Research Article Atomic Structure Calculations for Neutral...

Research ArticleAtomic Structure Calculations for Neutral Oxygen

Norah Alonizan Rabia Qindeel and Nabil Ben Nessib

Department of Physics and Astronomy College of Science King Saud University PO Box 2455 Riyadh 11451 Saudi Arabia

Correspondence should be addressed to Nabil Ben Nessib nbennessibksuedusa

Received 30 November 2015 Revised 28 March 2016 Accepted 4 May 2016

Academic Editor Karol Jackowski

Copyright copy 2016 Norah Alonizan et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Energy levels and oscillator strengths for neutral oxygen have been calculated using the Cowan (CW) SUPERSTRUCTURE (SS)and AUTOSTRUCTURE (AS) atomic structure codes The results obtained with these atomic codes have been compared withMCHF calculations and experimental values from the National Institute of Standards and Technology (NIST) database

1 Introduction

Oxygen atom (O I) is themost abundant element after hydro-gen andhelium in theUniverse Its spectroscopic study is veryimportant for the knowledge of the structure of stars galaxiesand in general the whole Universe It is also important forstudying the life on the earth and the possibility of life onother planets or exoplanetsThe studies of earthrsquos atmosphereand its radiative properties need these data Industrial andtechnical applications need the characteristics of this element

Pradhan and Saraph [1] calculated oscillator strengths fordipole transitions in O I using the SUPERSTRUCTURE (SS)code [2] with spectroscopic type orbitals for 1s 2s and 2p andcorrelation type orbitals for the 3d Tayal and Henry [3] cal-culated oscillator strengths and electron collisional excitationcross sections for O I They used the Hibbert CIV3 atomicstructure code [4] with the eight orthogonal one-electronorbitals 1s 2s 2p 3s 3p 3d 4s and 4p Using the sameCIV3 atomic structure code Bell and Hibbert [5] calculatedoscillator strengths for allowed transitions in O I with moresingle electron orbitals Hibbert et al (HBGV) [6] used theCIV3 code to calculate E1 transitions connecting the 119899 = 3

and 119899 = 4 energy levels in O I Biemont et al [7] calculateoscillator strengths of astrophysical interest for O I using theCIV3 configuration interaction code and the Hartree-Fockpseudorelativistic (HFR) suite of Cowan (CW) codes [8]Using the SS code Biemont and Zeippen [9] calculated oscil-lator strengths for 2p4-3s and 3s-3p allowed or spin-forbiddentransitions in O I Zheng and Wang [10] used the Weakest

Bound Electron Potential Model (WBEPM) theory to calcu-late radiative lifetime transition probabilities and oscillatorstrengths for atomic carbon and oxygen Using the Multi-configuration Hartree-Fock (MCHF) method [11] Tachievand Froese Fischer (TFF) [12] calculated ab initio Breit-Pauli energy levels and transition rates for nitrogen-like andoxygen-like sequences Froese Fischer and Tachiev (FFT) [13]calculated Breit-Pauli energy levels lifetimes and transitionprobabilities for the beryllium-like to neon-like sequences inthe adjusted with experimental values Fan et al [14] used theWBEPMT theory to calculate energy levels of high states inO I Celik and Ates [15] employed the WBEPMT theory tocalculate radial transition matrix elements and then atomictransition probabilities for O I

Using CW or SS or AS codes we did atomic structurecalculations for several atoms and ions [16ndash18] that areneeded for ab initio Stark broadening calculations [19 20] andfor emission line ratio calculations [21] butwe never compareresults obtained by the three codes for the same element

About O I atomic data in databases we used the NationalInstitute of Standards and Technology (NIST) data [22] forfine structure energy levels and oscillator strengths Thereare energy levels and oscillator strengths of O I withoutfine structure in the Opacity Project TOPbase [23] andNORAD-Atomic-Data [24] atomic structure databases TIP-base database [25] of the Opacity Project used NIST data forthe fine structure energy levels and Galavis et al [26] data forthe oscillator strengths fine structure data Galavis et al [26]used the SS atomic structure code with spectroscopic type

Hindawi Publishing CorporationInternational Journal of SpectroscopyVolume 2016 Article ID 1697561 7 pageshttpdxdoiorg10115520161697561

2 International Journal of Spectroscopy

Table 1 The scaling parameters used after minimization for the SS and AS atomic structure codes

Scaling parameters 1s 2s 2p 3s 3p 3d 4s120582119899ℓ(SS) 123103 123103 115865 123103 115865 092431 123103

120582119899ℓ(AS) 155498 116135 120894 107693 238871 091505 233806

orbitals for 1s 2s and 2p and correlation type orbitals for 3s3p 3d and 4f

In the Chianti project [27] they used the NIST databasefor experimental energy levels and oscillator strengths Fortheoretical energy levels they used the Zatsarinny and Tayal[28] and FFT [13] for the theoretical oscillator strengths

In this work we will calculate atomic data for transitionswith fine structure in O I using CW and SS and AS codesComparison with other theoretical and experimental dataavailable in the literature will be presented

2 Methods for Calculation

21 Hartree-Fock Pseudorelativistic (HFR) Method In thismethod a set of orbitals are obtained for each electronconfiguration by solving the Hartree-Fock equations [8]A totally antisymmetric wave-function is a combination ofsingle electron solution of the hydrogen atom Ψ (Slaterdeterminant)

Ψ =1

radic119873

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1205951(1) 120595

1(2) sdot sdot sdot 120595

1(119873)

1205952(1) 120595


2(119873)

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

120595119873(1) 120595

119873(2) sdot sdot sdot 120595

119873(119873)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1)

120595119895(119894) means that the 119894th electronrsquos space and spin are in the

one-electron state 120595119895 This will automatically satisfy the Pauli

principle because a determinant vanishes if two columns arethe same

Relativistic corrections are introduced by a Breit-PauliHamiltonian and treated by the perturbation theory Therelativistic corrections include the Blume-Watson spin-orbitmass-variation and one-body Darwin terms The Blume-Watson spin-orbit term contains the part of the Breit inter-action that can be reduced to a one-body operator

The Cowan (CW) atomic structure suite of codes (RCNRNC2 RCG and RCE) uses this HFRmethodThe three firstcodes are for ab initio atomic structure calculations and thefourth one (RCE) is used tomake least-squares fit calculationsusing an iterative procedure

