Commun. Thor. Phys. (Bijing, China) 47 (2007) pp. 1114 1120 c Intrnational Acadmic Publishrs Vol. 47, No. 6, Jun 15, 2007 Accurat Analytic Potntial Enrgy Function and Spctroscopic Study for G 1 Π g Stat of Dimr 7 Li 2 SHI D-Hng, 1,2, MA Hng, 2 SUN Jin-Fng, 2 and ZHU Zun-Lu 2 1 Collg of Physics & Elctronic Enginring, Xinyang Normal Univrsity, Xinyang 464000, China 2 Collg of Physics & Information Enginring, Hnan Normal Univrsity, Xinxiang 453007, China (Rcivd Jun 26, 2006) Abstract Th rasonabl dissociation limit for th G 1 Π g stat of dimr 7 Li 2 is dtrmind. Th quilibrium intrnuclar distanc, dissociation nrgy, harmonic frquncy, vibrational zro nrgy, and adiabatic xcitation nrgy ar calculatd using a symmtry-adaptd-clustr configuration-intraction mthod in complt activ spac in Gaussian03 program packag at such numrous basis sts as 6-311++G, 6-311++G(2df,2pd), 6-311++G(2df,p), cc-pvtz, 6-311++G(3df,3pd), CEP-121G, 6-311++G(2df,pd), 6-311++G(d,p),6-311G(3df,3pd), D95(3df,3pd), 6-311++G(3df,2p), 6-311++G(2df), 6-311++G(df,pd) D95V++, and DGDZVP. Th complt potntial nrgy curvs ar obtaind at ths sts ovr a wid intrnuclar distanc rang and hav last squars fittd to Murrll Sorbi function. Th conclusion shows that th basis st 6-311++G(2df,p) is a most suitabl on for th G 1 Π g stat. At this basis st, th calculatd spctroscopic constants T, D, E 0, R, ω, ω χ, α, and B ar of 3.9523 V, 0.813 06 V, 113.56 cm 1, 0.320 15 nm, 227.96 cm 1, 1.6928 cm 1, 0.004 436 cm 1, and 0.4689 cm 1, rspctivly, which ar in good agrmnt with masurmnts whnvr availabl. Th total 50 vibrational lvls and corrsponding inrtial rotation constants ar for th first tim calculatd and compard with availabl RKR data. And good agrmnt with masurmnts is obtaind. PACS numbrs: 31.50.Df, 31.15.Ar Ky words: vibrational frquncy, dissociation nrgy, Li 2, ab initio calculations 1 Introduction On of th most important problms in th fild of atomic and molcular physics is to obtain rliabl physical modls of bonding potntials so as to thoroughly undrstand molcular spctroscopic proprtis, sinc quantitativ molcular spctroscopic knowldg can b drivd from th molcular analytic potntial nrgy function (APEF). [1] Nowadays, with th dvlopmnt of modrn quantum chmical mthods and powrful computrs, ab initio calculations can giv mor and mor accurat potntial nrgy curv (PEC) with srial points, spcially for small molculs. And it is availabl to fit ths ab initio data using a suitabl analytic function with a root-man squar rror (RMSE) lowr than th chmical accuracy (1.0 Kcal/mol). [2] Thus, thr is a long-standing intrst in simpl yt rliabl analytical modls of chmical potntials, which should idally consist of physically idntifiabl trms and which should b basd on a limitd numbr of availabl thortical data. Li 2 is th simplst stabl homonuclar diatomics, nxt to H 2. Numrous thortical and xprimntal invstigations [3 13] hav bn publishd about its ground and low-lying xcitd singlt and triplt stats. Howvr, studis on th highly xcitd