On the Electronic Structure of the UO 2 Molecule

Transcription

1 0602 J. Phys. Chem. A 200, 05, On the Electronic Structure of the UO 2 Molecule Lur Gglirdi,*, Bjorn O. Roos, Per-Åke Mlmqvist, nd John M. Dyke Diprtimento di Chimic G. Cimicin, Vi F. Selmi 2, 4026 Bologn, Itly, Deprtment of Theoreticl Chemistry, Chemicl Center, P.O. Box 24, S Lund, Sweden, nd Deprtment of Chemistry, Highfield, UniVersity of Southmpton, Southmpton, SO7 BJ, U.K. ReceiVed: July 26, 200; In Finl Form: September 2, 200 The structure nd vibrtionl frequencies of the UO 2 molecule hve been determined using multiconfigurtionl wve functions (CASSCF/CASPT2), together with newly developed method to tret spin-orbit coupling. The molecule hs been found to hve (5fφ)(7s), Φ u, Ω ) 2 ground stte with U-O bond distnce of.77 Å. The computed ntisymmetric stretching σ u frequency is 92 cm - with 6/8 isotope rtio of.0525 which compres with the experimentl vlues of 95 cm - nd.0526, respectively. Clcultions of the first dibtic ioniztion energy gve the vlue 6.7 ev, which is 0.7 ev lrger thn the currently ccepted experimentl result. Resons for this difference re suggested.. Introduction The vibrtionl frequencies of the tritomics UO 2,UO + 2, nd UO 2- hve recently been mesured in solid neon nd rgon mtrixes using infrred spectroscopy, with lser bltion techniques. In ddition, the ioniztion energies of number of UO x systems hve been mesured in the gs phse using electron impct mss spectrometry. 2 Also, theoreticl studies utilizing the density functionl pproch (DFT/BLYP) hve been performed. This informtion mkes the urnium oxides good cndidtes for testing more dvnced quntum chemicl methods for hevy-element compounds. We hve recently reported equilibrium geometries nd vibrtionl frequencies for number of U(V) nd U(VI) tritomic molecules nd their positive ions XUY (X ) C, N, O). The computed frequencies were in greement with experiment provided tht extended bsis sets were used. These clcultions were performed using multiconfigurtionl (CAS) SCF theory with dynmic correltion effects dded with second-order perturbtion theory (CASPT2). Reltivistic effective core potentils (ECP) were used, nd no spin-orbit effects were included. Here we extend this study to the neutrl UO 2 molecule with two open-shell electrons in the 5f nd 7s orbitls. However, in the present study, we hve performed ll-electron clcultions, nd spin-orbit coupling hs been included. * Corresponding uthor. E-mil: lur.g@cim.unibo.it. Diprtimento di Chimic G. Cimicin, Bologn. Deprtment of Theoreticl Chemistry, Lund. University of Southmpton. 2. Method nd Detils of the Clcultions The study ws performed using the complete ctive spce (CAS) SCF method 4 with dynmic correltion dded using multiconfigurtionl second-order perturbtion theory (CASPT2). 5-7 Sclr reltivistic effects were included using Dougls-Kroll (DK) Hmiltonin. 8,9 The effects of spin-orbit (SO) coupling were introduced using newly developed method bsed on the CASSCF Stte Interction method (CASSI). 0, Here, the CASSCF wve function generted for number of electronic sttes re llowed to mix under the influence of spin-orbit Hmiltonin. The method hs recently been described, nd we refer to this rticle for detils. 