Spectroscopic constants and potential energy curves of Bi2 and Bi− 2K. Balasubramanian and DaiWei Liao Citation: The Journal of Chemical Physics 95, 3064 (1991); doi: 10.1063/1.460863 View online: http://dx.doi.org/10.1063/1.460863 View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/95/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Theoretical investigation of excited and Rydberg states of imidogen radical NH: Potential energy curves,spectroscopic constants, and dipole moment functions J. Chem. Phys. 126, 244302 (2007); 10.1063/1.2741260 Spectroscopic constants and potential energy curves of yttrium carbide (YC) J. Chem. Phys. 126, 224305 (2007); 10.1063/1.2743015 Spectroscopic constants and potential energy curves of tungsten carbide J. Chem. Phys. 112, 7425 (2000); 10.1063/1.481373 Spectroscopic constants and potential energy curves for 15 electronic states of Ag2 J. Chem. Phys. 98, 7092 (1993); 10.1063/1.464752 Electronic structure of the noble gas dimer ions. I. Potential energy curves and spectroscopic constants J. Chem. Phys. 69, 5151 (1978); 10.1063/1.436462

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Spectroscopic constants and potential energy curves of Bi2 and Bii K. Balasubramaniana ) and Dai-Wei Liao Department o/Chemistry, Arizona State University, Tempe, Arizona 85287-1604

(Received 26 February 1991; accepted 12 April 1991)

We compute the spectroscopic constants of26 electronic states ofBi2 and six electronic states of Bii . In addition, the potential energy curves of electronic states of Bi2 dissociating into Bi(4S) + Bi(4S), BWS) + Bi(ZD), Bi(4S) + BWP) , Bi(ZD) + BWD), and BWS) + Bi(4p) limits are computed. We use a complete active space multiconfiguration self-consistent field (CAS-MCSCF) followed by first-order configuration interaction (FOCI) and second-order configuration interaction (SOC!) methods. In addition, the spin-orbit effects are included through the relativistic configuration interaction (RCI) method. Our computed spectroscopic properties facilitate the assignment of recently observed negative ion photodetachment spectra as well as the electronic spectra accumulated up to now. The observed lifetime and transition moment dependence on internuclear distance are also explained based on computed potential energy curves.

I. INTRODUCTION

The spectroscopy of very heavy dimers and trimers of the sixth row atoms in general and Bi2 in particular has been the topic of several studies. I

-3o The recent review by one of

the authors25 summarizes the developments on spectroscop­ic constants and potential energy curves of heavy dimers and trimers.

The bismuth clusters, especially Bi2 and Bi4, have been studied by several experimental techniques. The Bi2 mole­cule appears to be the experimentally most studied among the sixth row heavy dimers. 1-26,28 The A-X system of Biz has been studied by several authors.8,9.12.13,17-20

The most comprehensive earlier study of Bi2 is due to Gerber et al. 8

,9 who have obtained the potential energy curves of several electronic states of Bi2 using the Rydberg­Klein-Rees (RKR) method from the experimentally de­rived molecular constants. Gerber et al. studied the Bi vapor excitation spectra in a cw Ar ion laser. They made a sugges­tion that there exists a new stateX' (CtJ. = 154cm -I) which lies 1500 cm - I below the X state, previously thought to be the ground state. However, in a subsequent study, Bondybey and English 12 showed that theX' state observed by Gerber et al. is actually due to Bi4 and the X(ot ) state is unambigu­ously the ground state ofBi2. This was further substantiated by the studies of Fabre et al. 16 and Effantin et al. 18 Gerber et af. observed five electronic transitions in the infrared-visible region.

The most studied system of Bi2 is the A(Ou+ )-X(O/) system.8,9,12,13,17,20 The A state is most probably the Ou+ com-ponent of the 3l:u- excited state ofBi2. Bondybey and Eng­lish 12 observed a laser-induced-fluorescence system with T. = 17859 cm -I and 0). = 132 cm - 1 in Ne and Ar matri­ces. These authors have also studied the spectra of Bi4. A striking feature of the Bi4 spectra is that they show no evi­dence of Jahn-Teller distortion in the excited states. The matrix spectra of Bi2 have also been studied by Teichman and Nixon. 10

a) Camille and Henry Dreyfus Teacher-Scholar.

Drosch and Gerber l9 have studied Bi2 using optically pumped cw laser. The A-X system was studied extensively leading to 150 line transitions attributed to the A-X system. Ehret and Gerber20 have obtained the lifetimes and transi­tion moments of the A-X system. A particularly striking feature of the A-X system is that the transition moments do not appear to change at all for internuclear distances between 2.6 and 3.3 A. The lifetimes of the vibrational levels (v' = 1-34) ranged between 50 to 600 ns.

Recently, Polak et al. 28 have studied the negative ion photodetachment spectra of Bii , Bi3- , and Bi4- . A unique feature of the photodetachment technique is that it facili­tates observation of dipole and other forbidden transitions. They find four excited electronic states ofBi2 lying above the XOg+ state. In addition, more than one electronic state ofBi2 is observed in the 13 500 em - 1 region, but this was consid­ered more tentative. They also observed the A (Ou+) elec­tronic state studied before by the other authors. The theo­retical calculation in this study was stimulated by the work of Lineberger and co-workers. 28

Fink et aeo have observed the band spectra for Bi2 in the near infrared region. The observed weak band sequences in the spectra between 7620 and 7800 cm - 1 were attributed to new states of Bi2, but no definitive assignments could be made from the observed spectral features.

The first objective of this study is to compute the spec­troscopic constants of all electronic states of Bi2 below 14000 cm - 1 of the ground state to aid in the interpretation of the photodetachment spectra. In addition, we compute several electronic states above the 14000 cm -1 region with the objective of aiding assignment of other observed spectra and possibly predicting electronic states which are yet to be observed. We also compute the electronic states ofBi2- . Sec­tion II outlines our method of theoretical calculations. Sec­tion III consists of results and discussion. Section IV de­scribes the nature of low-lying electronic states of Bi2.

II. METHOD OF CALCULATION

Table I shows the possible electronic states ofBi2 arising from 4S + 4S, 4S + 2D, 4S + 2p, 2D + 2D, 4S + 4p atoms in

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K. Balasubramanian and D. Liao: Potential energy curves of Bi2 and Bii 3065

TABLE I. Dissociation relationships for the low-lying A-S states of Bi2 •

A-sstates

I !.~+ , l!..+ , '!.,+ , 7!.u+

lI.~' , In., la" 'I.t, 'ng, 'a. l~.,~ , In,,, 3A

II, S~,t ,sn.,t Sa.,

l!.,- , In" .!.~- , 'n. l!.; , In., '!.- , 'n. '!..+ (3), 'I.; (2), 'n.(2), 'n.(2), 'a,(2),

'a., 't/I~, '';., 'r, 1I..+ (3),I!.,- (2),ln.(2),ln.(2),la.(2)

lA"ltfi.,ltfi., lr.

Dissociation limits Atomic states

the absence of spin-orbit coupling. The spin-orbit coupling would of course be very large for the Bi atom and split var­ious states in Table I into several spin-orbit states. The spin­orbit coupling would also mix two states with the same n quantum number. It is evident from Table I that Bi2 is the most complex main group dimer in having numerous elec­tronic states resulting from different spin multiplets and spin-orbit coupling. ..