stat G 1 Π g can hardly b found in th litraturs. [14 16] Th most rcnt xprimnts hav bn mad by Brnhim t al., [16] who publishd two possibl dissociation nrgis, on is 6390 cm 1 if th rasonabl dissociation limit corrsponds to (2 2 P )+ (2 2 P ), th othr is 7507 cm 1 if th rasonabl dissociation limit corrsponds to (2 2 P ) + (3 2 S). Ths valus wr basd on th most likly ground potntial valu of 8450 cm 1 givn by Konowalow t al. [17] Th most rcnt calculations hav bn prformd by Potau t al., [15] who only calculatd th quilibrium intrnuclar sparation R, dissociation nrgy D, harmonic frquncy ω, and adiabatic xcitation T. It is a pity that thy did not gav any othr information, such as th spctroscopic constants ω χ, E 0, and B, vibrational lvls G(ν), and inrtial rotation constants B ν. And no APEF can b found in th publications to dat. In this papr, w attmpt to calculat th accurat APEF and driv th main molcular spctroscopic proprtis. Compard with prvious thoris, this work shows xcllnt agrmnt with xprimnts, [16] and is mor complt ffort than prvious thoris. Thus, it is ncouraging. In this papr, th main spctroscopic constants, total 50 vibrational lvls and corrsponding inrtial rotation constants of th G 1 Π g stat for dimr 7 Li 2 ar calculatd using a symmtry-adaptd-clustr configurationintraction (SAC-CI) mthod [18,19] in full activ spac in Gaussian03 program packag. [19] In th nxt sction, w dscrib in dtail th dissociation limit and rcalculat th xprimntal dissociation nrgy for this stat. In Sc. 3, Th projct supportd by National Natural Scinc Foundation of China undr Grant No. 10574039 Corrsponding author, E-mail: scattring@sina.com.cn
No. 6 Accurat Analytic Potntial Enrgy Function and Spctroscopic Study for G 1 Π g Stat of Dimr 7 Li 2 1115 w prsnt th computd rsults and mak som usful discussion about thm. Concluding rmarks ar mad in Sc. 4. 2 Dissociation Limit for th G 1 Π g Stat Obviously, th APEF is diffrnt whn an lctronic stat is dissociatd in diffrnt channls. In ordr to corrctly calculat and dscrib th APEF of an lctronic stat, w must dtrmin its rasonabl dissociation limit. Th configuration of th ground Li atom is 1s 2 2s 1. Whn on lctron in 2s orbital is xcitd, th configurations 1s 2 2p 1, 1s 2 3s 1, 1s 2 3p 1, 1s 2 4s 1, 1s 2 3d 1 and so on can b formd. Whn an atom is in th configuration 1s 2 2s 1, 1s 2 3s 1 or 1s 2 4s 1, its atomic group rprsntation is 2 S g. And whn an atom is in th configuration 1s 2 2p 1 or 1s 2 3p 1, its atomic group rprsntation is 2 P u. If two Li atoms in th dissociation limit ar both in th ground stat, basd on th group thory and atomic and molcular raction statics, [20] th rprsntation 2 S g can b rsolvd into thos of D h (Li 2 ) as follows: Thir dirct product and rduction ar 2 S g 2 Σ + g. (1) 2 Σ + g 2 Σ + g 1 Σ + g 3 Σ + u. (2) It is obvious that quation (2) contains 1 Σ + g. According to th principl of rvrsibility for th microscopic procss, [20] th dissociation limit for th ground stat X 1 Σ + g may b Li 2 (X 1 Σ + g ) Li( 