Michael Seth

The chemistry of the superheavy elements. I. Pseudopotentials for 111 and 112 and relativistic coupled cluster calculations for (112)H+, (112)F2, and (112)F4

One- and two-component (spin–orbit coupled) relativistic and nonrelativistic energy adjusted pseudopotentials and basis sets for the elements 111 and 112 are presented. Calculations on the positively charged monohydride of the recently discovered superheavy element 112 are reported. Electron correlation is treated at the multireference configuration interaction and coupled cluster level and fine structure effects are derived from a single-reference configuration interaction treatment. Relativistic effects decrease the (112)H+ bond distance by 0.41 A. This bond contraction is similar to the one calculated recently for (111)H [Chem. Phys. Lett. 250, 461 (1996)]. As a result the bond distance of (112)H+ (1.52 A) is predicted to be smaller compared to those of the hydrides of the lighter congeners HgH+ (1.59 A), CdH+ (1.60 A) and similar to that of ZnH+ (1.52 A). We predict that (112)H+ is the most stable hydride in the Group 12 series due to relativistic effects. As in the case of (111)H the relativistic inc...

On the relation between time-dependent and variational density functional theory approaches for the determination of excitation energies and transition moments.

It is shown that it is possible to derive the basic eigenvalue equation of adiabatic time-dependent density functional theory within the Tamm-Dancoff approximation (TD-DFT/TD) from a variational principle. The variational principle is applied to the regular Kohn-Sham formulation of DFT energy expression for a single Slater determinant and leads to the same energy spectrum as TD-DFT/TD. It is further shown that this variational approach affords the same electric and magnetic transition moments as TD-DFT/TD. The variational scheme can also be applied without the Tamm-Dancoff approximation. Practical implementations of TD-DFT are limited to second order response theory which introduces errors in transition energies for charge transfer and Rydberg excitations. It is indicated that higher order terms can be incorporated into the variational approach. It is also discussed how the current variational method is related to traditional DFT schemes based on variational principles such as DeltaSCF-DFT, and how they can be combined.

A point-charge model for the nuclear quadrupole moment: Coupled-cluster, Dirac–Fock, Douglas–Kroll, and nonrelativistic Hartree–Fock calculations for the Cu and F electric field gradients in CuF

A point charge model for the nuclear quadrupole moment tensor (PCNQM) is developed in order to determine accurate electric field gradients (EFG) at the relativistic and correlated levels. The symmetric s contributions arising from the Poisson equation are avoided by using an appropriate point charge distribution in three-dimensional space. It is shown that the PCNQM model yields virtually the same EFGs compared to the conventional method of expectation values, if the point charges are set at small displacements from the nucleus (d<10−13 m) and the SCF energy is converged out to 12 significant figures. We further demonstrate that the choice of the point charge ζ is not very critical to the PCNQM perturbation, and that the correlation energy at both the nonrelativistic and relativistic level of theory depends linearly on ζ. This suggests that accurate EFG tensors can be obtained by performing only two correlated calculations for each atom and tensor component. The PCNQM model is tested on one-electron atoms...

Dependence of relativistic effects on electronic configuration in the neutral atoms of d- and f-block elements

Although most neutral d‐ and f‐block atoms have ndg−2(n + 1)s2 and (n − 1)fg−2(n + 1)s2 ground configurations, respectively, where g is the group number (i.e., number of valence electrons), one‐third of these 63 atoms prefer a higher d‐population, namely via (n + 1)s→nd “outer” to “inner” electron shift (particularly atoms from the second d‐row), or via (n − 1)f→nd “inner” to “outer” electron shift (particularly atoms from the second f‐row). Although the response to the modified self‐consistent field is orbital destabilization and expansion for (n + 1)s→nd, and stabilization and contraction for (n − 1)f→nd, the relativistic modification of the valence orbital responses is stabilization in both cases. This is explained by double perturbation theory. Accordingly, electron configuration and relativity trigger the orbital energies, the orbital populations and the chemical shell effects in different ways. The particularly pronounced relativistic effects in groups 10 and 11, the so‐called gold maximum, occur because of particularly efficient cooperative nonrelativistic shell effects and relativistic stabilization effects (inverse indirect effect) at the end of the d‐block.