We compute the spectroscopic constants and potential energy curves using a complete active space MCSCF (CAS­MCSCF) followed by configuration interaction (CI) meth­ods. We employed relativistic effective core potentials31

(RECPs) for the Bi atom which retained the outer 6:l6p3

shells in the valence space. The remaining electrons were replaced by RECPs. Hay and Wadt32 have also generated RECPs for Bi which give equally good results in the absence of spin-orbit coupling. but the RECPs generated by Ross et al. include the important spin-orbit effects for Bi.

We employed a (3s3p) valence Gaussian basis set aug­mented by a set of six-component d polarization functions with ad = 0.06. Thus our basis set is of triple zeta + polari­zation quality.

Both CASSCF and CI calculations were made in the D2h point group. We retained the valence 6s and 6p orbitals of the Bi atoms in the active space. This led to an active space consisting of two ag , two b3u ' one b2u ' one b2g • one bl'" one big. and one au orbitals in the D2h group. Ten outermost electrons of Bi2 were kept as active electrons. In the CASSCF, all these electrons are distributed in all possible

ways among the active space of orbitals. Separate CASSCF calculations were made for each electronic state of Bi2 with different spin multiplicity and spatial symmetry.

The potential energy curves for all internuclear dis­tances were computed using the first-order CI (FOCI) method. The FOCI method included all configurations in the CASSCF plus those configurations generated by distrib­uting nine electrons in the internal space and one electron in the orthogonal external space in all possible ways. The FOCI method was used to generate the natural orbitals for the rela­tivistic CI (RCI) calculations to be discussed later. The FOCI method was also used to compute the spectroscopic constants of the excited states of Bi2 .

The negative ion ofBi2 was treated on an equal footing with the neutral Bi2. However. it is well established that electron affinities are very sensitive to higher-order correla­tion effects. Hence we employed a more accurate second­order CI (SOCI) method to compute the ground state of Bi2- and the same SOCI method applied to the ground state of Bi2 • The SOCI method included all configurations in the FOCI and those configurations obtained by distributing nine electrons in the internal and two electrons in the exter­nal space in all possible ways for Bi2- • The SOC I calculations of the neutral Bi2 included all configurations in the FOCI plus configurations generated by distributing eight electrons in the internal and two electrons in the external space in all possible ways.

The effect of spin-orbit coupling was introduced using the relativistic configuration interaction (RCI) method fol­lowing the FOCI. The FOCI natural orbitals were used in the RCI. In the RCI, we included all low-lying electronic states which yield an n state of the desired symmetry as reference configurations. Subsequently, single and double excitations were allowed from these reference configura­tions. The introduction of spin-orbit coupling into the Ham­iltonian would mix all A-S states which give a n state of the desired symmetry. Table II shows the list of reference con­figurations included in the RCI.

As seen from Table II, the ot state calculations includ­ed reference configurations which constitute the ILt ground state, 311g , 5I.t (Og+), and excited 311g , 3I.g- and excited ILt states. The Ig state included 5Lg+ (1g), 311g (1 g). I I1g (1 g)' 3Lg- (1 g) states. The 1 u state included 5Lt (1g), 3I1g(1g), Il1g(1g), and 3I.g- (1g) states. The lu

TABLE II. A list of reference configurations included in the ReI. Numbers in parentheses denote the number of configuration spin functions with compatible spin combinations that yield an n state with the same symme­try as the reference state.

State

0+ •

Reference configurations

10: 10;20: bT~ (1), 10: 10;2O'g bT! bTg (4), 10: 10;20: 1 ~ 1 n; (16),

10: 10;20:20'. 1 ~ (4), 10: 10; 17r! 1 n; (4), 10: 10;20; I1T! (1),

10:10;20:1~1n;(8), 10: 10;20'. 11T! I1Tg(4), 10:10;11T!1n;(1) 10: 10;20: 1 ~ I1T. (8), 10: 10;2O'g2O'. I1T! (1)

10:10;20:1~I1Tg(8), 10:10;20'.20'. I1T! (2) 10: 10;20: 1 ~ I1T. (8) 10:10;20:1~ I1Tg(8) 10:20;20: 1 ~ I1T. (4)

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3066 K. Balasubramanian and D. Liao: Potential energy curves of Bi2 and Bii

state included 3~u+(lu)' 3Au(lu), and 3~u-(lu) states, while the 2u state included 3Au (2u) and IAu (2u). The Ou+ state included 3~u- (Ou+ ) and I~u+ (Ou+ ), while 3u included 3Au (3 u )' Hence our RCI included all important n states that will mix near reo All our preliminary calculations indi­cated that this array of reference configurations is complete­ly adequate for the ot state at all distances. For other states, the list is complete for properties near reo For example, high­lyexcited 3ITu (lu) could make a more important contribu­tion at longer internuclear distances to the 3~u+ (lu) state, but makes no significant contribution near the reo Hence 3ITu (Iu) was not included in the 3~u+ (lu)'

The RCI calculations of Bi2- l/2g state included two reference configurations from 10; 10;20; l1T! I1Tg and five reference configurations arising from 10; 10;2ug 11T~ I~ which constitute 4~; (l/2g) and 2~g+ (l/2g). The (3/2)g state included two reference configurations from 10; 10; 20; 11T~ I1Tg and five reference configurations from 10; 10;2ug 11T~ 10; which in tum constitute the 4~g- (3/2) and 2Ag (3/2) states.

All CASSCF /FOCI/SOCI calculations were done us­ing one of the author's (K.B.)33 modified versions of ALCHEMY II codes34 to include RECPs. The spin-orbit inte­grals for the RCI were obtained using Pitzer's ARGOS codes.35

,36 The RCI calculations were made using the codes based on the general polyatomic RCI described in Ref. 37. Our SOCI calculations included up to 304 000 configuration spin functions (CSFs) in the D2h group.

III. RESULTS AND DISCUSSIONS

A. Theoretical spectroscopic constants and potential energy curves of BI2

Table III shows our computed spectroscopic constants for Bi2. The spectroscopic constants of the X Og+ were ob­tained using the CASSCF/SOCI/RCI method, while the constants of the excited states were obtained using the CASSCF /FOCI/RCI method. The Te values were obtained using the FOCI/RCI method in all cases to maintain consis­tency. The properties of states containing no n designation in parentheses were obtained without the inclusion of the spin-orbit term. However, all states lying below the 21 000 cm - I region were treated with somewhat greater accuracy including spin-orbit effects.

Figure 1 shows our computed potential energy curves of electronic states ofBi2 in the absence of spin-orbit coupling. Figure 2 shows the potential energy curves of Bi2 including spin-orbit effects. As mentioned in Sec. II, our treatment of spin-orbit coupling is more accurate near re than at long distances, especially for the excited electronic states. Hence, we show potential energy curves for n states near the poten­tial well.

