results. Application of the semiclassical method, which utilises classical dynamics plus the superposition of probability amplitudes [456], has been pioneered by Marcus [457-466] and by Miller [456, 467-476],... 

It was recognized early on that the binding energy of the benzene dimer is quite sensitive to computational method. The potential energy surface of 77 is completely repulsive at the HF level, as well as with any DFT that does not include a dispersion correction, such as B3LYP. " Furthermore, the weakly bound benzene dimer is susceptible to basis set superposition error and counterpoise corrections are likely to be necessary. ... 

Calculated DFT properties listed in Table 1 were obtained from the fit of the ground-state potential energy curves to 12 points calculated around the energy minimum [32]. Dissociation energy has been corrected for basis set superposition error by a standard counterpoise technique. The local approximation to the exchange and correlation gives the best fit to bond distances, theoretical values differ by no more than 0.03 A (4%) from the experimental ones (see Table 1). Vibrational frequencies are also predicted to lie within 1 % off the experiment. One should remember, however, that other advanced quantum chemical methods give equally satisfactory results for these, basicaly one-electron quantities and that inclusion of nonlocal effects does not improve the DFT predictions. The dipole moment, fi, is much more sensitive... 

The results of Harrison and Bartlett illustrate that the problem of large correlated BSSE pertains to methods other than Mpller-Plesset, e.g., coupled cluster approach. Baum and Finney carried out their correlated calculations of the water dimer using a Cl procedure. They advocated using basis sets of high enough quality that the BSSE is reduced so as to minimize distortion of the potential energy surface, but noted the difficulty in achieving such low superposition error at correlated levels. 

The second difficulty with the superposition method is obtaining expressions for 0, and Z,. As we noted earlier, the natural starting point is to truncate a Taylor expansion for the potential energy around each minimum at second order giving the harmonic approximation. This truncation... 

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