Remigius Mastalerz

Analytic high-order Douglas-Kroll-Hess electric field gradients

In this work we present a comprehensive study of analytical electric field gradients in hydrogen halides calculated within the high-order Douglas-Kroll-Hess (DKH) scalar-relativistic approach taking picture-change effects analytically into account. We demonstrate the technical feasibility and reliability of a high-order DKH unitary transformation for the property integrals. The convergence behavior of the DKH property expansion is discussed close to the basis set limit and conditions ensuring picture-change-corrected results are determined. Numerical results are presented, which show that the DKH property expansion converges rapidly toward the reference values provided by four-component methods. This shows that in closed-shell cases, the scalar-relativistic DKH(2,2) approach which is of second order in the external potential for both orbitals and property operator yields a remarkable accuracy. As a parameter-dependence-free high-order DKH model, we recommend DKH(4,3). Moreover, the effect of a finite-nucleus model, different parametrization schemes for the unitary matrices, and the reliability of standard basis sets are investigated.

Relativistic Effects on the Topology of the Electron Density

The topological analysis of electron densities obtained either from X-ray diffraction experiments or from quantum chemical calculations provides detailed insight into the electronic structure of atoms and molecules. Of particular interest is the study of compounds containing (heavy) transition-metal elements, which is still a challenge for experiment as well as from a quantum-chemical point of view. Accurate calculations need to take relativistic effects into account explicitly. Regarding the valence electron density distribution, these effects are often only included indirectly through relativistic effective core potentials. But as different variants of relativistic Hamiltonians have been developed all-electron calculations of heavy elements in combination with various electronic structure methods are feasible. Yet, there exists no systematic study of the topology of the total electron density distribution calculated in different relativistic approximations. In this work we therefore compare relativistic Hamiltonians with respect to their effect on the electron density in terms of a topological analysis. The Hamiltonians chosen are the four-component Dirac-Coulomb, the quasi-relativistic two-component zeroth-order regular approximation, and the scalar-relativistic Douglas-Kroll-Hess operators.

Basis set representation of the electron density at an atomic nucleus

In this paper a detailed investigation of the basis set convergence for the calculation of relativistic electron densities at the position of finite-sized atomic nuclei is presented. The development of Gauss-type basis sets for such electron densities is reported and the effect of different contraction schemes is studied. Results are then presented for picture-change corrected calculations based on the Douglas-Kroll-Hess Hamiltonian. Moreover, the role of electron correlation, the effect of the numerical integration accuracy in density functional calculations, and the convergence with respect to the order of the Douglas-Kroll-Hess Hamiltonian and the picture-change-transformed property operator are studied.

On the R-dependence of the spin-orbit coupling constant: Potential energy functions of Xe2+ by high-resolution photoelectron spectroscopy and ab initio quantum chemistry

The pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of Xe(2) has been measured between 97 350 and 108 200 cm(-1), following resonant two-photon excitation via selected vibrational levels of the C 0(u) (+) Rydberg state of Xe(2). Transitions to three of the six low-lying electronic states of Xe(2) (+) could be observed. Whereas extensive vibrational progressions were observed for the transitions to the I(32g) and I(32u) states, only the lowest vibrational levels of the II(12u) state could be detected. Assignments of the vibrational quantum numbers were derived from the analysis of the isotopic shifts and from the modeling of the potential energy curves. Adiabatic ionization energies, dissociation energies, and vibrational constants are reported for the I(32g) and the I(32u) states. Multireference configurational interaction and complete active space self-consistent field calculations have been performed to investigate the dependence of the spin-orbit coupling constant on the internuclear distance. The energies of vibrational levels, measured presently and in a previous investigation (Rupper et al., J. Chem. Phys. 121, 8279 (2004)), were used to determine the potential energy functions of the six low-lying electronic states of Xe(2) (+) using a global model that includes the long-range interaction and treats, for the first time, the spin-orbit interaction as dependent on the internuclear separation.

Nuclear quadrupole moment of Sn-119

Second-order scalar-relativistic Douglas-Kroll-Hess density functional calculations of the electric field gradient, including an analytic correction of the picture change error, were performed for 34 tin compounds of which molecular structures and 119Sn Mössbauer spectroscopy parameters are experimentally known. The components of the diagonalized electric field gradient tensor, Vxx, Vyy, Vzz, were used to determine the quantity V, which is proportional to the nuclear quadrupole splitting parameter DeltaE. The slope of the linear correlation plot of the experimentally determined DeltaE parameter versus the corresponding calculated V data allowed us to obtain an absolute value of the nuclear quadrupole moment Q of 119Sn equal to Q = 13.2 +/- 0.1 fm2. This is about 11% larger than the picture-change-error-affected value and in good agreement with previous estimates of the picture change error in compounds of similar atomic charge. Moreover, despite the variety of the tin compounds considered in this study, the new result is in excellent agreement with the previously determined most accurate value of Q for 119Sn of Q = 12.8 +/- 0.7 fm2, but with a noticeably narrower error bar. The reliability of the calibration method in the calculation of the DeltaE parameter of tin compounds is within a margin of +/-0.3 mm s-1 when compared to experimental data and does not depend on the inclusion of the picture change correction in the density functional calculations but is essentially determined by the use of an atomic natural orbital relativistic core-correlated basis set for the description of the core electron density. The results obtained suggest that the present picture-change-corrected Douglas-Kroll-Hess approach provides reliable electric field gradients in the case of closed-shell metal compounds involving elements up to the fifth row of the periodic table for which spin-orbit coupling is negligible.

