Configuration Interaction Approximation Research Articles

Spectroscopy characteristics and decay properties of plasma-embedded atoms in external electric and magnetic fields

This paper describes a computational approach within the framework of relativity theory for explaining the spectral and decay properties of atoms and ions embedded in a plasma and also in the presence of applied external electric and magnetic fields. It uses the configuration interaction approximation and the analytical potential derived from general ion-sphere theory to represent the atomic interactions within the plasma. In the model, the Dirac–Coulomb–Hamiltonian is reconstructed and the effects of the weak electric and magnetic field are treated as small perturbations. The eigenvalues for the orbitals and (radial) wave functions are obtained through the Dirac equations. A diagonalization is performed to include these plasma, electric, and magnetic terms. As an example, an environment with a hot-dense plasma and weak electric and magnetic fields is considered, where the interaction is much weaker than the Coulomb interaction, yet much stronger than the spin–orbit interaction. The atomic structures and spectra of a selected hydrogen atom are presented for a wide range of electron densities, temperatures, and electric and magnetic fields. The behavior of the energy and radiative transitions with respect to these interactions is analyzed in detail. The results obtained from the proposed approach are critically compared with other available results. The present study not only advances our understanding of the electronic structures and radiation characteristics of atomic systems in external fields but may also be relevant for astrophysics and laboratory experiments, especially on the solar corona, laser-produced plasmas, and so on.

Determination of the atomic structure and radiative transition properties of atoms or ions under the dense and solid density magnetized plasmas

Simulating the magnetic field interactions with plasmas plays a paramount role in astrophysics, having significant impacts in several topics. Here, we propose a novel computational method within the framework of relativistic theory to the determination of the atomic structures and radiative properties of atoms or ions in presence of the dense and solid density magnetized plasma environments. In the method, the dense plasma effects on the atomic structure of highly charged ions are described by using the generalized b-potential model within the general framework of the ion sphere theory, which is somewhat simple and flexible and allows adjusting the b-parameter to consider finite temperature and density as well as solid density plasma environments. The weakly magnetic field effects are described using the perturbation term, which perturbs the Hamiltonian of the field-free case. Its special features include handling the effects of both electron correlation and interaction with the weakly magnetic field within the configuration interaction approximation. As a practical application, we present a systematic study of the plasma screening and magnetic field effects, separately and combined, on the structure and radiative properties of highly charged ions subjected to the magnetized plasma, using the atrophysically relevant He-like Mg10+ ion as an example. A comparison of our calculations with other theories, when available, is made. The present work not only originates a better understanding of the fundamentals of structure and radiative properties of ions in the presence of an external field, but also has some important relevance to applications in laboratory and space plasmas, particularly in solar corona, fusion, laser-produced plasmas, ect.

Comparative metathermodynamic description of thermal and correlation electron effects

Unified metathermodynamic description of thermal and correlation electron effects is proposed. It is based on the temperature-dependent populations of the common for all temperatures basis states of the (formally accurate) configuration interaction (CI) expansion of the components of the canonical ensemble. These populations are incorporated into the effective ensemble of the metathermodynamic approach through the partial effective tem- peratures. The extended temperature ${T}_{e}$ is introduced as the statistical average of those temperatures. The absolute zero of the ${T}_{e}$ scale represents a ``no-correlation'' Hartree-Fock state, while elevated ${T}_{e}$ describes the increase of the ``correlation motion'' and the conventional thermal motion. The diagonal double configuration interaction (DDCI) approximation is considered, in which the proposed metathermodynamic description of thermal and correlation electron effects is based on the temperature-dependent orbital populations.

