Second-order Many-body Perturbation Theory Research Articles

Impact of correlations on nuclear binding energies

A strong effort will be dedicated in the coming years to extend the reach of ab initio nuclear-structure calculations to heavy doubly open-shell nuclei. In order to do so, the most efficient strategies to incorporate dominant many-body correlations at play in such nuclei must be identified. With this motivation in mind, the present work analyses the step-by-step inclusion of many-body correlations and their impact on binding energies of Calcium and Chromium isotopes. Employing an empirically-optimal Hamiltonian built from chiral effective field theory, binding energies along both isotopic chains are studied via a hierarchy of approximations based on polynomially-scaling expansion many-body methods. More specifically, calculations are performed based on (i) the spherical Hartree–Fock–Bogoliubov mean-field approximation plus correlations from second-order Bogoliubov many-body perturbation theory or Bogoliubov coupled cluster with singles and doubles on top of it, along with (ii) the axially-deformed Hartree–Fock–Bogoliubov mean-field approximation plus correlations from second-order Bogoliubov many-body perturbation theory built on it. The corresponding results are compared to experimental data and to those obtained via valence-space in-medium similarity renormalization group calculations at the normal-ordered two-body level that act as a reference in the present study. The spherical mean-field approximation is shown to display specific shortcomings in Ca isotopes that can be understood analytically and that are efficiently corrected via the consistent addition of low-order dynamical correlations on top of it. While the same setting cannot appropriately reproduce binding energies in doubly open-shell Cr isotopes, allowing the unperturbed mean-field state to break rotational symmetry permits to efficiently capture the static correlations responsible for the phenomenological differences observed between the two isotopic chains. Eventually, the present work demonstrates that polynomially-scaling expansion methods based on unperturbed states that possibly break (and restore) symmetries constitute an optimal route to extend ab initio calculations to heavy closed- and open-shell nuclei.

The performance of approximate equation of motion coupled cluster for valence and core states of heavy element systems

The equation of motion coupled cluster singles and doubles model (EOM-CCSD) is an accurate, black-box correlated electronic structure approach to investigate electronically excited states and electron attachment or detachment processes. It has also served as a basis for developing less computationally expensive approximate models such as partitioned EOM-CCSD (P-EOM-CCSD), the second-order many-body perturbation theory EOM (EOM-MBPT(2)) and their combination (P-EOM-MBPT(2)) [S. Gwaltney et al., Chem. Phys. Lett. 248, 189–198 (1996)]. In this work we outline an implementation of these approximations for four-component based Hamiltonians and investigate their accuracy relative to EOM-CCSD for valence excitations, valence and core ionisations and electron attachment, and this for a number of systems of atmospheric or astrophysical interest containing elements across the periodic table. We have found that across the different systems and electronic states of different nature considered, partition EOM-CCSD yields results with the largest deviations from the reference, whereas second-order based approaches tend show a generally better agreement with EOM-CCSD. We trace this behaviour to the imbalance brought about by the removal of excited state relaxation in the partition approaches, with respect to degree of electron correlation recovered.

Modewise Johnson–Lindenstrauss embeddings for nuclear many-body theory

In this work, we explore modewise Johnson-Lindenstrauss embeddings (JLEs) as a tool to reduce the computational cost and memory requirements of nuclear many-body methods. JLEs are randomized projections of high-dimensional data tensors onto low-dimensional subspaces that preserve key structural features. Such embeddings allow for the oblivious and incremental compression of large tensors, e.g., the nuclear Hamiltonian, into significantly smaller random sketches that still allow for the accurate calculation of ground-state energies and other observables. Their oblivious character makes it possible to compress a tensor without knowing in advance exactly what observables one might want to approximate at a later time. This opens the door for the use of tensors that are much too large to store in memory, e.g., complete two-plus three-nucleon Hamiltonians in large, symmetry-unrestricted bases. Such compressed Hamiltonians can be stored and used later on with relative ease. As a first step, we analyze the JLE's impact on the second-order Many-Body Perturbation Theory (MBPT) corrections for nuclear ground-state observables. Numerical experiments for a wide range of closed-shell nuclei, model spaces and state-of-the-art nuclear interactions demonstrate the validity and potential of the proposed approach: We can compress nuclear Hamiltonians hundred- to thousand-fold while only incurring mean relative errors of 1\% or less in ground-state observables. Importantly, we show that JLEs capture the relevant physical information contained in the highly structured Hamiltonian tensor despite their random characteristics. In addition to the significant storage savings, the achieved compressions imply multiple order-of magnitude reductions in computational effort when the compressed Hamiltonians are used in higher-order MBPT or nonperturbative many-body methods.