Nuclear quadrupole moment of 119Sn.

Second-order scalar-relativistic Douglas-Kroll-Hess density functional calculations of the electric field gradient, including an analytic correction of the picture change error, were performed for 34 tin compounds of which molecular structures and 119Sn Mössbauer spectroscopy parameters are experimentally known. The components of the diagonalized electric field gradient tensor, Vxx, Vyy, Vzz, were used to determine the quantity V, which is proportional to the nuclear quadrupole splitting parameter DeltaE. The slope of the linear correlation plot of the experimentally determined DeltaE parameter versus the corresponding calculated V data allowed us to obtain an absolute value of the nuclear quadrupole moment Q of 119Sn equal to Q = 13.2 +/- 0.1 fm2. This is about 11% larger than the picture-change-error-affected value and in good agreement with previous estimates of the picture change error in compounds of similar atomic charge. Moreover, despite the variety of the tin compounds considered in this study, the new result is in excellent agreement with the previously determined most accurate value of Q for 119Sn of Q = 12.8 +/- 0.7 fm2, but with a noticeably narrower error bar. The reliability of the calibration method in the calculation of the DeltaE parameter of tin compounds is within a margin of +/-0.3 mm s-1 when compared to experimental data and does not depend on the inclusion of the picture change correction in the density functional calculations but is essentially determined by the use of an atomic natural orbital relativistic core-correlated basis set for the description of the core electron density. The results obtained suggest that the present picture-change-corrected Douglas-Kroll-Hess approach provides reliable electric field gradients in the case of closed-shell metal compounds involving elements up to the fifth row of the periodic table for which spin-orbit coupling is negligible.

Spin-Orbit Coupling and Potential Energy Functions of Ar2(+) and Kr2(+) by High-Resolution Photoelectron Spectroscopy and ab Initio Quantum Chemistry.

The dependence of the spin-orbit-coupling constant of the six low-lying electronic states of Ar2(+) and Kr2(+) on the internuclear distance R has been calculated ab initio. The spin-orbit-coupling constant varies by about 10% over the range of internuclear distances relevant for the interpretation of the high-resolution photoelectron spectra of Ar2 and Kr2 and can be accurately represented by a Morse-type function for the states of ungerade electronic symmetry and by an exponentially decreasing function for the states of gerade symmetry. The spin-orbit-coupling constant is larger than the asymptotic value (at R → ∞) for the gerade states and smaller for the ungerade states. The calculated R-dependent spin-orbit-coupling constants were used to derive a new set of potential energy functions for the low-lying electronic states of Ar2(+) and Kr2(+) and to quantify the errors resulting from the widely used approach consisting of approximating the spin-orbit-coupling constant by its asymptotic value. The effects of the R dependence on the potential energy functions of the six low-lying electronic states of the homonuclear rare-gas dimer ions are found to be very small for Ar2(+) (and by inference also for Ne2(+)) but significant for Kr2(+). The shifts arising in calculations of the potential energy functions from a neglect of the R dependence of the spin-orbit-coupling constant are the result of the interplay between the differences between the binding energies of the relevant (2)Π and (2)Σ(+) states, the magnitude of the spin-orbit-coupling constant, and the magnitude and sign of the deviations between the R-dependent spin-orbit-coupling constant and its asymptotic value at large internuclear distances.

Nuclear Quadrupole Moment of119Sn

Second-order scalar-relativistic Douglas-Kroll-Hess density functional calculations of the electric field gradient, including an analytic correction of the picture change error, were performed for 34 tin compounds of which molecular structures and 119Sn Mössbauer spectroscopy parameters are experimentally known. The components of the diagonalized electric field gradient tensor, Vxx, Vyy, Vzz, were used to determine the quantity V, which is proportional to the nuclear quadrupole splitting parameter DeltaE. The slope of the linear correlation plot of the experimentally determined DeltaE parameter versus the corresponding calculated V data allowed us to obtain an absolute value of the nuclear quadrupole moment Q of 119Sn equal to Q = 13.2 +/- 0.1 fm2. This is about 11% larger than the picture-change-error-affected value and in good agreement with previous estimates of the picture change error in compounds of similar atomic charge. Moreover, despite the variety of the tin compounds considered in this study, the new result is in excellent agreement with the previously determined most accurate value of Q for 119Sn of Q = 12.8 +/- 0.7 fm2, but with a noticeably narrower error bar. The reliability of the calibration method in the calculation of the DeltaE parameter of tin compounds is within a margin of +/-0.3 mm s-1 when compared to experimental data and does not depend on the inclusion of the picture change correction in the density functional calculations but is essentially determined by the use of an atomic natural orbital relativistic core-correlated basis set for the description of the core electron density. The results obtained suggest that the present picture-change-corrected Douglas-Kroll-Hess approach provides reliable electric field gradients in the case of closed-shell metal compounds involving elements up to the fifth row of the periodic table for which spin-orbit coupling is negligible.