Science, Faculty of
Non UBC
Computer Science, Department of
DSpace
Fischer, Charlotte Froese
Gaigalas, Gediminas
Jönsson, Per
All energy levels of the 3dᵏ,k=1,2,...,8,9,conﬁgurations for tungsten ions,computed using the GRASP2K fully relativistic code based on the variational multiconﬁguration Dirac–Hartree–Fock method, are reported. Included in the calculations are valence correlation where all 3s,3p,3d orbitals are considered to be valence orbitals, as well as core–valence and core–core effects from the 2s,2p subshells. Results are compared with other recent theory and with levels obtained from the wavelengths of lines observed in the experimental spectra. It is shown that the core correlation effects considerably reduce the disagreement with levels linked directly to observed wavelengths, but may differ signiﬁcantly from the NIST levels, where an unknown shift of the levels could not be determined from experimental wavelengths. For low values of k, levels were in good agreement with relativistic many-body perturbation levels, but for 2 < k < 8, the present results were in better agreement with observation.
atomsArticleCore Effects on Transition Energies for 3dkConfigurations in Tungsten IonsCharlotte Froese Fischer 1,*,†, Gediminas Gaigalas 2,† and Per Jönsson 3,†1 Department of Computer Science, University of British Columbia, Vancouver V6T 1Z4, BC, Canada2 Vilnius University, Institute of Theoretical Physics and Astronomy, Saule˙tekio av. 3,LT-10222 Vilnius, Lithuania; gediminas.gaigalas@tfai.vu.lt3 Materials Science and Applied Mathematics, Malmö University, SE-205 06 Malmö, Sweden;per.jonsson@mah.se* Correspondence: cff@cs.ubc.ca† These authors contributed equally to this work.Academic Editor: Joseph ReaderReceived: 20 December 2016; Accepted: 26 January 2017; Published: 8 February 2017Abstract: All energy levels of the 3dk, k = 1,2,. . . , 8, 9, configurations for tungsten ions, computed usingthe GRASP2K fully relativistic code based on the variational multiconfiguration Dirac–Hartree–Fockmethod, are reported. Included in the calculations are valence correlation where all 3s, 3p, 3dorbitals are considered to be valence orbitals, as well as core–valence and core–core effects fromthe 2s, 2p subshells. Results are compared with other recent theory and with levels obtained fromthe wavelengths of lines observed in the experimental spectra. It is shown that the core correlationeffects considerably reduce the disagreement with levels linked directly to observed wavelengths,but may differ significantly from the NIST levels, where an unknown shift of the levels could notbe determined from experimental wavelengths. For low values of k, levels were in good agreementwith relativistic many-body perturbation levels, but for 2 < k < 8, the present results were in betteragreement with observation.Keywords: core correlation effects; energy levels; multiconfiguration Dirac-Hartree-Fock; tungsten ions1. IntroductionBecause of their importance for the ITER project [1], spectra of tungsten ions have recently receivedmuch attention over a wide range of wavelengths. Of special interest are the NIST EBIT experimentsreported by Ralchenko et al. [2], who studied tungsten ions with the ground states 3d, 3d2, . . ., 3d8, and3d9. Detailed collisional-radiative modelling was undertaken to identify the measured spectral lines.For the modelling they relied on energy levels, radiative transition probabilities, and electron-impactcollisional cross-sections obtained using the relativistic Flexible Atomic Code (FAC) [3]. They foundthat many of the strong lines arose from magnetic dipole (M1) transitions. These lines were located ina narrow range of wavelengths, mostly well isolated with line ratios that could infer plasma properties,and were sensitive to electron densities. All these features make the M1 lines useful for plasmadiagnostics. The measured observed wavelengths for M1 transitions and the FAC energy levels wereanalyzed by Kramida [4] for spectra for these ions, and form the basis for the energy levels included inthe Atomic Spectra Database (ASD) [5].Atoms 2017, 5, 7; doi:10.3390/atoms5010007 www.mdpi.com/journal/atomsAtoms 2017, 5, 7 2 of 34At the same time, highly charged ions are of special interest for theory in that both correlationand relativistic effects are interrelated, and additional quantum electrodynamic (QED) corrections areneeded for accurate results. Quinet [6] reports an extensive summary of a large variety of theoreticalenergy levels and forbidden transitions for all levels of 3dk ground configurations, and comparedtheir energy levels with the NIST energies. Included among the various methods were results thathe obtained using the GRASP code developed by Norrington [7]. Most of the correlation included inthe calculation was valence correlation restricted to the n = 3 complex. More recently, Guo et al. [8]computed energy levels, wavelengths, and transition probabilities for the same configurations fora number of ions, including tungsten. The theoretical basis for their work was the relativisticmany-body perturbation theory (RMBPT) as described in [9], but small corrections for finite nuclearsize, nuclear recoil, vacuum polarization, and self-energy correction were also included using standardprocedures such as those in GRASP2K [10]. All basis orbitals were determined from the same centralfield, and all three types of correlation—valence–valence (VV), core–valence (CV), and core–core(CC)—where the core consists of the the full 1s, 2s, 2p core were included . Statistically, their energylevels were in much better agreement with NIST values than those of Quinet [6].The purpose of the present work was to evaluate the accuracy of energy levels obtained fromvariational multconfiguration Dirac–Hartree–Fock methods as implemented in the GRASP2K code [10].Included are all three correlation types as in the RMBPT calculation—except for the 1s2 core, that willbe assumed to be inactive.2. Multiconfiguration Dirac–Hartree–Fock (MCDHF) and Configuration Interaction MethodsIn the MCDHF method [11,12], as implemented in the GRASP2K program package [10], the wavefunction Ψ(γPJMJ) for a state labeled γPJMJ , where J and MJ are the angular quantum numbers andP is the parity, is expanded in antisymmetrized and coupled configuration state functions (CSFs)Ψ(γPJMJ) =M∑j=1cjΦ(γjPJMJ). (1)The labels {γj} denote other appropriate information about the CSFs, such as orbital occupancyand coupling of the subshells. The CSFs are built from products of one-electron orbitals, having thegeneral formψnκ,m(r) =1r(Pnκ(r)χκ,m(θ, ϕ)ıQnκ(r)χ−κ,m(θ, ϕ)), (2)where χ±κ,m(θ, ϕ) are two-component spin–orbit functions. The radial functions {Pnκ(r), Qnκ(r)} arerepresented numerically on a grid.Wave functions for a number of targeted states are determined simultaneously in the extendedoptimal level (EOL) scheme. Given initial estimates of the radial functions, the energies E andexpansion coefficients c = (c1, . . . , cM)t for the targeted states are obtained as solutions to theconfiguration interaction (CI) problemHc = Ec, (3)where H is the CI matrix of dimension M×M with elementsHij = 〈Φ(γiPJMJ)|H|Φ(γjPJMJ)〉. (4)Radial functions are solutions of systems of differential equations that define a stationary state ofan energy functional for a wave function expansion.Atoms 2017, 5, 7 3 of 34Two types of expansions may be used. In the past, both usually were the same, but for largecalculations, there are advantages to relaxing this restraint. The first is the expansion that determinesthe radial functions using the RMCDHF program of the GRASP2K package. For occupied orbitals,optimized radial functions can be obtained by applying the variational principal of an energyexpression. However, when correlation orbitals are to be determined, the most effective orbitalsare those that are in the same region of space as the occupied orbitals for a given type of correlation,as has been shown in partitioned configuration interaction (PCFI) studies [13]. In this work, weconsider two regions: the 3s, 3p, 3d region for valence–valence (VV) correlation and the 2s, 2p regionfor core–valence (CV) and core–core (CC) correlations.The second is an expansion for the relativistic configuration interaction (RCI) program thatdetermines the wavefunction and its associated energy for a given Hamiltonian and based on a givenorbital basis. In the present work, the Hamiltonian for RCI was the Dirac–Coulomb Hamiltonian(DC) plus the transverse photon interaction (DCB), the vacuum polarization effects as accountedfor by the Uehling potential, and electron self-energies as calculated with the screened hydrogenicformula [12,14], namely the DCBQ Hamiltonian. The RCI program is relatively simple to parallelizeefficiently [15,16] using message passing. As a result, much larger expansions are possible for RCIcalculations than RMCDHF ones that build the orbital basis. Present calculations were done withforty-eight (48) processors for the larger cases.The computational procedure was essentially the same for all ions. The first step was to performDirac–Hartree–Fock (DHF) calculations (in the EOL approximation) for all states associated withthe 3s23p63dk configuration. This calculation determined the 1s, 2s, 2p orbitals for all subsequentcalculations. Then, sequentially, orbital sets of increasing size, with maximum principal quantumnumbers n = 3, 4, 5, were determined from expansions