Computer Program for Ligand‐Field Analysis of F N Systems Within the Angular Overlap Model

Page 1of32 between this versionandtheVersionrecord. Pleasecitethis articleasdoi:10.1002/jcc.25096. through thecopyediting, typesetting, pagination andproofreading process,whichmay lead todifferences This istheauthor manuscriptaccepted forpublicationandhas undergonefullpeerreview buthasnotbeen oeue magnets, molecule ehd, at u rlal cluain using calculations approximatemethods are desirable reliable but these fast of cost methods, computational high the to Due Correspondence to: Thomas(E-mail: Bredow Angular Overlap ModelOverlap Angular Introduction Introduction

Prediction of physical properties ofproperties physical of Prediction 4 3 2 1 AnnaBronova, BonnMag - Computer Program Ligand-Fieldfor Analysi hoy CSP2 r NEV-PT2) or (CAS-PT2 theory ME) ME) (DV- method multi-electron discrete-variational Bonn, Germany Bonn, ataie os ae lo en tde with (LF-DFT) studied theory functional density field ligand been also have ions lanthanide Bonn, Germany Bonn, rnils ehd hv be applied, field self-consistent been space (CASSCF) first- have active accurate complete methods highly principles investigation, their

f neet u t ter aiu technical (white-light-diodes, various their to applications due interest of Private Institute of Theoretical Chemical Physics, Chemical Theoretical of Institute Private Uni Biosciences, Molecular and Chemistry of School Rheinis Chemistry, Theoretical for Center Mulliken Fried Rheinische Chemistry, Inorganic of Institute all Csall to due Splitting calculations. CASSCF/NEV-PT2 from BonnMag are shown.BonnMag of susceptibilities magnetic dependent calculate to developed been has BonnMag program The ABSTRACT ltrCno-hrly aaees n si-ri co spin-orbit and parameters Slater-Condon-Shortley backgrou theoretical the of description A coefficients accuracy. absorption relative the of estimation the within performed initio calculations, the transition energies of all of energies transition the calculations, initio n h cmaio bten hoy n eprmn, th experiment, and theory between comparison the on 4 2 DV-X , NaLnCl 2 , CASSCF combined with perturbation with combined CASSCF ,

α 6 1 (except Gd and Pm) are calculated using parameters using calculated are Pm) and Gd (except Thomas Thomas Bredow,

Accepted Article 5

Te f The . 1b SmCo

, 1c tastos in transitions d Nd Journal ofComputationalChemistry 2 Robert Glaum, 2 f Fe 3 1a ad the and , n systems is systems single 14 B

1d f ). For For ). n systems. The computations of the transition energi transition the of computations The systems. Via Dr. A. Sciarone Nr. 2, CH-6600 Muralto, CH-6600 2, Nr. Sciarone A. Dr. Via [email protected] rich-Wilhelms-Universität, Gerhard-Domagk-Straße 1, Gerhard-Domagk-Straße rich-Wilhelms-Universität, 6 che Friedrich-Wilhelms-Universität, Beringstr. 4, D 4, Beringstr. Friedrich-Wilhelms-Universität, che . versity of Queensland, Brisbane St. Lucia, QLD 4072 QLD Lucia, St. Brisbane Queensland, of versity Ln 1 Mark Riley J. AM. sn Jd-fl ter BnMg allows BonnMag theory Judd-Ofelt Using (AOM). 3+ ions are calculated and compared to the results the to compared and calculated are ions nd of the implemented methods is given. Using given. is methods implemented the of nd the ligand field as well as transition energies of energies transition as well as field ligand the f h eetoi tastos ih reasonable with transitions electronic the of pig ofiins o fe Ln free for coefficients upling established for ligand-field analysis of of analysis ligand-field for established ae at mtl opud. Previous (LUMPAC) compounds. methods metal semi-empirical on based been have approaches earth of structure rare electronic the of analysis the for Hamiltonians SURGEV SURGEV programs the in (implemented AOM the within o fe Ln free for energies transition electronic the calculations, model the of quality the investigate To systems. f model the approximations of framework using the within approach alternative rga BnMg Is oe er some bears computer code developed CAMMAG Its to resemblance BonnMag. newly program the present 1 f - ptnil n lmttos f h program the of limitations and potential e h asrto seta n temperature and spectra absorption the 3 and (AOM) 3 , and , UrlandWerner 13 f and LIGFIELD LIGFIELD and 11 reported in the literature. Based literature. the in reported f - 3+

9-12 s of s os n fr h chlorides the for and ions 8 13 ) I te rsn suy an study, present the In .

systems have been be treated be been have systems is presented. Up to now, only now, to Up presented. is f n Systems within the Systems within 7 16, 1716, r n effective on or 8 19,6618,

Switzerland ). In this study, we study, this In ). 4

nua overlap angular os rm ab from ions , which is well well is which , -53121 -53121 D-53121 D-53121 , Australia ,

es are es d

is given in Supportinggiven is the Information. file input example An B.). T. and B. (A. authors the from obtained be may BonnMag request On treated. e rae b itouig nstoi π- anisotropic introducing by treated be ofre fr ay cases) many for already (and assumed confirmed from is compounds parameterized transferability these chemically For be using parameters parameters. model can bonding this meaningful structure by described geometric symmetry) 2 f-f at to occur limited cm 25000 which (above energies higher excitations, is f-d approach transitions. present The approach). open-shell e of determination the for Gerloch by described are approaches solution of couple a However, problem. cases this overcome to underdetermined chance Schäffer no is there For by symmetry. the described Jørgenson is effect is This which effect. holohedrization so-called by caused parametrization, ambiguous the to lead note, can model overlap angular simple the should that one Nevertheless, interactions. Cs (octahedral [Ln(octahedral cee s el one i mlclr orbital molecular in theory. founded well is scheme parametrization its no and has restrictions It two symmetry approach. explicitly AOM the here of emphasize advantages to want We influence. Second sphere ligand effects effects field ligand sphere ligand calculated Second the influence. for way simple the a AOM in Thus, accounts of data. experimental fitting to metal-ligand properties the by of interactions parametrization the is and model this ligand of aspect fundamental A interaction. metal-ligand the assumptions with parameters of bonding of correlation the the to known due possible is Interpretation behavior well simplifications. the to due transparent is and power predictive has some AOM the Thus, systems. new considering

2 NaLnCl 9-12 6 80 hoohrs ih ifrn (low- different with Chromophores . It leads to the artificial increase of increase artificial the to leads It . ecp G ad m ae used are Pm) and Gd (except

Accepted Article III Cl

6 ] chromophores).]

18 (independent equations (independent This article isprotected by copyright. All rights reserved. σ o C Daul C. or ) Journal ofComputationalChemistry -1 20, 21 ,cno be cannot ), when when John Wiley& Sons,Inc. 79 81 and (two- 22 can antc rpris f ae at metal the of earth energies the rare on based of compounds and properties optical of magnetic calculation the for was developed (AOM) model overlap angular the 1970s, 12,23,24 lcrnc tts ti apoc ws later compounds). was metal transition approach to extended (this states electronic Δ describe the octahedral ligand-field (Eq 2) (Eq ligand-field octahedral the describe f-orbitals split into the three sets a sets three the into split f-orbitals d For containing complexes compounds. octahedral of homoleptical, of understanding series related and chemically modeling it the since preferable allows is parameters of transfer The separately. compound each for optimized the be can they for or systems novel of compounds consideration from transferred parameterized be already can parameters These the by described empiricalparameters e are terms interaction The Model Overlap Angular Δ (Figure1). In the AOM the global ligand field, which is is which field, ligand coordinated octahedral for given global the AOM the In hoohrs ih ifrn geometric ligands. different model. this individual by discriminated be can structures with the Chromophores of contributions iue . pitn o fobtl udr an under f-orbitals of ligandoctahedral Splitting field. 1. Figure For For by Eq.1. by 0q r Δ or 10Dq 1 0 n = 5e = 3e = ions the link between Δ between link the ions f n

ytm to aaees r nee to needed are parameters two systems π σ ˗ 4e /2 andΔ/2 21

π (1) o i dcmoe it the into decomposed is , 2 = e= 2 σ σ + + 3e ,e π ande o π , e , 2 (2) /2

n h 16s and 1960s the In σ and eand d δ .

2u n , t , systems by systems 2u π is given is , and t and , 3 . The . 1u 9- f

Page 2of32 Page 3of32 the ligands (φ = 45°), c) between f-orbitals f-orbitals between c) 45°), = (φ ligands the literature. of these parameters for parametersfor these of atom atom central of combination each for values specific attain and orbitals overlap ligand the and atom central the the of of orbitals respective the square between integral the to proportional The relations between relations The ligand-field The potential the metal and σ-orbitals of the ligands (φ = 0°), b 0°), = (φ ligands the of σ-orbitals and metal the h mgiue f h itrcin energies interaction the order the in decreases of magnitude The of terms 9. inRef. in matrices Urland W. by introduced were cosines direction rotation unitary the between f-orbitals between orbital). Figureadapted orbital). from literature. Figure 2. Angular dependence of σ- and π-interactio and σ- of dependence Angular 2. Figure ψ ψ = ψ ψ V|| | |Y | |V LF M ' c ' n+ 18-21 ∑∑ and ligand L depending on the the on depending L ligand and k q k These interaction parameters are parameters interaction These =−

Accepted Article k qq kq

f (z(x k e 2 c σ d -y kq > V n and 2 systems are found infound are systems LF )) of the metal and p-orbitals of the ligands (φ = = (φ ligands the of p-orbitals and metal the of )) This article isprotected by copyright. All rights reserved. e (3) is given by given Eq. is 3 π > > e e σ Journal ofComputationalChemistry δ ( . Compilations Compilations . e π ) as well as well as ) 26 John Wiley& Sons,Inc. f (z(x 18 . . 2 -y ) between f-orbital f-orbital between ) 2 )) of the metal and p-orbitals of the ligands (φ=0° ligands the of p-orbitals and metal the of )) ns for some f-orbitals. a) Between f-orbitals f-orbitals Between a) f-orbitals. some for ns distance distance where where oyer ifune te nry ees f the atom. central of levels energy the the influences of polyhedra structure geometric the atom, the central on the around ligands depend the of arrangement integrals spatial overlap the Since angulardescribes partthe the interaction. of subsumingradialintegrals, and 4). (Eq. part radial a and part angular an into split The harmonics. S S bab ab c ⋅θ = kq are the expansion are coefficients λ S λ is the radial part (λ = σ, π, δ) and δ) π, σ, = (λ part radial the is d (M-L). The overlap integral overlap The (M-L). (4) 25 f (z The σ- or π-interaction for some for π-interaction or σ- The 3 ) of the metal and σ orbitals of orbitals σ and metal the of ) 54.73°) (valid for (valid 54.73°) Y q k are spherical are

S f ab (z(x can be can f (z 2 3 -y ), d) ), ) of ) θ 2 ab )) 3 3

to the the to respect with π-bonding for interactions bonding anti- and bonding the 54.73°, = φ of case the In f rpris f h ligands. bonding the the of from a properties derived as is perturbation obtained This ion. free the of states are the of perturbation a coordination As specific atom. a in central cation a of levels energy the consequence, and ligands between factor F O parameters AOM the using f-shell, open an with ion an containing compounds of properties magnetic and spectra electronic the calculates program BonnMag The parameters AOM neatos Slater-Condon-Shortley parameters interactions, calculated from from calculated ria. o te -neato bten p between π-interaction the For orbital. F 4 F f(z the between σ-interaction which the integral, for 0°) = (φ 1 to overlap 90°) = (φ 0 from values the attains of part angular the of magnitude the determines φ angle The central 2. Figure in the shown are L ligand the and of M atom orbitals of alignments mutual ona, h gnrl etn o fobtl as f-orbitals inRef. given of setting general the BonnMag, aus f h fe in. o tasto metal transition For ions. free the of values the than smaller are complex a in atom an for (SCS) parameters Slater-Condon-Shortley The constant constant integral varies from from varies integral y ltrCno-hrly hoy with theory are ions Slater-Condon-Shortley parameters free the by of excited andaccessibleexperimentally approximated are the states and state electronic ground the between and7.