2 S g ) + Li( 2 S g ). (3) Whn two Li atoms in th dissociation limit ar both in th configuration 1s 2 2p 1, basd on th abov-mntiond rason, th rprsntation 2 P u is rsolvd into thos of D h (Li 2 ) as follows: 2 P u 2 Σ + u 2 Π u. (4) Thir dirct product and rduction ar 2 Σ + u 2 Π u ( 2 Σ + u 2 Π u ) 1 Σ + g (2) 1 Σ u 1 Π g 1 Π u 1 g 3 Σ + u (2) 3 Σ g 3 Π g 3 Π u 3 u. (5) Equation (5) contains 1 Π g. According to th principl of rvrsibility for th microscopic procss, [20] th dissociation limit for th G 1 Π g stat may b Li 2 (G 1 Π u ) Li( 2 P u ) + Li( 2 P u ). (6) Whn on Li atom in th dissociation limit is in th 1s 2 2s 1 and th othr in th 1s 2 2p 1, sinc 2 S g 2 Σ + g, 2 P u 2 Σ + u 2 Π u and 2 Σ + g 2 Σ + u 2 Π u ) 1 Σ + u 3 Σ + u 1 Π u 3 Π u, according to th principl of rvrsibility for th microscopic procss, [20] th dissociation limit may also b Li 2 (G 1 Π u ) Li( 2 S g ) + Li( 2 P u ). (7) Fig. 1 Potntial nrgy curvs of th ground and xcitd stats for a molcul. Fig. 2 PEC of th xcitd dimr Li 2. As shown in Fig. 1, th atomic xcitation nrgy E a for an xcitd stat of a molcul quals, E a = D + T D 0. (8) Hr, D is th dissociation nrgy for a givn xcitd stat. D 0 is th dissociation nrgy for th ground stat and quals 8517 cm 1 (about 1.0561 V) for dimr 7 Li 2, which has takn into considration th vibrational zro nrgy. [21] T is th adiabatic xcitation nrgy from th ground to a givn stat. And E a is th atomic xcitation nrgy sum
1116 SHI D-Hng, MA Hng, SUN Jin-Fng, and ZHU Zun-Lu Vol. 47 of th sparatd atoms for a givn xcitd stat in th dissociation limit whn th atomic xcitation nrgy sum of th sparatd atoms in th dissociation limit for th ground stat is st to zro. It has bn provd that quation (1) is th Li 2 ground-stat dissociation limit, in which th two sparatd atoms ar both in th ground stat. [22] According to Tabl 1, [23] th xcitation nrgy sum of th two Li atoms in th dissociation limit quals zro. Tabl 1 Enrgy lvls of two lithium atoms in svral lctronic configurations. [23] Configuration Excitation nrgy (cm 1 ) Configuration Excitation nrgy (cm 1 ) (1s 2 2s 1 ) + (1s 2 2s 1 ) 0 (1s 2 2s 1 ) + (1s 2 3s 1 ) 272 06 (1s 2 2s 1 ) + (1s 2 2p 1 ) 149 04 (1s 2 2p 1 ) + (1s 2 2p 1 ) 298 08 (1s 2 2s 1 ) + (1s 2 3p 1 ) 309 25 (1s 2 2s 1 ) + (1s 2 3d 1 ) 312 83 (1s 2 2p 1 ) + (1s 2 3p 1 ) 458 29 Th bst calculatd T and D valus for th stat G 1 Π g in this invstigation ar obtaind at th basis st 6-311++G(2df,p), which ar 3.9523 V and 0.813 06 V, rspctivly. Thrfor, E a = 3.709 26 V ( 29 913 cm 1 ) can b obtaind. According to Tabl 1, w conclud that th two Li atoms in th dissociation limit for this stat must b both in th configuration 1s 2 2p 1. Thus th rasonabl dissociation limit for th G 1 Π g stat must b Li 2 (G 1 Π u ) Li( 2 P u ) + Li( 2 P u ). (9) In th nxt, w rcalculat th xprimntal G 1 Π g stat dissociation nrgy according to th most rcnt ground stat dissociation nrgy [21] and th G 1 Π g stat T valu (about 31 868 cm 1 ) masurd in Rf. [16]. In th light of Eq. (8), D = 6457 cm 1 (about 0.800 67 V) is attaind. 