Functional counterpoise

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 ... 

Gutowski M, Van Duijneveldt FB, Chalasinski G, Piela L (1986) Does the boys and bernardi function counterpoise method actually overcorrect the basis set superposition error Chem Phys Lett 129 325-328... 

Gutowski M, Van Duijneveldt-Van der Rijdt JGCM, Van Lenthe JH, Van Duijneveldt FB (1993) Accuracy of the Boys and Bernardi function counterpoise method. J Chem Phys 98 4728-4737... 

Weak intermolecular interactions Large Diffuse polarization functions in addition to common polarization functions counterpoise correction should be tested... 

Chesnut, D. B. and Phung, C. G., Functional counterpoise corrections for the NMR chemical shift in a model dimeric water system, Chem. Phys. 147,91-97 (1990). 

Gutowski, M., van Duijneveldt, F. B., Chalasinski, G., and Piela, L., Does the Boys andBernardi function counterpoise method actually overcorrect the basis set superposition error , Chem. Phys. Lett. 129, 325-330 (1986). 

AE as well as AE should be corrected for the basis set superposition error which reflects the basis set inconsistency in the variation calculation of interaction energy. This problem was successfully solved by Boys and Bemardi [4] who formulated the function counterpoise principle eliminating the basis set superposition error completely. The introduction of the function counterpoise method however makes calculations more tedious because the energy of the subsystem (calculated in basis set of the dimer) depends on the geometry of the complex and must be ascertained for each point of the PES. Furthermore, and this is even more inconvenient, the gradient optimization method could not be applied for the optimization of the structure and energy of a complex. 

A rather novel objection " against the function counterpoise method is that it does not increase reliability, since does not remove the remaining errors in A . Thus the extra expense of performing counterpoise calculations is not warranted and it is better to increase the basis-set to the maximum affordable . This argument tacitly assumes that increasing the basis will simultaneously reduce both the BSSE and the remaining errors in A . While this may be true in some special cases (e.g. see Refs. 266 and 178), there are now several well-documented examples where increases in the basis set lead to increased bSSE . ... 

F. j. Olivares del Valle, S. Tolosa, E. A. Ojalvo, and j. j, Esperilla, ]. Chem. Phys., 85, 4448 (1986). The Polarization-Function Counterpoise Method, An Application of the Diagrammatic Perturbation Theory to the He-H2 Molecule in the Region of the van der Waals Minimum,... 

Boys and Bernardi proposed the function counterpoise method to correct for the effects of basis set superposition in calculations of small interaction energies, such as van der Waals interaction potential. For a supersystem X...Y, the function counterpoise method is employed in the following manner. The energies x and Ey of the subsystems X and Y are calculated using the full basis set employed in the calculation on the supersystem X... Y rather than just the basis sets for X or Y alone. The interaction energy is then given by... 

It is clear, however, that the function counterpoise method will overestimate the basis set superposition error. In the supersystem X... Y, the Pauli principle will prevent subsystem X from fully utilizing the basis set of subsystem Y, while in the ghost system the calculation of ExiR/Sx Sy) does not involve such a restriction. This had led some workers to propose modified function counterpoise correction procedures, none of which can be rigorously justified. 

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. 

Function counterpoise corrections for the ground state of the neon atom calculated within the matrix Hartree-Fock approximation for a systematic sequence of even-tempered basis sets of Gaussian-type functions. In this table G represents a set of ghost orbitals. The internuclear separation in the NeG system is 5.0 bour."... 

The importance of the non-pairwise additive components of the interaction energy between atoms and molecules is widely recognized and ab initio electronic structure calculations offer a route to important information about such effects. Attention has recently been drawn to the fact that there is no unique generalization of the Boys-Bernardi function counterpoise technique to clusters of molecules. Two possible generalizations have been introduced, as follows. 

In this approach it is assumed that the basis set superposition error in the many-body cluster can be approximated by the sum of the Boys-Bemardi function counterpoise corrections for pairs of bodies. Hence the total interactions for an N-body cluster using the pairwise additive function counterpoise correction is given by... 

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... 

A very important source of error is the basis set superposition error if the basis used for molecule A is inadequate, the virtual orbitals of molecule B may be able to improve the description of A in a way which has nothing to do with the interaction, and this leads to a spurious stabilization. It is conventional to correct for it by means of the functional counterpoise method [22] in which reference calculations are performed for each molecule in the presence of the basis functions, but not the electrons or nuclei, of the other. This procedure overcorrects for the effect, since it makes available to molecule A the occupied space of molecule B as well as the virtual space. It is possible to carry out a reference calculation for A in which the occupied orbitals of B are projected out of the basis[23], but although this gives better results than the normal procedure it is probably too cumbersome for routine use. Note that the function counterpoise method demands a separate reference calculation for each of the interacting molecules at every relative position, since the basis extension error varies with the position of the orbitals of the other molecule, and the procedure is therefore very time-consuming. 

Skwara et examined in depth the removal of basis set superposition error (BSSE) in supermolecule calculations of interaction-induced electric properties. The authors used the Valiron-Mayer function coimterpoise (VMFC), site-site function counterpoise (SSFQ and the TB scheme proposed by Mierzwicki and Latajka. The systems studied are the linear HF trimer and tetramer. The authors concluded that when large, flexible basis sets are used, all BSSE removal methods converge. Otherwise, quantitative differences are observed in the performance of the above cited methods. 

F.-M. Tao and Y. K. Pan,/. Phys. Chem., 96, 5815 (1992). Validity of the Function Counterpoise Method. Results from the Complete 4th-Otder MBPT Calculations. 

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