22 Thomas-Fermi-Dirac-Amaldi (TFDA) Method In thismethod and to have atomic parameters of an atom or ion astatistical TFDA potential is used For an atom or ion having119885 protons and 119873 electrons this potential is in the followingform [29]

119881 (119903) =119885eff (120582119899ℓ 119903)

119903= minus

119885

119903120601 (119909) (2)

where

120601 (119909) = 119890minus1198851199032

+ 120582119899ℓ(1 minus 119890

minus1198851199032) 119909 =

119903

120583(3)

with 120583 the constant

120583 =1

4(

119873

119873 minus 1)

23

(91205872

2119885)

13

asymp 08853 (119873

119873 minus 1)

23

119885minus13

(4)

and 120582119899ℓare the orbital scaling parameters

The function 120601 verifies the following equation

1198892120601

1198891199092=

1

radic119909120601 (119909)32 (5)

with the boundary conditions

120601 (0) = 1

120601 (infin) = minus119885 minus 119873 + 1

119885

(6)

The SUPERSTRUCTURE (SS) and AUTOSTRUCTURE(AS) atomic structure codes use this method Relativisticcorrections are also done by a perturbationmethod using theBreit-Pauli Hamiltonian The SS atomic structure code usedin this work [30] is an updated version of the original one of1974 [2] Some relativistic corrections are introduced in thisversion and orbital scaling parameters120582

119899ℓare dependent on 119899

and ℓ [31] and not like the original SS version of 1974 wherescaling parameters were depending only on ℓ (120582

ℓ) The AS

code [32 33] is an extension of the SS code incorporating var-ious improvements and new capabilities like two-body non-fine-structure operators of the Breit-Pauli Hamiltonian andpolarization model potentials Comparing the two atomicstructure codes SS and AS we can see that even they used thesame techniques in general they gave different results mainlybecause they incorporated different relativistic corrections ofthe Hamiltonian For the comparison between the two codeswe can refer to the work of Elabidi and Sahal-Brechot [34]where they studied excitation cross section by electron impactfor O V and O VI levels They showed that the incorporationof the two-body non-fine-structure operators (contact spin-spin two-body Darwin and orbit-orbit) in AS and not in theinitial SS code is the main reason of the different resultsobtained by the two codes

International Journal of Spectroscopy 3

Table 2 Energy levels for configuration 2s2 2p4 E(NIST) are fromNIST database [22] E(CW) E(SS) and E(AS) are energy levels calculatedusing respectively the Cowan SUPERSTRUCTURE and AUTOSTRUCTURE atomic codes E(TFF) are energy levels values from Tachievand Froese Fisher [12] All energies are in cmminus1

Configuration Term J E(NIST) E(CW) E(SS) E(AS) E(TFF)2s22p4 3P 2 0 0 0 0 02s22p4 3P 1 158 141 171 204 1562s22p4 3P 0 227 210 255 303 2232s22p4 1D 2 15868 14941 18881 17364 161222s22p4 1S 0 33793 37013 45746 42140 33844

Table 3 The same as Table 2 for configuration 2s2 2p3 3s

Configuration Term J E(NIST) E(CW) E(SS) E(AS) E(TFF)2s22p3(4S∘)3s 5S∘ 2 73768 70285 50342 67409 740122s22p3(4S∘)3s 3S∘ 1 76795 72704 54546 70365 769102s22p3(2D∘)3s 3D∘ 3 101135 96475 80769 99037 mdash2s22p3(2D∘)3s 3D∘ 2 101148 96474 80768 99036 mdash2s22p3(2D∘)3s 3D∘ 1 101155 96473 80767 99035 mdash2s22p3(2D∘)3s 1D∘ 2 102662 97684 82871 100502 mdash2s22p3(2P∘)3s 3P∘ 2 113911 113471 100024 119170 mdash2s22p3(2P∘)3s 3P∘ 1 113921 113469 100023 119169 mdash2s22p3(2P∘)3s 3P∘ 0 113928 113468 100022 119168 mdash2s22p3(2P∘)3s 1P∘ 1 115918 114666 101453 121545 mdash

Table 4 The same as Table 2 for configuration 2s2 2p3 3p except that we did not put the AS data because they are too far from the otherresults

Configuration Term J E(NIST) E(CW) E(SS) E(TFF)2s22p3(4S∘)3p 5P 1 86626 83148 62276 866452s22p3(4S∘)3p 5P 2 86628 83149 62279 866472s22p3(4S∘)3p 5P 3 86631 83152 62284 866502s22p3(4S∘)3p 3P 1 88631 85516 67495 885902s22p3(4S∘)3p 3P 2 88631 85519 67492 885912s22p3(4S∘)3p 3P 0 88631 85514 67497 885912s22p3(2D∘)3p 1P 1 113204 108935 91748 mdash2s22p3(2D∘)3p 3D 3 113295 108877 91674 mdash2s22p3(2D∘)3p 3D 2 113295 108871 91665 mdash2s22p3(2D∘)3p 3D 1 113298 108864 91655 mdash2s22p3(2D∘)3p 3F 4 113714 109075 92012 mdash2s22p3(2D∘)3p 3F 3 113721 109072 92007 mdash2s22p3(2D∘)3p 3F 2 113727 109069 92003 mdash2s22p3(2D∘)3p 1F 3 113996 109318 92419 mdash2s22p3(2D∘)3p 1D 2 116631 113447 101312 mdash2s22p3(2P∘)3p 3D 3 127283 126148 111485 mdash2s22p3(2P∘)3p 3D 2 127288 126149 111486 mdash2s22p3(2P∘)3p 3D 1 127292 126149 111485 mdash2s22p3(2P∘)3p 1P 1 127668 126335 111820 mdash2s22p3(2P∘)3p 1D 2 128595 127944 115611 mdash2s22p3(2P∘)3p 1S 0 130943 132423 111145 mdash2s22p3(2D∘)3p 3P 1 mdash 111274 96720 mdash2s22p3(2D∘)3p 3P 2 mdash 111280 96730 mdash2s22p3(2D∘)3p 3P 0 mdash 111272 96715 mdash2s22p3(2P∘)3p 3P 1 mdash 127427 113836 mdash2s22p3(2P∘)3p 3P 2 mdash 127418 113812 mdash2s22p3(2P∘)3p 3P 0 mdash 127432 113848 mdash