Multi-reference Epstein–Nesbet perturbation theory with density matrix renormalization group reference wavefunction

The accurate electronic structure calculation for strongly correlated chemical systems requires an adequate description for both static and dynamic electron correlation, and is a persistent challenge for quantum chemistry. In order to account for static and dynamic electron correlations accurately and efficiently, in this work we propose a new method by integrating the density matrix renormalization group (DMRG) method and multi-reference second-order Epstein–Nesbet perturbation theory (ENPT2) with a selected configuration interaction (SCI) approximation. Compared with previous DMRG-based dynamic correlation methods, the DMRG-ENPT2 method extends the range of applicability, allowing us to efficiently calculate systems with very large active space beyond 30 orbitals. We demonstrate this by performing calculations on H2S with an active space of (16e, 15o), hexacene with an active space of (26e, 26o) and 2D H64 square lattice with an active space of (42e, 42o).

Electron induced excitation of Furfural (C5H4O 2)

SynopsisThe present study reports excitation cross section for three low-lying excited states of furfural (C5 H4 O2). These states have a significant contribution to the elastic channel as well as dissociation processes. R-matrix method is used to study the e-C5H4O2 problem under configuration interaction (CI) approximation. The ground state geometry is considered for the construction of Hamiltonian of the problem. Results show resonances for these sates.

Ab initio MCDHF/RCI and semi-empirical HFR calculations of transition probabilities and oscillator strengths in Xe XI

The atomic structure of ten-times ionized xenon (Xe XI) has been computed by two independent methods, i.e. the ab initio relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) approach within the relativistic configuration interaction (RCI) approximation and the semi-empirical pseudo-relativistic Hartree–Fock (HFR) method. The transition probabilities and oscillator strengths of the 4d8 − (4p54d9 + 4d75p + 4d74f) transition array have been determined in both models and allowed us to estimate their accuracy taking into account both the gauge agreements and the cancellation effects on the line strengths. It has been found that core – core and core – valence correlations through the explicit inclusion of single- to triple-hole 4p-subshell configurations in our RCI model systematically decrease the transition rates by about 20% for the strong lines (with log gf > 0) with respect to our HFR values that did not consider those effects. Further opening of the core shells has also been investigated and did not give rise to significant systematic change on the transition probabilities.

Judd-Ofelt modelling and stimulated-emission cross-sections for Tb3+ ions in monoclinic KYb(WO4)2 crystal

Terbium (Tb3+) ions are promising for the development of visible lasers. We report on the spectroscopy of Tb3+ in the monoclinic KYb(WO4)2 (KYbW) crystal, including the Judd-Ofelt (J-O) modelling of the transition probabilities, evaluation of the absorption and stimulated-emission (SE) cross-sections with polarized light, and emission lifetime study. Within the strong configuration interaction (SCI) approximation of the J-O theory, the intensity parameters of Tb3+ are Ω2 =0.864, Ω4 =1.657, Ω6 =1.975 [10-20cm2] and Δ=38810cm–1. The maximum σabs for the 7F6 → 5D4 transition reaches 2.3×10-21cm2 at 486.7nm and the maximum σSE for the green emission according to the 5D4 → 7F5 transition is 2.3×10-21cm2 at 549.3nm (both for E || Nm). The measured lifetime of the 5D4 state for a 1at% Tb3+ doping is 395±5μs. Under blue excitation, Tb: KYbW exhibits intense green emission with the CIE 1931 coordinates of (0.312; 0.644).

Correlation Energy Extrapolation by Many-Body Expansion.

Accounting for electron correlation is required for high accuracy calculations of molecular energies. The full configuration interaction (CI) approach can fully capture the electron correlation within a given basis, but it does so at a computational expense that is impractical for all but the smallest chemical systems. In this work, a new methodology is presented to approximate configuration interaction calculations at a reduced computational expense and memory requirement, namely, the correlation energy extrapolation by many-body expansion (CEEMBE). This method combines a MBE approximation of the CI energy with an extrapolated correction obtained from CI calculations using subsets of the virtual orbitals. The extrapolation approach is inspired by, and analogous to, the method of correlation energy extrapolation by intrinsic scaling. Benchmark calculations of the new method are performed on diatomic fluorine and ozone. The method consistently achieves agreement with CI calculations to within a few mhartree and often achieves agreement to within ∼1 millihartree or less, while requiring significantly less computational resources.

