Combined Configuration Interaction Research Articles

Atomic properties of Cd-like and Sn-like ions for the development of frequency standards and search for the variation of the fine-structure constant

A high-precision relativistic calculations of Cd-like Nd$^{12+}$, Sm$^{14+}$ and Sn-like Pr$^{9+}$, Nd$^{10+}$ atomic properties is carried out using an approach that combines configuration interaction and a linearized coupled-cluster method. These ions have long-lived metastable states with transitions accessible by laser excitations, relatively simple electronic structure, high sensitivity to $\alpha$ variation, and stable isotopes. Breit and QED corrections were included into the calculations. Energies, transition wavelengths, electric- and magnetic-multipole reduced matrix elements, lifetimes, and sensitivity coefficients $q$ and $K$ to the variation of the fine-structure constant $\alpha$ were obtained. A detailed study of uncertainties was performed. Energies for similar Cd-like Ba$^{8+}$, La$^{9+}$, Ce$^{10+}$, Pr$^{11+}$ and Sn-like Ba$^{6+}$ ions were calculated and compared with experiment for further tests of the accuracy.

Highly charged Ag-like and In-like ions for the development of atomic clocks and the search forαvariation

We carried out a detailed high-precision study of Ag-like ${\mathrm{Nd}}^{13+}$ and ${\mathrm{Sm}}^{15+}$ and In-like ${\mathrm{Ce}}^{9+}$, ${\mathrm{Pr}}^{10+}$, ${\mathrm{Nd}}^{11+}$, ${\mathrm{Sm}}^{13+}$, and ${\mathrm{Eu}}^{14+}$ highly charged ions. These ions were identified to be of particular interest for the development of ultra-accurate atomic clocks, the search for variation of the fine-structure constant $\ensuremath{\alpha}$, and quantum information [Safronova et al., Phys. Rev. Lett. 113, 030801 (2014)]. The relativistic linearized coupled-cluster method was used for Ag-like ion calculations, and a hybrid approach that combines configuration interaction and a variant of the coupled-cluster method was used for the In-like ion calculations. Breit and QED corrections were included. Energies, transition wavelengths, electric-dipole, electric-quadrupole, electric-octupole, magnetic-dipole, magnetic-quadrupole, and magnetic-octupole reduced matrix elements, lifetimes, and sensitivity coefficients to $\ensuremath{\alpha}$ variation were calculated. A detailed study of various contributions was carried out to evaluate uncertainties of the final results. Energies for several similar ``reference'' ions where the experimental values are available were calculated and compared with experiment for further tests of the accuracy.

Relativistic all-order calculations of Th,Th+, andTh2+atomic properties

Excitation energies, term designations, and $g$-factors of Th, Th$^{+}$ and Th$^{2+}$ are determined using a relativistic hybrid configuration interaction (CI) + all-order approach that combines configuration interaction and linearized coupled-cluster methods. The results are compared with other theory and experiment where available. We find some "vanishing" $g$-factors, similar to those known in lanthanide spectra. Reduced matrix elements, oscillator strengths, transition rates, and lifetimes are determined for Th$^{2+}$. To estimate the uncertainties of our results, we compared our values with the available experimental lifetimes for higher $5f7p\ ^3G_{4}$, $7s7p\ ^3P_{0}$, $7s7p\ ^3P_{1}$, and $6d7p\ ^3F_{4}$ levels of Th$^{2+}$. These calculations provide a benchmark test of the CI+all-order method for heavy systems with several valence electrons and yield recommended values for transition rates and lifetimes of Th$^{2+}$.

Calculation of quadrupole polarizabilities with combined configuration interaction and coupled-cluster method

The recently developed method combining the configuration interaction and the coupled-cluster method was demonstrated to provide accurate treatment of correlation corrections in divalent atomic systems [Safronova, Kozlov, and Clark, Phys. Rev. Lett. 107, 143006 (2011)]. We have extended this approach to the calculation of quadrupole polarizabilities ${\ensuremath{\alpha}}_{2}$ and applied it to evaluate ${\ensuremath{\alpha}}_{2}$ for the ground state of Mg and Mg-like Si${}^{2+}$. Performing the calculations in three different approximations of increasing accuracy allowed us to place the upper bounds on the uncertainty of the final results. The recommended values ${\ensuremath{\alpha}}_{2}(3{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0})=35.86(13)$ a.u. for Si${}^{2+}$ and ${\ensuremath{\alpha}}_{2}(3{s}^{2}{\phantom{\rule{0.16em}{0ex}}}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0})=814(3)$ a.u. for Mg are estimated to be accurate to $0.4%$. Differences in quadrupole polarizability contributions in neutral Mg and Si${}^{2+}$ ion are discussed.