that defined valence–valence correlationexpansions. The latter were obtained from single- and double-excitations from the valence shellsto those of the orbital set. Since the 3d shell is unfilled, excitations such as 3s2 → 3d2 areallowed and increase the generalized occupation number for the 3d orbitals but decrease those of 3s.Variational methods determined the new orbitals introduced at each stage using the Dirac–CoulombHamiltonian. The n = 6 orbitals were targeted for core correlation effects. They were obtained fromcalculations that included CV correlation from the n = 2 shell where one orbital from the active core(either 2s or 2p) and one 3s, 3p, or 3d orbital were excited, as well as CC, where two n = 2 orbitalswere excited. At the same time, excitations from 3s, 3p subshells were limited to single excitationsfor 3s or 3p, thereby contracting the n = 6 orbitals to overlap more strongly with the n = 2 orbitalsand reducing the size of the expansions. For the configurations 3dk, k = 3, 4, 5, 6, 7, the expansionswere still exceedingly large and additional restrictions on interactions were imposed that define theenergy functional. First, what might be considered a zero-order approximation was obtained thatconsisted of the CSFs of the n = 5 VV expansion that accounted for 99.9 percent of the normalizedexpansion. All other terms of the n = 6 expansions were treated as first-order corrections. In derivingthe energy expression that determines the radial factors of the n = 6 orbitals, it was assumed that theinteraction between CSFs of the first-order corrections could be neglected. This procedure optimizesthe interaction of the n = 6 orbitals with the zero-order wave function, and has the effect of contractingthe core–valence orbitals.Each of these four orbital sets were then used in relativistic configuration interaction (RCI)calculations that included VV, CV, and CC correlation effects (excluding the 1s shell) for the threeHamiltonians—DC, DCB, and DCBQ. Again, for the cases where k = 3, 4, 5, 6, 7, the RCI calculationswere performed under the assumption that interactions between CSF of the first-order correction couldbe ignored.Table 1 summarizes the size of various expansions for the different 3dk configurations, whereasTable 2 shows how the mean radii of the n = 6 orbitals are contracted relative to the valence correlationorbitals. Note that the size increases rapidly as the number of electrons (or holes) increases from one tofive, as well as the number of J values and levels. The number of CSFs defining 99.9% of the waveAtoms 2017, 5, 7 4 of 34function composition is relatively small. Increasing this percentage to 99.99% would include somehigher order corrections. As for mean radii, it should be noted the the 3d orbitals (in non-relativisticnotation) have a mean radius closer to the core than either 3s or 3p. Listed in Table 2 are typicalvalues for the 3d5 configuration. The mean radii are also depicted graphically in Figure 1. Correlationincreases the generalized orbital occupation number of the 3d orbitals, but decreases those of all otheroccupied orbitals. The n = 4 and n = 5 orbitals have mean radii similar to those of the valence orbitals,whereas the n = 6 orbitals that are used to represent CC and CV correlation have mean radii eithersimilar to n = 2 orbitals or between n = 2 and n = 3, as in CV correlation.Table 1. Table showing the size (M) of the n = 6 relativistic configuration interaction (RCI) expansionsand the size of the zero-order space (m) for the different tungsten ions.J M m J M m3d 3d93/2 103 104 - 3/2 152 230 -5/2 130 021 - 5/2 193 718 -3d2 3d80 109 376 - 0 138 241 -1 306 873 - 1 388 664 -2 453 546 - 2 576 194 -3 526 871 - 3 672 708 -4 529 065 - 4 679 881 -3d3 3d71/2 508 854 514 1/2 584 675 7343/2 934 941 1 056 3/2 1 075 476 1 5645/2 1 217 067 1 062 5/2 1 402 693 1 5637/2 1 328 694 668 7/2 1 535 467 1 0209/2 1 281 840 737 9/2 1 486 446 1 05511/2 2216460 277 11/2 1 300 160 3533d4 3d60 433 540 925 0 462 613 1 1131 1 228 917 1 070 1 1 311 786 1 2442 1 840 515 1 688 2 1 965 798 2 0713 2 187 525 1 375 3 2 338 660 1 7384 2 261 243 1 624 4 2 420 366 1 9215 2 095 354 632 5 2 246 438 7616 1 771 535 572 6 1 902 774 6593d51/2 1 022 700 1 1193/2 1 888 910 1 6885/2 2 480 422 2 3527/2 2 741 429 1 8579/2 2 687 207 1 30611/2 2 387 571 91013/2 1 943 915 329Atoms 2017, 5, 7 5 of 34Table 2. Mean radii in a.u. of orbitals for the 3d5 configuration and their generalized occupationnumber w.nl 〈nl|r|nl〉 w1s 1.83433D-02 2.000002s 7.64525D-02 1.999922p− 6.33222D-02 1.999862p 7.10859D-02 3.999693s 1.91692D-01 1.999403p− 1.81324D-01 1.998533p 1.93743D-01 3.995773d− 1.67488D-01 2.001373d 1.71346D-01 3.002664s 2.04509D-01 1.24D-044p− 1.89988D-01 1.45D-044p 2.01490D-01 2.94D-044d− 1.71036D-01 1.73D-044d 1.70979D-01 2.82D-044 f− 1.94058D-01 5.94D-044 f 1.97398D-01 8.24D-045s 2.03090D-01 1.93D-055p− 1.95387D-01 2.23D-055p 1.97508D-01 4.08D-055d− 2.12303D-01 2.88D-055d 2.17420D-01 4.47D-055 f− 1.86560D-01 1.30D-055 f 1.85984D-01 2.01D-055g− 1.97882D-01 3.38D-055g 2.00859D-01 5.11D-056s 1.31230D-01 6.77D-066p− 1.19574D-01 8.04D-066p 1.20726D-01 1.40D-056d− 1.18546D-01 1.71D-056d 1.24725D-01 2.58D-056 f− 8.84520D-02 7.35D-066 f 9.29611D-02 1.10D-056g− 7.72823D-02 2.26D-066g 7.88248D-02 3.31D-066h− 1.62256D-01 2.42D-066h 8.04121D-02 7.65D-0700.050.10.150.20.25<nl|r|nl> in a.u.n=1n=2n=3n=4-5n=6Figure 1. Plot of the mean radii of orbitals of the 3d5 configuration in the order listed in Table 2.Atoms 2017, 5, 7 6 of 343. Results and Their ComparisonTable 3 reports some of the results for all levels of the 3dk configurations of tungsten ions fromRCI calculations for the DCBQ Hamiltonian. The classification of energy levels are presented in theLSJ- and jj-couplings. A set of three quantum numbers L, S, and seniority ν allows a one-to-oneclassification of 3dk (k = 3, 4, 5, 6, 7) energy levels in LSJ-coupling. These quantum numbers arepresented in Table 3 as (2S+1)Lν. The n = 5 results include only VV correlation, whereas n = 6 includeall three correlation effects. The next column is the energy levels as reported by NIST [5]. Includedhere are the different types of results. Energies with no square brackets are directly related to observedwavelengths—often these are in the lower portion of the spectrum. Then, there are levels that maybe linked to an observed wavelength but the shift of the energy levels relative to the ground stateis not known from experiment. These levels include a +x or +y in the table. Thus, the differencebetween two levels with the same +x is known accurately, but not the levels themselves. Taking thesefactors into account, it is clear that the inclusion of core effects has reduced the discrepancy with NISTvalues by about a factor of 1/2. In the next column, the values found by Quinet [6] are generallylike the VV results. From a general theoretical point of view, the the RMBPT results of Guo et al. [8]should be the most accurate. In the case of 3d2, RMBPT results have also been reported by Safronovaand Safronova [17], and are reported in the last column. These results are not as accurate as those ofGuo et al. In these tables, all energies are reported in the units of 1000 cm−1.Table 3. Energy level results for 3d, 3d2, . . ., 3d8, 3d9 ground configuration of tungsten ions. Shown isa unique label in LSJ- and jj-notation, the J value, the present n = 5 result for valence–valence (VV)correlation, and n = 6 result for all three types of correlation, the Atomic Spectra Database (ASD)value [5], the Quinet value [6], the Guo et al. RMBPTg value [8], and the Safronova & SafronovaRMBPTs value [17]. All energy levels are reported in 1000 cm−1.LabelJPresent WorkASD GRASP RMBPTg RMBPTsLSJ- jj-Couplings n = 5 n = 6W55+ (K-like)3d 2D 3d− (3/2,0) 3/2 0.00 0.00 0.00 0.00 0.003d 2D 3d+ (0,5/2) 5/2 625.23 626.17 626.49 624.7 626.56W54+ (Ca-like)3d2 3F 3d2− (2,0) 2 0.00 0.00 0.00 0.00 0.00 0.003d2 3P 3d2− (0,0) 0 186.42 186.23 [188] 186.9 184.86 187.113d2 3F 3d−3d+ (3/2,5/2) 3 584.05 584.75 585.48 583.5 585.80 582.853d2 3P 3d−3d+ (3/2,5/2) 2 667.45 667.96 668.49 667.6 668.00 666.213d2 3P 3d−3d+ (3/2,5/2) 1 706.35 706.75 709.46+x 707.1 706.78 705.413d2 1G 3d−3d+ (3/2,5/2) 4 695.68 696.10 [697] 697.1 696.74 693.813d2 3F 3d2+ (0,4) 4 1234.31 1235.57 [1234] 1234.1 1237.00 1231.643d2 3P 3d2+ (0,2) 2 1298.91 1300.18 [1299] 1298.6 1300.28 1296.733d2 1S 3d2+ (0,0) 0 1492.04 1493.71 [1493] 1491.0 1491.18 1491.54W53+ (Sc-like)3d3 4F3 3d3− (3/2,0) 3/2 0.00 0.00 0.00 0.00 0.003d3 4F3 3d2−3d+ (2,5/2) 5/2 528.39 529.07 530.03 528.2 530.513d3 4P3 3d2−3d+ (2,5/2) 3/2 579.43 579.99 580.86 579.9 580.863d3 2G3 3d2−3d+ (2,5/2) 7/2 610.41 610.86 [610] 611.7 611.863d3 4P3 3d2−3d+ (2,5/2) 1/2 622.72 623.22 623.95 623.6 623.533d3 2H3 3d2−3d+ (2,5/2) 9/2 609.94 610.32 [610]+x 612.0 611.623d3 2D1 3d2−3d+ (0,5/2) 5/2 811.84 812.07 812.22 814.2 811.773d3 4F3 3d−3d2+ (3/2,4) 7/2 1127.31 1128.60 [1126] 1127.1 1130.583d3 4F3 3d−3d2+ (3/2,4) 9/2 1164.81 1165.99 [1164] 1165.7 1168.15Atoms 2017, 5, 7 7 of 34Table 3. Cont.LabelJPresent WorkASD GRASP RMBPTg RMBPTsLSJ- jj-Couplings n = 5 n = 63d3 4P3 3d−3d2+ (3/2,2) 3/2 1206.41 1207.73 [1206] 1206.2 1208.343d3 2P3 3d−3d2+ (3/2,2) 1/2 1230.34 1231.58 [1230] 1230.5 1232.083d3 2D3 3d−3d2+ (3/2,4) 5/2 1243.67 1244.61 [1244] 1245.0 1245.393d3 2H3 3d−3d2+ (3/2,4) 11/2 1242.38 1243.30 1243.51+x 1245.2 1245.423d3 2F3 3d−3d2+ (3/2,2) 5/2 1314.58 1315.54 [1315] 1316.4 1315.843d3 2F3 3d−3d2+ (3/2,2) 7/2 1318.68 1319.55 [1320] 1321.5 1320.103d3 2D1 3d−3d2+ (3/2,0) 3/2 1479.96 1481.26 [1482] 1481.3 1479.893d3 2G3 3d3+ (0,9/2) 9/2 1762.93 1764.86 1762.9 1767.023d3 2P3 3d3+ (0,3/2) 3/2 1876.44 1878.32 1877.0 1878.543d3 2D1 3d3+ (0,5/2) 5/2 1958.00 1960.12 1957.9 1959.56W52+ (Ti-like)3d4 3P2 3d4− (0,0) 0 0.00 0.00 0.00 0.00 0.003d4 5D4 3d3−3d+ (3/2,5/2) 1 515.87 516.51 517.63 516.0 518.083d4 3H4 3d3−3d+ (3/2,5/2) 4 613.24 613.54 [613]+y 615.6 614.793d4 5D4 3d3−3d+ (3/2,5/2) 2 637.98 638.39 [638]+x 639.9 639.343d4 3F2 3d3−3d+ (3/2,5/2) 3 665.84 666.09 665.5621+x 668.6 667.043d4 5D4 3d2−3d2+ (2,2) 0 1101.86 1103.18 [1100] 1101.6 1104.663d4 5D4 3d2−3d2+ (2,4) 2 1106.82 1107.98 1109.69 1107.6 1110.023d4 3H4 3d2−3d2+ (2,4) 4 1125.54 1126.59 1127.27+y 1127.3 1129.113d4 5D4 3d2−3d2+ (2,4) 3 1142.02 1143.02 [1141] 1144.0 1145.193d4 3H4 3d2−3d2+ (2,4) 5 1172.24 1173.06 1173.35+y 1175.7 1175.603d4 3D4 3d2−3d2+ (2,2) 1 1213.52 1214.54 [1213] 1215.4 1215.643d4 1 I4 3d2−3d2+ (2,4) 6 1195.60 1196.31 [1195] 1200.00 1199.023d4 3F4 3d2−3d2+ (2,2) 3 1239.13 1239.92 [1240] 1242.5 1240.993d4 3G4 3d2−3d2+ (2,2) 4 1242.41 1243.17 [1243] 1245.7 1244.473d4 3F4 3d2−3d2+ (2,2) 2 1257.75 1258.62 [1258] 1260.6 1259.433d4 3F2 3d2−3d2+ (2,0) 2 1359.28 1360.44 [1361] 1361.1 1360.353d4 3F2 3d2−3d2+ (0,4) 4 1403.66 1404.22 1403.95+x 1408.6 1405.113d4 1D2 3d2−3d2+ (0,2) 2 1505.68 1506.35 [1509] 1510.3 1505.823d4 3P4 3d2−3d2+ (0,0) 0 1633.13 1634.15 [1637] 1636.5 1632.743d4 5D4 3d−3d3+ (3/2,9/2) 4 1714.26 1715.10 1715.3 1718.503d4 3F4 3d−3d3+ (3/2,9/2) 3 1725.24 1727.04 1725.9 1729.153d4 3D4 3d−3d3+ (3/2,3/2) 1 1766.70 1768.58 1767.1 1769.703d4 3G4 3d−3d3+ (3/2,9/2) 5 1773.76 1775.28 1776.4 1777.843d4 3H4 3d−3d3+ (3/2,9/2) 6 1778.76 1780.21 1782.4 1783.283d4 3F4 3d−3d3+ (3/2,3/2) 2 1841.18 1842.98 1842.9 1843.903d4 3D4 3d−3d3+ (3/2,3/2) 3 1857.70 1859.24 1860.2 1860.183d4 1S4 3d−3d3+ (3/2,3/2) 0 1922.88 1924.06 1925.8 1923.373d4 3P2 3d−3d3+ (3/2,5/2) 1 1983.87 1985.44 1987.2 1985.443d4 3F2 3d−3d3+ (3/2,5/2) 3 1979.96 1981.50 1983.6 1981.913d4 1G2 3d−3d3+ (3/2,5/2) 4 1985.00 1986.57 1988.7 1987.023d4 1D4 3d−3d3+ (3/2,5/2) 2 2018.63 2020.04 2022.8 2019.683d4 3F2 3d4+ (0,4) 4 2376.23 2378.86 2376.1 2380.513d4 1D2 3d4+ (0,2) 2 2460.51 2463.08 2461.4 2463.563d4 3P2 3d4+ (0,0) 0 2662.74 2665.52 2663.5 2663.60W51+ (V-like)3d5 4P3 3d4−3d+ (0,5/2) 5/2 0.00 0.00 0.00 0.00 0.003d5 6S5 3d3−3d2+ (3/2,4) 5/2 469.71 470.75 71.63 469.1 472.03Atoms 2017, 5, 7 8 of 34Table 3. Cont.LabelJPresent WorkASD GRASP RMBPTg RMBPTsLSJ- jj-Couplings n = 5 n = 63d5 4G5 3d3−3d2+ (3/2,4) 7/2 564.98 565.80 66.25 566.2 566.413d5 4D5 3d3−3d2+ (3/2,2) 3/2 579.61 580.50 80.89 579.8 580.443d5 2H3 3d3−3d2+ (3/2,4) 11/2 576.03 576.78 [577]+x 578.5 577.803d5 2G5 3d3−3d2+ (3/2,4) 9/2 620.92 621.61 [623] 623.7 622.203d5 4D5 3d3−3d2+ (3/2,2) 5/2 650.71 651.45 [652] 652.8 651.273d5 4P3 3d3−3d2+ (3/2,2) 1/2 679.60 680.38 [681] 680.8 679.833d5 2F5 3d3−3d2+ (3/2,2) 7/2 687.73 688.28 88.18 690.9 687.903d5 2D1 3d3−3d2+ (3/2,0) 3/2 823.99 824.95 [827] 825.5 823.603d5 6S5 3d2−3d3+ (2,9/2) 5/2 1025.98 1027.97 [1015] 1024.9 1029.113d5 4D5 3d2−3d3+ (2,9/2) 7/2 1096.84 1098.61 [1097] 1097.9 1099.593d5 4G5 3d2−3d3+ (2,9/2) 11/2 1100.79 1102.51 1103.43 1103.0 1104.043d5 4G5 3d2−3d3+ (2,9/2) 9/2 1116.98 1118.70 [1118] 1118.8 1119.703d5 4D5 3d2−3d3+ (2,3/2) 1/2 1155.66 1157.40 1156.6 1157.553d5 4P3 3d2−3d3+ (2,5/2) 3/2 1164.73 1166.79 1163.6 1166.643d5 2 I5 3d2−3d3+ (2,9/2) 13/2 1142.15 1143.78 [1143] 1145.6 1145.2723d5 2F5 3d2−3d3+ (2,3/2) 5/2 1174.89 1176.61 1176.3 1176.633d5 2H3 3d2−3d3+ (2,5/2) 9/2 1217.34 1219.21 1218.4 1219.393d5 2G5 3d2−3d3+ (2,3/2) 7/2 1237.88 1239.44 1240.9 1239.133d5 4F3 3d2−3d3+ (2,5/2) 5/2 1254.59 1256.46 1255.8 1256.023d5 2D5 3d2−3d3+ (2,3/2) 3/2 1259.49 1260.94 1262.1 1259.773d5 4P3 3d2−3d3+ (2,5/2) 1/2 1308.19 1309.93 1309.8 1308.633d5 2G3 3d2−3d3+ (2,5/2) 7/2 1307.82 1309.62 1309.9 1308.843d5 2G3 3d2−3d3+ (0,9/2) 9/2 1379.66 1381.18 1383.8 1380.573d5 2P3 3d2−3d3+ (0,3/2) 3/2 1504.94 1506.22 1510.4 1504.143d5 2D1 3d2−3d3+ (0,5/2) 5/2 1533.17 1534.71 1537.4 1532.743d5 4P3 3d−3d4+ (3/2,4) 5/2 1660.92 1663.98 1658.7 1664.073d5 4F3 3d−3d4+ (3/2,4) 7/2 1733.68 1736.62 1733.1 1736.603d5 4D5 3d−3d4+ (3/2,2) 3/2 1759.25 1762.30 1758.1 1761.853d5 2H3 3d−3d4+ (3/2,4) 11/2 1746.45 1749.34 1747.2 1749.913d5 2G5 3d−3d4+ (3/2,4) 9/2 1806.21 1808.95 1807.7 1808.863d5 2D3 3d−3d4+ (3/2,2) 5/2 1843.82 1846.49 1844.6 1845.213d5 2G3 3d−3d4+ (3/2,2) 7/2 1871.70 1874.38 1874.1 1873.743d5 2P3 3d−3d4+ (3/2,2) 1/2 1933.91 1936.39 1937.0 1934.463d5 2D1 3d−3d4+ (3/2,0) 3/2 2063.04 2065.78 2065.5 2062.963d5 2D1 3d5+ (0,5/2) 5/2 2362.48 2366.70 2359.4 2365.33W50+ (Cr-like)3d6 5D4 3d4−3d2+ (0,4) 4 0.00 0.00 0.00 0.00 0.003d6 3D4 3d4−3d2+ (0,2) 2 62.74 62.71 62.38 62.6 61.563d6 3P2 3d4−3d2+ (0,0) 0 207.31 207.66 [208]+x 205.9 205.743d6 5D4 3d3−3d3+ (3/2,9/2) 3 506.28 507.09 508.03 505.2 507.803d6 5D4 3d3−3d3+ (3/2,9/2) 4 518.36 519.02 519.78 518.0 519.833d6 5D4 3d3−3d3+ (3/2,3/2) 1 545.62 546.54 [545] 543.8 546.533d6 3G4 3d3−3d3+ (3/2,9/2) 5 582.70 583.09 583.67 584.2 583.743d6 3H4 3d3−3d3+ (3/2,9/2) 6 582.40 582.70 [583] 584.3 583.613d6 3F4 3d3−3d3+ (3/2,3/2) 2 637.99 638.51 [639] 638.1 637.593d6 3D4 3d3−3d3+ (3/2,3/2) 3 649.76 650.29 650.91 650.6 649.823d6 3P4 3d3−3d3+ (3/2,3/2) 0 725.01 725.35 [729] 727.9 723.983d6 3P2 3d3−3d3+ (3/2,5/2) 1 767.07 767.54 768.98+x 769.3 766.38Atoms 2017, 5, 7 9 of 34Table 3. Cont.LabelJPresent WorkASD GRASP RMBPTg RMBPTsLSJ- jj-Couplings n = 5 n = 63d6 3D4 3d3−3d3+ (3/2,5/2) 2 766.25 766.84 766.95 767.6 765.693d6 1G2 3d3−3d3+ (3/2,5/2) 4 760.65 761.12 761.21 762.5 760.283d6 3F2 3d3−3d3+ (3/2,5/2) 3 782.18 782.54 782.53 785.0 781.263d6 5D4 3d2−3d4+ (2,4) 2 1058.57 1060.19 1055.6 1060.643d6 5D4 3d2−3d4+ (2,2) 0 1083.07 1084.88 1079.6 1085.163d6 3H4 3d2−3d4+ (2,4) 4 1108.16 1109.55 1106.9 1110.133d6 5D4 3d2−3d4+ (2,4) 3 1135.23 1136.57 1134.6 1136.843d6 3H4 3d2−3d4+ (2,4) 5 1142.11 1143.32 1142.4 1144.113d6 1 I4 3d2−3d4+ (2,4) 6 1169.18 1170.23 1170.5 1171.163d6 3F4 3d2−3d4+ (2,2) 3 1196.79 1198.08 1197.0 1198.013d6 3D4 3d2−3d4+ (2,2) 1 1217.26 1218.50 1217.8 1217.793d6 1G4 3d2−3d4+ (2,2) 4 1232.82 1233.95 1234.1 1233.733d6 3F4 3d2−3d4+ (2,2) 2 1243.66 1244.79 1244.0 1243.753d6 3F2 3d2−3d4+ (2,0) 2 1336.95 1338.38 1336.9 1336.973d6 3F2 3d2−3d4+ (0,4) 4 1374.79 1375.77 1376.9 1375.033d6 1D2 3d2−3d4+ (0,2) 2 1518.97 1519.86 1523.2 1517.583d6 1S0 3d2−3d4+ (0,0) 0 1660.58 1661.58 1664.9 1658.283d6 3P2 3d−3d5+ (3/2,5/2) 1 1663.26 1665.83 1657.7 1665.573d6 1G2 3d−3d5+ (3/2,5/2) 4 1764.33 1766.52 1762.0 1766.293d6 3P2 3d−3d5+ (3/2,5/2) 2 1813.76 1815.87 1811.7 1814.753d6 3F2 3d−3d5+ (3/2,5/2) 3 1831.23 1833.30 1830.3 1832.643d6 3P2 3d6+ (0,0) 0 2321.86 2325.36 2314.1 2323.82W49+ (Mn-like)3d7 4F3 3d4−3d3+ (0,9/2) 9/2 0.00 0.00 0.00 0.00 0.003d7 2P3 3d4−3d3+ (0,3/2) 3/2 101.71 101.64 [103]+x 102.1 100.133d7 2D1 3d4−3d3+ (0,5/2) 5/2 158.95 159.10 158.75 158.7 157.623d7 4F3 3d3−3d4+ (3/2,4) 7/2 527.98 528.88 529.66 526.1 529.083d7 4F3 3d3−3d4+ (3/2,4) 9/2 583.50 584.16 584.59 583.1 584.183d7 4P3 3d3−3d4+ (3/2,2) 3/2 607.96 608.87 [608] 606.6 608.303d7 4P3 3d3−3d4+ (3/2,4) 5/2 624.97 625.72 628.02+x 624.9 625.413d7 4P3 3d3−3d4+ (3/2,2) 1/2 635.89 636.62 638.62+x 635.1 635.453d7 2H3 3d3−3d4+ (3/2,4) 11/2 650.16 650.58 650.70 651.8 650.553d7 2F3 3d3−3d4+ (3/2,2) 7/2 705.20 705.71 705.92 706.4 704.863d7 2F3 3d3−3d4+ (3/2,2) 5/2 742.86 743.30 [747] 745.4 742.073d7 2D1 3d3−3d4+ (3/2,0) 3/2 888.41 889.03 [893] 890.8 886.673d7 4F3 3d2−3d5+ (2,5/2) 5/2 1115.46 1117.19 1112.0 1116.933d7 4P3 3d2−3d5+ (2,5/2) 3/2 1147.62 1149.25 1145.1 1148.653d7 2P3 3d2−3d5+ (2,5/2) 1/2 1192.13 1193.65 1189.9 1192.533d7 2H3 3d2−3d5+ (2,5/2) 9/2 1185.68 1187.07 1184.9 1186.893d7 2F3 3d2−3d5+ (2,5/2) 7/2 1210.79 1212.16 1210.3 1211.443d7 2D1 3d2−3d5+ (0,5/2) 5/2 1410.07 1411.30 1411.0 1409.493d7 2D1 3d−3d6+ (3/2,0) 3/2 1751.87 1754.44 1746.4 1753.15W48+ (Fe-like)3d8 3F 3d4−3d4+ (0,4) 4 0.00 0.00 0.00 0.00 0.003d8 1D 3d4−3d4+ (0,2) 2 72.15 72.12 [73.4]+x 72.8 71.263d8 3P 3d4−3d4+ (0,0) 0 229.94 230.10 [233] 230.7 228.173d8 3F 3d3−3d5+ (3/2,5/2) 3 525.18 526.07 526.65 523.2 526.133d8 3P 3d3−3d5+ (3/2,5/2) 2 600.38 601.15 603.12+x 599.7 600.69Atoms 2017, 5, 7 10 of 34Table 3. Cont.LabelJPresent WorkASD GRASP RMBPTg RMBPTsLSJ- jj-Couplings n = 5 n = 63d8 3P 3d3−3d5+ (3/2,5/2) 1 642.01 642.71 644.76+x 642.7 642.143d8 1G 3d3−3d5+ (3/2,5/2) 4 643.89 644.43 644.70 645.0 644.033d8 3F 3d2−3d6+ (2,2) 2 1106.91 1108.59 [1106] 1103.6 1108.173d8 1S 3d2−3d6+ (0,0) 0 1304.16 1305.75 [1306] 1301.7 1304.07W47+ (Co-like)3d9 2D 3d4−3d5+ (0,5/2) 5/2 0.00 0.00 0.00 0.00 0.003d9 2D 3d3−3d6+ (3/2,0) 3/2 537.21 538.04 538.59 535.6 538.05The uncertainties of NIST energy levels not based on observed wavelengths are estimated asbeing less than 5000 cm−1, or 5.00 in our table. In order to better understand the importance of variouseffects in Table 4, we report the NIST energy levels that are based on observation and differencesof various theories for only those levels where NIST values are accurate, although there may be anunknown shift.Table 4. Difference from NIST energy levels derived from observation. Shown is the LS label, the Jvalue, the present n = 5 result for VV correlation, and n = 6 result for all three types of correlation, theASD value [5], the Quinet value [6], the Guo et al. RMBPTg value [8], and the Safranova & SafronovaRMBPTs value [17]. All energy levels are reported in 1000 cm−1.Label