Theoretical Investigation of Small Polyatomic Ions Observed in Inductively Coupled Plasma Mass Spectrometry: HxCO+ and HxN2+ (x = 1, 2, 3)

Transcription

1 Ames Lbortory Publictions Ames Lbortory Theoreticl Investigtion of Smll Polytomic Ions Observed in Inductively Coupled Plsm Mss Spectrometry: HxCO+ nd HxN2+ (x = 1, 2, 3) Kyle C. Sers Iow Stte University Jill Wisnewski Ferguson Iow Stte University Timothy J. Dudley Iow Stte University Robert S. Houk Iow Stte University, rshouk@istte.edu Mrk S. Gordon Iow Stte University, mgordon@istte.edu Follow this nd dditionl works t: Prt of the Chemistry Commons The complete bibliogrphic informtion for this item cn be found t meslb_pubs/337. For informtion on how to cite this item, plese visit howtocite.html. This Article is brought to you for free nd open ccess by the Ames Lbortory t Iow Stte University Digitl Repository. It hs been ccepted for inclusion in Ames Lbortory Publictions by n uthorized dministrtor of Iow Stte University Digitl Repository. For more informtion, plese contct digirep@istte.edu.

2 Theoreticl Investigtion of Smll Polytomic Ions Observed in Inductively Coupled Plsm Mss Spectrometry: HxCO+ nd HxN2+ (x = 1, 2, 3) Abstrct Two series of smll polytomic ions, HxCO+ nd HxN2+ (x = 1, 2, 3), were systemticlly chrcterized using three correlted theoreticl techniques: density functionl theory using the B3LYP functionl, spinrestricted second-order perturbtion theory, nd singles + doubles coupled cluster theory with perturbtive triples. On the bsis of thermodynmic dt, the existence of these ions in inductively coupled plsm mss spectrometry (ICP-MS) experiments is not surprising since the ions re predicted to be considerbly more stble thn their corresponding dissocition products (by kcl/mol). While ech pir of isoelectronic ions exhibit very similr thermodynmic nd kinetic chrcteristics, there re significnt differences within ech series. While the mechnism for dissocition of the lrger ions occurs through hydrogen bstrction, the tritomic ions (HCO+ nd HN2+) pper to dissocite by proton bstrction. These differing mechnisms help to explin lrge differences in the bundnces of HN2+ nd HCO+ observed in ICP-MS experiments. Disciplines Chemistry Comments Reprinted (dpted) with permission from Journl of Physicl Chemistry A 112 (2008): 2610, doi: / jp077209k. Copyright 2008 Americn Chemicl Society. This rticle is vilble t Iow Stte University Digitl Repository:

3 2610 J. Phys. Chem. A 2008, 112, Theoreticl Investigtion of Smll Polytomic Ions Observed in Inductively Coupled Plsm Mss Spectrometry: H x CO + nd H x N 2 + (x ) 1, 2, 3) Kyle C. Sers, Jill W. Ferguson, Timothy J. Dudley, R. S. Houk, nd Mrk S. Gordon* Ames Lbortory, U. S. Deprtment of Energy, Deprtment of Chemistry, Iow Stte UniVersity, Ames, Iow ReceiVed: September 7, 2007; In Finl Form: Jnury 4, 2008 Two series of smll polytomic ions, H x CO + nd H x N 2+ (x ) 1, 2, 3), were systemticlly chrcterized using three correlted theoreticl techniques: density functionl theory using the B3LYP functionl, spinrestricted second-order perturbtion theory, nd singles + doubles coupled cluster theory with perturbtive triples. On the bsis of thermodynmic dt, the existence of these ions in inductively coupled plsm mss spectrometry (ICP-MS) experiments is not surprising since the ions re predicted to be considerbly more stble thn their corresponding dissocition products (by kcl/mol). While ech pir of isoelectronic ions exhibit very similr thermodynmic nd kinetic chrcteristics, there re significnt differences within ech series. While the mechnism for dissocition of the lrger ions occurs through hydrogen bstrction, the tritomic ions (HCO + nd HN 2+ ) pper to dissocite by proton bstrction. These differing mechnisms help to explin lrge differences in the bundnces of HN 2+ nd HCO + observed in ICP-MS experiments. Introduction Smll, hydrogen-contining ctions ply n importnt role in numerous res of chemistry nd physics. Orgnic ctions such s the formyl ction (HCO + ) nd the formldehyde ction (H 2 CO + ) were mong the first polytomic ions observed in interstellr spce. 1 These ions hve lso been observed in dense clouds ssocited with formtion of strs nd gs plnets. 2-3 These ions ply n importnt prt in hydrocrbon combustion nd rections of O + with simple hydrocrbons such s methne. 4 Similr ions, contining nitrogen insted of crbon nd oxygen, hve been observed in roles tht re similr to their orgnic counterprts. The dizenylium ion (N 2 H + ) hs been observed in the sme type of interstellr medi s the formyl ction, 2-3 which is not surprising since they re isoelectronic. Smll polytomic ctions lso re prevlent in inductively coupled plsm mss spectrometry (ICP-MS), where tomic ions re preferred for multielement nlysis Using hightemperture (6000 K) tomiztion source such s n ICP ttenutes but often does not completely eliminte mny of these undesirble polytomic ions. These spectrl interferences become more troublesome for nlysis t the lowest possible concentrtions, which is importnt in key scientific res such s semiconductor production. Understnding how these ions form could lend insight into how to eliminte their production during n ICP-MS experiment. For exmple, experimentl mesurement of the dissocition constnt (K d ) ssocited with pir of ions cn indicte where such ions form, since the constnt is function of temperture. However, the temperture dependence of the constnt is determined through use of the prtition functions ssocited with ech species involved. 7,23 This in turn requires knowledge of energetic nd structurl dt for * To whom correspondence should be ddressed. E-mil: mrk@ si.msg.chem.istte.edu. Present ddress: Mterils Science Center, University of Wisconsins Eu Clire, Eu Clire, WI Present ddress: Deprtment of Chemistry, Villnov University, Villnov, PA ech species. Since mny polytomic ions re not very bundnt or long-lived, much of this dt cnnot be esily obtined through experiment. Theoreticl clcultions offer solution to such problem, since they cn provide severl useful quntities relted to prtition functions: electronic energies, moments of inerti from sttionry geometries, nd hrmonic vibrtionl frequencies. This work focuses on two clsses of smll polytomic ctions observed in ICP-MS experiments: H x CO + nd H x N 2 + (x ) 1, 2, 3). Numerous experimentl nd theoreticl studies hve been reported for mny of these ions, prticulrly the H x CO + series However, systemtic study of these ions using different levels of theory nd bsis sets hs only been reported for the x ) 1 tritomic HCO + ction 39 nd HN 2 + ction. 