No abstract

Study of the importance of relativistic, correlation, and relaxation effects on ionization energy of atoms by a relativistic and correlated local density method A solution (Dirac electron in crossed, constant electric and magnetic fields) that has found a problem (relativistic quantized Hall effect) Am.The lowest order relativistic effect theory for nuclear magnetic shieldings was derived from a two-component positive energy Hamiltonian. It was shown that the previous relativistic shielding theory based on the two-component Hamiltonian is not gauge invariant and the new terms have to be added to make a result gauge invariant. The presented theory is gauge invariant to the order of (Z/137) 4 where Z is the atomic number of the heaviest atom in the molecule. One of the new contributions to the relativistic magnetic shieldings is a second-order perturbation term due to the combination of the spin-orbit interaction and the Fermi-contact interaction. A numerical estimation for this term was performed for the four hydrogen halides, HF, HCl, HBr, and HI. The computational results showed that the contribution of this term to the hydrogen shieldings is negligibly small, but the contribution to the halogen atoms is considerable.

Spherically averaged electron momentum densities Π(p) are constructed by the numerical Hartree–Fock method for all 103 atoms from hydrogen (atomic number Z=1) to lawrencium (Z=103) in their experimental ground states. We find three different types of momentum densities spread across the periodic table in a very simple manner for the 98 atoms other than He, N, Mn, Ge, and Pd. Atoms in groups 1–6, 13, and 14, and all lanthanides and actinides have a unimodal momentum density with a maximum at p=0, atoms in groups 15–18 have a unimodal momentum density with a local minimum at p=0 and a maximum at p>0, and atoms in groups 7–12 have a bimodal momentum density with a primary maximum at p=0 and a small secondary maximum at p>0. Our results confirm the existence of nonmonotonic momentum densities reported in the literature, but also reveal some errors in the previous classification of atomic momentum densities. The physical origin for the appearance of the three different modalities in Π(p) is clarified by analysis of subshell contributions to momentum densities.

Nuclear magnetic shieldings in first-and second-row hydrides were calculated with electron correlation taken into account through third order. The calculation was performed using London's gauge-invariant atomic orbitals ͑GIAOs͒ and finite-field Mo "ller-Plesset perturbation theory ͑FF-MPPT͒. Furthermore, the vibrational motion corrections to the magnetic shieldings were evaluated. It was shown that the calculated isotropic shielding constants at the experimental geometries are higher than the experimental values, but that vibrational corrections are generally negative and improve the calculated shielding constants.

Ab initio self-consistent-field (SCF) and electron correlation calculations have been carried out for the dihedral angle dependence of the vicinal proton–proton coupling constants, 3JHH, in ethane molecule. The four contributions to 3JHH, (JFC, JSD, JOP, and JOD) have been computed with the three different basis sets, [5s2p1d/2s1p], [5s3p1d/3s1p], and [7s4p2d/5s2p]. The Fermi contact (FC) contribution was largest and the spin–dipole (SD) contribution was smallest. The FC and orbital paramagnetic (OP) contributions showed large basis set dependence, but the SD and orbital diamagnetic (OD) contributions presented little basis set dependence. The calculated total SCF contribution to 3JHH was higher than the experimental coupling. Using the Mo/ller–Plesset perturbation theory we have introduced electron correlation effects on the FC and OP terms. The correlation effects on the OP term was shown to be negligible. The second-order correlation in the FC term was very large and amounted to half of its SCF value in magnitude with opposite sign. However, the third-order correlation in the FC contribution was small. Unfortunately, the calculated 3JHH value including correlation corrections through third order was too small compared to the experimental one. The poor agreement between calculation and experiment is claimed to be due to higher than third-order correlations in the FC term.