Atomic orbitals core correlation

It is not possible to use normal AO basis sets in relativistic calculations The relativistic contraction of the inner shells makes it necessary to design new basis sets to account for this effect. Specially designed basis sets have therefore been constructed using the DKH Flamiltonian. These basis sets are of the atomic natural orbital (ANO) type and are constructed such that semi-core electrons can also be correlated. They have been given the name ANO-RCC (relativistic with core correlation) and cover all atoms of the Periodic Table.36-38 They have been used in most applications presented in this review. ANO-RCC are all-electron basis sets. Deep core orbitals are described by a minimal basis set and are kept frozen in the wave function calculations. The extra cost compared with using effective core potentials (ECPs) is therefore limited. ECPs, however, have been used in some studies, and more details will be given in connection with the specific application. The ANO-RCC basis sets can be downloaded from the home page of the MOLCAS quantum chemistry software (http //www.teokem.lu.se/molcas). 

In addition, for thermochemical purposes we are primarily interested in the core-valence correlation, since we can reasonably expect the core-core contributions to largely cancel between the molecule and its constituent atoms. (The partitioning between core-core correlation -involving excitations only from inner-shell orbitals - and core-valence correlation - involving simultaneous excitations from valence and inner-shell orbitals - was first proposed by Bauschlicher, Langhoff, and Taylor [42]). 

For all results in this paper, spin-orbit coupling corrections have been added to open-shell calculations from a compendium given elsewhere I0) we note that this consistent treatment sometimes differs from the original methods employed by other workers, e.g., standard G3 calculations include spin-orbit contributions only for atoms. In the SAC and MCCM calculations presented here, core correlation energy and relativistic effects are not explicitly included but are implicit in the parameters (i.e., we use parameters called versions 2s and 3s in the notation of previous papers 11,16,18)). 

This qualitative picture is taken into account in the unrestricted Hartree-Fock (UHF) approach, but it is found that UHF calculations normally overestimate Ajgo drastically. To obtain reliable results, the interactions between the electrons must be described much more accurately. Furthermore, in difference to most other electronic properties, such as dipole moments etc., a proper treatment of the hfcc s also requires special consideration of the inner valence and the Is core regions, since these electrons possess a large probability density at the position of the nucleus. Because the contributions from various shells are similar in magnitude but differ in sign, a balanced description of the electron correlation effects for all occupied shells is essential. All this explains the strong dependence of A on the atomic orbital basis and on the quality of the wavefunction used for the calculation. 

The Ni atoms are treated as one-electron systems in which the effects of the Ar-like core and the nine 3d electrons are replaced by a modified effective potential (MEP) as suggested by Melius et al./165/ A contracted gaussian basis set is used for Ni, which includes two functions to describe the 4s and one to describe the 4p atomic orbitals. Since a previous study/159/ found the O-Ni spacing and the vibrational frequency we insensitive to correlations in this open-shell system, the authors have adopted the SCF calculation scheme. To check the approximation of treating the Ni atoms as a one-electron system, they performed both the MEP and an all electron SCF calculation for the NisO cluster. They found that the MEP spacing is 0.37 A or 35% smaller than the all-electron value the MEP we value is 90 cm-1 or 24% smaller. Since the 3d... 

Depending on the chemical system of interest, however, it might be more prudent to correlate the motions of electrons in orbitals k and I rather than orbitals i and /. For example, (j),- and (j), might correspond to molecular core orbitals, while (j) and (j)/ might correspond to the atomic or molecular valence orbitals. Electron correlation can be particularly important in the latter set of functions because the valence orbitals are often directly involved in the formation of chemical bonds. In this case, the wavefunction would be written as... 

In this paper, we shall present a procedure for evaluating electron relaxation, inner-core correlation, and Breit, qed, and nuc corrections to 2p-core ionization energies and spin-orbit splitting in molecular systems, from tabulated results on atoms from Cl to Ba, excluding transition elements. 

It is quite common in correlated methods (including many-body perturbation theory, coupled-cluster, etc., as well as configuration interaction) to invoke the frozen core approximation, whereby the lowest-lying molecular orbitals, occupied by the inner-shell electrons, are constrained to remain doubly-occupied in all configurations. The frozen core for atoms lithium to neon typically consists of the Is atomic orbital, while that for atoms sodium to argon consists of the atomic orbitals Is, 2s, 2px, 2py and 2pz. The frozen molecular orbitals are those made primarily from these inner-shell atomic orbitals. 

This purely theoretical scheme yields, in principle, the best possible LCAO molecular orbitals for a given problem. However, the practice of the calcida-tion forces in a few errors, one of which is the use of a valence-state atomic orbitals on which one builds the molecular orbitals. Last, but not least, there is the intrinsic error contained in the concept itself of doubly occupied orbitals which permits two electrons of opposite spins to be at the same time at the same place, thus ignoring at least in part what is called their correlation . 

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