40 This work will nlyze the thermodynmics nd rection pthwys of the ions in ech series in order to shed light on the existence of these ions in even the hrshest environments. Similrly, nlyses involving comprisons between isoelectronic species will be performed in order to understnd similrities nd differences observed in ICP-MS experiments. Finlly, n nlysis of the performnce of vrious correlted methods in determining structures nd energies of smll polytomic ions will be performed. Computtionl Methods Geometries for ll structures were optimized using three methods: density functionl theory (DFT) with the B3LYP functionl, 41,42 second-order Z-verged perturbtion theory (ZAPT2), nd singles nd doubles coupled cluster theory with perturbtive triples, CCSD(T). 47 For open-shell systems, the restricted forms of ll of the previously mentioned techniques were used (e.g., RCCSD(T)) The bsis set used in ll optimiztions ws the Dunning triple-ζ bsis set (TZ) 48 with the Pople (2df,2pd) 49 polriztion set included. In this work, this bsis set will be referred to s TZ2P(f,d). Frequencies were clculted in order to determine the nture of the sttionry points on ech potentil energy surfce (PES). In ll cses, the frequencies were /jp077209k CCC: $ Americn Chemicl Society Published on Web 03/01/2008

4 Theoreticl Investigtion of Smll Polytomic Ions J. Phys. Chem. A, Vol. 112, No. 12, TABLE 1: Reltive Energies of Sttionry Points nd Dissocition Limits Associted with N 2 H + (Energies Are in kcl/mol) 1 1b N 2 + H + N 2+ + H B3LYP/TZ2P(f,d) ZAPT2/TZ2P(f,d) CCSD(T)/TZ2P(f,d) CR-CC(2,3)/cc-pVQZ Energy evluted t CCSD(T)/TZ2P(f,d)-optimized geometry. Figure 1. CCSD(T)/TZ2P(f,d) geometries of the dizenylium ion nd its trnsition stte ssocited with hydrogen migrtion. Vlues in ( ) re ZAPT2 prmeters, nd those in [ ] re B3LYP prmeters. Experimentl vlues re in {}nd were obtined from ref 61. Bond lengths re in ngstroms. clculted by numericlly differentiting nlytic grdients using centrl difference formul. Frequencies t ech level of theory cn be found in the Supplementl Informtion. Trnsition sttes were connected to their respective minim through intrinsic rection coordinte (IRC) clcultions using the second-order Gonzlez-Schlegel lgorithm, 50 with step size of 0.15 (mu) 1/2 bohr. IRC clcultions were only performed t the B3LYP nd ZAPT2 levels of theory. Constrined optimiztions using the multiconfigurtionl self-consistent field (MCSCF) method were used to determine the hydrogen tom/ion bstrction process for ech ction considered. Structures long these pths re expected to be configurtionlly mixed. For singlet structures, the MCSCF ctive spce consisted of two electrons in two orbitls: hydrogen-hevy tom σ nd σ* orbitls. For doublet structures, similr ctive spce ws utilized, except the unpired electron nd corresponding orbitl were lso included in the ctive spce (three electrons in three orbitls). Becuse of the number of low-lying minim on some of the PESs considered, clcultions involving lrger bsis set were performed to probe the ccurcy of the CCSD(T)/TZ2P(f,d) clcultions. Single-point energy clcultions were performed t ech CCSD(T)/TZ2P(f,d) optimized sttionry points using the cc-pvqz bsis set. The completely renormlized coupled cluster pproch (CR-CC(2,3)) 51,52 implemented in GAMESS 53 ws used to clculte the energies. This completely renormlized CC pproch correctly ccounts for dirdicl chrcter (ner degenercies) nd is therefore better ble thn trditionl CCSD- (T) to ccount for nondynmic correltion effects. All B3LYP, ZAPT2, MCSCF, nd CR-CC(2,3) clcultions were performed using GAMESS, nd ll CCSD(T) clcultions were performed using ACES II. 54 Defult tolernces were used in ll geometry optimiztions nd frequency clcultions. Results N 2 H +. The dizenylium ion (N 2 H + ) hs been previously chrcterized both theoreticlly 40,55-59 nd experimentlly Figure 1 shows the structures nd optimized geometricl prmeters for both sttionry points ssocited with the ground stte N 2 H + ction. The liner structure (1) is the potentil energy minimum, nd the ring structure (1b) is the trnsition stte ssocited with proton trnsfer between the two nitrogen toms. The B3LYP N-N bond lengths clculted for both structures in Figure 1 re bout 0.01 Å shorter thn the CCSD- (T) distnces, while the ZAPT2 distnces re bout 0.01 Å too long. The N-H bond length for the N 2 H + minimum grees to within Å t ll levels of theory, wheres the B3LYP N-H bond length in the trnsition-stte structure (1b) is Å longer thn tht determined t the CCSD(T) nd ZAPT2 levels of theory. The present clcultions gree quite well (within Å for ll bond lengths) with previously reported geometries t the CCSD(T)/ug-cc-pVXZ (x ) T, Q) nd MC-QCISD/6-31G- (d,p) levels of theory. 55,57 Tble 1 lists the reltive energies clculted t vrious levels of theory for the structures on the ground-stte PES of N 2 H +. At ll levels of theory, the dizenylium ion is clculted to be considerbly lower in energy thn the lowest two dissocition limits involving bstrction of the hydrogen moiety (either s proton or hydrogen tom). Excellent greement mong the methods is observed for the dissocition energy involving proton bstrction (within 2 kcl/mol reltive to coupled-cluster energies). However, the greement is worse for the hydrogen bstrction process, with the ZAPT2 dissocition energy being 11.4 kcl/mol lower thn the CCSD(T) vlue nd the B3LYP energy being 7.3 kcl/mol higher. The CCSD(T) dissocition energy for this process is 4.3 kcl/mol higher thn the CR-CC/ cc-pvqz energy. This notble difference in the dissocition energy ssocited with hydrogen tom bstrction is primrily due to differences in the Hrtree-Fock (HF) energies of the hydrogen tom using different bsis sets (4.2 kcl/mol) nd not due to indequcies of the bsis set in clculting correltion energy. A trend is observed (vide infr) in which the CCSD- (T)/TZ2P(f,d) energies gree quite well with the CR-CC/ccpVQZ energies (within 1.6 kcl/mol) except for dissocition limits involving hydrogen tom bstrction. However, the CCSD(T) clcultions consistently overestimte these limits by kcl/mol with respect to the CR-CC vlues, which is close to the difference in the HF energies of the hydrogen tom using the two bsis sets. Since the CCSD(T)/TZ2P(f,d) clcultions pper to dequtely describe the correltion energy of these polytomic ctions, the energies of the B3LYP nd ZAPT2 clcultions will be compred