Benchmarking calculations of wavelengths and transition rates with spectroscopic accuracy for W xlviii through W lvi tungsten ions

Atomic properties of $n=3$ levels for ${\mathrm{W}}^{47+}\ensuremath{-}{\mathrm{W}}^{55+}$ ions ($Z=74$) are systematically calculated using two different and independent methods, namely, the second-order many-body perturbation theory and the multiconfiguration Dirac-Hartree-Fock method combined with the relativistic configuration interaction approach. Wavelengths and transition rates for electric- and magnetic-dipole transitions involving the $n=3$ levels of ${\mathrm{W}}^{47+}\ensuremath{-}{\mathrm{W}}^{55+}$ are calculated. In addition, we discuss in detail the importance of the valence and core-valence electron correlations, the Breit interaction, the higher-order frequency-dependent retardation correction, and the leading quantum electrodynamical corrections for transition wavelengths. Spectroscopic accuracy is achieved for the present calculated wavelengths, and most of them agree with experimental values within $0.05%$. Our calculated wavelengths, combined with collisional radiative model simulations, are used to identify the yet unidentified 25 observed lines in the extremely complex spectrum between $27\phantom{\rule{0.16em}{0ex}}\AA{}$ and $34\phantom{\rule{0.16em}{0ex}}\AA{}$ measured by Lennartsson $et\phantom{\rule{4pt}{0ex}}al.$ [Phys. Rev. A 87, 062505 (2013)]. We provide additional data for 472 strong electric-dipole transitions in the wavelength range of 17--50 \AA{}, and 185 strong magnetic-dipole transitions between $36\phantom{\rule{0.16em}{0ex}}\AA{}$ and $4384\phantom{\rule{0.16em}{0ex}}\AA{}$, with a line intensity greater than $1\phantom{\rule{0.16em}{0ex}}\mathrm{photon}/\mathrm{s}$. These can provide benchmark data for future experiments and theoretical calculations.

Stochastic Vector Techniques in Ground-State Electronic Structure.

We review a suite of stochastic vector computational approaches for studying the electronic structure of extended condensed matter systems. These techniques help reduce algorithmic complexity, facilitate efficient parallelization, simplify computational tasks, accelerate calculations, and diminish memory requirements. While their scope is vast, we limit our study to ground-state and finite temperature density functional theory (DFT) and second-order many-body perturbation theory. More advanced topics, such as quasiparticle (charge) and optical (neutral) excitations and higher-order processes, are covered elsewhere. We start by explaining how to use stochastic vectors in computations, characterizing the associated statistical errors. Next, we show how to estimate the electron density in DFT and discuss effective techniques to reduce statistical errors. Finally, we review the use of stochastic vectors for calculating correlation energies within the second-order Møller-Plesset perturbation theory and its finite temperature variational form. Example calculation results are presented and used to demonstrate the efficacy of the methods.

Relativistic coupled-cluster calculation of the electric dipole polarizability and correlation energy of Cn, Nh+ , and Og: Correlation effects from lighter to superheavy elements

We employ a fully relativistic coupled-cluster theory to calculate the ground-state electric dipole polarizability and electron correlation energy of superheavy elements Cn, Nh$^+$ and Og. To assess the trend of electron correlation as function of $Z$, we also calculate the correlation energies for three lighter homologs--Zn, Cd and Hg; Ga$^+$, In$^+$ and Tl$^+$; Kr, Xe and Rn--for each superheavy elements. The relativistic effects and quantum electrodynamical corrections are included using the Dirac-Coulomb-Breit Hamiltonian with the corrections from the Uehling potential and the self-energy. The effects of triple excitations are considered perturbatively in the theory. Furthermore, large bases are used to test the convergence of results. Our recommended values of polarizability are in good agreement with previous theoretical results for all SHEs. From our calculations we find that the dominant contribution to polarizability is from the valence electrons in all superheavy elements. Except for Cn and Og, we observe a decreasing contribution from lighter to superheavy elements from the Breit interaction. For the corrections from the vacuum polarization and self-energy, we observe a trend of increasing contributions with $Z$. From energy calculations, we find that the second-order many-body perturbation theory overestimates the electron correlation energy for all the elements considered in this work.