3 Rsults and Discussion Th calculations dscribd hr ar prformd in Gaussian03 program packag. [19] By gomtry optimization (OPT) calculations for th G 1 Π g stat, w hav attaind th R valus at such basis sts as D95(3df,3pd), 6-311++G(2df,2pd), 6-311G(3df,3pd), 6-311++G(3df,2p), DGDZVP, 6-311++G(2df,p), CEP-121G, 6-311++G(2df,pd), 6-311++G(3df, 3pd), 6-311++G(2df), 6-311++G(df,pd), 6-311++G(d,p), D95V++, 6-311++G, and cc-pvtz. Som of th rsults ar tabulatd in Tabl 2. At th sam tim, by fin singl-point nrgy scanning (SPES) calculations nar th xprimntal quilibrium position at th sam basis st at a vry tiny intrval of 0.01 a 0, w hav obtaind th R valus, too. Som of th rsults ar also tabulatd in Tabls 2 and 3. Obviously, from Tabl 2 w can s that th two approachs, namd OPT and SPES, giv diffrnt quilibrium intrnuclar sparations at th sam basis st. It is asily undrstood, bcaus th uniqu GSUM algorithm usd in th SPES calculations is incompltly idntical with th on usd in th OPT computations. [18,19] It is th rason that th rsult obtaind by SPES calculations is quit intgratd into PEC, and all th spctroscopic proprtis including th quilibrium intrnuclar sparation can b drivd from APEF, thus th rsult obtaind by th SPES calculations should b mor rasonabl. Tabl 2 Comparison of quilibrium intrnuclar sparations (in nm) obtaind by OPT and by SPES calculations for th G 1 Π g stat of dimr 7 Li 2. 6-311++(df,pd) 6-311++G(2df,2pd) 6-311++G 6-311++G(2df,pd) 6-311++G(3df,2p) 6-311++G(2df,p) OPT 0.320 86 0.322 10 0.324 33 0.322 10 0.324 30 0.322 10 SPES 0.322 27 0.320 68 0.323 86 0.320 68 0.322 27 0.320 15 Thn, w comput th PECs for this stat at th abov-mntiond basis sts through th quilibrium positions obtaind by SPES at 0.3 a 0 intrvals. In ordr to guarant PEC convrgnc, th calculatd intrnuclar sparation rang should b larg nough at ach basis st. Murrll Sorbi (M-S) function is a widly usd potntial nrgy function, whos form is [24] n V (ρ) = D (1 + a i ρ i) xp( a 1 ρ), (10) i=1 whr ρ = R R, R is th intrnuclar distanc of diatomics. R is rgardd as a fixd paramtr in th fitting procss, which is attaind by fin SPES calculations in this papr. Th paramtrs a i ar dtrmind by th fitting mthod using ab initio data.
No. 6 Accurat Analytic Potntial Enrgy Function and Spctroscopic Study for G 1 Π g Stat of Dimr 7 Li 2 1117 Tabl 3 Equilibrium constants for th G 1 Π g stat of 7 Li 2. Sourc T (V) D (V) R (nm) ω (cm 1 ) E 0 (cm 1 ) Exprimnts [16] 3.9517 0.800 67 0.320 14 229.26 6-311++G(2df,p) 3.9523 0.813 06 0.320 15 227.96 113.56 6-311++G(2df,2pd) 3.9522 0.813 79 0.320 68 227.18 113.17 6-311++G(df,pd) 3.9406 0.788 37 0.322 27 230.29 114.71 6-311++G(2df,pd) 3.9522 0.813 06 0.320 68 227.13 113.16 6-311++G(3df,2p) 3.9388 0.821 19 0.322 27 222.59 110.87 6-311++G(3df,3pd) 3.9391 0.827 26 0.321 74 223.38 111.26 6-311++G 3.8818 0.738 36 0.323 86 230.65 114.85 6-311++G(2df) 3.9524 0.814 77 0.318 56 234.30 116.74 6-311++G(d,p) 3.9275 0.783 78 