(z(x

6 4 2 = 184041F = 1089F = 225F = 2 -y 28 28 k 2 )) orbital, the angular part of the the the overlapangular of orbital, part )) f . (z(x 2 20 (5) ζ 4

n te tvn obtl reduction orbital Stevens the and (6) The AOM assumes weak interaction weak assumes AOM The 2 F F 73 -y 6 2 (7) /25 2 2 is used. is , , , , 2 Accepted Article In other. each cancel orbital )) F

F F 4 4 2 , , , , , ,

F F F e 6 − 6 4 . te pn ri coupling orbit spin the , σ and and 27 and 2 2 5 1 hs prmtr are parameters These This article isprotected by copyright. All rights reserved. F 6 (φ = 90°) to 0 (0°). 0 to 90°) = (φ

via equations 5, 6 5, equations via e h differences The π o al M-L all for Journal ofComputationalChemistry 3 ad p and ) John Wiley& Sons,Inc. x and and z

ehluei efc i qie ml for small quite is effect nephelauxetic e relation e relation to 4 to f for smaller is effect nephelauxetic The systems. L) For example the value value the example For itne a fud hc ws xrse by metal-ligand expressed Δ was the which found and was distance splitting field ligand esrd pcr te neato eege e energies interaction the to spectra respect measured with AOM the of the parametrization For essential. is interaction spin-orbit the e The free ion parameters free The vrprmtiain h nme of number information.additional by restricted be can the parameters independent over-parametrization avoid To ligand. foreach determined be to have e and ion free SCS the to the For values. comparison as in reduction parameters similar a undergoes systems. complexes and for the former former metal the for transition and to complexes compared compounds ute apoiain h ratio the approximation further euto i dntd s nephelauxetic a as The values. denoted effect. ion free is the of reduction 90% to 80% of range the in are values reduced the complexes different bond lengths, a single esingle a lengths, bond different with ligands, identical chemically several with coupling constant coupling calculated using thecalculated above relationship. the the 4 odnSote prmtr ( parameters Condon-Shortley assumed to be isotropic. In many cases many In isotropic. be to assumed the three interaction parameters eparameters interaction three the complexlow-symmetric a For neglected. usually orbitals with ligand orbitals is smaller. is orbitals ligand with orbitals rsue eedne f Vvs pcr was spectra investigated UV/vis of dependence pressure ratio ratio parameters parameters π,iso π,y n d o min systems then for 3for then systems ~ , 5 , can be replaced by an isotropic π interaction π isotropic an by replaced be can d n te e the and between the metal and the ligand. As a a As ligand. the and metal the between f (M-L) n cno b ngetd ntecs of case the in neglected be cannot and d e F , 4 , 29 σ π 2 aus r salr o lanthanide for smaller are values r epoe bsds h Slater- the besides employed are The nephelauxeticratio The (ion in complex) / / complex) in (ion f and 5and 72 σ - ~ n h si-ri culn constant coupling spin-orbit The with 4 ≤ ≤ 4 with d f- e (M-L) σ 33,34 lcrn ytm cnieain of consideration systems electron and f σ systems. o te te lgns a be can ligands other the for n a eain ewe the between relation a and - ζ n e is often used. In complexes complexes In used. often is

π strongly increases from 3from increases strongly d are quite different for 3 for different quite are , because the overlap of of overlap the because , n

≤ 7 7 ≤ n h ery 90 the 1960s early the In β e 18-20,31-32 σ,max , , ζ and the ligand andthe field is used for for used is F 41 2 F Teeoe the Therefore . (free ion). The The ion). (free 2 β , ,

σ e The spin-orbit spin-orbit The describes thedescribes can be used. be can σ π F , e , e : : 4 π , , s often is π,x

e F Similarly,

σ σ 6 and eand e . e ). 1/3 = π,x d and and (M- δ is is f π,y d d ζ σ n f f ,

Page 4of32 Page 5of32 eie t le epniua t te plane the to perpendicular The n3. and n2 n1, atoms three the by defined lie to defined considered. considered. beshouldperpendicular π-interactions different connecting atoms n1 and n2. The The n2. and n1 atoms connecting neatos Dtie acut n these on term account electronic is coefficients given inSupporting Information. Detailed the for interactions. elements matrix hc ae n un eie fo te Clebsch- the from coefficients. Gordon derived turn in are which 3. The n3). from n2 n1 example (for file input the in list atom numbers the their using atoms three by set are systems coordinate coordinate ligand as well as global several The 3). Figure (see defined be calculations to have systems these For BonnMag in systems coordinate the of Definition | basis: field weak a in out carried is BonnMag in coupling spin-orbit and repulsion electron-electron ligand-field, the the of with inclusion levels energy the of calculation The BonnMag by used Coefficients [MO a in atoms oxygen all example for if bondingsituationoccurs simple A the improves 1/3 ratio the agreement with experiment. results our to According ions. metals transition for observed commonly is as 1/4 of ratio We a investigated 4. also Table in collected values literature the of average the to close is This 52). 24, 15, Ref. in compounds different for (observed used was ofiins f rcinl parentage fractional of from coefficients calculated are RME determined. exactly rae apoiaey s stoi. f the If isotropic. thespan ligand via of interaction is as approximately treated two the of be atomscan the oxygen at porbitals remaining π-interaction The orbital. hybrid sp- a via atom metal the between σ-interaction Racah configurations. configurations. elements socalled of use makes BonnMag 38 r apid o te aclto o the of calculation the for applied are RE fr h itrcin between interactions the for (RME) z 22,35,36 xs s aall o h vector the to parallel is axis Accepted Article 37

h cniuain arx is matrix configuration The

39,40 The CFP introduced by introduced CFP The n This article isprotected by copyright. All rights reserved. ] polyhedron have a have polyhedron ] Journal ofComputationalChemistry reduced matrixreduced α 2 hybrid, two hybrid,two ,l n (CFP), ,L,S,J,M y John Wiley& Sons,Inc. axis is is axis J >. 38 x

rhgnl to be orthogonal to product, vector a as constructed, is axis hie f hs lbl oriae ytm is system references to refer we coordinate topic, this on details global For required. this of choice careful a properties, dependent orientation of calculation the For system. coordinate handed iue . RE rpeetto of representation ORTEP 3. Figure oriae ytm ad o oe iad as ligand one with for (subscript example L). and given system) coordinate elpasolites (global atom central the for systems coordinate in chromophore to define define to order in chromophore the in ligand each for set be to have systems coordinate ligand local the addition, In eigenstates. the of representations global irreducible correct the get to order in molecule, The the of group point the in defined as axes same system. the using defined be to has system coordinate coordinate the of independent chosen however, are, energies ofiins t s osbe o aclt magnetic calculate to possible is it coefficients absorption and energies transition the Besides setting of spherical setting of f-orbital is functions used. general The calculations. the in for be accounted to has π-interaction anisotropic if systems coordinate ligand the of definition for used be of definition can sphere coordination second The facilitate directions. second to introduced, the be necessary, can if atoms "Dummy" used. and, are sphere coordination first the of σ and 8 19 18, z and π Te acltd transition calculated The . interactions. Here the atoms the Here interactions. 44 y

n t fr a right- a form to and

h [Lnthe

III L 73 6 5 5 ]

at ad eprtr-eedn magnetic (lower part)moments EuNbO of temperature-dependent (upper and spectra part) absorption (blue) measured and (black) calculated of Comparison 4. Figure are inlet) (see splitting reasonablecalculated with accuracy. the and transition 6 and moments) (and susceptibilities EuNbO of moments magnetic temperature-dependent and and spectra calculated absorption unpolarised the measured of comparison we Here the rather 75. show Ref. in with chromophores different oxo-compounds europium(III) UPO were discussed for the [UO the for discussed were theory Judd-Ofelt using coefficients absorption of calculation the as well as moments magnetic The BonnMag. temperature-dependent the of analysis detailed using electrons) f of numbers odd with systems for only currently latter (the

4 l n e. 2 n fr sre o nine of series a for and 42 Ref. in Cl 4 75

Accepted Article the of position The 4). (Figure

Journal ofComputationalChemistry 75

g tensors tensors John Wiley& Sons,Inc. 5 D 2

iue . eain ewe prmtr and parameters observables. between Relation 5. Figure of calculation the for used susceptibilitiesmagnetic (example inRef. 42). these Further are calculated. energies are levels energy BonnMag and and BonnMag ee acltd Uig h porm ORCA program the 4.0) (Version Using calculated. were tm wr dsrbd ih h recently the sets. with basis all-electron SARC2-QZVP-DKH described developed were lanthanide atoms The states. all considering theory) perturbation N-electron (second-order NEV-PT2 andfield) self-consistent space active (complete Ln cie pc cnitd f l possible all spin of f 14 the in consisted electrons n of configurations space The active formalism. account Douglas-Kroll-Hess the into within taken were coupling spin-orbit For the comparison between comparison the For Ln free the of Energies parameters and a spin-orbit coupling constant coupling spin-orbit a and parameters Slater-Condon-Shortley uses BonnMag 5. Figure in shown schematically is properties and calculated parameters the between connection The These energies for for energies These ion. free a of energies the of calculation the for M fr h tr itrcin ad AOM and interactions term parameters the for RME those given by the Dieke diagram. Dieke the by given those and BonnMag the energies for the freeLn the for energies the BonnMag and 3+ os ee acltd sn CASSCF using calculated were ions 46 eaiitc fet, ot importantly most effects, Relativistic e 45 σ and the excited state energies for all for energies state excited the ab ab initio e f π n for the ligand field the the field ligand the for ytm ae iia to similar are systems methods b initioab 3+ ions using using ions 31 Using the the Using methods

3+ ions

Page 6of32 Page 7of32 in Ref. 3. Slater-Condon-Shortley parameters Slater-Condon-Shortley 3. Ref. in reported those to similar very were manner this F ions (Ce ions lanthanide trivalent the free in several reported for literature values the to compared are parameters These energies. excitation CASSCF nry tts f l fe Ln free the all of NEV-PT2 data states Using energy NEV-PT2. experimental to from compared deviations larger F xie sae nris f h fe Ln free the of energies state Excited couplingspin-orbit parameters. by BonnMag and (SCS) in Slater-Condon-Shortley the way adjusting effective an in only included NEV-PT2 but in state effects excited each for correlation individually dynamical the are which 2).by Thesedeviations mainlycaused (Table are NEV-PT2 with calculated energies, those from deviating produces BonnMag and rvos RA eso ol high-spin only Tm for version except account into taken were configurations ORCA improves which previous account the In results. BonnMag the with into comparability taken were 3 configurations Ref. excitation all work in present the those in present because from The slightly differ therein. energies found be can setup computational the of Details orbitals. t ASF n NVP2 ee. h spin-orbit The constant coupling level. NEV-PT2 and CASSCF at ASF la t eege, ht are that energies, with obtained introductionof thecontrast, In CASSCF. to those from indistinguishable lead CASSCF, from parameters AOMusing BonnMag by framework the within calculations the expected As andCASSCFmade. were ahr iia t toe band from obtained those to for values CASSCF The 1). (Table experiment are similar NEV-PT2 from rather parameters The 1. Table T) hw ary od ac wt the with match good of comparison better a For fairly data. experimental show PT2) acltd ih oh E-T ad BonnMag and (with NEV-PT2 both with calculated using the the using BonnMag of framework the within Calculations to calculated rather a good approximation. 4 4 , , , F F 6 6 were obtained from the matrix elements matrix the from obtained were ζ nt hw) r mc lre ad show and larger much are shown) (not F rm E-T it cluain with calculations into NEV-PT2 from 3+ 2 , , . The . 3 and Yband F F 4 2 , , , , F F F 6 4 from NEV-PT2 and NEV-PT2 from 2 , , , ,

AcceptedF Article F 3

6 , Pr , 4 , , ζ , , was obtained by a fit to the to fit a by obtained was

ζ F 6 parameters from NEV-PT2 from parameters 47 , , , Eu , ζ parameters obtained in obtained parameters 48 This article isprotected by copyright. All rights reserved. , Pm , 3+ Journal ofComputationalChemistry os a be can ions 49 and Hoand ζ from NEV- from John Wiley& Sons,Inc. F 3+ 2 , , ions 49 F 4 ) in in ) , , F F F 2 2 6 , , ,

the free Lnfree the con ta te xiain nris f Gd of energies BonnMag excitation the into that taken is be account to has deviation and it Here Gd. absolute for transition obtained largest The NEV-PT2 the energies. overestimate 7). systematically results better (Figure slightly to leads NEV-PT2 cases most in BonnMag, by accuracy acceptable with relative deviation however,relative is, comparable. m 5. 5. 58 1075.9 936.2 802.2 5.83 685.4 5.60 5.25 52.1 49.9 0.00 356.6 52.1 342.7 0.0 Pm 324.2 Nd Pr 0.0 Pr Ce Ce Ln (incalculations cm NEVPT2 from param obtained coupling spinorbit and SCS ion Free 1. Table ( Slater-Condon- 2935.6 the states parameters Shortley by of dominated energies are the which Although 2671.3 6). 0.00 spin-orbit (Figure 2417.5 by defined deviation states same calculationsthe both nearly coupling is for absolute the mean for 7.60 2182.5 (MAD) 0.0 the 7.37 expected 1964.3 As 1761.7 69.9 7.08 1576.0 65.7 0.0 6.93 a)Experimental data for 6.69 467.4 1395.4 64.1 Yb 454.2 6.52 1231.3 61.5 Yb 59.4 Tm 6.26 440.8 Er 58.4 427.6 6.07 Ho 414.2 55.6 Ho 399.1 Dy 53.9 Tb 386.1 Gd 371.8 Eu Eu Sm Pm iue , n fr l ohr tts (mainly states other all for from resulting and 6, Figure rm E-T) n eprmn, were the for experiment, shown by only (defined multiplets are state ground results and The calculated. NEV-PT2) SCS (with from BonnMag between experimental as well and as data, results NEV-PT2 between deviations absolute mean the calculations both f a) 7 3+ a) a) a) a) a) ae ihr hn o te te in. The ions. other the for than higher )are 2. 5. 52 764.0 5.23 51.7 325.4 . 00 .0 2918.3 0.00 0.0 0.0 1320.0 6.06 55.4 401.0 . 00 .0 643.7 0.00 0.0 0.0 1. 6. 72 2163.0 7.27 68.8 414.6 4. 4. 52 1070.0 5.23 47.7 346.2