Europium doping in monoclinic KYb(WO4)2 crystal

We report on a detailed spectroscopic study of Eu3+ ions in the monoclinic KYb(WO4)2 crystal. The polarized room and low-temperature absorption spectra are measured. The maximum σabs corresponding to the 7F1 → 5D1 transition is 1.32×10–20cm2 at 534.2nm with a bandwidth of 0.7nm (for E||Nm). The Stark sub-levels of the excited mulitplets are determined. A Judd-Ofelt analysis is applied to the Eu3+:KYb(WO4)2 crystal to determine the probability of spontaneous transitions, radiative lifetimes and luminescence branching ratios. Within the strong configuration interaction (SCI) approximation, the intensity parameters are Ω2=4.757, Ω4=2.295, Ω6=1.644 [10–20cm2] and Δf=50160cm–1. The radiative lifetime of the 5D0 state is 351 µs. The maximum stimulated-emission cross-section corresponding to the 7F1 → 5D1 transition is 1.44×10–20cm2 at 703.2nm (for E||Nm). Under UV excitation, the Eu3+:KYb(WO4)2 crystal provides intense red photoluminescence with CIE coordinates, x=0.675, y=0.325.

Formation of silicon monoxide by radiative association: the impact of resonances

Detailed quantum chemistry calculations within the multireference configuration interaction approximation with the Davidson correction are presented using an aug-cc-pV6Z basis set, for the potential energy curves and transition dipole moments between low lying molecular states of singlet spin symmetry for the SiO molecule. The high quality molecular data are used to obtain radiative association cross sections and rate coefficients for collisions between ground state Si and O atoms. Quantal calculations are compared with semiclassical results. Using a quantum kinetic theory of radiative association in which quasibound levels are assumed to be in local thermodynamic equilibrium, we find that resonances play an important role in enhancing the rate coefficients at low temperatures by several orders of magnitude from that predicted by standard quantum scattering formulations. These new molecular formation rates may have important implications for applications in astrophysics.

Ab initio calculations of lower resonant states of two-electron systems

The complex scaling and the stabilization methods are applied to calculating the parameters of the lowest resonance states of He and Li+. The results obtained by both methods are in a good agreement with the published data. It is shown that the wave functions constructed using the restricted configuration interaction approximation provide fairly accurate estimates of the resonance parameters. The possibility of using the stabilization method for calculating the phase shift function is also discussed.

Length and velocity form calculations of generalized oscillator strengths of dipole, quadrupole and monopole excitations of argon

The quadrupole, monopole and dipole generalized oscillator strengths (GOSs) as a function of momentum transfer are respectively calculated for these 3p6 → 3p5 (4p, 5p, 6p) and 3p6 → 3p5 (4s, 5s, 6s) transitions. Configuration interaction (CI) and random phase approximation with exchange (RPAE) methods are used in the determination of these GOS, in the length and velocity forms. The code of Hibbert has been used to generate the wavefunctions from which a partial of argon GOSs are been computed. The present work has reduced the gap between the absolute values of the theoretical calculations of GOSs and those of the experimental results of Zhu et al for the quadrupole excitations to 3p5 (4p, 5p). The profile of our quadrupole GOS 3p6 → 3p55p transition agrees well with the experimental result of Zhu. The best agreement (0.7%) is observed between the (length) first maximum position and the experimental one for the quadrupole GOS 3p6 → 3p54p transition. The present velocity GOS minimum position for the dipole excitation in 3p6 → 3p54s and the calculated velocity GOS maximum position of the monopole 3p6 → 3p54p transition are in good agreement with the experimental observations (differences of 1.82% and 3.08%, respectively). Correlation effects decrease with increasing of the excited state principal quantum number and have no great influence on the extrema positions.

The single ionization cross-section of Rb atoms by electron impact

SynopsisThe 5s+core single ionization cross-section of Rb atoms was calculated for the incident electron energies up to 600 eV by using the relativistic distorted-wave, Coulomb-Born and binary-encounter-dipole approximations. The accuracy of the data was analyzed by the comparison with experimental data. The best agreement was observed for the calculations performed in configuration interaction approximation.

