Relativistic Coupling Effects Research Articles

Hydrogen-iodine scattering. I. Development of an accurate spin-orbit coupled diabatic potential energy model.

The scattering of H by I is a prototypical model system for light-heavy scattering in which relativistic coupling effects must be taken into account. Scattering calculations depend strongly on the accuracy of the potential energy surface (PES) model. The methodology to obtain such an accurate PES model suitable for scattering calculations is presented, which includes spin-orbit (SO) coupling within the Effective Relativistic Coupling by Asymptotic Representation (ERCAR) approach. In this approach, the SO coupling is determined only for the atomic states of the heavy atom, and the geometry dependence of the SO effect is accounted for by a diabatization with respect to asymptotic states. The accuracy of the full model, composed of a Coulomb part and the SO model, is achieved in the following ways. For the SO model, the extended ERCAR approach is applied, which accounts for both intra-state and inter-state SO coupling, and an extended number of diabatic states are included. The corresponding coupling constants for the SO operator are obtained from experiments, which are more accurate than computed values. In the Coulomb Hamiltonian model, special attention is paid to the long range behavior and accurate c6 dispersion coefficients. The flexibility and accuracy of this Coulomb model are achieved by combining partial models for three different regions. These are merged via artificial neural networks, which also refine the model further. In this way, an extremely accurate PES model for hydrogen iodide is obtained, suitable for accurate scattering calculations.

An improved spin-orbit coupling model for use within the effective relativistic coupling by asymptotic representation (ERCAR) method.

An improved atomic spin-orbit model is presented, which is designed to be used within the framework of the effective relativistic coupling by asymptotic representation method. This method is used for the generation of highly accurate coupled potential energy surfaces (PESs) to represent the fine structure energies of appropriate systems. The approach is demonstrated using CH3I and its photodissociation as a typical example. The method is based on a specific diabatization of electronic spin-space ("spin-free") states with respect to the asymptote at which a single relativistic atom is separated from a molecular non-relativistic fragment. Thus, the relativistic coupling effects can be treated entirely within the atomic framework. So far, an effective spin-orbit coupling operator which only accounts for intra-state coupling within each atomic spin-space state was used. In the present work, this approach is extended to account for inter-state couplings among different atomic spin-space states as well. It is shown that this extended approach improves the accuracy of the PESs significantly for higher excited states and also enhances the accuracy of low energy states. In particular, it improves the representation of the spin-orbit induced conical intersection among the 3Q0 and 1Q1 states of CH3I, which is of high relevance for the nonadiabatic quantum dynamics of the photodissociation.

Importance of Relativistic Effects and Electron Correlation in Structure Factors and Electron Density of Diphenyl Mercury and Triphenyl Bismuth.

This study investigates the possibility of detecting relativistic effects and electron correlation in single-crystal X-ray diffraction experiments using the examples of diphenyl mercury (HgPh2) and triphenyl bismuth (BiPh3). In detail, the importance of electron correlation (ECORR), relativistic effects (REL) [distinguishing between total, scalar and spin-orbit (SO) coupling relativistic effects] and picture change error (PCE) on the theoretical electron density, its topology and its Laplacian using infinite order two component (IOTC) wave functions is discussed. This is to develop an understanding of the order of magnitude and shape of these different effects as they manifest in the electron density. Subsequently, the same effects are considered for the theoretical structure factors. It becomes clear that SO and PCE are negligible, but ECORR and scalar REL are important in low- and medium-order reflections on absolute and relative scales-not in the high-order region. As a further step, Hirshfeld atom refinement (HAR) and subsequent X-ray constrained wavefunction (XCW) fitting have been performed for the compound HgPh2 with various relativistic and nonrelativistic wave functions against the experimental structure factors. IOTC calculations of theoretical structure factors and relativistic HAR as well as relativistic XCW fitting are presented for the first time, accounting for both scalar and spin-orbit relativistic effects.