Volume 117, number 4 CHEMICAL PHYSiCS Llt?I-lxRs 21June1985

AB INlTlo POTENTIA L CURVES AND EL.ECl-RONIC TRANSITION MOMENTS OF CS-”

Received 27 Mar& 1985

The complete acuve space SCF (CA.5 SCF) and contracted CI melhods have been used LO calculate potential energy curves and speclrosmpic constants for the X 2Ze, A211 and B2Z’ states of CS+ The CAS SCF wavehnctions were ah used LO calculate non-orthogonal electronic tratxitior. moments for the A-X, B-X and B-A transitions The calculated Wtion moments were used lo obtain radiative lifetimes of the A and B sLaLes and oscillator OLC~@IS of the astrophykaIIy inlereslmg A-X transition The calculated kfetimc for the B state is non in saCsfa%xy agccemen~ wirh the experimental result and tic r-n for this is dim. No cxpcrimtmtai results for the A stale are availabfe for comparison

1. Introduction

The CS+ ion has recently been tentatively identi-

fied in the diffuse interstellar clouds located III front of 5 Oph and S Sco by Fe&t et al_ [l] on the basis of an absorption feature detected near 6700 Ail. Simula- tions showed that this feature was probably the (3,0) band of the CS+.A2rIli11n-X *Z+transition. Several laboratory experiments on CS+ have been czried out in recent years_ Bands from the A 211-X 2Z,c+ transi- tion appearing in the red region (6000-8000 A) were analysed rotationally by Gauyacq and Honmi [Z] in the only work so far to achieve rotational resolution on CS*. The B 2IZ-X 211* transition in the region 2400-3400 W was observed and analysed vibrationaliy by Tsujl et al. [3,4] _ The presence of the B 22+-A 2iI transition in the unidentified group of emission bands in the 38004200 A region when CS2 is excited by He(2 3S) metastables [S] or bombarded with eiectrons at low pressure [2] has been the subject of some con- troversy. ~~0~~ works by Wu and Yen&a [6] and Tsuji et al. [4,7] now seem to have established the identification of the B-A transition, no band having the B 2Z+ state as the upper state has been rotationally analfled. Gauyacq and Horani [2] noted that B-A bands are Very complex, probably ‘due to perhuba- tions in the B and A states.

5ar1 and Larsson [8] measured the B 2IZ+ state

lifetime to be 425 ns with the high-frequency deflec- tion technique Obase et al. [9] derived the variation with internuclear distance of the electronic transition

moment of the B-X and B-A transitions from err&- &on data obtained from metastable reactions. The electromc transition moment of the A 2KI-X 2IZt transit&x has not been investigated-

The photoelectron spectrum of CS has been inves- tigated by several groups [lo--131 and interpreted with the help of theoretical calculations [13-l 5]_ It

was shown that the B 2Z‘c state corresponds to the well-known C 2ZF shake-up state of CO+ and lU$_ The calculations dealt only with vertical ionization ener- pies. No calculations of the full CS+ potential curves have hitherto been pubhshed.

In the present work we used the complete active spaoe SCF (CAS SCF} [16] and the contracted CI [17] methods to calculate th&X 2Z+, A 211 and B 2Z+ state potential curves. The CAS SCF wavefunctions were also used to generate the A-X, B-X and B-A electronic transition moments for a number of inter- nuclear distances. The most important aim of the presezi:rrt work is to provide data of astrophysical un- portance (tie A-X oscillator strength) and to go& knowledge about the experimentally elusive B state.

0 009-2614/85/S 03.30 0 Elsevier ScienceVPubli&ers B.V. (North-Holland Physics Pub-g Division)

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Volume 117. number 4 CHEMXXLi PHYSICS LETTERS 21 June 1985

2. Computatioti details

The Gausstan-type basis set used for sulphur was a modified version of the set given by Veillard [18] in contraction scheme number eight. The two most dif- fuse s functions were replaced by four with exponents 0.653,0.293,0_135 and 0.04. Like-e the two most diffuse p fiction were replaced by four with expo- nents 1 0,0.417,0.174 and 0.04. Contrary to scheme number eight, the last functions were not contracted. Four d functions with exponents 2.7, 1.1,0.4 and O-15 were added to the s,p basis set and the sulphur basis set IS #us [14s,lOp$d] contracted to (&,6p,4d). For carbon the Dunning-Huzinaga [19,20] lOs,6p basis set contracted to Ss,4p was extended by replacing the last two s exponents by three and the last three p exponents by four. The new exponents were for s, 060,O 25 and 0.10 and for p, 0.65,0.35,0.15 and 0.05. Two d functions were used with exponents 1 .O and 03. The total number of basis functions is 77 and the total SCF energy for the CS molecule at R = 2.80 au is 435333270 hartree. The CAS SCF method in a Newton-Raphson formulation 1161 was used in the first step of the calculations. The lo(1 ss), 2u(ls& 3u(2s& 40(2ps) and ln(2pS) orbit& were inactive (i.e. optimized but doubly occupied in all configura- tions) in the calcu*Mions on the X 2Z* state. The va- lence orbit& So, 60,7a, 80,2rr and 37r were used as active orbit&, i e. orbit& with occupation varying between zero and two. When nine valence electrons were distnbuted in all possible ways into these orbit& in Czv symmetry, the CAS SCF expansions comprised 616 and 588 confprations for the ZZ and lL symme- tries respectively. In order to make possrble the evalua- tion of non-orthogonal electronic transition moments between the X, A and B states according to the proce- dure described by Larsson et al. 1213, the core orbit& for the A and B states were frozen to the X state or- bitak in the CAS SCF calculations.