Radiative charge transfer in cold and ultracold sulphur atoms colliding with protons

Radiative decay processes at cold and ultra cold temperatures for sulfur atoms colliding with protons are investigated. The MOLPRO quantum chemistry suite of codes was used to obtain accurate potential energies and transition dipole moments, as a function of internuclear distance, between low-lying states of the SH+ molecular cation. A multi-reference configuration-interaction approximation together with the Davidson correction is used to determine the potential energy curves and transition dipole moments, between the states of interest, where the molecular orbitals are obtained from state-averaged multi-configuration-self-consistent field calculations. The collision problem is solved approximately using an optical potential method to obtain radiative loss, and a fully two-channel quantum approach for radiative charge transfer. Cross sections and rate coefficients are determined for the first time for temperatures ranging from 10 μK up to 10 000 K. Results are obtained for all isotopes of sulfur, colliding with H+ and D+ ions and comparison is made to a number of other collision systems.

Are natural orbitals useful for generating an efficient expansion of the wave function?

We investigate whether the natural orbitals (NOs) minimize ∥Ψ-Φ∥2, where Ψ is a wave function and Φ is a full configuration interaction (CI) approximation to Ψ in a reduced basis. We will show that the NOs rarely provide the optimal orbitals for Φ, except when (1) there are only two particles or (2) only one basis function is removed in the case of fermions. Further, we will show that the CI expansion coefficients of Ψ and Φ are identical up to a global scaling factor and demonstrate how the NOs can be used to generate the orbitals that minimize ∥Ψ-Φ∥2.

Electron-impact study of PO2using theR-matrix method

The $R$-matrix approach is used to study the electron scattering from ${\text{PO}}_{2}$ radical at low electron impact energies. The elastic scattering phenomenon is studied in static-exchange, one-state and many-states close-coupling approximation. The elastic differential cross sections, corresponding momentum-transfer cross sections, and collision frequency are calculated in the one-state configuration interaction approximation only. Calculations reveal a stable bound state of ${\text{PO}}_{2}^{\ensuremath{-}}$ having symmetry ${}^{1}{A}_{1}$, a configuration of $\ensuremath{\cdots}8{a}_{1}^{2},\ensuremath{\cdots}2{b}_{1}^{2},\ensuremath{\cdots}5{b}_{2}^{2},\ensuremath{\cdots}1{a}_{2}^{2}$, and vertical electron affinity of $2.94$ eV. The excited state of anion ${\text{PO}}_{2}^{\ensuremath{-}}$ having symmetry ${}^{3}{B}_{1}$ is also just bound relative to the ground state of ${\text{PO}}_{2}$ at its equilibrium geometry. The shape, core-excited, and Feshbach resonances are analyzed in different symmetries up to 7 eV. The partial waves up to $l=4$ are used to represent continuum electron. The converged cross sections are obtained for the partial waves having $l$ greater than 4 by applying Born correction. Certain interesting spectroscopic properties of radical are also reported.

Truncated configuration interaction expansions as solvers for correlated quantum impurity models and dynamical mean-field theory

The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nano-science to the dynamical mean-field theory (DMFT). Here we describe how configuration interaction (CI) approximations to exact diagonalization (ED) may be used as solvers in DMFT. CI approximations retain the main advantages of ED, such as the ability to treat general interactions and off-diagonal hybridizations and to obtain real spectral information, but are of polynomial cost. Furthermore, their errors can be controlled by monitoring the convergence of physical quantities as a function of the CI hierarchy. Using benchmark DMFT applications, such as single-site DMFT of the 1D Hubbard model and $2\times 2$ cluster DMFT of the 2D Hubbard model, we show that CI approximations allow us to obtain near-exact ED results for a tiny fraction of the cost. This is true over the entire range of interaction strengths including "difficult" regimes, such as in the pseudogap phase of the 2D Hubbard model. We use the ability of CI approximations to treat large numbers of orbitals to demonstrate convergence of the bath representation in the $2\times 2$ cluster DMFT using a 24 bath orbital representation. CI approximations thus form a promising route to extend ED to problems that are currently difficult to study using other solvers such as continuous-time quantum Monte Carlo, including impurity models with large numbers of orbitals and general interactions.