3+ ions F 2

1 F (see text). 2 , , F 4 F , , F 2 F , , F 4 6 F F 2 F ) in ) Figure7. , , 4 2 , , , , F F 4 6 F , , and 4 , , F 6 F were reproduced were 6 ζ ad ASF ( CASSCF and ) from literaturefor 6 ζ ζ ζ ) eters in , 3+ ζ 7 7 )

E T/ASF acltos Nvrhls, the parameters Nevertheless, Slater-Condon-Shortley calculations. PT2/CASSCF Yb rm hs rcdr fr w raos In reasons. SCS,(including parameterset large a of fitting two for the chromophores low-symmetry for procedure particular this from nris oprd o hs otie by obtained those of transition application to observed compared the energies with slightly a match show resultsbetter The literature. the in and ep h mdl s ipe s possible. as simple as parameters model higher-order the Considering the keep to states ion free the of parametrization the for and spin-orbit coupling constant constant coupling spin-orbit and 8 were calculations Ce for performed BonnMag Additionally, free ion energies only only energies ion free ligand- of the theand not match perfect on effects field the on focuses investigation our Since be of to therefore comparison the care. taken with has The theory (see 2). and matrices experiment Table solid in in comment doped ions to experimental reported but ions, gas-phase to the correspond not do values that noted and be to calculated has it Here between . ions free the for energies observed deviations to larger leads 44) Ref. in reported parametrization aaees r dfnd codn t the to according defined references in used conventions are parameters lcrnc tts s t a dsrbd for described was ion it free asCs the of states description elaborate electronic the more for a with model possible state excited is observed energies of fit better even An from derived available. experiment are parameters those no for where particular systems in benchmarks, as used be can and method NEV-PT2 the by determined parameters parameters simple four The only using ion free other. the of parametrization each of independent are (LF) AOM the ion free the for that parameters the and parameters assume to reasonable is [Ln

ave 2 3+ NaLnCl III , , using Cl P α 6 , , k chromophore.] k 246 i qie hlegn. These challenging. quite is 2,4,6) = (k β , , 6 γ n Cs and F , , 2 F , , T 2 F , , i (i = 2,3,4,6,7,8), 2,3,4,6,7,8), = (i 4 F Accepted Article , F

4 2 F , , 3+ , , 6

and 2 F Pr , NaYCl F 6 and and 4 , , 44 F 3+ 2 t rsn w refrain we present At F ζ , , Pm , 6 parameters reported parameters 6 F and :Ln This article isprotected by copyright. All rights reserved. ζ 4 , , cmae t the to (compared F 3+ 3+ 6 otiig the containing Eu , 67-71 and Journal ofComputationalChemistry M ζ rm NEV- from . Secondly, it it Secondly, . k 3+ (k = 0,2,4), = (k ζ ζ Ho , r well are F are used are 2 John Wiley& Sons,Inc. , , 3+ F 44,67-71 4 and , , F ζ 6 ,

h ftig rcdr of procedure fitting The procedurefitting a such (Table 3). for SCSBonnMag is the underdevelopment. in routine fitting least-squares a Currently Note: tt eege uig ona various currently are BonnMag as summarizedpossible, subsequently. strategies using parameterization energies state optimized re- the shows 2 Table NEV-PT2. from obtained energies and MAD for Prfor MAD and energies in BonnMag, the parameters the inBonnMag, states ion free the of fit improved an obtain To difficult very a procedure. parametrization to lead would ion free the for h fe in tts s eurd te more the and required, is ( parameters four states all of fitting complex ion free of fitting the accurate highly If 7). and 6 Figure 2, Table (see NEV-PT2 from originally obtained as o te aclto f h re Ln free the of calculation the For smaller MAD compared to those using those to compared MAD smaller the ratios the whereby varied, were calculations PT2/CASSCF • • • • ζ

) should ) considered. be Fitting PT2/CASSCF Taking aaees ihu te ihr order parameters) four higher the these without fitted parameters has reference the F Taking ζ ζ Fitting all four parameters four all Fitting 2

/ F

F F 2 2 6 / and ratios F 4 F F and F 2 2 and , , 2 ζ , , F values, as well as calculated as well as values, 4 F , , F 2 F / 4 ζ ζ 6 , , F and 6

with constant with were keptconstantwere as F 3+ 6 and , Eu , F ζ ζ 2 F and

2 from literature (if literature from 3+ and and Gdand ζ ζ 3+ F ζ

o excited ion ζ ζ 2 rm NEV- from , , from NEV- from ed to leads F F 4 F F 2 , , 2 / 3+ 2 , , F and F from from 6 4 F and and and and 4 , , F ζ 6

Page 8of32 Page 9of32 Ln 50. Ref from energies Experimental NEVPT2. and BonnMag cm energi experimental the between Comparison 2. Table Sm Pm Nd Ce Pr Pr 3+ 1

fr h fe Ln free the for )

3 3 3 1 3 3 1 1 3 4 4 4 4 4 6 6 6 6 6 6 6 6 6 6 6 5 5 5 5 5 5 5 5 5 5 4 4 4 2 4 4 4 4 2 4 4 4 4 4 3 2 3 state I I I F F F F F F F H F H H H H F F S F F F I I I I G G G G G F S F H F F I I I P I P P D G F F F H H F 9/2 7/2 8 7 6 5 15/2 13/2 11/2 6 11/2 3/2 5/2 11/2 9/2 7/2 5/2 3/2 1/2 5 4 3 2 1 9/2 7/2 5/2 3/2 4 3 2 7/2

2 3/2 2 1 0 15/2 13/2 11/2 9/2 7/2 9/2 2 6 5 11/2 9/2 7/2 7/2 5/2 4

2400.0 2399.0 2253.0 2253

20980 20560 20010 18860 17860 10470 9080 7910 7050 6540 6470 6290 4990 3610 2290 1080 23160 22211 22007 21389 17334 9921 6854 6415 4996 4389 2152 15800 14470 14100 13520 12670 12230 6580 4820 3110 1490 94 19440 19290 18890 17100 16980 14570 13370 13280 12470 12320 11290 5910 3860 1880 exp

Accepted Articlea)

3+ os n toe acltd using calculated those and ions

23833.0 22009.0 22590.0 21976.0 17950.0 10202.0 7080.0 6516.0 5099.0 4375.0 2132.0 15916.0 14606.0 14373.0 13654.0 12735.0 12292.0 6934.0 5101.0 3305.0 1586.0 E BonnMag b) This article isprotected by copyright. All rights reserved. E . 21056.0 20756.0 20065.0 19208.0 18607.0 10756.0 9288.0 8046.0 7135.0 6610.0 6861.0 6352.0 5304.0 3800.0 2384.0 1099.0 23955.0 22112.0 22627.0 21971.0 18005.0 10471.0 7201.0 6613.0 5112.0 4597.0 2246.0 16262.0 14876.0 14591.0 13860.0 12957.0 12486.0 6983.0 5113.0 3298.0 1576.0 19565.0 20121.0 19634.0 17732.0 16525.0 15257.0 13875.0 13717.0 12996.0 12835.0 11727.0 6300.0 4107.0 1992.0 BonnMag Journal ofComputationalChemistry c E . John Wiley& Sons,Inc. 22463.8 21990.4 21593.7 20281.5 19414.9 10836.2 9379.2 8147.4 7238.9 6701.9 6881.3 6430.8 5310.1 3797.0 2377.6 1094.1 23469.3 22126.5 22511.3 21463.7 17664.2 10411.2 7103.3 6495.7 4978.9 4603.4 2250.8 16454.3 15059.0 14477.0 14026.4 13340.5 12667.6 7013.6 5158.9 3304.8 1579.4 20610.4 20240.5 19892.0 17663.5 16918.2 15305.9 13920.1 13827.3 13343.1 12759.4 11672.5 6310.1 4107.6 1990.4 NEVPT2 es (in es

. b) Using free Ln free averages ionsfrom doped the intoLaCl a)Some of these experimental energy aretak levels field of splitting the multiplets. c) Using c) (Table1 a) set Tm Gd Ho Dy Eu Yb Tb Er Er 3 3 3 1 3 3 6 6 6 6 6 6 6 4 4 4 6 2 4 4 4 4 6 6 6 G F F H H F H H 4 5 5 5 3 5 7 7 7 7 7 7 7 7 7 7 7 7 5 5 5 5 5 H H P P P S I I F F F F F F F F F 5 5 5 5 F I F D D D K S F F F F F F F F F F F F 11/2 13/2 F F F F F 2 2 3 4 4 5 I I I I 3+ 9/2 11/2 13/2 4 9/2 5/2 3/2 5/2 7/2 9/2 3/2 5/2 7/2 3/2 5/2 7/2 3/2 5/2 7/2 4 5 6 7

2 0 1 2 3 4 5 6 5 4 3 2 1 2 1 2 3 4 5 8 2 2 1 0

, , ions(Table 1) , ,

01 1240 07. 10275.0 10275.0 10214.0 10214

F 4 4 , , , , 33290 32720 32120 5653 5431 4977 4292 3314 2051 22180 21240 20960 20510 18450 18320 15370 13180 11110 8550 5050 21510 19030 17270 4940 3910 2860 1890 1040 370 21320 14850 14350 12500 8090 5640 22410 22070 20400 18290 15180 12350 10110 6480 13060 12270 10870 10100 9060 8950 5780 3460 F F 6 6 and and ζ ζ fromab initio calculations thefor from literature from for free the Ln

22366.1 21317.0 21137.0 20568.0 18480.0 18220.0 15403.0 13350.0 11255.0 8648.0 5087.0 21573.0 19155.0 17508.0 5014.0 3915.0 2861.0 1883.0 1031.0 373.0

34667.0 33960.0 33342.0 5833.0 5598.0 5121.0 4403.0 3389.0 2093.0 23077.0 20949.0 21766.0 21416.0 19365.0 18858.0 16146.0 13446.0 11348.0 8742.0 5159.0 22224.0 19670.0 17906.0 5303.0 4147.0 3036.0 2004.0 1101.0 400.0 21482.0 15198.0 14517.0 12709.0 8323.0 5670.0 23012.0 22731.0 20991.0 18980.0 15595.0 12456.0 10270.0 6612.0 13566.0 12777.0 11342.0 10391.0 9356.0 9299.0 5935.0 3531.0 3 ignoring ligand 35484.8 34836.2 34228.9 5826.5 5595.3 5123.9 4410.2 3399.0 2081.9 22626.5 21899.0 21363.8 20882.0 18797.5 18656.6 15692.8 13439.3 11332.6 8714.2 5137.6 23228.3 20643.8 18850.3 5288.0 4120.9 3004.7 1974.3 1079.2 389.9 21467.7 15008.1 14383.2 12679.0 8335.3 5584.2 22696.3 22439.4 20729.8 18446.3 15472.1 12574.2 10334.1 6616.6 13392.6 12574.4 11133.9 10352.6 9169.8 9267.2 5905.6 3514.5 en asen 3+ ions

9 9

iue . en boue deviation absolute Mean states ion mainlyresulting from free the for Exp./NEV-PT2 and 6. Exp./BonnMag Figure 10 Gd Eu Pr Ln th of calculations procedure . the for free for used energies transitions Parameters 3. Table

F 2 F , , 1520.0 1320.0 2 385.0 373.0 770.0 317.0 F , , 6.28 56.4 6.04 53.7 5.13 50.9 F 4 , ,

4 F , , F 6 , Accepted6 Article ζ

ζ,

energies andMADin cm 32720 32120 22211 22007 21389 17334 9921 6854 6415 4996 4389 2152 21510 19030 17270 4940 3910 2860 1890 1040 370 33290 23160 E Ln Exp. os band rm fitting a from obtained ions E This article isprotected by copyright. All rights reserved. 33428 32748 32151 21407 18997 17360 23349 21566 22083 21457 17562 10147 5006 3907 2855 1880 1030 6996 6423 4987 4411 2153 BonnMag 373 ζ Journal ofComputationalChemistry . MAD 1 John Wiley& Sons,Inc. . 146.7 65.7 35.9

e band rm h Wbun parameters Wybourne the from obtained F Cs chlorides elpasolite-type of spectra Absorption Csseries the for ligand-field the to due splitting and energies deviation transition of Calculation absolute Mean states ion mainlyresulting from free the for Exp./NEV-PT2 7. and Exp./BonnMag Figure ee ae fo rfrne 4 ad 2 for 52 and 44 Cs references from taken were 4. Table in given are values These gadolinium(III). parameters Slater-Condon-Shortley The ligand the to field. due splitting the of the magnitude the of for especially quality BonnMag using the calculations evaluate to benchmarks O parameters AOM 6 , the spin-orbit coupling constant coupling spin-orbit the , 2 2 NaLnCl NaLnCl 6 6 2 xet o poehu(I) and promethium(III) for except as used were Gd) and Pm (except NaLnCl 6

e σ L-l and (Ln-Cl) F 2 , , F 4 ζ , , e as well as well as F π,iso 6 . . (Ln-Cl) (Ln-Cl) F

