Basis sets convergence errors

It has been pointed out by Dunning [66] that "It is quite possible and even probably that the binding energies computed without the counterpoise correction are closer to the complete basis set limit than the uncorrected values. This situation is due to the fact that BSSE and basis set convergence error are often of opposite sign". Since it cannot be established a priori if that is the case, we have modeled the closest system to our reactant complexes with known experimental binding energy the water dimer. The experimental value for the electronic... 

The basis set convergence error is separate from the accuracy of the particular electronic structure method used to solve the Schrodinger equation (Hartree-Fock, singles and doubles configuration interaction, second-order perturbation theory, etc.). The methods error is defined by... 

Figure 3 Basis set convergence errors in the (a) Hartree carbon, oxveen. and neon atoms...

Figure 4 Basis set convergence errors in Z)c c for HF and valence-CASSCF calculations on the CO molecule...

We now turn our attention to the heart of this article - the use of correlation consistent basis sets in correlated calculations on molecules. It is not our intent here to compare the relative merits of various methods for treating electron correlation. This is addressed in other articles. Rather, our focus is on the convergence of the computed structures, energies, and properties of molecules with basis set, for this allows us to ascertain the basis set needed to obtain a given level of basis set convergence error, both in an absolute sense and in a relative sense. 

Figure 6 Basis set convergence errors in Dc and for RCCSD(T) calculations on the CH molecule and CCSD(T) calculations on the HF, N2, and CO molecules...

Figure 8 Basis set convergence errors in Z>c and r for CCSD(T) calculations on the Ar-HF ( , ) and Ar-FH ( , O) isomers of the ArHF complex. Del , aug-cc-pVnZ , O d-aug-cc-pVnZ...

From the data plotted in Figure 9 it is clear that doubly augmented sets are required to obtain reasonable basis set convergence errors in Ne2. The basis set errors for the aug-cc-pV/iZ sets are significantly larger than those for the d(t)-aug-cc-pVnZ sets even for n =6. Calculations with the aug-cc-pVDZ set yield only 35% of De(Ne2) obtained at the... 

Figure 11 Basis set convergence errors in A rxn and AFb for R-UCCSD(T) calculations on the F -f- H2 and O H- H2 reactions with the standard ( , ) and augmented ( , O) correlation consistent basis sets...

In Table 25 the PAgS of hydrogen fluoride, carbon monoxide, and ammonia calculated with the CCSD(T) method are listed. Both the standard and augmented correlation consistent basis sets have been considered. The corresponding basis set convergence errors are plotted in Figure 12. A number of conclusion can be drawn from the data in Table 25 and Figure 12. The first is that the accuracy of the CCSD(T) method is at least comparable to the measured values of the electronic proton affinities - in all cases the calculated proton... 

Figure 12 Basis set convergence errors in the proton affinities (PAc) of HF, CO, and NH3 aug-cc-pVnZ ( ) and aug -cc-pV/iZ (O) basis sets...

The augmented correlation consistent basis sets, when combined with coupled cluster or multireference configuration interaction methods, have been found to provide an accurate description of atomic electron affinities. The calculated EAs of boron and fluorine are summarized in Table 26 and the basis set convergence errors are plotted in Figure 13. The values of the EAs of these two atoms, 6.39 0.23 kcal mol (B) and 78.82 kcal mol" (F), respectively (corrected for spin-orbit effects), bracket the EAs of the other first-row atoms. 

There have been only a few calculations of the electron affinities of molecules with the correlation consistent basis sets. The EAs of O2 and CN from RCCSD(T) calculations with the aug-cc-pVnZ basis sets are listed in Table 27 and the basis set convergence errors are also plotted in Figure 13. As... 

Figure 13 Basis set convergence errors in the electron affinities of the boron ( ) and fluorine ( ) atoms and the O2 (A) and CN ( ) molecules for RCCSD(T) calculations with the aug-cc-pVwZ basis sets...

Since the computational requirement of the CCSD(T) method grows as N, calculations with the larger correlation consistent sets quickly become computationally intractable for all but the simplest molecules. Nonetheless, as the calculations on the CH bond strengths in the CH and C2H series illustrated, for some molecular properties it may be possible to chose smaller basis sets that lead to consistent basis set convergence errors for a subset of molecules. With careful control of the basis set errors, it should be possible to predict reliably the relative properties of many molecules even if the absolute values cannot be predicted. 

Since 1989 there have been over one thousand papers published in the literature that make use of the correlation consistent basis sets. In this Appendix we provide a listing of the papers reporting the development of the correlation consistent basis sets as well as a partial listing of those papers that have explored the basis set convergence errors associated with the use of these sets. Many of these papers also report the intrinsic errors associated with the electronic structure methods. 

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