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Xantheas Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P. O. Box 999, MS K1-96, Richland, WA 99352 USA George S. Fanourgakis(a), Stavros C. Farantos(a) and M. Velegrakis Institute of Electronic Structure and Laser, Foundation for Research and Technology-Hellas, P. O. Box 1527, 711 10 Heraklion, Greece ABSTRACT We present the first non-empirically calculated spectroscopic constants for the recently observed [J. Chem. Phys. 105, 2167 (1996)] ground (X-2S+) and excited (A-2P) states of Sr+Ar. Our best results yield De=694 cm-1, Re=3.662  and we=38.7 cm-1 for the ground and De=1967 cm-1, Re=3.169  and we=99.1 cm-1 for the excited state. The calculated Deдs are within the error bars of the experimentally determined one for the ground state favoring the low end and underestimate the corresponding one for the excited state by about 7%. The equilibrium separations (Reдs) for the two states have not been experimentally determined, however our results accurately reproduce the estimated shift, DRe, between the two states. The interaction is mainly electrostatic for the ground state for which the contribution of dynamic electron correlation was found to be more important than for the excited state. Clusters of noble gas atoms serve as prototype systems in modeling solvation phenomena. Metal atoms embedded in these clusters function as "chromophores" used to probe their optical properties. The potential energy surfaces (PESs) of the metal atom-noble gas diatomic molecules are of particular importance since they represent the cornerstones in the parametrization of interaction potentials used to study the energetic and dynamical properties of the larger clusters.1 Recently, LŸder and Velegrakis2 have studied the photofragmentation spectrum of the Sr+Ar complex in the 418-448 nm wavelength region. They observed vibrational progressions which they attributed to transitions from the X-2S1/2 electronic ground state to the excited A-2P1/2 and A-2P3/2 states. From the experimental studies it was possible to deduce the harmonic frequencies (we) and anharmonicities (wece) of the X-2S1/2 and A-2Pi states but not the corresponding equilibrium separations (Re). Furthermore, the experimental data allowed determination of the dissociation energies with respect to the corresponding asymptotes arising from the Sr+(52S1/2) and Sr+(52P1/2,3/2) limits with error bars amounting to 30% for the X-2S1/2 and 10% for the 2Pi states, respectively. It should be noted that the only available theoretical results for this system prior to this study were obtained using pseudopotential models3 which, however, differ significantly with respect to the experimental data as noted by LŸder and Velegrakis.2 In particular, the empirical calculations underestimate the dissociation energy for the excited A-2Pi states by about 1000 cm-1 (or 40%) as well as the shift in the equilibrium separation between the ground X-2S1/2 and A-2Pi excited states by 0.15  (the empirical calculations predict DRe=0.35  vs. 0.50Б0.05  determined experimentally). To this end our study aims in complementing the experimental data by producing accurate potential energy curves for the ground and the excited states of Sr+Ar towards our long term research effort to parametrize interaction potentials in order to study the energetic and dynamical properties of the Sr+(Ar)n clusters.4 Previous theoretical studies5 by Bauschlicher, Partridge and Langhoff on metal noble-gas positive ions M+Ar (M=Li, Na, K, Mg, Sc, Ti, Mn, Fe, Co, Cu, V) have accounted for an excellent overview of the bonding in these systems. These authors have elaborated on the importance of the rare gas atom basis set in accurately describing its polarizability, a requirement arising from the predominantly electrostatic interaction in these systems with the leading term being the one corresponding to the charge-induced dipole. They have also noted the possibility of charge donation from the ligand (rare gas atom) to the metal depending on the difference between the metal and ligand ionization potentials (IPs). However, for the system at hand, the large difference between the Ar and Sr IPs (15.77 and 5.692 eV respectively6) suggests that this is most probably unlikely. In this