2 , , F 51 4 , Page 10of32

Page 11of32 9 shows the correlation between between correlation the shows 9 F E-T/ASF te nris f h fe Ln free the of energies the NEV-PT2/CASSCF, atomic number except for Eufor except number atomic with decreases procedure fitting our by derived pure nearly the to respect with procedure fitting a by derived Ref. Ref. ih h eprmna energies experimental the with BonnMag with calculated energies excited-state parameters parameters aaees r raoal (iue a. The 9a). AOM (Figure the reasonable that are parameters confirming both for sets, data parameter experimental the with match the good a using show energies transition calculated The reproduced better from Tableparameters 3. be can ions and NEV-PT2/CASSCF from obtained The ratio ratio The Ln transi the of energiesfor calculations BonnMag the in used were 5 and 44 (Refs. literature from Parameters 4. Table hl sre o clrds Cs chlorides of series whole from the literature. The parameter parameter The literature. the from oi rdi f Ln of radii ionic e and a fitted value for for value fitted a and sets. lit: sets. parameter following the using 9 Figure in given O parameters AOM derived of The 4. range Table in the shown values in literature is which S1) and 1 (Table 1/3 u t te iadfed ee additionally were ligand-field parameters the using the calculated to splitting the due as well as energies state excited m 4. 5. 55 17 2. 100 0.31 100.0 326.5 1167 5.5 51.7 344.5 Sm m 4. 6. 70 64 0. 196 0.39 119.6 305.3 2624 7.0 65.7 449.4 Tm o 2. 6. 63 19 2. 132 0.44 143.2 325.1 2129 6.3 0.37 62.9 156.0 0.35 420.0 419.0 137.2 Ho 623 391.1 872 0 4.8 48.6 0 315.1 Nd 0 Ce b 0 29 260 1. 0.48 114.0 236.0 2897 0 0 0.46 0 138.0 300.5 Yb 1920 6.3 60.9 412.1 Dy 372.8 Eu b 9. 5. 58 64 1. 196 0.44 139.6 315.3 1694 5.8 58.8 398.1 Tb r 3. 6. 65 36 9. 100 0.41 120.0 292.0 2356 6.5 63.8 431.4 Er 299.2 Pr 2 σ and 3+ (Ln-Cl), (Ln-Cl),

44 ; fit1: fit1: ; F ζ 2 F given in Table 3 and a fitted value for value fitted a and 3 Table in given

2 e Ln

, , e π F / π in Csin 51 . 12 342 3. 0.36 136.4 384.2 1324 0.41 5.6 184.8 55.1 447.4 756 4.4 45.5 e F 4 F / F , , e 2 σ 2 4 , , , , varies from 0.31 to 0.48 over the over 0.48 to 0.31 from varies F σ σ F 6

AcceptedF Article F 2

, , J NaLnCl 13 Sne h fe ion free the Since 1/3. = 4 4 tts ih h ratio the with states ζ , , , , 3+ e ,

F 6 Te oprsn f the of comparison The . σ σ e e ζ 6 6 , , σ , , e r cmaal t those to comparable are (Ln-Cl), and(Ln-Cl), ζ σ 6 ζ . . (Ln-Cl), , from NEV-PT2/CASSCF from F r oeetmtd by overestimated are 2 , , This article isprotected by copyright. All rights reserved. F 4 , , 3+ F and Tmand 6 e σ , π

Journal ofComputationalChemistry ζ F 2 / e , NaLnCl 44 2 e e e , , π σ σ σ ep) are (exp.) (Ln-Cl) from (Ln-Cl) σ F , = 1/3; fit2: 1/3; = L-l and (Ln-Cl) e 4 e , , π π 3+ in cm John Wiley& Sons,Inc. e e e F e . Figure Figure . σ σ 6 6 π and (Ln-Cl) (Ln-Cl) . The The . ) that 2) / e 1 π tion σ σ . / e = 3+ σ ζ

o a etr ecito o te ligand-field the of description influence. better a for necessaryiscalculations initioab in space active the of extension an that indicates This spectra. absorption the fitting the by obtained than parameters lower significantly are values These e aus o te hl sre o Cs of series whole the for values In Reference 3 the the 3 Reference In ligands inthe different compounds. and elements earth rare the between bonding the of splitting becan states studyexcited used the chemicalto the Furthermore moments. magnetic the of dependency temperature the and susceptibilities ligand-field magnetic the the for of calculation crucial the is state ground of the of splitting description proper The procedure vs. ionic radiiprocedure vs. of Ln setting the ratiosetting allow will sublevels resolved well the of analysis detailed principle, In systems. new considering mhszd n iue b o oe selected one for Ln 9b each for transition Figure in emphasized is which good values, observed in the with agreement are splittings ligand-field calculated

(except Pm and Gd) are reported using AILFT using reported are Gd) and Pm (except of fitting the procedure as well as NEV-PT2 from obtained nlec. h parameters The field ligand influence. the of magnitude the well rather Figure 8. 8. Figure π,iso L-l ue i tee acltos describe calculations these in used (Ln-Cl) e σ L-l otie fo te fitting the from obtained (Ln-Cl) e e σ π (Ln-L) can be applied by by applied be can (Ln-L) / e σ . 3+ e ion. Thus, ion. σ L-l and (Ln-Cl) 3+ F . 2 74 74 , , F 4 e , , σ (Ln-Cl) and (Ln-Cl) e F π,iso 6 2 and NaLnCl (Ln-Cl) 53 11 11 ζ 6 .

fitted fitted excited state energies in IR/vis range, b) splittin b) range, IR/vis in energies state excited ligandeffect.field iue . eetd acltd n eprmna tran experimental and calculated Selected 9. Figure 12 nrisotie using obtained energies

e σ (Ln-Cl) and (Ln-Cl) Accepted Article

e π / e σ σ = 1/3 (fit1); (fit1); 1/3 = F 2 This article isprotected by copyright. All rights reserved. , , F 4 , , F Journal ofComputationalChemistry 6 , , ζ and F 2 John Wiley& Sons,Inc. and e σ L-l fo ltrtr (lit.); literature from (Ln-Cl) ζ from Table 3 with fitted with 3 Table from g pattern for the various excited states to visuali to states excited various the for pattern g iin nris o Ln for energies sition e σ F (Ln-Cl) and (Ln-Cl) 2 , , 3+ F 4 n Cs in , , F 6 , , ζ 2 rm E-T with NEV-PT2 from NaLnCl e π / e σ σ = 1/3 (fit2) a) (fit2) 1/3 = 6 Calculated .

ze the ze Page 12of32

Page 13of32 e ubr xet Eu except number (8) PrCl for state ground the (except energies state the of shift observed The h distances the between difference The S1). (Table symmetry discussed. chromophores low-symmetry. with the for BonnMag alreadyusing reproduced ligand-field well be can the to due as splitting the However, constant spin-orbit and coupling parameters Condon-Shortley Slater- overestimated the by caused is numbers rsne i tee opud hv site have compounds these symmetry in presented chromophores The systems. low-symmetry for BonnMagofquality the assess toused were Ho) were accounted foraccountedwereby relation(8). ih t lwsmer lgn fed is fields ligand low-symmetry PrCl for demonstrated to high- the for fromparameters AOM the of transferability The experiment the orthophosphates. with good agreement in is splitting calculated The elpasolites. PrCl of spectra Absorption PrCl for the ligand-field to due splitting the of Calculation The value value The n osre dt. al S (I sos the shows (SI) S3 value Table data. observed and calculated of comparison visual by derived was LnPO orthophosphates LnPOorthophosphates Tbe ) Te Slater-Condon-Shortley of value fit” “best The compounds. all for used The were constant NEV-PT2/CASSCF from obtained coupling spin-orbit and 5). parameters splitting calculated the (Table to compared is field ligand- the to due splitting level experimental EuPO dP l)) ) Cl (d(Pr e ) d ( e σ σ σ (Pr-Cl) was taken from Cs from taken was (Pr-Cl) 4 e 77 4 σ (Ln: Pr, Sm, Eu, Tb and Ho) Ho) and Tb Eu, Sm, Pr, (Ln: ⋅ − = ) or or ) (Ln-O) C e σ 3 h (Ln-O) 2.38Å (PrCl d

Accepted ArticleD P-l i PrCl in (Pr-Cl) 2 for for the orthophosphates. d (TbPO

3+ 2 .38 Å 3 s led fud o the for found already as 78 ), ), 4 min erae wt atomic with decreases 3 (Ln: Pr, Sm, Eu, Tb and Tb Eu, Sm, Pr, (Ln: Te O parameter AOM The . 3 C and phosphates phosphates and 1 4 This article isprotected by copyright. All rights reserved. 2 (PrPO 14 NaPrCl       3 t hge wave higher to ) HoPO , (rC ) Cl d(Pr 3 (rC ) Cl d(Pr n Cs and Journal ofComputationalChemistry 3 n five and 4 6 − 41 76 with with − SmPO , 4 14 John Wiley& Sons,Inc. 2 e NaPrCl ). The The ). min σ O (Ln-O) h site site 7 4 77

6 , ,

susceptibilities and susceptibilities of of

C Sm C Pr C Pr and[LnO cmin (LFS transition selected a for field t to due splitting calculated and Observed 5. Table eedn mgei moments magnetic temperature- and dependent susceptibilities magnetic energies, transition electronic of calculation the allows BonnMag program developed newly The Conclusions a)Pr D Ho D Tb C Eu ytm wti te rmwr o te angular the of framework the within systems

Ln 1 1 3h 2d 2d 1 a)

electrons) 3+ in PrCl state 6 9 1 1 3 5 5 F 5 ] or ] [LnO D D H D D I

9/2 4 2 2 4 4 2

16779.5 16731.2 16630.5 133 133 96.1 33.2 0 9338 9319 9306 9277 9254 17021 16906 16720 16663 16579 20622 20598 20575 20551 20539 20497 20487 13414 13387 13344 13317 13293 13258 13220 13134 21647 21633 21614 21607 21590 8 18 E ] chromophoresin LnPO Exp. for the complete range of of range complete the for LFS g -tensors (for odd numbers odd (for -tensors 149 3 20781 135 280 4 18016 442 4 9360 84 7 22195 57

exp. E 1 ) for [PrClfor ) 18131 18113 17985 20902 20886 20863 20820 20803 20797 22251 22238 22220 22208 18462 18279 18205 18070 13758 13678 13633 13575 13559 13506 13506 13468 9433 9401 9389 9376 BonnMag 217 135 134 118 96 11 4 0 . 42 crystal , LFS he ligand he 9 ] in PrClin ] 121 217 146 446 290 73 56

calc. f 13 13 n 3

states for Lnfor states transition electronic measured The techniques. parameters implemented. parameters be will AOM obtain automatically to spectra of fitting field ligand least-square and modeling magnetic dependent of field- theory, ligand-fieldinitio ab from matrices introduction parameters, the Mössbauer of calculation The of included. options be will further development BonnMag program ongoing computer the Within usingBonnMag. opttoal demanding and computationally sophisticated described more than the accuracy similar a of with results to leads modeling and properties physical the well for is AOM suited that shows, BonnMag program 14 the for used parameters for energies transitions the of calculations AOM S1. Table forInputBonnMag S5. files susceptibilitiesmagnetic Calculation S4. the transitionenergies of and Implementation S3.1. inBonnMag Calculation S3. the absorptioncoefficients of Reduced elementsMatrix Coefficients S2. Fractional of andParentage symbols and6-j Clebsch-Gordon S1. CoefficientsandWigner 3-j- Supportinginformation available. elements,absorptionspectra, BonnMag Keywords: The possible. fast is between comparison and chromophores simple for different calculations the of number large experimental a to procedure, Due with intensities. agreement absorption yield reasonable theory Judd-Ofelt calculated on based The coefficients model. overlap tts u t te iad il fr h series the for field ligand Cs the to due states Cs

2 2 NaLnCl NaLnCl 6 6 nua oelp oe, rare-earth model, overlap angular . LnPO and e 3+ π : : and the splitting of the parental the of splitting the and

e Accepted Article

σ σ = = 1/3.

b initio ab -1 . John Wiley& Sons,Inc. Ln in

al S. acltd n experimental and Ln for Calculated energies transition S2. Table from NEV-PT2/CASSCF with fitted fitted with NEV-PT2/CASSCF from References and Notes Notes and References and fitted fitted e al S. O prmtr ue fr the for used parameters for energies transitions the of calculations AOM S3. Table andEu). O) acltd nris band using obtained energies Calculated LnPO π / 2.38 e 5. 4. 2. 1. 9. 8. 7. 3. 6. σ σ e Å 4 13 ft) (fit1); 1/3 =

