Spectrochimica Acta Part A 55 (1999) 467475
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
Relativistic effective core potential calculations, including configuration interaction and spinorbit coupling, arereported for the lowest-lying electronic states of the BaI2 dication, and the results are compared with the data forthe isovalent CaX2 (XCl, Br, I) systems studied earlier within the same approach. The X1
2P3:2 and X2 2P1:2states 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 V1:2 state. All other low-lying electronicstates of CaX2 are repulsive. Electric-dipole moments are calculated for the AXl, X2 transitions. The correspond-ing radiative lifetimes are computed to be: t(AX1)5.0 ms and t(AX2)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 AXl, X2 transition energies andhighest transition probabilities. 1999 Elsevier Science B.V. All rights reserved.
Keywords: Core potential calculations; Low-energy spectrum; BaI2 dication
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.  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 ) it is sufficientthat a simple parameter D, defined as DIP2(A)IP1(B), where IP1,2 denote first and sec-
* Corresponding author. Tel.: 49-202-439-2509; Fax: 49-202-439-2581; e-mail: firstname.lastname@example.org.
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A.B. Alekseye6 et al. : Spectrochimica Acta Part A 55 (1999) 467475468
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.  have reported the first mass-spectrometricobservation of this type of systems, among othersCaBr2 and BaX2, where XF, Cl, Br, I.Stimulated by this experimental study we havecarried out ab initio calculations of the CaX2
(XCl, Br, I) dications [6,7] and have shown thatall of them possess a fairly strongly bound X2Pground state (by 0.961.55 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 A2SX1 2P3:2, X22P1:2 radiative transitions have been predicted tolie in the IR 640012250 cm1 spectral range,and electric-dipole moments and lifetimes forthese transitions have been calculated. Compari-son of the computed spectroscopic data for thethree CaX2 (XCl, Br or I) dications showsthat the most favourable situation for experimen-tal observation of the AXl, 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 spinorbit interaction increases theAX2 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 AX 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  and Refs.therein) and the conventional MRD-CI procedure. 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 AX 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. , 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 , 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 10.0019.9010.45410.11I 19.09
a Experimental data from Ref. .
A.B. Alekseye6 et al. : Spectrochimica Acta Part A 55 (1999) 467475 469
Table 2Excitation energies E (in eV) for the lowest-lying LS 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. . 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. , 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. 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 spinorbit interaction is introduced at the last stage.The CI calculations are carried out using theconventional multireference single- and double-excitation (MRD-CI) method , includingconfiguration selection, energy extrapolation and
the generalized Davidson correction [15,16],which accounts for higher excitations. The TableCI algorithm  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 130200 reference configurations and up to three rootsof each LS symmetry, generating (64109)106symmetry adapted fuctions, from which 700020000 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 a0interval centered at the ground state equilibriumdistance, and with some selected points at smallerand larger separations.
The next step in the present treatment is toemploy t