2 All clcultions hve been performed with the softwre MOLCAS-5. Three sets of clcultions hve been performed. All used ANO-type bsis sets for U nd O. The U exponents were optimized using the DK Hmiltonin. The primitive set is 24s9p4df. 4 A smll bsis set (BS) used this bsis set for U contrcted to 9s8p7d5f, nd this ws combined with the ANO-L bsis of the MOLCAS librry 5 for oxygen, contrcted to 4sp2d. BS ws used in the first nd second set of clcultions with the smll nd lrge ctive spce (see below). The third set used the lrge ctive spce nd the lrger bsis set (BS2), where two g-type functions were dded to the U set nd one f-type function ws dded to the O set. The ground stte of UO 2 hs been suggested to be (5f)(7s) Φ u nd not (5f) 2, s might hve been intuitively expected by considering some isoelectronic molecules such s, for exmple, NpO ,7 In light of this, we decided to use s n ctive spce the 5f nd 7s orbitls (2 electrons in 8 orbitls, 2/8). This miniml ctive spce gives rise to seven singlet nd seven triplet ungerde sttes rising from the (5f)(7s) electronic configurtion nd 28 singlet nd 2 triplet gerde sttes from the (5f) 2 configurtion. Stte verge clcultions were performed for ll these sttes in the first set of clcultions. Since the gerde nd ungerde sttes do not mix under the influence of spinorbit coupling, one spin-orbit Hmiltonin ws constructed for the 9 gerde SO sttes nd one for the 28 ungerde SO sttes. In our recent study of the U(V) nd U(VI) systems XUY (X, Y ) C, N, O), we found tht it ws importnt to include in the ctive spce the oxygen 2p orbitls nd the corresponding UO ntibonding orbitls of σ nd π type. A second lrger ctive spce ws therefore constructed, which comprised the six oxygen 2p orbitls nd the corresponding σ- nd π-type orbitls on U. They will be hybrid orbitls mixing 5f, 6d, nd 7s. In ddition, we hve included the four 5fδ nd 5fφ orbitls. In totl, this yields 4 electrons in 6 orbitls. CASSCF/CASPT2 clcultions of this size re not yet possible. Therefore, the ctive spce ws reduced to 4 electrons in 4 orbitls (4/4) by computing only the ground stte with this ctive spce. The effect of spin-orbit coupling ws tken into ccount using the results obtined with the smller ctive spce. 0.02/jp02888z CCC: $ Americn Chemicl Society Published on Web 0/25/200

2 Electronic Structure of the UO 2 Molecule J. Phys. Chem. A, Vol. 05, No. 46, TABLE : Anlysis of the Spin-Orbit Mixing in the Five Lowest Electronic Sttes of UO 2 (BS nd 2/8 ctive spce) Ω 2 u u u 2 u 4 g energy (ev) r(uo) (Å): force (u) b decomposition in % Φ u u Π u Φ u u Π u H g Γ g Γ g Reltive energies in ev. b Symmetric force constnt, σ g. Figure. Reltive energies (in u) for the lowest electronic sttes of UO 2 s function of the UO distnce t the CASPT2 level of theory (28098 u hve been dded to the totl energies). Solid lines, triplet ungerde sttes; dotted lines, singlet ungerde sttes; dshed lines, triplet gerde sttes; dot-dshed lines, singlet gerde sttes. Figure 2. Reltive energies (in u) for the lowest electronic sttes of UO 2 s function of the UO distnce t the CASPT2-SO level of theory (28098 u hve been dded to the totl energies). Solid lines, ungerde sttes; dotted lines, gerde sttes. A numericl grid ws used to compute the geometry nd force constnts. The molecule ws ssumed to hve D h symmetry, but only inversion symmetry ws used in the geometry optimiztion in order to llow verging over ll sttes of given spin symmetry. Clcultions of the symmetric stretching force constnt were mde without imposing symmetry. The clcultions with the lrger ctive spce were, however, performed using symmetry, D 2h or C 