Table 5 The same as Table 2 for configuration 2s2 2p3 3d

Configuration Term J E(NIST) E(CW) E(SS) E(AS) E(TFF)2s22p3(4S∘)3d 5D∘ 4 97421 94227 72721 89755 971472s22p3(4S∘)3d 5D∘ 3 97421 94227 72721 89755 971472s22p3(4S∘)3d 5D∘ 2 97421 94227 72721 89755 971472s22p3(4S∘)3d 5D∘ 1 97421 94227 72721 89755 971472s22p3(4S∘)3d 5D∘ 0 97421 94227 72721 89754 971482s22p3(4S∘)3d 3D∘ 1 97488 94299 72820 89836 972052s22p3(4S∘)3d 3D∘ 2 97488 94299 72820 89836 972052s22p3(4S∘)3d 3D∘ 3 97489 94299 72821 89836 972052s22p3(2D∘

32)3d 3P∘ 2 123297 120045 102401 120957 mdash

2s22p3(2D∘32)3d 3P∘ 1 123356 120049 102405 120959 mdash

2s22p3(2D∘32)3d 3P∘ 0 123387 120050 102406 120961 mdash

2s22p3(2D∘52)3d 3F∘ 4 124214 119938 102042 120523 mdash

2s22p3(2D∘52)3d 3F∘ 3 124219 119935 102039 120520 mdash

2s22p3(2D∘52)3d 3F∘ 2 124224 119934 102037 120518 mdash

2s22p3(2D∘)3d 3G∘ 4 124239 119945 102051 120530 mdash2s22p3(2D∘)3d 3G∘ 5 124240 119946 102053 120531 mdash2s22p3(2D∘

52)3d 1S∘ 0 124243 119935 102037 120519 mdash

2s22p3(2D∘52)3d 3D∘ 3 124247 119957 102070 120544 mdash

2s22p3(2D∘)3d 3G∘ 3 124253 119944 102051 120529 mdash2s22p3(2D∘

52)3d 3D∘ 2 124258 119958 102072 120545 mdash

2s22p3(2D∘32)3d 1G∘ 4 124259 119952 102061 120538 mdash

2s22p3(2D∘52)3d 3D∘ 1 124264 119959 102072 120546 mdash

2s22p3(2D∘52)3d 1P∘ 1 124274 120043 103055 120030 mdash

2s22p3(2D∘32)3d 1D∘ 2 124319 120017 102181 120609 mdash

2s22p3(2D∘32)3d 1F∘ 3 124327 120033 102174 120629 mdash

2s22p3(2D∘32)3d 3S∘ 1 124336 120002 102133 120577 mdash

2s22p3(2P∘)3d 1D∘ 2 137928 137105 121625 141057 mdash2s22p3(2P∘)3d 3P∘ 0 137947 137093 121609 141050 mdash2s22p3(2P∘)3d 3P∘ 1 137947 137094 121611 141052 mdash2s22p3(2P∘)3d 3P∘ 2 137947 137097 121615 141054 mdash2s22p3(2P∘)3d 3D∘ 1 137963 137117 121642 141063 mdash2s22p3(2P∘)3d 3D∘ 2 137963 137119 121645 141066 mdash2s22p3(2P∘)3d 3D∘ 3 137963 137121 121647 141067 mdash2s22p3(2P∘)3d 1P∘ 1 137981 137186 121755 141153 mdash2s22p3(2P∘)3d 3F∘ 4 mdash 137084 121596 141041 mdash2s22p3(2P∘)3d 3F∘ 3 mdash 137085 121597 141041 mdash2s22p3(2P∘)3d 3F∘ 2 mdash 137085 121597 141041 mdash2s22p3(2P∘)3d 1F∘ 3 mdash 137136 121667 141098 mdash

3 Results and Discussion

31 Energy Levels We performed ab initio calculations ofenergy levels for O I using the three atomic structure codesCW SS and AS with the 5 configurations expansion 2p4 2p3

3s 2p3 3p 2p3 3d and 2p3 4sThis same set of configurationsexpansion was used by Tachiev and Froese Fischer (TFF)in the ab initio calculations [12] and by Froese Fischer andTachiev in the adjusted with experimental values calculations[13] For the SS and AS atomic codes the scaling parametersare determined variationally byminimizing the sum of all thenonrelativistic term energies (Table 1)

In Tables 2ndash6 calculated fine structure energy levels arepresented The obtained values are compared with the NISTatomic database [22] and with Tachiev and Froese Fischer abinitio calculations [12] using the Multiconfiguration Hartree-Fock (MCHF) method [11]

For the fundamental configuration 2s2 2p4 CW codegives 7 difference fromNIST values while SS and AS codesgive respectively 15 and 19 difference from NIST valuesWith CW code and for the other four excited configurations(2p3 3ℓ ℓ = 0 1 2 and 2p3 4s) the agreement with NISTvalues is about 3 while SS and AS give an agreement ofabout 20 with the NIST values except for 2p3 3s where



Configuration Term J E(NIST) E(CW) E(SS) E(AS) E(TFF)2s22p3(4S∘)4s 5S∘ 2 95477 92425 71070 110558 955762s22p3(4S∘)4s 3S∘ 1 96225 93053 72757 122242 962642s22p3(2D∘)4s 3D∘ 3 122420 118248 100741 144123 mdash2s22p3(2D∘)4s 3D∘ 2 122433 118247 100740 144121 mdash2s22p3(2D∘)4s 3D∘ 1 122441 118246 100739 144121 mdash2s22p3(2D∘

32)4s 1D∘ 2 122798 118560 101552 149959 mdash

2s22p3(2P∘)4s 3P∘ 0 135682 135369 120288 164620 mdash2s22p3(2P∘)4s 3P∘ 1 135682 135370 120289 164621 mdash2s22p3(2P∘)4s 3P∘ 2 135682 135372 120291 164623 mdash2s22p3(2P∘)4s 1P∘ 1 136353 135684 121113 170467 mdash

Table 7 Oscillator strengths for 3 multiplets 2p4-2p3(4S) 3s 3S∘ 119892119894and 119892

119896are respectively the statistical weights of initial and final

levels of the transition gf(NIST) are from NIST database [22] gf(CW) gf(SS) and gf(AS) are calculated using respectively the CowanSUPERSTRUCTURE and AUTOSTRUCTURE atomic codes gf(FFT) are values from Froese Fisher and Tachiev [13] and gf(HBGV) arevalues from Hibbert et al [6]