directly to the CCSD(T) energies. Such comprison should be more insightful nd consistent since ll three methods utilize the sme bsis set. The experimentl 64 energy difference between the two dissocition limits nlyzed in Tble 1 is 46.1 kcl/mol. From Tble 1, one cn see tht the coupled cluster energy differences re quite good (46.4 kcl/mol for CCSD(T) nd 43.7 kcl/mol for CR-CC), while ZAPT2 significntly underestimtes the difference (37.2 kcl/mol) nd B3LYP overestimtes the difference by similr mrgin (55.5 kcl/mol). Note tht the vibrtionl zero point energy (ZPE) correction ws not included in these clcultions nd would only hve smll effect on the differences (<0.3 kcl/mol). The CCSD(T) trnsition stte corresponding to hydrogen tom trnsfer from one nitrogen tom to the other in the dizenylium ion is predicted to be 49.9 kcl higher in energy thn the ssocited minim. The other methods predict similr vlue. Note tht the clcultions indicte tht the preferred pthwy for dissocition of N 2 H + is proton loss to N 2 nd H +. However, the ICP-MS experiments mesure the bundnce rtio N + 2 /N 2 H + nd use n estimte for the number density of hydrogen toms in the ICP. 65 Although pek cn be mesured for H + from the ICP, it is not esy to estimte the sensitivity of the MS t m/z 1, since there re no nerby metl ions to use s mss bis clibrnts.

5 2612 J. Phys. Chem. A, Vol. 112, No. 12, 2008 Sers et l. Figure 2. CCSD(T)/TZ2P(f,d) geometries of the formyl nd isoformyl ctions long with tht of the ssocited trnsition stte. Vlues in ( ) re ZAPT2 prmeters, nd those in [ ] re B3LYP prmeters. Experimentl vlues re in {}nd were obtined from refs 68, 73, nd 81. Bond lengths re in ngstroms. TABLE 2: Reltive Energies of Sttionry Points nd Dissocition Limits Associted with COH + (Energies Are in kcl/mol) 2 2b 2c CO + H + CO + + H B3LYP/TZ2P(f,d) ZAPT2/TZ2P(f,d) CCSD(T)/TZ2P(f,d) CR-CC(2,3)/cc-pVQZ Energy evluted t CCSD(T)/TZ2P(f,d)-optimized geometry. HCO +. The formyl ction (HCO + ) hs been chrcterized extensively using experimentl nd theoreticl 39,74-77 techniques. The isoformyl ction (COH + ) hs received less ttention, prticulrly in experimentl studies Figure 2 shows the optimized structures for both the formyl (2) nd isoformyl (2b) ctions, long with the trnsition stte corresponding to H-tom trnsfer between the two structures (2c). The C-O bond length in the formyl ction is predicted to be Å longer t the ZAPT2 level nd Å shorter t the B3LYP level thn tht clculted t the CCSD(T) level of theory (1.108 Å). The C-H bond length grees quite well mong the different clcultions (within Å). Similrly, the isoformyl ction O-H bond lengths gree quite well (within Å) mong the three methods. The C-O bond lengths determined t ech level of theory exhibit even better greement (within Å). The C-H nd O-H bond lengths clculted t the vrious levels gree to within 0.01 Å in lmost ll cses with the B3LYP C-H bond length being the only exception. Geometries determined t ech level of theory gree quite well with experimentlly determined geometries. The only exception is the O-H bond in the isoformyl ction, which is overestimted by t lest Å t ll levels of theory. This result is not unexpected bsed on previous studies of this system by Schefer et l. 39 The very low frequency bending vibrtion ssocited with this molecule is believed to be the reson for the discrepncies between theory nd experiment for this system. Tble 2 lists the reltive energies of the vrious sttionry points on the ground-stte PES of COH + long with the lowest two dissocition limits ssocited with bstrcting the hydrogen tom or the proton from the C-O frgment. Both the formyl nd isoformyl ctions re quite stble compred to either dissocition limit shown in Tble 2, with the formyl ction being more stble by 40.4 kcl/mol t the CCSD(T) level. The B3LYP nd CCSD(T) reltive energy differences between the two minim re in good greement, wheres ZAPT2 is off by 6.0 Figure 3. CCSD(T)/TZ2P(f,d) geometries of the iso-, cis-, nd trnsdizene ctions. Vlues in ( ) re ZAPT2 prmeters, nd those in [ ] re B3LYP prmeters. Bond lengths re in ngstroms. kcl/mol. Similrly, the B3LYP nd CCSD(T) isomeriztion brriers leding from the formyl ction gree to within 1 kcl/ mol, while the ZAPT2 vlue is too high by 4.1 kcl/mol. The predicted dissocition energy for proton bstrction grees quite well mong ll of the methods (within 2.5 kcl/mol), with the CCSD(T) dissocition energy clculted to be kcl/mol. The ZAPT2 nd CCSD(T) dissocition energies for hydrogen tom bstrction gree to within 1 kcl/mol, while B3LYP overestimtes this dissocition energy by bout 5 kcl/mol. The coupled cluster dissocition energies (10.5 nd 7.7 kcl/mol for CCSD(T) nd CR-CC, respectively) re in resonble greement with the experimentl 64 vlue of 9.2 kcl/mol. The ZAPT2 dissocition energy difference (10.1 kcl/mol) lso grees well with the experimentl vlue, while B3LYP is off by nerly fctor of 2 (17.6 kcl/mol). H 2 N 2 +. Figure 3 shows the structures nd geometricl prmeters of the three low-lying minim on the ground-stte PES for H 2 N 2 +. The N-H bond lengths for ll structures in Figure 3 re nerly identicl regrdless of the level of theory. The spred in the predicted N-N bond length in trns-dizene ction (3) is lrger, 0.02 Å, with CCSD(T) in the middle (1.169 Å), ZAPT2 too long, nd B3LYP too short. All levels of theory predict decrese in the N-N bond length (by Å) in the cis-dizene (3c) ction reltive to the trns structure. There is considerble elongtion of the N-N bond in the iso-dizene (3b) ction compred to both the trns nd cis structures. Few theoreticl clcultions hve been reported for these systems, with some discrepncies existing mong vrious interprettions of the PES. The present clcultions, in greement with erlier lower-level studies by Pople nd Curtiss, 82 indicte tht there re three locl minim on the groundstte PES. Recent RCCSD[T] clcultions by Pludoux nd Hochlf 83 suggest tht the cis structure is ctully sddle point nd tht two other nonplnr minim exist on the ground-stte surfce. Figure 4 shows the structures for two trnsition sttes tht correspond to isomeriztions between pirs of minim on the ground stte PES of H 2 N 2 +. The hydrogen-bridging structure (3d) corresponds to the trnsition stte between the trns- nd iso-dizene ctions. Neither ZAPT2 nor B3LYP is in consistently good greement with the CCSD(T) geometries. Much closer greement is seen for the second trnsition stte tht is ssocited with the isomeriztion between the cis- nd trnsdizene ions (3e).