2V. The bending force constnt ws not computed, nd only liner geometries were studied.. Results Figure shows the energies s function of the UO distnce t the CASPT2 level of theory (BS, 2/8). The four lowest sttes belong to the (5f)(7s) ungerde configurtion, Φ u, u, Φ u, nd u. The first gerde stte is H g.figure 2 shows the effect of spin-orbit coupling. The ungerde sttes re now strongly mixed resulting in two pirs of lmost prllel potentil curves. In Tble, we present the results for the five lowest sttes, corresponding to Ω ) 2,,, 2, nd 4. The results hve been TABLE 2: Reltive Energies, Bond Distnces, nd Symmetric Force Constnts for the Lowest Electronic Sttes in the UO 2 Molecule (BS, 2/8) method T e (ev) bond distnce (Å) force (u) CASSCF, Φ u CASSCF, u CASSCF, H g CASPT2, Φ u CASPT2, u CASPT2, H g SO (Ω ) 2) u SO (Ω ) ) u SO (Ω ) ) u SO (Ω ) 2) u SO (Ω ) 4) g obtined with the smller bsis set nd ctive spce. This shows how spin-orbit coupling mixes the different sttes, computed t n UO distnce of.5 u. The ground stte hs Ω ) 2, with extr stbiliztion due to the interction of the Φ u stte with u nd u. Only 0.05 ev bove is the Ω ) stte, which is mixture of Φ u, u, nd Φ u, still dominted by the Φ u stte. The next stte (Ω ) ) is dominted by u. The first gerde stte ( H g, Ω ) 4) is found 0.52 ev bove the lowest stte. We note tht the interction with Γ g stbilizes the Ω ) 4 component nd mkes it the lowest gerde stte. In perturbtion theory, first-order spin-orbit term is responsible for the Ω ) 6 stte being the lowest-ω gerde stte, while second-order spinorbit term is responsible for the Ω ) 4 stte being the lowest-ω gerde stte. This second-order effect thus overrules the firstorder spin-orbit effect. Actully the Ω ) 6 stte is found.2 ev bove the first gerde stte. The tble lso gives the reltive energies, bond distnces, nd symmetric force constnts. The ungerde sttes hve lmost the sme bond length nd force constnt, while the force constnt is lrger for the first gerde stte. More detils re given in the Tble 2. We notice here tht the CASSCF bond lengths re bout 0. Å too short. The CASPT2 results for the ground stte for the bond length nd force constnt re.84 Å nd 0.72 u, which re modified to.84 Å nd 0.86 u by spin-orbit coupling. Thus, the bond length is not ffected, but the force constnt is becuse the force constnt for the u stte is lrger thn tht for the Φ u stte. The vibrtionl frequencies re presented in Tble, which lso gives the results obtined with the lrger 4/4 ctive spce nd bsis set (BS2). Both these extensions modify the geometry nd the force field. As ws seen in our erlier studies, the effect of extending the ctive spce is to mke the bond shorter nd

3 0604 J. Phys. Chem. A, Vol. 05, No. 46, 200 Gglirdi et l. TABLE : Bond Distnces nd Vibrtionl Frequencies (Intensities within Prentheses) for the Ground Stte of the UO 2 Molecule method r(uo) Å σ g(6) σ u(6) σ u(8) 8/6 rtio Smll Bsis Set, Smll Active Spce CASSCF (242) 754(28).05 CASPT ( ) 84( ).054 SO (Ω ) 2) ( ) 88( ).05 SO (Ω ) ) ( ) 8( ).05 SO (Ω ) ) ( ) 8( ).054 Smll Bsis Set, Lrge Active Spce CASPT (472) 848(27).054 SO (Ω ) 2) ( ) 89( ).054 Lrge Bsis Set, Lrge Active Spce CASPT (485) 885(9).05 SO (Ω ) 2) ( ) 877( ).052 BLYP-RECP on U, 6-G(d,p) on O (42) Expt (-) 869(-).052 From ref. stronger. Thus, the bond length decreses (CASPT2) by 0.08 Å. A further decrese of Å is obtined by extending the bsis set. It is cler tht precise