As seen from Fig. I, we computed all of the potential energy curves dissociating into 4S + 4S ground state atoms e~g+, 3~u+' 5~g+, 7~u+)' Since there are numerous elec­tronic states dissociating into 4S + 2D, 4S + 2p, 2D + 2D, and 4S + 4p, it was not possible to study exhaustively all these states. However, we chose selected states of impor­tance in either assigning the existing spectra or in the predic-

TABLE III. Theoretical spectroscopic properties of Bi2 .•

State R. (A) T.(cm- I ) w. (cm- I)

I~t (0,+) 2.76 (2.84) 0.0 151 (171) 3~.+ (I.) 3.00 6651 114 3~.+ (0.- ) 3.03 11780 112 36..(2.) 2.97 12833 133 S~g+ (Og+) 3.22 13700 III S~g+ Og) 3.24 14424 96 3ng(Ot) 3.00 18892 99 36..(3.) 2.93 18905 138 3ng(O,- ) 2.90 21062 139 A 3~.- 2.87 22300 140 3n, (2,) 2.97 23657 122 I~,+ (II) 3.09 22170 137 16.. 2.91 22481 145 In, 2.92 25948 123 I~u- 2.89 26308 152 36.. (II) 3.22 28786 96 I~t (Ill) 3.22 30855 88 3n,(II) 3.38 31815 75 In. 3.16 34107 99 I~: 3.05 36208 119 In,(Il) 3.33 37931 92 III. (II) 3.34 37995 71 'n,(III) 3.34 40 179 97 36.. (II) 3.32 42575 107 16.. (II) 3.29 45004 112 I~u+ (II) 3.33 51657 105

• T. 's without n designation in parentheses are splittings relative to I ~,+ in the absence of spin--orbit coupling. Numbers in parentheses obtained using 15 electron RECPs, (4s4p4d) basis set, and MRSDCI method (Ref. 26).

0.26

0.24

0.22,

0.20

0.18

0.16

III 0.14 II> II> ... 0.12 -... c J: 0.10

1 0.08

0.06 W

0.04

0.02

0

-O.OZ

-0.04

-0.06 I

2.0 I

3.0 I

4.0 I

5.0 6.0 7.0 8.0

FIG. I. Potential energy curves ofBi2 in the absence of spin--orbit coupling.

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K. Balasubramanian and D. Liao: Potential energy curves of Bi2 and Bii 3067

0.0.8

006

0,04

0,02

0 I/) Q) Q)

-0,02 ... -... 0 :t: -0,0.4

1 -0,06

LaJ -0,0.8

-0..10.

-0..12

-0.,14

-0.,16 I

2.0. I

£..iW_--,t.---3

I1g (2 9 )

1~'----1C-_3L~ wt)

r-.f-h'---.LL-,3t.u (j u )

3I1gWg+)

I 3.0. 4,0.

I 5,0. o

R~A

I 6,0.

1 7,0.

FIG, 2. Potential energy curves ofBi2 including spin-orbit effects.

tion of new spectra. Consequently, we believe that this theo­retical study should shed significant light on the possible low-lying states of Bi2 .

The ground state of Biz is now experimentally estab­lished as the X I~g+ (Og+) state. Even though this state is predominantly I ~g+ even near its re , mixing with 3IIg (Og+ ) as a result of spin-orbit coupling is very significant.

The electron correlation effects were found to be very significant similar to the lighter group V trimers. This is because in the molecular region of the well, the ground elec­tronic state has a closed-shell I ~g+ symmetry, while at the dissociation limit, it forms two open shell 4S atoms. The full second-order CI (SOCI) correlating all 10 valence electrons yieldedre =2.76A,UJ. = 15Icm- l ,andDe = 1.88 eV. The previous MRSDCI26 together with 15 electron potentials and a (4s4p4d) basis yielded improved UJe of 171 cm - I, but failed to yield a better reo The experimental re of the X 0 + is

• 0 g well establIshed as 2.6596 A. Hence even the SOCI method correlating 10 electrons overestimates the re by almost 0.1 A. We believe that there are two sources of discrepancies. One has to do with the basis set especially in regards to the d polarization functions. An additional set of d polarization functions is quite likely to decrease re and increase UJe. The other factor has to do with d-correlation effects, although it is believed that d-electron correlation effects arising from the 5d 10 shells would be much smaller for Bi2 compared to other early sixth row dimers such as T12 • 29 The previous stud­ies26

•38 included 5d 10 shells in the ECPs, but did not corre­

late the d shells. Considering this, the most pro.bable so.urce

of errors in theoretical results is the basis set and the use of RECPs.

Although an accuracy o.f ± 0.02 A in re o.f ± 10 cm- I

canno.t be achieved with the treatment emplo.yed here fo.r such a heavy dimer as Bi2 , the theo.retical results give ade­quate info.rmatio.n o.n the relative trends. This is extremely useful as the co.mputed results aid in the assignment of the observed spectra and provide important insight into the na­ture of the low-lying electronic states in the observed systems and possible candidates perturbing or predissociating the ob­served bands. We estimate that the r;s of most of the elec­tro.nic states in Table III have less than 5% error and in mo.st of the cases the computed r;s are expected to' be lo.nger than experiment. The expected erro.r in vibratio.nal frequencies o.f electro.nic states o.fBi2 is 10%-15%. The co.mputed Te val­ues fo.r electronic states with Te < 18 000 cm - I are expected to' be accurate to' ± 3000 cm - I. Fo.r electro.nic states with Te > 20 000 cm - I, we expect a larger error of up to 20% mainly because spin-orbit effects could not be included for these states. However, based on the symmetry, and spectral properties of the observed states, we were able to assign al­most all observed systems.

B. Assignment of the observed spectra

1. Electronic states below 11 000 cm-1

A comprehensive summary of the observed states and our suggested assignment can be found in Table IV. Gerber and Broida8 had proposed the existence of a state that they labeled B(O) with Te = 6500 ± 1000 cm -I. Po.lak et al.28

have observed an electronic state in this regio.n in their nega­tive ion photodetachment spectra with a Te value o.f 5460 cm - I. Our calculations reveal that the first excited state of Bi2 is the 3~ u+ ( 1 u ) state with a theoretical Te of 6651 cm - I

rather close to the experimentally observed B state with Te = 5460 cm - I (previous value 6500 ± 1000 cm - I). Our computations support the assignment of the observed B state to the 1 u component rather than 0 - suggested by Gerber and Broida.8

Bondybey and English 12 as well as Effantin et al. 18 ar­gued correctly that the state labeled X' (below the X state of Bi2) first thought to be attributed to Bi2 by Gerber and Broida8 is actually due to Bi4. As seen from our co.mputa­tions, there is no electronic state below the X(O/ ) state of Bi2. Therefore the previous assignment of X to.Og+ and theX' state to' Bi4 is fully suppo.rted by o.ur calculatio.ns and all works subsequent to Bondybey and English. 12

An electronic state labeled A' ( 0 ) was observed by Gerber and Broida8 with Te = 9500 ± 2000 cm -I and UJe = 141 cm -I. The most recent negative ion photodetach­ment spectra by Polak et al. 28 place this state somewhat low­er at Te = 8220 cm - I with UJe = 132 cm - 1 (listed in Table IV). As seen from Table IV, the 3~: (Ou-) component with a theoretical Te = 10 013 cm -I is the most consistent state, although the nearby 3!l.u (2u) cannot be completely ruled o.ut. Hence, we tentatively assign theA' state to. 3~: (Ou- ). It is interesting to note that our computed 3l:.;" (lu )_3l:.;" (Ou-) splitting o.f 5100 cm -1 is somewhat

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3068 K. Balasubramanian and D. Liao: Potential energy curves of Bi2 and Bii

TABLE IV. Assignment of experimentally observed systems consistent with theoretical constants.

