Many-body Perturbation Theory Methods Research Articles

Wavelengths and transition rates for nl–n′l′ transitions in Be-, B-, Mg-, Al-, Ca-, Zn-, Ag- and Yb-like tungsten ions

We present a comprehensive theoretical study of atomic characteristics of eight isoelectronic sequences of tungsten ions in a broad range of wavelengths and transitions. In particular, excitation energies, oscillator strengths and transition probabilities are calculated for nl–n′l′ transitions in W70 +, W69 +, W62 +, W61 +, W54 +, W44 +, W27 + and W4 + ions. Atomic structure and radiative characteristics of Be-like ([He]2lnl′, n = 2, 3), B-like ([He]2l2l′2l″), Mg-like ([Ne]3l3l′), Al-like ([Ne]3l3l′3l″), Ca-like ([Ar]3d4l), Zn-like ([Ni]4l4l′), Ag-like [Kr]4d10nl) and Yb-like ([Xe]4f145l6l′) tungsten ions are computed by the relativistic many-body perturbation theory (RMBPT) method. The calculations start from a 1s2 Dirac–Fock potential for Be- and B-like W, from the 1s22s22p6 Dirac–Fock potential for Mg- and Al-like W; from the 1s22s22p63s23p6 and 1s22s22p63s23p63d10 Dirac–Fock potentials for Ca- and Zn-like W, respectively. Evaluation of properties of Ag-like and Yb-like ions starts from a Dirac–Fock potential with only partially filled n = 4 shell (1s22s22p63s23p63d104s24p64d10) and n = 5 shell (1s22s22p63s23p63d104s24p64d104f145s25p6), respectively. First-order perturbation theory is used to obtain intermediate coupling coefficients, and second-order RMBPT is used to determine the matrix elements. The contributions from negative-energy states are included in the second-order E1 matrix elements to achieve agreement between length-form and velocity-form amplitudes. Our calculations present benchmark data for many yet unmeasured properties of tungsten ions and are in particular important in diagnostics of tungsten plasma of a broad range of temperatures as well as for future ITER plasmas.

Excitation energies, radiative and autoionization rates, dielectronic satellite lines and dielectronic recombination rates for excited states of Mg-like W from Na-like W

Energy levels, radiative transition probabilities and autoionization rates for 1s22s22p63l′nl (n = 3–13, l ⩽ n − 1), 1s22s22p64l′nl (n = 4–7, l ⩽ n − 1) and 1s22s22p53l′3l″nl (n = 3–4, l ⩽ n − 1) states in Mg-like tungsten (W62+) are calculated using the Hartree–Fock-relativistic method (COWAN code), the multiconfiguration relativistic Hebrew University Lawrence Atomic Code (HULLAC code) and the relativistic many-body perturbation theory method (RMBPT code). Autoionizing levels above the thresholds 1s22s22p63l and 1s22s22p64l are considered. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the first excited odd- and even-parity states. It is shown that the contribution of the highly excited states is very important for the calculation of total DR rates. Contributions to DR rate coefficients from the excited 1s22s22p63l′nl states with n ⩾ 14 and 1s22s22p64l′nl states with n ⩾ 8 and additionally from core-excited 1s22s22p53l′3l″nl states with n ⩾ 5 are estimated by extrapolation of all atomic parameters. The orbital angular momentum quantum number l distribution of the rate coefficients shows two peaks at l = 2 and l = 5. The total DR rate coefficient is derived as a function of electron temperature. The dielectronic satellite spectra of W62+ are important for L-shell diagnostic of very high-temperature laboratory plasmas such as future ITER plasmas.

Entanglement in disordered and non-equilibrium systems

We calculate an entanglement witness for a disordered spin system using the method of functional many-body perturbation theory, comparing the effect of taking a quenched and an annealed average over the disorder. We find, on considering the example of an XX Heisenberg spin chain with a Dzyaloshinskii–Moriya interaction, that disorder in the Dzyaloshinskii–Moriya interaction increases the region of entanglement detected by the witness. We also discuss a method of detecting entanglement in far from equilibrium systems.