study we present the potential energy curves for the ground (X-2S+) and the excited (A-2P) states of Sr+Ar, arising from the interaction of Ar(1S) with electrons in the 5s and 5p orbitals of Sr+, respectively. The A-2P state is the second one of that symmetry, the lower one arising from the interaction of Ar with the 4d electrons of Sr+ which lie energetically between the 5s and 5p and produce a manifold of states (2S, 2P, 2D) which, however, have not been observed experimentally for Sr+Ar but they have been observed for Ca+Ar.7 For the ground (X-2S+) state, the calculations were performed at the coupled cluster level of theory including single and double excitations with a perturbative estimation8 of the triple excitations [RCCSD(T)] from a restricted Hartree-Fock (RHF) reference wavefunction. In addition, we considered the internally contracted multi reference single and double excitation configuration interaction (icMRCI) method9 from a multi configuration self-consistent field (MCSCF) wavefunction. We have chosen two active spaces in the MCSCF calculations one including the Ar(3s,3p) with the Sr(5s) electrons (MCSCF-1: 9e-/5 orbitals) the other the Ar(3s,3p) with the Sr(4s, 4p, 5s) electrons (MCSCF-2: 17e-/9 orbitals). The number of internally contracted/uncontracted CSFs are 7896/26020 and 25946/155658 in the icMRCI for the two active spaces, respectively. The RCCSD(T) calculations corresponding to the two previous active spaces are denoted as RCCSD(T)/9e- and RCCSD(T)/17e-. We finally considered a larger active space (MCSCF-3: 17e-/12 orbitals) in order to incorporate the states that arise from the Sr+(4d) and (5p) orbitals. For the calculations with the last active space we have performed a 4-state average MCSCF calculation (15128 CSFs) with equal weights for the ground state, the 2S and 2D states coming from the Sr+(4d) orbitals and the repulsive B-2S+ state arising from the Sr+(4p) orbitals and subsequently successive projected icMRCI calculations for four states. It should be noted that the repulsive B-2S+ state is needed in order to parametrize10 classical interaction potentials for the triatomic Sr+(Ar)2 system; results regarding the B-2S+ state obtained from these calculations will be reported in subsequent publications together with the potential development.4 The states of P symmetry were obtained by a similar procedure, viz. a 2-state average MCSCF (14204 CSFs) and subsequent projected icMRCI calculations for two states. The corresponding number of internally contracted CSFs in the icMRCI is 2140732 for the  EMBED Equation.2 =0 and 2122179 for the  EMBED Equation.2 =1 states out of about 135 million uncontracted. In the icMRCI calculations the в+Qг designation denotes the multireference analog11 of the Davidson correction12 that provides an estimate of higher-than-double excitations from the MCSCF active space. For the Sr atom we used the quasi-relativistic effective core potential (ECP) from the Stuttgart group13 (28 core electrons) in conjunction with the (6s6p5d) valence set contracted to [4s4p2d] for the remaining electrons. This ECP/valence set combination yields a second ionization potential (IP) of 10.80 eV for Sr+ at the CCSD(T) level of theory (compared to 11.03 eV experimentally6) and a 52S-52P excitation of 2.93 eV for Sr+ (compared to the averaged spin-orbit value6 of 2.99 eV). For Ar we used the doubly augmented correlation-consistent polarized valence double zeta (d-aug-cc-pVDZ) basis set.14 This consists of the regular aug-cc-pVDZ set15 augmented with one additional diffuse function of each symmetry (s, p, d) whose exponents are determined in an even-tempered fashion. The d-aug-cc-pVDZ set produces 11.05 a.u. for the polarizability of Ar at the CCSD(T) level of theory, a value very close to the basis set limit of 11.19 a.u. We computed the potential energy curves using the energies of 14-17 internuclear separations around the minimum. A Dunham analysis16 was used to extract the equilibrium bond length (Re), the dissociation energy (De), the harmonic frequency (we) and the anharmonicity (wece). The largest difference between the calculated energies and those predicted by the fit was 10-6 hartree (0.22 cm-1). The dissociation limit for the separated atoms was calculated using the