Origin and Magnitude of BSSE

The first part of this chapter defined the BSSE effect and explained why it occurs. The remainder of this chapter discusses the size, importance, and accuracy of BSSE corrections, and finally gives practical guides for making corrections for the effect within the standard computer packages now available. 

Returning to the BSSF calculations themselves, let us consider what would happen if we were to calculate the energy of a simple but real system, such as H2. Let us also start our modeling by using a simple basis set, namely, one function per atom. When we determine the energy of each atom, we use one function, but when we calculate the energy of a diatomic we use two functions, one centered on each nucleus. If the one function were the exact solution, the 

Consider now what happens if we try to determine the difference in energy of the atoms and the molecule. The answer will depend on how the atomic energy is determined, i.e., whether one or two functions were used for each atom in this case. Which way is correct The answer is not obvious. Why would we use a basis set for an atom that contains functions from another center The reason is that we would be using the same basis set for both the atomic and the molecular system, and consequently we would be consistent. 

The BSSE is difficult to calculate accurately. We know there will be a BSSE for any finite basis set, but most of the time we do not know its magnitude. Later in this chapter we will discuss the counterpoise method invented by Boys and Bernardi, a common method to estimate the error using basis sets from both centers to calculate both the atom and the diatomic. The method often works well, but it does have an inherent error. The error is the following what we desire is really the energy of, say, the diatomic and the energy of the separate atoms calculated with the same functions as used by the diatomic. In our hydrogen molecule example, the occupancy of each atomic function from its own center is not exactly one because the functions overlap. So we should use only part of the atomic function from the other center in our calculations of the atomic energy to get an absolutely equivalent basis for both atom and molecule. That proves to be almost impossible to do except in certain cases that are explored later. 

The magnitude of the BSSE effect is affected by the size of the basis sets used, whether localized or bond orbitals are used, the type of system treated, and the level of calculation (Hartree-Fock or post-Hartree-Fock). 

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