Counterpoise procedure

The term BSSE was first introduced in 1973 by Liu and McLean (Liu and McLean, 1973). However, as early as 1970 Boys and Bernard (Boys and Bernard , 1970) had proposed the function counterpoise procedure (CP) as a strategy to correct for BSSE. In this procedure the monomer calculations are given the same flexibility that is available to the monomers in the dimer calculation, namely, the monomer energies are evaluated in the complete dimer basis set. The counterpoise-corrected interaction energy then becomes ... 

As seen above, application of the counterpoise procedure or the addition of diffuse functions may result in Rg(nZ) or coAnZ) curves which are better behaved. As another example. Figure 9 shows the harmonic frequency of HCl, computed with the cc-pVnZ and aug-cc-pVnZ basis sets. As for HF, application of the counterpoise correction improves the convergence behavior of computed with the regular sets, although the convergence behavior of the corrected co, s is far from simple. Addition of the set of diffuse functions to the basis as well as use of the counterpoise correction results in a very smooth dependence of on basis set. 

As mentioned earlier in this section, the convergence behavior of computed properties generally becomes less exponential as the quantities become less related to energies. By way of illustration, neither the application of the counterpoise procedure nor the addition of diffuse functions to the basis set improves the convergence behavior of the computed anharmonicities co x of the HF molecule (see Figure 10). Even in this case, however, both the uncorrected and corrected curves appear to be converging to the same limits. 

For strongly bound diatomics like Nj, HF, and HCl, the counterpoise procedure can improve the convergence behavior of r and co, (although the counterpoise-corrected values are not always well represented by a simple exponential formula). For highly ionic molecules like HF and HCl, it was found that addition of diffuse functions to the basis set in addition to the counterpoise correction also improves the convergence of r and co. ... 

Although many researchers ackowledged that there was some inconsistency in using a larger basis set for the complex than for the monomers, there was initial reluctance to accept the counterpoise procedure as a valid means to correct the problem when it was first introduced. The chief source for this skepticism lay in the numerical results. Many of the early calculations of H-bonded complexes relied on fairly small and inflexible basis sets. It is now known that bases of this type tend toward potentials that are much less attractive than the true potential. Limitations of the era also prohibited application of correlation in most cases, eliminating a major attractive component. As a result, the H-bond attractions corresponding to these treatments are much too weak. It was only the superposition errors that were hidden in the calculations that permitted the final results to be even slightly attractive. In other words, if one does not analyze the results carefully, one can easily be misled since the spurious attractive nature of the BSSE can compensate in some sense for the unsatisfactory character of the calculations themselves. 

The energetics of formation of the H20 --H20--HC1 complex are reported in Table 5.31, in a format comparable to that for H20"-HF"HF in Table 5.29. All data were obtained at the MP2 level and are corrected for BSSE by the counterpoise procedure. The three basis sets all contain polarization functions and yield comparable results. The binding of HCl to the pre-formed water dimer (step lb) is considerably more favorable than its binding to a water monomer, as in step 2a. This enhancement is referred to as E p in Table 5.31, and amounts to between 2 and 3 kcal/mol. (The same quantity is identically equal to the enhancement of binding of water to HjO—HCl as compared to HCl.) It is worth noting that whereas the total binding energy in the appropriate row of Table 5.31 is rather insensitive... 

Table 6.2 Characteristics of various complexes, computed at MP2/TZP level, and corrected by counterpoise procedure. ...

The correction for superposition error (BSSE) in the cluster energies for stationary states is calculated using the counterpoise procedure (CP) first described by Boys and. Bernardi " and implemented in Gaussion 03 using the procedure of Dannenberg. ... 

Johansson et al were the first to conclude that the counterpoise procedure overestimates the basis-set superposition error. They proposed to scale the correction by a factor reflecting the reduced number of ghost virtual orbitals available to a monomer in the dimer situation and obtained good agreement with larger basis sets for their STO-3G SCF calculations on hydrogen-bonded systems. Their idea has had few followers and little. Nevertheless, their conclusion that the BSSE is overestimated... 

The counterpoise procedure must be applied in order to avoid the basis-set superposition error. 

Alternate language that one may come across in the literature refers to the process of correcting AT to AE by including the ghost orbitals of each partner as the (Boys-Bernardi) counterpoise procedure.Using the basis set of the full complex at all stages (Eq. 4) is sometimes referred to as the dimer-centered basis set (DCBS) method, whereas discarding the basis functions of the partner for each subunit (Eq. 5) is termed the monomer-centered basis set (MCBS). 

In an effort to design basis sets of small size that could be used with some confidence for molecular interactions, Kolos demonstrated that one could obtain quite reasonable results with a minimal basis set if (1) it is well-balanced and (2) the superposition error is corrected by the counterpoise procedure. By reasonable, it is meant here that the interaction potentials mimic rather closely those calculated with much larger basis sets, also at the Hartree-Fock level. More specifically, Kolos advised against the use of STO-nG for molecular inter-... 

It appears clear that one must correct the superposition error at both SCF and correlated levels via the counterpoise procedure. What one then obtains is the true interaction energy associated with a given basis set and not the... 

Figure 5 Calculated SCF interaction energies, corrected by counterpoise procedure, in water dimer. (From ref. 42.)...

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