T,(em- ' ) al. (em-I)

State Expt. Theory Expt. Theory Footnote

x 0,+ 0 0 173 151(171) a, h B 3!,.+ (1.) 5460 (6500) 6651 134 114 a A • 3!,.+ (0.- ) 8225 11780 132 112 a,g a 3.6..(2.) 9875 12833 125 133 a,e

(12395) 123 B' '!,,+ (0,+ ) 10 826 13700 91 (106) 111 a,b b 3.6..(3u) 15246 18905 132 138 e 3n, (0,+ ) 16850 18892 143 145 d cB" 1.6..(2.) 17336 22481 145 140 d A 3!,u- (0.+ ) 17739 22300 132 140 e E 3n,(0,± ) (26505) 31815 64 75 e G I!,,+ (29609) 30855 107 88 e V'!,;; (0.+) 30172 32 b H'n,(1I) (32657) 37931 92 e [3n,(l1I) 32167 40 179 156 97 e C I!,.+ 36456 36208 155 119 e R I!,.+ (II) 53200 51657 140 105 f

• Experimental constants from Ref. 28. bThe experimental al. of 106 em -I was obtained by Effantin et al. (Ref. 18) for this state. cExperimental T. of 12395 em - I in the Ar matrix from Ref. 10. d Experimental constants in the Ar matrix from Ref. 10. e Experimental values from Ref. 44. 'Experimental constants from Ref. 15. I An earlier experimental value of 6500 ± 1000 em - I is reported in Ref. 8. hThe number in parentheses obtained using 15e REeps and a (4s4p4d) basis set (Ref. 26).

larger than the experimental value of 2760 cm - I. It should also be emphasized that the theoretical me's are consistently 15% lower than the corresponding experimental constants as expected since the theoreticalm.'s of especially excited states are likely to be in greater error as they are obtained using the FOCI/RCI (lower level) levels of theory. At pres­ent, there exists no rotational analyses of these systems to provide'e values for these states.

Polak et al.28 find an electronic state with a Te of 9870 cm - 1. As seen from Table IV, the most consistent state in this region with our computation is an electronic state which we label 3 au (2u), but it is actually a mixture oe au (2u) and lau (2u)' The spin-orbit coupling term introduces 3% 3au - I a u mixing in this state and thus lowers this state in relationship to other spin-orbit components of 3 au' We be­lieve that this state is the same as the state labeled a by Teich­man and Nixon. lo These authors recorded the absorption spectra of matrix-isolated Bi2 • The new system with origin Voo at 12 395 cm - I resulting from the X Og+ state was found to have an me of 123 cm -I by Teichman and Nixon. We do not find any u state other than 3au (2u) in this region and thus assign this to 3au (2u).

In an interesting laser-induced fluorescence study of Bi2 , Effantin et al. 18 used the ultraviolet lines of both Ar + and Kr+ lasers to observe a new system of Biz. They assign this to VO: -X I~g+. They found that the VOu+ state radi­ates to yet another new state labeled B ' Og+ . Effantin et af. assigned the B ' Og+ to the ot component of the S~g+ state dissociating into 4S + 4S ground state Bi atoms (see Table I).

Effantin et al. 18 placed the B' Og+ state with an me of 106 cm -I at 10 826 cm -I above the xot state. Polak et al. 28

also find a system in their negative detachment spectra at­tributed to an electronic state with Te = 10 820 cm - I and me =91 cm- I

.

As seen from Table IV, our computation evidently sup­ports the existence of 5~g+ (ot) with a theoretical Te = 13 700 cm - I and me = 111 cm - I. The smaller me is consistent with the computed longer re (see Table III). We will discuss the nature of the VO u+ state subsequently, but although the B' ot state is predominantly 5~t (ot ), it is contaminated significantly by 3~g- (ot).

2. Electronic states in the 15000-30000 cm-' region

Teichman and Nixon lO found in the Ar matrix an elec­tronic state labeled b with Voo = 15246 cm - I attributed to Bi2 in absorption from the X Og+ state. The most consistent electronic state with our computations is the 3au (3u) state which is computed theoretically to have a Te of 18905 cm - I. Considering that our computed Te's are consistently higher than experimental values, we are inclined to argue that this system is due to the forbidden 3a" (3" )-X(ot) transition. Indeed, Teichman and Nixon find that the ab­sorption systems resulting from the new states are all weak and have speculated that these are due to possibly forbidden electronic transitions. Polak et al. 28 also appear to find some bands in this region, but no definitive analyses could be made as there appears to be more than one state in this region.

An electronic state with an approximate experimental

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K. Balasubramanian and D. Liao: Potential energy curves of Bi2 and Bii 3069

T~ of 16 850 cm -I deduced from the negative ion photode­tachment spectra ofBi2 28 appears to be most consistent with the 3ITg (Og+ ) state that we compute. Our computed con­stants of this state support the assignment of this system of 3Dg(Og+ ).

Teichman and Nixon lO find an electronic state which they label c. This state is attributed to the third absorption system below the well characterized A (Ou+ )-X(Og+ ) system. The origin band of this system in the Ar matrix appears to be at 17 336 cm - I with an CtJe of 145 cm - I. Effantin et al. 18

label the same state B 1/ and speculate that this state should be of u symmetry. As seen from Table IV, we indeed find I ~u (2u ) with a theoretically computed Te of 22 481 cm - I. The observed state most consistent with this value is the I ~u (2u ) state. It should be mentioned that 3 ~u (1 u ) is raised relative to J~u since the 3,£u+ (lu) is lowered relative to 3,£u+

due to spin-orbit mixing of 3,£u+ Ou) and 3Llu (1u)' This means that the 3 Llu ( 1 u ) component could be in this region, although we could not compute this state since it is a higher root. Consequently, the B 1/ (c) state is either 3 Llu (1 u) or I Llu (2u ), although the forbidden nature of the ILlu (2u )-X(Og+ ) transition is consistent with the weak c-x bands observed by Teichman and Nixon.

The experimentally most studied system ofBi2 is the A­X system. The rotational analysis of the A-X system has now been made by Gerber et al. 8,9 All experimental studies assign the A state to a Ou+ state of Bi2. As seen from Table IV, our computations reveal that the A state is the 0: component of 3,£u- • Evidently, the theoretical Te is too high mainly be­cause the spin-orbit coupling could not be included in the computed properties of this state. Nevertheless, our comput­ed r. of the 3,£; state, viz., 2.87 A is in remarkable accord with the experimental value of 2.863 A obtained from the rotational analysis. Our computed CtJe of 140 cm - I for the 3,£u- (Ou+ ) state is also in reasonable agreement with the ex­perimental value of 165 cm - I. The A state is unambiguously assigned to the 3,£u- (0: ) state.

Gerber and Broida8 have observed a new doublet photo­luminescence system labeled the E-B system. The B state is the 3,£u+ (1 u) component in Table IV. This means that the E state is of g symmetry. The experimental CtJ e of the E state is 63.5 cm - I and the deduced Te value is 26 505 cm - I. As seen from Table IV, the most consistent state with the E state is an excited 3Dg (Og±). We are not sure if it is Og+ or 0; since both can radiate to the 3,£: ( 1 u ) state. Our computed Te of 31 815 cm - I in the absence of spin-orbit coupling could be lowered further when spin-orbit effects are included. The small theoretical CtJe of75 cm - I supports the assignment of E to this 3D, state.

