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Spectrochimica Acta Part A 55 (1999) 467–475

Low-energy spectrum of the thermodynamically stableBaI2+ dication

Aleksey B. Alekseyev a, Heinz-Peter Liebermann a, Rainer M. Lingott a,Robert J. Buenker a,*, James S. Wright b

a Bergische Uni6ersitat-Gesamthochschule Wuppertal, Fachbereich 9-Theoretische Chemie, Gaussstr. 20,D-42097 Wuppertal, Germany

b Department of Chemistry, Carleton Uni6ersity, 1125 Colonel By Dri6e, Ottawa ON K1S 5B6, Canada

Received 24 March 1998; accepted 20 April 1998

Abstract

Relativistic effective core potential calculations, including configuration interaction and spin–orbit coupling, arereported for the lowest-lying electronic states of the BaI2+ dication, and the results are compared with the data forthe isovalent CaX2+ (X=Cl, Br, I) systems studied earlier within the same approach. The X1

2P3/2 and X22P1/2

states are found to be thermodynamically stable by 0.92 and 0.56 eV, as also is the first excited state, A2S+, althoughits potential curve is crossed at large internuclear distances by a repulsive V=1/2 state. All other low-lying electronicstates of CaX2+ are repulsive. Electric-dipole moments are calculated for the A�Xl, X2 transitions. The correspond-ing radiative lifetimes are computed to be: t(A�X1)=5.0 ms and t(A�X2)=141 ms (the values given are for6%=0). It is concluded that the most favourable situation for spectroscopic observation of this group of dicationsoccurs for the heavier CaI2+ and BaI2+ species because they exhibit the largest A–Xl, X2 transition energies andhighest transition probabilities. © 1999 Elsevier Science B.V. All rights reserved.

Keywords: Core potential calculations; Low-energy spectrum; BaI2+ dication

1. Introduction

Molecular dications characterized by physicalproperties interesting for both fundamental re-search and applications have attracted much at-tention from experimentalists and theoreticiansalike (for review see Ref. [1] and references

therein). Most of these systems are thermodynam-ically unstable due to a repulsive ground stateresulting from the electrostatic interaction of twopositively charged fragments. It is not so difficult,however, to find thermodynamically stable sys-tems of this type, or at least those which havewell-bound ground states and are very long-lived.To achieve this goal for diatomic AB2+ dications(see the discussion in Refs [2–4]) it is sufficientthat a simple parameter D, defined as D=IP2(A)−IP1(B), where IP1,2 denote first and sec-

* Corresponding author. Tel.: +49-202-439-2509; Fax: +49-202-439-2581; e-mail: [email protected].

1386-1425/99/$ - see front matter © 1999 Elsevier Science B.V. All rights reserved.

PII: S1386 -1425 (98 )00255 -8

A.B. Alekseye6 et al. / Spectrochimica Acta Part A 55 (1999) 467–475468

ond ionization potentials, have negative values.This means that the A2+ +B dissociation limitlies lower than the A+ +B+ asymptote, andsince interaction of the doubly positive ion with aneutral atom is attractive due to the strong polar-ization of the latter, while interaction of twopositive ions is Coulomb repulsive, this occur-rence is indicative of thermodynamical stabilityfor the AB2+ dication in its ground state.

It is obvious that in order to satisfy the abovecondition, one can combine electropositive alka-line earth atoms characterized by low second ion-ization potentials with halogen or rare gas atomshaving very high IPl values. Recently, Falcinelli etal. [5] have reported the first mass-spectrometricobservation of this type of systems, among othersCaBr2+ and BaX2+, where X=F, Cl, Br, I.Stimulated by this experimental study we havecarried out ab initio calculations of the CaX2+

(X=Cl, Br, I) dications [6,7] and have shown thatall of them possess a fairly strongly bound X2Pground state (by 0.96–1.55 eV) and thus areeither thermodynamically stable (CaCl2+,CaBr2+) or at least very long-lived (CaI2+) dueto a high and broad barrier to dissociation. It hasalso been found in the calculations that anothercommon feature of all these systems is a low-lyingbound A2S+ state. The A2S+�X1