supermolecule approach at the icMRCI (the energy is computed at an internuclear separation of 100Ъa0) and the sum of the separated atoms at the RCCSD(T) levels of theory, respectively. All calculations were performed using the MOLPRO program suite.17 The results of our calculations are listed in Table I; the potential energy curves for the two states are shown in Figure 1. For the ground X-2S+ state, dynamic electron correlation results in a contraction of Re by almost 0.8  with a five-fold increase in the corresponding De. The effect of correlation of the Sr(4s,4p) electrons is also large as evident from the difference between both the icMRCI (+Q) with the MCSCF-1 and MCSCF-2 active spaces and the RCCSD(T) 9e-/17e- results. It amounts to a contraction of 0.24  for Re and an increase of 326 cm-1 for De at the RCCSD(T) level of theory. The effect on Re is similar at the icMRCI level of theory (0.22 ), although the differential effect on De is only 70% of that at the RCCSD(T) level. The в+Qг correction seems, however, to compensate for this yielding differential correlation effects of 0.23  and 298 cm-1 for Re and De respectively, values that are closer to the ones obtained at the RCCSD(T) level of theory. The largest [RCCSD(T)/17e- and icMRCI+Q/MCSCF-3] calculations for the ground state yield dissociation energies within 11 cm-1 from each other, both lying within the experimental error favoring the lower end. The corresponding harmonic frequencies are within 1 cm-1 from each other, both ~10 cm-1 smaller than experiment. In addition, the predicted Re values between the two methods are within 0.034  from each other. For the ground state the interaction is mainly electrostatic as indicated by the magnitude of the charge-induced dipole term V=q2a/2R4 which yields 78% of De (a is the dipole polarizability of Ar). For the A-2P excited state we compute a dissociation energy (De) of 1126 cm-1 at the MCSCF and 1814 cm-1 at the icMRCI levels of theory; the в+Qг correction increases our estimate to 1967 cm-1. The effect of dynamic electron correlation for the A-2P state is important, although not to the extreme observed for the ground state. For instance, the ratio of the CASSCF to icMRCI+Q Deеs is 0.38 for the ground and 0.57 for the excited state. Furthermore, the calculated Re is 3.183  at the icMRCI level of theory, decreasing to 3.169  when the в+Qг correction is taken into account. Our estimated shift in the corresponding Reеs between the ground and the A-2P excited state (cf. Figure 2) is therefore 0.526  (icMRCI) and 0.493  (icMRCI+Q), in excellent agreement with the experimentally2 estimated value of ЦRe=0.50Б0.05 . Our best estimate for the harmonic frequency of the excited state is 20 cm-1 lower than the one determined experimentally. In conclusion, we present the first non-empirical calculations for the ground and the first observed excited state of Sr+Ar. Our calculations produce a dissociation energy for the ground state that is within the experimental error bar favoring the lower end while underestimate the one for the excited state by about 7%; they also accurately reproduce the observed contraction of the equilibrium separation in the excited state with respect to the ground state. Our results are in much better agreement with the available experimental data for this system than the results of previous empirical calculations.3 To this end our calculations complement the available experimental data for this system by providing accurate equilibrium distances (Reеs) and potential energy curves for the two states, information which will be used to parametrize interaction potentials in subsequent studies.4 Acknowledgment: This work was performed under the auspices of the Division of Chemical Sciences, Office of Basic Energy Sciences, US Department of Energy under Contract DE-AC06-76RLO 1830 with Battelle Memorial Institute, which operates the Pacific Northwest National Laboratory. Computer resources were provided by the Division of Chemical Sciences and by the Scientific Computing Staff, Office of Energy Research, at the National Energy Research Supercomputer Center (Berkeley, CA). SSX and SCF gratefully acknowledge support from the Hellenic General Secretariat for Research and Technology under the program for support of scientific staff PENED-1994 (15774/296). REFERENCES 1. G. S. Fanourgakis and S. C. Farantos, J. Phys. Chem. 100, 3900, 1996. 