Theoretical Study of Vibrationally Averaged Dipole Moments for the Ground and Excited C═O Stretching States of trans-Formic Acid.

Recent experimental studies of trans-formic acid (FA) in solid para-hydrogen (pH2) highlighted the importance of vibrationally averaged dipole moments for the interpretation of the high-resolution infrared (IR) spectra, in particular for the C═O stretch (ν3) mode. In this report, dipole moments for the ν3 ground (v = 0) and excited (v = 1, 2, 3, and 4) anharmonic vibrational states in trans-FA are investigated using two different approaches: a single mode approximation, where the vibrational states are obtained from the solution of the one-dimensional Schrödinger equation for the harmonic normal coordinate, and a limited vibrational configuration interaction (VCI) approximation. Density functional theory (B3LYP, BPW91) and correlated ab initio (MP2 and CCSD(T)) electronic methods were employed with a number of double- and triple-ζ and correlation consistent basis sets. Both single mode and VCI approaches show comparable agreement with experimental data, which is more dependent on the level of theory used. In particular, the BPW91/cc-pVDZ level appears to perform remarkably well. Effects of solvation of FA in solid state Ar and pH2 matrices were simulated at the BPW91/cc-pVDZ level using a conductor-like polarized continuum model (CPCM). The Ar and pH2 solid-state matrices cause quite a substantial increase in the FA dipole moments. Compared to gas-phase calculations, the CPCM model for pH2 better reproduces the experimental FA spectral shifts caused by interaction with traces of ortho-hydrogen (oH2) species in solid pH2. The validity of the single mode approach is tested against the multidimensional VCI results, suggesting that the isolated (noninteracting) mode approximation is valid up to the third vibrationally excited state (v = 3). Finally, the contribution of the ground anharmonic vibrational states of the remaining modes to the resulting ν3 single mode dipole moments is examined and discussed.

Symmetry-decomposed reduced transition operators for degenerate atomic states-Their generation and their utility

The p-particle reduced transition operator between the (ML = L, Ms = S) member of one degenerate (L, S) manifold and the (ML′ = V, MS′ = S′) member of a (possibly different) (L′, S′) manifold of eigenstates of a nonrelativistic atomic Hamiltonian contains sufficient information to construct the p-particle reduced transition operator between any member of the first manifold and any member of the second manifold. The procedure for such a construction has been given, and applied computationally to generate the symmetry-decomposed one-particle reduced transition operators among all the ML, MS states of a degenerate (L, S) manifold, from the nondecomposed one-particle reduced density operator of the (ML = L, MS = S) member of this manifold; thereby expediting the calculation of the one-particle reduced density operator of an arbitrary linear superposition of these degenerate states. To illustrate their applicability, these results were used to obtain the densities of the cubic-symmetry-adapted states of an atomic 1D manifold, (in a configuration-interaction approximation) which densities are shown graphically (using the PLOT79 graphics program). The computer program uses the coding of Carlos Bunge's atomic CI program, and can be appended directly to it or to its wavefunction or density-matrix output.

The hydrogen atom in the hydrogen molecule

Accurate two-electron wavefunctions which are localized in the sense that they are least distorted from a product of hydrogen atom wave functions, have been calculated for the X, 1∑+ and the b3∑+ states of H2 at nuclear separations of 1.0 to 4.0 bohrs. The calculations were done in the full configuration interaction approximation. These localized wavefunctions have been used as the basis for an analysis of the interaction energies in the manner of Heitler and London. The analysis shows the importance of the exchange energy for bonding. In addition, the localized wavefunctions have been used to define and calculate the densities of the H atoms in the molecule and to define an electronic exchange density. Contour plots of the densities are used to show how the atoms adjust to the molecular environment and how these changes are reinforced by exchange to give the molecular electronic density.