determintions of the geometry of these compounds cn only be obtined by creful considertion of both bsis sets nd ctive spces. Spin-orbit coupling lso hs considerble effect on the bond length when the lrger ctive spce is used. A decrese of Å is obtined with BS, while decrese of Å is obtined with BS2. The finl bond length is.766 Å. It is interesting to compre the CASPT2 bond length,.806 Å, with our erlier results for UO 2 2+ nd UO 2 +. The results were.705 nd.77 Å obtined with BS2 but without g-type functions on U, which were shown to hve only smll effect. Thus, the ddition of one 5f electron on going from the urnyl ion to UO 2 + increses the bond length by 0.07 Å. The further ddition of the 7s electron gives n dditionl increse of 0.0 Å. Only the ntisymmetric stretching frequency, ω(σ u )ofuo 2 cn be compred to the experiment. The neon mtrix vlue reported by Zhou et l. is 94.8 cm - for 6 O nd cm - for 8 O, with 6/8 rtio of The best present results give 92, 877, nd.0525 cm -, respectively. The mtrix effect is estimted to be bout 0 cm -. In ddition, the present results correspond to hrmonic frequencies. The nhrmonic correction cn, however, be expected to be smll for the σ u vibrtion. Thus, there is greement between theory nd experiment. We note tht the smller bsis set nd ctive spce underestimte the frequency. The results of clcultions using DFT (BLYP with reltivistic effective core potentils) re lso reported in Tble. The results re in resonble greement with experiment nd identicl to the results obtined by Zhou et l. The results re similr to the b initio vlues. One should, however, be creful to conclude tht the DFT pproch cn generlly be used to study this clss of compounds. Our experience with other similr systems is much less optimistic. Not much experimentl informtion is vilble for gseous UO 2. In ddition to the mesurements of the ntisymmetric vibrtionl frequencies reported bove, the ioniztion energies (IE) hve lso been mesured. The first ioniztion energy of UO 2 hs been determined by electron impct mss spectrometry on t lest two previous occsions. In 974, Ruh nd Ackermnn determined vlue of 5.4 ( 0. ev, 8 nd in 999, Cpone et l. 2 reproduced this result using moleculr bem TABLE 4: Computed Adibtic Ioniztion Energy (in ev) for UO 2 with Different Bsis Sets nd Active Spces method r(uo) Å IE Smll Bsis Set, 2/8, /7 Active Spces CASSCF CASPT CASPT2-SO Smll Bsis Set, 4/4, / Active Spces CASPT Lrge Bsis Set, 4/4, / Active Spces CASPT BLYP-RECP on U, 6-G(d,p) on O Bond distnce in UO 2+. smple. Gibson obtins 5.5 ev in similr experiment. 9 In recent review pper by Hildenbrnd, 20 electron impct ioniztion energies re compred with ioniztion energies determined by more precise methods (e.g., photoelectron spectroscopy), nd it is concluded tht n electron impct ioniztion energy is expected to gree with the dibtic ioniztion energy to within (0.0 ev. Thus, the bove vlue for the first ioniztion energy of UO 2 might be relible within the quoted error limits nd should be tken s the dibtic vlue. In work reported in 988, He(I) photoelectron spectroscopy ws used to mesure the ioniztion energies, but insufficient intensity ws obtined for UO 2 in the low ioniztion energy region (5-0 ev). 