Terms 119892119894

119892119896

120582 (A) gf(NIST) gf(CW) gf(SS) gf(AS) gf(FFT) gf(HBGV)3P-3S∘ 1 3 130603 519119864 minus 02 726119864 minus 02 139119864 minus 01 513119864 minus 02 478119864 minus 02 529119864 minus 02

3P-3S∘ 3 3 130486 156119864 minus 01 218119864 minus 01 417119864 minus 01 154119864 minus 01 143119864 minus 01 159119864 minus 01


1D-3S∘ 5 3 164131 222119864 minus 06 604119864 minus 06 131119864 minus 05 695119864 minus 06 213119864 minus 06 mdash1S-3S∘ 1 3 232474 112119864 minus 08 308119864 minus 09 160119864 minus 08 550119864 minus 08 159119864 minus 10 mdash

Table 8 The same as Table 7 for 4 multiplets 2p3(4S)3s S∘-2p3(4S) 3p P∘

Terms 119892119894

119892119896

120582 (A) gf(NIST) gf(CW) gf(SS) gf(AS) gf(FFT) gf(HBGV)5S∘-5P∘ 5 3 777539 100119864 + 00 109119864 + 00 950119864 minus 01 200119864 + 00 967119864 minus 01 101119864 + 00

5S∘-5P∘ 5 5 777417 167119864 + 00 181119864 + 00 158119864 + 00 333119864 + 00 161119864 + 00 168119864 + 00

5S∘-5P∘ 5 7 777194 234119864 + 00 254119864 + 00 222119864 + 00 467119864 + 00 226119864 + 00 235119864 + 00

5S∘-3P∘ 5 3 672654 131119864 minus 05 573119864 minus 07 921119864 minus 06 710119864 minus 05 102119864 minus 05 mdash5S∘-3P∘ 5 5 672628 400119864 minus 05 177119864 minus 06 281119864 minus 05 218119864 minus 04 351119864 minus 05 mdash3S∘-5P∘ 3 3 1016935 916119864 minus 06 286119864 minus 06 168119864 minus 05 443119864 minus 05 791119864 minus 06 mdash3S∘-5P∘ 3 5 1016726 280119864 minus 05 465119864 minus 08 551119864 minus 06 136119864 minus 04 274119864 minus 05 mdash3S∘-3P∘ 3 1 844625 344119864 minus 01 388119864 minus 01 381119864 minus 01 420119864 minus 01 339119864 minus 01 360119864 minus 01

3S∘-3P∘ 3 3 844676 103119864 + 00 116119864 + 00 114119864 + 00 126119864 + 00 102119864 + 00 108119864 + 00

3S∘-3P∘ 3 5 844636 172119864 + 00 194119864 + 00 191119864 + 00 210119864 + 00 170119864 + 00 180119864 + 00

the agreement of AS with NIST is 4 and 7 for 2p3 3dAS gives bad energy levels (one hundred greater values) forthe 2p3 3p configuration comparing to the other data andthe calculated values are not reported in Table 4 TFF energylevels are less than 1near theNIST values but there aremanymissed values (they give energy levels for only 24 of theNIST data for the 4 excited configurations 2p3 119899ℓ)

We obtain six energy levels for the 2p3 3p configuration(2p3(2D∘)3p 3P

012and 2p3(2P∘)3p 3P

012) and four new

energy levels for the 2p3 3d configuration (2p3(2P∘)3d 3F234

and 2p3(2P∘)3d 1F3) which are not in the NIST atomic

database (see the end of Tables 4 and 5)

32 Oscillator Strengths We have also computed oscillatorstrengths for threemultiplets of the transition 2p4-2p3 3s four

multiplets of the transition 2p3 3s-2p3 3p onemultiplet of thetransition 2p4-3d and fourmultiplets of the transition 2p3 3p-2p3 3d using the atomic structure codes CW SS and AS (seeTables 7ndash10) They are compared with those of FFT [13] andHBGV [6] and tabulated in NIST [22] Our calculations withCW code give an agreement of about 2 with NIST valueswhile FFT gives 8 with the NIST ones The HBGV valueshave an agreement of 2 with the NIST ones but many dataare missing

4 Conclusions

The comparison between the energy levels calculated bythe different atomic codes indicates that the agreementwith NIST data is generally less than 20 except for the


Table 9 The same as Table 7 for the multiplet 2p4 3P-2p3(4S) 3d 3D∘

Terms 119892119894

119892119896

120582 (A) gf(NIST) gf(CW) gf(SS) gf(AS) gf(FFT) gf(HBGV)3P- 3D∘ 5 7 102576 845119864 minus 02 35119864 minus 01 129119864 + 00 105119864 minus 01 817119864 minus 02 893119864 minus 02

3P-3D∘ 5 5 102576 151119864 minus 02 624119864 minus 02 231119864 minus 01 187119864 minus 02 146119864 minus 02 159119864 minus 02





3P-5D∘ 5 7 102647lowast mdash 845119864 minus 09 100119864 minus 06 579119864 minus 09 435119864 minus 07 mdash3P-5D∘ 5 5 102647lowast mdash 113119864 minus 07 325119864 minus 06 436119864 minus 08 365119864 minus 08 mdash3P-5D∘ 5 3 102647lowast mdash 664119864 minus 08 160119864 minus 06 387119864 minus 08 714119864 minus 09 mdash3P-5D∘ 3 5 102812lowast mdash 132119864 minus 08 176119864 minus 08 366119864 minus 08 110119864 minus 07 mdash3P-5D∘ 3 3 102812lowast mdash 448119864 minus 08 133119864 minus 06 mdash 107119864 minus 07 mdash3P-5D∘ 1 3 102883lowast mdash 385119864 minus 08 562119864 minus 07 mdash 144119864 minus 07 mdashlowastWavelengths are from FFT

Table 10 The same as Table 7 for 4 multiplets 2p3(4S) 3p P-2p3(4S) 3d D∘

Terms 119892119894

119892119870

120582 (A) gf(NIST) gf(CW) gf(SS) gf(AS) gf(FFT) gf(HBGV)5P-3D∘ 5 7 920493 148119864 minus 04 105119864 minus 05 115119864 minus 05 183119864 minus 05 844119864 minus 05 150119864 minus 04