0.319 09 237.84 118.44 D95V++ 3.8220 0.709 68 0.323 86 244.21 121.54 6-311G(3df,3pd) 4.3094 0.461 26 0.351 37 155.07 77.16 cc-pvtz 4.2516 0.527 03 0.338 67 185.92 92.55 CEP-121G 4.1905 0.377 26 0.345 55 190.87 94.78 D95(3df,3pd) 4.3119 0.440 77 0.351 90 160.36 79.83 DGDZVP 5.4285 0.435 90 0.369 37 158.09 78.67 By itrating a systm of normal quations basd on a last-squars fitting, th paramtrs a i and D in Eq. (10) ar fittd at various basis sts. In ordr to attain satisfactory rsults, w try it from n = 3 to n = 8, and find th bst rsults for n = 6. From th fitting rsults, th quadratic forc constant f 2 is calculatd, f 2 = D (a 2 1 2a 2 ). (11) According to th RKR mthod, w hav ω = f 2 8πcµR 2, (12) whr µ and c ar th rducd mass of dimr 7 Li 2 and th vlocity of light in vacuum, rspctivly. Th calculatd ω valus ar listd in Tabl 3, too. Tabl 3 tabulats T, D, R, ω, and th vibrational zro nrgy E 0 of th G 1 Π g stat at various basis sts. From ths rsults w find that th basis st 6-311++G(2df,p) [25,26] is an xcllnt on, sinc th calculatd T, R, and ω valus at this basis st ar in agrmnt with th masurmnts [16] within 0.0006 V or 0.015%, 0.000 01 nm or 0.003%, and 1.3 cm 1 or 0.567%, rspctivly, though D is somwhat largr than th masurmnts [16] by 0.012 36 nm or 1.579%. Thus, furthr calculations will b prformd using th APEF obtaind at th basis st 6-311++G(2df,p). Tabl 4 Paramtrs of M-S APEF for 7 Li 2(G 1 Π g) at th SAC-CI/6-311++G(2df,p) lvl of thory. D (V) R (nm) a 1 (nm 1 ) a 2 (nm 2 ) a 3 (nm 3 ) a 4 (nm 4 ) a 5 (nm 5 ) a 6 (nm 6 ) RMSE (V) 0.813 07 0.320 15 13.247 06 43.835 38 48.091 12 326.595 69 704.933 24 2531.8496 0.0026 Th APEF paramtrs at 6-311++G(2df,p) ar all tabulatd in Tabl 4 for intgrality. At th sam tim, in ordr to invstigat th PEC dtails of this stat, th ab initio data ar tabulatd in Tabl 5, and th fitting rsults and th curv of th ab initio calculatd points ovr th intrnuclar sparation rang from about 2.4a 0 to 37a 0 ar intuitivly illustratd in Fig. 2, too. In ordr to valuat th fitting quality of APEF at 6-311++G(2df,p), w calculat th RMSE, RMSE = 1 N (V APEF V ab initio ) N 2, (13) i=1 whr V APEF and V ab initio ar nrgis attaind by th fitting and ab initio calculations, rspctivly. N is th numbr of fittd points (hr N = 116). Th prsnt RMSE for th G 1 Π g stat is only 0.0026 V ( 0.06 Kcal/mol). Obviously, our fitting accuracy about th APEF is gratly suprior to th chmical accuracy (1.0 Kcal/mol). [2] Thus, th APEF of th G 1 Π g stat is crdibl.
1118 SHI D-Hng, MA Hng, SUN Jin-Fng, and ZHU Zun-Lu Vol. 47 Tabl 5 Potntial nrgis E(R) at diffrnt intrnuclar sparations R for th G 1 Π g stat at SAC-CI/6-311++G(2df,p) lvl of thory. R (nm) E(R) (Hartr) R (nm) E(R) (Hartr) R (nm) E(R) (Hartr) 0.161 399 0 14.686 714 0.510 656 0 14.769 071 1.209 169 9 14.757 221 0.193 149 7 14.737 069 0.558 282 0 14.764 782 1.272 671 2 14.757 188 0.224 900 3 14.764 821 0.605 907 9 14.761 849 1.336 172 5 14.757 165 0.256 650 9 14.779 058 0.653 533 9 14.760 121 1.399 673 