2P3/2, X22P1/2 radiative transitions have been predicted tolie in the IR 6400–12250 cm−1 spectral range,and electric-dipole moments and lifetimes forthese transitions have been calculated. Compari-son of the computed spectroscopic data for thethree CaX2+ (X=Cl, Br or I) dications showsthat the most favourable situation for experimen-tal observation of the A�Xl, X2 transitions oc-curs for the heavier species, in particular forCaI2+. The stronger polarization of the heavierhalogen atoms stabilizes the Xl, X2 and A states,while stronger spin–orbit interaction increases theA�X2 transition probability. It is worth notingat this point that, although reports of mass-spec-trometric detection of various molecular dicationsare quite numerous, studies of such systems bymeans of optical spectroscopy are still very rare,especially for the thermodynamically stablespecies.

Based on the above experience, one can sup-pose that BaI2+ should be another suitable sys-tem for the spectroscopic observation ofthermodynamically stable dications. As one cansee from the experimental ionization potentialvalues of the Ba and I atoms presented in Table 1,the thermodynamical stability of the BaI2+ dica-tion is practically guaranteed by the fact that thesecond ionization potential (IP2) of the Ba atom islower than the first ionization potential of I. Onecan also expect that due to the presence of theheavy I atom the A–X transitions must be fairlystrong. So the goal of the present study is toobtain accurate ab initio information for theBaI2+ dication by employing the same approachas used before for CaX2+ [6,7]. This approach isbased on relativistic effective core potentials(RECPs) (see review articles [9–11] and Refs.therein) and the conventional MRD-CI procedure[12]. It allows one to drastically reduce the num-ber of electrons which are treated explicitly, whilestill accurately describing correlation energy andrelativistic effects. Special attention in the presentstudy is paid to description of the A–X radiativetransitions, and the resulting data will be com-pared with those for the CaX2+ dications.

2. Computational method

In the present theoretical treatment core elec-trons of the barium atom are described by theRECP of Ross et al. [13], with the 5s, 5p, and 6selectrons included in the valence space. A RECPof the same shape-consistent type is also em-ployed for the iodine atom [14], for which onlyseven outer 5s and 5p electrons are treated explic-itly via basis functions. The atomic basis set em-

Table 1Computed ionization energies for Ba and I (in eV), comparedto experimental valuesa

Experimental ExperimentalIP1 IP2Species

5.15Ba 5.210 10.0019.90–10.45410.11I 19.09

a Experimental data from Ref. [8].

A.B. Alekseye6 et al. / Spectrochimica Acta Part A 55 (1999) 467–475 469

Table 2Excitation energies E (in eV) for the lowest-lying L–S states of the BaI2+ dication and the corresponding atomic dissociation limitsa

I state Ea (eV) BaI2+ stateBa state

I 2P0 0.0Ba2+ 1S 2S+, 2P0.453 2S−, 4S−, 2P, 4PBa+ 2S I+ 3P

3P 1.062D 2S+, 2S−(2), 4S+, 4S−(2), 2P(3), 4P(3), 2D(2), 4D(2), 2F, 4F2.15 2S+, 2P, 2D1D2S

a Experimental data from Ref. [8]. Energy values for the lowest multiplet components I+(3P2) and Ba+(2D3/2) have been used.