5P-5D∘ 3 3 926085 129119864 + 00 151119864 + 00 122119864 + 00 243119864 minus 01 133119864 + 00 152119864 + 00

5P-5D∘ 3 5 926094 100119864 + 00 118119864 + 00 949119864 minus 01 189119864 minus 01 103119864 + 00 118119864 + 00


5P-5D∘ 5 5 926267 167119864 + 00 196119864 + 00 158119864 + 00 315119864 minus 01 172119864 + 00 168119864 + 00

5P-5D∘ 5 7 926278 267119864 + 00 313119864 + 00 253119864 + 00 504119864 minus 01 275119864 + 00 269119864 + 00


5P-5D∘ 7 7 926593 133119864 + 00 157119864 + 00 127119864 + 00 252119864 minus 01 138119864 + 00 134119864 + 00

5P-5D∘ 7 9 926601 515119864 + 00 605119864 + 00 488119864 + 00 973119864 minus 01 531119864 + 00 519119864 + 00

3P-3D∘ 3 5 1128632 222119864 + 00 197119864 + 00 964119864 minus 01 307119864 minus 01 202119864 + 00 220119864 + 00


3P-3D∘ 5 7 1128691 413119864 + 00 368119864 + 00 180119864 + 00 571119864 minus 01 377119864 + 00 410119864 + 00






configuration 2p3 3p where the SS gives 20 greater valuesthan NIST and CW gives only 3 greater values than NIST

We obtained respectively six and four energy levelscorresponding to the configurations 2p3 3p and 2p3 3d whichare not in the NIST atomic database

TFF energy levels values are nearly the same comparedto NIST ones with less than 1 difference but many energylevels are missed in these calculations

When comparing oscillator strengths calculated by AScode we obtain good agreement with NIST

We can say that there is no best atomic code to use andwe have to calculate atomic structure data with more thanone code to compare results between them and with othertheoretical and experimental sources

Competing Interests

The authors declare that there are no competing interestsregarding the publication of this paper

Acknowledgments

The project was supported by the Research Center College ofScience King Saud University

References

[1] A K Pradhan andH E Saraph ldquoOscillator strengths for dipoletransitions in neutral oxygenrdquo Journal of Physics B Atomic andMolecular Physics vol 10 no 17 pp 3365ndash3376 1977


[2] W Eissner M Jones and H Nussbaumer ldquoTechniques for thecalculation of atomic structures and radiative data includingrelativistic correctionsrdquoComputer Physics Communications vol8 no 4 pp 270ndash306 1974

[3] S S Tayal and R J W Henry ldquoOscillator strengths and electroncollisional excitation cross sections for atomic oxygenrdquo PhysicalReview A vol 39 no 9 pp 4531ndash4536 1989

[4] A Hibbert ldquoCIV3mdasha general program to calculate configura-tion interaction wave functions and electric-dipole oscillatorstrengthsrdquo Computer Physics Communications vol 9 no 3 pp141ndash172 1975

[5] K L Bell and A Hibbert ldquoOscillator strengths for allowedtransitions in atomic oxygenrdquo Journal of Physics B vol 23 no 16pp 2673ndash2685 1990

[6] A Hibbert E Biemont M Godefroid and N Vaeck ldquoE1 tran-sitions of astrophysical interest in neutral oxygenrdquo Journal ofPhysics B Atomic Molecular and Optical Physics vol 24 no 18pp 3943ndash3958 1991

[7] E Biemont A Hibbert M Godefroid N Vaeck and B CFawcett ldquoAccurate oscillator strengths of astrophysical interestfor neutral oxygenrdquoTheAstrophysical Journal vol 375 no 2 pp818ndash822 1991

[8] R D CowanTheory of Atomic Structure and Spectra Universityof California Press Berkeley Calif USA 1981

[9] E Biemont and C J Zeippen ldquoElectric dipole transitions inatomic oxygen and the lifetimes of the 2p(3)(4S0)3s5S0 and 3S0statesrdquo Astronomy amp Astrophysics vol 265 no 2 pp 850ndash8561992

[10] N Zheng and T Wang ldquoRadiative lifetimes and atomic tran-sition probabilities for atomic carbon and oxygenrdquo The Astro-physical Journal Supplement Series vol 143 no 1 p 231 2002

[11] C Froese Fischer T Brage and P Jonsson ComputationalAtomic Structure An MCHF Approach Institute of PhysicsPublishing Bristol UK 1997

[12] G I Tachiev and C F Fischer ldquoBreit-Pauli energy levels andtransition rates for nitrogen-like and oxygen-like sequencesrdquoAstronomy and Astrophysics vol 385 no 2 pp 716ndash723 2002

[13] C Froese Fischer and G Tachiev ldquoBreit-Pauli energy levelslifetimes and transition probabilities for the beryllium-like toneon-like sequencesrdquoAtomicData andNuclearData Tables vol87 no 1 pp 1ndash184 2004

[14] J Fan N W Zheng D X Ma and T Wang ldquoCalculation of theenergy levels to high states in atomic oxygenrdquo Physica Scriptavol 69 no 5 pp 398ndash402 2004

[15] G Celik and S Ates ldquoThe calculation of transition probabilitiesfor atomic oxygenrdquo European Physical Journal D vol 44 no 3pp 433ndash437 2007

[16] N BenNessib H Elabidi M Cornille and J Dubau ldquoRadiativeand collisional atomic data for neon-like siliconrdquo PhysicaScripta vol 72 no 1 pp 23ndash30 2005

[17] H Elabidi S Sahal-Brechot and N B Nessib ldquoFine structurecollision strengths for S VII linesrdquo Physica Scripta vol 85 no 6Article ID 065302 2012

[18] R Hamdi and N Ben Nessib ldquoElectric dipole transition prob-abilities in Al IV and Al V ionsrdquoMemorie della SAIt vol 7 pp228ndash229 2005

[19] N Ben Nessib ldquoAb initio calculations of Stark broadeningparametersrdquo New Astronomy Reviews vol 53 no 7-10 pp 255ndash258 2009

[20] R Hamdi N Ben Nessib M S Dimitrijevic and S Sahal-Brechot ldquoStark broadening of Pb IV spectral linesrdquo Monthly

