The scalar relativistic contributions to bond or atomization energies of homo- or hetero-polar s-p-bonded atoms, △relE(bond), correlate well with the changes on bond formation of the electron density, integrated throughout the spatial K-shell region of the heavy nucleus, △bondFK-region, times Z4, where Z is the nuclear charge. The "bond density changes" in the innermost atomic core regions, however, have no direct simple relationship to the electron density reorganizations in the outer atomic valence shell regions, which determine the nonrelativistic main contribution to the bond energy, △nonrelE(bond). Also, scalar relativistic bond energy changes and bond length changes, △relRe, are not directly correlated. Namely, △relE(bond) correlates with the difference △bondFK-region, whereas △relRe correlates with the derivative (dFK-region/dR). Reducing the internuclear distance from the separated to the united atom limit through the equilibrium distance value, Re, the density around the nucleus at first decreases in many cases, goes through a minimum, and finally increases again. Therefore (dFK-region/dR) may be positive or negative at Re.

Density functional calculations including relativistic as well as nonlocal exchange and correlation corrections have been performed on group 14 molecules MO. MH4, MCI4 (M=C, Si, Ge, Sn, Pb). Good bond lengths, and reasonable bond energies and force constants have been obtained. The dipole moments of the MO series are quite good, and dμ/dR of CO is close to the experimental results. Relativistic corrections are important for the heavier molecules (M=Ge, Sn, Pb). Fractional relativistic changes of bond energies, bond lengths and force constants are nearly exactly proportional to Z2 (Z: heavy nuclear charge). The origin of the relativistic changes has been analyzed: the change upon bond formation of the valence orbitals near the heavy nucleus is decisive.

In contrast to former ligand field predictions, the standard energetic order of the metal 3d orbitals, δ<π<σ, is not reproduced here. Throughout, the 3ds molecular orbital (MO) level is found rather low lying because of s-donating ligand induced 3d-4s hybridization in these linear dicoordinated compounds, while the 3dp is rather high due to the pronounced p-donor character of the halogen ligands at the short distances of the digonal halides. This results in an unexpected electron distribution for the ground state and in an unusual order of electronic states. The calculations are in general consistent with recent experimental findings. The approach yields semiquantitatively correct geometric parameters and vibrational frequencies, and qualitatively correct trends for the dissociation energies. Those properties show a secondary periodicity, similar to the one known for octahedral high-spin complexes, though for different electronic reasons. Unknown structures, vibrational frequencies, and dissociation energies are predicted.

l surrounding was simulated by a Madelung field. The influence of the surrounding alkali metal ions was examined. The electronic structure differs from that of the isoelectronic dihalides M'X2 (M'=M+1). Orbital mixing is more pronounced in [MO2]3-. The M3d-πg atomic orbital (a.o.) correlates in [MO2]3- with an antibonding M3d-O2p-π* molecular orbital (m.o.), the M3d-σg a.o. correlates with a strongly mixed nonbonding M3d-4s-σg hybrid-m.o. There is significant covalency in the dioxometallate(Ⅰ) anions in contrast to the more ionic dihalides. As a result the orders of calculated levels are different in some cases. The charge distribution may be symbolized by [M2δ-O2(1.5-δ)-]. The M-O bond length varies significantly with the π* occupation. The assignment of the electronic ground states and electronic spectra is still an unsolved problem. Its solution would throw light on the reliability of present-day DFT approaches.

Density functional (DF) calculations including gradient-exchange and correlation corrections have been performed on the LnH, LnO, and LnF series (Ln = La, Gd, Yb, and Lu). Relativistic first-order perturbations including S-0 couplings are accounted for. The calculated molecular constants are in reasonable agreement with the experimental ones. The calculated lanthanide contractions of the three series, i.e. R(La-X) - R(Lu-X), are quite different, 0.198, (0.19 A) for LnH, 0.108, (0.11 A) for LnF, and only 0.05 A (0.04A) for LnO. There is good agreement between the calculated values and the experimental ones (values in parentheses). This astonishing variation has two origins, a monoatomic and a diatomic one, which are related to each other. The first point is the noninteger 4f-shell population. Participation of unoccupied 4f-AOs in outervalence shell bonding is important for strongly bound lighter lanthanides. The second point is the "rigidity" of the bond: the larger the bond energy or the force constant, the smaller the lanthanide contraction.