The Molecular Structure and Ionization Potential of Si 2 : The Role of the Excited States in the Photoionization of Si 2

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1 36 J. Phys. Chem. A 000, 104, The Moleculr Structure nd Ioniztion Potentil of Si : The Role of the Excited Sttes in the Photoioniztion of Si Dvid A. Dixon* nd Dvid Feller EnVironmentl Moleculr Sciences Lbortory, Pcific Northwest Ntionl Lbortory, P.O. Box 999, Richlnd, Wshington 9935 Kirk A. Peterson Deprtment of Chemistry, Wshington Stte UniVersity, Richlnd, Wshington 9935 nd EnVironmentl Moleculr Sciences Lbortory, Pcific Northwest Ntionl Lbortory, P.O. Box 999, Richlnd, Wshington 9935 Jmes L. Gole School of Physics, Georgi Institute of Technology, Atlnt, Georgi 3033 ReceiVed: June, 1999; In Finl Form: December 1, 1999 The ioniztion potentils (IP) of Si ( g- ) to form the X 4 Σ g- nd Π u sttes of Si + hve been clculted t very high levels of b initio moleculr orbitl theory (CCSD(T) with ugmented correltion-consistent bsis sets extrpolted to the complete bsis set limit). The clculted vlue of the IP to form the X 4 Σ g - ground stte of the ion is ev s compred to n experimentl vlue of ev. The Π u stte is predicted to lie 0.5 ev bove the X 4 Σ g- ground stte of Si +. The 1 3 u, 3 u, u-, nd u- excited sttes of Si, s well s the X 4 Σ g-, Π u, nd Π u sttes of Si +, hve been clculted t the multireference configurtion interction level. The greement of the clculted positions of the sttes with the known experimentl vlues is quite good (better thn 0.1 ev). The clculted wve functions for the excited sttes of Si show significnt multireference chrcter. This is especilly true for the H stte which hs been used s n intermedite stte in photoioniztion experiments. The multireference chrcter of the H stte redily llows the connection of this stte to the ground X 4 Σ g- electronic stte of Si + vi one electron photoioniztion process. Introduction The study of the structures nd properties of smll silicon clusters hs been very ctive re of reserch becuse of silicon s importnce in both fundmentl nd pplied science The discovery of emissive nnometer-scle silicon clusters hs further heightened this interest. 3 Fundmentl to the buildup of nnometer-size silicon clusters is n understnding of the underlying silicon-silicon interctions existing in the cluster which, to first order, re strongly influenced by the nture of the two-body Si-Si interction (i.e., the silicon dimer bond). The ioniztion potentil (IP) of the silicon dimer provides n importnt link in the understnding of the moleculr electronic structure of the dimer, its chemicl rectivity, nd vrious dissocition processes. The IP lso serves s sensitive probe of the ccurcy of theoreticl clcultions which extend from the evlution of smll silicon clusters to surfce modeling. 1,13 Here we pproch this description with chemiclly ccurte clcultions on the silicon dimer nd its ion. Si hs two low-lying sttes. The - g ground stte, corresponding to n orbitl occupncy of...4σ g 4σ u 5σ g π u, lies bout 330 cm -1 below the first excited stte, of 3 Π u symmetry nd...4σ g 4σ u 5σ g1 π u3 occupncy. Both sttes hve been the focus of high level clcultions 1,6 nd experimentl mesurements. 