6 Theoreticl Investigtion of Smll Polytomic Ions J. Phys. Chem. A, Vol. 112, No. 12, Figure 5. CCSD(T)/TZ2P(f,d) geometries of the formldehyde nd hydroxymethylene ctions long with the ssocited trnsition stte. Vlues in ( ) re ZAPT2 prmeters, nd those in [ ] re B3LYP prmeters. Bond lengths re in ngstroms. Figure 4. CCSD(T)/TZ2P(f,d) geometries of the trnsition sttes ssocited with trns-/iso-dizene ction isomeriztion nd trns-/cisdizene ction isomeriztion. Vlues in ( ) re ZAPT2 prmeters, nd those in [ ] re B3LYP prmeters. Bond lengths re in ngstroms. TABLE 3: Reltive Energies of Sttionry Points nd Dissocition Limits Associted with N 2 H 2+ (Energies Are in kcl/mol) 3 3b 3c 3d 3e N 2H + + H N 2H + H + B3LYP/TZ2P(f,d) ZAPT2/TZ2P(f,d) CCSD(T)/TZ2P(f,d) CR-CC(2,3)/ cc-pvqz Energy evluted t CCSD(T)/TZ2P(f,d)-optimized geometry. Tble 3 lists the reltive energies of ll previously described sttionry points on the ground-stte H 2 N 2 + PES. All three minim re reltively close in energy, nd ll levels of theory predict the trns-dizene ion to be the globl minimum. All methods re generlly in excellent greement with ech other, except ZAPT2 predicts reltive energy for the iso-dizene ion (3b) tht is much too high. This leds to n incorrect prediction tht the cis-dizene ion (3c) is more stble thn the iso-dizene ion, in disgreement with both coupled cluster nd B3LYP, s well s with erlier G2 clcultions by Pople nd Curtiss. 82 The 14.2 kcl/mol CCSD(T) brrier to isomeriztion between the cis nd trns isomers (3e) is in good greement with the B3LYP brrier, while ZAPT2 overestimtes the brrier by 3.0 kcl/mol. The CCSD(T) isomeriztion brrier connecting the iso nd trns isomers (3d) is much higher in energy, 54.0 kcl/mol, with similr vlues predicted by both B3LYP nd ZAPT2. The CCSD(T) dissocition limit corresponding to the removl of hydrogen tom from N 2 H 2 + is only 39.3 kcl/mol higher in energy thn the globl minimum (3). While ZAPT2 predicts similr result, B3LYP overestimtes the dissocition energy by 8.5 kcl/mol. Removl of proton from N 2 H 2 + requires much more energy (>100 kcl/mol) thn hydrogen tom bstrction. Experimentlly, 84 the difference between the two dissocition limits ws determined to be kcl/mol. The CCSD(T) clcultions predict the difference to be kcl/mol, underestimting the difference by 8 kcl/mol with the CR- CC clcultions being in slightly better greement (127.7 kcl/ TABLE 4: Reltive Energies of Sttionry Points nd Dissocition Limits Associted with H 2 CO + (Energies Are in kcl/mol) 4 4b 4c HCO + + H HCO + H + B3LYP/TZ2P(f,d) ZAPT2/TZ2P(f,d) CCSD(T)/TZ2P(f,d) CR-CC(2,3)/cc-pVQZ Energy evluted t CCSD(T)/TZ2P(f,d)-optimized geometry. mol) with experiment. The B3LYP clcultions underestimte the difference by 17.2 kcl/mol, more thn twice tht of the CCSD(T) clcultion. Interestingly, the ZAPT2 energy difference is much closer to the experimentl vlue thn the B3LYP nd coupled-cluster clcultions (132.4 kcl/mol). H 2 CO +. The formldehyde ction (4) nd hydroxymethylene ction (4b) hve been previously chrcterized through numerous experimentl nd theoreticl studies, prticulrly the formldehyde ction. Figure 5 shows the structures nd geometricl prmeters clculted for the two minim nd the ssocited trnsition stte (4c) on the ground stte H 2 CO + PES. In generl ZAPT2 underestimtes bond distnces reltive to CCSD(T), nd B3LYP overestimtes them, but ll three levels of theory re in resonble greement. In the trnsition stte, the ZAPT2 O-H nd C-H bond lengths tht re ssocited with the bridging hydrogen re considerbly different from those predicted by both CCSD(T) nd B3LYP, which gree quite closely with one nother. The ZAPT2 O-H bond length is nerly Å shorter, nd the C-H bond length is nerly 0.02 Å longer. Tble 4 lists the reltive energies of the vrious sttionry points on the H 2 CO + PES, including two relted dissocition limits. The most noticeble trend in this tble is the severe underestimtion of reltive energies t the ZAPT2 level of theory. While CCSD(T) nd B3LYP predict the formldehyde ction to be the globl minimum nd the hydroxymethylene ction to be bout 5 kcl/mol higher in energy, ZAPT2 predicts the hydroxymethylene ction to be bout 3 kcl/mol lower in energy. This inbility of perturbtion theory to correctly predict the reltive energies of these structures is well documented, despite the fct tht the geometries re in good greement with those obtined from higher-level clcultions. ZAPT2 lso underestimtes the reltive energies of the trnsition stte nd