Atomic properties of Pb III

We carry out a systematic study of Pb iii properties using a hybrid method that combines configuration interaction and linearized coupled-cluster approaches. The calculations start from a [Xe]$4{f}^{14}5{d}^{10}$ Dirac-Fock potential. Excitation energies and lifetimes of the $6{p}^{2}$, $6sns$, $6snp$, and $6snd$ ($n\ensuremath{\le}9$) states are evaluated. Reduced matrix elements, oscillator strengths, and transition rates are determined for allowed electric-dipole transitions including these states. Extensive comparison with other theoretical and experimental values is carried out. Electric-dipole polarizabilities of the $6{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}\phantom{\rule{-0.16em}{0ex}}{S}_{0}$, $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{0}$, and $6s6p{\phantom{\rule{0.16em}{0ex}}}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}$ states in Pb iii and ground state polarizability of Pb${}^{4+}$ are reported.

Solvatochromic Shifts of the n → π* Transition of Acetone from Steam Vapor to Ambient Aqueous Solution: A Combined Configuration Interaction QM/MM Simulation Study Incorporating Solvent Polarization.

A hybrid quantum mechanical and molecular mechanical potential is used in Monte Carlo simulations to examine the solvent effects on the electronic excitation energy of the n → π(*) transition of acetone in ambient and supercritical water fluid, in which the temperature is in the range of 25-500 °C with pressures of 1-2763 atm. In the present study, the acetone molecule is described by the AM1 Hamiltonian, and the water molecules are treated classically. Two sets of calculations are performed. The first involves the TIP4P model for water, and the second employs a polarizable model, POL2, for the solvent. The first calculation yields the excitation energy by using the static ground-state solvent charge distribution obtained from QM-CI/MM calculations. The latter takes into account the effect of solvent polarization following the solute electronic excitation. The trend of the computed n → π(*) blue-shifts for acetone as function of the fluid density is in good agreement with experimental results. The present simulations of acetone in the supercritical, near supercritical, dense-liquid, and ambient water fluids reveal that the solvatochromic shifts are dominated by the electrostatic interactions between acetone and water molecules during the solute excitation. Additionally, the solvent charge redistribution following the solute electronic excitation has a small correlation (0 to -37 cm(-1)) to the total solvatochromic shift and decreases linearly with water density. Both the solvatochromic shift and solvent polarization correction are more obvious in the ambient water than in the supercritical water because the solvent stabilization of the ground state over the excited state is more significant in the former condition.

Many‐Body Perturbation Theory Wavelengths of High‐ n X‐Ray Transitions of Fe and Ni L‐shell Ions

Using a combined configuration interaction and many-body perturbation theory method, we compute the wavelengths of n → 2 (3 ≤ n ≤ 7) transitions of Fe and Ni L-shell ions. The uncertainties of the results are determined to be a few mA through extensive comparisons with existing laboratory measurements. We provide a complete line list of these X-ray transitions of Fe and Ni and incorporate them in the emissivity tables of the Astrophysical Plasma Emission Database (APED).

Energies of 1s 22l q (1 ⩽ q ⩽ 8) states for Z ⩽ 60 with a combined configuration interaction and many-body perturbation theory approach

Using a combined configuration interaction and many-body perturbation theory approach, we calculate the level energies of 1s 22l q (1 ⩽ q ⩽ 8) states for ions with Z ⩽ 60. Comparison with experimental results wherever available indicates that the calculated energies are accurate to within a few 1000 cm −1 for all ions except for near-neutral systems which are less than 2–3 times ionized. The ground state ionization energies of these ions are also reported and compared with experimental values.

Wavelengths of 2l→3l′ Transitions in L‐Shell Ions of Iron and Nickel: A Combined Configuration Interaction and Many‐Body Perturbation Theory Approach

Using a combined configuration interaction and many-body perturbation theory approach, we calculate the level energies of 1s22lq and 1s22lq-13l' (1 ≤ q ≤ 8) complexes in iron and nickel ions. Comparison of 1s22lq energies with experimental results shows that the calculation is accurate to within ~0.15 eV for these levels. The accuracy of 1s22lq-13l' energies can be slightly worse, at ~0.5 eV. The theoretical wavelengths of 2→3 transitions of iron ions are compared with the published experimental measurements, and discrepancies are found to be mostly within ±10 mA. Similar accuracy is expected for wavelengths of nickel ions. Such accuracy is a significant improvement over that obtainable with standard configuration interaction methods. A complete table of 2l → 3l' transition wavelengths of all L-shell ions of iron and nickel is presented.

