Functional counterpoise method

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... 

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. 

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. 

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. 

The molecular orbitals in the nonrelativistic and one-component calculations and the large component in the Dirac-Fock functions were spanned in the Cd s Ap9d)l[9slp6d basis of [63] and the H (5s 2p)/[35 l/>] set [61]. Contraction coefficients were taken from corresponding atomic SCF calculations. The basis for the small components in the Dirac-Fock calculations is derived by the MOLFDIR program from the large-component basis. The basis set superposition error is corrected by the counterpoise method [64]. The Breit interaction was found to have a very small effect and is therefore not included in the results. 

The effect of basis set superposition error (BSSE) was estimated for this series using the counterpoise method of Boys and Bemardi (16), The isotropic shielding value of methane by itself was calculated to be 31.8276 ppm. Isotropic shielding values corrected for BSSE for the proximal proton of methane were calculated for each distance from ethene (Table I). The difference between the isotropic shielding value calculated for methane alone and the isotropic shielding values at each geometry for the proximal proton of methane obtained for the methane-ethene pair in a counterpoise calculation including the basis functions of ethene (but no electrons) is... 

Johansson, A., Kollman, P., and Rothenberg, S., An application of the functional Boys-Bernardi counterpoise method to molecular potential surfaces, Theor. Chim. Acta 29, 167-172 (1973). 

Tao, F.-M., The counterpoise method and bond functions in molecular dissociation energy calculations, Chem. Phys. Lett. 206, 560-564 (1993). 

Figure 2 Orientational dependence of SCF and correlation components to interaction energy in the water dimer as a function of deviation of H-bond from linearity. A refers to second-order Mpller-Plesset correlation contribution, corrected by the counterpoise method Eji p is a shorthand notation for the perturbation value of Edisp -...

A. Johansson, P. Kollman, and S. Rothenberg, Theor. Chim. Acta, 29, 167 (1973). An Application of the Functional Boys-Bernardi Counterpoise Method to Molecular Potential Surfaces. 

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