2 Assignments were mde with the id of Hrtree-Fock-Slter (LCAO-XR) clcultions. A (5f) 2 configurtion ws, however, ssumed for the UO 2 ground stte, which is different from the results obtined in lter studies (including the present). We hve computed the first IE of UO 2. The clcultions were performed with both bsis sets nd with both ctive spces. For UO 2 +, the smller ctive spce comprised the seven f-orbitls with one ctive electron. The lrge ctive spce dded the six O(2p) orbitls nd the corresponding ntibonding orbitls ( electrons in orbitls). The geometry of UO 2+ ws determined in order to compute the dibtic IE. DFT/BLYP clcultions were lso performed. The results re presented in Tble 4. The ground stte of UO 2 + is 2 Φ u, Ω ) 5 / 2 with computed bond distnce of.72,.807,.806 Å t the CASSCF, CASPT2, nd CASPT2-SO levels, respectively. The CASPT2 vlue is slightly different from the vlue obtined in our erlier work,.78 Å, where ECP s were used for the U tom. The computed IP s re 5.4, 6.2, nd 6.2 ev, respectively. We note tht the effect of spin-orbit coupling is smll. This is explined by the fct tht the ionized electron resides in n orbitl dominted by U(7s). Both the ion nd the neutrl molecule hve one 5fφ orbitl occupied. No spin-orbit coupling ws included in the clcultions with the lrge bsis set. The vlue for the IE is 6.2 ev independent of the method nd bsis set used. Also, the BLYP clcultions give the sme result, nd this confirms the vlue obtined by Zhou et l. of 6.27 ev. The difference between this vlue nd the experimentl vlue, 5.4 ev, of 0.7 ev is surprisingly lrge. With the lrge ctive spce nd both the smll nd lrge bsis, we obtin verticl IE of 6. ev. To investigte the difference between the experimentl nd computed dibtic IE, number of checks were mde. First of ll the UO Σ g stte, obtined on (7s) - ioniztion from the UO 2 ground stte, ws considered, but this ws found to lie more thn ev bove the 2 Φ u stte. Second, the possibility tht UO 2 + could be bent in its ground stte ws investigted. However, bent UO 2 + ws found to be higher in energy thn

4 Electronic Structure of the UO 2 Molecule J. Phys. Chem. A, Vol. 05, No. 46, liner UO 2 +. We therefore concluded tht there is no obvious reson our computed vlue of 6.2 ev for the first dibtic IE should be in error. The photoelectron spectrum of urnium recorded with HeI rdition 2 exhibits contributions from ioniztion of the ground stte s well s excited sttes populted t the high tempertures (c K) used for evportion. The bnd intensities re lso ffected by utoioniztion processes. This is lso likely to be the cse for UO 2 prepred by high-temperture evportion nd ionized by photon or electron impct in the energy region ev. The clcultions with the smll ctive spce nd smll bsis sets revel tht severl excited sttes of different symmetry lie in the ev energy region. Among the gerde sttes, two singlets nd two triplets re found t c. 5.6 ev, two triplets t c. 6.0 ev nd two singlets t c ev. If these re positioned bove the first ioniztion energy (c. 6.2 ev), then utoioniztion to the ionic ground stte cn occur. Inspection of Tble 2 shows tht there is H g stte of UO 2 t 0.75 ev bove the ground stte t the CASPT2 level, which corresponds to n excittion energy of 0.52 ev to Ω ) 4, g stte, when SO coupling in included. The min electronic configurtion of the outermost orbitls for this stte is 5f 2. Clerly, the ground stte of UO 2 + is obtined vi (7s) - ioniztion from the ground stte of UO 2, nd vi (5f) - ioniztion from the H stte. From tbultion of tomic photoioniztion cross-sections of Yeh nd Lindu, 22 the 7s:5f crosssection rtio is expected to be