Ephraim Eliav

Formulation and implementation of the relativistic Fock-space coupled cluster method for molecules

An implementation of the relativistic multireference Fock-space coupled cluster method is presented which allows simultaneous calculation of potential surfaces for different oxidation states and electronic levels of a molecule, yielding values for spectroscopic constants and transition energies. The method is tested in pilot calculations on the I2 and HgH molecules, and is shown to give a good and balanced description of various electronic states and energies.

Intermediate Hamiltonian Fock-space coupled-cluster method: Excitation energies of barium and radium

An intermediate Hamiltonian Fock-space coupled cluster method is introduced, based on the formalism developed by Malrieu and co-workers in the context of perturbation theory. The method is designed to make possible the use of large P spaces while avoiding convergence problems traceable to intruder states, which often beset multireference coupled cluster schemes. The essence of the method is the partitioning of P into a main Pm and an intermediate Pi serving as buffer, with concomitant definition of two types of wave and excitation operators. Application to atomic barium and radium yields converged results for a large number of states not accessible by traditional Fock-space coupled cluster. Moreover, states calculated by both methods exhibit better accuracy (by a factor of 2–5) in the intermediate Hamiltonian approach. Energies are given for low-lying states of Ra which have not been observed experimentally.

A Fock space coupled cluster study on the electronic structure of the UO2, UO2+, U4+, and U5+ species

The ground and excited states of the UO(2) molecule have been studied using a Dirac-Coulomb intermediate Hamiltonian Fock-space coupled cluster approach (DC-IHFSCC). This method is unique in describing dynamic and nondynamic correlation energies at relatively low computational cost. Spin-orbit coupling effects have been fully included by utilizing the four-component Dirac-Coulomb Hamiltonian from the outset. Complementary calculations on the ionized systems UO(2) (+) and UO(2) (2+) as well as on the ions U(4+) and U(5+) were performed to assess the accuracy of this method. The latter calculations improve upon previously published theoretical work. Our calculations confirm the assignment of the ground state of the UO(2) molecule as a (3)Phi(2u) state that arises from the 5f(1)7s(1) configuration. The first state from the 5f(2) configuration is found above 10,000 cm(-1), whereas the first state from the 5f(1)6d(1) configuration is found at 5,047 cm(-1).

Electronic structure of eka-lead (element 114) compared with lead

The electronic level structure of eka-lead (element 114), the synthesis of which was reported last year, is studied by the recently developed intermediate Hamiltonian Fock-space coupled-cluster method. Very large basis sets are used, with l up to 8, and 36 electron are correlated. The accuracy of the resulting transition energies is tested by applying the same method to Pb; calculated ionization potentials and excitation energies agree with experiment within a few hundredths of an eV, and similar accuracy is expected for the heavier element. Ionization potentials and excitation energies of E114 are considerably higher than for Pb, due to the relativistic stabilization of the 7s and 7p1/2 orbitals. This indicates that eka-lead will probably be more inert and less metallic than lead.

Measurement of the first ionization potential of astatine by laser ionization spectroscopy

The radioactive element astatine exists only in trace amounts in nature. Its properties can therefore only be explored by study of the minute quantities of artificially produced isotopes or by performing theoretical calculations. One of the most important properties influencing the chemical behaviour is the energy required to remove one electron from the valence shell, referred to as the ionization potential. Here we use laser spectroscopy to probe the optical spectrum of astatine near the ionization threshold. The observed series of Rydberg states enabled the first determination of the ionization potential of the astatine atom, 9.31751(8) eV. New ab initio calculations are performed to support the experimental result. The measured value serves as a benchmark for quantum chemistry calculations of the properties of astatine as well as for the theoretical prediction of the ionization potential of superheavy element 117, the heaviest homologue of astatine.

High-Accuracy Calculations for Heavy and Super-Heavy Elements

Energy levels of heavy and super-heavy (Z>100) elements are calculated by the relativistic coupled cluster method. The method starts from the four-component solutions of the Dirac-Fock or Dirac-Fock-Breit equations, and correlates them by the coupled-cluster approach. Simultaneous inclusion of relativistic terms in the Hamiltonian (to order α 2 , where α is the fine-structure constant) and correlation effects (all products and powers of single and double virtual excitations) is achieved. The Fock-space coupled-cluster method yields directly transition energies (ionization potentials, excitation energies, electron affinities). Results are in good agreement (usually better than 0.1 eV) with known experimental values. Properties of superheavy atoms which are not known experimentally can be predicted. Examples include the nature of the ground states of elements 104 and 111. Molecular applications are also presented.