7 14.757 147 0.288 401 6 14.785 346 0.717 035 1 14.758 928 1.463 175 0 14.757 134 0.304 276 9 14.786 595 0.780 536 4 14.758 316 1.526 676 2 14.757 124 0.320 152 2 14.786 970 0.844 037 6 14.757 946 1.590 177 5 14.757 116 0.336 027 5 14.786 687 0.891 663 6 14.757 750 1.653 678 8 14.757 109 0.367 778 2 14.784 758 0.955 164 9 14.757 560 1.717 180 0 14.757 104 0.399 528 8 14.781 697 1.018 666 1 14.757 427 1.796 556 6 14.757 099 0.431 279 4 14.778 093 1.082 167 4 14.757 333 1.875 933 2 14.757 094 0.463 030 1 14.774 350 1.1456 687 14.757 268 1.955 309 8 14.757 091 Basd on th following Eqs. (14) (18), th forc constants f 3, f 4 and thn th spctroscopic constants B, α, and ω χ ar calculatd. Th calculatd spctroscopic rsults ar tabulatd in Tabl 6. For convnint comparison, w also tabulat prsnt T, R, D, and ω valus in Tabl 6 togthr with th masurmnts [16] and othr thoris. [14,15] ( ) f 3 = 6D a 3 a 1 a 2 + a3 1, (14) 3 f 4 = D (3a 4 1 12a 2 1a 2 + 24a 1 a 3 ), (15) h B = 8πcµR 2, (16) ( α = 6B2 f3 R ) + 1, (17) ω 3f 2 ω χ = B [ f 4R 2 ( + 15 1 + ω ) α 2 ] 8 f 2 6B 2. (18) Hraftr, w calculat th vibrational zro nrgy E 0 at various basis sts (th calculatd E 0 rsults ar tabulatd in Tabl 3), E 0 = 1 2 ω 1 4 ω χ. (19) Tabl 6 Comparison with masurmnts and othr thoris about T, R, D, ω, ω χ, B, and α for dimr 7 Li 2 (G 1 Π g) at SAC-CI/6-311++G(2df,p) lvl of thory. Sourc T (V) R (nm) D (V) ω (cm 1 ) ω χ (cm 1 ) B (cm 1 ) α (cm 1 ) This work 3.9523 0.320 15 0.813 06 227.96 1.6928 0.4689 0.004 436 Exp. [16] 3.9517 0.320 14 0.800 67 229.26 0.468 87 Thory [14] 0.3405 0.493 52 189.5 2.25 Thory [15] 3.9581 0.3201 0.793 35 229.1 From Tabl 6, w find that th bst R, D, and ω valus of prvious thoris ar prsntd by Potau t al. [15] Thir discrpancis dviatd from th masurmnts [16] ar 0.0125% for R, 0.914% for D, and 0.07% for ω, rspctivly. Ths discrpancis ar quivalnt to ours as a whol. Sinc w prsnt th complt APEF for th first tim and furthr calculat othr main spctroscopic constants ω χ, B, α, E 0, total 50 vibrational lvls and th corrsponding inrtial rotation constants, thus w say that our calculations ar mor complt than prvious thoris and rprsnt an improvmnt. Howvr, w cannot carry out any comparison for α and E 0, bcaus no masurmnts and thoris can b found in th litraturs to th bst of our knowldg. Bsids, w considr that th ω χ valu givn in Rf. [14] is possibly unrliabl, sinc thir R, D, and ω valus ar gratly dviatd from th masurmnts. [16] Now w comput th vibrational lvl G(ν) and th corrsponding inrtial rotation constant B ν by solving th following radial Schrödingr quation of nuclar motion in th adiabatic approximation, [ h2 2µ d 2 dr 2 + h2 2µr 2 J(J + 1) + V (r) ] Ψ ν.j (r) = E ν,j Ψ ν.j (r). (20)