7 2614 J. Phys. Chem. A, Vol. 112, No. 12, 2008 Sers et l. TABLE 5: Reltive Energies of Sttionry Points nd Dissocition Limits Associted with H 3 N 2+ (Energies Are in kcl/mol; B3LYP, ZAPT2, nd CCSD(T) Energies Clculted Using TZ2P(f,d) Bsis Set) B3LYP ZAPT2 CCSD(T) CR-CC(2,3)/ cc-pvqz H 3N (trns)h 2N 2+ + H (iso)h 2N 2+ + H (cis)h 2N 2+ + H (trns)h 2N 2 + H (cis)h 2N 2 + H (iso)h 2N 2 + H Energy evluted t CCSD(T)/TZ2P(f,d)-optimized geometry. Figure 6. CCSD(T)/TZ2P(f,d) geometries of the globl minimum on the H 3CO + nd H 3N 2+ PESs. Vlues in ( ) re ZAPT2 prmeters, nd those in [ ] re B3LYP prmeters. Bond lengths re in ngstroms. TABLE 6: Reltive Energies of Sttionry Points nd Dissocition Limits Associted with H 3 CO + (Energies Are in kcl/mol; B3LYP, ZAPT2, nd CCSD(T) Energies Clculted Using TZ2P(f,d) Bsis Set) B3LYP ZAPT2 CCSD(T) CR-CC(2,3)/cc-pVQZ H 3CO H 2CO + + H HCOH + + H H 2CO + H HCOH + H Energy evluted t CCSD(T)/TZ2P(f,d)-optimized geometry. both dissocition limits by kcl/mol. This is rther lrge error, considering the CCSD(T) reltive energy for the trnsition stte is only 45.9 kcl/mol nd tht for the lowest dissocition limit is 31.8 kcl/mol. B3LYP reltive energies re in reltively good greement with the CCSD(T) results, prticulrly for the bound structures. B3LYP overestimtes the dissocition energy for the lowest dissocition limit by lmost 8 kcl/mol compred to the CCSD(T) vlue but grees well with the CCSD(T) vlue for the higher dissocition limit. The energy difference between the dissocition limits t the coupled cluster levels (126.7 nd kcl/mol for CCSD(T) nd CR- CC, respectively) compre quite well to the experimentl vlue 84 of kcl/mol. The ZAPT2 clcultions overestimte this difference by lmost 4 kcl/mol, while the B3LYP clcultions underestimte the vlue by just over 8 kcl/mol. H 3 N 2 + nd H 3 CO +. The triplet methoxy ction hs been extensively studied due to its rectivity through nondibtic processes On the bsis of preliminry clcultions, this structure nd the isoelectronic triplet dinitrogen species were not considered in this work since these ions re considerbly higher in energy (>50 kcl/mol) thn the corresponding globl minim nd re probbly not importnt in the relevnt experiments (i.e., in n ICP t T 6000 K). Figure 6 depicts the geometries for the globl minimum structures for the H 3 N 2 + nd H 3 CO + singlet ctions, which re both plnr. Although these structures re considerbly more stble thn their triplet counterprts, few clcultions on these species hve been reported. 37,89-91 The ZAPT2 nd B3LYP geometricl prmeters for the H 3 N 2 singlet ction gree quite well with the CCSD(T) vlues. Most bond lengths gree to within Å, nd the ngles gree to within 1. Similr comments pply to the H 2 - COH + singlet ction; ll bond lengths gree to within Å of the CCSD(T) result, nd most bond ngles gree to within 1. Attempts to find nonplnr minim comprble in energy to the ground-stte minim (within 50 kcl/mol) for both ions were unsuccessful. Tble 5 lists the reltive energies of the dissocition limits ssocited with H 3 N 2 + t vrious levels of theory. The bstrction of hydrogen tom from H 3 N 2 + requires lrge mount of energy ( 100 kcl/mol), with the proton bstrction process requiring pproximtely twice s much energy. The B3LYP nd CCSD(T) reltive energies gree quite well (within 2 kcl/mol), while the ZAPT2 energies devite from the CCSD(T) vlues by 2-8 kcl/mol. Tble 6 lists the energies of the dissocition limits ssocited with the H 2 COH + ction t the sme levels of theory. Qulittively the energies re similr to those for the nitrogen-contining nlog: hydrogen bstrction requires lrge mount of energy (t lest 100 kcl/mol), nd the corresponding proton bstrction process requires considerbly more energy (>50 kcl/mol). Discussion Since the HCO + nd N 2 H + ctions re isoelectronic, one expects tht they will hve similr thermodynmic nd kinetic prmeters. Tbles 1 nd 2 show tht the thermodynmic stbilities of these species compred with their respective dissocition limits re both quite lrge (>120 kcl/mol). Despite the similrities in the thermodynmics ssocited with these two ions, ICP-MS experiments 65 hve shown tht the bundnce rtios N + 2 /CO + nd N 2 H + /HCO + re bout four nd ten, respectively. While thermodynmic rguments cn explin the bundnce of N 2 H + compred to N + 2, it provides no insight into the differences between the two isoelectronic species. The ioniztion energies of neutrl N 2 H nd HCO re in the rnge 7.8 to 8.2 ev 84 close enough tht differences in the extent of ioniztion re unlikely to be responsible for the different bundnces of N 2 H + nd HCO +. Exmintion of the mechnisms for dissocition of HCO + nd N 2 H + does give n indiction of why there re different bundnces of these ions. Simple MCSCF clcultions revel tht these ions dissocite smoothly into neutrl ditomic molecule nd proton when they re pulled prt. These dissocition limits re lso significntly lower in energy thn the corresponding hydrogen bstrction processes. Thus, the ssocition of the neutrl ditomic molecule nd proton within the experimentl pprtus could led to higher thn expected