JPresent WorkASD GRASP RMBPTg RMBPTsn = 5 n = 6W55+ (K-like)3d 2D 3/2 0.00 0.00 0.00 0.00 0.003d 2D 5/2 1.25 0.32 626.49 2.49 −0.07W54+ (Ca-like)3d2 3F 2 0.00 0.00 0.00 0.00 0.00 0.003d2 3F 3 1.43 0.73 585.48 1.98 −0.32 2.633d2 3P 2 1.04 0.53 668.49 0.89 0.49 2.283d2 3P 1 3.11 2.71 709.46+x 2.36 2.68 4.05W53+ (Sc-like)3d3 4F3 3/2 0.00 0.00 0.00 0.00 0.003d3 4F3 5/2 1.64 0.96 530.03 1.83 −0.483d3 4P3 3/2 1.43 0.87 580.86 0.96 0.03d3 4P3 1/2 1.23 0.73 623.95 0.35 0.423d3 2D1 5/2 0.38 0.15 812.22 −1.98 0.453d3 2H3 11/2 1.13 0.21 1234.51+x −1.69 0.45W52+ (Ti-like)3d4 3P2 0 0.00 0.00 0.00 0.00 0.003d4 5D4 1 1.76 1.12 517.63 1.63 −0.453d4 3F2 3 −0.28 −0.53 665.5621+x −3.04 −1.483d4 5D4 2 2.87 1.71 1109.69 2.09 −0.333d4 3H4 4 1.73 0.68 1127.27+y −0.03 −1.843d4 3H4 5 1.11 0.29 1173.35+y −2.35 −22.253d4 3F2 4 0.29 −0.27 1403.95+x −4.65 −1.16Atoms 2017, 5, 7 11 of 34Table 4. Cont.Label JPresent WorkASD GRASP RMBPTg RMBPTsn = 5 n = 6W51+ (V-like)3d5 4P3 5/2 0.00 0.00 0.00 0.00 0.003d5 6S5 5/2 1.92 0.88 471.63 2.53 −0.403d5 4G5 7/2 1.27 0.45 566.25 0.05 −0.163d5 4D5 3/2 1.28 0.39 580.89 1.09 0.453d5 2F5 7/2 0.45 −0.10 688.18 −2.72 0.283d5 4G5 11/2 2.64 0.92 1103.43 0.43 −0.61W50+ (Cr-like)3d6 5D4 4 0.00 0.00 0.00 0.00 0.003d6 3D4 2 −0.36 −0.29 62.38 −0.22 0.823d6 5D4 3 1.75 1.04 508.03 2.83 0.233d6 5D4 4 1.41 0.74 519.78 1.78 0.053d6 3G4 5 0.97 0.44 583.67 −0.53 −0.073d6 3D4 3 1.15 0.56 650.91 0.31 1.093d6 3P2 1 1.91 1.44 768.98+x −0.32 2.603d6 3D4 2 0.70 0.11 766.95 −0.65 1.263d6 1G2 4 0.56 −0.04 761.21 −1.29 0.933d6 3F2 3 0.35 −0.08 782.53 −2.47 1.27W49+ (Mn-like)3d7 4F3 9/2 0.00 0.00 0.00 0.00 0.003d7 2D1 5/2 −0.20 −0.35 158.75 0.05 1.133d7 4F3 7/2 1.68 0.78 529.66 3.56 0.583d7 4F3 9/2 1.09 0.43 584.59 1.49 0.413d7 4P3 5/2 3.05 2.30 628.02+x 3.12 2.613d7 4P3 1/2 2.73 2.00 638.62+x 3.52 3.173d7 2H3 11/2 0.54 0.12 650.70 −1.10 0.153d7 2F3 7/2 0.72 0.21 705.92 −0.48 1.06W48+ (Fe-like)3d8 3F 4 0.00 0.00 0.00 0.003d8 3F 3 1.47 0.58 526.65 3.45 0.523d8 3P 2 2.74 1.97 603.12+x 3.42 2.433d8 3P 1 2.73 2.05 644.76+x 2.06 2.62W47+ (Co-like)3d9 2D 5/2 0.00 0.00 0.00 0.00 0.003d9 2D 3/2 1.38 0.55 538.59 2.99 0.54Table 4 shows clearly that the uncertainties of the present n = 6 results are smaller by about afactor of a half when no shifts are indicated in the NIST value. For these levels, the n = 6 resultsstatistically differ less than the Quinet values that are similar to the less accurate n = 5 values. Themost accurate results for 3d and 3d9 are the RMCDHFg results, although for 3d9, the n = 6 are almostof the same accuracy. RMBPTg is the more accurate for 3d2, with n = 6 almost the same. For 3d8,the two lower levels, RMBPTg is the more accurate, whereas n = 6 is the more accurate for the twoupper levels. A similar pattern seems to hold for other spectra. An interesting case is 3d7 4P J = 5/2and 1/2, where both levels have an unknown shift. An exact theoretical value and an exact NISTvalue (except for the shift) would have the same difference for the two levels. In the present case, theAtoms 2017, 5, 7 12 of 34n = 6 differences are more similar than the RMCDHFg differences. In fact, from this table, we canconclude that any NIST value for which the theoretical difference from NIST for both methods is morethan 1.00 has a noticeable error. Thus, for example, the 3P1 level of 3d8 with an energy levelof 644.70 Kcm−1 suggests that the NIST values is not accurate to two decimal places.The errors in different theoretical results are shown in Figure 2. Note the similarity in accuracy ofthe present n = 6 results and values reported by Guo et al. [8].0 200 400 600 800 1000 1200 1400-4-2024Energy ASD (Kcm-1)Energy - Energy ASD (Kcm-1)n=5n=6QuinetGuoFigure 2. Plot comparing the accuracy of different theoretical methods.The accuracy of theoretical energy levels are best evaluated by comparing theoretical wavelengthswith wavelengths of observed lines in the spectrum. In Table 5, all wavelengths for M1 transitionsbetween the 3dk levels for the present n = 5, 6 results are compared with experimental results and othertheory, when available. This table clearly shows the improvement in accuracy of n = 6 calculations overn = 5, as well as the GRASP results reported by Quinet [6], and in many cases the very close agreementwith Guo et al. [8]. Two exceptions are the 3d7 4F3 − 3d7 2F3 (J = 9/2 to J = 7/2) transition, for whichthe observed wavelength is 14.166(3) nm, the present n = 6 is 14.170 nm, and the Guo et al. valueis 14.187 nm. Similarly, the 3d8 3F− 3d8 1G (J = 4 to J = 4) transition has an observed wavelengthof 15.511(3) nm, whereas the present value is 15.518 nm and the Guo et al. value is 15.463 nm.Table 5. Wavelengths from theory for observed M1 transitions compared with observed wavelengths(in nm). Included are some long wavelengths for transitions between close-lying levels.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])W55+ (K-like)3d 2D 3/2 3d 2D 5/2 15.994 15.970 15.962(3) 16.008 15.960 16.035W54+ (Ca-like)3d2 3F 2 3d2 3F 3 17.122 17.101 17.080(3) 17.138 17.071 17.2183d2 3F 2 3d2 3P 2 14.982 14.971 14.959(3) 14.980 14.970 14.9243d2 3F 2 3d2 3P 1 14.157 14.1493d2 3F 2 3d2 3P 2 7.699 7.6913d2 3P 0 3d2 3P 1 19.233 19.211 19.177(3) 19.222 19.160 19.4223d2 3F 3 3d2 3P 2 119.908 120.1683d2 3F 3 3d2 1G 4 89.580 89.8053d2 3F 3 3d2 3F 4 15.378 15.3653d2 3F 3 3d2 3P 2 13.989 13.977Atoms 2017, 5, 7 13 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d2 3P 2 3d2 3P 1 257.054 257.7933d2 3P 2 3d2 3P 2 15.836 15.8173d2 3P 1 3d2 3P 2 16.876 16.8513d2 3P 1 3d2 1S 0 12.728 12.7073d2 1G 4 3d2 3F 4 18.566 18.537W53+ (Sc-like)3d3 4F3 3/2 3d3 4F3 5/2 18.925 18.901 18.867(3) 18.933 18.850 19.1203d3 4F3 3/2 3d3 4P3 3/2 17.258 17.242 17.216(3) 17.243 17.216 17.3153d3 4F3 3/2 3d3 4P3 1/2 16.059 16.046 16.027(3) 16.035 16.038 16.0383d3 4F3 3/2 3d3 2D1 5/2 12.318 12.314 12.312(3) 12.282 12.319 12.2253d3 4F3 3/2 3d3 4P3 3/2 8.289 8.2803d3 4F3 3/2 3d3 2P3 1/2 8.128 8.1203d3 4F3 3/2 3d3 2D3 5/2 8.041 8.0353d3 4F3 3/2 3d3 2F3 5/2 7.607 7.6013d3 4F3 3/2 3d3 2D1 3/2 6.757 6.7513d3 4F3 3/2 3d3 2P3 3/2 5.329 5.3243d3 4F3 3/2 3d3 2D1 5/2 5.107 5.1023d3 4F3 5/2 3d3 4P3 3/2 195.953 196.3903d3 4F3 5/2 3d3 2G3 7/2 121.923 122.2643d3 4F3 5/2 3d3 2D1 5/2 35.279 35.3363d3 4F3 5/2 3d3 4F3 7/2 16.697 16.6803d3 4F3 5/2 3d3 4P3 3/2 14.749 14.7353d3 4F3 5/2 3d3 2D3 5/2 13.981 13.9753d3 4F3 5/2 3d3 2F3 5/2 12.720 12.7153d3 4F3 5/2 3d3 2F3 7/2 12.654 12.6513d3 4F3 5/2 3d3 2D1 3/2 10.509 10.5023d3 4F3 5/2 3d3 2P3 3/2 7.418 7.4123d3 4F3 5/2 3d3 2D1 5/2 6.995 6.9883d3 4P3 3/2 3d3 4P3 1/2 230.965 231.3043d3 4P3 3/2 3d3 2D1 5/2 43.026 43.0893d3 4P3 3/2 3d3 4P3 3/2 15.949 15.9303d3 4P3 3/2 3d3 2P3 1/2 15.364 15.3473d3 4P3 3/2 3d3 2D3 5/2 15.055 15.0463d3 4P3 3/2 3d3 2F3 5/2 13.603 13.5953d3 4P3 3/2 3d3 2D1 3/2 11.105 11.0953d3 4P3 3/2 3d3 2P3 3/2 7.710 7.7023d3 4P3 3/2 3d3 2D1 5/2 7.254 7.2463d3 2H3 9/2 3d3 2G3 7/2 21322.871 18591.1623d3 2H3 9/2 3d3 4F3 7/2 19.329 19.2953d3 2H3 9/2 3d3 4F3 9/2 18.022 17.9963d3 2H3 9/2 3d3 2H3 11/2 15.812 15.798 15.785(3) 15.792 15.778 15.8763d3 2H3 9/2 3d3 2F3 7/2 14.110 14.1003d3 2H3 9/2 3d3 2G3 9/2 8.673 8.6613d3 2G3 7/2 3d3 2D1 5/2 49.645 49.7003d3 2G3 7/2 3d3 4F3 7/2 19.346 19.3153d3 2G3 7/2 3d3 4F3 9/2 18.037 18.0143d3 2G3 7/2 3d3 2D3 5/2 15.791 15.7793d3 2G3 7/2 3d3 2F3 5/2 14.201 14.191Atoms 2017, 5, 7 14 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d3 2G3 7/2 3d3 2F3 7/2 14.119 14.1103d3 2G3 7/2 3d3 2G3 9/2 8.677 8.6653d3 2G3 7/2 3d3 2D1 5/2 7.421 7.4113d3 4P3 1/2 3d3 4P3 3/2 17.132 17.1083d3 4P3 1/2 3d3 2P3 1/2 16.459 16.4383d3 4P3 1/2 3d3 2D1 3/2 11.665 11.6543d3 4P3 1/2 3d3 2P3 3/2 7.976 7.9683d3 2D1 5/2 3d3 4F3 7/2 31.700 31.5923d3 2D1 5/2 3d3 4P3 3/2 25.344 25.2743d3 2D1 5/2 3d3 2D3 5/2 23.157 23.1193d3 2D1 5/2 3d3 2F3 5/2 19.891 19.8623d3 2D1 5/2 3d3 2F3 7/2 19.730 19.7053d3 2D1 5/2 3d3 2D1 3/2 14.968 14.9433d3 2D1 5/2 3d3 2P3 3/2 9.393 9.3793d3 2D1 5/2 3d3 2D1 5/2 8.725 8.7103d3 4F3 7/2 3d3 4F3 9/2 266.613 267.4483d3 4F3 7/2 3d3 2D3 5/2 85.937 86.1973d3 4F3 7/2 3d3 2F3 5/2 53.397 53.4923d3 4F3 7/2 3d3 2F3 7/2 52.253 52.3703d3 4F3 7/2 3d3 2G3 9/2 15.733 15.7173d3 4F3 7/2 3d3 2D1 5/2 12.038 12.0263d3 4F3 9/2 3d3 2H3 11/2 128.917 129.3453d3 4F3 9/2 3d3 2F3 7/2 64.991 65.1223d3 4F3 9/2 3d3 2G3 9/2 16.719 16.6983d3 4P3 3/2 3d3 2P3 1/2 418.463 419.2263d3 4P3 3/2 3d3 2D3 5/2 268.399 271.1103d3 4P3 3/2 3d3 2F3 5/2 92.445 92.7513d3 4P3 3/2 3d3 2D1 3/2 36.557 36.5593d3 4P3 3/2 3d3 2P3 3/2 14.925 14.9123d3 4P3 3/2 3d3 2D1 5/2 13.305 13.2913d3 2P3 1/2 3d3 2D1 3/2 40.056 40.0513d3 2P3 1/2 3d3 2P3 3/2 15.477 15.4623d3 2H3 11/2 3d3 2G3 9/2 19.211 19.1733d3 2D3 5/2 3d3 2F3 5/2 141.016 140.9843d3 2D3 5/2 3d3 2F3 7/2 133.312 133.4503d3 2D3 5/2 3d3 2D1 3/2 42.321 42.2573d3 2D3 5/2 3d3 2P3 3/2 15.804 15.7803d3 2D3 5/2 3d3 2D1 5/2 13.999 13.9763d3 2F3 5/2 3d3 2F3 7/2 2440.155 2497.0853d3 2F3 5/2 3d3 2D1 3/2 60.469 60.3433d3 2F3 5/2 3d3 2P3 3/2 17.798 17.7693d3 2F3 5/2 3d3 2D1 5/2 15.542 15.5143d3 2F3 7/2 3d3 2G3 9/2 22.510 22.4563d3 2F3 7/2 3d3 2D1 5/2 15.642 15.6113d3 2D1 3/2 3d3 2P3 3/2 25.222 25.1853d3 2D1 3/2 3d3 2D1 5/2 20.919 20.8833d3 2P3 3/2 3d3 2D1 5/2 122.606 122.246Atoms 2017, 5, 7 15 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])W52+ (Ti-like)3d4 3P2 0 3d4 5D4 1 19.385 19.361 19.319(3) 19.379 19.302 19.6053d4 3P2 0 3d4 3D4 1 8.241 8.2343d4 3P2 0 3d4 3D4 1 5.660 5.6543d4 3P2 0 3d4 3P2 1 5.041 5.0373d4 5D4 1 3d4 5D4 2 81.888 82.0533d4 5D4 1 3d4 5D4 0 17.065 17.0453d4 5D4 1 3d4 5D4 2 16.922 16.907 