No. 6 Accurat Analytic Potntial Enrgy Function and Spctroscopic Study for G 1 Π g Stat of Dimr 7 Li 2 1119 Hr V (r) is th adiabatic rotationlss potntial nrgy function tabulatd in Tabl 4. ν and J ar th vibrational and rotational quantum numbrs, rspctivly. Th rotational sublvls of a givn vibrational lvl ar rprsntd by th following powr sris, [27] E ν,j = G(ν) + B ν [J(J + 1)] D ν [J(J + 1)] 2 + H ν [J(J + 1)] 3 + L ν [J(J + 1)] 4 + (21) Tabl 7 Th first 21 vibrational lvls, inrtial rotation constants and th corrsponding comparison with availabl RKR data for th 7 Li 2 (G 1 Π g) (J = 0) stat at SAC-CI/6-311++G(2df,p) lvl of thory. ν SAC-CI/6-311++G(2df,p) RKR data [16] G(ν) cm 1 B ν cm 1 G(ν) cm 1 B ν cm 1 0 115.5774 0.466 643 5 114.226 0.466 134 9 1 344.8050 0.4622246 340.254 0.460 658 3 2 571.6019 0.457 746 2 563.068 0.455 181 7 3 795.8886 0.453 202 8 782.686 0.449 705 1 4 1017.5849 0.448 588 6 999.121 0.444 228 5 5 1236.6097 0.443 897 9 1212.384 0.438 751 9 6 1452.8807 0.439 124 9 1422.480 0.433 275 3 7 1666.3144 0.434 263 4 1629.409 0.427 798 7 8 1876.8255 0.429 307 4 1833.167 0.422 322 1 9 2084.3267 0.424 250 2 2033.747 0.416 845 4 10 2288.7287 0.419 085 0 2231.136 0.411 368 8 11 2489.9396 0.413 804 5 2425.318 0.405 892 2 12 2687.8646 0.408 400 8 2616.271 0.400 415 6 13 2882.4059 0.402 865 5 2803.969 0.394 939 0 14 3073.4616 0.397 189 6 2988.384 0.389 462 4 15 3260.9262 0.391 363 1 3169.480 0.383 985 8 16 3444.6893 0.385 375 1 3347.219 0.378 509 2 17 3624.6353 0.379 213 8 3521.558 0.373 032 6 18 3800.6427 0.372 865 7 3692.450 0.367 556 0 19 3972.5834 0.366 316 1 3859.842 0.362 079 4 20 4140.3217 0.359 548 3 4023.680 0.356 602 8 Tabl 8 Vibrational lvls and inrtial rotation constants from ν = 21 to ν = 49 for th 7 Li 2(G 1 Π g) (J = 0) stat at SAC-CI/ 6-311++G(2df,p) lvl of thory. ν G(ν) (cm 1 ) B ν (cm 1 ) ν G(ν) (cm 1 ) B ν (cm 1 ) 21 4314.0025 0.353 731 9 36 6237.5782 0.197 148 2 22 4484.9259 0.346 570 2 37 6301.1156 0.177 755 2 23 4651.2126 0.339 134 0 38 6353.6101 0.155 927 6 24 4812.6879 0.331 395 8 39 6394.6853 0.132 969 3 25 4959.1624 0.323 323 8 40 6425.7658 0.113 495 5 26 5100.4296 0.314 880 3 41 6450.4244 0.100 819 8 27 5236.2631 0.306 020 5 42 6471.6307 0.092 257 1 28 5366.4126 0.296 690 3 43 6490.5528 0.085 111 0 27 5490.5991 0.286 823 6 44 6507.5022 0.078 232 4 30 5608.5088 0.2763 380 45 6522.4770 0.071 031 7 31 5719.7855 0.265 130 9 46 6535.3186 0.063 014 2 32 5824.0197 0.253 068 8 47 6545.7359 0.053 485 3 33 5920.7355 0.239 978 2 48 6553.2426 0.040 904 1 34 6009.3731 0.225 628 5 49 6556.8625 0.016 580 7 35 6163.8752 0.214 299 0 W hav obtaind a total of 50 vibrational lvls for this stat whn J = 0. For ach vibrational lvl G(ν), on inrtial rotation constant B v and six cntrifugal distortion constants D ν, H ν, L ν, M ν, N ν, and O ν ar attaind. Hr only 50 vibrational lvls and th corrsponding inrtial rotation constants togthr with availabl RKR data [16] ar tabulatd in Tabls 7 and 8 du to th lngth of th papr. From Tabl 7, on can asily find that th calculatd rsults
