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<ul><li><p>Spectrochimica Acta Part A 55 (1999) 467475</p><p>Low-energy spectrum of the thermodynamically stableBaI2 dication</p><p>Aleksey B. Alekseyev a, Heinz-Peter Liebermann a, Rainer M. Lingott a,Robert J. Buenker a,*, James S. Wright b</p><p>a Bergische Uni6ersitat-Gesamthochschule Wuppertal, Fachbereich 9-Theoretische Chemie, Gaussstr. 20,D-42097 Wuppertal, Germany</p><p>b Department of Chemistry, Carleton Uni6ersity, 1125 Colonel By Dri6e, Ottawa ON K1S 5B6, Canada</p><p>Received 24 March 1998; accepted 20 April 1998</p><p>Abstract</p><p>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</p><p>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.</p><p>Keywords: Core potential calculations; Low-energy spectrum; BaI2 dication</p><p>1. Introduction</p><p>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</p><p>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 [24]) it is sufficientthat a simple parameter D, defined as DIP2(A)IP1(B), where IP1,2 denote first and sec-</p><p>* Corresponding author. Tel.: 49-202-439-2509; Fax: 49-202-439-2581; e-mail: buenker@wrcs1.urz.uni-wupper-tal.de.</p><p>1386-1425:99:$ - see front matter 1999 Elsevier Science B.V. All rights reserved.</p><p>PII: S1386 -1425 (98 )00255 -8</p></li><li><p>A.B. Alekseye6 et al. : Spectrochimica Acta Part A 55 (1999) 467475468</p><p>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.</p><p>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 XF, Cl, Br, I.Stimulated by this experimental study we havecarried out ab initio calculations of the CaX2</p><p>(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.</p><p>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 [911] 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 AX radiativetransitions, and the resulting data will be com-pared with those for the CaX2 dications.</p><p>2. Computational method</p><p>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-</p><p>Table 1Computed ionization energies for Ba and I (in eV), comparedto experimental valuesa</p><p>Experimental ExperimentalIP1 IP2Species</p><p>5.15Ba 5.210 10.0019.9010.45410.11I 19.09</p><p>a Experimental data from Ref. [8].</p></li><li><p>A.B. Alekseye6 et al. : Spectrochimica Acta Part A 55 (1999) 467475 469</p><p>Table 2Excitation energies E (in eV) for the lowest-lying LS states of the BaI2 dication and the corresponding atomic dissociation limitsa</p><p>I state Ea (eV) BaI2 stateBa state</p><p>I 2P0 0.0Ba2 1S 2S, 2P0.453 2S, 4S, 2P, 4PBa 2S I 3P</p><p>3P 1.062D 2S, 2S(2), 4S, 4S(2), 2P(3), 4P(3), 2D(2), 4D(2), 2F, 4F2.15 2S, 2P, 2D1D2S</p><p>a Experimental data from Ref. [8]. Energy values for the lowest multiplet components I(3P2) and Ba(2D3:2) have been used.</p><p>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.</p><p>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 [12], includingconfiguration selection, energy extrapolation and</p><p>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 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.</p><p>The next step in the present treatment is toemploy the LS eigenfunctions as basis for thefinal spinorbit 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 withMsS and applying spin-projection techniquesand the WignerEckart theorem. All states con-verging to the two lowest LS 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 spinorbit CI method may be found in earlier work[1820]. As our recent analysis [20] has shown,the LS contracted SOCI approach employedin the present study gives an adequate descriptionof the spinorbit interaction in such heavy halo-gen atoms as iodine and astatine and thereforeshould be suitable for calculations of the alkalineearth halide dications.</p></li><li><p>A.B. Alekseye6 et al. : Spectrochimica Acta Part A 55 (1999) 467475470</p><p>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 theNumerovCooley 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.</p><p>3. Results and discussion</p><p>3.1. Potential energy cur6es</p><p>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 FranckCondon re-gion and is strongly split into 3:2 and 1:2components, both converging to the Ba2(1S)</p><p>Fig. 1. Computed potential curves of the lowest-lying states of BaI2.</p></li><li><p>A.B. Alekseye6 et al. : Spectrochimica Acta Part A 55 (1999) 467475 471</p><p>Table 3Computed spectroscopic properties of BaI2 (excitation en-ergy Te, equilibrium bond length re and vibrational frequencyve)</p><p>re (A) ve (cm1)Te (cm</p><p>1)State</p><p>3.502 99.2X12P3:2 0</p><p>90.23.503X22P1:2 2873</p><p>3.518 78.4A 2S 10404</p><p>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 cm1 as compared to 12245 cm l</p><p>in CaI2.The spinorbit interaction within the X2P,</p><p>A2Sgroup of states has a number of specificfeatures and deserves a brief discussion. The first-order splitting of the X2II state is equal to2px HSO py. This spinorbit matrix element isapproximately equal to the atomic5pI,x HSO 5pI,ya:2534 cm l matrix ele-ment, which is responsible for the ground statesplitting in the iodine atom: DE(2P1:22P3:2)3a7603.15 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 spinorbit interaction. This effect israther small, but nevertheless worth noting becauseit causes an additional stabilization of the X1 2II3:2ground state relative to the LS level of treatment,which is quite unusual for molecular systems, forwhich an opposing fairly strong destabilizationeffect due to the spinorbit interaction is observedin most cases. It simultaneously explains why, inspite of the very strong spinorbit 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 spinorbit 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</p><p>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 2P1:2state can be esti...</p></li></ul>

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