16.890(3) 16.903 16.894 16.9583d4 5D4 1 3d4 3D4 1 14.334 14.3263d4 5D4 1 3d4 3F4 2 13.479 13.4753d4 5D4 1 3d4 3F2 2 11.857 11.8493d4 5D4 1 3d4 1D2 2 10.103 10.1033d4 5D4 1 3d4 3P4 0 8.950 8.9473d4 5D4 1 3d4 3D4 1 7.995 7.9873d4 5D4 1 3d4 3F4 2 7.545 7.5393d4 5D4 1 3d4 1S4 0 7.107 7.1053d4 5D4 1 3d4 3P2 1 6.812 6.8083d4 5D4 1 3d4 1D4 2 6.654 6.6513d4 5D4 1 3d4 1D2 2 5.142 5.1373d4 5D4 1 3d4 3P2 0 4.658 4.6533d4 3H4 4 3d4 3F2 3 190.114 190.2623d4 3H4 4 3d4 3H4 4 19.520 19.491 19.445(3) 19.543 19.443 19.6963d4 3H4 4 3d4 5D4 3 18.912 18.8863d4 3H4 4 3d4 3H4 5 17.889 17.872 17.846(3) 17.855 17.831 18.0653d4 3H4 4 3d4 3F4 3 15.977 15.9653d4 3H4 4 3d4 3G4 4 15.894 15.8823d4 3H4 4 3d4 3F2 4 12.652 12.6473d4 3H4 4 3d4 5D4 4 9.083 9.0713d4 3H4 4 3d4 3F4 3 8.993 8.9813d4 3H4 4 3d4 3G4 5 8.617 8.6083d4 3H4 4 3d4 3D4 3 8.036 8.0283d4 3H4 4 3d4 3F2 3 7.317 7.3103d4 3H4 4 3d4 1G2 4 7.290 7.2833d4 3H4 4 3d4 3F2 4 5.672 5.6653d4 5D4 2 3d4 3F2 3 358.990 360.9073d4 5D4 2 3d4 5D4 2 21.329 21.2953d4 5D4 2 3d4 5D4 3 19.840 19.8163d4 5D4 2 3d4 3D4 1 17.375 17.3563d4 5D4 2 3d4 3F4 3 16.635 16.6243d4 5D4 2 3d4 3F4 2 16.135 16.1233d4 5D4 2 3d4 3F2 2 13.864 13.8493d4 5D4 2 3d4 1D2 2 11.525 11.5213d4 5D4 2 3d4 3F4 3 9.197 9.1863d4 5D4 2 3d4 3D4 1 8.860 8.8483d4 5D4 2 3d4 3F4 2 8.311 8.3023d4 5D4 2 3d4 3D4 3 8.199 8.1913d4 5D4 2 3d4 3F2 3 7.452 7.4453d4 5D4 2 3d4 3P2 1 7.430 7.4243d4 5D4 2 3d4 1D4 2 7.243 7.238Atoms 2017, 5, 7 16 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d4 5D4 2 3d4 1D2 2 5.487 5.4803d4 3F2 3 3d4 5D4 2 22.677 22.6303d4 3F2 3 3d4 3H4 4 21.753 21.7163d4 3F2 3 3d4 5D4 3 21.001 20.9683d4 3F2 3 3d4 3F4 3 17.443 17.4273d4 3F2 3 3d4 3G4 4 17.344 17.3293d4 3F2 3 3d4 3F4 2 16.895 16.8773d4 3F2 3 3d4 3F2 2 14.421 14.4023d4 3F2 3 3d4 3F2 4 13.554 13.548 13.543(3) 13.513 13.549 13.4953d4 3F2 3 3d4 1D2 2 11.907 11.9013d4 3F2 3 3d4 5D4 4 9.538 9.5253d4 3F2 3 3d4 3F4 3 9.439 9.4263d4 3F2 3 3d4 3F4 2 8.508 8.4973d4 3F2 3 3d4 3D4 3 8.390 8.3813d4 3F2 3 3d4 3F2 3 7.610 7.6023d4 3F2 3 3d4 1G2 4 7.581 7.5733d4 3F2 3 3d4 1D4 2 7.392 7.3863d4 3F2 3 3d4 3F2 4 5.847 5.8393d4 3F2 3 3d4 1D2 2 5.572 5.5653d4 5D4 0 3d4 3D4 1 89.555 89.7983d4 5D4 0 3d4 3D4 1 15.041 15.0283d4 5D4 0 3d4 3P2 1 11.338 11.3343d4 5D4 2 3d4 5D4 3 284.116 285.3463d4 5D4 2 3d4 3D4 1 93.723 93.8403d4 5D4 2 3d4 3F4 3 75.583 75.7913d4 5D4 2 3d4 3F4 2 66.257 66.3823d4 5D4 2 3d4 3F2 2 39.611 39.6103d4 5D4 2 3d4 1D2 2 25.072 25.1023d4 5D4 2 3d4 3F4 3 16.170 16.1533d4 5D4 2 3d4 3D4 1 15.154 15.1383d4 5D4 2 3d4 3F4 2 13.617 13.6053d4 5D4 2 3d4 3D4 3 13.318 13.3113d4 5D4 2 3d4 3F2 3 11.453 11.4483d4 5D4 2 3d4 3P2 1 11.402 11.3963d4 5D4 2 3d4 1D4 2 10.967 10.9643d4 5D4 2 3d4 1D2 2 7.387 7.3803d4 3H4 4 3d4 5D4 3 606.876 608.7613d4 3H4 4 3d4 3H4 5 214.114 215.2063d4 3H4 4 3d4 3F4 3 88.039 88.2433d4 3H4 4 3d4 3G4 4 85.561 85.7813d4 3H4 4 3d4 3F2 4 35.956 36.0203d4 3H4 4 3d4 5D4 4 16.986 16.9663d4 3H4 4 3d4 3F4 3 16.675 16.6543d4 3H4 4 3d4 3G4 5 15.427 15.4163d4 3H4 4 3d4 3D4 3 13.658 13.6493d4 3H4 4 3d4 3F2 3 11.704 11.6973d4 3H4 4 3d4 1G2 4 11.635 11.6283d4 3H4 4 3d4 3F2 4 7.996 7.9863d4 5D4 3 3d4 3F4 3 102.978 103.203Atoms 2017, 5, 7 17 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d4 5D4 3 3d4 3G4 4 99.604 99.8523d4 5D4 3 3d4 3F4 2 86.407 86.5073d4 5D4 3 3d4 3F2 2 46.028 45.9953d4 5D4 3 3d4 3F2 4 38.221 38.2853d4 5D4 3 3d4 1D2 2 27.498 27.5243d4 5D4 3 3d4 5D4 4 17.475 17.4533d4 5D4 3 3d4 3F4 3 17.146 17.1233d4 5D4 3 3d4 3F4 2 14.303 14.2873d4 5D4 3 3d4 3D4 3 13.973 13.9623d4 5D4 3 3d4 3F2 3 11.934 11.9263d4 5D4 3 3d4 1G2 4 11.863 11.8553d4 5D4 3 3d4 1D4 2 11.408 11.4023d4 5D4 3 3d4 3F2 4 8.102 8.0923d4 5D4 3 3d4 1D2 2 7.584 7.5753d4 3H4 5 3d4 1 I4 6 428.184 430.1203d4 3H4 5 3d4 3G4 4 142.509 142.6373d4 3H4 5 3d4 3F2 4 43.213 43.2613d4 3H4 5 3d4 5D4 4 18.450 18.4183d4 3H4 5 3d4 3G4 5 16.625 16.6053d4 3H4 5 3d4 3H4 6 16.488 16.4703d4 3H4 5 3d4 1G2 4 12.304 12.2923d4 3H4 5 3d4 3F2 4 8.306 8.2933d4 1 I4 6 3d4 3G4 5 17.296 17.2723d4 1 I4 6 3d4 3H4 6 17.148 17.1263d4 3D4 1 3d4 3F4 2 226.092 226.8683d4 3D4 1 3d4 3F2 2 68.606 68.5413d4 3D4 1 3d4 1D2 2 34.228 34.2693d4 3D4 1 3d4 3P4 0 23.832 23.8323d4 3D4 1 3d4 3D4 1 18.077 18.0493d4 3D4 1 3d4 3F4 2 15.932 15.9123d4 3D4 1 3d4 1S4 0 14.097 14.0943d4 3D4 1 3d4 3P2 1 12.981 12.9723d4 3D4 1 3d4 1D4 2 12.421 12.4153d4 3D4 1 3d4 1D2 2 8.019 8.0093d4 3D4 1 3d4 3P2 0 6.900 6.8923d4 3F4 3 3d4 3G4 4 3040.724 3074.7753d4 3F4 3 3d4 3F4 2 536.990 534.7153d4 3F4 3 3d4 3F2 2 83.228 82.9733d4 3F4 3 3d4 3F2 4 60.779 60.8643d4 3F4 3 3d4 1D2 2 37.516 37.5333d4 3F4 3 3d4 5D4 4 21.047 21.0053d4 3F4 3 3d4 3F4 3 20.571 20.5293d4 3F4 3 3d4 3F4 2 16.610 16.5823d4 3F4 3 3d4 3D4 3 16.166 16.1473d4 3F4 3 3d4 3F2 3 13.498 13.4853d4 3F4 3 3d4 1G2 4 13.407 13.3933d4 3F4 3 3d4 1D4 2 12.829 12.8193d4 3F4 3 3d4 3F2 4 8.794 8.7803d4 3F4 3 3d4 1D2 2 8.187 8.176Atoms 2017, 5, 7 18 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d4 3G4 4 3d4 3F2 4 62.019 62.0933d4 3G4 4 3d4 5D4 4 21.194 21.1493d4 3G4 4 3d4 3F4 3 20.711 20.6673d4 3G4 4 3d4 3G4 5 18.820 18.7933d4 3G4 4 3d4 3D4 3 16.253 16.2323d4 3G4 4 3d4 3F2 3 13.559 13.5443d4 3G4 4 3d4 1G2 4 13.466 13.4523d4 3G4 4 3d4 3F2 4 8.820 8.8053d4 3F4 2 3d4 3F2 2 98.494 98.2133d4 3F4 2 3d4 1D2 2 40.334 40.3673d4 3F4 2 3d4 3F4 3 21.391 21.3483d4 3F4 2 3d4 3D4 1 19.648 19.6093d4 3F4 2 3d4 3F4 2 17.140 17.1133d4 3F4 2 3d4 3D4 3 16.668 16.6493d4 3F4 2 3d4 3F2 3 13.846 13.8343d4 3F4 2 3d4 3P2 1 13.772 13.7593d4 3F4 2 3d4 1D4 2 13.143 13.1333d4 3F4 2 3d4 1D2 2 8.314 8.3023d4 3F2 2 3d4 1D2 2 68.306 68.5363d4 3F2 2 3d4 3F4 3 27.325 27.2783d4 3F2 2 3d4 3D4 1 24.544 24.5013d4 3F2 2 3d4 3F4 2 20.751 20.7243d4 3F2 2 3d4 3D4 3 20.063 20.0483d4 3F2 2 3d4 3F2 3 16.111 16.1023d4 3F2 2 3d4 3P2 1 16.011 16.0003d4 3F2 2 3d4 1D4 2 15.166 15.1613d4 3F2 2 3d4 1D2 2 9.081 9.0693d4 3F2 4 3d4 5D4 4 32.196 32.0743d4 3F2 4 3d4 3F4 3 31.096 30.9773d4 3F2 4 3d4 3G4 5 27.020 26.9503d4 3F2 4 3d4 3D4 3 22.024 21.9773d4 3F2 4 3d4 3F2 3 17.352 17.3233d4 3F2 4 3d4 1G2 4 17.201 17.1723d4 3F2 4 3d4 3F2 4 10.282 10.2603d4 1D2 2 3d4 3F4 3 45.544 45.3123d4 1D2 2 3d4 3D4 1 38.310 38.1333d4 1D2 2 3d4 3F4 2 29.806 29.7063d4 1D2 2 3d4 3D4 3 28.407 28.3373d4 1D2 2 3d4 3F2 3 21.085 21.0463d4 1D2 2 3d4 3P2 1 20.912 20.8733d4 1D2 2 3d4 1D4 2 19.495 19.4673d4 1D2 2 3d4 1D2 2 10.473 10.4523d4 3P4 0 3d4 3D4 1 74.865 74.3853d4 3P4 0 3d4 3P2 1 28.511 28.4663d4 5D4 4 3d4 3F4 3 910.088 905.5303d4 5D4 4 3d4 3G4 5 168.067 168.6823d4 5D4 4 3d4 3D4 3 69.712 69.8103d4 5D4 4 3d4 3F2 3 37.636 37.6653d4 5D4 4 3d4 1G2 4 36.935 36.959Atoms 2017, 5, 7 19 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d4 5D4 4 3d4 3F2 4 15.106 15.0863d4 3F4 3 3d4 3F4 2 86.253 86.2533d4 3F4 3 3d4 3D4 3 75.495 75.6423d4 3F4 3 3d4 3F2 3 39.260 39.3003d4 3F4 3 3d4 1G2 4 38.498 38.5323d4 3F4 3 3d4 1D4 2 34.085 34.1303d4 3F4 3 3d4 3F2 4 15.361 15.3423d4 3F4 3 3d4 1D2 2 13.600 13.5863d4 3D4 1 3d4 3F4 2 134.268 134.4203d4 3D4 1 3d4 1S4 0 64.031 64.3173d4 3D4 1 3d4 3P2 1 46.049 46.1133d4 3D4 1 3d4 1D4 2 39.694 39.7693d4 3D4 1 3d4 1D2 2 14.413 14.3993d4 3D4 1 3d4 3P2 0 11.160 11.1493d4 3G4 5 3d4 3H4 6 1997.212 2027.1603d4 3G4 5 3d4 1G2 4 47.338 47.3293d4 3G4 5 3d4 3F2 4 16.598 16.5683d4 3F4 2 3d4 3D4 3 605.307 614.8283d4 3F4 2 3d4 3F2 3 72.059 72.1933d4 3F4 2 3d4 3P2 1 70.085 70.1933d4 3F4 2 3d4 1D4 2 56.355 56.4793d4 3F4 2 3d4 1D2 2 16.146 16.1263d4 3D4 3 3d4 3F2 3 81.796 81.7973d4 3D4 3 3d4 1G2 4 78.556 78.5393d4 3D4 3 3d4 1D4 2 62.140 62.1923d4 3D4 3 3d4 3F2 4 19.285 19.2453d4 3D4 3 3d4 1D2 2 16.589 16.5613d4 1S4 0 3d4 3P2 1 163.968 162.9263d4 3F2 3 3d4 1G2 4 1982.892 1971.6593d4 3F2 3 3d4 1D4 2 258.586 259.4743d4 3F2 3 3d4 3F2 4 25.235 25.1663d4 3F2 3 3d4 1D2 2 20.809 20.7653d4 3P2 1 3d4 1D4 2 287.662 289.0683d4 3P2 1 3d4 1D2 2 20.980 20.9363d4 3P2 1 3d4 3P2 0 14.730 14.7043d4 1G2 4 3d4 3F2 4 25.560 25.4913d4 1D4 2 3d4 1D2 2 22.630 22.571W51+ (V-like)3d5 4P3 5/2 3d5 6S5 5/2 21.290 21.243 21.203(3) 21.317 21.185 21.4923d5 4P3 5/2 3d5 4G5 7/2 17.700 17.674 17.660(3) 17.660 17.655 17.8263d5 4P3 5/2 3d5 4D5 3/2 17.253 17.227 17.215(3) 17.247 17.228 17.2493d5 4P3 5/2 3d5 4D5 5/2 15.368 15.3503d5 4P3 5/2 3d5 2F5 7/2 14.541 14.529 14.531(3) 14.475 14.537 14.5133d5 4P3 5/2 3d5 2D1 3/2 12.136 12.1223d5 4P3 5/2 3d5 6S5 5/2 9.747 9.7283d5 4P3 5/2 3d5 4D5 7/2 9.117 9.1023d5 4P3 5/2 3d5 4P3 3/2 8.586 8.5713d5 4P3 5/2 3d5 2F5 5/2 8.511 8.499Atoms 2017, 5, 7 20 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d5 4P3 5/2 3d5 2G5 7/2 8.078 8.0683d5 4P3 5/2 3d5 4F3 5/2 7.971 7.9593d5 4P3 5/2 3d5 2D5 3/2 7.940 7.9313d5 4P3 5/2 3d5 2G3 7/2 7.646 7.6363d5 4P3 5/2 3d5 2P3 3/2 6.645 6.6393d5 4P3 5/2 3d5 2D1 5/2 6.522 6.5163d5 4P3 5/2 3d5 4P3 5/2 6.021 6.0103d5 4P3 5/2 3d5 4F3 7/2 5.768 5.7583d5 4P3 5/2 3d5 4D5 3/2 5.684 5.6743d5 4P3 5/2 3d5 2D3 5/2 5.424 5.4163d5 4P3 5/2 3d5 2G3 7/2 5.343 5.3353d5 4P3 5/2 3d5 2D1 3/2 4.847 4.8413d5 4P3 5/2 3d5 2D1 5/2 4.233 4.2253d5 6S5 5/2 3d5 4G5 7/2 104.969 105.2143d5 6S5 5/2 3d5 4D5 3/2 90.995 91.1193d5 6S5 5/2 3d5 4D5 5/2 55.250 55.3413d5 6S5 5/2 3d5 2F5 7/2 45.868 45.9713d5 6S5 5/2 3d5 2D1 3/2 28.226 28.2333d5 6S5 5/2 3d5 6S5 5/2 17.977 17.9463d5 6S5 5/2 3d5 4D5 7/2 15.946 15.9273d5 6S5 5/2 3d5 4P3 3/2 14.388 14.3673d5 6S5 5/2 3d5 2F5 5/2 14.181 14.1673d5 6S5 5/2 3d5 2G5 7/2 13.018 13.0093d5 6S5 5/2 3d5 4F3 5/2 12.741 12.7273d5 6S5 5/2 3d5 2D5 3/2 12.662 12.6553d5 6S5 5/2 3d5 2G3 7/2 11.932 11.9213d5 6S5 5/2 3d5 2P3 3/2 9.660 9.6573d5 6S5 5/2 3d5 2D1 5/2 9.403 9.3993d5 6S5 5/2 3d5 4P3 5/2 8.395 8.3813d5 6S5 5/2 3d5 4F3 7/2 7.912 7.9003d5 6S5 5/2 3d5 4D5 