σ . e . . (Ln-Cl) from literature (lit.); (lit.); literature from (Ln-Cl) σ e Yin, Yin, M. Xia, S. Duan, C.-K. Reid, M.F. Hu, L. 178 . sgwr, . aaae H. Watanabe, Tanaka, I. S. Ikeno, H. Brik, M.G. Ishii, T. Toyoshima, Osagawara, K. . a dn evl S Calvello, S. Heuvel, den A.Soncini, van W. 1968 Matsuura, Matsuura, Y. Yamamoto, H. Togawa, N. Fujimura, a) T. Jüstel, H. Nikol, C. Ronda, Ronda, C. Nikol, H. Jüstel, T. a) W. Urland, W. Wegh, R.T. Meijerink, A. Peijzel, P.S. Chem. Int. Ed. Int. Chem. Chem Burdick, G.W. Reid, M.F. Comput. ChemComput. Freire, R.O. Bispo, T.D. Dutra, J.D.L. aeci n R Sessoli, R. Commun. and A. Favre, Ganeschi A. Mannini, M. Perfetti, M. . rvn, . tnsv F Neese, F. Atanasov, Inorg.Chem M. Aravena, D. 2016 Velge, K.H.J. Buschow, Buschow, K.H.J. Velge, . ua C Wcldr n W Urland, Phys. Chem. Lett. W. and Wickleder C. H. Suta, M. Daul, Cimpoesu, C. Herden, B. F. Ramanan-toanina, García-Fuente, A. 045501. (Ln-Cl) and (Ln-Cl) π : : , , 412. J. Phys. Condens. MatterCondens. Phys. J. e , , . σ σ 18 2005 39 = 1/3. 1/3. = , , 15807. 11. d M Sgw, S. Sagawa, M. d) 1717.; , J.Appl. Phys 2011 Chem.Phys e . oi Sae Chem State Solid J. hs Ce. hm Phys Chem. Chem. Phys. , . F 178 π 2016 2 /

and and e 1998 . σ σ 2014 e , , , , 448. = 1/3 (fit2) (only for Pr for (only (fit2) 1/3 = σ 2015 , 47 , 55 , , e ζ rm al 3 with 3 Table from 35. c W.A.J. c) 3751.; , 37 , , π 3+ n cm in , , 4457. 35 , . n Cs in . , 3084; b) P. Car, P. b) 3084; , 622 1976 1984 ,772. . p. Phys App. J. . oi State Solid J. e , 120. , σ F -1 , , F (Ln-Cl) and (Ln-Cl) , , 2

2 for 14 55 , , 2011 , , 2 NaLnCl

F F , 393. , . Angew. , 2083. , 4 4 Chem. , , , , 2005 d Ln , , F F (Ln- 6 6 23 , , in , , 6 J. ζ ζ . . . , . , Page 14of32

Page 15of32 18. 21. 19. 20. 12. 22. 11. 13. 24. 23. 10. 25. 26. 15. 27. 28. 14. 16. 17.

1983 TheoryField Gerloch, M. . . . Lever, spectroscopy P. B. A. University of Gießen, University of Soc. DaltonSoc. McMeeking, F. R. Gerloch, M. VCH New VCHNew York, Hitchman, Applications Its A. and Theory Field M. Figgis, N. B. 372. 372. . asn G N LaMar, N. G. Larsen, E. . enn MA Aaao, .L Lee, S.-L. Chem. Coord. Rev Atanasov, M.A. Reinen, D. 1422. VCH D. E. Richardson, E. D. 1974 . Urland, Gießen, University of W. oriain hmsr, Lausanne, Switzerland, Chemistry, Coordination 29th 445. 445. 457. . Urland, W. Urland, W. H.-H. Pappalardo, Schmidtke R. Jørgensen, K. C. 1973 Slade, Parameters R. Gerloch, M. R. Glaum, Glaum, R. 105. 105. . Urland, W. Press Press Spectra Atomic of Shortley,H. G. Condon, U. E. L. H. Gade, H. L. . . ulc, . . rsi ad . A. L. and Grossie Boatner A. D. Mullica, F. D. 296. 296. Chem Schäffer, E. Brorson, M. Bendix, J. rga Pcae o Ligand-Field Computer Personal a for on Calculations Package Program Bendix, J.

1998 . , . . 1967 51 1993, nentoa Cneec on Conference International

Accepted Article Acta Chim. Inorg. ,

, , 633. . J Ce. Phys Chem. J. , .

Cmrde nv Press, Univ. Cambridge , Koordinationschemie 1975 hm Py. Lett Phys. Chem. Lett Phys. Chem. hm Py. Lett Phys. Chem. 1992.

,Elsevier, New York, 32 Cmrde nv Press, Univ. Cambridge , Lgil" A Extensive An "Ligfield": hss of Thesis ants ad Ligand and Magnetism , , 2838. 2000 , 2443. , . J. Chem. Ed. Chem. J. aiiain thesis Habilitation

1999 1980 , 175 Journal ofComputationalChemistry

. . . hm Ed Chem. J. iad Field Ligand Habilitation . , 91. , . . . The Theory The 1985 1963

1977 1977 1978 1993 John Wiley& Sons,Inc. . Chem. J. , Wiley- , , Wiley- ,

Ligand 1998 109, , Inorg. , , , , , , 53, 53, , , , 70 50 46 39 .

, , , , , , . , , 38. 37. 36. 35. 34. 33. 29. 30. 42. 40. 39. 41. 32. 31. 45. 46. 43. 44. 47. 49. 48.

A219 AbelschenFunktionen G. Racah, Racah, G. G. Racah, Racah, G. ruz S R Leh M J Riley, J. Chem., M. Luethi R. S. R. E. Krausz, Bernhardt, V. P. Flanagan, M. B. Chem., Chem., S.R. Bernhardt, Krausz, E.R. and Riley M.J. Luethi, P.V. Flanagan, B.M. hmsr ad hsc o Solids of Physics Pressure andChapmanHall, London High and the Chemistry and transitions Frank, W. C. Drickamer, G. H. Phys Drickamer, G. H. Minomura, S. C. E. Schäffer and C. K. Jørgensen, Jørgensen, K. Inorg.Nuclear.Chem C. and Schäffer E. C. . . . Stevens, H. W. K. W. Urland, W. and Glaum, R. Bredow, T. Bronova, A. LondonA., . lbc, . Gordon, P. Clebsch, A. Butler H. P. W. Urland, W. rnprn Rr Erh Compounds New Press Academic York, Earth Rare Hüfner,Transparent S. Publishers, New York,Publishers, ae at in i crystals in ions earth rare H.G.Dieke, 83 Mülheim, package SCF-MO semiempirical 4.0, ORCA Chem. TheoryComput. Chem. Pantazis, A. D. Neese, F. Aravena, D. antc ucpiiiis Oxford Susceptibilities, Press, University London,1932. Magnetic Vleck, van H. n R D Smith, D. R. and Dallara J. J. Reid, F. M. Richardson, S. F. J.Sugar, 2171. Phys Runciman, A. W. Crozier, H. M. G. S. Ofelt, Ofelt, S. G. , , 3813. . . , , 542. 1961 1961 2002 2001 Phys. Rev. LettPhys. Phys. Rev Phys. Phys. Rev Phys. 2017 1975,

, , Inorg.Chem Chem.Phys 35 35 Spectra and energy levels of levels andSpectra energy , , , , . hm Phys Chem. J. n b nto DT and DFT initio, ab An 41 40 , The Theory of Electric and Electric of Theory The hl Tas Ry Soc. Roy. Trans. Phil. , , 903. , , 1392. . , 5024. , , 5401. , pia Seta of Spectra Optical

277 . hm Phys. Chem. J. rc Ry Soc Roy. Proc. . .

1943 1942 . , , 545.

, Leipzig, , 1958 1968

. 2016 . 1979 1965 2016 , , , , Interscience , 63 62 1978 , , . 1973 hoi der Theorie , , 8 . , , , , 367. , , 438. , , 12 , , 143. , , 38 1963 1866 Electronic 14 55 J. Chem. J. . J. Chem. J. , , 1148. . , 407. , , 731. ,

, 6853. ,

MPI , . Inorg. 1954 1985 Inorg , , .

38 15 15

J. J. , , , , ,

68. 63. 58. 54. 50. 53. 51. 67. 59. 52. 66. 60. 62. 65. 61. 64. 55. 56. 57.

tmc nry ees Te Rare-Earth The – Levels Energy Atomic f 1976 Crosswhite, and J. G. Conway, Conway, G. M. J. H. and Crosswhite, H.Crosswhite, Carnall, T. W. B. R. Judd,R. B. 1976 Press, Press, Structure I Structure Slater, J.C. E. P. Wigner, Wigner, P. E. 116. 116. NSRDS-NBS 60, 422 pp. (Nat. Bur. Bur. (Nat. pp. U.S.,Stand., 1978). 422 60, NSRDS-NBS Ser., Data Ref. Stand. Nat. in Hagan, L. and R. Zalubas, C. W. Martin, Elements, 55. 2012 143 Vol. Molecular K II. Complexes Neese, Ganyushin, structures Electronic of TransitionMetal F. D. Sivalingam, Atanasov, M. . . yore Spectroscopic Wybourne, 1965. NY, Sons, & Wiley Earth, Rare G. of Properties B. aea ad . Sarup, W. R. and F. Kaseta, Crosswhite, H. Crosswhite, M. . Krane, K. . Urland, W. Wiley, Wiley, M. J. Riley, J. M. B. R. Judd,R. B. . . . oel n R Orbach, R. Phys. Soc and Powell D. J. M. 325. 325. Phys Morrison, A. C. and Leavitt P R. G. S.Ofelt,G. . . Kruppke, F. W. Press, New York, Press, 1972 1972 Shelejain, 106 Band Seiten" L.A. verschiedenen Smorodinski, " A. J. R. Boca, R. C. W. Nielson, G. F. Koster, Koster, F. G. Nielson, p for Coefficients Spectroscopic W. C. lbc-odnKefzetn von Clebsch-Gordon-Koeffizienten n Configurations

. , , . (Russian).

1980 64 1963 64

Accepted1987 Article Struct. Bond ,3582. . , , 1981. Srne, eln Germany, Berlin Springer, ,

1961 ,McGraw-HillNY, nrdcoy ula Physics Nuclear Introductory , Proc.Roy Phys. Rev Phys. J. Chem. Phys . Inorg. Chim. Acta Chim. Inorg. Quantum Theory of Atomic Atomic of Theory Quantum . 73 hm Phys Chem.

, , 749. In Structure and Bonding Bonding and Structure In ru Theory Group

, ,

. . 2006 1957 1962 . . . . hm Phys Chem. J. Journal ofComputationalChemistry Lett. 1962 , , , , . 117 A241 127 1960 Academic , 1966 1998

1981 , , , , 1-264. , , 750. n John Wiley& Sons,Inc. 37 J. Chem. J. , d , , , 414. . UFN, , , ,

, , 511. , , n Proc. , , and 145 268 ibid 83 . , , , ,

79. 80. 81. 78. 77. 76. 75. 72. 74. 71. 73. 70. 69.

Acta Anorganischen ChemieAnorganischen 1367. A C. F. Schäffer, Schäffer, F. C. iad il TheoryAmsterdam, Field Ligand Jørgensen, K. C. . aaataia W Uln, F. Urland, Daul, C. W. Cimpoesu, Ramanantoanina, H. Phys. J. S. Margolis, Margolis, S. J. 71. el ad . . Boatner A. W. L. G. and Mullica, Beall F. D. Mulligan, O. W. . . ulc, . . rsi ad . A. L. and Grossie Boatner A. D. Mullica, F. D. . rnv, . annißr n R. and Glaum, Kannengießer N. Bronova, A. Chem Yeung, Y. Y. and Tanner A. P. 10.1021/acs.inorgchem.7b01287 Berlin, Germany, Berlin, . olmn E Wiberg, E. Holleman, A. . . anl, . rswie H M. H. Crosswhite, H.Crosswhite, Carnall, T. W. LaboratoryReport Computer Program Computer 3002. K. Rajnak, and J. B. Mann, Mann, of Boston, Reidel, Properties B. the J. Lanthanides and and Systematics Rajnak, K. Crosswhite, H. Beitz, V. J. Carnall, T. W. . . rswie H Cosht, N. Crosswhite, Rajnak, K. and Edelstein, H. Crosswhite, M. H. ac.uk/orbitron/AOs/4f/, 2017. http://winter.group.shef. Sheffield, of

1967 1983

. 2014 2013 , 297, 96., Inorg. ChemInorg. J Sld tt Chem. State Solid J. , , 70, 70, , 133. , 16, 12282. , A , eie b S P Sinha, P. S. by edited , 1971. 117 Proc. R. Soc. London Ser. London Soc. R. Proc. . hm Phys. Chem. J. 1983

1995. ron National Argonne , , 10726. , ,

1977 oen set of Aspects Modern . 2017 . Orbitron hs Ce. Chem. Chem. Phys. .

North-Holland, , 101, de Gruyter, de 101,

ibid Iog Chim. Inorg. , , eruh der Lehrbuch in print. print. in , University , .,

1961 1985 1976 J. Phys. Phys. J.

