Correlation levels, calculations

The most advanced relativistic approach in relativistic calculations of X-ray spectra, is most likely that based on the Dirac-Coulomb-Breit Hamiltonian and quantum electrodynamic contributions accounted for. In addition, one should also carry out the corresponding correlated-level calculation within these relativistic formalism. To illustrate the role and size of relativistic and QED corrections the core and valence ionisation potentials and excitation energies of noble gases are shown. The relativistic fOTC CASSCE/CASPT2 method together with the restricted active space... 

More recently, the Duiming group has focused on developing basis sets that are optimal not for use in SCF-level calculations on atoms and molecules, but that have been optimized for use in correlated calculations. These so-called correlation-consistent bases [43] are now widely used because more and more ab initio calculations are being perfonned at a correlated level. 

There are several types of basis functions listed below. Over the past several decades, most basis sets have been optimized to describe individual atoms at the EIF level of theory. These basis sets work very well, although not optimally, for other types of calculations. The atomic natural orbital, ANO, basis sets use primitive exponents from older EIF basis sets with coefficients obtained from the natural orbitals of correlated atom calculations to give a basis that is a bit better for correlated calculations. The correlation-consistent basis sets have been completely optimized for use with correlated calculations. Compared to ANO basis sets, correlation consistent sets give a comparable accuracy with significantly fewer primitives and thus require less CPU time. 

Cl calculations can be used to improve the quality of the wave-function and state energies. Self-consistent field (SCF) level calculations are based on the one-electron model, wherein each electron moves in the average field created by the other n-1 electrons in the molecule. Actually, electrons interact instantaneously and therefore have a natural tendency to avoid each other beyond the requirements of the Exclusion Principle. This correlation results in a lower average interelectronic repulsion and thus a lower state energy. The difference between electronic energies calculated at the SCF level versus the exact nonrelativistic energies is the correlation energy. 

The numerical value of hardness obtained by MNDO-level calculations correlates with the stability of aromatic compounds. The correlation can be extended to a wider range of compounds, including heterocyclic compounds, when hardness is determined experimentally on the basis of molar reffactivity. The relatively large HOMO-LUMO gap also indicates the absence of relatively high-energy, reactive electrons, in agreement with the reduced reactivity of aromatic compounds toward electrophilic reagents. 

Kello, V. and Sadlej, A.J. (1996) Standardized basis sets for high-level-correlated relativistic calculations of atomic and molecular electric properties in the spin-averaged Douglas-Kroll (nopair) approximation 1. Groups Ib and 11b. Theoretica Chimica Acta, 94, 93-104. 

At the correlated level the many-body perturbation theory is applied, the localized version of which (LMBPT) has already proven to be useful in the study of molecular electronic structure. The LMBPT is a double perturbation theory, and the perturbational correction are calculated as ... 

That study at the MP2 correlated level for the dimers investigated are summarized in Table 7. In Table 7, we use the following notations SM denotes the values obtained in the super-molecule, while CP denotes those obtained in the counter-poise corrected calculations. The results clearly show, that the E(intra/net) values are close to each other (using any basis sets) for the monomers in both of SM and CP systems. This suggests that the SMO-LMBPT scheme takes into account the benefit effect of the basis set superposition. The deviations found in the intra terms between the SM and CP systems are explained recently (Kapuy etal, 1998) in detail. 

According to the formulae used in the SMO-LMBPT procedure (see those concerning the correlated level as given in Chapter 6), the following quantities are calculated the intra-correlated part as well as the inter-correlated part of the energy terms at the second (MP2), third (MP3) and the fourth (MP4) level of correlation. The MINI basis... 

---