Dirac-Fock-Breit self-consistent-field method: Gaussian basis-set calculations on many-electron atoms

Correlated Dirac-Coulomb-Breit multiconfigurational self-consistent-field methods

The fully correlated frequency-independent Dirac-Coulomb-Breit Hamiltonian provides the most accurate description of electron-electron interaction before going to a genuine relativistic quantum electrodynamics theory of many-electron systems. In this work, we introduce a correlated Dirac-Coulomb-Breit multiconfigurational self-consistent-field method within the frameworks of complete active space and density matrix renormalization group. In this approach, the Dirac-Coulomb-Breit Hamiltonian is included variationally in both the mean-field and correlated electron treatment. We also analyze the importance of the Breit operator in electron correlation and the rotation between the positive- and negative-orbital space in the no-virtual-pair approximation. Atomic fine-structure splittings and lanthanide contraction in diatomic fluorides are used as benchmark studies to understand the contribution from the Breit correlation.

Efficient Evaluation of the Breit Operator in the Pauli Spinor Basis

The frequency-independent Coulomb-Breit operator gives rise to the most accurate treatment of two-electron interaction in the non-quantum-electrodynamics regime. The Breit interaction in the Coulomb gauge consists of magnetic and gauge contributions. The high computational cost of the gauge term limits the application of the Breit interaction in relativistic molecular calculations. In this work, we apply the Pauli component integral-density matrix contraction scheme for gauge interaction with a maximum spin- and component separation scheme. We also present two different computational algorithms for evaluating gauge integrals. One is the generalized Obara-Saika algorithm, where the Laplace transformation is used to transform the gauge operator into Gaussian functions and the Obara-Saika recursion is used for reducing the angular momentum. The other algorithm is the second derivative of inverse Coulomb interaction evaluated with Rys-quadrature. This work improves the efficiency of performing Dirac-Hartree-Fock with variational treatment of Breit interaction for molecular systems. We use this formalism to examine relativistic trends in the periodic table, and analyze the relativistic two-electron interaction contributions in heavy-element complexes.

RELATIVISTIC MR-MP ENERGY LEVELS FOR L-SHELL IONS OF SULFUR AND ARGON

Calculated level energies for valence and K-vacancy states are provided for the ion series S VII - S XIV and Ar IX - Ar XVI. The calculations were performed with the relativistic Multi-Reference Mxller-Plesset Perturbation Theory method (MR-MP). The data set includes all the level energies with configurations 1s 22(s, p) q , 1s 22(s, p) q-1 nl, 1s 12(s, p) q+1, 1s 12(s, p) q nl, 2(s, p) q+2 and 2(s, p) q+1 nl, where 1 ≤ q ≤ 8, n ≤ 5 and l ≤ 3. We have compared our results with data from the National Institute of Standards and Technology (NIST) on-line database and with previous calculations. The average deviation of valence level energies ranges from 0.16 eV in Ne-like ions to 0.01 eV in Li-like ions, showing that the present MR-MP valence level energies are highly accurate. In the case of K-vacancy states, the deviation is generally below 0.3 eV for Li-like S XIV and Ar XVI. The deviation for K-vacancy energies in other L-shell ions (Be-, B-, C-, N- and O-like Ar ions) is higher but likely because the NIST-recommended values have a higher uncertainty. The data set includes many n = 4 and n = 5 valence and K-vacancy levels in L-shell ions of S and Ar not previously reported. The data can be used for line identification and modeling of L-shell ions of S and Ar in astrophysical and laboratory-generated plasmas, and as energy references in the absence of more accurate laboratory measurements.

RELATIVISTIC MR-MP ENERGY LEVELS FOR L-SHELL IONS OF SILICON

Level energies are reported for Si V, Si VI, Si VII, Si VIII, Si IX, Si X, Si XI and Si XII. The energies have been calculated with the relativistic Multi-Reference Møller-Plesset Perturbation Theory method and include valence and K-vacancy states with nl up to 5f. The accuracy of the calculated level energies is established by comparison with the recommended data listed in the National Institute of Standards and Technology (NIST) on-line database. The average deviation of valence level energies ranges from 0.20 eV in Si V to 0.04 eV in Si XII. For K-vacancy states, the available values recommended in the NIST database are limited to Si XII and Si XIII. The average energy deviation is below 0.3 eV for K-vacancy states. The extensive and accurate dataset presented here greatly augments the amount of available reference level energies. We expect our data to ease the line identification of L-shell ions of Si in celestial sources and laboratory generated plasmas, and to serve as energy references in the absence of more accurate laboratory measurements.

Electron and nuclear dynamics in many-electron atoms, molecules and chlorophyll-protein complexes: a review

It has been shown [V.A. Shuvalov, Quantum dynamics of electrons in many-electron atoms of biologically important compounds, Biochemistry (Mosc.) 68 (2003) 1333-1354; V.A. Shuvalov, Quantum dynamics of electrons in atoms of biologically important molecules, Uspekhi biologicheskoi khimii, (Pushchino) 44 (2004) 79-108] that the orbit angular momentum L of each electron in many-electron atoms is L=mVr=nPlanck's and similar to L for one-electron atom suggested by N. Bohr. It has been found that for an atom with N electrons the total electron energy equation E=-(Z(eff))(2)e(4)m/(2n(2)Planck's(2)N) is more appropriate for energy calculation than standard quantum mechanical expressions. It means that the value of L of each electron is independent of the presence of other electrons in an atom and correlates well to the properties of virtual photons emitted by the nucleus and creating a trap for electrons. The energies for elements of the 1st up to the 5th rows and their ions (total amount 240) of Mendeleev' Periodical table were calculated consistent with the experimental data (deviations in average were 5 x 10(-3)). The obtained equations can be used for electron dynamics calculations in molecules. For H(2) and H(2)(+) the interference of electron-photon orbits between the atoms determines the distances between the nuclei which are in agreement with the experimental values. The formation of resonance electron-photon orbit in molecules with the conjugated bonds, including chlorophyll-like molecules, appears to form a resonance trap for an electron with E values close to experimental data. Two mechanisms were suggested for non-barrier primary charge separation in reaction centers (RCs) of photosynthetic bacteria and green plants by using the idea of electron-photon orbit interference between the two molecules. Both mechanisms are connected to formation of the exciplexes of chlorophyll-like molecules. The first one includes some nuclear motion before exciplex formation, the second one is related to the optical transition to a charge transfer state.

The generator coordinate Dirac–Fock method applied to beryllium-like atomic species

The recently formulated generator coordinate Dirac–Fock method for relativistic closed-shell atoms is applied to the Be atom and Be-like ions Ne6+, Ar14+, and Sn46+ in order to assess its efficacy for light atomic systems. The Dirac–Fock equations are integrated numerically in the generator coordinate Dirac–Fock method so as to generate Gaussian basis sets for the atomic species under study. The results obtained with the application of the generator coordinate Dirac–Fock method in this work for Dirac–Fock–Coulomb and Dirac–Fock–Breit energies for Be-like ions are in excellent agreement with Declaux's benchmark numerical calculations, and are better than the Dirac–Fock–Coulomb and Dirac–Fock–Breit energies obtained with even-tempered Gaussian-type function calculations. For the Be atom, the Dirac–Fock–Coulomb energy result obtained with the generator coordinate Dirac–Fock method is lower than the corresponding value obtained with the Declaux's numerical finite-difference program. Key words: Dirac–Fock–Coulomb energy, Dirac–Fock–Breit energy, Gaussian basis sets, generator coordinate Dirac–Fock method.