Relativistic Fock-space Coupled Cluster Method Research Articles

Ionization potentials and electron affinities of Rg, Cn, Nh, and Fl superheavy elements

The successive ionization potentials (IPs) and electron affinities (EAs) for superheavy elements with $111\ensuremath{\le}Z\ensuremath{\le}114$, namely, Rg, Cn, Nh, and Fl, are reexamined using the relativistic Fock-space coupled-cluster method with nonperturbative single (S), double (D), and triple (T) cluster amplitudes (FS-CCSDT). For most of the considered quantities, the triple-amplitude contributions turn out to be important. The Breit and frequency-dependent Breit corrections are evaluated by means of the configuration-interaction method. The quantum-electrodynamics corrections to the IPs and EAs are taken into account within the model-QED-operator approach. The obtained results are within 0.10 eV uncertainty.

Tin resonance-ionization schemes for atomic- and nuclear-structure studies

This paper presents high-precision spectroscopic measurements of atomic tin using five different resonance-ionization schemes performed with the collinear resonance-ionization spectroscopy technique. Isotope shifts were measured for the stable tin isotopes from the $5{s}^{2}5{p}^{2}\phantom{\rule{0.28em}{0ex}}^{3}{P}_{0,1,2}$ and ${}^{1}{S}_{0}$ to the $5{s}^{2}5p6s\phantom{\rule{0.28em}{0ex}}^{1}{P}_{1},^{3}{P}_{1,2}$ and $5{s}^{2}5p7s{\phantom{\rule{0.28em}{0ex}}}^{1}{P}_{1}$ atomic levels. The magnetic dipole hyperfine constants ${A}_{\mathrm{hf}}$ have been extracted for six atomic levels with electron angular momentum $Jg0$ from the hyperfine structures of nuclear spin $I=1/2$ tin isotopes, $^{115,117,119}\mathrm{Sn}$. State-of-the-art atomic calculations using a relativistic Fock-space coupled-cluster method and the configuration interaction approach combined with many-body perturbation theory allow accurate and reliable calculations of both field- and mass-shift factors for the studied transitions, in addition to the hyperfine magnetic fields and electric-field gradients of the atomic levels. The excellent agreement with the experimental results highlights the accuracy of modern atomic theory and establishes an important foundation for precision measurements of nuclear moments and charge radii of the most exotic isotopes of tin.

Theoretical study of YbOH173 to search for the nuclear magnetic quadrupole moment

CP-violating interaction of the nuclear magnetic quadrupole moment (MQM) with electrons in the ytterbium mono-hydroxide molecule, $^{173}$YbOH, is considered. Both the magnetic quadrupole moment (MQM) of the $^{173}$Yb nucleus and the molecular interaction constant WM are estimated. Electron correlation effects are taken into account within the relativistic Fock-space coupled cluster method. Results are interpreted in terms of the strength constants of CP-violating nuclear forces, neutron EDM, QCD vacuum angle $\theta$, quark EDM and chromo-EDM.

A four-component quadratic vibronic coupling approach to the Renner–Teller effect in linear triatomic molecules. The , manifold of BrCN+ and ClCN+

In this work, we present the four-component quadratic vibronic coupling model for the description of the Renner–Teller effect (RTE) in the presence of the spin–orbit coupling. The interaction of the two potential energy surfaces emerging from the cationic 2Π states of singly ionized linear triatomic molecules is described by the quadratic coupling constant c for the genuine RT repulsion and the second parameter, d, for a nonconstant spin–orbit coupling varying with the bond angle of the triatomic. The emergence of a linear RT constant in the presence of the spin–orbit operator was originally shown by Poluyanov and Domcke (2004 Chem. Phys. 301 111–27) and is based on the application of the Breit–Pauli Hamiltonian in combination with nonrelativistic wavefunctions. In contrast to this methodology, we generate the diabatic RT Hamiltonian in a 4-spinor basis where the symmetry transformation properties of the electronic and vibrational wavefunctions completely determine the RT matrix structure. Explicit access to highly correlated wavefunctions is not required in our approach. In addition, the four-component vibronic coupling model takes into account the full spatial orbital relaxation upon the inclusion of the spin–orbit coupling and is therefore well suited for heavy systems. The third parameter, p, accounting for a possible pseudo-Jahn–Teller interaction is not considered here, but it does not introduce a principal difficulty. As the initial systems for this study, we considered the BrCN+ and ClCN+ cations and determined the c and d parameters by a numerical fit to accurate adiabatic potential energy surfaces obtained by the relativistic Fock-space coupled-cluster method. New values for the computed linear RT parameter d amount to 14.7 ± 0.5 cm−1 for ClCN+ and 73.2 ± 0.7 cm−1 for BrCN+.