c. :6. Hence, lthough the popultion of the excited H stte is expected to be low t the evportion tempertures used, its enhnced cross-section my give rise to extr signl below the true dibtic ioniztion energy in the electron impct ioniztion efficiency curve. This my be the reson the experimentl vlue for the first ioniztion energy of UO 2 determined by electron impct mss spectrometry is too low by c. 0.7 ev. Also, we note tht the excited stte hs Ω ) 4 wheres the ground stte hs Ω ) 2. The selection rule Ω ) 0, ( would imply tht the excited stte is metstble in nture with the trnsition to the ground stte formlly forbidden. As well s contributions from the low-lying excited sttes below the first ioniztion energy to the electron-impct ioniztion efficiency curve, there is lso the possibility tht excited sttes bove the first ioniztion energy, populted on electron impct, would give rise to distortion of the ioniztion efficiency curve. Hence, we present these s possible resons why the electron impct ioniztion efficiency curve will be distorted nd the ioniztion energy obtined on extrpoltion to zero signl could be in error. Clerly, there is need for determintion of the first dibtic ioniztion energy of UO 2 by more ccurte methods other thn electron impct mss spectrometry, such s photoelectron spectroscopy or Rydberg series extrpoltion methods. The second IE of UO 2 hs lso been determined experimentlly, by Cornehl et l., 2 who reported vlue of 5.4(2.6) ev. We computed the second IE with the lrge ctive spce nd both the smll nd lrge bsis by optimizing UO 2 2+ in its Σ g ground stte t the 2/2 CASPT2 level. This gve n equilibrium distnce of.75 Å with the smll bsis nd.70 with the lrge bsis. (In our erlier work, we obtined.705 nd.698 Å t ECP s/caspt2 nd ECP s/dft level, respectively.) The vlue for the second IE is 4.02 ev with the smll bsis nd 4.6 ev with the lrge bsis. (In our erlier work, we obtined 4.4 nd 5.25 ev t ECP s/caspt2 nd ECP s/ DFT level, respectively.) CASPT2 in generl gives lower vlue for the second IE thn DFT. However, ll these computed vlues re within the experimentl rnge. 4. Conclusions We hve presented results of clcultions on the electronic structure nd vibrtionl frequencies of the UO 2 molecule. The im hs been to use this molecule s test of newly developed method to include spin-orbit coupling into multiconfigurtionl wve functions. 2 The method hs been found to work well for systems contining trnsition metls nd min group elements, but this is the first test for n ctinide compound. It is cler from the computed vibrtionl frequencies tht the method gives stisfctory description of the energy surfce round the equilibrium geometry. The effect of spin-orbit coupling is lrge for the symmetric stretching mode but less significnt for the mesured ntisymmetric stretch. The frequency decreses by 0 cm - on including spin-orbit interction. The molecule hs ground stte of ungerde symmetry (Ω ) 2), which is best described s the electronic configurtion (5fφ)(7s) with D h symmetry nd bond length of.77 Å. The corresponding (Ω ) ) stte is, however, locted only 0.05 ev bove. Spin-orbit coupling mixes sttes of symmetry Φ u, Φ u, u, nd u. The first gerde stte H g (Ω ) 4) is locted 0.5 ev bove the ground stte. Clcultions of the first ioniztion energy give vlue of 6.2 ev, which is 0.7 ev bove the generlly ccepted experimentl vlue of 5.4 ev. Our results re very consistent, nd they gree with the theoreticl