Notices of the Royal Astronomical Society vol 431 no 2 pp1039ndash1047 2013

[21] N Ben Nessib N Alonizan R Qindeel S Sahal-Brechot andM S Dimitrijevic ldquoThe OIV 14073 A 14011 A emission-lineratio in a plasmardquo Advances in Space Research vol 54 no 7 pp1190ndash1194 2014

[22] A Kramida Yu Ralchenko J Reader and NIST ASD TeamNIST Atomic Spectra Database (ver 53) National Instituteof Standards and Technology Gaithersburg Md USA 2015httpphysicsnistgovasd

[23] httpcdswebu-strasbgfrtopbasetopbasehtml[24] httpwwwastronomyohio-stateedusimnaharnahar radiative-

atomicdataindexhtml[25] httpcdswebu-strasbgfrtipbasehomehtml[26] M EGalavis CMendoza andC J Zeippen ldquoAtomic data from

the IRON Project-XXII Radiative rates for forbidden transi-tions within the ground configuration of ions in the carbon andoxygen isoelectronic sequencesrdquo Astronomy and Astrophysicsvol 123 no 1 pp 159ndash171 1997

[27] httpwwwchiantidatabaseorgchiantihtml[28] O Zatsarinny and S S Tayal ldquoElectron collisional excitation

rates for O I using the B-spline R-matrix approachrdquo Astrophysi-cal Journal Supplement Series vol 148 no 2 pp 575ndash582 2003

[29] A K Pradhan and S N Nahar Atomic Astrophysics and Spec-troscopy Cambridge University Press Cambridge UK 2011

[30] S NNaharW Eissner G-X Chen andA K Pradhan ldquoAtomicdata from the Iron Project LIII Relativistic allowed and for-bidden transition probabilities for Fe XVIIrdquo Astronomy andAstrophysics vol 408 no 2 pp 789ndash801 2003

[31] H Nussbaumer and P J Storey ldquoBound-bound radiative transi-tions in C Irdquo Astronomy amp Astrophysics vol 140 no 2 pp 383ndash389 1984

[32] N R Badnell ldquoOn the effects of the two-body non-fine-structure operators of the BreitmdashPauli Hamiltonianrdquo Journal ofPhysics B Atomic Molecular and Optical Physics vol 30 no 1pp 1ndash11 1997

[33] N R Badnell ldquoA Breit-Pauli distorted wave implementation forautostructurerdquo Computer Physics Communications vol 182 no7 pp 1528ndash1535 2011

[34] H Elabidi and S Sahal-Brechot ldquoExcitation cross-sections byelectron impact for OV and OVI levelsrdquoMonthly Notices of theRoyal Astronomical Society vol 436 no 2 pp 1452ndash1464 2013

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Inorganic ChemistryInternational Journal of

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014

International Journal ofPhotoenergy


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Advances in

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Hindawi Publishing Corporationhttpwwwhindawicom

Analytical Methods in Chemistry

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Bioinorganic Chemistry and ApplicationsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

SpectroscopyInternational Journal of


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Applied ChemistryJournal of



Theoretical ChemistryJournal of


Journal of

Spectroscopy

Analytical ChemistryInternational Journal of


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Quantum Chemistry


Organic Chemistry International

ElectrochemistryInternational Journal of



CatalystsJournal of


Table 1 The scaling parameters used after minimization for the SS and AS atomic structure codes

Scaling parameters 1s 2s 2p 3s 3p 3d 4s120582119899ℓ(SS) 123103 123103 115865 123103 115865 092431 123103

120582119899ℓ(AS) 155498 116135 120894 107693 238871 091505 233806

orbitals for 1s 2s and 2p and correlation type orbitals for 3s3p 3d and 4f

In the Chianti project [27] they used the NIST databasefor experimental energy levels and oscillator strengths Fortheoretical energy levels they used the Zatsarinny and Tayal[28] and FFT [13] for the theoretical oscillator strengths

In this work we will calculate atomic data for transitionswith fine structure in O I using CW and SS and AS codesComparison with other theoretical and experimental dataavailable in the literature will be presented

2 Methods for Calculation

21 Hartree-Fock Pseudorelativistic (HFR) Method In thismethod a set of orbitals are obtained for each electronconfiguration by solving the Hartree-Fock equations [8]A totally antisymmetric wave-function is a combination ofsingle electron solution of the hydrogen atom Ψ (Slaterdeterminant)

Ψ =1

radic119873

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

1205951(1) 120595


1(119873)

1205952(1) 120595


2(119873)

sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot sdot

120595119873(1) 120595

119873(2) sdot sdot sdot 120595

119873(119873)

100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816100381610038161003816

(1)

120595119895(119894) means that the 119894th electronrsquos space and spin are in the

one-electron state 120595119895 This will automatically satisfy the Pauli

principle because a determinant vanishes if two columns arethe same

Relativistic corrections are introduced by a Breit-PauliHamiltonian and treated by the perturbation theory Therelativistic corrections include the Blume-Watson spin-orbitmass-variation and one-body Darwin terms The Blume-Watson spin-orbit term contains the part of the Breit inter-action that can be reduced to a one-body operator

The Cowan (CW) atomic structure suite of codes (RCNRNC2 RCG and RCE) uses this HFRmethodThe three firstcodes are for ab initio atomic structure calculations and thefourth one (RCE) is used tomake least-squares fit calculationsusing an iterative procedure

22 Thomas-Fermi-Dirac-Amaldi (TFDA) Method In thismethod and to have atomic parameters of an atom or ion astatistical TFDA potential is used For an atom or ion having119885 protons and 119873 electrons this potential is in the followingform [29]

119881 (119903) =119885eff (120582119899ℓ 119903)

119903= minus

119885

119903120601 (119909) (2)

where

120601 (119909) = 119890minus1198851199032

+ 120582119899ℓ(1 minus 119890

minus1198851199032) 119909 =

119903

120583(3)

with 120583 the constant

120583 =1

4(

119873

119873 minus 1)

23

(91205872

2119885)

13

asymp 08853 (119873

119873 minus 1)

23

119885minus13

(4)

and 120582119899ℓare the orbital scaling parameters

The function 120601 verifies the following equation

1198892120601

1198891199092=

1

radic119909120601 (119909)32 (5)

with the boundary conditions

120601 (0) = 1

120601 (infin) = minus119885 minus 119873 + 1

119885

(6)

