Basis set superposition effects

H. Wells, S. Wilson, Van der Waals interaction potentials many-body basis set superposition effects. Chem. Phys. Lett. 101,429-434 (1983)... 

Sokalski S, Roszak WA, Harlharan PC, Kaufman JJ (1983) Improved scf interaction energy decomposition scheme corrected for basis set superposition effect. Int J Quantum Chem 23 847-854... 

Karlstrom, G. and Sadlej, A. J., Basis set superposition effects on properties of interacting systems. Dipole moments and polarizabilities, Theor. Chim. Acta 61, 1-9 (1982). 

Wells, B. H. and Wilson, S., van der Wools interaction potentials. Basis set superposition effects in electron correlation calculations. Mol. Phys. 50, 1295-1309 (1983). 

B. H. Wells and S. Wilson, Mol. Phys., 50, 1295 (1983). Van der Waals Interaction Potentials. Basis Set Superposition Effects in Electron Correlation Calculations. See also. Mol. Phys., 54,787... 

G. Karlstrom and A. J. Sadlej, Theor. Chim. Acta, 61, 1 (1982). Basis Set Superposition Effects on Properties of Interacting Systems. Dipole Moments and Polarizabilities. 

The use of multi-centre basis set often leads to overestimates of interaction energies between atoms and/or molecules. Such effects are particularly problematic in calculations small interaction energies such as van der Waals interaction energies, where they can completely mask the true interaction. " This error is mainly attributable to basis set superposition effects. 

It should be emphasized that basis set superposition effects exist in all theoretical and computational methods which involve the algebraic approximation, in matrix Hartree-Fock calculations, in configuration interaction and in many-body perturbation theory. It is frequently found that basis set superposition effects are larger in calculations which take account of electron correlation effects than they are in orbital theories such as the matrix Hartree-Fock method. We shall discuss this aspect further in Section VII.C. It should... 

For extensive basis sets, an optimal description of the subsystems X and Y and the supersystem X... Y will be obtained. The basis set superposition error will then be very small. In recent work. Wells and Wilson did not use the function counterpoise correction in the usual fashion described above. They pointed out not only that the Boys-Bemardi procedure overcorrects for basis set superposition effects but also that it cannot be uniquely generalized for the calculation of a many-body interaction. Wells and Wilson argue that the function counterpoise correction should be used as a test for basis set superposition errors. 

The total interaction energy in the absence of basis set superposition effects may be written in the form... 

If the basis set employed in a particular study is so large that basis set superposition effects can be neglected, then these equations serve to define the many-body potential. However, if the site-site function counterpoise approximation is used to take account of superposition effects in calculations performed with basis sets which are not so large, then equation (76) is replaced by... 

J. Andzelm, M. Klobukowski, and E. Radzio-Andzelm, J. Comput. Chem., 5, 146 (1984). Compact Contracted Gaussian-Type Basis Sets for Halogen Atoms. Basis Set Superposition Effects on Molecular Properties. 

Finally one should point out the occurrence of the basis set superposition effect (each unit cell in a quasi-ID polymer is better described because the basis functions of its neighbours also exert an effect, rather than as a single molecule). The basis set superposition causes only an error if one wants to calculate the cohesion energy of a chain or of a 2D or 3D periodic system, because then one has to calculate the energy difference of the extended system and the sum of its constituents. This basis superposition effect occurs both at the HF and at the correlation corrected (QP) level and causes that already at the MP2 level, if one uses a double basis with polarization functions, and one obtains 70-75% of the correlation energy. 

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