ployed for Ba is adapted from the (5s5p4d) Gaus-sian set of Ref. [13], which has been optimized atthe SCF level for use with the above RECP. Inthe Ba atomic tests carried out in the presentstudy, it has been found useful to augment it withan s exponent of 2.0, and the two smallest dexponents have been reoptimized at the CI level inthe Ba+(2D) calculations to values of 0.21 and0.07. Finally, two f polarization functions withexponents of 0.9 and 0.25, and (1s1p) diffusefunctions (0.012 for s and 0.0045 for p) have beenadded, producing a (7s6p4d2f) basis set for the Baatom, employed in fully uncontracted form. The Iatomic basis is a (6s7p3d1f) uncontracted set andis described in more detail in our previous work[7]. Before carrying out molecular calculations anumber of atomic tests have been performed forboth atoms, in particular the relevant ionizationpotentials of Ba and I have been computed. Asone can see from Table 1, the calculated atomicIP values, though being somewhat underesti-mated, agree reasonably well with the experimen-tal data and thus should lead to the qualitativelycorrect asymptotic behaviour for the calculatedmolecular potential curves.

The first step in the present molecular calcula-tions is a self-consistent-field (SCF) computationof the …s2p3 2P ground state. At this stage, aswell as in the configuration interaction (CI) step,calculations are carried out with the spin-indepen-dent part of the RECP (ARECP) and includeonly scalar relativistic effects, whereas the spin–orbit interaction is introduced at the last stage.The CI calculations are carried out using theconventional multireference single- and double-excitation (MRD-CI) method [12], includingconfiguration selection, energy extrapolation and

the generalized Davidson correction [15,16],which accounts for higher excitations. The TableCI algorithm [17] is employed for efficient han-dling of the various open-shell cases generated.All calculations are carried out in C26 symmetry.The MRD-CI calculations typically include 130–200 reference configurations and up to three rootsof each L–S symmetry, generating (64–109)·106

symmetry adapted fuctions, from which 7000–20000 have been selected by using a threshold of10 mH. Results are obtained at a series of internu-clear distances ranging from 4.5 to 50 a0, with astandard increment of 0.05 a0 in the 91.0 a0

interval centered at the ground state equilibriumdistance, and with some selected points at smallerand larger separations.

The next step in the present treatment is toemploy the L–S eigenfunctions as basis for thefinal spin–orbit CI calculations. The estimatedfull CI energies described above are placed on thediagonal of the Hamiltonian matrices, whereasoff-diagonal matrix elements are obtained by em-ploying pairs of selected CI wavefunctions withMs=S and applying spin-projection techniquesand the Wigner–Eckart theorem. All states con-verging to the two lowest L–S limits (see Table 2)have been included in the calculations as well as anumber of higher-lying roots, leading to secularequations of order 28. More details of the spin–orbit CI method may be found in earlier work[18–20]. As our recent analysis [20] has shown,the L–S contracted SO–CI approach employedin the present study gives an adequate descriptionof the spin–orbit interaction in such heavy halo-gen atoms as iodine and astatine and thereforeshould be suitable for calculations of the alkalineearth halide dications.


Finally, the resulting potential curves are fit topolynomials which serve as the potentials in one-dimensional nuclear motion Schrodinger equa-tions solved numerically by means of theNumerov–Cooley method [21,22]. The electronictransition moments are averaged over variouspairs of vibrational functions obtained above andare combined with transition energy data to com-pute Einstein spontaneous emission coefficients.The radiative lifetimes of a given upper vibra-tional state are obtained by summing over itsEinstein coefficients with all lower-lying levels andthen inverting.

3. Results and discussion

3.1. Potential energy cur6es

Computed potential energy curves for the low-est-lying states of BaI2+ are shown in Fig. 1 andthe corresponding spectroscopic constants for thebound states are given in Table 3. As for theisovalent CaX2+ dications, the X2II ground stateis characterized predominantly by a …s2p3 elec-tronic configuration in the Franck–Condon re-gion and is strongly split into 3/2 and 1/2components, both converging to the Ba2+(1S)+

Fig. 1. Computed potential curves of the lowest-lying states of BaI2+.