Gerber, Sakuri, and Broida9 observed weak photolumi­nescence attributed to an N-G system, wherein the lower G state was believed by these authors to be the same as the one participating in the G-A system observed by Reddy and Ali.4 The constants of the G state deduced by Gerber et al.9

were similar to those of Reddy and Ali.4 This suggests that the G state should be of g symmetry. An approximate Te value of 26 505 cm - I was deduced for the G state.

As seen from Table IV, the most consistent state with

the G state is an excited l'£g+ state. Our computed Te

(30 855 cm - I) is only a bit larger than the experiment. Further, the theoretical CtJe also seems to support this assign­ment, although we consider this only a tentative assignment.

3. States with Te >30 000 cm-' Effantin et al. 18 observed a new electronic transition

which they labeled VO u+ -B I Og+ system. The B I state as­signed to S~g+ (ot) was discussed before. The VO u+ state needs to be assigned. We found a s~u+ state dissociating into 4S + 2D. This state although very shallow and predominant­ly repulsive in the absence of spin-orbit coupling, may form a long-range minimum upon introduction of spin-orbit cou­pling via mixing with a I,£u+ (0: ) near this state as well as 3,£; (0: ). The fact that the CtJe deduced experimentally by Effantin et al. 18 is only 32 cm - I is consistent with the shal­low nature of the s'£u+ state deduced from our computation. Furthermore, the s,£: _S'£t transition is strongly allowed, which would explain the origin of the V-B experimental sys­tem.

Reddy and Ali4 have observed an emission system which they call the H .... A system. The A state is the well­characterized 3~u- (Ou+ ) state. This suggests that the H state should be of g symmetry. We indeed find a IDg (II) state (i.e., the second excited state of IITg symmetry with a theo­retical Te of 37 931 cm - I). Reddy and Ali could observe only the v' = 0 state of the H state and thus there exists no experimental CtJ e for the H state. Weare tempted to assign the H state to IDg (II), but our assignment will be more defini­tive if further experimental studies will yield the re and CtJe of the H state in question.

Reddy and Ali4 also observe another emission system with the band origin Voo = 15487 cm - I terminating to the A (Ou+ ) state designated as the I -.A system. Experimental Te = 33 217 cm- I andCtJe = l56.4cm -I have been deduced for the I state. We find a 3Dg (III) state with a computed Te = 40 179 cm - I most consistent with this state. Again, the theoretical constants do not include the spin-orbit ef­fects for the IDg (II) state which could alter the Te by 7000 cm - I. The theoretical CtJe is, however, too small compared to an experimental value of 156 cm - 1. While it is evident that the I state must be a g state, our assignment of I to I ITg (III) is very tentative. The ot or Ig components arising from the 3~; state dissociating into BieD) + BieD) could certain­ly be more strongly bound and can be a potential candidate for the I state.

Damany et al. ls observed five new systems in the 160-230 nm region. One of these corresponds to the same C <- X absorption spectrum studied by Almy and Sparks I in the earlier part of this century. The C state has well-character­ized spectroscopic constants of Te = 36 456 cm - I and CtJe = 155cm- l

• We find a 1,£: electronicstateofBi2 with a theoretical Te of 36 208 cm - I. Weare not too surprised by the fortuitious agreement with the experimental Te since the spin-orbit effect on Te for this state appears to be similar to the ground state effectively canceling the effect on Te' Our computed (t) e trend is also consistent with the trend for other

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3070 K. Balasubramanian and D. Liao: Potential energy curves of Bi2 and Bii

electronic states. There exists a I IT u (II) state with a comput­ed Te of38 OOOcm - 1, but with a rather small CUe = 71 cm -I. Since the experimental estate's CUe is almost twice this value, we argue that the C state should be assigned to the 12.u+ state supporting strongly allowed C 12.u+ -X 12.g+ (ot ) emission. This appears to be akin to the A 12.u+ -X 12.g+ systems of AS2 which occurs in the 40 350 cm - I region. 39

Damany et al. ls have observed a number of electronic states of Bi2 in the 46 500-59 700 cm - I region which they label F, Q, R, S, and T, respectively. All these states are attributed to the Rydberg states ofBi2 dissociating into Ryd­berg states of the Bi atom. Our FOCI method and basis sets are not expected to be completely adequate for the computa­tion of Rydberg states. Yet we find a 12.u+ (II) state with re = 3.33 A, CUe = 140 cm -I, and Te = 51657 cm -I. This state appears to be consistent with the R state of Damany et al., although their re = 2.96 A is considerably shorter. How­ever, we are not surprised by such a difference for a state with Te - 52 000 cm - I since as mentioned before the basis set is not adequate for these states.

C. Dissociation energy of Bi2

Rovner et al. 3 as well as Kohl et al. Z have deduced the D g value of Biz as 2.03 eV from the mass spectrum assuming a 12. ground state. If this value is corrected for the zero-point energy, one gets' a De of2.05 eV.

Ehret and Gerber24 have employed double resonance polarization spectroscopy to investigate the excited elec­tronic states of Biz. One of the obtained spectral systems (with two-step excitation) converges to the dissociation lim­it of a new electronic state. From this, these authors deduced the ground stateD. ofBi2 to be 16 778 ± 5 cm -I or 2.08 eV. This value is very close to the value deduced from the mass spectra.

Our CASSCF/SOCI/RCI De of Biz is 1.88 eV. This value is evidently lower than the established experimental results. It is clear that the addition of one more set of d polar­ization functions and further extension of the sand p basis sets could improve the De. The present value of 1.88 eV is, however, improved considerably compared to a previous theoretical value26 of 1.38 eV mainly because the present calculation includes a full second-order configuration inter­action of all 10 valence electrons.

D. Predissociations

Ehret and Gerber10•21 have studied the A-X system ex­

tensively. They find that the lifetimes of the vibrational lev­els (v = 1-34) of the A state varied between 50 and 600 ns. The transition moment of the A-X stysem was obtained as 1.4 ± 0.4 D.

As seen from Fig. 1, the A 32.u- curve crosses the 32.u+ (II) curve dissociating to 4S + zD. Likewise, the 72.u+ repulsive curve dissociating to the ground state 4S + 4S atoms crosses the A 32.u-' The crossing of 32.u+ (II) with A 32.'; occurs at - 3.75 A, while the crossing of the 7~u+ state occurs at - 3.35 A. Consequently, the crossing of the repulsive 7~u+ curve occurs prior to 32.u+ (II) and would be a

more decisive state in the predissociation to the ground state atoms.

According to Herzberg,4O the selection rule for case (c) predissociation is g"""+g, u"""+u, An = 0, ± 1. Since the state in question is a 32.u- (Ou+ ) state, only u states could predisso­ciate this state. Consequently, the repulsive 72.u+ state is the most attractive candidate for the predissociation. This state yields Ou-' lu, 2u, and 3u spin-orbit components. Among them the 72. u+ ( 1 u) state is the most consistent state for pre­dissociation.