1 Given the closeness of the two neutrl sttes, the ground stte of the Si + ction could result from the removl of either π or σ electron, resulting in Π u stte (...4σ g 4σ u 5σ g π u 1 ) or 4 Σ g - stte (...4σ g 4σ u 5σ g 1 π u ), respectively. It hs been previously shown 6 t the G level 14 tht the ground stte of the ion is the 4 Σ g - stte, with the Π u stte lying 9.6 kcl/mol (0.4 ev) higher in energy. There hve been severl experimentl determintions of the IP of Si. Trevor et l. 10 determined lower bound of 7.87 ev, while Fuke et l. determined the ioniztion energy to be higher thn 8.49 ev. More recently, Boo nd Armentrout 9 reported vlue tht ws e8.04 ev, bsed on their mesurement of the enthlpy of formtion of Si + nd the JANAF enthlpy of formtion of Si. Winsted et l. 15 used mss-selected resonnt two-photon ioniztion spectroscopy through the u - stte to brcket the IP between 7.9 nd 8.08 ev, in good greement with the results of Trevor et l. nd Boo nd Armentrout. Most recently, Mrijnissen nd ter Meulen 16 hve used mss-selected photoioniztion spectroscopy through the intermedite N 3 Σ u - (...4σ g 4σ u 5σ g 1 π u 5σ u 1 in single-determinnt formlism) excited stte of Si to determine the dibtic ioniztion energy of 8 Si s ev. In the course of tht study, the uthors rised questions bout the vlidity of the selected route for the two-photon ioniztion studies of Winsted et l., who ccessed the intermedite u - (...4σ g 4σ u 5σ g π u 1 π g 1 in singledeterminnt formlism) excited stte of Si in their brcketing experiment. We hve been developing computtionl chemistry methods to predict the energetics of rnge of first- nd second-row /jp99078b CCC: $ Americn Chemicl Society Published on Web 0/05/000

2 Moleculr Structure nd Ioniztion Potentil of Si J. Phys. Chem. A, Vol. 104, No. 11, molecules to chemicl ccurcy. Our pproch does not rely on empiricl corrections. 17 We hve recently been clculting the thermodynmic properties of severl silicon-contining molecules. 17i Here, we report clcultions on the spectroscopic properties nd dissocition energies for the ground stte nd for severl low-lying excited sttes of the Si molecule relevnt to the photoioniztion process. We lso clculte the energies of the three lowest lying sttes of Si +. This study provides further confirmtion of the ioniztion potentil, the energetics of severl excited sttes of Si nd the reltive energetics of the three lowest sttes of the ion, nd the optiml bond lengths of the considered sttes. In the present study, we lso evlute the conclusions of Mrijnissen nd ter Meulen 16 in light of the result tht mny of the low-lying sttes of Si re not well described by single configurtion. Approch Clcultions on the ground stte of Si nd on the two lowest lying sttes of Si + were crried out t the coupled cluster level of theory with single nd double excittions nd perturbtive correction for the triple excittions [CCSD(T)]. 18 The initil energetics were clculted within the frozen core (FC) pproximtion in which the 10 inner shell electrons (1s s p 6 ) on ech silicon tom were excluded from the correltion tretment. When combined with lrge bsis sets, the CCSD- (T)(FC) level of theory is cpble of recovering significnt frction of the vlence correltion energy. There re currently three widely used CCSD(T) pproches for hndling open shell systems. 