8 Theoreticl Investigtion of Smll Polytomic Ions J. Phys. Chem. A, Vol. 112, No. 12, levels of the tritomic ctions. The higher bundnce of N 2 H + thn HCO + in the mss spectrum my thus be relted to different bundnces of the corresponding neutrl N 2 nd CO in the ICP. The thermodynmics of H 2 CO + nd N 2 H 2 + exhibit numerous similrities s expected. The minim on ech surfce re more thermodynmiclly stble thn the dissocition products but not nerly to the extent seen for the tritomic ctions described bove. The one significnt difference between these two systems is tht no minimum corresponding to cis-like species ws found for H 2 CO +. Ech PES exhibits multiple minim tht re reltively close in energy: H 2 CO + hs two minim within 6 kcl/mol of ech other, nd N 2 H 2 + hs three minim within 7 kcl/mol rnge. Despite these closely spced minim, the PESs re not shllow nd fetureless. Reltively lrge brriers (45-55 kcl/mol) corresponding to hydrogen trnsfer between hevy toms exist on both PESs. On the N 2 H 2 + surfce, considerbly smller brrier (14 kcl/mol) ws found leding to isomeriztion between the cis nd trns isomers. The dissocition pthwys for the formldehyde ction nd the iso-dizene ion were found to be similr in tht they both dissocite to form hydrogen tom nd the corresponding tritomic ction (HCO + or HN 2 + ). This is significntly different thn the mechnism found for the tritomic ctions themselves, which pper to form through protontion of neutrl ditomic molecule rther thn through rdicl rection involving hydrogen tom nd ditomic ction. Similrly, the dissocition of the trns-dizene ion leds to the hydrogen tom nd N 2 H +. Thus, the formtion of both the H 2 CO + nd N 2 H 2 + ctions ppers to be dependent on the concentrtion of hydrogen toms nd HCO + nd N 2 H + ctions. Though the singlet H 2 COH + nd H 3 N 2 + ctions pper to be globl minim, few clcultions hve been reported for these structures. The two structures re very similr in mny respects. They both hve plnr geometries nd re very stble with respect to the lowest dissocition limits (bout 100 kcl/mol). MCSCF clcultions show tht dissocition of the hydroxy hydrogen in H 2 COH + leds to the formtion of hydrogen tom nd the formldehyde ction. The similr process for H 3 N 2 + leds to formtion of hydrogen tom nd the iso-dizene ction. The bstrction of hydrogen from H 3 N 2 + to form trnslike species results in the removl of hydrogen tom to form the trns-dizene ction. These processes more closely resemble the dissocitions of the tetr-tomic ctions s opposed to the tritomic ctions. The biggest discrepncy between geometries using different methods ws observed for the trnsition sttes involving bridged hydrogen. The ZAPT2 hydrogen-hevy tom bond lengths involving the bridging hydrogen re often significntly different from the B3LYP nd CCSD(T) vlues. These differences re usully lrger thn 0.01 Å nd s high s 0.03 Å. The B3LYP distnces generlly gree to within 0.01 Å with the CCSD(T) vlues. The ZAPT2 reltive energies re often considerbly different from those determined t the CCSD(T) level of theory; in some cses (H 2 CO + nd H 2 N 2 + ) ZAPT2 predicts incorrect energy ordering for the minim. In most cses, the B3LYP energies gree very well with the CCSD(T) results nd predict the correct ordering of minim for ll structures. The effect of the bsis set hs miniml role in determining the energetics of the smll polytomic ctions considered. The TZ2P(f,d) bsis set ppers to be dequte in determining the correltion energy of the species considered. However, the indequcies of this bsis set in determining the HF energy of the hydrogen tom did show significnt, though predictble, differences in the energies ssocited with hydrogen tom bstrction processes. Anlysis of the T1 mplitudes from the CR-CC single-point clcultions indictes tht essentilly ll of the structures nlyzed hve very little multireference chrcter, including trnsition-stte structures. The one exception is the formldehyde ction, which does exhibit some multireference chrcter (lrgest T1 mplitude )-0.154). This fct could explin the difficulty perturbtion theory hs in determining the proper energy ordering of the formldehyde nd hydroxymethylene ctions. It ppers tht geometries re not very sensitive to the choice of method used. This is good news for the intended fundmentl studies of polytomic ions in ICP-MS s resonble estimte of the geometry is probbly sufficient to llow clcultion of the vibrtionl nd rottionl prtition functions. Also, lrger systems similr to the ones studied in this work could be ccurtely probed using reltively simple correlted methods to obtin geometries. However, one must be cutious of using perturbtive methods to obtin reltive energies, s the dissocition constnt is highly temperture sensitive. Conclusions Two series of smll polytomic ions, H x CO + nd H x N + 2 (x ) 1, 2, 3), were systemticlly chrcterized using CCSD(T), ZAPT2, nd B3LYP. Despite lrge difference in the bundnces of HCO + nd HN + 2 in recent ICP-MS experiments, these isoelectronic ions re found to hve similr dissocition energies nd pthwys bsed on theoreticl clcultions. Ech pthwy corresponds to deprotontion of the ion to form neutrl ditomic molecule. This observtion could explin the concentrtion differences since the experiments were performed under tmospheric conditions. Also, protontion of the ditomic molecules leds to much more thermodynmiclly stble species (>120 kcl/mol). For the tetr-tomic species, H 2 CO + nd H 2 N + 2, both the thermodynmics nd kinetics differ significntly from the tritomic ions. The dissocition pthwy ssocited with these species corresponds to