The crossing of 72.u+ (lu) withA 32.u- (Ou+ ) is estimated to occur at -3.3 A. Consequently, only those vibrational levels of the A 32.u- (Ou+ ) with classical turning points below -3.3 A could be observed in the A-X system. Our predicted curve crossing of 72.u+ (lu) with 32.'; (Ou+ ) explains nicely why the observed transition moment of the A-X system does not change much for internuclear distances between 2.6 and 3.3 A and then changes sharply. The crossing of 72.u+ (lu)

with A 32.u- (Ou+ ) at - 3.3 A will cut offall vibrational levels above this curve crossing. Furthermore, the crossing of re­pulsive 72.u+ with 32.u- and other states will induce an avoid­ed crossing of the corresponding lu spin-orbit components. As seen from Fig. 1, there is no repulsive curve crossing between 2.6 and 3.3 A in the A 32.u- curve.

The 72.: state also crosses the 3 Au, 12.'; , 1 Au, 12.u+ , and a few other u states. Consequently, these states will also be predissociated. On the other hand, the crossing of the repul­sive 32.u+ (II) state would have little impact on predissocia­tion since it crosses most of these curves at longer internu­clear distances. Thus we conclude that the observed predissociation in the A-X system is due to the predissocia­tion of32.u- (Ou+ ) by 72. u+ (1u)' This also explains the depen­dence of the lifetimes ofthe A state on the v quantum number and transition moment invariance between 2.6 and 3.3 A observed by Ehret and Gerber.

E. Spectroscopic properties of Bii

1. Constants and potential energy curves

Figure 3 shows the potential energy curves ofBi2- , while Table V shows the spectroscopic constants of Biz- . The most favored orbital for the attachment of an electron to Biz is the lowest unoccupied molecular orbital (LUMO) which is the 1T'g orbital of Biz . Hence the ground state of Biz- is predicted to be a 2Ug state in the absence of spin-orbit coupling.

As evidenced from Table V and Fig. 3, the spin-orbit coupling is very significant for Bi2- • It splits the 2ITg state into 0/2)g and (3/2)g spin-orbit components. The ( 112) g-( 3/2) g splitting of Bi2- is 8500 cm - I as seen from Table V. The mixing of zITg (112) with 42.g- (112) and 22.t (112) was found to be significant. Likewise the 2Ug (3/2) mixes heavily with the 42.g- (3/2) state.

The attachment of an electron to the unoccupied 20' u

antibonding orbital of neutral Bi2 results in the 22.u+ state. As seen from Fig. 3 and Table V, this state forms only a shallow minimum. This state lies 19 700 cm - I above the 2ITg ( 112) ground state of Bi2- •

There are two excited zITg states of Bi2- as well as a

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K. Balasubramanian and D. Liao: Potential energy curves of Bi2 and Bii 3071

028

0.24 Bi;

0.20

..... 0,16 en GI CD ...

0,12 -... c ::I:

0,08

r 2ng(II)

0,04

w ° ~:,:,

-0.04 n g ('2Q)

-0,08 :::1I,(-i" -0,12

j I I I I 2.0 3.0 4.0 5.0 6.0

0

R~A

FIG. 3. Potential energy curves of low-lying states of Bi2- .

2'J.U+ (II) state with a Te = 34300 cm- I. However, these

states cannot be populated in the negative ion generation as they are well above the ground state. In any case, they are rather weakly bound and would undergo autodetachment.

2. Electron affinity of 812

At the CASSCF and FOCI levels of theories, the 2Ilg state of Bi2- lies above the Il:g+ ground state. Only a full second-order CI (SOCI) theory stabilizes the 2Ilg state of Bi2- relative to Bi2, indicating the significance of electron correlation effects in the computation of electron affinities of clusters.

The spin-orbit effect has an important role in the deter­mination of the electron affinity. The 2IIg (1/2) state of Bi2-is much more stabilized by spin-orbit coupling than the X ground state of Bi2 due to its open-shell character. While there is spin-orbit stabilization of the Og+ state of Bi2 through the mixing ofll:g+ with 3IIg, this stabilization is less than the 2IIg ( 1/2) lowering of Bi2- due to spin-orbit cou-

TABLE V. Spectroscopic properties of Bi2- . a

State R, (A) Te (em-I) We (em -I)

2n,{1.) 2.83 - 5 200 144 2n,{h) 2.78 3306 151 2:I.+ 3.58 14524 70 2n, (II) 3.48 22060 107 2n,(I1I) 3.54 24735 104 2:I: (II) 3.70 29131 87

• All To's relative to the 0; ground state of Bi2 •

piing. Consequently, spin-orbit effects increase the electron affinity of Bi2 .

Our final computed electron affinity of Bi2 is 5200 cm - I. Polak et al.28 have recently measured the electron affinity ofBi2 from their photodetachment spectra as 10 250 cm -I. Consequently, our computation underestimates the electron affinity of Bi2 too much, as we expected. The main source of error is the basis set limitation. It is necessary to have a much larger basis set augmented with at least two more sets of d polarization functions for the accurate compu­tation of electron affinity. Nevertheless, these computations shed significant light on the nature of the ground state ofBi2-in relation to the neutral X(ot ) state ofBi2.

IV. THE NATURE OF ELECTRONIC STATES OF Bi2 AND Bi2"

Since spin-orbit coupling of the Bi atom is very large, it would be interesting to analyze the mixing of various states ofBi2 which would otherwise not mix in the absence of spin­orbit coupling. Table VI shows the composition of the low­lying spin-orbit states of Bi2 and Bi2- . As seen from Table VI, even the predominantly closed-shell 1 'J.t ground state of Bi2 is contaminated heavily by 3IIg (ot) (19%). In the lu component of3'J.: , the mixing with 3~u (lu) is quite signifi­cant. This has the effect of lowering the I u component of 3l: u+ . The Ou- component of the 3l: u+ state is relatively pure (mixing with I l:,; is less than 1%).

The second ot state [Og+ (II)] exhibits an interesting behavior as a function of internuclear distance. Near the r. of the XOg+ state, the Og+ (II) state is predominantly 3IIg (Og+ ), although as seen from Table VI, mixing with the ll:t ground states 5l:t (Og+) and 3l:; (Og+) is significant. At 3.2 A (near its r.), the Og+ (II) state is almost purely sl:t (Og+). This suggests an avoided crossing of the 3IIg (ot ) and sl:g+ (Og+ ) components.

The ot (III) state is influenced considerably by the avoided crossing of 3IIg (ot ) with 5l:t (Og+ ). At 2.6 A, the Og+ (III) state is purely sl:g+ (ot ), while at 2.8 A, it be­comes 58% 3IIg, 8% 1 l:t ,6% 3l:; ,and 5% sl:g+ . At longer

TABLE VI. The RCI compositions of n states of Bi2 and Bi; .'

State

0+ g

3l:: Ou)

3l:: (0.- ) 3au (2u)

Og+ (II) at its R.

ot (II) at 2.6 A Og+ (Ill) 2.6 A Og+ (III) 2.8 A ot (III) 3.0 A Ig 3.25 A 3l:; (O:)

l/2g 3/2g

Compositions

65% Il:g+. 16.5% 3lIg 66% 3l:u+. 20% 3au

80% 3l::. 0.6% Il:u-81% 3au • 3% lau

90% ':It (Og+ ). 11 % Il:g+ • 60% 3lIg• 10% 'l:g+ • 6% 3l:g-88% 'l:g+ (Og+ )

58% 3ng• 8% l:Ig+. 6% 3l:; .5% ':It 43% 3lIg• 12% 'l:t. 1% Il:t. 5% 3l:g-76% ':It. 18% ':Ig-. 0.5% 'ng 90% 3:I; 76% 2ng• 7% 4:I; • 5% 2l:g+ 65% 2ng• 14% 4:I;. 8% 2Ag

'States with odd n quantum numbers correspond to Bi2- •

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3072 K. Balasubramanian and D. Liao: Potential energy curves of Bi2 and Bii

distances, the mixing of3n, (Og+ ) with other states becomes significant.