19 The clcultions on the ions were done with ROHF orbitls, but with the spin constrint relxed in the coupled cluster portion of the clcultion. Energies obtined from this hybrid procedure re denoted R/UCCSD(T). The clcultions for the neutrl were done with unrestricted Hrtree-Fock (UHF) orbitls, denoted s UCCSD(T). For Si the UCCSD(T) nd R/UCCSD(T) methods produce energies tht gree to within E h. Spectroscopic constnts were obtined vi the usul Dunhm 0 nlysis using coefficients from polynomil fits in r ) r - r e for 6 to 7 points of ech potentil energy curve. The orbitls for the multireference configurtion interction (MRCI) clcultions were obtined s nturl orbitls from complete ctive spce self-consistent field (CASSCF) clcultions with full vlence ctive spce, i.e., ll moleculr orbitls rising from the vlence tomic orbitls were included in the ctive spce. The core orbitls were optimized, but constrined to be doubly occupied. In ll cses for the neutrl, stte verge of five sttes ws crried out corresponding to the 3 Σ g- ground stte, the two lowest lying 3 u sttes, nd the two lowest lying 3 Σ - u sttes. The former were found to be reltively low-lying sttes in preliminry CCSD(T) clcultions, nd the ltter were necessry for treting the H-stte of the neutrl. This common set of orbitls ws then used in internlly contrcted 1 MRCI (icmrci) clcultions with reference function identicl to the CASSCF ctive spce (9 configurtion stte functions). Only the vlence electrons were correlted. In the icmrci clcultions, lthough the ground stte ws clculted seprtely, the four excited sttes were clculted simultneously s the first four roots in A u symmetry (D h symmetry ws used throughout). A similr tretment ws lso used for the positive ion. The orbitls were obtined in stte-verged CASSCF (X 4 Σ - g, 1 Π u, nd Π u ), nd the MRCI clcultions consisted of seprte clcultion for the ground stte nd two-stte icmrci for the Π u sttes. The MRCI results were lso corrected for higher order excittions through the use of the multireference Dvidson +Q correction. Spectroscopic constnts were TABLE 1: UCCSD(T)(FC) Results for Si ( g- ) bsis D e (kcl/mol) R e (Å) ω e ω ex e E (E h) cc-pvdz cc-pvtz cc-pvqz cc-pv5z ug-cc-pvdz ug-cc-pvtz ug-cc-pvqz ug-cc-pv5z ug-cc-pv6z CBS(TQ5/exp) CBS(TQ5/mix) CBS(Q56/exp) CBS(Q56/mix) expt Reference 9. obtined vi the usul Dunhm nlysis using coefficients from polynomil fits in r ) r - r e for 6 to 7 points of ech potentil energy curve. All clcultions were performed with the correltion consistent (cc-pvnz or ug-cc-pvnz) bsis sets. 3 The geometries for the ions were optimized in pointwise fshion with the norml cc-pvnz bsis sets for n ) D, T, Q, nd 5. Energies were lso clculted with the diffuse function ugmented sets, denoted ug-cc-pvnz, t the cc-pvnz geometry for the sme n. For the neutrl nd in ll MRCI clcultions, the geometries were lso optimized with the ug-cc-pvnz bsis sets. These sequences of bsis sets hve been extensively demonstrted to provide relible thermochemicl nd structurl properties, with rre exceptions. 17 Only the sphericl components (i.e., 5-d, 7-f, 9-g, etc.) of the Crtesin bsis functions were used. All clcultions were performed with the MOLPRO-96/97 4 nd Gussin 94 5 progrms on Silicon Grphics PowerChllenge compute servers. To estimte energies t the complete bsis set (CBS) limit, we used mixed exponentil/gussin function of the form E(n) ) A CBS + B*exp[-(n - 1)] + C*exp[-(n - 1) ] (1) where n ) (DZ), 3 (TZ), etc., first proposed by Peterson et l. 6 We denote this s CBS(TQ5/mix). As crude hndle on the likely error ssocited with the CBS extrpoltion, we use the spred in the CBS estimtes obtined from the mixed expression nd simple exponentil: 7 E(n) ) A CBS + B*exp(-Cn) () In the study of Feller nd Peterson, 17 the mixed expression produced the smllest men bsolute devition with respect to experiment by smll mesure s compred to other extrpoltion methods such s the simple exponentil. Hving estimted energies t the CCSD(T)(FC)/CBS level of theory, we then include number of dditionl corrections