3/2 7.755 7.7433d5 6S5 5/2 3d5 2D3 5/2 7.277 7.2693d5 6S5 5/2 3d5 2G3 7/2 7.133 7.1243d5 6S5 5/2 3d5 2D1 3/2 6.276 6.2693d5 6S5 5/2 3d5 2D1 5/2 5.283 5.2743d5 4G5 7/2 3d5 2G5 9/2 178.750 179.1563d5 4G5 7/2 3d5 4D5 5/2 116.648 116.7523d5 4G5 7/2 3d5 2F5 7/2 81.465 81.6453d5 4G5 7/2 3d5 6S5 5/2 21.692 21.6373d5 4G5 7/2 3d5 4D5 7/2 18.802 18.7683d5 4G5 7/2 3d5 4G5 9/2 18.116 18.0863d5 4G5 7/2 3d5 2F5 5/2 16.396 16.3723d5 4G5 7/2 3d5 2H3 9/2 15.329 15.3043d5 4G5 7/2 3d5 2G5 7/2 14.861 14.8453d5 4G5 7/2 3d5 4F3 5/2 14.501 14.4793d5 4G5 7/2 3d5 2G3 7/2 13.462 13.4443d5 4G5 7/2 3d5 2G3 9/2 12.275 12.2643d5 4G5 7/2 3d5 2D1 5/2 10.329 10.3213d5 4G5 7/2 3d5 4P3 5/2 9.125 9.106Atoms 2017, 5, 7 21 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d5 4G5 7/2 3d5 4F3 7/2 8.557 8.5413d5 4G5 7/2 3d5 2G5 9/2 8.057 8.0443d5 4G5 7/2 3d5 2D3 5/2 7.820 7.8083d5 4G5 7/2 3d5 2G3 7/2 7.653 7.6423d5 4G5 7/2 3d5 2D1 5/2 5.563 5.5533d5 2H3 11/2 3d5 2G5 9/2 222.726 223.0303d5 2H3 11/2 3d5 4G5 11/2 19.056 19.021 18.996(3) 19.064 19.002 19.1853d5 2H3 11/2 3d5 4G5 9/2 18.486 18.4533d5 2H3 11/2 3d5 2 I5 13/2 17.664 17.6373d5 2H3 11/2 3d5 2H3 9/2 15.593 15.5663d5 2H3 11/2 3d5 2G3 9/2 12.443 12.4323d5 2H3 11/2 3d5 2H3 11/2 8.544 8.5283d5 2H3 11/2 3d5 2G5 9/2 8.129 8.1163d5 4D5 3/2 3d5 4D5 5/2 140.653 140.9443d5 4D5 3/2 3d5 4P3 1/2 100.009 100.1203d5 4D5 3/2 3d5 2D1 3/2 40.920 40.9073d5 4D5 3/2 3d5 6S5 5/2 22.403 22.3483d5 4D5 3/2 3d5 4D5 1/2 17.360 17.3343d5 4D5 3/2 3d5 4P3 3/2 17.091 17.0563d5 4D5 3/2 3d5 2F5 5/2 16.799 16.7753d5 4D5 3/2 3d5 4F3 5/2 14.815 14.7943d5 4D5 3/2 3d5 2D5 3/2 14.708 14.6963d5 4D5 3/2 3d5 4P3 1/2 13.725 13.7093d5 4D5 3/2 3d5 2P3 3/2 10.807 10.8023d5 4D5 3/2 3d5 2D1 5/2 10.487 10.4803d5 4D5 3/2 3d5 4P3 5/2 9.248 9.2303d5 4D5 3/2 3d5 4D5 3/2 8.477 8.4623d5 4D5 3/2 3d5 2D3 5/2 7.910 7.8993d5 4D5 3/2 3d5 2P3 1/2 7.384 7.3753d5 4D5 3/2 3d5 2D1 3/2 6.741 6.7333d5 4D5 3/2 3d5 2D1 5/2 5.609 5.5983d5 2G5 9/2 3d5 2F5 7/2 149.683 150.0053d5 2G5 9/2 3d5 4D5 7/2 21.012 20.9643d5 2G5 9/2 3d5 4G5 11/2 20.839 20.7953d5 2G5 9/2 3d5 4G5 9/2 20.159 20.1173d5 2G5 9/2 3d5 2H3 9/2 16.767 16.7343d5 2G5 9/2 3d5 2G5 7/2 16.209 16.1863d5 2G5 9/2 3d5 2G3 7/2 14.558 14.5353d5 2G5 9/2 3d5 2G3 9/2 13.180 13.1653d5 2G5 9/2 3d5 4F3 7/2 8.987 8.9693d5 2G5 9/2 3d5 2H3 11/2 8.885 8.8673d5 2G5 9/2 3d5 2G5 9/2 8.437 8.4223d5 2G5 9/2 3d5 2G3 7/2 7.995 7.9823d5 4D5 5/2 3d5 2F5 7/2 270.094 271.5163d5 4D5 5/2 3d5 2D1 3/2 57.709 57.6363d5 4D5 5/2 3d5 6S5 5/2 26.647 26.5593d5 4D5 5/2 3d5 4D5 7/2 22.415 22.3633d5 4D5 5/2 3d5 4P3 3/2 19.454 19.4043d5 4D5 5/2 3d5 2F5 5/2 19.077 19.042Atoms 2017, 5, 7 22 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d5 4D5 5/2 3d5 2G5 7/2 17.031 17.0073d5 4D5 5/2 3d5 4F3 5/2 16.560 16.5293d5 4D5 5/2 3d5 2D5 3/2 16.426 16.4073d5 4D5 5/2 3d5 2G3 7/2 15.218 15.1943d5 4D5 5/2 3d5 2P3 3/2 11.706 11.6993d5 4D5 5/2 3d5 2D1 5/2 11.332 11.3223d5 4D5 5/2 3d5 4P3 5/2 9.899 9.8763d5 4D5 5/2 3d5 4F3 7/2 9.234 9.2153d5 4D5 5/2 3d5 4D5 3/2 9.021 9.0023d5 4D5 5/2 3d5 2D3 5/2 8.381 8.3683d5 4D5 5/2 3d5 2G3 7/2 8.190 8.1773d5 4D5 5/2 3d5 2D1 3/2 7.080 7.0703d5 4D5 5/2 3d5 2D1 5/2 5.842 5.8303d5 4P3 1/2 3d5 2D1 3/2 69.257 69.1693d5 4P3 1/2 3d5 4D5 1/2 21.006 20.9633d5 4P3 1/2 3d5 4P3 3/2 20.613 20.5593d5 4P3 1/2 3d5 2D5 3/2 17.245 17.2253d5 4P3 1/2 3d5 4P3 1/2 15.909 15.8843d5 4P3 1/2 3d5 2P3 3/2 12.116 12.1093d5 4P3 1/2 3d5 4D5 3/2 9.262 9.2433d5 4P3 1/2 3d5 2P3 1/2 7.973 7.9623d5 4P3 1/2 3d5 2D1 3/2 7.228 7.2183d5 2F5 7/2 3d5 6S5 5/2 29.564 29.4383d5 2F5 7/2 3d5 4D5 7/2 24.443 24.3703d5 2F5 7/2 3d5 4G5 9/2 23.296 23.2333d5 2F5 7/2 3d5 2F5 5/2 20.527 20.4783d5 2F5 7/2 3d5 2H3 9/2 18.882 18.8353d5 2F5 7/2 3d5 2G5 7/2 18.177 18.1433d5 2F5 7/2 3d5 4F3 5/2 17.641 17.6003d5 2F5 7/2 3d5 2G3 7/2 16.127 16.0943d5 2F5 7/2 3d5 2G3 9/2 14.452 14.4323d5 2F5 7/2 3d5 2D1 5/2 11.828 11.8143d5 2F5 7/2 3d5 4P3 5/2 10.275 10.2493d5 2F5 7/2 3d5 4F3 7/2 9.561 9.5393d5 2F5 7/2 3d5 2G5 9/2 8.941 8.9233d5 2F5 7/2 3d5 2D3 5/2 8.650 8.6343d5 2F5 7/2 3d5 2G3 7/2 8.446 8.4313d5 2F5 7/2 3d5 2D1 5/2 5.971 5.9583d5 2D1 3/2 3d5 6S5 5/2 49.507 49.2563d5 2D1 3/2 3d5 4D5 1/2 30.151 30.0803d5 2D1 3/2 3d5 4P3 3/2 29.348 29.2533d5 2D1 3/2 3d5 2F5 5/2 28.498 28.4373d5 2D1 3/2 3d5 4F3 5/2 23.224 23.1753d5 2D1 3/2 3d5 2D5 3/2 22.962 22.9363d5 2D1 3/2 3d5 4P3 1/2 20.653 20.6193d5 2D1 3/2 3d5 2P3 3/2 14.685 14.6783d5 2D1 3/2 3d5 2D1 5/2 14.101 14.0893d5 2D1 3/2 3d5 4P3 5/2 11.948 11.9193d5 2D1 3/2 3d5 4D5 3/2 10.692 10.668Atoms 2017, 5, 7 23 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d5 2D1 3/2 3d5 2D3 5/2 9.806 9.7893d5 2D1 3/2 3d5 2P3 1/2 9.010 8.9973d5 2D1 3/2 3d5 2D1 3/2 8.071 8.0593d5 2D1 3/2 3d5 2D1 5/2 6.500 6.4863d5 6S5 5/2 3d5 4D5 7/2 141.121 141.5593d5 6S5 5/2 3d5 4P3 3/2 72.074 72.0353d5 6S5 5/2 3d5 2F5 5/2 67.156 67.2783d5 6S5 5/2 3d5 2G5 7/2 47.192 47.2883d5 6S5 5/2 3d5 4F3 5/2 43.743 43.7663d5 6S5 5/2 3d5 2D5 3/2 42.824 42.9243d5 6S5 5/2 3d5 2G3 7/2 35.481 35.5053d5 6S5 5/2 3d5 2P3 3/2 20.879 20.9103d5 6S5 5/2 3d5 2D1 5/2 19.717 19.7343d5 6S5 5/2 3d5 4P3 5/2 15.749 15.7233d5 6S5 5/2 3d5 4F3 7/2 14.130 14.1113d5 6S5 5/2 3d5 4D5 3/2 13.638 13.6183d5 6S5 5/2 3d5 2D3 5/2 12.227 12.2173d5 6S5 5/2 3d5 2G3 7/2 11.824 11.8153d5 6S5 5/2 3d5 2D1 3/2 9.643 9.6363d5 6S5 5/2 3d5 2D1 5/2 7.482 7.4703d5 4D5 7/2 3d5 4G5 9/2 496.548 497.8613d5 4D5 7/2 3d5 2F5 5/2 128.131 128.2143d5 4D5 7/2 3d5 2H3 9/2 82.993 82.9243d5 4D5 7/2 3d5 2G5 7/2 70.903 71.0093d5 4D5 7/2 3d5 4F3 5/2 63.393 63.3533d5 4D5 7/2 3d5 2G3 7/2 47.397 47.3923d5 4D5 7/2 3d5 2G3 9/2 35.359 35.3903d5 4D5 7/2 3d5 2D1 5/2 22.919 22.9313d5 4D5 7/2 3d5 4P3 5/2 17.728 17.6883d5 4D5 7/2 3d5 4F3 7/2 15.703 15.6743d5 4D5 7/2 3d5 2G5 9/2 14.097 14.0783d5 4D5 7/2 3d5 2D3 5/2 13.387 13.3713d5 4D5 7/2 3d5 2G3 7/2 12.906 12.8913d5 4D5 7/2 3d5 2D1 5/2 7.901 7.8863d5 4G5 11/2 3d5 4G5 9/2 617.468 617.5723d5 4G5 11/2 3d5 2 I5 13/2 241.792 242.2973d5 4G5 11/2 3d5 2H3 9/2 85.801 85.6913d5 4G5 11/2 3d5 2G3 9/2 35.859 35.8853d5 4G5 11/2 3d5 2H3 11/2 15.488 15.4603d5 4G5 11/2 3d5 2G5 9/2 14.176 14.1553d5 4G5 9/2 3d5 2H3 9/2 99.648 99.4963d5 4G5 9/2 3d5 2G5 7/2 82.713 82.8223d5 4G5 9/2 3d5 2G3 7/2 52.399 52.3783d5 4G5 9/2 3d5 2G3 9/2 38.069 38.0983d5 4G5 9/2 3d5 4F3 7/2 16.215 16.1833d5 4G5 9/2 3d5 2H3 11/2 15.887 15.8573d5 4G5 9/2 3d5 2G5 9/2 14.509 14.4873d5 4G5 9/2 3d5 2G3 7/2 13.250 13.2333d5 2 I5 13/2 3d5 2H3 11/2 16.548 16.513Atoms 2017, 5, 7 24 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d5 4D5 1/2 3d5 4P3 3/2 1102.758 1064.9963d5 4D5 1/2 3d5 2D5 3/2 96.307 96.5833d5 4D5 1/2 3d5 4P3 1/2 65.560 65.5623d5 4D5 1/2 3d5 2P3 3/2 28.630 28.6683d5 4D5 1/2 3d5 4D5 3/2 16.568 16.5323d5 4D5 1/2 3d5 2P3 1/2 12.849 12.8373d5 4D5 1/2 3d5 2D1 3/2 11.021 11.0093d5 4P3 3/2 3d5 2F5 5/2 984.197 1018.7573d5 4P3 3/2 3d5 4F3 5/2 111.284 111.5253d5 4P3 3/2 3d5 2D5 3/2 105.523 106.2163d5 4P3 3/2 3d5 4P3 1/2 69.704 69.8633d5 4P3 3/2 3d5 2P3 3/2 29.393 29.4613d5 4P3 3/2 3d5 2D1 5/2 27.141 27.1803d5 4P3 3/2 3d5 4P3 5/2 20.153 20.1133d5 4P3 3/2 3d5 4D5 3/2 16.820 16.7933d5 4P3 3/2 3d5 2D3 5/2 14.726 14.7123d5 4P3 3/2 3d5 2P3 1/2 13.001 12.9943d5 4P3 3/2 3d5 2D1 3/2 11.132 11.1243d5 4P3 3/2 3d5 2D1 5/2 8.349 8.3343d5 2F5 5/2 3d5 2G5 7/2 158.747 159.1553d5 2F5 5/2 3d5 4F3 5/2 125.471 125.2343d5 2F5 5/2 3d5 2D5 3/2 118.195 118.5783d5 2F5 5/2 3d5 2G3 7/2 75.224 75.1823d5 2F5 5/2 3d5 2P3 3/2 30.298 30.3393d5 2F5 5/2 3d5 2D1 5/2 27.911 27.9253d5 2F5 5/2 3d5 4P3 5/2 20.575 20.5183d5 2F5 5/2 3d5 4F3 7/2 17.896 17.8573d5 2F5 5/2 3d5 4D5 3/2 17.113 17.0743d5 2F5 5/2 3d5 2D3 5/2 14.949 14.9283d5 2F5 5/2 3d5 2G3 7/2 14.351 14.3313d5 2F5 5/2 3d5 2D1 3/2 11.259 11.2463d5 2F5 5/2 3d5 2D1 5/2 8.420 8.4033d5 2H3 9/2 3d5 2G5 7/2 486.710 494.2183d5 2H3 9/2 3d5 2G3 7/2 110.511 110.6033d5 2H3 9/2 3d5 2G3 9/2 61.605 61.7393d5 2H3 9/2 3d5 4F3 7/2 19.367 19.3273d5 2H3 9/2 3d5 2H3 11/2 18.900 18.8633d5 2H3 9/2 3d5 2G5 9/2 16.982 16.9573d5 2H3 9/2 3d5 2G3 7/2 15.282 15.2633d5 2G5 7/2 3d5 4F3 5/2 598.575 587.6003d5 2G5 7/2 3d5 2G3 7/2 142.974 142.4923d5 2G5 7/2 3d5 2G3 9/2 70.533 70.5533d5 2G5 7/2 3d5 2D1 5/2 33.865 33.8673d5 2G5 7/2 3d5 4P3 5/2 23.638 23.5553d5 2G5 7/2 3d5 4F3 7/2 20.170 20.1133d5 2G5 7/2 3d5 2G5 9/2 17.595 17.5593d5 2G5 7/2 3d5 2D3 5/2 16.503 16.4733d5 2G5 7/2 3d5 2G3 7/2 15.777 15.7503d5 2G5 7/2 3d5 2D1 5/2 8.892 8.871Atoms 2017, 5, 7 25 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d5 4F3 5/2 3d5 2D5 3/2 2038.287 2231.1273d5 4F3 5/2 3d5 2G3 7/2 187.841 188.1083d5 4F3 5/2 3d5 2P3 3/2 39.944 40.0383d5 4F3 5/2 3d5 2D1 5/2 35.896 35.9393d5 4F3 5/2 3d5 4P3 5/2 24.610 24.5393d5 4F3 5/2 3d5 4F3 7/2 20.873 20.8263d5 4F3 5/2 3d5 4D5 3/2 19.815 19.7693d5 4F3 5/2 3d5 2D3 5/2 16.971 16.9483d5 4F3 5/2 3d5 2G3 7/2 16.205 16.1833d5 4F3 5/2 3d5 2D1 3/2 12.369 12.3563d5 4F3 5/2 3d5 2D1 5/2 9.026 9.0073d5 2D5 3/2 3d5 4P3 1/2 205.353 204.1233d5 2D5 3/2 3d5 2P3 3/2 40.742 40.7703d5 2D5 3/2 3d5 2D1 5/2 36.540 36.5273d5 2D5 3/2 3d5 4P3 5/2 24.911 24.8123d5 2D5 3/2 3d5 4D5 3/2 20.010 19.9463d5 2D5 3/2 3d5 2D3 5/2 17.114 17.0783d5 2D5 3/2 3d5 2P3 1/2 14.828 14.8053d5 2D5 3/2 3d5 2D1 3/2 12.445 12.4253d5 2D5 3/2 3d5 2D1 5/2 9.066 9.0443d5 2G3 7/2 3d5 2G3 9/2 139.208 139.7473d5 2G3 7/2 3d5 2D1 5/2 44.377 44.4273d5 2G3 7/2 3d5 4P3 5/2 28.321 28.2203d5 2G3 7/2 3d5 4F3 7/2 23.482 23.4193d5 2G3 7/2 3d5 2G5 9/2 20.065 20.0273d5 2G3 7/2 3d5 2D3 5/2 18.657 18.6263d5 2G3 7/2 3d5 2G3 7/2 17.735 17.7073d5 2G3 7/2 3d5 2D1 5/2 9.482 9.4603d5 4P3 1/2 3d5 2P3 3/2 50.826 50.9453d5 4P3 1/2 3d5 4D5 3/2 22.170 22.1063d5 4P3 1/2 3d5 2P3 1/2 15.982 15.9633d5 