Electron correlation and properties of many-electron systems

Different computational methods of quantum chemistry, which are currently employed in accurate calculations of atomic and molecular properties, are discussed and their advantages and disadvantages are investigated in calculations of electric properties of Be, FH, and H2O. A complete fourth-order many-body perturbation theory (MBPT) approach based on the coupled Hartree–Fock (CHF) solution for the perturbed problem reveals that in several cases the fourth-order correlation correction to the CHF result is dominated by those terms which involve triply substituted intermediate states. Moreover, in some cases a complete fourth-order MBPT result appears to be inferior to those obtained in approximate MBPT treatments which involve only certain classes of intermediate states. Hence, a complete fourth-order MBPT approach may not be sufficient for accurate predictions of atomic and molecular properties. The applicability of the complete active space (CAS) SCF method is studied in calculations of electric properties of FH. Although this method offers some advantages over the MBPT approach, its usefulness may be limited by the requirement of rather large active orbital spaces which have to be used in order to achieve sufficiently high accuracy. The CAS SCF results can be improved by using multireference CI methods with reference functions built of the CAS SCF natural orbitals. A good performance of the MBPT method limited to singly and doubly substituted intermediate states suggests that reasonable results can also be obtained in similar configuration interaction (CI) calculations, provided the latter are corrected for the erratic treatment of unlinked clusters. It is shown that the unlinked cluster corrections due to Davidson and Siegbahn result in reasonable estimates of the total correlation contribution to different properties. Because of its fairly routine character the CI method limited to single and double substitutions may in this way provide useful data with relatively small computational effort.

Excitation energies, radiative and autoionization rates, dielectronic satellite lines, and dielectronic recombination rates for excited states of Na-like W from Ne-like W

Energy levels, radiative transition probabilities, and autoionization rates for 1 s 2 2 s 2 2 p 5 3 l ′ nl , 1 s 2 2 s 2 p 6 3 l ′ nl ( n = 3 – 7 , l ⩽ n - 1 ) and 1 s 2 2 s 2 2 p 5 4 l ′ nl , 1 s 2 2 s 2 p 6 4 l ′ nl ( n = 4 – 6 , l ⩽ n - 1 ) states in Na-like tungsten ( W 63 + ) are calculated. Cowan’s relativistic Hartree–Fock method, the relativistic multiconfiguration method implemented in the Hebrew University Lawrence Livermore Atomic Code, and the relativistic many-body perturbation theory method, are used. Autoionizing levels above the threshold 1 s 2 2 s 2 2 p 6 are considered. It is found that configuration mixing [ 3 sns + 3 pnp + 3 dnd ] , [ 3 snp + 3 pns + 3 pnd + 3 dnp ] plays an important role for all atomic characteristics. Also strong mixing between states with 2 s and 2 p holes ( 1 s 2 2 s 2 2 p 5 3 l 1 nl 2 + 1 s 2 2 s 2 p 6 3 l 3 nl 4 ) occurs. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the excited 1 s 2 2 s 2 2 p 6 nl ( n = 3 – 7 , l ⩽ n - 1 ) states. It is shown that the contribution of the highly excited states is very important for calculation of total DR rates. Contributions from the autoionizing states 1 s 2 2 s 2 2 p 5 3 l ′ nl , 1 s 2 2 s 2 p 6 3 l ′ nl ( n ⩾ 8 ) and 1 s 2 2 s 2 2 p 5 4 l ′ nl , 1 s 2 2 s 2 p 6 4 l ′ nl ( n ⩾ 7 ) to the DR rate coefficients are estimated by extrapolation of all atomic parameters. The orbital angular momentum ( l) distribution of the rate coefficients shows a peak at l = 2 . The total DR rate coefficient is derived as a function of electron temperature. The dielectronic satellite spectra of W 63 + are important for L-shell diagnostics of very high-temperature laboratory plasmas such as future ITER fusion plasmas.

Atomic data for dielectronic satellite lines and dielectronic recombination into Ne 5+

Energy levels, radiative transition probabilities, and autoionization rates for B-like neon (Ne 5+) including 1s 22s 2 nl, 1s 22s2p nl, and 1s 22p 2 nl ( n = 2–11 and l = 0–7) states were calculated using a multiconfigurational Hartree–Fock method (Cowan code) and a relativistic many-body perturbation theory method (RMPT) code. Autoionizing levels above three thresholds (1s 22s 2 1S, 1s 22s2p 3P, 1s 22s2p 1P) were considered. We find that configuration mixing (2s 2 nl + 2p 2 nl) plays an important role for all atomic characteristics. Branching ratios relative to the first threshold and the intensity factor were calculated for satellite lines and dielectronic recombination rate coefficients for the 190 odd-parity and 198 even-parity excited states. The dielectronic recombination rate coefficients including 1s 22s 2 nl, 1s 22s2p nl, and 1s 22p 2 nl ( n = 2–11 and l = 0–7) states were calculated. The contributions from the excited states higher than n = 11 were estimated by extrapolation of all atomic characteristics to derive the total dielectronic recombination rate coefficient. It is found that the distribution of the rate coefficients as a function of the orbital angular momentum quantum number shows a peak at l = 5. The total dielectronic recombination rate coefficient was derived as a function of electron temperature. The dielectronic satellite lines were also obtained. The state selective dielectronic recombination rate coefficients to excited states of B-like neon were obtained, which are useful for modeling Ne VI spectral lines in a recombining plasma.