M1 transition energy and rate in the ground configuration of Ag-like ions with 62 ⩽ Z ⩽ 94

Systematic calculations and assessments are performed for the magnetic dipole (M1) transition energies and rates between the levels in the ground configuration 4d104f along the Ag-like isoelectronic sequence with 62 ⩽ Z ⩽ 94 based on the second-order many-body perturbation theory implemented in the Flexible Atomic Code. The electron correlations, Breit interaction and quantum electrodynamics effects are taken into account in the present calculations. The accuracy and reliability of our results are evaluated through comprehensive comparisons with available measurements and other theoretical results. For transition energies, our results are in good agreement with the recent experimental data obtained from the electron beam ion traps within 0.18%. The maximum discrepancy between our results and those obtained with the large-scale multiconfiguration Dirac–Hartee–Fock calculations by Grumer et al. [Phys. Rev. A 89 062501 (2014)] is less than 0.13% along the isoelectronic sequence. Furthermore, the corresponding M1 transition rates are also reported. The present results can be used as the benchmark and useful for spectra simulation and diagnostics of astrophysical and fusion plasmas.

Benchmarking calculations with spectroscopic accuracy of level energies and wavelengths in W LVII–W LXII tungsten ions

Atomic properties of n=3 states of the W56+ - W61+ ions are systematically investigated through two state-of-the-art methods, namely, the second-order many-body perturbation theory, and the multi-configuration Dirac–Hartree–Fock method combined with the relativistic configuration interaction approach. The contributions of valence-valence and core-valence electron correlations, the Breit interaction, the higher-order retardation correction beyond the Breit interaction through the transverse photon interaction, and the quantum electrodynamical corrections to the excitation energies are studied in detail. The excitation energies and wavelengths obtained with the two methods agree with each other within ≈0.01%. The present results achieve spectroscopic accuracy and provide a benchmark test for various applications and other theoretical calculations of W56+ - W61+ ions. They will assist spectroscopists in their assignment and direct identification of observed lines in complex spectra.

Determination of the dipole polarizability of the alkali-metal negative ions

We present electric dipole polarizabilities ($\alpha_d$) of the alkali-metal negative ions, from H$^-$ to Fr$^-$, by employing four-component relativistic many-body methods. Differences in the results are shown by considering Dirac-Coulomb (DC) Hamiltonian, DC Hamiltonian with the Breit interaction, and DC Hamiltonian with the lower-order quantum electrodynamics interactions. At first, these interactions are included self-consistently in the Dirac-Hartree-Fock (DHF) method, and then electron correlation effects are incorporated over the DHF wave functions in the second-order many-body perturbation theory, random phase approximation and coupled-cluster (CC) theory. Roles of electron correlation effects and relativistic corrections are analyzed using the above many-body methods with size of the ions. We finally quote precise values of $\alpha_d$ of the above negative ions by estimating uncertainties to the CC results, and compare them with other calculations wherever available.

Time-dependent optimized coupled-cluster method for multielectron dynamics. III. A second-order many-body perturbation approximation.

We report successful implementation of the time-dependent second-order many-body perturbation theory using optimized orthonormal orbital functions called time-dependent optimized second-order many-body perturbation theory to reach out to relatively larger chemical systems for the study of intense-laser-driven multielectron dynamics. We apply this method to strong-field ionization and high-order harmonic generation of Ar. The calculation results are benchmarked against ab initio time-dependent complete-active-space self-consistent field, time-dependent optimized coupled-cluster double, and time-dependent Hartree-Fock methods, as well as a single active electron model to explore the role of electron correlation.

Energy levels, transition rates and electron impact excitation rates for B-like Kr XXXII

Energy levels and transition rates for electric-dipole, electric-quadrupole, electric-octupole, magnetic-dipole, and magnetic-quadrupole transitions among the levels arising from the n≤ 5 configurations in B-like Kr XXXII are calculated by using two state-of-the-art methods, namely, the multi-configuration Dirac–Hartree–Fock (MCDHF) approach and the second-order many-body perturbation theory (RMBPT). Our results are compared with several available experimental and other theoretical values. Electron-impact excitation (EIE) collision strengths are calculated via the independent process and isolated resonance approximation using distorted-wave (denoted by IPIRDW). Radiation damping effects on the resonance excitation contributions are included. Effective collision strengths are calculated as a function of electron temperature by assuming a Maxwellian electron velocity distribution. Spectral line intensities are modelled by using collision radiative model, and several line pairs pointed out might be useful for density diagnostics.