to ccount for core-vlence, spin-orbit effects, nd moleculr sclr reltivistic effects. Zero point vibrtionl energies re lso evluted. The frequencies for the ion were clculted with the cc-pvqz bsis set. Core-vlence corrections to the dissocition energy were obtined from fully correlted CCSD(T) clcultions with the cc-pcvtz bsis set 36 t the CCSD(T)/cc-pVTZ geometry. Experience hs shown tht the cc-pcvtz bsis set recovers 75% or more of the effect seen with the lrger ccpcvqz bsis. A finl correction to ccount for sclr reltivistic effects is lso pplied. We evlute the sclr reltivistic correction using configurtion interction wve functions with

3 38 J. Phys. Chem. A, Vol. 104, No. 11, 000 Dixon et l. TABLE : Detils of the Clcultion of D e nd the Ioniztion Potentils of Si molecule CBS D e 1/ ω e (VQZ) E e CV E f SR E g SO ΣD 0 IP (ev) expt Si ( g- ) b ( h Si + (X 4 Σ g- ) c d (7.918) j ev i Si + ( Π u) c d (8.444) j Results re given in kcl/mol except for the ioniztion potentils which re given in ev. The totl theoreticl vlue is defined s: E[CCSD(T)(FC)/ CBS] - 1/ω e + CV + sclr reltivistic + tomic/moleculr SO. b Clculted with the UCCSD(T) method. c Clculted with the R/UCCSD(T) method. d The negtive vlue corresponds to the fct tht Si + is unbound reltive to two ground stte Si toms. e Core-vlence corrections were obtined with the cc-pwcvtz bsis set t the optimized CCSD(T)/ug-cc-pVTZ geometries. A positive sign indictes tht CV effects increse the stbility of the molecule reltive to the tomic symptotes. f The sclr reltivistic correction is bsed on CISD(FC)/cc-pVTZ clcultions of the 1-electron Drwin nd mss-velocity terms evluted t the CCSD(T)(FC)/ug-cc-pVTZ geometry. g Correction due to the incorrect tretment of the tomic symptotes s n verge of spin multiplets. h Reference 9. i Reference 16. j First vlue is CBS(TQ5/mix) nd the vlue in prentheses is CBS(TQ5/exp). TABLE 3: Si Results from MRCI Clcultions on the Ground Stte nd Selected Excited Sttes r e (Å) ω e ω ex e E (E h) E (ev) E ug-cc-pvtz X 3 - Σ g Q u Q u Q u Q u Q ug-cc-pvqz - g Q u Q u Q u Q K 3 - Σ u Q ug-cc-pv5z - g Q u Q u Q H 3 - Σ u Q u Q expt b - g H 3 - Σ u u Rows lbeled with +Q include the multireference Dvidson correction. b Reference 9. single nd double excittions (CISD/cc-pVTZ). 8 Specificlly, the sclr reltivistic energy lowering is defined to be the sum of the expecttion vlues of the 1-electron Drwin nd mssvelocity terms in the Breit-Puli Hmiltonin. Tests show this pproch to be cpble of reproducing sclr reltivistic corrections obtined from more ccurte methods to within bout 0.1 kcl/mol. Results The UCCSD(T) results for the ground stte of Si re given in Tbles 1 nd. The multireference CI results for Si ( - g, 1 3 u, 3 u, u-, nd u- ) re given in Tble 3. The R/UCCSD(T) results for the two lowest sttes of the ion Si + re given in Tbles nd 4, while the MRCI results for Si + re shown in Tble 5. The clculted bond length for ground-stte Si using the ugcc-pvqz nd higher bsis sets re within 0.01 Å of the experimentl vlue. 9 The remining error is due primrily to core-vlence correltion effects. 37 The frequencies clculted t the highest levels for the ground stte re within 4 cm -1 of the experimentl vlues. 9 To clculte D e for the ground stte, we hve included correction for core-vlence interctions of