4P3 1/2 3d5 2D1 3/2 13.248 13.2303d5 2G3 9/2 3d5 4F3 7/2 28.247 28.1343d5 2G3 9/2 3d5 2H3 11/2 27.264 27.1623d5 2G3 9/2 3d5 2G5 9/2 23.444 23.3773d5 2G3 9/2 3d5 2G3 7/2 20.324 20.2763d5 2P3 3/2 3d5 2D1 5/2 354.267 351.0293d5 2P3 3/2 3d5 4P3 5/2 64.110 63.3893d5 2P3 3/2 3d5 4D5 3/2 39.323 39.0513d5 2P3 3/2 3d5 2D3 5/2 29.510 29.3883d5 2P3 3/2 3d5 2P3 1/2 23.312 23.2473d5 2P3 3/2 3d5 2D1 3/2 17.918 17.8713d5 2P3 3/2 3d5 2D1 5/2 11.661 11.6213d5 2D1 5/2 3d5 4P3 5/2 78.275 77.3593d5 2D1 5/2 3d5 4F3 7/2 49.873 49.5273d5 2D1 5/2 3d5 4D5 3/2 44.232 43.9393d5 2D1 5/2 3d5 2D3 5/2 32.191 32.0733d5 2D1 5/2 3d5 2G3 7/2 29.540 29.4403d5 2D1 5/2 3d5 2D1 3/2 18.873 18.830Atoms 2017, 5, 7 26 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d5 2D1 5/2 3d5 2D1 5/2 12.058 12.0193d5 4P3 5/2 3d5 4F3 7/2 137.450 137.6583d5 4P3 5/2 3d5 4D5 3/2 101.706 101.7093d5 4P3 5/2 3d5 2D3 5/2 54.677 54.7893d5 4P3 5/2 3d5 2G3 7/2 47.445 47.5283d5 4P3 5/2 3d5 2D1 3/2 24.869 24.8883d5 4P3 5/2 3d5 2D1 5/2 14.254 14.2303d5 4F3 7/2 3d5 2G5 9/2 137.868 138.2553d5 4F3 7/2 3d5 2D3 5/2 90.796 91.0133d5 4F3 7/2 3d5 2G3 7/2 72.454 72.5913d5 4F3 7/2 3d5 2D1 5/2 15.903 15.8713d5 2H3 11/2 3d5 2G5 9/2 167.319 167.7683d5 4D5 3/2 3d5 2D3 5/2 118.248 118.7673d5 4D5 3/2 3d5 2P3 1/2 57.255 57.4423d5 4D5 3/2 3d5 2D1 3/2 32.917 32.9513d5 4D5 3/2 3d5 2D1 5/2 16.577 16.5453d5 2G5 9/2 3d5 2G3 7/2 152.705 152.8403d5 2D3 5/2 3d5 2G3 7/2 358.662 358.6343d5 2D3 5/2 3d5 2D1 3/2 45.616 45.6023d5 2D3 5/2 3d5 2D1 5/2 19.280 19.2233d5 2G3 7/2 3d5 2D1 5/2 20.376 20.3123d5 2P3 1/2 3d5 2D1 3/2 77.440 77.2833d5 2D1 3/2 3d5 2D1 5/2 33.396 33.231W50+ (Cr-like)3d6 5D4 4 3d6 5D4 3 19.752 19.720 19.684(3) 19.796 19.693 19.8353d6 5D4 4 3d6 5D4 4 19.291 19.267 19.239(3) 19.303 19.237 19.4253d6 5D4 4 3d6 3G4 5 17.162 17.150 17.133(3) 17.118 17.131 17.2593d6 5D4 4 3d6 3D4 3 15.390 15.378 15.363(3) 15.370 15.289 15.3163d6 5D4 4 3d6 1G2 4 13.147 13.139 13.137(3) 13.114 13.153 13.0503d6 5D4 4 3d6 3F2 3 12.785 12.779 12.779(3) 12.739 12.800 12.6423d6 5D4 4 3d6 3H4 4 9.024 9.0133d6 5D4 4 3d6 5D4 3 8.809 8.7983d6 5D4 4 3d6 3H4 5 8.756 8.7463d6 5D4 4 3d6 3F4 3 8.356 8.3473d6 5D4 4 3d6 1G4 4 8.111 8.1043d6 5D4 4 3d6 3F2 4 7.274 7.2693d6 5D4 4 3d6 1G2 4 5.668 5.6613d6 5D4 4 3d6 3F2 3 5.461 5.4553d6 3D4 2 3d6 5D4 3 22.546 22.5033d6 3D4 2 3d6 5D4 1 20.709 20.6683d6 3D4 2 3d6 3F4 2 17.384 17.3673d6 3D4 2 3d6 3D4 3 17.035 17.0193d6 3D4 2 3d6 3D4 2 14.214 14.202 14.193(3) 14.184 14.202 14.1703d6 3D4 2 3d6 3P2 1 14.198 14.1883d6 3D4 2 3d6 3F2 3 13.900 13.892 13.886(3) 13.843 13.895 13.8483d6 3D4 2 3d6 5D4 2 10.042 10.0253d6 3D4 2 3d6 5D4 3 9.324 9.3123d6 3D4 2 3d6 3F4 3 8.818 8.808Atoms 2017, 5, 7 27 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d6 3D4 2 3d6 3D4 1 8.662 8.6523d6 3D4 2 3d6 3F4 2 8.468 8.4603d6 3D4 2 3d6 3F2 2 7.848 7.8393d6 3D4 2 3d6 1D2 2 6.867 6.8633d6 3D4 2 3d6 3P2 1 6.248 6.2383d6 3D4 2 3d6 3P2 2 5.711 5.7043d6 3D4 2 3d6 3F2 3 5.655 5.6483d6 3P2 0 3d6 5D4 1 29.559 29.5093d6 3P2 0 3d6 3P2 1 17.865 17.861 17.826(3) 17.750 17.837 17.9213d6 3P2 0 3d6 3D4 1 9.901 9.8933d6 3P2 0 3d6 3P2 1 6.868 6.8583d6 5D4 3 3d6 5D4 4 827.797 838.1073d6 5D4 3 3d6 3F4 2 75.926 76.0903d6 5D4 3 3d6 3D4 3 69.700 69.8303d6 5D4 3 3d6 1G2 4 39.314 39.3653d6 5D4 3 3d6 3D4 2 38.467 38.4993d6 5D4 3 3d6 3F2 3 36.246 36.3043d6 5D4 3 3d6 5D4 2 18.107 18.0803d6 5D4 3 3d6 3H4 4 16.615 16.5993d6 5D4 3 3d6 5D4 3 15.900 15.8863d6 5D4 3 3d6 3F4 3 14.482 14.4723d6 5D4 3 3d6 1G4 4 13.764 13.7583d6 5D4 3 3d6 3F4 2 13.562 13.5563d6 5D4 3 3d6 3F2 2 12.038 12.0293d6 5D4 3 3d6 3F2 4 11.514 11.5123d6 5D4 3 3d6 1D2 2 9.875 9.8743d6 5D4 3 3d6 1G2 4 7.949 7.9403d6 5D4 3 3d6 3P2 2 7.648 7.6413d6 5D4 3 3d6 3F2 3 7.547 7.5403d6 5D4 4 3d6 3G4 5 155.438 156.0803d6 5D4 4 3d6 3D4 3 76.108 76.1773d6 5D4 4 3d6 1G2 4 41.274 41.3053d6 5D4 4 3d6 3F2 3 37.905 37.9483d6 5D4 4 3d6 3H4 4 16.955 16.9343d6 5D4 4 3d6 5D4 3 16.211 16.1933d6 5D4 4 3d6 3H4 5 16.032 16.0183d6 5D4 4 3d6 3F4 3 14.740 14.7263d6 5D4 4 3d6 1G4 4 13.997 13.9873d6 5D4 4 3d6 3F2 4 11.676 11.6723d6 5D4 4 3d6 1G2 4 8.026 8.0163d6 5D4 4 3d6 3F2 3 7.617 7.6093d6 5D4 1 3d6 3F4 2 108.263 108.7303d6 5D4 1 3d6 3P4 0 55.744 55.9243d6 5D4 1 3d6 3D4 2 45.325 45.3933d6 5D4 1 3d6 3P2 1 45.157 45.2483d6 5D4 1 3d6 5D4 2 19.495 19.4683d6 5D4 1 3d6 5D4 0 18.606 18.5763d6 5D4 1 3d6 3D4 1 14.889 14.8823d6 5D4 1 3d6 3F4 2 14.326 14.322Atoms 2017, 5, 7 28 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d6 5D4 1 3d6 3F2 2 12.637 12.6293d6 5D4 1 3d6 1D2 2 10.274 10.2743d6 5D4 1 3d6 1S0 0 8.969 8.9683d6 5D4 1 3d6 3P2 1 8.947 8.9343d6 5D4 1 3d6 3P2 2 7.886 7.8783d6 5D4 1 3d6 3P2 0 5.630 5.6223d6 3H4 6 3d6 3G4 5 33171.897 25414.2523d6 3H4 6 3d6 3H4 5 17.866 17.8373d6 3H4 6 3d6 1 I4 6 17.042 17.0203d6 3G4 5 3d6 1G2 4 56.196 56.1703d6 3G4 5 3d6 3H4 4 19.031 18.9953d6 3G4 5 3d6 3H4 5 17.876 17.8503d6 3G4 5 3d6 1 I4 6 17.051 17.0323d6 3G4 5 3d6 1G4 4 15.382 15.3643d6 3G4 5 3d6 3F2 4 12.625 12.6153d6 3G4 5 3d6 1G2 4 8.463 8.4503d6 3F4 2 3d6 3D4 3 850.017 848.7313d6 3F4 2 3d6 3D4 2 77.967 77.9273d6 3F4 2 3d6 3P2 1 77.469 77.4993d6 3F4 2 3d6 3F2 3 69.354 69.4313d6 3F4 2 3d6 5D4 2 23.777 23.7153d6 3F4 2 3d6 5D4 3 20.111 20.0783d6 3F4 2 3d6 3F4 3 17.895 17.8713d6 3F4 2 3d6 3D4 1 17.263 17.2423d6 3F4 2 3d6 3F4 2 16.511 16.4943d6 3F4 2 3d6 3F2 2 14.307 14.2883d6 3F4 2 3d6 1D2 2 11.351 11.3463d6 3F4 2 3d6 3P2 1 9.754 9.7343d6 3F4 2 3d6 3P2 2 8.505 8.4943d6 3F4 2 3d6 3F2 3 8.381 8.3703d6 3D4 3 3d6 1G2 4 90.179 90.2323d6 3D4 3 3d6 3D4 2 85.841 85.8053d6 3D4 3 3d6 3F2 3 75.516 75.6173d6 3D4 3 3d6 5D4 2 24.461 24.3963d6 3D4 3 3d6 3H4 4 21.815 21.7743d6 3D4 3 3d6 5D4 3 20.598 20.5653d6 3D4 3 3d6 3F4 3 18.280 18.2553d6 3D4 3 3d6 1G4 4 17.151 17.1333d6 3D4 3 3d6 3F4 2 16.838 16.8213d6 3D4 3 3d6 3F2 2 14.552 14.5333d6 3D4 3 3d6 3F2 4 13.792 13.7843d6 3D4 3 3d6 1D2 2 11.505 11.5003d6 3D4 3 3d6 1G2 4 8.972 8.9593d6 3D4 3 3d6 3P2 2 8.591 8.5793d6 3D4 3 3d6 3F2 3 8.464 8.4533d6 3P4 0 3d6 3P2 1 237.757 237.0233d6 3P4 0 3d6 3D4 1 20.315 20.2783d6 3P4 0 3d6 3P2 1 10.658 10.6333d6 1G2 4 3d6 3F2 3 464.412 466.858Atoms 2017, 5, 7 29 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d6 1G2 4 3d6 3H4 4 28.776 28.7003d6 1G2 4 3d6 5D4 3 26.696 26.6353d6 1G2 4 3d6 3H4 5 26.215 26.1643d6 1G2 4 3d6 3F4 3 22.928 22.8863d6 1G2 4 3d6 1G4 4 21.178 21.1493d6 1G2 4 3d6 3F2 4 16.283 16.2693d6 1G2 4 3d6 1G2 4 9.963 9.9463d6 1G2 4 3d6 3F2 3 9.341 9.3273d6 3D4 2 3d6 3P2 1 12130.770 14130.0823d6 3D4 2 3d6 3F2 3 627.813 636.8453d6 3D4 2 3d6 5D4 2 34.209 34.0883d6 3D4 2 3d6 5D4 3 27.101 27.0473d6 3D4 2 3d6 3F4 3 23.226 23.1893d6 3D4 2 3d6 3D4 1 22.172 22.1403d6 3D4 2 3d6 3F4 2 20.946 20.9223d6 3D4 2 3d6 3F2 2 17.522 17.4973d6 3D4 2 3d6 1D2 2 13.285 13.2803d6 3D4 2 3d6 3P2 1 11.148 11.1243d6 3D4 2 3d6 3P2 2 9.546 9.5333d6 3D4 2 3d6 3F2 3 9.390 9.3773d6 3P2 1 3d6 5D4 2 34.306 34.1713d6 3P2 1 3d6 5D4 0 31.646 31.5123d6 3P2 1 3d6 3D4 1 22.213 22.1753d6 3P2 1 3d6 3F4 2 20.982 20.9543d6 3P2 1 3d6 3F2 2 17.548 17.5183d6 3P2 1 3d6 1D2 2 13.300 13.2923d6 3P2 1 3d6 1S0 0 11.192 11.1853d6 3P2 1 3d6 3P2 1 11.158 11.1323d6 3P2 1 3d6 3P2 2 9.554 9.5393d6 3P2 1 3d6 3P2 0 6.432 6.4193d6 3F2 3 3d6 5D4 2 36.181 36.0163d6 3F2 3 3d6 3H4 4 30.677 30.5803d6 3F2 3 3d6 5D4 3 28.324 28.2463d6 3F2 3 3d6 3F4 3 24.119 24.0653d6 3F2 3 3d6 1G4 4 22.190 22.1533d6 3F2 3 3d6 3F4 2 21.669 21.6333d6 3F2 3 3d6 3F2 2 18.025 17.9913d6 3F2 3 3d6 3F2 4 16.875 16.8573d6 3F2 3 3d6 1D2 2 13.572 13.5633d6 3F2 3 3d6 1G2 4 10.182 10.1633d6 3F2 3 3d6 3P2 2 9.694 9.6773d6 3F2 3 3d6 3F2 3 9.532 9.5173d6 5D4 2 3d6 5D4 3 130.436 130.9303d6 5D4 2 3d6 3F4 3 72.345 72.5243d6 5D4 2 3d6 3D4 1 63.013 63.1683d6 5D4 2 3d6 3F4 2 54.026 54.1713d6 5D4 2 3d6 3F2 2 35.921 35.9473d6 5D4 2 3d6 1D2 2 21.720 21.7553d6 5D4 2 3d6 3P2 1 16.537 16.511Atoms 2017, 5, 7 30 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d6 5D4 2 3d6 3P2 2 13.242 13.2333d6 5D4 2 3d6 3F2 3 12.942 12.9353d6 5D4 0 3d6 3D4 1 74.520 74.8403d6 5D4 0 3d6 3P2 1 17.236 17.2133d6 3H4 4 3d6 5D4 3 369.368 370.1053d6 3H4 4 3d6 3H4 5 294.589 296.0753d6 3H4 4 3d6 3F4 3 112.825 112.9593d6 3H4 4 3d6 1G4 4 80.216 80.3823d6 3H4 4 3d6 3F2 4 37.506 37.5633d6 3H4 4 3d6 1G2 4 15.240 15.2213d6 3H4 4 3d6 3F2 3 13.830 13.8173d6 5D4 3 3d6 3F4 3 162.444 162.5793d6 5D4 3 3d6 1G4 4 102.469 102.6833d6 5D4 3 3d6 3F4 2 92.227 92.4023d6 5D4 3 3d6 3F2 2 49.574 49.5523d6 5D4 3 3d6 3F2 4 41.744 41.8053d6 5D4 3 3d6 1D2 2 26.059 26.0903d6 5D4 3 3d6 1G2 4 15.896 15.8743d6 5D4 3 3d6 3P2 2 14.738 14.7213d6 5D4 3 3d6 3F2 3 14.368 14.3533d6 3H4 5 3d6 1 I4 6 369.318 371.6373d6 3H4 5 3d6 1G4 4 110.232 110.3373d6 3H4 5 3d6 3F2 4 42.977 43.0213d6 3H4 5 3d6 1G2 4 16.071 16.0463d6 3F4 3 3d6 1G4 4 277.541 278.7173d6 3F4 3 3d6 3F4 2 213.361 214.0663d6 3F4 3 3d6 3F2 2 71.346 71.2753d6 3F4 3 3d6 3F2 4 56.181 56.2763d6 3F4 3 3d6 1D2 2 31.039 31.0763d6 3F4 3 3d6 1G2 4 17.620 17.5923d6 3F4 3 3d6 3P2 2 16.208 16.1873d6 3F4 3 3d6 3F2 3 15.762 15.7433d6 3D4 1 3d6 3F4 2 378.830 380.3493d6 3D4 1 3d6 3F2 2 83.550 83.4183d6 3D4 1 3d6 1D2 2 33.145 33.1823d6 3D4 1 3d6 1S0 0 22.557 22.5693d6 3D4 1 3d6 3P2 1 22.422 22.3553d6 3D4 1 3d6 3P2 2 16.764 16.7403d6 3D4 1 3d6 3P2 0 9.053 9.0353d6 1G4 4 3d6 3F2 4 70.440 70.5143d6 1G4 4 3d6 1G2 4 18.815 18.7773d6 1G4 4 3d6 3F2 3 16.711 16.6853d6 3F4 2 3d6 3F2 2 107.190 106.8533d6 3F4 2 3d6 1D2 2 36.323 36.3543d6 3F4 2 3d6 3P2 1 23.832 23.7513d6 3F4 2 3d6 3P2 2 17.541 17.5113d6 3F4 2 3d6 3F2 3 17.019 16.9923d6 3F2 2 3d6 1D2 2 54.939 55.1013d6 3F2 2 3d6 3P2 1 30.646 30.539Atoms 2017, 5, 7 31 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d6 