BSSE, counterpoise method

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... 

For discussions of BSSE and the counterpoise method see (a) Clark T (1985) A handbook of computational chemistry. Wiley, New York, pp 289-301. (b) Martin JM (1998) In Irikura KK, Frurip DJ (eds) Computational thermochemistry. American Chemical Society, Washington, D.C., p 223. (c) References [104] give leading references to BSSE and [104 (a)] describes a method for bringing the counterpoise correction closer to the basis set limit... 

Basis set superposition error (BSSE) is a particular problem for supermolecule treatments of intermolecular forces. As two moieties with incomplete basis sets are brought together, there is an unavoidable improvement in the overall quality of the supermolecule basis set, and thus an artificial energy lowering. Various approximate corrections to BSSE are available, with the most widely used being those based on the counterpoise method (CP) proposed by Boys and Bemardi [3]. There are indications that potential energy surfaces corrected via the CP method may not describe correctly the anisotropy of the molecular interactions, and there have been some suggestions of a bias in the description of the electrostatic properties of the monomers (secondary basis set superposition errors). 

All the structures were first optimized at the MP2/6-31+g (d, p) level and improved energy were recalculated at the MP4/6-31+g (d, p) level except for some large hydrates. BSSE, which is corrected by the most common counterpoise method [22], was employed in the present work for the interaction energy calculations. 

VASP code. Correcting for the BSSE, via the counterpoise method [48], it is nicely... 

The counterpoise method proposed by Boys and Bemardi attempts to remove some of the effect of BSSE. The counterpoise correction is defined as... 

The standard procedure to correct the BSSE is the counterpoise method proposed by Boys and Bemardi [17], that relies on using for A and B isolated the same basis set as for the complex A-B. It has been pointed that this correction is not completely satisfactory and can cause other errors, due to an ill-balanced description, that now favors the isolated species. Other Authors [18] have suggested to reduce the BSSE by employing, in addition to the proper orbitals of species A, only the virtual orbitals of species B and viceversa. It should also be noticed that the counterpoise correction can have... 

Finally, in view of the current uncertainty with regard to the proper scheme to correct for BSSE, some authors regard the full counterpoise-corrected and the uncorrected interaction energies as results bracketing the real interaction energy for the basis or the experimental interaction energy - °. The counterpoise method is sometimes only used as an indication for the reliability of the calculation Note, however, that a small BSSE may be due... 

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 . ... 

A method to overcome this error is to use both basis sets in the calculation of the energy of each atom on its own so that the phantom component of the atomic energies can be determined and subtracted in what is known as the counterpoise method. BSSE can lead to over-estimations of molecular binding energies and so to the prediction of incorrect molecular geometries and charge density distributions. 

For the calculation of interaction energies the basis set superposition error (BSSE) has to be taken into account. It leads to a lowering of the energy of the polyad with respect to the energies of the individual bases. BSSE is identically zero in the limit of a complete basis set and usually it is corrected by the counterpoise method. Details regarding BSSE may be found in other reviews. 

In the supermolecular method there is a need to compensate for what is called the basis set superposition error (BSSE). The error appears because due to the incompleteness of the atomic basis set fl ), the individual subsystem A with the interaction switched off profits from the ilj basis set only, while when interacting lowers its energy due to the total fiji U basis set (the same pertains to any of the subsystems). As a result a part of the calculated interaction energy does not come from the interaction, but from the problem of the basis set used (BSSE) described above. A remedy is called the counterpoise method, in which all quantities (including the energies of the individual subsystems) are calculated within the U Up basis set. 

Several schemes have been proposed for estimating the BSSE. The most widely used is the counterpoise method, which defines the BSSE for a dimer as the sum over both monomers of (monomer in monomer basis) — (monomer in full dimer basis). Some authors caution against allowing the electrons on monomer A to utilize the funaion space corresponding to the occupied orbitals on monomer More recently diis controversy seems... 

The calculated dissociation energies reported here have not been corrected for the basis set superposition error (BSSE). There are two types of error in calculations using a truncated basis set the BSSE and the basis set incompletion error (BSIE). These two errors have opposite sign. Both errors can, in principle, be corrected by saturating the basis set, which is not possible in this case. However, correcting for the BSSE would leave the BSIE uncorrected. We think that for a comparison with experimental values, directly calculated bond energies should be used rather than estimated data obtained from correction procedures such as the counterpoise method. For a discussion of the BSSE, see Reference 114. 

The complexes of metal cations Fe, Co, NF+, and with guanine tetrads (G ) of C, and symmetry) were studied in [100]. The system contained two water molecules above and under the G -cation plane, with six-coordinated metal ion. G -Co and G -Cu being open shell species were treated using unrestricted method UB3LYP and 6-3 lG(d) basis set. BSSE (Basis Set Superposition Error) correction was evaluated according to the counterpoise method of Boys and Bemardi [101]. Bader s AIM (atoms in molecules) theory [102] was applied to determine a strong hydrogen bond [103]. The main conclusiorrs were as follows ... 

Gradient optimization of a two-quartet stracture (i.e. G-octet) can result in BSSE error originating from the incompleteness of the basis set of atomic oibitals and causing an artefactual stabilization of complexes. As has been already mentioned, this error can be corrected for single-point calculations by employing the standard counterpoise method [101]. It should be mentioned that empirical dispersion corrections are also able to absorb small BSSE effects [120]. 

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. 

The aim of this chapter is to show, on the basis of several examples, how the location of the bond path may be useful to characterize, define and/or verify the specific, considered interaction. Mainly the QTAIM approach [4-7] is considered here however sometimes there are also references to other methods and concepts as for example the Namral Bond Orbitals (NBO) method [21, 22] or the o-hole concept [25-27]. This is worth to note that the results presented hereafter are mainly based on the MP2/aug-cc-pVTZ level of calculations those results are taken from earlier studies or the calculations were carried out especially for the purposes of this chapter. Consequently the QTAIM calculations were performed on the MP2/aug-cc-pVTZ wave functions. The binding energies (Ebin s) were calculated as differences between the energy of the complex and the sum of energies of monomers optimized separately and they were corrected for the basis set superposition error (BSSE) by the counterpoise method [28]. Since the NBO method is based on the Hartree-Fock method thus the corresponding NBO results, i.e. orbital-orbital interactions or atomic charges, if presented, are based on the HF/aug-cc-pVTZ//MP2/aug-cc-pVTZ level. Hence there is rather not indicated the level of calculations for the next systems discussed hereafter unless the results presented were obtained within other levels of calculations. 

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. 

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