Prediction of the adsorption behavior of elements 112 and 114 on inert surfaces from ab initio Dirac-Coulomb atomic calculations

The interaction of elements 112 and 114 with inert surfaces has been studied on the basis of fully relativistic ab initio Dirac-Coulomb CCSD(T) calculations of their atomic properties. The calculated polarizabilities of elements 112 and 114 are significantly lower than corresponding Hg and Pb values due to the relativistic contraction of the valence ns and np(12) orbitals, respectively, in the heavier elements. Due to the same reason, the estimated van der Waals radius of element 114 is smaller than that of Pb. The enthalpies of adsorption of Hg, Pb, and elements 112 and 114 on inert surfaces such as quartz, ice, and Teflon were predicted on the basis of these atomic calculations using a physisorption model. At the present level of accuracy, -DeltaH(ads) of element 112 on these surfaces is slightly (about 2 kJ/mol) larger than -DeltaH(ads)(Hg). The calculated -DeltaH(ads) of element 114 on quartz is about 7 kJ/mol and on Teflon is about 3 kJ/mol smaller than the respective values of -DeltaH(ads)(Pb). The trend of increasing -DeltaH(ads) in group 14 from C to Sn is thus reversed, giving decreasing values from Sn to Pb to element 114 due to the relativistic stabilization and contraction of the np(12) atomic orbitals. This is similar to trends shown by other atomic properties of these elements. The small difference in DeltaH(ads) of Pb and element 114 on inert surfaces obtained within a picture of physisorption contrasts with the large difference (more than 100 kJ/mol) in the chemical reactivity between these elements.

Mixed-sector intermediate Hamiltonian Fock-space coupled cluster approach.

An alternative formulation of the intermediate Hamiltonian Fock-space coupled cluster scheme developed before is presented. The methodological and computational advantages of the new formulation include the possibility of using a model space with determinants belonging to different Fock-space sectors. This extends the scope of application of the multireference coupled cluster method, and makes possible the use of quasiclosed shells (e.g., p2, d4) as reference states. Representative applications are described, including electron affinities of group-14 atoms, ionization potentials of group-15 elements, and ionization potentials and excitation energies of silver and gold. Excellent agreement with experiment (a few hundredths of an electronvolt) is obtained, with significant improvement (by a factor of 5-10 for p3 states) over Fock-space coupled cluster results. Many states not reachable by the Fock-space approach can now be studied.

Intermediate Hamiltonian Fock-space coupled cluster method in the one-hole one-particle sector: Excitation energies of xenon and radon

The intermediate Hamiltonian Fock-space coupled cluster method developed recently is applied to excitations in the one-hole one-particle sector, taking xenon and radon atoms as test cases. Virtual orbitals are modified to yield better approximations to orbitals occupied in excited states. The usual Fock-space coupled cluster scheme diverges for these systems, but the intermediate Hamiltonian approach converges for large P spaces and yields excitation energies in very good agreement with experiment. The average error in the calculated values for the lowest excitation energies (about 20 for each atom) is 0.6%. Predictions are made for the unobserved 8s Rydberg states of Rn.

The relativistic Fock-space coupled-cluster method for molecules: CdH and its ions

The relativistic coupled-cluster method starts from the Dirac–Coulomb–Breit Hamiltonian in its low-frequency approximation and includes correlation by Fock-space coupled-cluster with single and double excitations. One- and two-component approximations using the Douglas–Kroll transformation are also tested. Significant relativistic effects are found for CdH, with bond length contracting from 1.820 to 1.778 A (experimental 1.781 A) and binding energies decreasing from 0.87 to 0.70 eV (experimental 0.68 eV). The binding energy of the cation increases by 0.1 eV upon inclusion of relativity. The electron affinity of the molecule is 0.44 eV. The Douglas–Kroll values include nearly all the relativistic correction.