, , , 57, , DOI: , , 35, 67 in , Page 16of32

Page 17of32

Accepted Article

u 8. 5. 62 1395.4 1231.3 6.26 1075.9 936.2 6.07 55.6 802.2 5.83 53.9 685.4 5.60 386.1 5.25 52.1 371.8 49.9 0.00 Eu 356.6 52.1 Sm 342.7 0.0 Pm Pm 324.2 Nd 0.0 Pr Pr Ce Ce Ln (incalculations cm NEVPT2 from param obtained coupling spinorbit and SCS ion Free 1. Table 2935.6 2671.3 0.00 2417.5 7.60 2182.5 0.0 7.37 1964.3 1761.7 69.9 7.08 1576.0 65.7 0.0 6.93 a)Experimental fordata 6.69 467.4 64.1 Yb 454.2 6.52 61.5 Yb 59.4 Tm 440.8 Er 58.4 427.6 Ho 414.2 Ho 399.1 Dy Tb Gd Eu the free Lnfreethe a) 3+ a) a) a) a) a) 2. 5. 52 764.0 5.23 51.7 325.4 . 00 .0 2918.3 0.00 0.0 0.0 1320.0 6.06 55.4 401.0

1. 6. 72 2163.0 7.27 68.8 414.6 643.7 0.00 0.0 0.0 4. 4. 52 1070.0 5.23 47.7 346.2

ions F 2

Accepted Article 1 (see text). F F 2 , , 4 F F F 4 2 , , This article isprotected by copyright. All rights reserved. , , F 6 6 F and 4 , , F Journal ofComputationalChemistry 6 ζ ad ASF ( CASSCF and ) from literaturefor 6 ζ ζ John Wiley& Sons,Inc. eters ζ ) ) Page 18of32 Page 19of32 Ln 50. Ref from energies Experimental NEVPT2. and BonnMag cm(in energi experimental the between Comparison 2. Table Sm Pm Nd Nd Ce Eu Pr 3+

1 5 5 5 5 5 4 4 4 2 4 4 4 4 2 4 4 4 4 4 3 2 4 4 4 4 4 6 6 6 6 6 6 6 6 6 6 6 5 5 5 5 5 1 3 3 3 3 3 1 3 3 1 state ) for the free Lnfree the for ) F G G G G G F S F H F F P P P D G F F F H H F F F F F F F F H F H H H H F F S F F I I I I I I I I I I I 5 7 7 7 7 7 7 11/2 9/2 7/2 8 7 6 5 15/2 13/2 11/2 6 D F F F F F F 4 4 3 2 7/2 3/2 5/2 11/2 9/2 7/2 5/2 3/2 1/2 5 4 3 2 1 9/2 7/2 5/2 3/2 2 3/2 2 1 0 15/2 13/2 11/2 9/2 7/2 9/2 2 6 5 11/2 9/2 7/2 7/2 5/2 4

6 5 4 3 2 1

0 2400.0 2399.0 2253.0 2253

23160 22211 22007 21389 17334 9921 6854 6415 4996 4389 2152 15800 14470 14100 13520 12670 12230 6580 4820 3110 1490 17270 4940 3910 2860 1890 1040 370 20980 20560 20010 18860 17860 10470 9080 7910 7050 6540 6470 6290 4990 3610 2290 1080 Accepted 19440 19290 18890 17100 16980 14570 13370 Article13280 12470 12320 11290 5910 3860 1880 E

exp a)

3+ 23833.0 22009.0 22590.0 21976.0 17950.0 10202.0 7080.0 6516.0 5099.0 4375.0 2132.0 15916.0 14606.0 14373.0 13654.0 12735.0 12292.0 6934.0 5101.0 3305.0 1586.0 17508.0 5014.0 3915.0 2861.0 1883.0 1031.0 373.0 E ions and those calculated using calculated those and ions BonnMag This article isprotected by copyright. All rights reserved. b) E . Journal ofComputationalChemistry 19565.0 20121.0 19634.0 17732.0 16525.0 15257.0 13875.0 13717.0 12996.0 12835.0 11727.0 6300.0 4107.0 1992.0 23955.0 22112.0 22627.0 21971.0 18005.0 10471.0 7201.0 6613.0 5112.0 4597.0 2246.0 16262.0 14876.0 14591.0 13860.0 12957.0 12486.0 6983.0 5113.0 3298.0 1576.0 17906.0 5303.0 4147.0 3036.0 2004.0 1101.0 400.0 21056.0 20756.0 20065.0 19208.0 18607.0 10756.0 9288.0 8046.0 7135.0 6610.0 6861.0 6352.0 5304.0 3800.0 2384.0 1099.0 BonnMag c E . John Wiley& Sons,Inc. 20610.4 20240.5 19892.0 17663.5 16918.2 15305.9 13920.1 13827.3 13343.1 12759.4 11672.5 6310.1 4107.6 1990.4 23469.3 22126.5 22511.3 21463.7 17664.2 10411.2 7103.3 6495.7 4978.9 4603.4 2250.8 16454.3 15059.0 14477.0 14026.4 13340.5 12667.6 7013.6 5158.9 3304.8 1579.4 18850.3 5288.0 4120.9 3004.7 1974.3 1079.2 389.9 22463.8 21990.4 21593.7 20281.5 19414.9 10836.2 9379.2 8147.4 7238.9 6701.9 6881.3 6430.8 5310.1 3797.0 2377.6 1094.1 NEVPT2 es

. free Lnfree averages dopedfrom ionsintothe LaCl Some thesea) of experimental energy aretak levels b) Using b) c) Using c) (Table a) set 1 ions field of splitting multiplets.the Tm Gd Ho Dy Yb Tb Tb Er 1 3 3 3 3 3 6 6 6 6 6 6 6 4 4 4 6 6 6 6 2 4 4 4 4 G F F H H F H H 4 5 5 5 3 5 5 7 7 7 7 7 7 5 5 5 H H P P P S I I F F F F F F F F F 5 5 5 5 I F D D S 11/2 13/2 K F F F F F F F F F F F F 2 2 3 4 I I I I 4 5 9/2 3+ 11/2 13/2 4 4 3/2 5/2 7/2 9/2 5/2 3/2 5/2 7/2 9/2 3/2 5/2 7/2 3/2 5/2 7/2 4 5 6 7

2 5 0 1 2 3 4 5 2 1 2 3 4 2 8 2 1

, , (Tableions 1) ,

01 1240 07. 10275.0 10275.0 10214.0 10214

F 4 4 , , , , 33290 32720 32120 21510 19030 13060 12270 10870 10100 9060 8950 5780 3460 22410 22070 20400 18290 15180 12350 10110 6480 5653 5431 4977 4292 3314 2051 22180 21240 20960 20510 18450 18320 15370 13180 11110 8550 5050 21320 14850 14350 12500 8090 5640 F F 6 6 6 and and ζ ζ fromab initio calculations thefor from literature from freefor Ln the

21573.0 19155.0

22366.1 21317.0 21137.0 20568.0 18480.0 18220.0 15403.0 13350.0 11255.0 8648.0 5087.0

34667.0 33960.0 33342.0 22224.0 19670.0 13566.0 12777.0 11342.0 10391.0 9356.0 9299.0 5935.0 3531.0 23012.0 22731.0 20991.0 18980.0 15595.0 12456.0 10270.0 6612.0 5833.0 5598.0 5121.0 4403.0 3389.0 2093.0 23077.0 20949.0 21766.0 21416.0 19365.0 18858.0 16146.0 13446.0 11348.0 8742.0 5159.0 21482.0 15198.0 14517.0 12709.0 8323.0 5670.0 3 ignoringligand 35484.8 34836.2 34228.9 23228.3 20643.8 13392.6 12574.4 11133.9 10352.6 9169.8 9267.2 5905.6 3514.5 22696.3 22439.4 20729.8 18446.3 15472.1 12574.2 10334.1 6616.6 5826.5 5595.3 5123.9 4410.2 3399.0 2081.9 22626.5 21899.0 21363.8 20882.0 18797.5 18656.6 15692.8 13439.3 11332.6 8714.2 5137.6 21467.7 15008.1 14383.2 12679.0 8335.3 5584.2 enas 3+

Pr Ln th of calculations procedure. the for free for used energies transitions Parameters 3. Table Ln transi the of calculations BonnMag energiesfor the in 5 used and 44 were (Refs. literature from Parameters 4. Table Gd Eu Sm 344.5 51.7 5.5 1167 326.5 100.0 0.31 0.31 100.0 326.5 1167 5.5 51.7 344.5 Sm Tm 449.4 65.7 7.0 2624 305.3 119.6 0.39 0.39 119.6 305.3 2624 7.0 65.7 449.4 Tm Ho 420.0 62.9 6.3 2129 325.1 143.2 0.44 0.44 143.2 325.1 2129 0.37 6.3 62.9 0.35 156.0 420.0 419.0 137.2 Ho 623 391.1 872 0 4.8 0 48.6 315.1 Nd 0 Ce Yb 0 0 0 2897 236.0 114.0 0.48 0.48 114.0 236.0 2897 0 0 0.46 0 138.0 300.5 Yb 1920 6.3 60.9 412.1 Dy 372.8 Eu Tb 398.1 58.8 5.8 1694 315.3 139.6 0.44 0.44 139.6 315.3 1694 5.8 58.8 398.1 Tb Er 431.4 63.8 6.5 2356 292.0 120.0 0.41 0.41 120.0 292.0 2356 6.5 63.8 431.4 Er 299.2 Pr 3+ 3+

F 2 F

2 F Ln , 1520.0 1320.0 2 770.0 317.0 385.0 373.0 F , , 5.13 50.9 6.28 56.4 6.04 53.7 in Cs in 4 Accepted Article F 55.1 5.6 1324 384.2 136.4 0.36 0.36 136.4 384.2 0.41 1324 5.6 184.8 55.1 447.4 756 4.4 45.5

, ,

4 F F , , 4 6 6 F F

, , 6 2 ζ , NaLnCl

ζ, energies andMAD in cm 6 ζ 32720 32120 21510 19030 17270 4940 3910 2860 1890 1040 370 22211 22007 21389 17334 9921 6854 6415 4996 4389 2152 33290 23160 E 6 Ln . Exp. This article isprotected by copyright. All rights reserved. F os band rm fitting a from obtained ions 2 E , F 4 , F Journal ofComputationalChemistry 23349 21566 22083 21457 17562 10147 21407 18997 17360 33428 32748 32151 e 6 6996 6423 4987 4411 2153 5006 3907 2855 1880 1030 BonnMag 373 , , σ

ζ , e σ MAD MAD , John Wiley& Sons,Inc. e e π π 1 in cm e . 146.7 35.9 65.7 ) that 2) 1 . π / tion e e σ

Page 20of32 Page 21of32 C Pr and[LnO cm in (LFStransition selected a for field t to due splitting calculated and Observed 5. Table a)Pr D Ho D Tb C Eu C Sm C Pr

Ln 2d 2d 1 1 1 3h a)

3+ in in PrCl state 6 9 3 5 5 1 1 F 5 ] or ] [LnO D H D D D I

9/2 9/2 4 4 2 2 2 4

3 Accepted Article

] chromophoresinLnPO Exp. LFS

exp. E Journal ofComputationalChemistry 1 ) for [PrClfor ) 22251 22238 22220 22208 13758 13678 13633 13575 13559 13506 13506 13468 18131 18113 17985 20902 20886 20863 20820 20803 20797 18462 18279 18205 18070 9433 9401 9389 9376 BonnMag 217 135 134 118 96 11 4 0 . John Wiley& Sons,Inc. LFS he ligand he 9 ] in PrCl in ] 290 290 146 146 217 121 121 446 446 56 56 73 73

calc. 3

BonnMag Ligand Computer - for FieldAnalysi Program of the free Ln free the of the for used is BonnMag program developed newly The Model elpasolites elpasolites Cs Anna Bronova, Thomas Robert Bredow, Glaum, J. R Mark GRAPHICALABSTRACT n si-ri culn cntn fo CSC ad NE and CASSCF Additionally,framework the of within from constant coupling spin-orbit and

Accepted Article

2 3+ NaLnCl ions . These calculations are performed using the the using performed are calculations These . ions 6 using fit the parameter This article isprotected by copyright. All rights reserved. Journal ofComputationalChemistry

John Wiley& Sons,Inc. angular overlap model overlap angular e σ is done and compared from theto results literatur s of calculations of the transition state energies state transition the of calculations -T fr oprsn f hs methods. these of comparison for V-PT2 iley, and iley, Werner Urland f the ligand-field splitting for the series of of series for the ligand-field thesplitting n within Systems the Angular Overlap Slater-Condon-Shortley parameters Slater-Condon-Shortley

e. Page 22of32 Page 23of32 In simplify to order calculation the of CGC the 3- The Clebsch-Gordon coefficients (CGC) coefficients Clebsch-Gordon The Clebsch-Gordon Coefficients Wigner and and 6 3-j- S1 It is possible to define a scalar independent from independent scalar a define to possible is It Anna Bronova, Thomas Robert Bredow, Glaum, BonnMag- Ligand-Field Computerfor Program Analysi Supporting information The elements < momentum ofsystems independent the 1). (Eq. following relation (6) (2) The symbols vanish the if selection rules not are f theAngular Overlap Model , |                             m m m all > > < = > − < + > − = >< = ∑ N n n j j j j j j j j 3 2 1 mj 2 1 3 2 1 m m m − j j j j j j 3 2 1 m j m j m j j j )( ),;,|, | , ; , 1) (2 1) ( j m j m m m m m m m

1 5 6 4 2 2 4 6 5 1 = + + 3 2 1 + ≤ ≤ − m 2 3 2 1 = + + j j j 1) ( 2 2 1 1 2 2 1 1 5 64 6 2 4 6 5 1 ∑ ∑ ∑ ∑ 5 3 5 4 −=− =− −=− =− ⋅ − 4 4 j j j j 0 >= 2 1 2 1 m j j 34 6 5 4 3 5 − − 3 2 1 j j j m m

− − ∑ i m j i i

Accepted− Article

, =       j m j m m j j j

= ( 1 3 3 2 1 2 1 3 − − − , , | , ; , , ; , |   j j j m m m j ò ⋅ ⋅ 2 3 2 1 m j m m j j m m j j 2 2 1 2 1 2 1 2 1 m m j j m m j j ; j j j 3 2 1 (5) 2 1 2 1 2 1 2 1 3 2 1 m , , ; , | j,m | , ; , − ) 1 2 1 (4) (3) ) , This article isprotected by copyright. All rights reserved. m 2 | j , m Journal ofComputationalChemistry > of of transformation the > matrix Clebsch-Gord are the 6 John Wiley& Sons,Inc.