3F2 2 3d6 3P2 2 20.973 20.9433d6 3F2 2 3d6 3F2 3 20.232 20.2053d6 3F2 4 3d6 1G2 4 25.671 25.5923d6 3F2 4 3d6 3F2 3 21.909 21.8573d6 1D2 2 3d6 3P2 1 69.307 68.5083d6 1D2 2 3d6 3P2 2 33.922 33.7833d6 1D2 2 3d6 3F2 3 32.025 31.9053d6 1S0 0 3d6 3P2 1 3732.652 2353.5613d6 3P2 1 3d6 3P2 2 66.443 66.6483d6 3P2 1 3d6 3P2 0 15.184 15.1623d6 1G2 4 3d6 3F2 3 149.470 149.7533d6 3P2 2 3d6 3F2 3 572.500 573.976W49+ (Mn-like)3d7 4F3 9/2 3d7 4F3 7/2 18.940 18.908 18.880(3) 19.006 18.901 18.9433d7 4F3 9/2 3d7 4F3 9/2 17.138 17.119 17.106(3) 17.149 17.118 17.1323d7 4F3 9/2 3d7 2H3 11/2 15.381 15.371 15.368(3) 15.343 15.372 15.3803d7 4F3 9/2 3d7 2F3 7/2 14.180 14.170 14.166(3) 14.156 14.187 14.0633d7 4F3 9/2 3d7 2H3 9/2 8.434 8.4243d7 4F3 9/2 3d7 2F3 7/2 8.259 8.2503d7 2P3 3/2 3d7 2D1 5/2 174.708 174.0563d7 2P3 3/2 3d7 4P3 3/2 19.753 19.7153d7 2P3 3/2 3d7 4P3 5/2 19.111 19.081 19.047(3) 19.130 19.037 19.2713d7 2P3 3/2 3d7 4P3 1/2 18.720 18.692 18.670(3) 18.764 18.680 18.7333d7 2P3 3/2 3d7 2F3 5/2 15.597 15.5853d7 2P3 3/2 3d7 2D1 3/2 12.711 12.7003d7 2P3 3/2 3d7 4F3 5/2 9.864 9.8473d7 2P3 3/2 3d7 4P3 3/2 9.561 9.5463d7 2P3 3/2 3d7 2P3 1/2 9.171 9.1573d7 2P3 3/2 3d7 2D1 5/2 7.643 7.6363d7 2P3 3/2 3d7 2D1 3/2 6.060 6.0503d7 2D1 5/2 3d7 4F3 7/2 27.098 27.0433d7 2D1 5/2 3d7 4P3 3/2 22.271 22.2333d7 2D1 5/2 3d7 4P3 5/2 21.458 21.4303d7 2D1 5/2 3d7 2F3 7/2 18.307 18.294 18.276(3) 18.258 18.274 18.4253d7 2D1 5/2 3d7 2F3 5/2 17.126 17.1173d7 2D1 5/2 3d7 2D1 3/2 13.709 13.7003d7 2D1 5/2 3d7 4F3 5/2 10.455 10.4373d7 2D1 5/2 3d7 4P3 3/2 10.115 10.0993d7 2D1 5/2 3d7 2F3 7/2 9.507 9.4963d7 2D1 5/2 3d7 2D1 5/2 7.993 7.9863d7 2D1 5/2 3d7 2D1 3/2 6.278 6.2683d7 4F3 7/2 3d7 4F3 9/2 180.107 180.9083d7 4F3 7/2 3d7 4P3 5/2 103.103 103.2593d7 4F3 7/2 3d7 2F3 7/2 56.428 56.5503d7 4F3 7/2 3d7 2F3 5/2 46.537 46.6373d7 4F3 7/2 3d7 4F3 5/2 17.022 16.9983d7 4F3 7/2 3d7 2H3 9/2 15.204 15.1933d7 4F3 7/2 3d7 2F3 7/2 14.645 14.635Atoms 2017, 5, 7 32 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d7 4F3 7/2 3d7 2D1 5/2 11.337 11.3323d7 4F3 9/2 3d7 2H3 11/2 150.021 150.5593d7 4F3 9/2 3d7 2F3 7/2 82.173 82.2653d7 4F3 9/2 3d7 2H3 9/2 16.606 16.5863d7 4F3 9/2 3d7 2F3 7/2 15.942 15.9233d7 4P3 3/2 3d7 4P3 5/2 587.816 593.2703d7 4P3 3/2 3d7 4P3 1/2 357.969 360.2833d7 4P3 3/2 3d7 2F3 5/2 74.127 74.3873d7 4P3 3/2 3d7 2D1 3/2 35.657 35.6933d7 4P3 3/2 3d7 4F3 5/2 19.704 19.6733d7 4P3 3/2 3d7 4P3 3/2 18.530 18.5063d7 4P3 3/2 3d7 2P3 1/2 17.118 17.1003d7 4P3 3/2 3d7 2D1 5/2 12.467 12.4623d7 4P3 3/2 3d7 2D1 3/2 8.742 8.7293d7 4P3 5/2 3d7 2F3 7/2 124.648 125.0143d7 4P3 5/2 3d7 2F3 5/2 84.823 85.0513d7 4P3 5/2 3d7 2D1 3/2 37.960 37.9783d7 4P3 5/2 3d7 4F3 5/2 20.388 20.3473d7 4P3 5/2 3d7 4P3 3/2 19.133 19.1013d7 4P3 5/2 3d7 2F3 7/2 17.070 17.0523d7 4P3 5/2 3d7 2D1 5/2 12.737 12.7293d7 4P3 5/2 3d7 2D1 3/2 8.874 8.8603d7 4P3 1/2 3d7 2D1 3/2 39.602 39.6183d7 4P3 1/2 3d7 4P3 3/2 19.542 19.5083d7 4P3 1/2 3d7 2P3 1/2 17.978 17.9523d7 4P3 1/2 3d7 2D1 3/2 8.961 8.9463d7 2H3 11/2 3d7 2H3 9/2 18.673 18.6393d7 2F3 7/2 3d7 2F3 5/2 265.490 266.0613d7 2F3 7/2 3d7 4F3 5/2 24.375 24.3033d7 2F3 7/2 3d7 2H3 9/2 20.812 20.7743d7 2F3 7/2 3d7 2F3 7/2 19.779 19.7453d7 2F3 7/2 3d7 2D1 5/2 14.187 14.1733d7 2F3 5/2 3d7 2D1 3/2 68.707 68.6193d7 2F3 5/2 3d7 4F3 5/2 26.839 26.7463d7 2F3 5/2 3d7 4P3 3/2 24.706 24.6343d7 2F3 5/2 3d7 2F3 7/2 21.371 21.3283d7 2F3 5/2 3d7 2D1 5/2 14.988 14.9703d7 2F3 5/2 3d7 2D1 3/2 9.911 9.8903d7 2D1 3/2 3d7 4F3 5/2 44.043 43.8303d7 2D1 3/2 3d7 4P3 3/2 38.579 38.4303d7 2D1 3/2 3d7 2P3 1/2 32.925 32.8283d7 2D1 3/2 3d7 2D1 5/2 19.169 19.1473d7 2D1 3/2 3d7 2D1 3/2 11.581 11.5553d7 4F3 5/2 3d7 4P3 3/2 310.962 311.9193d7 4F3 5/2 3d7 2F3 7/2 104.893 105.2903d7 4F3 5/2 3d7 2D1 5/2 33.943 34.0003d7 4F3 5/2 3d7 2D1 3/2 15.713 15.6923d7 4P3 3/2 3d7 2P3 1/2 224.661 225.2053d7 4P3 3/2 3d7 2D1 5/2 38.102 38.159Atoms 2017, 5, 7 33 of 34Table 5. Cont.Label and J Label and J Present Work ExptGRASP RMBPTg RCIgfor Lower for Upper n = 5 n = 6 (Ref. [2])3d7 4P3 3/2 3d7 2D1 3/2 16.549 16.5243d7 2P3 1/2 3d7 2D1 3/2 17.865 17.8323d7 2H3 9/2 3d7 2F3 7/2 398.243 398.6113d7 2F3 7/2 3d7 2D1 5/2 50.182 50.2153d7 2D1 5/2 3d7 2D1 3/2 29.257 29.143W48+ (Fe-like)3d8 3F 4 3d8 3F 3 19.041 19.009 18.988(3) 19.114 19.007 19.0273d8 3F 4 3d8 1G 4 15.531 15.518 15.511(3) 15.503 15.463 15.5253d8 1D 2 3d8 3F 3 22.073 22.0293d8 1D 2 3d8 3P 2 18.931 18.902 18.878(3) 18.978 18.888 18.9663d8 1D 2 3d8 3P 1 17.548 17.525 17.502(3) 17.548 17.517 17.4893d8 1D 2 3d8 3F 2 9.664 9.6483d8 3P 0 3d8 3P 1 24.268 24.2363d8 3F 3 3d8 3P 2 132.993 133.1893d8 3F 3 3d8 1G 4 84.240 84.4893d8 3F 3 3d8 3F 2 17.190 17.1673d8 3P 2 3d8 3P 1 240.207 240.6003d8 3P 2 3d8 3F 2 19.742 19.7073d8 3P 1 3d8 3F 2 21.510 21.4653d8 3P 1 3d8 1S 0 15.102 15.082W47+ (Co-like)3d9 2D 5/2 3d9 2D 3/2 18.615 18.586 18.567(3) 18.671 18.586 18.5804. ConclusionsThe present study has shown that the inclusion of core correlation effects improves the accuracy oftheoretical transition wavelengths for M1 transitions in 3dk configurations of tungsten ions. Omitted inour work were correlation effects arising from the 1s2 core. Further studies are needed to determinewhether the discrepancy with observation arises from the limited orbital set for core correlation orfrom the inactive 1s2 shell in our present work.Acknowledgments: Computations were performed on resources at the High Performance Computing Center“HPC Sauletekis” in Vilnius University Faculty of Physics (Lithuania). Per Jönsson acknowledge support from theSwedish Research Council under contract 2015-04842.Author Contributions: All authors have participated in the development of the programs that made thesecalculations possible and in preparation of this manuscript.Conflicts of Interest: The authors declare no conflict of interest.References1. Hawryluk, R.J.; Campbell, D.J.; Janeschitz, G.; Thomas, P.R.; Albanese, R.; Ambrosino, R.; Bachmann, C.;Baylor, L.; Becoulet, M.; Benfatto, I.; et al. Principal physics developments evaluated in the ITER designreview. Nucl. Fusion 2009, 49, 065012.2. Ralchenko, Y.; Draganic´, I.N.; Osin, D.; Gillaspy, J.; Reader, J. Spectroscopy of diagnostically importantmagnetic-dipole lines in highly charged 3dn ions of tungsten. Phys. Rev. A 2011, 83, 032517.3. Gu, M.F. The flexible atomic code. Can. J. Phys. 2008, 86, 675–689.4. Kramida, A. Recent progress in spectroscopy of tungsten. Can. J. Phys. 2011, 89, 551–570.Atoms 2017, 5, 7 34 of 345. Kramida, A.; Ralchenko, Y.; Reader, J.; NIST ASD Team. NIST Atomic Spectra Database (Ver. 5.2); National Instituteof Standards and Technology: Gaithersburg, MD, USA, 2014. Available online: http://physics.nist.gov/asd(accessed on 28 December 2014).6. Quinet, P. Dirac-Fock calculations of forbidden transitions within the 3pk and 3dk ground configurations ofhighly charge tungsten ions (W47+ – W61+). J. Phys. B: At. Mol. Opt. Phys. 2011, 44, 195007.7. Norrington, P.H. GRASP0 Manual. 2009, unpublished.8. Guo, X.L.; Huang, M.; Yan, J.; Li, S.; Si, R.; Li, C.Y.; Chen, C.Y.; Wang, Y.S.; Zou, Y.M. Relativistic many-bodycalculations on wavelengths and transition probabilities for forbidden transitions within the 3dk groundconfigurations in Co- through K-like ions of hafnium, tantalum, tungsten, and gold. J. Phys. B Atomic Mol.Opt. Phys. 2015, 48, 144020.9. Lindgren, I. The Rayleigh-Schrodinger perturbation and the linked-diagram theorem for a multi-configurationalmodel space. J. Phys. B Atomic Mol. Opt. Phys. 1974, 7, 2441.10. Jönsson, P.; Gaigalas, G.; Bieron´, J.; Froese Fischer, C.; Grant, I.P. New Version: Grasp2K relativistic atomicstructure package. Comput. Phys. Commun. 2013, 184, 2197–2203.11. Grant, I.P. Relativistic Quantum Theory of Atoms and Molecules; Springer: New York, NY, USA, 2007.12. Froese Fischer, C.; Godefroid, M.; Brage, T.; Jönsson, P.; Gaigalas, G. Advanced multiconfiguration methodsfor complex atoms: Part I—Energies and wave functions. J. Phys. B Atomic Mol. Opt. Phys. 2016, 49, 182004.13. Verdebout, S.; Rynkun, P.; Jönsson, P.; Gaigalas, G.; Froese Fischer, C.; Godefroid, M. A partitioned correlationfunction interaction approach for describing electron correlation in atoms. J. Phys. B Atomic Mol. Opt. Phys.2013, 46, 085003.14. McKenzie, B.J.; Grant, I.P.; Norrington, P.H. A program to calculate transverse Breit and QED corrections toenergy levels in a multiconfiguration Dirac-Fock environment. Comput. Phys. Commun. 1980, 21, 233–246.15. Bentley, M; Fischer, C.F. Hypercube conversion of serial codes for atomic structure calculations.Parallel Comput. 1992, 18, 1023–1031.16. Fischer, C.F.; Tong, M.; Bentley, M.; Shen, Z.; Ravimohan, C. The Distributed-memory implementation of theMCHF atomic structure package. J. Supercomput. 1994, 8, 117–134.17. Safronova, U.I.; Safronova, A.S. Wavelengths and transition rates for nl− n′l′ transitions in Be-, B-, Mg-, Al-,Ca-, Zn-, Ag-, and Yb-like tungsten ions. J. Phys. B Atomic Mol. Opt. Phys. 2010, 43, 074026.c© 2017 by the authors; licensee MDPI, Basel, Switzerland. This article is an open accessarticle distributed under the terms and conditions of the Creative Commons Attribution(CC BY) license (http://creativecommons.org/licenses/by/4.0/).
Article
eng
Reviewed
Vancouver : University of British Columbia Library
Multidisciplinary Digital Publishing Institute
CC BY 4.0
Faculty
Corecorrelationeffects
Energylevels
MulticonfigurationDirac-Hartree-Fock
Tungstenions
Core Effects on Transition Energies for 3dk Conﬁgurations in Tungsten Ions
Text