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).

Large-scale calculation of dielectronic recombination parameters for Mg-like Fe

Energy levels, radiative transition probabilities and autoionization rates for 1s22s22p63l′nl (n = 3–12, l ⩽ n − 1) and 1s22s22p64l′nl (n = 4–7, l ⩽ n − 1) states in Mg-like iron (Fe14+) are calculated by the Hartree–Fock-relativistic method (Cowan code) and the relativistic many-body perturbation theory method (RMBPT code). Autoionizing levels above three thresholds 1s22s22p63s, 1s22s22p63p and 1s22s22p63d are considered. It is found that configuration mixings [3sns + 3pnp + 3dnd] and [3snp + 3pns + 3pnd + 3dnp] play an important role for all atomic characteristics. Branching ratios relative to the first threshold and intensity factors are calculated for satellite lines, and dielectronic recombination (DR) rate coefficients are determined for the excited 444 odd-parity and 419 even-parity states. It is shown that the contribution of the highly-excited states is very important for calculation of total DR rates. Contributions from the excited 1s22s22p63l′nl states with n ⩾ 12 and 1s22s22p64l′nl states with n ⩾ 7 to DR rate coefficients are estimated by extrapolation of all atomic parameters. The total DR rate coefficient is derived as a function of electron temperature.

Ab initio calculations with CI+MBPT of large number of energy levels for beryllium-like neon

Previously, ab initio precision configuration–interaction many-body perturbation theory (CI+MBPT) method was applied only to low energy levels. In this work, we consider highly excited states with this method and show that many theoretical levels agree well with experiment and can be easily identified. The precision of the method for lowest levels can be achieved at the level of tens of cm−1; however, for a large number of levels the precision is lower, a few 100 cm−1. This is due to slower convergence of bases obtained in large cavities to avoid cavity effects on the states of interest. Available experimental data have been used for label assignment and as a test of our method. This is the first attempt to apply ab initio precision method to hundreds of levels including moderately highly excited states. The method can be useful for level identification and for calculations of properties of Rydberg states in the regime where ion-core correlations are important and can be used to test other methods designed for these states.

Excitation energies, hyperfine constants, E1 transition rates and lifetimes of 4s2nl states in neutral gallium

Energies of the 4s2npj (n = 4–8), 4s2ns1/2 (n = 5–8), 4s2ndj (n = 4–7), 4s2nfj (n = 4–5) and 4s25gj states in neutral gallium are obtained using a relativistic many-body perturbation theory (RMBPT) method. First-, second-, third- and all-order Coulomb energies and first-order Breit and second-order Coulomb–Breit corrections are calculated. Reduced matrix elements, oscillator strengths, transition rates and lifetimes are determined for the 130 possible electric-dipole transitions. Hyperfine constants A are determined for 28 4s2nlj states in 69Ga I and 71Ga I isotopes. All above-mentioned properties are obtained in the relativistic single–double (SD) approximation, where single and double excitations of Dirac–Fock wavefunctions are included to all orders of perturbation theory. Using SD wavefunctions, accurate values are obtained for energies of the lowest states and for the possible electric-dipole matrix elements between these states. With the aid of the SD wavefunctions, we also determine transition rates, oscillator strengths and lifetimes. These calculations provide a theoretical benchmark for comparison with experiment and theory.