Table 3Computed spectroscopic properties of BaI2+ (excitation en-ergy Te, equilibrium bond length re and vibrational frequencyve)

re (A) ve (cm−1)Te (cm−1)State

3.502 99.2X12P3/2 0

90.23.503X22P1/2 2873

3.518 78.4A 2S+ 10404

X2P ground state by an electron excitation fromthe bonding s to the nonbonding p orbital andthis leads to much less binding (#0.46 eV) for theA state than for Xl. This is also indicated by thesmaller ve value and the larger equilibrium dis-tance computed for this state (see Table 3). Asmentioned above, the s orbital is less bonding inBaI2+ than in CaI2+, which results in a smallerexcitation energy of the A state in the formersystem, 10404 cm−1 as compared to 12245 cm− l

in CaI2+.The spin–orbit interaction within the X2P,

A2S+group of states has a number of specificfeatures and deserves a brief discussion. The first-order splitting of the X2II state is equal to2�px � HSO � py�. This spin–orbit matrix element isapproximately equal to the atomic�5pI,x � HSO � 5pI,y�=a:2534 cm− l matrix ele-ment, which is responsible for the ground statesplitting in the iodine atom: DE(2P1/2−

2P3/2)=3a=7603.15 cm− l. This is not surprising since asmentioned above the px,y MOs are localized almostcompletely on the I atom. It is interesting to note,however, that this matrix element is even some-what larger in the BaI2+ and CaI2+ dications thanthat in the iodine atom, 2566 and 2592 cm− l,respectively. This happens due to a partial transferof charge from the I atom, which slightly contractsthe px,y(5px,y) MOs and thus increases the corre-sponding spin–orbit interaction. This effect israther small, but nevertheless worth noting becauseit causes an additional stabilization of the X1

2II3/2

ground state relative to the L–S level of treatment,which is quite unusual for molecular systems, forwhich an opposing fairly strong destabilizationeffect due to the spin–orbit interaction is observedin most cases. It simultaneously explains why, inspite of the very strong spin–orbit interactionin BaI2+, a pure electrostatic approach employedin Ref. [5] to estimate bond strength of theX2II ground state gives a value of 0.95 eV whichis in very good agreement with the present resultof 0.92 eV. The second-order spin–orbit interac-tion between the X2

2II1/2 and A2S+ states pushesthe former state down but does not influencethe position of the X1

2P3/2 state, thus decreas-ing the final X2II splitting. This effect is strongerin BaI2+ than in CaI2+ because, as discussed

I(2P3/2) dissociation limit. The p orbital is local-ized completely on the iodine atom, while thebonding s orbital has mainly iodine 5pz character,with some admixture of the iodine 5s, barium 5s,6s, 6pz and more diffuse AOs on both atoms. The1s22s21p43s2 inner shells, which accomodate thebarium 5s25p6 and the iodine 5s2 electrons areomitted in the above notation and in the follow-ing discussion because they do not play an impor-tant role in the BaI2+ low-energy spectrum. It isworth noting, however, that excitations from allthese MOs have been allowed in the CI calcula-tions. The dissociation energy for the X2

2P1/2

state can be estimated as the difference of theenergy values at the equilibrium distance and atr=50 a0, which gives De(X1)=0.92 eV. This issignificantly less than the 1.53 eV value calculatedfor the potential well depth of the CaI2+ groundstate [7], and this can be explained by the fact thatthe much larger core of the Ba ion prevents sucha close approach of the I atom as in the CaI2+

dication. Therefore polarization interaction,which is mainly responsible for binding in bothsystems, is somewhat smaller in the case of theBaI2+ dication. Using the quantum chemistrylanguage, one can also say that the s orbital hasless bonding character in BaI2+ than in thelighter CaI2+ system. The analogous estimate forthe De(X2) value gives 0.56 eV. As one can seefrom Table 3, the X2

2P1/2 state has a noticeablysmaller vibrational frequency than X1, which canbe explained quite simply on the basis of the factthat both these states converge to the same disso-ciation limit.

