Superposition effect

This is synonymous with the region of significant overlap of orbital charge distributions, where the Pauli restriction (1.6) and quantal superposition effects become important. 

H. Wells, S. Wilson, Van der Waals interaction potentials many-body basis set superposition effects. Chem. Phys. Lett. 101,429-434 (1983)... 

Sokalski S, Roszak WA, Harlharan PC, Kaufman JJ (1983) Improved scf interaction energy decomposition scheme corrected for basis set superposition effect. Int J Quantum Chem 23 847-854... 

Karlstrom, G. and Sadlej, A. J., Basis set superposition effects on properties of interacting systems. Dipole moments and polarizabilities, Theor. Chim. Acta 61, 1-9 (1982). 

Wells, B. H. and Wilson, S., van der Wools interaction potentials. Basis set superposition effects in electron correlation calculations. Mol. Phys. 50, 1295-1309 (1983). 

The last row of Table 2.3 reveals the profound difficulties in using the 6-311G basis set where the triple split of the valence set might normally be expected to be an improvement over 6-3IG. Instead, the SCF BSSE is more than doubled, and an increase of similar magnitude occurs in the correlated superposition error. Indeed, the correlation component is completely distorted by superposition effects Essentially all the (1.93 kcal/mol) stabilization predicted by MP2 with this basis set is due to the artifact of superposition. Removal of this error leaves only a net stabilization of less than 0.1 kcal/mol. 

Stage 2 (superposition effect). At a rubber-particle content of more than 15 vol%, the stress concentration directly at the particle surface is increased by the stress fields of neighboring particles (Figure 9). This fact favors the formation of broad crazes and long craze bands. 

The stress concentration at rubber particles starts to increase by the superposition effect if the interparticle distance, A, is smaller than about 0.5D, that is, if the rubber volume content is higher than 15 vol% (Figure 11). There is an increasing tendency of craze formation with increasing stress concentration, which means with decreasing particle modulus and increasing rubber volume content. 

B. H. Wells and S. Wilson, Mol. Phys., 50, 1295 (1983). Van der Waals Interaction Potentials. Basis Set Superposition Effects in Electron Correlation Calculations. See also. Mol. Phys., 54,787... 

G. Karlstrom and A. J. Sadlej, Theor. Chim. Acta, 61, 1 (1982). Basis Set Superposition Effects on Properties of Interacting Systems. Dipole Moments and Polarizabilities. 

The use of multi-centre basis set often leads to overestimates of interaction energies between atoms and/or molecules. Such effects are particularly problematic in calculations small interaction energies such as van der Waals interaction energies, where they can completely mask the true interaction. " This error is mainly attributable to basis set superposition effects. 

It should be emphasized that basis set superposition effects exist in all theoretical and computational methods which involve the algebraic approximation, in matrix Hartree-Fock calculations, in configuration interaction and in many-body perturbation theory. It is frequently found that basis set superposition effects are larger in calculations which take account of electron correlation effects than they are in orbital theories such as the matrix Hartree-Fock method. We shall discuss this aspect further in Section VII.C. It should... 

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. 

The total interaction energy in the absence of basis set superposition effects may be written in the form... 

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... 

Fig. 11. Comparison of the action of homogeneous and core-shell particles in toughened polymers concerning the single mechanism at particles and the superposition effect between particles.

J. Andzelm, M. Klobukowski, and E. Radzio-Andzelm, J. Comput. Chem., 5, 146 (1984). Compact Contracted Gaussian-Type Basis Sets for Halogen Atoms. Basis Set Superposition Effects on Molecular Properties. 

Superposition effect Stress fields around the rubber particles overlap when the particle distance is smaller than half the particle diameter (i.e., particle content larger than about 15 vol.%) higher stress concentrations create thicker crazes and long craze bands, so large material volumes contribute to toughness. 

Rgure 5.13 Comparison of the role played by homogeneous rubber particles in contrast to core-shell particles in rubber toughened polymers similar single mechanism but different superposition effect [12]... 

Perturbation theory offers some advantages in this respect. It is also subject to basis superposition error, but the contributions in which such errors may occur can be identified, and it is possible to make an estimate of the error and to correct for it to some extent. The charge-transfer energy is subject to basis superposition error, but it is possible to estimate the contribution of this error to the result. The extension correlation and double charge transfer terms are wholly due to basis superposition effects, to lowest order in overlap at least[l8], and can be discarded. The charge-transfer correlation and dispersion terms, on the other hand, can have no basis superposition error at all because they can only arise when occupied orbitals of both molecules are present[193. 

A summary of Macosko s results is given in Table 11, adapted from Reference 213, while Figure 18, also taken from Reference 213, shows the adiabatic temperature rise data for the block copolymer formation and the excellent agreement with Malkin s model. The additional temperature rise at longer times is due to polymer crystallization, underlining that the two phenomena, polymerization and crystallization, can be kept well separated by choosing proper experimental setup, thus, avoiding any superposition effect. 

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