hydrogen tom bstrction leding to the previously mentioned tritomic ction. Though formtion of the tetr-tomic ctions leds to more thermodynmiclly stble structures, the difference in energy between these structures nd their dissocition limits (<40 kcl/ mol) is much smller thn for the tritomic/ditomic systems. One significnt difference observed between these two isoelectronic species is the bsence of cis-like sttionry point on the H 2 CO + PES. The H 3 CO + nd H 3 N + 2 ctions re very similr in tht they both re roughly 100 kcl/mol more stble thn their dissocition products. The dissocition products for these structures re hydrogen tom nd the corresponding tetr-tomic ction. For ech series, the formtion of the lrger polytomic ction is energeticlly fvored by considerble mount, though this vlue differs significntly depending on the ion formed. Thus, it is not surprising tht such ions re detected in experiments in which even complete tomiztion source, such s n ICP, is used. The primry difference within ech series is tht the formtion of the tritomic ion is through protontion process rther thn through ddition of hydrogen tom, which my be why HCO + nd HN + 2 re present t very different bundnces in ICP-MS experiments. An nlysis of the relibility of the three methods used for predicting geometries nd reltive energies suggests tht B3LYP nd ZAPT2 geometries typiclly gree well with those determined t the CCSD(T) level of theory. The ZAPT2 clcultions hve more difficulty predicting the geometries of trnsition sttes tht involve bridging hydrogen. Reltive energies determined t the ZAPT2 level re in mny cses in reltively poor

9 2616 J. Phys. Chem. A, Vol. 112, No. 12, 2008 Sers et l. greement with CCSD(T) vlues, while B3LYP energies re typiclly in good greement. On the bsis of T1 mplitudes generted t the CR-CC(2,3)/cc-pVQZ level nd the very smll differences between the CR-CC nd CCSD(T) energies, there is very little multireference chrcter in the ctions considered. Therefore, using simple correlted methods to predict geometries for such systems ppers to be resonble pproch, though energy clcultions re very sensitive to the method used nd must be nlyzed crefully. Acknowledgment. This work ws supported by Ntionl Science Foundtion, Anlyticl nd Surfce Chemistry Progrm, Grnt No K.S. ws supported in prt by Ntionl Science Foundtion REU grnt nd in prt by funds generously provided by the ISU chemistry deprtment. Supporting Informtion Avilble: B3LYP, ZAPT2, nd CCSD(T) vibrtionl frequencies for ll sttionry points reported in this work re included. This mteril is vilble free of chrge vi the Internet t References nd Notes (1) Buhl, D.; Snyder, L. E. Nture 1970, 228, (2) Cselli, P.; Myers, P. C.; Thddeus, P. Astrophys. J. 1995, 455, L77. (3) Ziurys, L. M.; Apponi, A. J. Astrophys. J. 1995, 445, L73. (4) Wrntz, J. In Combustion Chemistry; Grdiner, W. C., Jr., Ed.; Springer-Verlg: Berlin, 1984; (5) Houk, R. S.; Fssel, V. A.; Flesch, G. D.; Svec, H. J.; Gry, A. L.; Tylor, C. E. Anl. Chem. 1980, 52, (6) Niu, H.; Houk, R. S. Spectrochim. Act, Prt B 1996, 51, (7) Houk, R. S.; Prphirksit, N. Spectrochim. Act, Prt B 2001, 56, (8) Tylor, V. F.; Mrch, R. E.; Longerich, H. P.; Stdey, C. J. Int. J. Mss Spectrom. 2005, 243, (9) Nonose, N. S.; Mtsud, N.; Fudgw, N.; Kubot, M. Spectrochim. Act, Prt B 1994, 49, (10) Tnner, S. D. J. Anl. At. Spectrom. 1995, 10, (11) Tnner, S. D.; Brnov, V. I.; Bndur, D. R. Spectrochim. Act, Prt B 2002, 57, (12) Nonose, N.; Kubot, M. J. Anl. At. Spectrom. 2001, 16, (13) Nonose, N.; Kubot, M. J. Anl. At. Spectrom. 2001, 16, (14) Nonose, N. J. Mss Spectrom. Soc. Jpn. 1997, 45, (15) Tnner, S. D. J. Anl. At. Spectrom. 1993, 8, (16) Becker, J. S.; Dietze, H.-J. J. Anl. Chem. 1997, 359, (17) Evns, E. H.; Ebdon, L.; Rowley, L. Spectrochim. Act Prt B 2002, 57, (18) Frser, M. M.; Beuchemin, D. Spectrochim. Act Prt B 2001, 56, (19) Hollidy, A. E.; Beuchemin, D. J. Anl. At. Spectrom. 2003, 18, (20) Guenther, D.; Longerich, H. P.; Jckson, S. E.; Forsythe, L. J. Anl. Chem. 1996, 355, (21) Zhrn, N. F.; Hell, A. I.; Amr, M. A.; Abdel-Hfiez, A.; Mohsen, H. T. Int. J. Mss Spectrom. 2005, 226, (22) Reed, N. M.; Cirns, R. O.; Hutton, R. C.; Tkku, Y. J. Anl. At. Spectrom. 1994, 9, (23) Houk, R. S. Spectrochim. Act, Prt B 2006, 61, (24) Dlgrno, A.; Blck, J. H. Rep. Prog. Phys. 1976, 39, (25) Smith, D.; Adms, N. G. Astrophys. J. 1977, 217, 741. (26) Huntress, W. T. Astrophys. J. Suppl. Ser. 1977, 33, 495. (27) Bohme, D. K.; Goodings, J. M.; Ng, C.-W. Int. J. Mss Spectrom. 1977, 24, 335. (28) Liu, J.; Vn Devener, B.; Anderson, S. L. J. Chem. Phys. 2003, 119, (29) Liu, J.; Anderson, S. L. J. Chem. Phys. 2004, 120, (30) M, N. L.; Smith, B. J.; Collins, M. A.; Pople, J. A.; Rdom, L. J. Phys. Chem. 1989, 93, (31) Tkeshit, K. J. Chem. Phys. 1991, 94, (32) Cesr, A.; Ågren, H.; Helgker, T.; Jørgensen, P.; Jensen, H. J. A. J. Chem. Phys. 1991, 95, (33) M, N. L.; Rdom, L.; Collins, M. A. J. Chem. Phys. 1992, 96, (34) M, N. L.; Smith, B. J.; Rdom, L. Chem. Phys. Lett. 1992, 193, (35) Nguyen, M. T.; Creve, S.; Vnquickenborne, L. G. J. Phys. Chem. 1996, 100, (36) Frncisco, J. S.; Thomn, J. W. Chem. Phys. Lett. 1999, 300, (37) Frncis, G. J.; Wilson, P. F.; Mclgn, R. G. A. R.; Freemn, C. G.; Meot-Ner, M.; McEwn, M. J. J. Phys. Chem. A 2004, 108, (38) Levndier, D. J.; Chiu, Y.