Ghost basis

The superscripts AB indicate that the monomer energies are computed in the dimer basis set, AuB. The B basis in theEj calculation and the A basis in the calculation are usudly referred to as "ghost basis sets. Eq. (1) represents the uncorrected interaction energy, which subsequently will be referred to as AE" AEbsse is usually defined as the difference between AE and AE" , i.e.,... 

One or two issues involving BSSE surface periodically in the literature. One is the question as to whether a counterpoise correction should be determined with a ghost basis that includes or excludes the occupied orbitals of the ghost fragment. 

The physical definition of ES (electrostatic interactions among rigid partners) clearly indicates that there is no room here for CP corrections, which would involve some shift of the monomer s charge onflie ghost basis functions offlie partner. This physical observation corresponds to the structure of the blocks of the Hamiltonian matrix used to compute ES no elements regarding the BS of the partner are present in conclusion and thus no corrections to ES are possible. 

We have used here as ghost basis the occupied orbitals of the second monomer, following the suggestions given by the physics of the interaction. 

There are variations of this method. For example may it be argued that the full set of ghost orbitals should not be used, since some of the functions in the complex are used for describing the electrons of the other component, and only the virtual orbitals are available for artificial stabilization. However, it appears that the method of full counterpoise corection (using all basis functions as ghost orbitals) gives the best results. Note that A cp is an approximate correction, it gives an estimate of the BSSE effect, but it does not provide either an upper or lower limit. 

In the early 1990s, Bakker and Van den Akker (1991, 1994) introduced an approximate but effective Euler Euler approach (see also A. Bakker s PhD Thesis, 1992) on the basis of a single-phase RANS flow field calculated by FLUENT, a code named GHOST calculated local and averaged values of bubble size db, gas hold-up a, and specific mass transfer rate kfl. 

Considering the different calculated values for an individual complex in Table 11, it seems appropriate to comment on the accuracy achievable within the Hartree-Fock approximation, with respect to both the limitations inherent in the theory itself and also to the expense one is willing to invest into basis sets. Clearly the Hartree-Fock-Roothaan expectation values have a uniquely defined meaning only as long as a complete set of basis functions is used. In practice, however, one is forced to truncate the expansion of the wave function at a point demanded by the computing facilities available. Some sources of error introduced thereby, namely ghost effects and the inaccurate description of ligand properties, have already been discussed in Chapter II. Here we concentrate on the... 

Table 5. The Basis Set Superposition Error (BSSE) for CH5(H2). The Monomers in Parentheses are Ghost Molecules. " AE Indicates the Difference between the Energy of the Monomer within the Monomer vs. the Dimer Basis...

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