Core correlation bond distances

The generally accepted mechanism via which core holes are produced during atomic collisions is described within the electron promotion model introduced by Fano, Lichten, and coworkers (Fano and Lichten 1965 Lichten 1967 Barat and Lichten 1972). This describes the formation/modification of MOs from the respective AOs of the two colliding atoms as they approach each other from an infinite distance to distances substantially less than equilibrium bond distances. This modification can be understood as the energy of an MO formed as defined by the interatomic distance (see Section 2.2.2). Correlation diagrams relay the modification of MO energies for all levels of interest as a function of interatomic (intemuclear) distance. 

Non-Bom-Oppenheimer (BODC), relativistic, and core-valence correlation corrections, tacitly neglected in most quantum chemical studies, result in small shifts of the calculated PES values. BODC and relativistic correction to the force constant are usually negligble for species involving first- and second-row. atoms. On the other hand, advances in the continuing development of quantitatively accurate ab initio methods have revealed the necessity of a full understanding of the consequences of core-core and core-valence electron correlation (see Core-Valence Correlation Effects) on calculated force fields. It has been found that (a) equilibrium bond distances of first-row diatomic molecules experience a considerable contraction, about 0.002 A for multiple bonds and 0.001 A for single bonds, reducing the errors in Rq predictions... 

In this section, we investigate the accuracy of ab initio electronic-structure predictions of bond distances [21. In Section 15.3.1, we review the experimental data on which the investigation is based. Next, in Sections 15.3.2-15.3.5, we consider the statistical measures of errors, piecing together a picture of the performance of the standard models with respect to the calculation of equilibrium bond distances. After a discussion of higher-order effects at the CCSDT level in Section 15.3.6 and core correlation in Section 15.3.7, we attempt to rationalize the behaviour of the different models in Section 15.3.8. We conclude our discussion in Section 15.3.9, which... 

We now examine the contribution to the bond lengths from the correlation of the core electrons. As the core-correlation energy to a large extent is independent of the geometry, it is expected to have a small effect on geometries. Tliis was demonstrated in Section 8.3.1, where correlation of the core reduced the bond distance of BH by just 0.2 pm. The contributions discussed here are therefore important only for applications that require high precision. 

To examine the effect of core correlation, we have in Table 15.6 listed the statistical data that describe the differences in the MP2 bond distances between all-electron cc-pCVXZ calculations and frozen-core cc-pVXZ calculations. Core correlation is seen to shorten the bonds, with an average reduction of about 0.20 pm for the cc-pCVTZ and cc-pCVQZ sets. The cc-pCVDZ basis is too small to give a reliable description of core correlation. 

Table 15,6 The effect of core correlation on bond distances (in pm) at the MP2 level. The statistical mea.sures are based on the molecules in Table 15.1...

In Table 15.7, we have collected the equilibrium bond distances of the molecules in Table 15.1, calculated using the core-valence cc-pCVQZ basis set, correlating all the electrons in the system. For the CCSD(T) model, a comparison with experiment shows that, for 22 of the 29 bond lengths, the difference is less than or equal to 0.1 pm. This error is less than the intrinsic error of the CCSD(T) model and arises from a cancellation of errors. 

The first point to note about the correlation-consistent basis sets in Table 8.16 is that the convergence is in all cases uniform and systematic - for the energies, for the bond distances, and for the bond angle. Scrutiny of the table reveals that, with each increment in the cardinal number, all errors are reduced by a factor of at least 3 or 4. Clearly, the correlation-consistent basis sets provide a convenient framework for the quantitative study of molecular systems at the Hartree-Fock level. We also note that the results for the cc-pVXZ and cc-pCVXZ basis sets are very similar. Apparently, the molecular core orbitals are quite atom-like and unpolarized by chemical bonding. In Hartree-Fock calculations, therefore, the use of the smaller valence cc-pVXZ sets is recommended. 

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