Divergence of Many-Body Perturbation Theory for Noncovalent Interactions of Large Molecules.

Prompted by recent reports of large errors in noncovalent interaction (NI) energies obtained from many-body perturbation theory (MBPT), we compare the performance of second-order Mo̷ller-Plesset MBPT (MP2), spin-scaled MP2, dispersion-corrected semilocal density functional approximations (DFAs), and post-Kohn-Sham random phase approximation (RPA) for predicting binding energies of supramolecular complexes contained in the S66, L7, and S30L benchmarks. All binding energies are extrapolated to the basis set limit, corrected for basis set superposition errors, and compared to reference results of the domain-based local pair-natural orbital coupled-cluster (DLPNO-CCSD(T)) or better quality. Our results confirm that MP2 severely overestimates binding energies of large complexes, producing relative errors of over 100% for several benchmark compounds. RPA relative errors consistently range between 5 and 10%, significantly less than reported previously using smaller basis sets, whereas spin-scaled MP2 methods show limitations similar to MP2, albeit less pronounced, and empirically dispersion-corrected DFAs perform almost as well as RPA. Regression analysis reveals a systematic increase of relative MP2 binding energy errors with the system size at a rate of approximately 0.1% per valence electron, whereas the RPA and dispersion-corrected DFA relative errors are virtually independent of the system size. These observations are corroborated by a comparison of computed rotational constants of organic molecules to gas-phase spectroscopy data contained in the ROT34 benchmark. To analyze these results, an asymptotic adiabatic connection symmetry-adapted perturbation theory (AC-SAPT) is developed, which uses monomers at full coupling, whose ground-state density is constrained to the ground-state density of the complex. Using the fluctuation-dissipation theorem, we obtain a nonperturbative "screened second-order" expression for the dispersion energy in terms of monomer quantities, which is exact for non-overlapping subsystems and free of induction terms; a first-order RPA-like approximation to the Hartree, exchange, and correlation kernel recovers the macroscopic Lifshitz limit. The AC-SAPT expansion of the interaction energy is obtained from Taylor expansion of the coupling strength integrand. Explicit expressions for the convergence radius of the AC-SAPT series are derived within RPA and MBPT and numerically evaluated. While the AC-SAPT expansion is always convergent for nondegenerate monomers when RPA is used, it is found to spuriously diverge for second-order MBPT, except for the smallest and least polarizable monomers. The divergence of the AC-SAPT series for MBPT is numerically confirmed within RPA; prior numerical results on the convergence of the SAPT expansion for MBPT methods are revisited and support this conclusion once sufficiently high orders are included. The cause of the failure of MBPT methods for NIs of large systems is missing or incomplete "electrodynamic" screening of the Coulomb interaction due to induced particle-hole pairs between electrons in different monomers, leaving the effective interaction too strong for AC-SAPT to converge. Hence, MBPT cannot be considered reliable for quantitative predictions of NIs, even in moderately polarizable molecules with a few tens of atoms. The failure to accurately account for electrodynamic polarization makes MBPT qualitatively unsuitable for applications such as NIs of nanostructures, macromolecules, and soft materials; more robust nonperturbative approaches such as RPA or coupled cluster methods should be used instead whenever possible.

Extensive and accurate energy levels, transition rates, lifetimes, hyperfine structures and isotope shifts for the Rb XXXVI spectrum of plasma interest