1120 SHI D-Hng, MA Hng, SUN Jin-Fng, and ZHU Zun-Lu Vol. 47 ar in good agrmnt with availabl RKR data as a whol. Thrfor, th vibrational lvls and th corrsponding inrtial rotation constants tabulatd in Tabl 8 should b rliabl. 4 Conclusions W hav attaind th rasonabl dissociation limit for dimr 7 Li 2 (G 1 Π g ), calculatd th intraction potntials using SAC-CI mthod at numrous basis sts and found that th bst potntial can b obtaind at 6-311++G(2df,p). Employing prsnt potntial obtaind at 6-311++G(2df,p), w hav computd th main spctroscopic constants D, E 0, R, ω, ω χ, α, and B, and for th first tim calculatd th vibrational lvls G(ν) and th inrtial rotation constants B ν. Favorabl agrmnt has bn found in comparing with availabl RKR data as a whol. Th rsults obtaind hr ar mor complt than prvious thortical invstigations, thus rprsnt an improvmnt. Rfrncs [1] K.T. Tang, J.P. Tonnis, and W. Myr, J. Chm. Phys. 95 (1991) 1144. [2] A. Aguado and M. Paniagua, J. Chm. Phys. 96 (1992) 1265. [3] M.D. Halls, H.B. Schlgl, M.J. DWitt, and G.W.F. Drak, Chm. Phys. Ltt. 339 (2001) 427. [4] C. Linton, F. Martin, A.J. Ross, t al., J. Mol. Spctrosc. 196 (1999) 20. [5] A.M. Maniro and P.H. Acioli, Int. J. Quant. Chm. 103 (2005) 711. [6] W.T. Zmk and W.C. Stwally, J. Chm. Phys. 111 (1999) 4962. [7] L. Li, G. Lazarov, and A.M. Lyyra, J. Mol. Spctrosc. 191 (1998)387. [8] A.A. Zavitsas, J. Mol. Spctrosc. 221 (2003) 67. [9] Y. Huang and R.J. LRoy, J. Chm. Phys. 119 (2003) 7398. [10] K. Urbanski, S. Antonova, A. Yiannopoulou, t al., J. Chm. Phys. 104 (1996) 2813. [11] D. Danovich, W. Wu, and S. Shaik, J. Am. Chm. Soc. 121 (1999) 3165. [12] N. Bouloufa, P. Cacciani, R. Vttr, and A. Yiannopoulou, J. Chm. Phys. 114 (2001) 8445. [13] X. Xi and R.W. Fild, J. Chm. Phys. 83 (1985) 6193. [14] D.D. Konowalow and J.L. Fish, Chm. Phys. 84 (1984) 463. [15] R. Potau and F. Spiglmann, J. Mol. Spctrosc. 171 (1995) 299. [16] R.A. Brnhim, L.P. Gold, P.B. Klly, T. Tipton, and D.K. Virs, J. Chm. Phys. 74 (1981) 749. [17] D.D. Konowalow and M.L. Olson, J. Chm. Phys. 71 (1979) 450. [18] H. Nakatsuji, M. Hada, M. Ehara, t al., SAC/SAC- CI Program Combind with Gaussian for Calculating Ground, Excitd, Ionizd, and Elctron-Attachd Stats and Singlt, Doublt, Triplt, Quartt, Quintt, Sxtt, and Sptt Spin Stats and Thir Analytical Enrgy Gradints, Kyoto Univrsity Prss, Kyoto (2002). [19] M.J. Frisch, G.W. Trucks, H.B. Schlgl, t al., Gaussian 03 Rvision A1, Gaussian Inc., Pittsburgh, PA (2003). [20] Z.H. Zhu, Atomic and Molcular Raction Statics, Scinc Prss, Bijing (1996). [21] B. Barakat, R. Bacis, F. Carrot, S. Churassy, P. Crozt, and F. Martin, Chm. Phys. 102 (1986) 215. [22] D.H. Shi, J.F. Sun, X.D. Yang, Z.L. Zhu, and Y.F. Liu, Chin. Phys. 14 (2005) 1566. [23] C.E. Moor, Atomic Enrgy Lvls, US Govrnmnts Printing Offic, Washington (1971). [24] J.N. Murrll, S. Cartr, S.C. Farantos, P. Huxly, and J.C. Varandas, Molcular Potntial Enrgy Functions, John Wily & Sons, Chichstr (1984). [25] R. Krishnan, J.S. Binkly, R. Sgr, and J.A. Popl, J. Chm. Phys. 72 (1980) 650. [26] M.J. Frisch, J.A. Popl, and J.S. Binkly, J. Chm. Phys. 80 (1984) 3265. [27] G. Hrzbrg, Molcular Spctra and Molcular Structur, Vol. 1, Van Nostrand Rinhold, Nw York (1951).