Nuclear quadrupole moment of Au197 from high-accuracy atomic calculations

The electric field gradient (EFG) at the gold nucleus is calculated using a finite field approach, to make the extraction of the nuclear quadrupole moment Q from experimental nuclear quadrupole coupling constants possible. The four-component Dirac-Coulomb Hamiltonian serves as the framework, 51 of the 79 electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the contribution of the Gaunt term, the main part of the Breit interaction, is evaluated. Large basis sets (up to 26s22p18d12f8g5h uncontracted Gaussians) are employed. Energy splittings of the 2D5/2 and 2D3/2 levels, rather than level shifts, are used to extract the EFG constants, as the former remain linear with Q up to 10(-5) a.u., whereas the latter display significant nonlinearity even at Q=10(-8) a.u. Larger Q values lead to larger energy changes and better precision. Excellent agreement (0.1%) is obtained between Q values derived from 2D5/2 and 2D3/2 data. Systematic errors connected with neglecting triple and higher excitations, truncating the basis and orbital active space, and approximating the Gaunt contribution are evaluated. The final value of Q(197Au) is 521(7) mb. It is lower than the muonic 547(16) mb and agrees within error bounds with the recent value of 510(15) mb obtained from molecular calculations.

High-accuracy calculation of nuclear quadrupole moments of atomic halogens

Electric field gradients at the nuclei of halogen atoms are calculated using a finite field approach. The four-component Dirac-Coulomb Hamiltonian serves as the framework, all electrons are correlated by the relativistic Fock-space coupled cluster method with single and double excitations, and the Gaunt term, the main part of the Breit interaction, is included. Large basis sets (e.g., 28s24p21d9f4g2h Gaussian-type functions for I) are used. Combined with experimental nuclear quadrupole coupling constants, accurate estimates of the nuclear quadrupole moments are obtained. The calculated values are Q(35Cl)=-81.1(1.2) mb, Q(79Br)=302(5) mb, and Q(127I)=-680(10) mb. Currently accepted reference values [Pyykko, Mol. Phys. 99, 1617 (2001)] are -81.65(80), 313(3), and -710(10) mb, respectively. Our values are lower for the heavier halogens, corroborating the recent work of van Stralen and Visscher [Mol. Phys. 101, 2115 (2003)], who obtained Q(127I)=-696(12) mb in a series of molecular calculations.

Potential Functions of Al2 by the Relativistic Fock-Space Coupled Cluster Method

Potential functions of the ground and low excited states of Al2 are calculated by the relativistic Fock-space coupled cluster method in the framework of the projected Dirac-Coulomb Hamiltonian. A moderate-size basis [16s11p3d3f/6s6p3d2f] is used. 3Πu is confirmed as the ground state of the system. Its spin orbit splittings are reproduced well, with the Λ = 1, 2 states lying 32.5 and 66.1 cm−1, respectively, above the Λ = 0 minimum (experimental values are 30.4 and 63.4 cm−1). The bond is somewhat too weak, with De 0.14 eV below experiment, Re too high by 0.08 ˚A, and ωe 21 cm−1 too low. It is speculated that the better agreement obtained in earlier calculations may be due to neglect of basis set superposition errors. The description of bonding in the molecule may be improved by the use of a better basis and the inclusion of more correlation by the intermediate Hamiltonian coupled cluster method, which makes it possible to handle larger P spaces and extend the potential functions to the whole range of internuclear separations.

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.

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 Å (experimental 1.781 Å) 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.

Transition energies of ytterbium, lutetium, and lawrencium by the relativistic coupled-cluster method.