We present relativistic multiconfiguration Dirac-Hartree-Fock (MCDHF) spectrum calculations for Rb XXXVI with correlations within the n = 8 complex. An extensive and accurate set of energy levels, wavelengths, line strengths, weighted oscillator strengths, lifetimes, isotope shifts, hyperfine structure and Landé gJ factors has been calculated for lower 127 odd- and even-parity states arising from the 1s2 and 1snl(n=1−8,0≤l≤n−1) configurations in He-like-Rb. Transition rates for electric-multipole (dipole (E1), quadrupole (E2), and octupole (E3)) and magnetic-multipole (dipole (M1), quadrupole (M2), and octupole (M3)) have been also calculated. For the accuracy of our results, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the Second-Order Many-Body Perturbation Theory (MBPT) method. Additionally, Breit interaction and leading quantum electrodynamic effects (QED) have been included as perturbations in extensive relativistic configuration interaction (RCI) calculations. The results arising in the two sets of calculations MCDHF and MBPT are quite close. Our results are compared with other available theory reported in the literature as well as the experimental data listed in the Atomic Spectra Database (ASD) of the National Institute of Standards and Technology (NIST) online database. Good agreement between them has been found. The present complete and consistent results can be used in line identification, plasma modeling and diagnostics of astrophysical plasma.

An adiabatic connection for doubly-occupied configuration interaction wave functions.

An adiabatic connection (AC) is developed as an electron correlation correction for doubly occupied configuration interaction (DOCI) wave functions. Following the work of Pernal [Phys. Rev. Lett. 120, 013001 (2018)], the working equations of the approach, termed AC-DOCI, are rooted in the extended random phase approximation (ERPA) and require knowledge of only the ground-state two-electron reduced density matrix (2RDM) from the DOCI. As such, the AC is naturally suited to modeling electron correlation in variational 2RDM (v2RDM)-based approximations to the DOCI. The v2RDM-driven AC-DOCI is applied to the dissociation of molecular nitrogen and the double dissociation of water; the approach yields energies that are similar in quality to those from second-order multireference perturbation theory near equilibrium, but the quality of the AC-DOCI energy degrades at stretched geometries. The exact adiabatic connection path suggests the assumption that the one-electron reduced-density matrix is constant along the AC path is invalid at stretched geometries, but this deficiency alone cannot explain the observed behavior. Rather, it appears that the ERPA's single-particle-transition ansatz cannot, in general, provide good approximations to the 2RDM along the AC path. The AC-DOCI is also applied to a set of 45 reaction energies; for these systems, the approach has an average accuracy that is comparable to that of single-reference second-order many-body perturbation theory.

Extended calculations of energy levels, radiative properties, and lifetimes for nitrogen-like Zr XXXIV

Highly accurate calculations are performed for the lowest 272 fine-structure levels arising from the 2s22p3, 2s2p4, 2p5, 2s22p23l, 2s2p33l, and 2p43l configurations in N-like Zr XXXIV using two state-of-the-art methods, second-order many-body perturbation theory and multiconfiguration Dirac–Fock. Complete and consistent atomic data, including excitation energies, wavelengths, E1, E2, M1, M2 line strengths, oscillator strengths, transition rates, and lifetimes for these 272 levels, are provided. Comparisons are made between the present two data sets, as well as with other available results. The present data are accurate enough for identification and deblending of emission lines involving the n=3 levels and are also useful for modeling and diagnosing fusion plasmas. These data can be considered as a benchmark for other calculations.

Extended calculations of energy levels, radiative properties, and lifetimes for oxygen-like Mo XXXV

Employing two state-of-the-art methods, second-order many-body perturbation theory and multiconfiguration Dirac–Fock, highly accurate calculations are performed for the lowest 318 fine-structure levels arising from the 2s22p4, 2s2p5, 2p6, 2s22p33l, 2s2p43l, 2p53l, and 2s22p34l configurations in O-like Mo XXXV. Complete and consistent atomic data, including excitation energies, lifetimes, wavelengths, and E1, E2, M1 line strengths, oscillator strengths, and transition rates among these 318 levels are provided. Comparisons are made between the present two data sets, as well as with other available experimental and theoretical values. The present data are accurate enough for identification and deblending of emission lines involving the n=3,4 levels and are also useful for modeling and diagnosing fusion plasmas. These data can be considered as a benchmark for other calculations.