The SUPERSTRUCTURE (SS) and AUTOSTRUCTURE(AS) atomic structure codes use this method Relativisticcorrections are also done by a perturbationmethod using theBreit-Pauli Hamiltonian The SS atomic structure code usedin this work [30] is an updated version of the original one of1974 [2] Some relativistic corrections are introduced in thisversion and orbital scaling parameters120582

119899ℓare dependent on 119899

and ℓ [31] and not like the original SS version of 1974 wherescaling parameters were depending only on ℓ (120582

ℓ) The AS

code [32 33] is an extension of the SS code incorporating var-ious improvements and new capabilities like two-body non-fine-structure operators of the Breit-Pauli Hamiltonian andpolarization model potentials Comparing the two atomicstructure codes SS and AS we can see that even they used thesame techniques in general they gave different results mainlybecause they incorporated different relativistic corrections ofthe Hamiltonian For the comparison between the two codeswe can refer to the work of Elabidi and Sahal-Brechot [34]where they studied excitation cross section by electron impactfor O V and O VI levels They showed that the incorporationof the two-body non-fine-structure operators (contact spin-spin two-body Darwin and orbit-orbit) in AS and not in theinitial SS code is the main reason of the different resultsobtained by the two codes











32)3d 3P∘ 2 123297 120045 102401 120957 mdash

2s22p3(2D∘32)3d 3P∘ 1 123356 120049 102405 120959 mdash

2s22p3(2D∘32)3d 3P∘ 0 123387 120050 102406 120961 mdash

2s22p3(2D∘52)3d 3F∘ 4 124214 119938 102042 120523 mdash

2s22p3(2D∘52)3d 3F∘ 3 124219 119935 102039 120520 mdash

2s22p3(2D∘52)3d 3F∘ 2 124224 119934 102037 120518 mdash


52)3d 1S∘ 0 124243 119935 102037 120519 mdash

2s22p3(2D∘52)3d 3D∘ 3 124247 119957 102070 120544 mdash

2s22p3(2D∘)3d 3G∘ 3 124253 119944 102051 120529 mdash2s22p3(2D∘

52)3d 3D∘ 2 124258 119958 102072 120545 mdash

2s22p3(2D∘32)3d 1G∘ 4 124259 119952 102061 120538 mdash

2s22p3(2D∘52)3d 3D∘ 1 124264 119959 102072 120546 mdash

2s22p3(2D∘52)3d 1P∘ 1 124274 120043 103055 120030 mdash

2s22p3(2D∘32)3d 1D∘ 2 124319 120017 102181 120609 mdash

2s22p3(2D∘32)3d 1F∘ 3 124327 120033 102174 120629 mdash

2s22p3(2D∘32)3d 3S∘ 1 124336 120002 102133 120577 mdash










32)4s 1D∘ 2 122798 118560 101552 149959 mdash





Terms 119892119894

119892119896






Terms 119892119894

119892119896


5S∘-5P∘ 5 5 777417 167119864 + 00 181119864 + 00 158119864 + 00 333119864 + 00 161119864 + 00 168119864 + 00

5S∘-5P∘ 5 7 777194 234119864 + 00 254119864 + 00 222119864 + 00 467119864 + 00 226119864 + 00 235119864 + 00


3S∘-3P∘ 3 3 844676 103119864 + 00 116119864 + 00 114119864 + 00 126119864 + 00 102119864 + 00 108119864 + 00

3S∘-3P∘ 3 5 844636 172119864 + 00 194119864 + 00 191119864 + 00 210119864 + 00 170119864 + 00 180119864 + 00



012and 2p3(2P∘)3p 3P

012) and four new






4 Conclusions




Terms 119892119894

119892119896









Terms 119892119894

119892119870



5P-5D∘ 3 3 926085 129119864 + 00 151119864 + 00 122119864 + 00 243119864 minus 01 133119864 + 00 152119864 + 00

5P-5D∘ 3 5 926094 100119864 + 00 118119864 + 00 949119864 minus 01 189119864 minus 01 103119864 + 00 118119864 + 00


5P-5D∘ 5 5 926267 167119864 + 00 196119864 + 00 158119864 + 00 315119864 minus 01 172119864 + 00 168119864 + 00

5P-5D∘ 5 7 926278 267119864 + 00 313119864 + 00 253119864 + 00 504119864 minus 01 275119864 + 00 269119864 + 00


5P-5D∘ 7 7 926593 133119864 + 00 157119864 + 00 127119864 + 00 252119864 minus 01 138119864 + 00 134119864 + 00

5P-5D∘ 7 9 926601 515119864 + 00 605119864 + 00 488119864 + 00 973119864 minus 01 531119864 + 00 519119864 + 00

3P-3D∘ 3 5 1128632 222119864 + 00 197119864 + 00 964119864 minus 01 307119864 minus 01 202119864 + 00 220119864 + 00


3P-3D∘ 5 7 1128691 413119864 + 00 368119864 + 00 180119864 + 00 571119864 minus 01 377119864 + 00 410119864 + 00