A revised electronic Hessian for approximate time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) at the generalized gradient level of approximation (GGA) has shown systematic errors in the calculated excitation energies. This is especially the case for energies representing electron transitions between two separated regions of space or between orbitals of different spatial extents. It will be shown that these limitations can be attributed to the electronic ground state Hessian G(GGA). Specifically, we shall demonstrate that the Hessian G(GGA) can be used to describe changes in energy due to small perturbations of the electron density (Deltarho), but it should not be applied to one-electron excitations involving the density rearrangement (Deltarho) of a full electron charge. This is in contrast to Hartree-Fock theory where G(HF) has a trust region that is accurate for both small perturbations and one-electron excitations. The large trust radius of G(HF) can be traced back to the complete cancellation of Coulomb and exchange terms in Hartree-Fock (HF) theory representing self-interaction (complete self-interaction cancellation, CSIC). On the other hand, it is shown that the small trust radius for G(GGA) can be attributed to the fact that CSIC is assumed for GGA in the derivation of G(GGA) although GGA (and many other approximate DFT schemes) exhibits incomplete self-interaction cancellation (ISIC). It is further shown that one can derive a new matrix G(R-DFT) with the same trust region as G(HF) by taking terms due to ISIC properly into account. Further, with TD-DFT based on G(R-DFT), energies for state-to-state transitions represented by a one-electron excitation (psi(i)-->psi(a)) are approximately calculated as DeltaE(ai). Here DeltaE(ai) is the energy difference between the ground state Kohn-Sham Slater determinant and the energy of a Kohn-Sham Slater determinant where psi(i) has been replaced by psi(a). We make use of the new Hessian in two numerical applications involving charge-transfer excitations. It is concluded that higher than second order response theory (involving ISIC terms) must be used in approximate TD-DFT, in order to describe charge-transfer excitations.

Range-Separated Exchange Functionals with Slater-Type Functions

An implementation of range-separated density functionals utilizing the Yukawa potential and Slater-type functions is described. The density-functional part of the range-separated regime is straightforward. The exact exchange part makes use of established methods for evaluating exchange integrals over Slater-type functions but still requires new one- and two-center integrals. Equations for the one-center integrals are derived. The two-center integrals are evaluated through a combination of new equations and techniques taken from procedures for evaluating two-center Coulomb integrals over Slater-type functions. In a first application, the performance of range-separated functionals in the prediction of transition metal thermochemistry is evaluated using a database of average ligand removal energies. The range-separated functionals perform better than a GGA parent and similarly to commonly used hybrid and meta-hybrid functionals. The results were relatively insensitive to the chosen value of the attenuation parameter.