Energy levels, weighted oscillator strengths, transition rates, lifetimes, hyperfine structures and isotope shifts of He-like-Sn deduced from the relativistic multiconfiguration Dirac–Hartree–Fock and second-order many-body perturbation theory calculations

We disclose relativistic multiconfiguration Dirac–Hartree–Fock (MCDHF) spectrum calculations for SnXLIX. Energy levels, weighted oscillator strengths, isotope shifts, hyperfine structure and Landé gJ factors are calculated for 127 odd- and even-parity states as well as lifetimes and transition rates between these states. To scrutinize the accuracy of our results, we have implemented parallel calculations using a Flexible Atomic Code (FAC) by introducing the Second-Order Many-Body Perturbation Theory (MBPT) method. Additionally, the Breit interaction and leading quantum electrodynamic effects (QED) are included as perturbations in extensive relativistic configuration interaction (RCI) calculations. We signal that, our calculations for SnXLIX are made for the first time and they provide to date the most accurate and complete atomic data related to this ion.

Natural orbitals for ab initio no-core shell model calculations

We explore the impact of optimizations of the single-particle basis on the convergence behavior and robustness of ab initio no-core shell model calculations. Our focus is on novel basis sets defined by the natural orbitals of a correlated one-body density matrix that is obtained in second-order many-body perturbation theory. Using a perturbatively improved density matrix as starting point informs the single-particle basis about the dominant correlation effects on the global structure of the many-body state, while keeping the computational cost for the basis optimization at a minimum. Already the comparison of the radial single-particle wavefunctions reveals the superiority of the natural-orbital basis compared to a Hartree-Fock or harmonic oscillator basis, and it highlights pathologies of the Hartree-Fock basis. We compare the model-space convergence of energies, root-mean-square radii, and selected electromagnetic observables with all three basis sets for selected p-shell nuclei using chiral interactions with explicit three-nucleon terms. In all cases the natural-orbital basis provides the fastest and most robust convergence, making it the most efficient basis for no-core shell model calculations. As an application we present no-core shell model calculations for the ground-state energies of all oxygen isotopes and assess the accuracy of the normal-ordered two-body approximation of the three-nucleon interaction in the natural-orbital basis.

Tensor-decomposition techniques for ab initio nuclear structure calculations: From chiral nuclear potentials to ground-state energies

The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input Hamiltonian on ground-state energies of closed-shell nuclei calculated via second-order many-body perturbation theory is benchmarked. With the aid of the factorized Hamiltonian, the second-order perturbative correction to ground-state energies is decomposed and the scaling properties of the underlying tensor network are discussed. The employed tensor formats are found to lead to an efficient data compression of two-body matrix elements of the nuclear Hamiltonian. In particular, the sophisticated \emph{tensor hypercontraction} (THC) scheme yields low tensor ranks with respect to both harmonic-oscillator and Hartree-Fock single-particle bases. It is found that the tensor rank depends on the two-body total angular momentum $J$ for which one performs the decomposition, which is itself directly related to the sparsity the corresponding tensor. Furthermore, including normal-ordered two-body contributions originating from three-body interactions does not compromise the efficient data compression. Ultimately, the use of factorized matrix elements authorizes controlled approximations of the exact second-order ground-state energy corrections. In particular, a small enough error is obtained from low-rank factorizations in $^{4}$He, $^{16}$O and $^{40}$Ca.

Theoretical determination of energies, wavelengths, and transition probabilities for EUV and SXR spectral lines in Rb XXXIV, Sr XXXV, Zr XXXVII, and Nb XXXVIII

Energy levels, radiative processes and lifetimes are studied among the 98 lowest levels of the 1s22snl and 1s22pnl (n = 2–4, l = 0–3) configurations of Rb XXXIV, Sr XXXV, Zr XXXVII, and Nb XXXVIII. The GRASP2K (General-purpose Relativistic Atomic Structure Package) is adopted, in which the orbital set is systematically expanded within the orbital space up to n = 9, and the Breit interaction and leading quantum electrodynamical corrections are considered. Results are provided for four types of transitions:electric dipole, electric quadrupole, magnetic dipole, and magnetic quadrupole. Similar data for the 166 lowest states belonging to the n ≤ 5 configurations are also determined using the second-order relativistic many-body perturbation theory to assess the accuracy of the calculations, taking Sr XXXV as an example. Good agreement is found between results of this work and available values from the Atomic Spectra Database of the National Institute of Standards and Technology and other theoretical reports. The accuracy for energies and radiative rates is estimated to be about 0.02% and 5%, respectively. These accurate theoretical data can aid line identifications in extreme ultraviolet (EUV) and soft X-ray (SXR) spectra. The present work should be useful for diagnostics of hot plasmas in fusion applications.