Direct measurement of the energy thresholds to conformational isomerization in Tryptamine: Experiment and theory

The methods of stimulated emission pumping-hole filling spectroscopy (SEP-HFS) and stimulated emission pumping population transfer spectroscopy (SEP-PTS) were applied to the conformation-specific study of conformational isomerization in tryptamine [TRA, 3-(2-aminoethyl)indole]. These experimental methods employ stimulated emission pumping to selectively excite a fraction of the population of a single conformation of TRA to well-defined ground-state vibrational levels. This produces single conformations with well-defined internal energy, tunable over a range of energies from near the zero-point level to well above the lowest barriers to conformational isomerization. When the SEP step overcomes a barrier to isomerization, a fraction of the excited population isomerizes to form that product. By carrying out SEP excitation early in a supersonic expansion, these product molecules are subsequently cooled to their zero-point vibrational levels, where they can be detected downstream with a third tunable laser that probes the ground-state population of a particular product conformer via a unique ultraviolet transition using laser-induced fluorescence. The population transfer spectra (recorded by tuning the SEP dump laser while holding the pump and probe lasers fixed) exhibit sharp onsets that directly determine the energy thresholds for conformational isomerization in a given reactant-product conformer pair. In the absence of tunneling effects, the first observed transition in a given X-Y PTS constitutes an upper bound to the energy barrier to conformational isomerization, while the last transition not observed constitutes a lower bound. The bounds for isomerizing conformer A of tryptamine to B(688-748 cm(-1)), C(1)(860-1000 cm(-1)), C(2)(1219-1316 cm(-1)), D(1219-1282 cm(-1)), E(1219-1316 cm(-1)), and F(688-748 cm(-1)) are determined. In addition, thresholds for isomerizing from B to A(<1562 cm(-1)), B to F(562-688 cm(-1)), and out of C(2) to B(<747 cm(-1)) are also determined. The A-->B and B-->A transitions are used to place bounds on the relative energies of minima B relative to A, with B lying at least 126 cm(-1) above A. The corresponding barriers have been computed using both density functional and second-order many-body perturbation theory methods in order to establish the level of theory needed to reproduce experimental results. While most of the computed barriers match experiment well, the barriers for the A-F and B-F transitions are too high by almost a factor of 2. Possible reasons for this discrepancy are discussed.

Excitation energies, radiative and autoionization rates, dielectronic satellite lines, and dielectronic recombination rates to excited states for B-like oxygen

Energy levels, radiative transition probabilities, and autoionization rates for B-like oxygen (O 3+) including 1s 22s 2 nl, 1s 22s2p nl, and 1s 22p 2 nl ( n = 2–8, l ⩽ n − 1) states are calculated using the multiconfiguration interaction Cowan code and a relativistic many-body perturbation theory method (RMBPT) code. Autoionizing levels above three thresholds (1s 22s 2 1S, 1s 22s2p 3P, and 1s 22s2p 1P) are considered. Configuration mixing (2s 2 nl + 2p 2 nl) plays an important part in all of the atomic properties considered. Branching ratios relative to the first threshold and the intensity factor are calculated for satellite lines and dielectronic recombination rate coefficients for the excited 105 odd-parity and 94 even-parity states. The dielectronic recombination rate coefficients are calculated including 1s 22s 2 nl, 1s 22s2p nl, and 1s 22p 2 nl ( n = 2–8, l ⩽ n − 1) states. The contribution from the excited states higher than n = 8 are estimated by extrapolation of all atomic properties to derive the total dielectronic recombination rate coefficient. The orbital angular momentum quantum number distribution of the rate coefficients shows a peak at l = 5. The total dielectronic recombination rate coefficient is derived as a function of electron temperature and the dielectronic satellite lines are also obtained. The state selective dielectronic recombination rate coefficients to excited states of B-like oxygen are obtained, which are useful for modeling O IV spectral lines in a recombining plasma.

Algebraic modifications to second quantization for non-Hermitian complex scaled hamiltonians with application to a quadratically convergent multiconfigurational self-consistent field method

The algebraic structure for creation and annihilation operators defined on orthogonal orbitals is generalized to permit easy development of bound-state techniques involving the use of non-Hermitian Hamiltonians arising from the use of complex-scaling or complex-absorbing potentials in the treatment of electron scattering resonances. These extensions are made possible by an orthogonal transformation of complex biorthogonal orbitals and states as opposed to the customary unitary transformation of real orthogonal orbitals and states and preserve all other formal and numerical simplicities of existing bound-state methods. The ease of application is demonstrated by deriving the modified equations for implementation of a quadratically convergent multiconfigurational self-consistent field (MCSCF) method for complex-scaled Hamiltonians but the generalizations are equally applicable for the extension of other techniques such as single and multireference coupled cluster (CC) and many-body perturbation theory (MBPT) methods for their use in the treatment of resonances. This extends the domain of applicability of MCSCF, CC, MBPT, and methods based on MCSCF states to an accurate treatment of resonances while still using L2 real basis sets. Modification of all other bound-state methods and codes should be similarly straightforward. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

Relativistic effects in two valence-electron atoms and ions and the search for variation of the fine-structure constant

We perform accurate calculations of the dependence of transition frequencies in two valence electron atoms and ions on a variation of the fine structure constant, alpha. The relativistic Hartree-Fock method is used with many-body perturbation theory and configuration interaction methods to calculate transition frequencies. The results are to be used in atomic-clock-type laboratory experiments designed to test whether alpha varies in time.