The 19 (I) state is 76% 5~g+ (1g), 18% 3~g- (1g) at its reo Contrary to the Og+ (II) state, we do not find avoided crossing of3n g (1g) with 5~g+ (1g) mainly because 3ng (1g) is raised relatively to 3ng. Similarly, 5~t (2g )_3ng (2g) mixing is not significant. The 3~: (0: ) state was found to be relatively purer near its reo

As seen from Table VI, the 1I2g ground state of Bi2- is 76% 2ng(1I2)g, 7% 4~g- (112), and 5% 2~g+ (112). Like­wise the (3/2)g state is 65% 2ng(3/2), 14% 4~8-' and 8% 2ag(3/2). Consequently, it is concluded that most of the electronic states ofBi2 and Bi2- are contaminated heavily by spin-orbit coupling.

Table VII shows the composition of the electronic states ofBi2 in the absence of spin -orbit coupling. This table gives insight into the importance of various configurations consti­tuting the electronic states of Bi2. This table also contains useful information on several excited states ofBi2 for which spectroscopic constants are shown in the absence of spin­orbit coupling. As seen from Table VII, the I ~/ state ofBi2 is 70% 10:20: 10: l1r! and 19% 10:20: 10: l~ In;. Clearly a double excitation from 1Tu to 1Tg is more important than a double excitation from 2ug to 2uu near reo

The 5~g+ , 3 au, 3~u- , I au states are relatively simpler in

that leading configuration(s) make up more than 80% con­tribution. The upper roots of 1~8+ symmetry as well as 3ng, I~g+, 3au (II), and lau (III) are significantly more complex as seen from Table VII.

Table VIII shows the leading configurations of the elec­tronic states of Bi; in the absence of spin-orbit coupling. The 2ng ground state is a 76%-12% mixture of 10: 10: 20; 11T! 11T g and 10;20; 1 0: ~ ~ at the FOCI level. This illustrates the significance of electron correlation ef­fects from a multireference list of configurations. Likewise the excited states of Bi2- are even more complex, although most of these states have only shallow minima.

It is interesting to compare Bi2 with its lighter analogs, namely Sb2

41 and AS2 .39 The previous study by Balasubra­manian and Li41 on Sb2 reveals that the X 0,+ ground state of Sb2 is composed of 82% I~g+ (20: 11T!), 12% I~,+ (20;1~10;), and 2% 3ng (2ug11T!11Tg). This evidently demonstrates that spin-orbit coupling is dramatically larger for Bi2 compared to Sb2. Likewise the contamination of 3 au (1 u ) in the 1 u state is only 3% for Sb2 compared to 20% for Bi2.

A critical comparison of the Mulliken populations of the electronic states ofBi2 and Sb2 reveals that the 6s shell is nearly complete in Bi2, while the 6s popUlation is 1.87 for Sb2. This is a consequence of the relativistic mass-velocity

TABLE VII. Leading configurations in the FOCI wave functions for some states of Bi2 .

State

'~6+ (II) 3~.-

'A. 'II. I~.-

3A. (II)

I~t (III)

3II. (II)

'A. (III)

Configuration and weight

70% lo!2o!l~n-Z.19% lo!2o!l~In;I~ 72% lo!2o!l~1T!tr!, 14% lo!2o!l~~1T~,2% lo!2u!I~2u~1T! 90% lo!2~1~n;~, 3% lo!2u!I~2~1T!tr! 94% lo!2u!1~2~n;~ 80% lo!2~1~1T!tr!, 8% lo!2o!l~~1T~ 76% lo!2u!I~1T!1T!, 11% lo!2u!I~~~, 2% lo!2o!l~2~n;1T~. 1% lo!2o!lu~n;tr! 61% lo!2~1~n-Z. 26% lo!2o!l~n;~ 83% 1~2~1~1T~tr!, 7% 1~2o!l~~1T~ 87% lo!2o!l~1T!tr!, 9% lo!2o!l~~1T~ 79% lo!2u!I~1T!1T!, 10% lo!2u!I~~~ 87% lo!2o!l~1T!tr!, 2% lo!2o!l~~1T~ 42% lo!2u!I~2~n;~. 34% lo!2u!I~2u~1T! 8% lo!2o!l~1T!tr!, 7% lo!2u!1~2u~~ 90% lo!2o!l~n;~ 45% lo!2~1~2u~tr!, 20% lo!2o!l~2u~n;1T~, 14% lo!2u!I~1T!1T!, 5% 1~2u!I~2~1T!~, 3% lo!2u!1~~~, 2% lo!2u!I~2~~, 1% lo!2u!I~~~ 48% lo!2o!l~1T!tr!. 22% lo!2u!I~2u~~. 19% lo!2o!l~~1T~, 1% lo!2u!I~2u~n-: 71% lo!2o!l~2u~tr!, 13% lo!2o!l~2u~n;1T~, 2% 1~2u!1~1T!n-Z. 1% lo!2o!l~2u~3~n;, 1% lo!2u!1~2~1T!~ 48% lo!2u!I~~~, 12% 1~2o!l~2u~n;1T~, 12% 1~2~lu~n;tr!, 10% lo!2oil~1T!~, 5% lo!2o!l~2~tr!, 3% lo!2u!I~2~1T!~ 38% lo!2o!l~~1T~, 29% lo!2u!I~2u~n;~. 11% 1~2~1~1T!tr!, 4% lo!l~~tr!. 3% lo!2o!l~2~1T!1T~ 52% loi2o!l~~1T~.15% loi2o!~tr!. 15% lo!2u!I~2u~n;~. 3% loi2o!l~2~1T!1T~. 3% lo!l~2~1T!tr! 72% lo!2oil~~1T~. 15% loi2u!1~2~n;~, 3% 1~2o!lo!1T!tr!

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K. Balasubramanian and D. Liao: Potential energy curves of Bi2 and Bii 3073

TABLE YIII. Leading configurations in the FOCI wave functions for some states of Bi2- •

State Configuration and weight

2n. 2'I..+ ~n.(II)

'n.(lII)

76% 10;20;IO:1T~1T~, 12% 10;20;IO:~~, 2% 10;2q~lo:2q~n;~ 64% 10;20;1o:2q~ 1T!, 23% 10;20; lo:2q~ n;~, 2% 10;20;1o:2q~ 1T~ 78% 10;20;Io:~~, 5% 10;2q~lo:2q~n;~, 4% 10;20;IO:1T~1T~ 83% 10;20;1o:~~, 3% 10;2q~1<Tu2q~n;~, 2% la;2(T~1<Tu2(T~~~

stabilization of the 6~ shell which makes the 6.? shell "inert" for Bi2.