2. C. LŸder and M. Velegrakis, J. Chem. Phys. 105, 2167 (1996). 3. H. Harima, T. Ihara, Y. Urano and K. Tachibana, Phys. Rev. A 34, 2911 (1986). 4. G. S. Fanourgakis, S. C. Farantos, S. S. Xantheas, C. LŸder and M. Velegrakis, work in progress. 5. C. W. Bauschlicher, Jr., H. Partridge and S. R. Langhoff, J. Chem. Phys. 91, 4733 (1989); H. Partridge, C. W. Bauschlicher, Jr. and and S. R. Langhoff, J. Phys. Chem. 96, 5350 (1992); C. W. Bauschlicher, Jr., H. Partridge, Chem. Phys. Lett. 239, 241 (1995). 6. C. E. Moore, Atomic Energy Levels, Natl. Bur. Stand. Circ. 467, Vols. I-III (1949). 7. T. Buthelezi, D. Bellert, V. Lewis and P. J. Brucat, Chem. Phys. Lett. 246, 145, (1995). 8. C. Hampel, K. Peterson, and H.-J. Werner, Chem. Phys. Lett. 190, 1 (1992); J. D. Watts, J. Gauss and R. J. Bartlett, J. Chem. Phys. 98, 8718 (1993). 9. H.-J. Werner and P.J. Kn_920667960џџџџ РF€dFMpМ€dFMpМOle џџџџџџџџџџџџPIC џџџџLPICT џџџџџџџџџџџџ1 roll sub 256 div 384 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /MT-Extra f1 (l) -8 261 sh end MTsave restore  ПЁdMATH   ‹l  џаЯрЁБс;џў ўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў   ‹lаЯрЁБсаЯрЁБс;џў LЇ­№шшCompObj џџџџYObjInfoџџџџ џџџџEquation Native џџџџџџџџџџџџ(_920668048џџџџџџџџ РF€dFMpМћЋFMpМowles, J. Chem. Phys. 89, 5803 (1988); P.J. Knowles and H.-J. Werner, Chem. Phys. Lett. 145, 514 (1988); H.-J. Werner and E.A. Reinsch, J. Chem. Phys. 76, 3144 (1982); H.-J. Werner, Adv. Chem. Phys. LXIX, 1 (1987). 10. L. C. Balling and J. J. Wright, J. Chem. Phys. 79, 2941, (1983). 11. M. R. A. Blomberg, P. E. M. Siegbahn, J. Chem. Phys. 78, 5682 (1983). 12. S. R. Langhoff, E. R. Davidson, Int. J. Quantum Chem. 8, 61 (1974). 13. M. Kaupp, P. v. R. Schleyer, H. Stoll, H. Preuss, J. Chem. Phys. 94, 1360 (1991). 14. D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 100, 2975 (1994). 15. D. E. Woon and T. H. Dunning, Jr., J. Chem. Phys. 98, 1358 (1993); R. A. Kendall, T. H. Dunning, Jr., and R. J. Harrison, ibid., 96, 6796 (1992); T. H. Dunning, Jr., ibid., 90, 1007 (1989). 16. J. L. Dunham, Phys. Rev. 41, 713 (1932). 17. MOLPRO is a package of ab initio programs written by H.-J. Werner and P. J. Knowles, with contributions from J. Almlšf, R. D. Amos, A. Berning, D. L. Cooper, M. J. O. Deegan, F. Eckert, S. T. Elbert, C. Hampel, R. Lindh, W. Meyer, M. E. Mura, A. Nicklass, K. Peterson, R. Pitzer, P. Pulay, M. ShŸltz, H. Stoll, A. J. Stone, P. R. Taylor and T. Thorsteinsson. For the RCCSD(T) implementation in MOLPRO see P. J. Knowles, C. Hampel and H.-J. Werner, J. Chem. Phys. 99 5219 (1993). FIGURE CAPTIONS Figure 1 Calculated potential energy curves for the X-2S+ and A-2P states of Sr+Ar at the icMRCI/MCSCF-3 level of theory. Figure 2 Area around the two minima to indicate the contraction of Re for the A-2P state with respect to the ground state. (a) Also at Department of Chemistry, University of Crete, 711 10 Heraklion, Crete, Greece Xantheas et. al. вSpectroscopic constants of the 2S and 2P states of Sr+Ar...г ŽЁ™ ›hœтѓЇ ЈјјЉјј|HHк(џсџтљFG(ќHHи(d'`iаЯрЁБс;џў џџџўџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџOle џџџџџџџџџџџџPIC  џџџџLPICT џџџџџџџџџџџџJCompObjџџџџ'YаЯрЁБс;џў J џ џџџџ ЁdЗxpr  Œ , гMT Extra г   *  "  ОЁР currentpoint  П" О( lЁРj/MTsave save def 40 dict begin currentpoint 3 -1 roll sub neg 3 1 roll sub 256 div 384 3 -1 roll exch div scale currentpoint translate 64 59 translate /cat { dup length 2 index length add string dup dup 5 -1 roll exch copy length 4 -1 roll putinterval } def /ff { dup FontDirectory exch known not { dup dup length string cvs (|______) exch cat dup FontDirectory exch known {exch} if pop } if findfont } def /fs 0 def /cf 0 def /sf {exch dup /fs exch def dup neg matrix scale makefont setfont} def /f1 {ff dup /cf exch def sf} def /ns {cf sf} def /sh {moveto show} def 384 /MT-Extra f1 (l) -8 261 sh end MTsave restore  ПЁdMATH   ‹l  џаЯрЁБс;џў ўџџџџџРFMicrosoft Equation Editor 2.0ўџџџDNQE Equation.2аЯрЁБс;џў аЯрЁБс;џў   ‹lаЯрЁБсўџ ђŸ…рOљhЋ‘+'Гй0b ˜Щх ы ї  +F NZџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџџ)APS 235i:Applications:MS Word 6.0:NormalSotiris S. 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