Correlation relativistic correction

Very recently Azzam et al. [50] presented new DMSs (called ALYT2013) computed ab initio using the CCSD(T)/aug-cc-pV(6+ d)Z level of theory supplemented by a core-correlation/relativistic corrective surfaces based on CCSD[t]/aug-cc-pCV5Z-DK. Calculated transitions intensities show very good agreement with the HITRAN database for 14 vibrational bands. The... 

The effect of core-electron correlation is small, as shown in Table 11.16. It should be noted that the valence and core correlation energy per electron pair is of the same magnitude, however, the core correlation is almost constant over the whole energy surface and consequently contributes very little to properties depending on relative energies, like vibrational frequencies. It should be noted that relativistic corrections for the frequencies are expected to be of the order of 1 cm" or less. ... 

It is perhaps somewhat surprising that, for Al3+, the relativistic corrections are of the same order of magnitude as the correlation... 

Froman, A., Calculation of correlation energies and relativistic corrections of some He- and Ne-like systems/ ... 

The prerequisites for high accuracy are coupled-cluster calculations with the inclusion of connected triples [e.g., CCSD(T)], either in conjunction with R12 theory or with correlation-consistent basis sets of at least quadruple-zeta quality followed by extrapolation. In addition, harmonic vibrational corrections must always be included. For small molecules, such as those contained in Table 1.11, such calculations have errors of the order of a few kJ/mol. To reduce the error below 1 kJ/mol, connected quadruples must be taken into account, together with anhar-monic vibrational and first-order relativistic corrections. In practice, the approximate treatment of connected triples in the CCSD(T) model introduces an error (relative to CCSDT) that often tends to cancel the... 

In systems where a large number of inner-shell electrons makes the inner-shell correlation (and, to a lesser extent, scalar relativistic) steps in W1 and W2 theory unfeasible, the use of a bond equivalent model for the inner-shell correlation and scaled B3LYP/cc-pVTZuc+l scalar relativistic corrections offers an alternative under the name of Wlc and Wlch theories. 

Two key pieces of theoretical data are required to obtain an empirical estimate of the correlation energy from the experimental data collected in the preceding section the total molecular Hartree-Fock energy and the relativistic corrections . It is implicit in the definition of the correlation energy presented in Eq. (1) that the total electronic energy ofa given molecule, Ef, may be divided into three constituent parts,... 

In order to establish the plausibility of the argument that the calculation of relativistic corrections to the second-order correlation energy in Be-like ions may be used to estimate reliably the corresponding quantity in many-electron molecules, we have included a calculation, in Table 8, of the many-body corrections to Ne. The relativistic correction to the correlation derived from these calculations is 1.257 x 10 hartree, which should be compared with our previous calculations [38] of the same quantity in 1.277 x 10 hartree, and with the independent calculations by Drake... 

From this, we may deduce that the relativistic correction to the correlation energy is dominated by the contribution from the s electron pair, and that the total relativistic effect involving the exchange of a single transverse Breit photon is obtained to sufficient accuracy for our present purposes at second-order in many-body perturbation theory. 

Thus, introducing parameters a, / and T we can account for the essential part of the correlation effects. However, it turned out that in the framework of the semi-empirical approach, all relativistic corrections of the second order of the Breit operator improving the relative positions of the terms, are also taken into consideration (operators H2, and H s, described by formulas (1.19), (1.20) and (1.22), respectively). Indeed, as we have seen in Chapter 19, the effect of accounting for corrections Hj and H s in a general case may be taken into consideration by modifications of the integrals of electrostatic interaction, i.e. by representing them in form... 

It can be seen that the calculated shielding values agree qualitatively with experimental values. The predicted shieldings are in correct order with Rb2 being most shielded and Rbl being least shielded. In the absence of relativistic corrections and correlation effects, the calculated shieldings at the Hartree-Fock level are already promising. 

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