-H.; Dressler, R. A.; Sun, L.; Schtz, G. C. J. Phys. Chem. A 2004, 108, (39) Ymguchi, Y.; Richrds, C. A.; Schefer, H. F. J. Chem. Phys. 1994, 101, (40) Sheng, Y.; Leszczynski, J. J. Chem. Phys. A 2002, 106, (41) Becke, A. J. Chem. Phys. 1993, 98, (42) Lee, C. T.; Yng, W. T.; Prr, R. G. Phys. ReV. B: Condens. Mtter 1988, 37, (43) Lee, T. J.; Jytilk, D. Chem. Phys. Lett. 1993, 201, (44) Lee, T. J.; Rendell, A. P.; Dyll, K. G.; Jytilk, D. J. Chem. Phys. 1994, 100, (45) Fletcher, G. D.; Gordon, M. S.; Bell, R. L. Theor. Chem. Acc. 2002, 107, (46) Aikens, C. M.; Fletcher, G. D.; Schmidt, M. W.; Gordon, M. S. J. Chem. Phys. 2006, 124, (47) Pople, J. A.; Hed-Gordon, M.; Rghvchri, K. J. Chem. Phys. 1987, 87, (48) Dunning, T. H. J. Chem. Phys. 1971, 55, (49) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80, (50) Gonzles, G.; Schlegel, H. B. J. Chem. Phys. 1989, 90, (51) Piecuch, P.; Kuchrski, S. A.; Kowlski, K.; Musil, M. Comput. Phys. Commun. 2002, 149, (52) Piecuch, P.; Wloch, M. J. Chem. Phys. 2005, 123, (53) Schmidt, M. W.; Bldridge, K. K.; Botz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. H.; Koseki, S.; Mtsung, N.; Nguyen, K. A.; Su, S. J.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, (54) ACES II is progrm product of the Quntum Theory Project, University of Florid. Authors: Stnton, J. F.; Guss, J.; Perer, S. A.; Yu, A. D.; Wtts, J. D.; Nooijen, M.; Oliphnt, N.; Szly, P. G.; Luderdle, W. J.; Gwltney, S. R.; Beck, S.; Blkov, A.; Bernholdt, D. E.; Beck, K.-K.; Rozyczko, P.; Sekino, H.; Huber, C.; Pittner, J.; Brtlett, R. J. Integrl pckges included re VMOL (J. Almlof nd P. R. Tylor), VPROPS (P. Tylor), nd ABACUS (T. Helgker, H. J. A. Jensen, P. Jørgensen, J. Olsen, nd P. R. Tylor). (55) Grunenberg, J.; Streubel, R.; Frntzius, G.; Mrten, W. J. Chem. Phys. 2003, 119, (56) Bickelhupt, F. M.; DeKock, R. L.; Berends, E. J. J. Am. Chem. Soc. 2002, 124, (57) Seo, Y.; Kim, Y.; Kim, Y. Chem. Phys. Lett. 2001, 340, (58) Nizkorodov, S. A.; Meuwly, M.; Mier, J. P.; Dopfer, O.; Bleske, E. J. J. Chem. Phys. 1998, 108, (59) Hirok, K.; Ktsurgw, J.; Minmitsu, A.; Igncio, E. W.; Ymbe, S. J. Phys. Chem. A 1998, 102, (60) Gudemn, C. S.; Begemnn, M. H.; Pfff, J.; Syklly, R. J. J. Chem. Phys. 1983, 78, (61) Owrutsky, C.; Gudemn, C. S.; Mrtner, C. C.; Tck, L. M.; Rosenbum, N. H.; Syklly, R. J. J. Chem. Phys. 1986, 84, (62) Kbbdj, Y.; Huet, T. T.; Rehfuss, B. D.; Gbrys, C. M.; Ok, I. J. Mol. Spectrosc. 1994, 163, (63) Gudemn, C. S.; Syklly, R. J. Ann. ReV. Phys. Chem. 1984, 35, (64) Herzberg, G.; Huber, K.-P. Constnts of Ditomic Molecules; Vn Nostrnd Reinhold: New York, (65) Ferguson, J. W.; Dudley, T. J.; Sers, K. C.; Gordon, M. S.; Houk, R. S. submitted to Spectrochim. Act, Prt B. (66) Woods, R. C.; Dixon, T. A.; Syklly, R. J.; Sznto, P. G. Phys. ReV. Lett. 1975, 35, (67) Woods, R. C.; Syklly, R. J.; Anderson, T. G.; Dixon, T. A.; Sznto, P. G. J. Chem. Phys. 1981, 75, (68) Bogey, M.; Demuynck, C.; Destombes, J. L. Mol. Phys. 1981, 43, (69) Sstry, K. V. L. N.; Herbst, E.; De Luci, F. C. J. Chem. Phys. 1981, 75, (70) Vn den Heuvel, F. C.; Dymnus, A. Chem. Phys. Lett. 1982, 92, (71) Gudemn, C. S.; Begemnn, M. H.; Pfff, J.; Syklly, R. J. Phys. ReV. Lett. 1983, 50, (72) Whlgren, U.; Liu, B.; Person, P. K.; Schefer, H. F. Nture 1973, 246, 4. (73) Woods, R. C. Philos. Trns. R. Soc. A 1988, 324, 141.

10 Theoreticl Investigtion of Smll Polytomic Ions J. Phys. Chem. A, Vol. 112, No. 12, (74) Woods, R. C. In Ion nd Cluster Ion Spectroscopy nd Structure; Mier, J. P., Ed.; Elsevier: Amsterdm, (75) Boum, W. J.; Burgers, P. C.; Holmes, J. L.; Rdom, L. J. Am. Chem. Soc. 1986, 108, (76) Øiestd, Å. M. L.; Uggerud, E. Int. J. Mss Spectrom. Ion Process 2000, 201, (77) vn Mourik, T.; Dunning, T. H.; Peterson, K. A. J. Phys. Chem. A 2000, 104, (78) Gudemn, C. S.; Woods, R. C. Phys. ReV. Lett. 1979, 48, (79) Woods, R. C.; Gudemn, C. S.; Dickmn, R. L.; Goldsmith, P. F.; Huguenin, G. R.; Irvine, W. M.; Hjlmrson, Å.; Nymn, L.-Å.; Olofsson, H. Astrophys. J. 1983, 270, 583. (80) Blke, G. A.; Helminger, P.; Herbst, E.; De Luci, F. C. Astrophys. J. 1983, 264, L69. (81) Berry, R. J.; Hrmony, M. D. J. Mol. Spectrosc. 1988, 128, (82) Pople, J. A.; Curtiss, L. A. J. Chem. Phys. 1991, 95, (83) Pludoux, J.; Hochlf, M. J. Chem. Phys. 2004, 121, (84) Vlues obtined from NIST Chemistry WebBook t (85) Ruscic, B.; Berkowitz, J. J. Chem. Phys. 1991, 95, (86) Yrkony, D. A. J. Am. Chem. Soc. 1992, 114, (87) Aschi, M.; Hrvey, J. N.; Schlley, C. A.; Schröder, D.; Schwrz, H. Chem. Commun. 1998, (88) Hrvey, J. N.; Aschi, M. Phys. Chem. Chem. Phys. 1999, 1, (89) Boum, W. J.; Nobes, R. H.; Rdom, L. Org. Mss Spectrom. 1982, 17, 315. (90) Curtiss, L. A.; Kock, D.; Pople, J. A. J. Chem. Phys. 1991, 95, (91) Øiestd, Å. M. L.; Uggerud, E. Int. J. Mss Spectrom. Ion Process 1997, 167/168,