4 Moleculr Structure nd Ioniztion Potentil of Si J. Phys. Chem. A, Vol. 104, No. 11, TABLE 4: R/UCCSD(T) Results for the X 4 Σ g- nd Π u Sttes of Si + r e (Å) ω e ω ex e E min (E h) E min (E h) ugmented X 4 Σ - g cc-pvdz cc-pvtz cc-pvqz cc-pv5z CBS(TQ5/exp) CBS(TQ5/mix) Π u cc-pvdz cc-pvtz cc-pvqz cc-pv5z CBS(TQ5/exp) CBS(TQ5/mix) TABLE 5: Si + Results from MRCI Clcultions on the Ground Stte nd Selected Excited Sttes ug-cc-pv5z r e (Å) ω e ω ex e E (E h) E (ev) b X 4 Σ - g Q Π u Q Π u Q Rows lbeled with +Q include the multireference Dvidson correction. b Reltive to the MRCI/ug-cc-pV5Z results for the ground stte of the neutrl. Zero-point vibrtionl energy corrections re not included. 0.5 kcl/mol, sclr reltivistic correction of -0.1 kcl/mol, nd n tomic spin-orbit correction of -0.9 kcl/mol. The clculted vlues for D 0 re likely to be more ccurte thn the vilble experimentl ones. The CBS(TQ5) nd CBS(Q56) vlues in Tble 1 show tht the bsis set extrpoltion is stble with respect to further increses in the 1-prticle bsis set. Spectroscopic mesurements yield D 0 ) 70 ( 4 kcl/mol, with n upper limit of D 0 ) 74.0 kcl/mol. 30 Knudsen cell/third lw mesurements on the Si-Si equilibrium yield D 0 vlues of 73.3, 74.3, nd 70.4 kcl/mol (verge ) 7.7 kcl/mol). 31 The CCSD(T)/CBS vlue of D 0 (Si ) ) 74.4 ( 0.4 kcl/mol clculted in this study is t the high end of these vlues 30-3 but in good greement with the 74.0 kcl/mol, which is bsed on severl experimentl mesurements, recommended by Huber nd Herzberg. 8 The contribution of the electronic energy to the dibtic ioniztion potentil for the ground stte of Si ( 3 Σ - g ) is clculted to be ev (18.48 kcl/mol) t the CBS(TQ5/ mix) level. A similr clcultion t the CBS(TQ5/exp) level yields ev. Thus, there is difference of only ev between the two extrpoltion methods. To clculte vrious correction fctors to obtin the electronic energy of the ion, we hve determined the tomiztion energy of Si + by the following process (note tht it gives negtive D e ): e - + Si + f Si( 3 P) (3) With core-vlence correction of ev (0.3 kcl/mol), sclr reltivistic correction of ev (-0. kcl/mol), nd negligible neutrl-ion zero point energy difference, we obtin predicted IP of 7.9 ( 0.0 ev for Si ( g- ) to form Si + (X 4 Σ g - ). This vlue is in excellent greement with the experimentl vlue of 7.906(9) ev. 16 The G vlue 6 of 7.94 ev for the X 4 Σ g - stte is in very good greement with our clculted vlue t the CBS limit. In similr fshion, the electronic energy contribution to the dibtic ioniztion potentil for the Π u stte is clculted to be ev, with the two extrpoltion procedures differing by only ev. For the Π u stte, the core-vlence correction is ev (0.4 kcl/mol), the sclr reltivistic correction is ev (-0.3 kcl/mol), nd the zero point correction is ev (0.13 kcl/mol). The predicted dibtic IP for Si ( - g ) to form Si + ( Π u ) is 8.44 ( 0.0 ev. Thus, the Π u stte of the ction is predicted to lie 0.5 ev bove the X 4 Σ - g stte. Becuse the clculted bond distnce for the ground stte of Si,.55 Å, is very similr to the vlue predicted for the ground stte of Si + (X 4 Σ - g ),.67 Å, the verticl nd dibtic ioniztion potentils will be very similr. However, the clculted bond distnce for the Si + Π u stte is significntly longer t.451 Å. Thus, verticl ioniztion to the Π u stte is expected to require n dditionl 0.8 ev energy increment. We note tht the G vlue 6 of 8.36 ev for the dibtic IP of the Π u stte is in resonble greement with our clculted vlue t the CBS limit. The clculted spectroscopic prmeters for the excited 1 3 u, 3 u, - u, nd - u sttes of Si t the MRCI level with different correltion consistent bsis sets re given in Tble 3. Figure 1 presents the clculted potentil energy curves. We note tht the MRCI