39,40 are obtained by summation of the orbital, spin and spin orbital, the of summation by obtained are

j Mark Riley, J. andUrland Werner were symbols byintroduced Wigner 2). (Eq. ulfilled (Eq. 3-5). m (1) . The product of the four 3- four the of product The . -j symbols -j s of s f n Systems withinSystems j symbols leads to the to leads symbols on on coefficients. 54

total total

Racah introduced the unit tensor operators. RME for RME operators. tensor unit the introduced Racah acM (c eso b M Rly ad nld U include and Riley) M. by version (pc CalcRME symbols and(Eq. 11).10 (8) elements matrix Reduced tabulated for all possible possible all for tabulated The result of sum is 6- this is aof matrix element the tensor operator the angular momentum coupling of the additional ele additional the of coupling momentum angular the Coefficients of these combinations are represented are combinations these of Coefficients All anti-symmetric All CoefficientsFractional of Parentage Reducedand S2 with the electron equation is given in 7 using Cleb (11) (11) all for Tables (7) The sum configurations the with of ( l; ,l l | × × × ) − ( ⋅ ⋅ ) ( LMM vLSM l S L v G G =++ + 1)] >= ' + 1)(2 [(2 1) + ' (2 1) (2 δ >= < < > ⋅| > ⋅ > < aet parentsparents parents S L v L T L M L T M L M M ∑ ∑ ∑ ∑ G 1 1 1 parents S L v 1 n ,'(1 || ' || || 1) ( ' ', | | , ∑ n p vLS n c L L n S L v l U vLS l m lsm M M S L v SM m M S L s s s n h S L v l V vLS l , , 1 1 1 S S L L ∑ − n K n n n , , S L v n S L S L v n 1 1 1 1 1 1 1 <> ≡< ≡ 1 1 - 1 , + + + + ' ' ' , S M LSM S L v 1 1 1 1 s l S L S s S Q 1) ( ) ( 1 1 1 K M L K G G -)() ) ( (-1) || 2 )( 1) ' (2 1) (2L ' ' ' || || || )21)] 1)(2 ( [ ' ' ' || || 1 1 1 2 2 2 − n 1 1 n , n n , L, 1 1 1 ,S ,L 1,v L S L v n vLS n − − ' ' ' , * , , , S L 1,v S L 1,v l | | s l S L S L de addedadded 12 11 1 1 1

1 1 m m             + + + + + Accepted 1 1 1 1 1 1 Article l l L s s Ss s lL l L L' k S S' S l LL' k s l

f − = n systems originally given by Nielson and Koster and Nielson by given originally systems S L ⋅ > < |}l , l n 1 1 − 1 n -electron states are obtained by linear combination linear by obtained are states -electron MmLM m lM L >= − − 1 1 ×       G -M Q -MQ M' L L' K S L v n vLSn - 1 , This article isprotected by copyright. All rights reserved. * , 58 L l L p

j 1 1 1 37 symbol n SS , ' ,

| d ( L T L Journal ofComputationalChemistry n , || ' || || k l L L f 1 + + + n k configurations 55 n which is usedcalculation the for the of RME. John Wiley& Sons,Inc. -1) electrons leads to theelectrons to -1) CFP leads (Eq. 8). 1 1 2 2       ) S L are defined as given in Equation 9 whereby 9 Equation in given as defined are ll L LL' k (9) T Q K 1 2

between initial the state

(10) (10) . sch-Gordon coefficients.

57 2 U , RME can be calculated using CFP and Wigner 6- Wigner and CFP using calculated be can RME by CFP. The product of the (the of product The CFP. by these operators these 4 ctron and parent states with (with states parent and ctron U, elements Matrix 6 V, 11 57 arcs s el s ai st and sets basis as well as matrices were calculated using the program the using calculated were L U of the states calculated from from calculated states the of , 2 M M , 56 U and the and final state

3 , U 4 , n -1) electron states electron -1) U 5 ( , M L T M L n ,' ', | | , U -1) electrons. electrons. -1) 6 and Q K V L' 11 , are M' ) . . j

Page 24of32 Page 25of32 admix states from configurations of opposite parity opposite of configurations from states admix n h frt prxmto n electric no approximation first the In resulting matrix elements givenare theby followin ion to the excited state state excited the to ion The oscillator strength strength oscillator The Calculation of the absorption coefficients S3 59 number of a coefficients These elements. matrix electrostatic D f i χ v h m D that resultingthe matrix elements n ae f aeerh os o cluain f h o the of crys the calculationand integrals radial |B') for to (B| component ions rare-earth of case In with where odd λ and is Y k C     C r D f D i h mv P            × − + + = λ Ξ )(1 21) (2 1) ( ') | | ( = initial state = initial = final state term term containing index of mediumrefractive the the frequency of bandthe A B D B Planck's constant (1) q p p q q 0 0 0 0 0 0 1 qjj j kq j j q j j q j q ) ( l t l l l ) ( ) ( mass the of electron 21( ) 1) 1)( ' 1)(2 (2 2 ) , ( π χ = can be terms given polarin the coordinatesof res k k k k l l t . The most important configurations in that case wo case that in configurations important most The . 21 ) , ( 1) (2 / 4 ) , ( ϕ θ = ϕ θ + π = ϕ θ ' ' 1 q − − ( 1 )     ∑ | ) | | ( | / 8 λ 1 2 (1) 2 j ∑ f electrons.

Accepted + λ − = Article [ ∑ t

) , ( || )(,) , ( ') || || ( tp t A U A , , λ q p ) ( × λ + 2 P f ) )/('') ' ( / ') ' | r | ')( ' | r | ( (13) This article isprotected by copyright. All rights reserved. corresponding to the electric dipole transition fr transition dipole electric the to corresponding q p can be described by the following formula accordinfollowing formula the bydescribed be can lnln l n l n nl l n nl + ] 1/2 λ Ξ Journal ofComputationalChemistry (12) (12) l l + ' ') | | (       B D B tp 1 l l l John Wiley& Sons,Inc. (14) (14) f t where(23) - q (1 ) λ f ' dpl tastos cusLpre ue. t s ne is It rule). occurs(Laporte transitions dipole ' t can substitute can substitute Y g relation g relation re automatically read by BonnMag for the given the for BonnMag by read automatically re tal field parameters Aparameters field tal to kq pectively Equation 13. is a spherical harmonic. clao srnt o te rniin rm the from transition the of strength scillator (15) (15) l N uld be configurations of the type the of configurations be uld to obtain non-vanishing matrix elements of of elements matrix non-vanishing obtain to in whichin ion is the embedded. ) | | ( f D i q ( 1 ) in 12. Eq. om the ground state state ground the om tp have to be estimated, so estimated, be to have g to Fermi’s Golden Rule Rule Golden Fermi’s to g esr to cessary l N-1 l l i of an of '. The '.

equation 22. o values calculated and measured between deviations and The matrix elements Uelements matrix The (21) (21) AThe o itrrtto o te xeietl aa te fo the data,parameters experimental the of interpretation For (Eq. 15). repr η' and is η ρ(η) and states final and initial the complex, of numbers the of coordinate normal the Equation isto 21 thereplaced orientarbitrary due where λ and is even fixed direction space in disappear, f following the qu all that fact, the and 16 and 14 equations Using dimensionless and is related line-str simply the to oscillator the of terms in reported are Intensities where is n index of refractive medium, the Two new terms introducedare for ofsimplification which tabulated byare Nielson and Koster. vh mv T ρηΞλ Ξ η ×ρ S P t A B J l U J f l D i T P J h mv P η η + λ Ξ × + λ + = × + λ = ∑ J l U J l S λ tp t ψ ψ = = + π χ = ψ ψ = λ λ t ) (t, | | ) ( + = × + λ π χ = t 21 21 ' | | 1) (2 1) (2 ' ∑ ∑ 21 t 21) (2 / ) (t, 1) (2 21) (2 3 ∑ J h tp     21 21 t ) (t, | | 1) (2 1) (2 J B t 2) ( 8     + λ 21 | ) | | ( | 1) (2 3 / 8 λ= with odd values for t are the odd-parity terms in terms odd-parity the are t for values odd with λ 21) (2 3 / 8 ∂ + π + λ Ξ + ∂ p A 21) (2 / | | Q 2 2 2 2,4,6 λν 1 2 (1) 2 cn mc tp 2 i || ') ' || || (

Accepted Articlet 2 2

2 N ) ( N 2 λ λ 2 ∑

      ∑ ( λ N ) ( N =2,4,6) are called Judd-Ofelt parameters and can be can and parameters Judd-Ofelt called are =2,4,6) pt pt , ' , , , 9 λ n ηη || ' ' || || A t (λ) 2 This article isprotected by copyright. All rights reserved. . (19) (19) . are the doubly reduced matrix elements of the sphe the of elements matrix reduced doubly the are λ ∑ Q t − 2 2 1 (23) (23) (18) (18) Journal ofComputationalChemistry − tp 1 (17) (17) 2 2 John Wiley& Sons,Inc. (22) (22) i (16) (16) (20) (20) λ 2

the mean of wave is thelength transition. the density of states. Ξ(t,λ) contains radial inte radial contains Ξ(t,λ) states. of density the ormula isobtained. ength by relationshipfollowing the ationof the byrare-earth ions spherical a average strength or P number as given above, which is is which above, given as number P or strength equation equation 17. antum numbers and suffixes that depend on a on depend that suffixes and numbers antum f so called transition line-strength S given by given S line-strength transition called so f lwn apoiain a b ue. Three used. be can approximation llowing the static crystal field expansion. Qexpansion. field crystal static the esent the totality of vibrational quantum quantum vibrational of totality the esent 60-63 varied for minimization of the the of minimization for varied

rical tensor operators, tensor rical 32,64,65 32,64,65 i denotes denotes grals

Page 26of32 Page 27of32 written as followedma The equations". "master p the in is summarized theory elements matrix required all of evaluation The calculated from the eigenvectors and eigenvalues. is matrix total The perturbations. various the for prope fieldligand computationof the issecond the the integrals integrals the energy the of calculation the for used are matrices S4 three-valent rare-earth ions doped in LaF valu c default as the BonnMag for in used used are that are parameters values these file data input the ob are strengths line as ionsthree-valent rare-earthall for parameters that so parameters Judd-Ofelt f results three the integrals the of squaring After intensities of the electric dipole transitions. The transitions. dipole electric the of intensities The spin-orbitconstructedcoupling matrix usingis state. state. h egnetr ad h obtlui tno operat tensor orbital-unit the and eigenvectors The Implementationin BonnMag S3.1 perturbation (Eq. 8) is first the parts: two of consist calculations The ground state are multiplied with the matrix Umatrix the with multiplied are state ground α α ⋅ ⋅ × + ⋅ V j i U H + + − = ) (       α α U c c U c J U l c U J l 1 2 ) ( N ) ( N (') ' )( ( ) ( M q M j i j i j j i i J k J +ζ + = ϕ ϕ = ϕ ϕ Y|'l'''' ' ' ' l ' | |Y l l = Ψ Ψ = ψ ψ || ' l ' || || l n n J J ∑ ∑ ∑ n n 1 2 1 2 1 i i j i N N N < SMLSJM J S L LSJM || | | || || SULS L U LS || ||| || ' ' || || l k M S L J J + + + + + + Calculation of the transition energies and magnetic and energies transition of the Calculation       ) ( ) ( ) , ( λ ' 1 2 λ λ ' J q J k 4 k

Acceptedπ Article +

' k J l U J l J N ) ( N

      21 ψ ψ / S J L k L J ' ' Fiii i i LF 56 ] [ ' ' || || ∑∑

      j i s l r l k l 0 0 0 J J λ This article isprotected by copyright. All rights reserved. j i Journal ofComputationalChemistry (8) 2 for λ = 2 ,4 and 6. The coefficients from the eige the from coefficients The 6. and ,4 2 = λ for ) ( λ 21 John Wiley& Sons,Inc. / (9) (9) 3 (Ref. 65). (24) (24) (λ) and coefficients from the eigenvector of the excit the of eigenvector the from coefficients and U default values, so that if no parameters are givenare parameters no if that values,sodefault tedaoaiaino h ekfedbss under basis field weak the of diagonalization the or λ =2 ,4 and 6 are summed and multiplied with with multiplied and summed are 6 and ,4 =2 λ or the secondthe master equation (Eq.10) (λ) rties. The corresponding matrices are constructed are matricescorresponding The rties. levels. At first the subroutine MPROG calculates MPROG subroutine the first At levels. ignlzd n te iad il poete are properties field ligand the and diagonalized are already present the program because these these because program the present already are oie b te ahnr o tensor-operator of machinery the by rovided luain f ie tegh. Te Judd-Ofelt The . strengths. line of alculation r U or s r toe ht ae en band from obtained been have that those are es ster equation for all ligand field elements is elements field ligand all for equation ster and BnMg otis h Judd-Ofelt the contains BonnMag tained. (λ) are used for the calculation of the the of calculation the for used are susceptibilities

