On Relativity, Bonding, and Valence Electron Distribution

Abstract

The scalar relativistic contributions to bond or atomization energies of homo-or hetero-polar s-p-bonded atoms, ∆ rel E(bond), correlate well with the changes on bond formation of the electron density, integrated throughout the spatial K-shell region of the heavy nucleus, ∆ bond F K-region , times Z 4 , 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, ∆ nonrel E(bond). Also, scalar relativistic bond energy changes and bond length changes, ∆ rel R e , are not directly correlated. Namely, ∆ rel E(bond) correlates with the difference ∆ bond F K-region , whereas ∆ rel R e correlates with the derivative (dF K-region /dR). Reducing the internuclear distance from the separated to the united atom limit through the equilibrium distance value, R e , the density around the nucleus at first decreases in many cases, goes through a minimum, and finally increases again. Therefore (dF K-region /dR) may be positive or negative at R e .

Vibrational dependence of the torsional tunneling splitting and the a to b intensity evolution in the OH overtone spectra of CH3OH

“…Similar inversion has been discovered for the ν 11 (A ) out-of-plane CH 3 rock around 1140 cm −1 [13], and analysis of the high-resolution CH 2 -bending fundamental region also suggests an anomalous structure for one of the bending vibrations [14]. This frequently observed inversion pattern might arise naturally for a wide class of methyl-top-containing molecules, as suggested by Wang and Perry [11] on the basis of their successful explanation of the inversion for the CH stretches of methanol through an internal coordinate local-mode approach.…”

“…Interestingly, the torsional E/A ordering has been found to be reversed for a number of excited vibrational modes, contrary to the requirement of the conventional model. In the 3 µm region, inverted torsional patterns have been observed [10,11] for the two asymmetric CH stretches, ν 9 (A ) and ν 2 (A ), while the symmetric ν 3 (A ) mode is normal [12]. Similar inversion has been discovered for the ν 11 (A ) out-of-plane CH 3 rock around 1140 cm −1 [13], and analysis of the high-resolution CH 2 -bending fundamental region also suggests an anomalous structure for one of the bending vibrations [14].…”

Relativistic and quantum electrodynamic effects in superheavy elements

“…The matrices α and β are the Dirac matrices in the standard representation, 3 the σ i are the Pauli matrices, I n denotes the n × n unit matrix, and the projection operator + makes sure that only positive energy states are occupied (no-virtual pair approximation, NVPA) [69], which also circumvents the Brown-Ravenhall continuum dissolution [39,70,71]. We note that the projection operator + depends on the actual potential used, and numerical examples for Hartree-Fock orbital energies using different projections together with a detailed discussion can be found in Ref.…”

“…It is now well established that relativistic effects in the electronic structure of heavy elements are important to the extent that they can significantly alter their chemical and physical behaviour [1][2][3][4][5]. Simple extrapolations from the lighter to the heavier elements to deduce the physical or chemical behaviour of the heaviest elements in the periodic table [6] is therefore not always possible.…”

Prescreening and efficiency in the evaluation of integrals over ab initio effective core potentials

“…the core electrons) have substantial relativistic character, meaning that neglecting these effects can lead to significant errors. [14][15][16][17] While methods do exist to include such terms in a calculation, it is much more efficient to include them in the fitting process of the ECP. In this way, the accuracy of results may even be improved 18,19 , despite a substantial number of electrons being frozen.…”