results without the +Q correction seem to yield vlues of E in somewht better greement with experiment thn MRCI+Q by few hundredths of n ev. However, the predicted bond distnces seem to be predicted better with the +Q correction. For the clcultions with the ug-cc-pv5z bsis set, the greement with the experimentlly determined vlues of r e, ω e, ω e x e, nd T e of the H nd K sttes is, overll, excellent. At the MRCI level for the H stte, the bond distnce is within 0.04 Å, ω e within 11 cm -1, nd E within 0.04 ev. At the MRCI+Q level, the bond distnce is within 0.01 Å, ω e within 1 cm -1, nd E within 0.07 ev. Thus, we re ble to relibly reproduce the prmeters of the u- stte. A similr high level of greement is found for the K stte with the geometry t the MRCI level now within 0.0 Å nd both vlues for E within 0.04 ev. The results presented in Tble 3 for the excited sttes of Si re the most ccurte vilble to dte. In Tble 6, we summrize the dominnt reference configurtions for the clculted excited sttes of Si. Not surprisingly, we note tht the excited sttes of Si hve significnt multireference chrcter. This is especilly true for the 3 u, - u, nd - u sttes. Our bility to ccurtely clculte the spectroscopic prmeters of the - u nd - u sttes of Si suggests tht we hve obtined very relible descriptions of these multireference excited sttes. We especilly note tht the

5 330 J. Phys. Chem. A, Vol. 104, No. 11, 000 Dixon et l. TABLE 6: Dominnt Configurtions for the Ground nd Selected Excited Sttes of Si Bsed on MRCI Clcultions stte coefficient excittion configurtion - g r e(x) σ g 4σ u 5σ g π u π u f π g 4σ g 4σ u 5σ g π g 1 3 u verticl π u f π u1 π 4σ g 4σ u 5σ g π u1 π σ g π u f π u3 π 4σ g 4σ u π u3 π 3 u verticl σ g π u f π u3 π 4σ g 4σ u π u3 π 0.36 π u f π u1 π 4σ g 4σ u 5σ g π u1 π σ g π u f π u1 π g 3 4σ g 4σ u π u1 π g σ u π u f π u3 π 4σ g 5σ g π u3 π - u verticl π u f π u1 π 4σ g 4σ u 5σ g π u1 π σ g π u f π u3 π 4σ g 4σ u π u3 π σ g f 5σ g1 5σ 4σ g 4σ u 5σ g1 π u 5σ - u r e(h) π u f π u1 π 1 4σ g 4σ u 5σ g π u1 π g σ g π u f π u3 π 4σ g 4σ u π u3 π σ g f 5σ g1 5σ 4σ g 4σ u 5σ g1 π u 5σ σ g π u f 5σ g1 5σ u1 π g 4σ g 4σ u 5σ g1 5σ u1 π g - u verticl σ g π u f π u3 π 4σ g 4σ u π u3 π π u f π u1 π 4σ g 4σ u 5σ g π u1 π σ g f 5σ g1 5σ 4σ g 4σ u 5σ g1 π u 5σ σ u π u f π u3 π 4σ g 5σ g π u3 π TABLE 7: Si u- r g- Dipole Trnsition Mtrix Elements (in Debye) from MRCI Dipole Trnsition Moments nd MRCI+Q Potentil Energy Functions with the ug-cc-pv5z Bsis Set V \V The clculted dipole trnsition moment vries from.34 D t the X stte r e to.35 D t the H stte r e, with mximum of bout.64 D ner r ).43 Å. Figure 1. Ground nd excited stte curves for Si nd Si + clculted t the MRCI/ug-cc-pV5Z level of theory. Note tht ddition of the multireference Dvidson correction (+Q) shifts the Si + sttes by bout +0.1 ev reltive to the Si ground stte. multireference nture of the u- stte is very dependent on the vlue of the internucler distnce r. The chrcter of the wve function in the region ner the minimum of this excited stte is quite different from tht predicted for the region which corresponds to the vlue of r e for the ground stte nd thus the verticl Frnck-Condon region. The multireference nture of the u - stte hs significnt implictions for the experimentl determintion of the Si ioniztion potentil. We lso note tht the coefficients shown in Tble 6 re not sensitive to our choice of stte-verged orbitls. For exmple, clcultions employing orbitls seprtely optimized for the H stte t its r e yield MRCI coefficients for