55 nvector of the the of nvector

ed ed in

hs cluain ae efre fr l sx indepe six all for performed are calculations These The calculation of molecular magnetic susceptibilit LGND 2 1 3 1 4 LGND 1 1 2 1 5 XREF 2 1 4 O -0.5 0.0 0.0 O 0.5 0.0 0.0 O -0.5 0.0 0.0 O 0.0 0.5 0.0 O 0.0 0.0 -0.5 O 0.0 0.0 0.5 Ln 0.0 0.0 0.0 MULT 1 CELL 90.0 90.0 90.0 8.0 8.0 8.0 CONF 3 2 TITLE Pr3+ ion- free Setup: Input files BonnMag for S5 calculation of molecular or first- either for products numerator The tensor. The same product matrix elements can be used eq in ] [ ⋅ ⋅ = χ + + + = × − δ δ = ∑ SLS L LS l l l lsjk s kl j s kl i j i α α ()l|V| ' l ' || ||V l ) )( ( αβ l j s i s j l i k i i||j||i | j | | |i | j | | l j l i k s j s i + + ≡     ' ' ' ' l ' | | l 2 JMM M JJ |i | j | |          α α + + n n ' β β α α β α 2 2 − ∑ 1 2 1 SMLSJM J S L LSJM i||j||i | j | | |i | j | | ' ∑ |i | j | | j β α '' β α β α 0 J J j β α N j i         ' A |i | j | | J J ) (

Accepted i j i Article j i

∑ β α ∑ i||j|| | j | | |i | j | | 1 n + i i e kT α β β α

L' − 21 sl 2 2 e kT E / i i + + − i 0 J S kT E / i 0 / n n       S J L This article isprotected by copyright. All rights reserved. k L J g E E ' ' αβ j i ) ( ) ( 0 0 values for given a temperature. 2 2 − 11 Journal ofComputationalChemistry John Wiley& Sons,Inc. (10) (10) ies is given vantheby relation Vleck (eq. 11).          (12) (12) second order terms are given by equation 12 for 12 equation by given are terms order second (11) (11) uations anduations 12 13. dn cmoet of components ndent 19

χ αβ f h susceptibility the of 43

Page 28of32 Page 29of32 LATT 0 KVAL 1.0 TEMP 1.74 120 400. VLEC 6000. 0.5 12000. EPIY 0.0 EPIX 0.0 ESIG 0.0 SCSZ 324.2 52.1 5.25 802.2 MOLS 4 GTEN 0 MAGN 0 EORF 1 NVEC 9 Run: END LGND 6 1 7 1 2 LGND 5 1 6 1 2 LGND 4 1 5 1 2 LGND 3 1 4 1 2 90.0 93.3 93.3 103.3 270.0 106.6 110.0 280.0 280.0 126.6 Yb 310.0 Tm 113.3 320.0 Er 330.0 130.0 Ho 136.6 380.0 Dy 140.0 340.0 Tb Eu 390.0 Sm 410.0 Pm 420.0 Nd Pr Ce Ln e for energies transitions the of calculations the for used parameters AOM S1. Table π in cm 3+ Ln

in Csin 1 . e 2 σ NaLnCl

Accepted Article

e Journal ofComputationalChemistry σ , John Wiley& Sons,Inc.

2 2 Tablewith3 fitted e en transition experimental and Calculated S2. Table 4 4 4 6 6 6 6 6 6 G F G F F F H H H F F σ state state 3/2 9/2 7/2 5/2 7/2 5/2 E 4); (Table literature (LnCl) from 9/2 7/2 5/2 7/2 5/2

20130.0 19972.0 18808.0 18108.0 17764.0 9180.0 9155.0 9100.0 8080.0 7955.0 7183.0 7107.0 2431.0 2379.0 2272.0 1220.0 1044.0 162.0 0.0 3048.0 2662.0 2160.0 570.0 0.0 E E

Acceptedobs Articleobs

. . e

Sm Ce σ (LnCl)and 2406 2297 1211 1069 151 0.0 3047 2661 2160 571 0.0 20135 19343 19295 18044 17538 17193 8993 8953 8884 7885 77744 7181 7104 2454 E E lit lit. .

This article isprotected by copyright. All rights reserved. e π 2518 2411 1270 1122 161 0 3259 2859 2372 563 0 21034 20832 20782 19295 18959 18588 9502 9458 9389 8331 8183 7376 7297 2571 / e E E fit1 σ fit1 fit1 =1/3 (only(Table S1) Prforand Eu) Journal ofComputationalChemistry : : F

2 , , F 4 5 5 5 7 7 7 7 7 3 1 1 3 3 3 3 3 3 , , D D D F F F F F P D G F F F H H H F state state John Wiley& Sons,Inc. 4 3 2 1 0 4 3 2 1 2 6 5 4 2 1 0 4 6

, ,

, 1 ζ I 6 from NEVPT2 (Table 1) with fitted withfitted (Table 1) NEVPT2 from

ergies for Ln for ergies 6973.0 6631.0 6620.0 5297.0 5204.0 5005.0 4976.0 4884.0 4695.0 4447.0 2773.0 2654.0 2402.0 2330.0 703.0 422.0 241.0 0.0 21486.0 21385.0 18961.0 17206.0 3036.0 3010.0 2976.0 2660.0 1964.0 1903.0 1798.0 1093.0 872.0 360.0 0.0 21218.0 21167.0 21058.0 17256.0 16663.0 9898.0 9786.0 7288.0 7049.0 7017.0 E E obs obs . . 3+ 6927 6802 6747 6741 5371 5303 4989 4964 4888 4707 4506 4447 2792 2683 2436 2329 734 410 244 0 20926 20851 18426 16690 3109 3074 3035 2736 2013 1956 1853 1026 897 377 0 21221 21160 21005 17321 16725 10413 9835 9774 7356 7022 6992 in Cs in E E Eu Eu Pr Pr lit. lit.

2 NaLnCl 7532 7138 7088 7073 5628 5564 5217 5183 5106 4984 4759 4708 2862 2755 2559 2443 673 417 243 0 22288 22197 19685 17924 3220 3193 3161 2856 2087 2027 1929 1166 936 390 0 22329 22202 22096 18741 18214 11319 10715 10687 10631 7856 7596 7574 E E fit1 fit1 6 . Calculated energies Calculated .

e σ (LnCl) and 7329 6948 6899 6884 5550 5439 5030 4997 4924 4798 4573 4523 2768 2661 2465 2351 671 416 243 0 21473 21383 19014 17365 3043 3014 2980 2679 1964 1906 1806 1091 866 362 0 21783 21657 21551 18299 17769 10997 10390 10363 10306 7651 7392 7371 E E fit2 fit2

e 4 2 4 4 4 4 4 5 7 7 7 7 7 7 4 4 2 4 4 F H F F I I I D F F F F F F G G G G F π 13/2 11/2 9/2 state state 7/2 5/2 3/2 / 1 2 3 4 5 6 9/2 9/2 4 9/2 7/2 7/2 5/2 e

E = 1/3 (Table S1); (Table1/3 = lit . : obtained using obtained : 13368.0 13334.0 12632.0 12565.0 12418.0 12329.0 11373.0 4104.0 4092.0 3875.0 3867.0 2149.0 2131.0 1933.0 1924.0 342.0 98.0 0.0 20551.0 20501.0 20488.0 20474.0 5617.0 5295.0 5108.0 4565.0 4444.0 4414.0 3670.0 3427.0 3378.0 3331.0 2354.0 2319.0 2249.0 2087.0 375.0 352.0 289.0 83.0 39.0 0.0 19288.0 19157.0 18860.0 18778.0 18627.0 17262.0 17177.0 17035.0 16916.0 16676.0 14558.0 14498.0 13445.0 E E obs obs . . Nd Tb Tb 13293 13273 12455 12353 12340 12282 12219 11246 4120 4085 4077 3848 3841 2141 2114 1910 1902 334 86 0 19268 19167 19145 19116 5611 5285 5100 4534 4435 4398 3653 3413 3363 3313 2356 2322 2243 2096 359 336 276 77 36 0 19285 19185 18878 18864 18627 16948 16931 16830 17129 16663 14658 14483 14424 13354 E E E F fit2 2 lit. lit. : : ,

F F 2 4 and , , F Page 30of32 20951 20859 20838 20810 5853 5504 5312 4702 4614 4565 3785 3513 3486 3460 2407 2367 2316 2130 360 336 269 80 36 0 20391 20269 19765 19669 19360 17864 17856 17742 18042 17536 15543 15368 15309 14104 14038 14017 13222 13125 13119 13002 12903 11875 4403 4368 4362 4134 4124 2279 2252 2049 2043 336 95 0 6 , , ζ E E ζ from and fit1 fit1

Page 31of32 6 6 6 6 3 3 3 3 3 3 4 6 6 6 F F H H F H F F F F H F H H state state 2 3 4 9/2 3/2 5/2 7/2 9/2 4 5 6 7/2 11/2 15/2

15124.0 14959.0 14451.0 14427.0 12886.0 12607.0 12538.0 8458.0 8272.0 8238.0 5936.0 5864.0 5814.0 5544.0 110.0 55.0 0.0 21255.0 20975.0 20967.0 13248.0 12482.0 12387.0 11111.0 11080.0 11040.0 9330.0 9202.0 9168.0 9010.0 6038.0 6008.0 5947.0 5936.0 399.0 331.0 177.0 31.0 0.0 E E obs Acceptedobs Article

. .

Tm Tm Dy 498 467 311 154 72 0 20621 20596 20480 13553 21810 12740 11425 11386 11348 9330 9159 9471 9420 6059 6033 5965 5956 378 304 176 29 0 15098 14934 14479 14472 14404 12911 12751 12640 12534 8627 8507 8321 8282 5863 5793 5740 5433 E E lit. lit.

This article isprotected by copyright. All rights reserved. 471 442 274 144 68 0 21584 21543 21474 13814 13044 12973 11632 11599 11572 9681 9586 9481 9350 6197 6147 6105 6096 394 324 159 34 0 15527 15389 14793 14785 14713 13198 13028 12908 12829 8744 8623 8457 8419 6090 6036 5997 5702 E E fit1 fit1 Journal ofComputationalChemistry

2 2 5 5 3 5 5 5 5 5 F F G G K F F F I I 7 8 state state John Wiley& Sons,Inc. 5/2 7/2 2 4 5

8 5 6

21267.0 21266.0 21093.0 20986.0 18556.0 18521.0 18516.0 15556.0 15528.0 15401.0 15357.0 5268.0 5245.0 5225.0 5118.0 5115.0 242.0 200.0 40.0 10.0 0.0 10708.0 10243.0 573.0 225.0 0.0 23990.0 23977.0 23802.0 23783.0 22238.0 22213.0 22127.0 21941.0 21882.0 21826.0 21397.0 21394.0 21360.0 21318.0 21277.0 E E obs obs . . 19873 19872 21498 21370 19092 19074 19046 16010 15979 15825 15764 5281 5268 5247 5150 5144 284 283 240 211 28 8 0 10622 10270 519 227 0 24137 24125 24041 24029 22863 22842 22775 22649 22603 22575 19999 19994 19982 19911 19899 E Ho E Yb Yb lit. lit.

21085 21067 22042 21920 19604 19557 19529 16436 16407 16267 16205 5413 5380 5371 5358 5255 296 291 259 214 52 13 0 10822 10440 577 285 0 24923 24909 24825 2481 23631 23606 23519 23388 23353 23304 21436 21192 21185 21165 21105 E E fit1 fit1

4 2 4 4 4 4 2 4 F H F I I I G F 11/2 13/2 15/2 state 7/2 7/2 5/2 11/2 9/2

20437.0 20388.0 19181.0 19143.0 19058.0 19020.0 15347.0 15242.0 15152.0 10208.0 10182.0 10176.0 10151.0 6683.0 6660.0 6532.0 6517.0 6492.0 284.0 257.0 55.0 25.0 0.0 24529.0 24470.0 24407.0 22067.0 22038.0 20460.0 E obs

. 20593 20529 19038 19018 18984 18981 15395 15323 15224 10102 10100 10018 10007 6681 6675 6522 6506 6480 294 265 59 30 0 24190 24177 24042 22188 22132 20600 E

lit.

Er Er

21125 21058 19811 19792 19763 19735 15809 15734 15645 10432 10430 10347 10338 6833 6819 6670 6662 6638 291 245 56 24 0 24969 24930 24819 22888 22827 21159 E fit1

r 0 201.3 604 Pr Ln cm for energies transitions the of calculations the for used parameters AOM S3. Table 1 o 6 121.3 128.0 134.6 131.3 364 384 404 Ho 394 Tb Eu Sm G 3+ 4 1

for

in LnPO in d (LnO) 21422.0 21356.0 20851.0 21498.0 e σ

Accepted Article4 . . 2.38

e π Å : : .

σ 21937 21907 21848 21411 , , e π in Journal ofComputationalChemistry

John Wiley& Sons,Inc.

Page 32of