The first excited state, A2S+, is mainly charac-terized by a …sp4 configuration in the Franck–Condon region. This state thus arises from the


above, the A2S+ lies lower in the former sys-tem. The corresponding �A2S+ � HSO � X2P�=�p � HSO � s�5�5pI,x � HSO � 5pI,z� matrix elementis also slightly larger in BaI2+, 2437 versus 2421cm−1 in CaI2+ owing to a higher weight of the5pI,z AO in the BaI2+ s orbital. These effectstaken together give a fairly large difference in theX2P splitting, 2873 cm−1 in BaI2+ as comparedto 3544 cm−1 in CaI2+, though the physicalorigin of this effect in both systems is essentiallythe same, namely the spin–orbit interaction in the5p shell of the iodine atom, and the distributionof the electron density is qualitatively very similar.

All other low-lying states of BaI2+ are repul-sive. The lowest four of them, 2,4S−(s2p2s*) and2,4P(sp3s*), go to the Ca+(2S)+Br+(3P) dissoci-ation limit (see Table 2). The s* molecular orbitalis localized mainly on the barium atom, andtherefore the leading configurations of these statesgiven above in parentheses correspond to a chargetransfer from Ba2+ to the I atom and explain therepulsive character of their potential curves. Thelowest five V states (1/2(2),3/2(2),5/2) belonging tothis group are shown in Fig. 1. At the groundstate equilibrium distance (#6.6 a0) these stateslie in the energy interval of 41–43·103cm− l andtheir influence on the X1,2 and A states is veryweak because the corresponding spin–orbit ma-trix elements are all smaller than 400 cm− l. Theyconverge, however, to the Ba+(2S)+I+(3P2)atomic limit, which lies only 0.453 eV higher thanthe Ba2+(1S)+I(2P3/2) asymptote, or 0.49 eVlower than the Ba2+(1S)+I(2P1/2) limit, to whichthe A2S+ state goes diabatically. This means thatall these curves cross the A2S+ potential curve,with such crossings occurring at very large inter-nuclear distances of 45–50 a0 according to thepresent calculations. The A2S+ curve exhibits anavoided crossing with the lowest of the repulsive1/2 states, and thus converges adiabatically to theBa+(2S)+I+(3P2) limit. Adding the above valueof 0.453 eV to the X1

2P1/2 state dissociationenergy, one obtains for the A2S+adiabatic poten-tial curve an asymptotic energy of 11060 cm− l

with respect to the BaI2+ ground state minimum.This is approximately 650 cm−1 higher than theA2S+Te value and means that this state is ther-modynamically stable. Therefore an important

conclusion which can be made from the presentanalysis is that all three of the lowest states ofBaI2+, X1, X2 and A, are thermodynamicallystable, in contrast to the CaI2+ case [7]. One cannote, however, that in the latter system all thesestates must be very long-lived due to the high andbroad barriers to dissociation.

3.2. Transition moments and radiati6e lifetimes

Electric-dipole moments for the A–X1, X2 tran-sitions in the BaI2+ dication are shown as afunction of internuclear distance in Fig. 2. TheA2S+−X2P perpendicular transition is symme-try-allowed at the L–S level of molecular treat-ment, but vanishes (mx=my=0) when r��because the X and A states converge to the sameBa2+(1S)+I(2P) atomic limit. This gives a quali-tative explanation for the weakness of the A–X1

transition in this class of molecular systems, ashas also been found earlier for the CaX2+ dica-tions [6,7]. This transition gains its intensitymainly from halogen atom polarization and there-fore is a bit weaker in BaI2+ relative to that inCaI2+. At shorter internuclear distances, the A–X1 transition moment becomes smaller due tointermolecular charge transfer, and even changesits sign at distances corresponding to the repulsivelimbs of the potential curves. As one can see fromFig. 2, the mx dipole moment curves for the A�X1 and A�X2 transitions are very similar. This iseasily understandable since these are equivalentDV=1 transitions (1/2�3/2, 1/2�−1/2) withthe same L–S origin. Some difference is causedby the A–X2 spin–orbit mixing as well as byspin–orbit coupling with the higher-lying states.