Competing Interests


Acknowledgments


References













































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of











32)3d 3P∘ 2 123297 120045 102401 120957 mdash

2s22p3(2D∘32)3d 3P∘ 1 123356 120049 102405 120959 mdash

2s22p3(2D∘32)3d 3P∘ 0 123387 120050 102406 120961 mdash

2s22p3(2D∘52)3d 3F∘ 4 124214 119938 102042 120523 mdash

2s22p3(2D∘52)3d 3F∘ 3 124219 119935 102039 120520 mdash

2s22p3(2D∘52)3d 3F∘ 2 124224 119934 102037 120518 mdash


52)3d 1S∘ 0 124243 119935 102037 120519 mdash

2s22p3(2D∘52)3d 3D∘ 3 124247 119957 102070 120544 mdash

2s22p3(2D∘)3d 3G∘ 3 124253 119944 102051 120529 mdash2s22p3(2D∘

52)3d 3D∘ 2 124258 119958 102072 120545 mdash

2s22p3(2D∘32)3d 1G∘ 4 124259 119952 102061 120538 mdash

2s22p3(2D∘52)3d 3D∘ 1 124264 119959 102072 120546 mdash

2s22p3(2D∘52)3d 1P∘ 1 124274 120043 103055 120030 mdash

2s22p3(2D∘32)3d 1D∘ 2 124319 120017 102181 120609 mdash

2s22p3(2D∘32)3d 1F∘ 3 124327 120033 102174 120629 mdash

2s22p3(2D∘32)3d 3S∘ 1 124336 120002 102133 120577 mdash










32)4s 1D∘ 2 122798 118560 101552 149959 mdash





Terms 119892119894

119892119896






Terms 119892119894

119892119896


5S∘-5P∘ 5 5 777417 167119864 + 00 181119864 + 00 158119864 + 00 333119864 + 00 161119864 + 00 168119864 + 00

5S∘-5P∘ 5 7 777194 234119864 + 00 254119864 + 00 222119864 + 00 467119864 + 00 226119864 + 00 235119864 + 00


3S∘-3P∘ 3 3 844676 103119864 + 00 116119864 + 00 114119864 + 00 126119864 + 00 102119864 + 00 108119864 + 00

3S∘-3P∘ 3 5 844636 172119864 + 00 194119864 + 00 191119864 + 00 210119864 + 00 170119864 + 00 180119864 + 00



012and 2p3(2P∘)3p 3P

012) and four new






4 Conclusions




Terms 119892119894

119892119896









Terms 119892119894

119892119870



5P-5D∘ 3 3 926085 129119864 + 00 151119864 + 00 122119864 + 00 243119864 minus 01 133119864 + 00 152119864 + 00

5P-5D∘ 3 5 926094 100119864 + 00 118119864 + 00 949119864 minus 01 189119864 minus 01 103119864 + 00 118119864 + 00


5P-5D∘ 5 5 926267 167119864 + 00 196119864 + 00 158119864 + 00 315119864 minus 01 172119864 + 00 168119864 + 00

5P-5D∘ 5 7 926278 267119864 + 00 313119864 + 00 253119864 + 00 504119864 minus 01 275119864 + 00 269119864 + 00


5P-5D∘ 7 7 926593 133119864 + 00 157119864 + 00 127119864 + 00 252119864 minus 01 138119864 + 00 134119864 + 00

5P-5D∘ 7 9 926601 515119864 + 00 605119864 + 00 488119864 + 00 973119864 minus 01 531119864 + 00 519119864 + 00

3P-3D∘ 3 5 1128632 222119864 + 00 197119864 + 00 964119864 minus 01 307119864 minus 01 202119864 + 00 220119864 + 00


3P-3D∘ 5 7 1128691 413119864 + 00 368119864 + 00 180119864 + 00 571119864 minus 01 377119864 + 00 410119864 + 00











Competing Interests


Acknowledgments


References













































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of




32)4s 1D∘ 2 122798 118560 101552 149959 mdash





Terms 119892119894

119892119896






Terms 119892119894

119892119896


5S∘-5P∘ 5 5 777417 167119864 + 00 181119864 + 00 158119864 + 00 333119864 + 00 161119864 + 00 168119864 + 00

5S∘-5P∘ 5 7 777194 234119864 + 00 254119864 + 00 222119864 + 00 467119864 + 00 226119864 + 00 235119864 + 00


3S∘-3P∘ 3 3 844676 103119864 + 00 116119864 + 00 114119864 + 00 126119864 + 00 102119864 + 00 108119864 + 00

3S∘-3P∘ 3 5 844636 172119864 + 00 194119864 + 00 191119864 + 00 210119864 + 00 170119864 + 00 180119864 + 00



012and 2p3(2P∘)3p 3P

012) and four new






4 Conclusions




Terms 119892119894

119892119896









Terms 119892119894

119892119870



5P-5D∘ 3 3 926085 129119864 + 00 151119864 + 00 122119864 + 00 243119864 minus 01 133119864 + 00 152119864 + 00

5P-5D∘ 3 5 926094 100119864 + 00 118119864 + 00 949119864 minus 01 189119864 minus 01 103119864 + 00 118119864 + 00


5P-5D∘ 5 5 926267 167119864 + 00 196119864 + 00 158119864 + 00 315119864 minus 01 172119864 + 00 168119864 + 00

5P-5D∘ 5 7 926278 267119864 + 00 313119864 + 00 253119864 + 00 504119864 minus 01 275119864 + 00 269119864 + 00


5P-5D∘ 7 7 926593 133119864 + 00 157119864 + 00 127119864 + 00 252119864 minus 01 138119864 + 00 134119864 + 00

5P-5D∘ 7 9 926601 515119864 + 00 605119864 + 00 488119864 + 00 973119864 minus 01 531119864 + 00 519119864 + 00

3P-3D∘ 3 5 1128632 222119864 + 00 197119864 + 00 964119864 minus 01 307119864 minus 01 202119864 + 00 220119864 + 00


3P-3D∘ 5 7 1128691 413119864 + 00 368119864 + 00 180119864 + 00 571119864 minus 01 377119864 + 00 410119864 + 00











Competing Interests


Acknowledgments


References













































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of



Terms 119892119894

119892119896









Terms 119892119894

119892119870



5P-5D∘ 3 3 926085 129119864 + 00 151119864 + 00 122119864 + 00 243119864 minus 01 133119864 + 00 152119864 + 00

5P-5D∘ 3 5 926094 100119864 + 00 118119864 + 00 949119864 minus 01 189119864 minus 01 103119864 + 00 118119864 + 00


5P-5D∘ 5 5 926267 167119864 + 00 196119864 + 00 158119864 + 00 315119864 minus 01 172119864 + 00 168119864 + 00

5P-5D∘ 5 7 926278 267119864 + 00 313119864 + 00 253119864 + 00 504119864 minus 01 275119864 + 00 269119864 + 00


5P-5D∘ 7 7 926593 133119864 + 00 157119864 + 00 127119864 + 00 252119864 minus 01 138119864 + 00 134119864 + 00

5P-5D∘ 7 9 926601 515119864 + 00 605119864 + 00 488119864 + 00 973119864 minus 01 531119864 + 00 519119864 + 00

3P-3D∘ 3 5 1128632 222119864 + 00 197119864 + 00 964119864 minus 01 307119864 minus 01 202119864 + 00 220119864 + 00


3P-3D∘ 5 7 1128691 413119864 + 00 368119864 + 00 180119864 + 00 571119864 minus 01 377119864 + 00 410119864 + 00











Competing Interests


Acknowledgments


References













































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of












































Journal of

Chemistry


Advances in

Physical Chemistry



Journal of

Volume 2014














Journal of

Spectroscopy



Journal of


Quantum Chemistry






CatalystsJournal of

Research Article Atomic Structure Calculations for Neutral...

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