The relativistic Fock-space coupled-cluster method was applied to the Yb, Lu, and Lr atoms, and to several of their ions. A large number of transition energies was calculated for these systems. Starting from an all-electron Dirac-Fock or Dirac-Fock-Breit function, many electrons (30--40) were correlated to account for core-valence polarization. High-l virtual orbitals were included (up to l=5) to describe dynamic correlation. Comparison with experiment (when available) shows agreement within a few hundred wave numbers in most cases. Fine-structure splittings are even more accurate, within 30 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ of experiment. Average errors are at least three times smaller than for previous calculations. Two bound states of ${\mathrm{Lu}}^{\mathrm{\ensuremath{-}}}$ are predicted, 6p5d $^{1}$${\mathit{D}}_{2}$ and 6${\mathit{p}}^{2}$ $^{3}$${\mathit{P}}_{0}$, with binding energies of about 2100 and 750 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, respectively. The ground state of lawrencium is $^{2}$${\mathit{P}}_{1/2}$, relativistically stabilized relative to $^{2}$${\mathit{D}}_{3/2}$, the ground state of Lu. Two states of the ${\mathrm{Lr}}^{\mathrm{\ensuremath{-}}}$ anion are bound, 7${\mathit{p}}^{2}$ $^{3}$${\mathit{P}}_{0}$ (by 2500 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$) and 7p6d $^{1}$${\mathit{D}}_{2}$ (by 1300 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$).

Relativistic coupled-cluster method: Intrashell excitations in the f2 shells of Pr+3 and U+4.

The relativistic Fock-space coupled-cluster method for the direct calculation of ionization potentials and excitation energies (including fine structure) is applied to the 4${\mathit{f}}^{2}$ levels of ${\mathrm{Pr}}^{+3}$ and the 5${\mathit{f}}^{2}$ levels of ${\mathrm{U}}^{+4}$. The no-pair Dirac-Coulomb-Breit Hamiltonian is taken as the starting point. Correlation is treated by the coupled-cluster singles-and-doubles approximation, which includes single and double virtual excitations in a self-consistent manner, incorporating therefore the effects of the Coulomb and Breit interactions to all orders in these excitations. Extensive basis sets of kinetically balanced four-component Gaussian spinors are used to span the atomic orbitals. All levels appear in correct order. The average error of the excitation energies with the best basis is 222 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for ${\mathrm{Pr}}^{+3}$ and 114 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ for ${\mathrm{U}}^{+4}$. Fine-structure splittings are obtained with even better accuracy.

Ionization potentials and excitation energies of the alkali-metal atoms by the relativistic coupled-cluster method.

Ground- and excited-state energies, as well as ionization potentials and electron affinities, are calculated for all the alkali-metal atoms Li--Fr by the relativistic Fock-space coupled-cluster method. The coupled-cluster singles and doubles approximation, which includes single and double virtual excitations in a self-consistent manner, is implemented. The no-pair Dirac-Coulomb-Breit Hamiltonian is taken as the starting point. Rather extensive basis sets of balanced Gaussian spinors are used to span the atomic orbitals. The average error for the ionization potentials is 0.09% and for excitation energies 0.2%. Electron affinities are less accurate, particularly for the heavier atoms, with errors of 4--9 % for K, Rb, and Cs.

Open-shell relativistic coupled-cluster method with Dirac-Fock-Breit wave functions: Energies of the gold atom and its cation

The relativistic Fock-space coupled cluster method for the direct calculation of ionization potentials and excitation energies (including fine structure) is presented and applied to atomic Au and its ions. The no-pair Dirac-Coulomb-Breit Hamiltonian is taken as the starting point. The CCSD approximation is implemented (where CCSD indicates coupled cluster with single and double excitations), which includes single and double virtual excitations in a self-consistent manner, incorporating therefore the effects of the Coulomb and Breit interactions to all orders in these excitations. A rather large basis set (21s17p11d7f) of kinetically balanced Gaussian spinors is used to span the atomic orbitals. All calculated energies (ionization potential and electron affinity of Au, excitation energies of Au and ${\mathrm{Au}}^{+}$) agree with experiment to 0.1 eV or better, with an average error of 0.06 eV. Fine-structure splittings are accurate to better than 0.01 eV.

The relativistic open shell coupled cluster method: Direct calculation of excitation energies in the Ne atom

The relativistic Fock space coupled-cluster method for the direct calculation of excitation energies (including fine structure) is presented and applied to excitations of atomic Ne. The coupled clusters with single and double excitations (CCSD) approximation, which includes single and double virtual excitations in a self-consistent manner, is implemented. The no-pair Dirac–Coulomb Hamiltonian is taken as the starting point. Mean length basis sets of balanced Gaussian spinors are used to span the atomic orbitals. The model (P) space is quasicomplete, consisting of determinants with one valence hole and one valence particle. Fourteen excitation energies of the atom are calculated. They all agree with experiment to 0.08 eV or better, with an average error of 0.02 eV. Fine structure splittings are also in very good agreement with experiment.