Electronic excitation and singlet-triplet coupling in uracil tautomers and uracil-water complexes

Electronic spectra of uracil in its diketo (lactam) form and five enol (lactim) tautomeric forms have been investigated by means of combined density functional and configuration interaction methods. We have simulated the effects of hydrogen bonding with a protic solvent by recomputing the spectrum of uracil in the presence of two, four, or six water molecules. Geometries of the electronic ground state and several low-lying excited states have been optimized. Spin-orbit coupling has been determined for correlated wavefunctions employing a non-empirical spin-orbit mean-field approach. In accord with experiment, we find the diketo tautomer to be the most stable one. The calculations confirm that the first absorption band arises from the 1( π↦π*) S0↦S2 excitation. The experimentally observed vibrational structure in this band originates from a breathing mode of the six ring. Complexation with water molecules is seen to cause a significant blue shift of n↦π* excitations while leaving π↦π* excitations nearly uninfluenced. Computed radiative lifetimes are presented for the experimentally known weak phosphorescence from the π↦π* excited T1 state. Among the uracil lactim tautomers, one is particularly interesting from a spectroscopic point of view. In this tautomer, the π↦π* excitation gives rise to the S1 state.

Influence of the Pauli antisymmetry and exclusion principle on the electronic structure of π systems — a combined Green function quantum Monte Carlo and configuration interaction study

It is demonstrated that the Pauli antisymmetry principle (PAP) is a hidden variable in π electron calculations of polyenes and annulenes with 4 n + 2 π electrons ( n = 0, 1, 2,...). Here the π electrons behave as a hard core bosonic ensemble which represents a superposition of fermionic on-site and bosonic intersite properties. In 4 n rings ( n = 1, 2,...) the PAP leads to a destabilization of the π electronic system. With an increasing π electron count the Pauli exclusion principle (PEP) raises the normalized π energy of annulenes. The influence of the PEP and PAP on the π electron localization properties is analyzed in terms of charge fluctuations.

Electronic Structure of Bis(2,4-pentanedionato-O,O')oxovanadium(IV). A Photoelectron Spectroscopy, Electronic Spectroscopy, and ab Initio Molecular Orbital Study.

The electronic structure of the title VO(acac)(2) complex has been investigated using effective core potential configuration interaction ab initio calculations, UV-photoelectron spectroscopy, and electronic spectroscopy. The metal-ligand bonding with the equatorial acac(-) ligands is dominated by sigma interactions involving the filled ligand orbitals and the empty orbitals of the d(1) vanadium(IV) ion. The oxovanadium interactions involve a larger metal-d participation thus resulting in a strong V-O bonding having partial triple-bond character. Additional three-orbital-four-electron stabilizing interactions involving the filled acac(-) MOs and the oxovanadium orbitals further reinforce both the axial and equatorial bonds. The unpaired metal-d electron is completely localized in the nonbonding d(x)()()2(-)(y)()()2 orbital. The low ionization energy of the photoelectron spectrum has been fully assigned on the basis of combined DeltaSCF and configuration interaction calculations. The same theoretical approach has, in addition, provided a good fitting of frequencies associated with "d-d" and charge transfer electronic transitions.

Changes in l-shell correlation energies with a combined density functional and configuration interaction method

A recently developed method which supplements configuration interaction calculations with density functional correlation energies is applied to correlation contributions to: a) the ionization energies and electron affinities of H, Li and N, b) sp-transfer energies in B+, 0 + and Ne + .The accuracy (~ 0.01 hartree) is similar to that observed In previous calculations with the same method.

A systematic study of molecular vibrational anharmonicity and vibration—rotation interaction by self-consistent-field higher-derivative methods. Asymmetric top molecules

Recently developed analytic third-derivative methods for self-consistent-field (SCF) wavefunctions have made it possible to theoretically determine a number of anharmonic molecular properties, including vibration—rotation interaction constants, vibrational anharmonic constants, fundamental vibrational frequencies, sextic centrifugal distortion constants, and rotational constants which include zero-point vibrational and centrifugal distortion corrections. Application has been made here to a variety of asymmetric top molecules including H 2O, H 2S, H 2CO, HCO, CH 2( 3B 1), CH 2( 1A 1), CH 2( 1B 1), C 2H 4, and several isotopomers. The formulas employed for the various spectroscopic constants are those derived from standard spectroscopic perturbation theory. For most of these molecules the anharmonic molecular constants which are available from experiments are well reproduced theoretically using a double-zeta plus polarization (DZP) basis set. Particularly good agreement is found for fundamental vibrational frequencies obtained by combining configuration interaction singles and doubles (CISD) harmonic frequencies with SCF anharmonic corrections within the same basis set. This work also provides insight into the applicability of standard spectroscopic perturbation theory to such molecules. Moreover, the methods used here are immediately applicable to molecules significantly larger than those studied here.

A combined density functional and configuration interaction method

Correlation energies are divided into two parts. One contribution is given by a configuration interaction calculation in the space of the natural orbitals with occupation numbers larger than an arbitrary threshold u. The remaining part is obtained from a u-dependent functional of the electronic density. Representative examples (for which the existing spin-density functionals fail) are (1) the correlation energies in the He and Be series and (2) the contribution of the correlation energy to the dissociation energy of the first-row dimers. It is shown that even for large values of v the errors remain on the order of 0.01 hartree.