The situation is quite different for the parallelA–X2 transition, which only becomes allowed dueto the spin–orbit interaction. Since the latter isfairly strong in BaI2+, the corresponding mz tran-sition moment is significantly larger than mx(Fig.2). Thus the main channel of the A2S+state ra-diative decay in BaI2+ is the parallel transition tothe X2

2P1/2 state. One can also see this fromTable 4, in which the calculated partial radiativelifetimes for transitions from the seven lowestvibrational levels of the A state to X1 and X2 arepresented. The t (A,6%=0�X2) value for BaI2+


is calculated to be 148 ms, noticeably longer thanthe 53.8 ms value, obtained for the same transitionin CaI2+ [7]. The reason for this distinction is ahigher n3 frequency factor combined with a largerdifference between the dipole moments of the Aand X states in the lighter system which gives themain contribution to the mz(A–X2) transitionmoment.

The radiative lifetime for the X2�X1 transitionhas also been esimated in the present study for theapproximate equilibrium distance of both states,6.6 a0. The computed t value of 0.4 s as well as avery small transition energy of 2873 cm−1 indi-

cate that attempts to observe this very weak tran-sition may be extremely difficult.

4. Conclusion

The spin–orbit CI method based on RECPshas been employed to study low-lying electronicstates of the BaI2+ dication. The three loweststates, X1

2P3/2, X22P1/2 and A2S+, are all found

to be thermodynamically stable, although the po-tential curve of the latter state exhibits an avoidedcrossing at very large internuclear distances (�50

Fig. 2. Computed electric-dipole moments mx,z for the A–X1 and A–X2 transitions in the BaI2+ dication as a function ofinternuclear distance. The dication is located on the z axis.


Table 4Calculated partial radiative lifetimes for the A�X1 and A�X2 transitions from the lowest vibrational levels 6% of the Astate of BaI2+

6% A�X1 A�X1, X2A�X2

tA (ms)t (ms)tÞ (ms) tÞ (ms) t (ms)

145148 1418.30 5.0144 1421 4.9 1387.7142 1402 4.6 7.4 135

137140 1337.03 4.5135 1314 4.4 6.7 138132 1295 4.3 6.4 135

133 1306 4.2 6.2 126

sults available prior to publication and for use-ful discussions. One of us (J.S.W.) would like tothank the Natural Sciences and Engineering Re-search Council of Canada for financial support.This work was supported in part by theDeutsche Forschungsgemeinschaft in the form ofa Forschergruppe grant (Bu 152/12) and withinthe Schwerpunktprogramm ‘Relativistische Ef-fekte’ (Bu 450/6). The financial support of theFonds der Chemischen Industrie is also herebygratefully acknowledged.

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a0) with the repulsive 1/2 state going to theBa+(2S)+I(3P2) dissociation limit.

The electric-dipole moments and partial radia-tive lifetimes for transitions from the 6%=0–6vibrational levels of the A to the X1 and X2

states have also been calculated. Comparison ofthe computed spectroscopic data for BaI2+ andthe three CaX2+ (X=Cl, Br, I) dications stud-ied earlier within the same approach [6,7] showsthat the best situation for experimental observa-tion of the A�X1, X2 radiative transitions oc-curs for the heavier species, namely BaI2+ andCaI2+. The latter system may be considered asa favourite for such studies, although the X1, X2

and A states of CaI2+ are not thermodynami-cally stable. They are extremely long-lived withrespect to non-radiative decay, however, due tovery broad and high barriers to dissociation [7],and possess the largest A–X1, X2 transition en-ergies and Einstein coefficients among the dis-cussed systems, which indicates that observationof these transitions in CaI2+ is more feasible.The BaI2+ dication is another good candidatefor this type of experiment, having the advan-tage of possessing thermodynamically stable X1,X2, and A states with a fairly large A–X2 tran-sition probability.

Acknowledgements

The authors are very grateful to R.N. Zareand F. Fernandez-Alonso for making their re-


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