Understanding relativistic effects of chemical bonding

Abstract

mTo elucidate the physical origin of relativistic changes of molecular properties, exact theorems, perturbation theory, and Hartree-Fock-Slater-Pauli calculations are exploited. The relativistic molecular virial theorem offers insight into the relativistic and nonrelativistic, kinetic, and potential energy contributions to the bond energy. In general, there exist two contributions to the relativistic correction of a molecular property: the relativistic change at the nonrelativistic equilibrium geometry and the change of the nonrelativistic property due to the relativistic change of the equilibrium geometry. Sometimes the first and sometimes the second contribution is the dominant one. Accurate numerical results for Hl-like systems are obtained using direct relativistic double perturbation theory. In some cases, near-degenerate perturbation theory is mandatory. Relativistic changes of chemical bond energies are often proportional to the density change in the K-shell when the bond is formed. Relativistic corrections to many properties (and also to the 1 s2-correlation energy) are often proportional to Z2a2. 0 1996 John Wiley & Sons, Inc. so-called relativistic corrections are well defined in 1 . Introduction theory, although nonobservable quantities. Since the common thinking is nonrelativistic, and since While the world of chemical perception is claswe have much experience with classical and nonsical, the underlying world of microscopic matter relativistic theories, the relativistic corrections-as is a relativistic quantum world. Nonrelativistic differences between common understanding and theories of massive charged particles with spin microscopic reality-deserve theoretical under-(see, e.g., [ 11) are well developed. Accordingly, the standing. Relativity, indeed, plays a very signifi-

On Relativity, Bonding, and Valence Electron Distribution

“…The relativistic energy contributions of hydrogen-like atomic orbitals vary with the nuclear charge as Z 4 . Indeed Δ scal.rel E (bond) correlates well with Δ bond 〈ρ〉 K-region · Z 4 for a large set of s−p−σ-bonded molecules with a single heavy atom (Figure , see also refs and ), where k = 0.95: The respective slope of − 21 V for heavy atomic molecules agrees well with the one from Figure for oxygen compounds, which is − 22.5 V (i.e., − 103 V· Z 4 /c 2 , where Z / c is 8/137 for oxygen). Most molecules with a heavy s-block element in Figure show relativistic bond energy increases, whereas most molecules with a heavy p−d−f-block element show relativistic bond energy decreases, as do the oxygen systems.…”

“…This explains why also the heavy-atomic compounds with large indirect orbital reorganizations lie near the correlation lines of Figures and . Scalar relativistic bond effects can be attributed dominantly to the contributions from the first half wave of atomic s orbitals (compare also refs , , and 28).…”

“…Several years ago Wang 1 and Schwarz et al, 2 and again more recently other researchers, [3][4][5][6][7] found that the scalar relativistic effects reduce the absolute value of the bond or atomization energies (atomization energy is the sum of two-atomic bond energies) of many light p-block molecules (i.e., raise the values of their bond energies, which are defined as negative). On the other hand, positiVe and negatiVe relativistic contributions to bond energies were obtained for a more comprehensive set of molecules.…”

“…On the other hand, positiVe and negatiVe relativistic contributions to bond energies were obtained for a more comprehensive set of molecules. 1,2,8,9 The scalar relatiVistic effects comprise the direct massvelocity and scalar spin-Darwin contributions, and the so-called indirect effects caused by the Coulomb repulsion between the relatiVistically modified orbitals. In addition, there are also the Vectorial spin-dependent relativistic bond energy contributions, which are of orders of magnitude similar to the scalar ones.…”

Lanthanide Diatomics and Lanthanide Contractions

“…We note that the direct relativistic effects originate in the vicinity of the nucleus.47•48 There is a linear relation between the change of electron charge in the spatial K-shell upon bond formation times Z4 and relativistic corrections to the bond energy. 48 This relation also holds for the lanthanide molecules, as shown in Figure 1. So we have traced back the large relativistic destabilization of GdO to the large decrease of electronic charge in the K shell of Gd upon formation of GdO from the atoms.…”