Lithium hyperfine splitting

We present an approach for the calculation of relativistic $m{\ensuremath{\alpha}}^{6}$ corrections to the lithium ground-state hyperfine splitting. It is based on the effective Hamiltonian derived from relativistic quantum electrodynamic theory. This approach with the help of appropriate nonrelativistic correlated basis sets has the potential to be more accurate than currently available relativistic computational methods such as the relativistic many-body perturbation theory, configuration interaction, or multiconfiguration Dirac-Fock method.

αdependence of transition frequencies for ions Si II, Cr II, Fe II, Ni II, and Zn II

We perform an improved calculation of the $\ensuremath{\alpha}$ dependence $(\ensuremath{\alpha}{=e}^{2}/hc)$ of the transition frequencies for ions, which are used in a search for the variation of the fine-structure constant $\ensuremath{\alpha}$ in space-time. We use the Dirac-Hartree-Fock method as a zero approximation and then the many-body perturbation theory and configuration-interaction methods to improve the results. The important problem of level pseudocrossing (as a function of $\ensuremath{\alpha})$ is considered. Near the crossing point the derivative of the frequency over $\ensuremath{\alpha}$ varies strongly (including a change of sign). This makes it very sensitive to the position of the crossing point. We propose a semiempirical solution of the problem, which allows us to obtain accurate results.

Spectra of Ar–CO2 from ab initio potential energy surfaces

Potential energy surface for the interaction of Ar with CO2 has been calculated using different levels of symmetry-adapted perturbation theory (SAPT) and the supermolecular many-body perturbation theory (MBPT) and coupled-cluster methods. These potentials have been used to compute the rovibrational spectra of Ar–CO2 and the interaction virial coefficients. The best reproduction of experimental data was achieved by the SAPT potential at the level of theory similar to the second-order of MBPT. The accuracy of this potential is in fact very close to that of the recent semiempirical surface of Hutson et al. [J. Chem. Phys. 106, 9130 (1996)] which was fitted to this set of data. Somewhat surprisingly, the more advanced methods considered here performed not as well.

Analytic second derivatives in high-order many-body perturbation and coupled-cluster theories: Computational considerations and applications

The history of analytic first- and second-derivative methods in quantum chemistry is discussed, with special emphasis given to approaches that are associated with electron correlation treatments based on many-body perturbation theory (MBPT) and the coupled-cluster (CC) approximation. The computational requirements of recently developed analytical second derivative methods for high-order MBPT and CC methods are discussed in detail and compared with those associated with finite-difference procedures. Applications of these techniques to the calculation of anharmonic force fields used to deduce equilibrium geometries and fundamental vibrational frequencies for polyatomic molecules are reviewed.

Calculated Raman and Rayleigh properties of the CaC molecule

The dipole moment, static dipole polarizability and hyperpolarizability of CaC are calculated using high-level many-body perturbation theory and coupled-cluster methods with large basis sets. These moments and the corresponding gradients are used to predict the Rayleigh and Raman activities. The effects of the electron correlation on the calculated properties are discussed. At the highest level, CCSD(T), the dipole moment is 1.6a.u. (4.1D), and the average dipole polarizability is 111.5a.u. (16.52Å3) with a large and negative anisotropy of 7.4a.u. (1.1Å3). The average dipole hyperpolarizability is 1720.0a.u. (14.862×10−30cm5esu−1). Analysis of the polarizability gradient indicates a very large Raman depolarization of the light scattered by CaC with the depolarization being 96%, 93% and 77% for natural, planar and circular polarizations, respectively.

Structures and electron detachment energies of uracil anions

Uracil and its radical anions were studied with second-order, many-body perturbation theory, coupled-cluster theory and electron propagator methods with large, diffuse, atom-centered basis sets. All structures were optimized and two minima were found for anionic forms: one corresponding to a 2 A′, diffuse-bound state and another corresponding to a 2 A, non-planar, covalent-bound state. The optimized 2 A′ anionic structure is lower in energy than the neutral form. The vertical electron detachment energy (VEDE) of this structure is very close to the experimentally observed value. A large, positive VEDE was found for the 2 A, covalent-bound anion.