The 3I.u+ (1 u )-X(Og+ ) separation is 8760 cm - 1 for Sb2 ,

while it is 6650 cm - 1 for Bi2 • The corresponding 3I.u+ -X( lI.g+) theoretical separation for AS2 is 14500 em - I, while the experimental c 3I.; -x lI.t separation is 11 860 cm - I. Hence this separation decreases as one goes down the group.

The 3I.u+ (1u )_3l:u+ (0;) separation of 5129 cm -I is dramatically larger than the corresponding separation of only 120 cm - 1 for Sb2 • Hence it is evident that relativistic effects are dramatically larger for Biz compared to Sb2 • It is interesting to note the 3~u+ ( 1 u )_3~u+ (Ou-) separation of Bi2 (5129 cm - I) is similar to the 3~g- (ot )_3l:g- Og) sepa­ration of 4150 cm - 1 for Pb2 • 42 The corresponding experi­mental value is known to be .,;;5500 cm - 1.43

The 3~u- (Ou+ )-XOg+ separations for As2 , Sb2 , and Bi2 are 24640, 19068, and 17 739 cm - I, respectively. This trend is consistent with the 3~u+ -X 0/ energy separation. Hence we conclude that in general the energy separations of excited states of group V dimers decrease as one goes down the group in the absence of spin-orbit coupling.

V. CONCLUSION

In this study CASSCF IFOCI/SOCI/RCI calculations which included up to 304 000 configurations were made on Bi2 and Bi2-. We found 26 bound electronic states for Bi2 with Te < 50 000 cm - I. Our computations facilitated the as­signment of some 16 observed spectroscopic systems of Bi2 including the most recent photodetachment spectra. Our computations reveal the existence of at least six bound states for Bi2 of which the 2IIg ( 1/2) state is the ground state. The computed potential energy curves of Bi2 explained the pre­viously observed predissociation of the well-studied A-X system ofBi2. The crossing of the repulsive 7l:; state disso­ciating to the ground state atoms with theA 3l:; (0; ) curve explained the observed lifetimes and predissociations. Simi­lar predissociations for other states were predicted.

ACKNOWLEDGMENT

This research was supported in part by the National Science Foundation through Grant No. CHE8818869.

1 G. M. Alrny and I. M. Sparks, Phys. Rev. 44, 365 (1933). 2 E. J. Kohl, O. M. Oscarard, and K. D. Carlson, J. Chern. Phys. 47, 2667

(1967).

3 L. H. Rovner, A. Drowart, and J. Drowart, Trans. Faraday Soc. 63, 2906 (1967).

4S. P. Reddy and M. K. Ali, J. Mol. Spectrosc. 35, 285 (1970). ~T. V. Rao and S. V. J. Lakshrnan, Indian J. Pure Appl. Phys. 8, 785

(1970). 60. P. Strauz, J. Connor, and P. J. Young, J. Am. Chern. Soc. 93, 822

(1971). 7 J. Singh, P. R. Naer, and D. K. Rai, Spectrosc. Lett. 4,313 (1971). 8G. Gerber and H. P. Broida, J. Chern. Phys. 64, 3423 (1976). 9G. Gerber, K. Sakuri, and H. P. Broida, J. Chern. Phys. 64,3410 (1976). lOR. A. Teichman III and E. R. Nixon, J. Chern. Phys. 67, 2470 (1977). II Y. E. Bondybey, G. P. Schwartz, J. E. Griffiths, and J. H. English, Chern.

Phys. Lett. 76, 30 (1980). l2V. E. Bondybey and J. H. English, J. Chern. Phys. 73, 42 (1980). 13 K. Manzel, V. Engelhardt, H. Abe, W. Schulze, and F. W. Froben, Chern.

Phys. Lett. 77,514 (1981). 14F. Ahmed and E. R. Nixon, J. Chern. Phys. 74, 2156 (1981). "N. Darnany, J. Figuet, and A. Topouzkhanian, Chern. Phys. 63, 157

(1981 ). 16G. Fabre, J. P. Baci, C. Athenour, R. Stringat, and P. F. Bernath, Can. J.

Phys. 60, 73 (1982). 17 G. Gerber, H. Hoenninger, and J. James, Chern. Phys. Lett. 85, 415

(1982). 18C. Etrantin, A. Topouzkhanian, J. Figuet, J. D'lncan, R. F. Barrow, and

J. Verger, J. Phys. B 15, 3829 (1982). 19S. Drosch and G. Gerber, J. Chern. Phys. 77,123 (1982). 20G. Ehret and G. Gerber, Chern. Phys. 66, 27 (1982). 21 G. Ehret and G. Gerber, Opt. Cornrnun. 51,145 (1984). 22B. Eberle, H. Sontag, and R. Weber, Chern. Phys. 92, 417 (1985). 23B. Eberle, H. Sontag, and R. Weber, Surf. Sci. 156,751 (1985). 24G. Ehret and G. Gerber, Springer Ser. Opt. Sci. 49, 140 (1985). 25 J. H. Glownia, J. A. Misewich, and P. P. Sorokin, J. Chern. Phys. 92,3375

(1990). 26L. S. Wang, Y. T. Lee,D. A. Shirley,K. Balasubrarnanian, and P. Feng,J.

Chern. Phys. 93, 6310 (1990). 27K. Balasubrarnanian, Chern. Rev. 90, 93 (1990). 28M. Polak, J. Ho, G. Gerber, and W. C. Lineberger, J. Chern. Phys. 95,

3053 (1991). 29K. S. Pitzer, Int. J. Quantum Chern. 25,131 (1984); P. A. Christiansen

and K. S. Pitzer, J. Chern. Phys. 74, 1162 (1981); P. Christiansen, ibid. 79,2928 (1983).

JOE. H. Fink, K. D. Setzer, D. A. Ramsay, and M. Vervloet, Chern. Phys. Lett. (in press).

31 R. B. Ross, J. M. Powers, T. Atashroo, W. C. Ermler, L. A. LaJohn, and P. A. Christiansen, J. Chern. Phys. 93, 6654 (1980).

32 P. J. Hay and W. R. Wadt, J. Chern. Phys. 82, 299 (1985). 33K. Balasubrarnanian, Chern. Phys. Lett. 127, 5851 (1986). 34 The major authors of ALCHEMY II are B. Liu, B. Lengsfield, and M. Yoshi-

mine. 35 R. M. Pitzer, ARGOS codes. 36R. M. Pitzer and N. Winter, J. Phys. Chern. 92, 3061 (1988). 37K. Balasubrarnanian, J. Chern. Phys. 89,5731 (1987). 38 P. A. Christiansen, Chern. Phys. Lett. 109, 145 (1984). 39 K. Ba1asubrarnanian, J. Mol. Spectrosc. 121, 465 (1987). 4OG. Herzberg, Spectra of Diatomic Molecules (Van Nostrand-Reinhold,

Princeton, 1950). 41 K. Balasubrarnanian and J. Q. Li, J. Mol. Spectrosc. 135, 169 (1989). 42 K. S. Pitzer and K. Balasubrarnanian, J. Phys. Chern. 86, 3068 (1982). 43y. E. Bondybey and J. H. English, J. Chern. Phys. 76, 2165 (1982). 44K. P. Huber and G. Herzberg, Constants of Diatomic Molecules (Yan

Nostrand-Reinhold, New York, 1979).

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