the three most dominnt reference configurtions of 0.79, 0.8, nd 0.33 s compred to the stte-verged results shown in Tble 6 of 0.78, 0.7, nd Such smll differences hve no impct on the qulittive discussion of the interctions of the vrious sttes s discussed below. The dipole trnsition moments hve lso been clculted between the X nd H sttes of the neutrl using MRCI/ug-ccpV5Z wve functions. Rottionless trnsition dipole moment vibrtionl mtrix elements were then determined using numericl vibrtionl wve functions clculted 35 from the MRCI+Q potentil energy functions. These results re shown in Tble 7. Since the equilibrium bond length of the H stte is significntly longer thn tht of the ground stte, the lrgest mtrix elements nd hence Frnck-Condon fctors occur when the ground stte nd H stte re in excited vibrtionl sttes. For trnsitions rising from V ) 0 of the ground electronic stte, the lrgest mtrix elements occur for V > 5. This is in good greement with the lser-induced fluorescence (LIF) results of Winsted et l., where the trnsitions shown for V ) 0 nd V ) 5 were more intense thn those with smller vlues of V. The MRCI results for Si + shown in Tble 5 re very similr to the CCSD(T) results shown in Tble 4 for the ground nd first excited stte. The Π u stte is clculted to lie 0.55 ev bove the X 4 Σ g- stte of the ion t the MRCI/ug-cc-pV5Z level of theory. Addition of the multireference Dvidson correction decreses this to 0.49 ev. The R/UCCSD(T)/cc-pV5Z result shown in Tble 4, 0.53 ev, is in excellent greement. As lso shown in Figure 1, second Π u stte (...4σ g 4σ u π u3 in single-determinnt formlism) lies bout 0.8 ev bove the Π u stte. At short bond distnces, i.e., less thn.3 Å, these two Π u sttes strongly interct nd exhibit n voided crossing ner. Å. It should be noted tht the MRCI+Q/ug-cc-pV5Z ioniztion potentil of 7.87 ev is only slightly lower thn the estimted CBS limit IP e clculted t the R/UCCSD(T) level

6 Moleculr Structure nd Ioniztion Potentil of Si J. Phys. Chem. A, Vol. 104, No. 11, TABLE 8: Si u- /Si + X 4 Σ g- Vibrtionl Stte Overlps from MRCI+Q/ug-cc-pV5Z Potentil Energy Functions V \V of 7.91 ev (see bove). Using MRCI+Q/ug-cc-pV5Z potentil energy functions, the nucler motion contribution (vibrtionl) to the stte overlps between the Si u - nd Si + X 4 Σ g - sttes hve been clculted using numericl 35 vibrtionl wve functions. These results re shown in Tble 8. Discussion Mrijnissen nd ter Meulen, 16 in obtining the most ccurte evlution of the 8 Si ioniztion potentil, (7) cm -1 ) ev, hve used the N 3 Σ - u stte of Si t cm -1 s the intermedite stte in their two-photon photoioniztion process. These uthors hve rgued tht this intermedite stte is dominted by single determinnt...4σ g 4σ u 5σ π u 5σ electronic configurtion which gives rise to the...4σ g 4σ u 5σ g1 π u electronic configurtion (X 4 Σ - g ) of the ground stte of the ion. These rguments re indeed vlid, lthough these uthors did not consider tht there is likely to be significnt multireference chrcter in the excited sttes of Si. Without considertion of the multireference chrcter of the excited stte wve functions, Mrijnissen nd ter Meulen 16 hve rgued tht the brcketing of the Si ioniztion potentil between 7.90 nd 8.08 ev by Winsted et l. 15 from resonnt two-photon ioniztion spectroscopy is invlid nd tht their observed IP does not correlte to the ground stte of the Si + ion but rther to n excited stte. Mrijnissen nd ter Meulen rgue tht the u- intermedite stte ccessed by Winsted et l. in their experiment rises from the...4σ g 4σ u 5σ g π π electronic configurtion, wheres the X 4 Σ - g ground stte of the ion belongs to the...4σ g 4σ u 5σ π u electronic configurtion. This suggests tht ioniztion from the u- stte of Si would require tht two electrons chnge their moleculr orbitls, photoioniztion process with low probbility. Furthermore, these uthors 16 suggest tht the - u stte correltes with the...4σ g 4σ u 5σ g π electronic excited stte of Si + (i.e., the Π u stte). The results given in Tble 6 demonstrte tht the rguments of Mrijnissen nd ter Meulen re oversimplified due to their lck of considertion of the multireference chrcter of the excited sttes of Si. The vlidity of the single determinnt model is plced in serious doubt if one simply surveys the plethor of Si excited sttes clculted by Peyerimhoff nd Buenker 33 in their erly multireference study which clerly estblished tht the possibility for excited stte mixing is significnt. It is somewht surprising tht Mrijnissen nd ter Meulen ccepted the G results 6 for the first IP of Si to form the ground stte of the ion yet ignored the clculted energy difference of 0.4 ev for the difference in the energy of the ground nd first excited Π u stte of Si +, especilly in view of the good greement between their determined vlue nd the lower bound of Winsted et l. 15 One cnnot esily invoke the existence of very lowlying (<0.4 ev) excited stte to explin the good greement between these two photoioniztion results. A possible source of error in the photoioniztion experiments of Winsted et l. would be tht different stte other thn the ground stte of Si ws excited in their photoioniztion experiments. This possibility nd the potentil cndidte A 3 Π u stte were certinly eliminted by the extensive spectroscopic study of Winsted et l. 34 on the H-X bnd system which demonstrted clen 3 Σ u - to 3 Σ g - spectrum with no evidence for involvement of the A 3 Π u stte in the cold expnsion of Si under the sme conditions s used in the photoioniztion experiments. A simple rgument tht cn be evoked to explin the experimentl results of Winsted et l. 15 is tht the H stte of Si is not dominted by single configurtion to the exclusion of other configurtions tht would prevent coupling to the ground stte of the ion. Wheres Tble 6 clerly shows tht the ground stte of Si is dominted by the single configurtion,...4σ g 4σ u 5σ g π u, the H stte, s noted bove, is composed of strongly mixed configurtions. As well, its multireference chrcter chnges s function of internucler distnce. The two configurtions of gretest import to the two-photon ioniztion process through the u - stte to form the ground stte ion re...4σ g 4σ u 5σ g 1 π u 5σ u 1, significnt t both r.3 Å (verticl excittion region) nd r.7å(r e for the H stte of Si ), nd...4σ g 4σ u 5σ g1 π g 5σ u 1, significnt t r.7 Å. The former directly correltes with the ground stte of the ion by loss of the 5σ u 1 electron. At r.3 Å, this stte hs coefficient of 0. nd t the lrger r.7 Å, it hs n even lrger coefficient, The contributions of these configurtions re sufficiently lrge so s to hve direct impct on the photoioniztion process in producing the ground stte of the ion. It is perhps lso worth mentioning tht the reltive mgnitudes of these coefficients re not strongly dependent on the choice of orbitls used in the MRCI. Test clcultions using pseudocnonicl orbitls optimized only for the ground electronic stte resulted in CI coefficients nerly identicl to those shown in Tble 6. Acknowledgment. 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