vlue previously determined by Zhou et l. of 6.27 ev. We thus hve no obvious reson to suspect tht the computed vlue of 6.2 ev is in error. It is suggested tht the possible reson for this difference is tht low vlue for the first ioniztion energy hs been mesured in electron impct mss spectrometric experiments, which involve popultion of neutrl excited sttes under the high-temperture evportion conditions used to prepre UO 2 in the gs phse. At lest one of these excited sttes, 0.52 ev bove the ground stte, is long-lived, s the trnsition to the ground stte is forbidden. Further experimentl mesurements will be required to investigte this suggestion. Clcultions of the second ioniztion energy give vlues in the region ev, which is within the error limits of the experimentl vlue (5.4 ( 2.6 ev), Acknowledgment. This work ws prtilly supported by Ministero dell Università e dell Ricerc Scientific, (MURST), nd the Swedish Nturl Science Reserch council (NFR). The uthors thnk Professor Lester Andrews (Virgini) for inspiring the project nd useful discussions. References nd Notes () Zhou, M.; Andrews, L.; Ismil, N.; Mrsden, C. J. Phys. Chem. A 2000, 04, (2) Cpone, F.; Colle, Y.; Hiernut, J. P.; Ronchi, C. J. Phys. Chem. A 999, 0, () Gglirdi, L.; Roos, B. O. Chem. Phys. Lett. 2000,, 229. (4) Roos, B. O. In AdV. in Chem. Phys.; Ab Initio Methods in Quntum Chemistry - II; Lwley, K. P., Ed.; John Wiley & Sons Ltd.: Chichester, Englnd, 987; p 99. (5) Andersson, K.; Mlmqvist, P.-Å.; Roos, B. O.; Sdlej, A. J.; Wolinski, K. J. Phys. Chem. 990, 94, 548. (6) Andersson, K.; Mlmqvist, P.-Å.; Roos, B. O. J. Chem. Phys. 992, 96, 28. (7) Roos, B. O.; Andersson, K.; Fülscher, M. P.; Mlmqvist, P.-Å.; Serrno-Andrés, L.; Pierloot, K.; Merchán, M. InAdVnces in Chemicl Physics: New Methods in Computtionl Quntum Mechnics; Prigogine, I., Rice, S. A., Eds.; John Wiley & Sons: New York, 996; Vol. XCIII, pp 29-. (8) Dougls, N.; Kroll, N. M. Ann. Phys. 974, 82, 89.

5 0606 J. Phys. Chem. A, Vol. 05, No. 46, 200 Gglirdi et l. (9) Hess, B. Phys. ReV. A986,, 742. (0) Mlmqvist, P.-Å. Int. J. Quntum Chem. 986, 0, 479. () Mlmqvist, P. Å.; Roos, B. O. Chem. Phys. Lett. 989, 55, 89. (2) Mlmqvist, P.-Å.; Roos, B. O.; Schimmelpfennig, B. Chem. Phys. Lett., in press. () Andersson, K.; Bryz, M.; Bernhrdsson, A.; Blomberg, M. R. A.; Boussrd, P.; Cooper, D. L.; Fleig, T.; Fülscher, M. P.; Hess, B.; Krlström, G.; Lindh, R.; Mlmqvist, P.; Neogrdy, P.; Olsen, J.; Roos, B. O.; Sdlej, A. J.; Schimmelpfennig, B.; Schütz, M.; Seijo, L.; Serrno, L.; Siegbhn, P. E.; Stålring, J.; Thorsteinsson, T.; Veryzov, V.; Whlgren, U.; Widmrk, P. MOLCAS, Version 5.0; University of Lund: Lund, Sweden, (4) Whlgren, U. Privte communiction, (5) Widmrk, P.-O.; Mlmqvist, P.-Å.; Roos, B. O. Theor. Chim. Act 990, 77, 29. (6) Mtsik, S.; Pitzer, R. M.; Reed, D. T. J. Phys. Chem. A 2000, 04, 98. (7) Mtsik, S.; Zhng, Z.; Brozell, S. R.; Bludeu, J.-P.; Wng, Q.; Pitzer, R. M. J. Phys. Chem. A 200, 05, 825. (8) Ruh, E. G.; Ackermn, R. J. J. Chem. Phys. 974, 60, 96. (9) Gibson, J. K. Rdiochim. Act 998, 8, 8. (20) Hildenbrnd, D. L. Int. J. Mss Spectrom. 2000, 97, 27. (2) Allen, G. C.; Berends, E. J.; Vernooijs, P.; Dyke, J. M.; Ellis, A. M.; Fehér, M.; Morris, A. J. Chem. Phys. 988, 89, 56. (22) Yeh, J. J.; Lindu, I. At. Dt Nucl. Dt Tbles 985, 2,. (2) Cornehl, H. H.; Heinemnn, C.; Mrclo, J.; de Mtos, A. P.; Schwrz, H. Angew. Chem., Int. Ed. Engl. 996, 5, 89.