THE CHEMISTRY OF SUPERHEAVY ELEMENTS. III. THEORETICAL STUDIES ON ELEMENT 113 COMPOUNDS

The chemistry of element 113 is investigated by theoretical methods. The results of fully relativistic calculations for (113)H and (113)F are compared with those derived by other techniques to obtain an indication of the accuracy of the more approximate models as well as the importance of including scalar and/or spin–orbit relativistic effects. Both of these effects are found to be important. The spin–orbit coupled pseudopotential approximation yields results of satisfactory accuracy, but the two relativistic methods that do not include spin–orbit coupling (Douglas–Kroll and scalar relativistic pseudopotential method) do not agree so well with each other. The calculated properties of (113)H and (113)F and a number of other hydrides and halides of element 113 are compared with the properties of the equivalent compounds of the lighter group 13 elements. In general, element 13 exhibits behavior that is consistent with its placement in group 13 of the periodic table. Some of its properties are found to be somewhat unusual however, e.g., the element is relatively electronegative, the molecules (113)H3, (113)F3, and (113)Cl3 are predicted to be T-shaped rather than trigonal planar, and the 6d electrons of element 113 participate to a significant extent in chemical bonding. Compounds where element 113 is present in the +5 oxidation state are considered as well but are predicted to be thermodynamically unstable.The chemistry of element 113 is investigated by theoretical methods. The results of fully relativistic calculations for (113)H and (113)F are compared with those derived by other techniques to obtain an indication of the accuracy of the more approximate models as well as the importance of including scalar and/or spin–orbit relativistic effects. Both of these effects are found to be important. The spin–orbit coupled pseudopotential approximation yields results of satisfactory accuracy, but the two relativistic methods that do not include spin–orbit coupling (Douglas–Kroll and scalar relativistic pseudopotential method) do not agree so well with each other. The calculated properties of (113)H and (113)F and a number of other hydrides and halides of element 113 are compared with the properties of the equivalent compounds of the lighter group 13 elements. In general, element 13 exhibits behavior that is consistent with its placement in group 13 of the periodic table. Some of its properties are found to be som...

Large relativistic effects in molecular properties of the hydride of superheavy element 111

Abstract Relativistic and electron correlation contributions in the hydride of the recently discovered superheavy element 111 were studied using ab-initio methods within different relativistic approaches. Relativistic effects decrease the (111)H bond distance by 0.42 A. As a result of this large bond contraction, the bond distance of (111)H (1.51 A) is comparable to that of the hydride of its lighter congener AuH (1.52 A), but below that of AgH (1.60 A). The dissociation energy is relativistically increased by approximately 1.2 eV and the stretching force constant is more than quadrupled from 1.1 mdyn/A at the nonrelativistic level to 5.0 mdyn/A at the relativistic level.

The chemistry of the superheavy elements. II. the stability of high oxidation states in group 11 elements: Relativistic coupled cluster calculations for the di-, tetra- and hexafluoro metallates of Cu, Ag, Au, and element 111

The stability of the high oxidation states +3 and +5 in Group 11 fluorides is studied by relativistic Mo/ller–Plesset (MP) and coupled cluster methods. Higher metal oxidation states are stabilized by relativistic effects. As a result, the hexafluoro complex of the Group 11 element with nuclear charge 111 and oxidation state +5 is the most stable compared to the other congeners. The results also suggest that AgF6− is thermodynamically stable and, therefore, it might be feasable to synthesize this compound. For the copper fluorides we observe very large oscillations in the Mo/ller–Plesset series up to the fourth order. Nonrelativistic calculations lead to the expected trend in the metal–fluorine bond distances for the MF2− compounds, CuF2−<AgF2−<AuF2−<(111)F2−. However, relativistic effects change this trend to CuF2−<AuF2−<(111)F2−<AgF2−. Vibrational frequencies are predicted for all compounds. Where experimental data are available, they generally agree very well with our calculated results.

Calculation of the A term of magnetic circular dichroism based on time dependent-density functional theory I. Formulation and implementation

A procedure for calculating the A term and the A/D ratio of magnetic circular dichroism (MCD) within time-dependent density functional theory (TD-DFT) is described. Utilizing an implementation of the MCD theory within the Amsterdam Density Functional program, the A term contributions to the MCD spectra of MnO(4) (-), CrO(4) (2-), VO(4) (3-), MoO(4) (2-), VO(4) (3-), MoS(4) (2-), Se(4) (2+), Te(4) (2+), Fe(CN)(6) (4-), Ni(CN)(4) (2-), trichlorobenzene, hexachlorobenzene, tribromobenzene, and hexabromobenzene are calculated. For the most part, agreement between theory and experiment for A/D ratios and the relative magnitude of A terms is found to be good, leading to simulated spectra that are similar in appearance to those derived from measurements. The A terms are found to be too small whenever comparison with experiment was possible, probably due to the neglect of environment effects on the incident radiation and the relative low accuracy of dipole strengths calculated within TD-DFT.