In the second step highly correlated wavefunctions were constructed with the multireference contracted CI method [ 171 in order to improve the potent& curves_ The reference states were chosen on the basis of theu weights along the full potential curves in the preceding CAS SCF calculation- Configurations with a coefficient larger than 4.07 for the X state and x0.10 for the A and B states anywhere along the curves were mcluded in the set of reference states.

332

This procedure quahfied 11 configurations as refer- ence confgurations for the X and B states and 13 for the A state. The CI expansions comprised between 350000 and 385000 configurations. The calculations were danied out at about fifteen nuclear geometries in therange 2.20 to 1010 au for each state.

3. Results and discussion

The final vanational CI energies for the X 2Z+, A 2ff and B 25;* states are plotted as a function of in- ternuclear distance in fig. 1. In general appearance these potential curves are ve@ similar to the Morse potentials given by Tsuji et al. [3] _ The most note- worthy point with the electronic states of CS+ is, as al- ready mentioned, that the third state is not the one with the dominant configuration (KKL)(So)~6rr) (2n)4(7u)2 as would be expected from an analogy with CO+. Rather, as was clearly demonstrated by Okuda and Jonathan [14] from semiempirical and by Domcke et al. [15] from ab initio calculations. the B state is of shake-up character. The present calculations show that the B state wavefunction is do_minated by the (KKL)(5~)~(6~~~(2rr)~(7~) configuration at short internuclear distances and by the ~~SU)~~U)~- (2~)3(7~~3~) and ~~5~)z~6~)(2~~(7u)2 eoufig- urations around the equilibrium nuclear geometry. The I3 2E+ state is thus strongly mixed through con- figuration interaction with both ‘&e X 2X+ and C2Z* [CS X 1Z*(6u)-1) states.

E4 -W48-

-L35.2 -

I I I I * I I I I 30 4.0 sci R{auJ

Fr;. 1. Potential energy CUI-+TS for the X %+, A 2n and B 2~+ states of CS+ Tom mriational contracted-Cl calculations.

Volume 117. number 4 CHEMICAL PHYSICS UTTERS 21 June 1985

Table 1 Spectroscopic mnstants (IZIII-~) for the B ‘Z+. A *II and X %* states of CS*

B =Z+

this work, CI =xp- r31

A%

this work, CI =xp- I21

x 2z+

this work, CI =P- PI

re (A) 1.667 1.665 a) 1.653 1.6399 1.501 1.4925 Be 0.6953 0.7074 0.7184 0.8575 0.8673 pe 0.0079 00086 0 -0065 0 0060 0.0065 we. 920.6 911 988.34 1013.79 1358.45 1376 6 “eXe 644 65 6.41 6.78 7.64 7.8

D\ "T%n (eV)

910.17 974.75 1343.17 1361 b,

369935 36509 11875.8 11984 96 d)

5.60 0 0 0.0 6.38 =)

a) Ref. [ll],from photoelectron data. b) Ref. [5]. ‘1 Ref. [22]_ d) CI energy: 435 223520

In order to check the quality of the potential curves, the computed CI energies were fitted to poly- nomials of degree ten or eleven and the rovibrational Schrodinger equation was solved numerically. The computed energy levels were titted to a Dunham ex- pansion and the resulting constants are listed in table 1. The errors in the calculated equilibrium bond lengths are 0.013 A (0.0212 A at CAS SCF level) for the A211 state and 0.0085 A (0.0115 A CAS SCF) for the X2Zf state. The close agreement between calcu- lated and experimental re values for the B 21;+ state is

fortuitous. The experimental bond lengths of the B state given in table 1 were not deternuned from a rota- tional analysis but from the Hppearance of the shake- UT band at 16.1 eV in the photoelectron spectrum of CS [l l] _ It should be noted that the corresponding procedure for the A and X states gave bond lengths of the order of 0.005-0.008 A longer than the analysis

of the optical emission data [2] _ If 0.008 A is sub- tracted from 1.665 A, the error in the calculated equi- librium bond length is O.OiO A and of the same order of magnitude as for the A and X states. The error at the CAS SCF level was 0.0346 A, in other words some- what larger than for the other states The calculated

equibbrium geometries are slightly improved by the variational CI procedure. No further improvements were obtained when the CI energies were extrapolated to the full CI knit with the correction suggested by Davidson [23] _ In fact it is most probable that the de- ficiencies in the equiliirium geometries can only be reduced if the CAS SCF calculations are repeated with a larger active space. Pettersson and Siegbahn [24]

have shown that when a diatomic contains at least one second-row atom it is important to add one further narbital and one &orbital to the valence space in the orbital optimization step. Very long CAS SCF expan- sions are then obtained, but Sicgbabn [25] has devel- oped a new method to handle this problem. The com- puted excitation energies are in excellent agreement with the experimental values and satisfactory agree- ment is also obtained for the vibration-rotation con- stants. The ground-state dissociation ener= is too low by almost 0 8 eV. A larger active space would have re- duced this error according to ref. [24], but the lack of an f function in the sulphur basis is probably also an important source of error.

The main aim of the present work was to investi- gate the radiative properties of CS+. The non-ortho- gonal electronic transition Imoments for the A-X, B-X and B-A transitions evaluated with the CAS SCF

wavefunctions are shown m fig. 2 as a function of in- ternuclear distance_ Obase et al. [9] determined experi- mentally the B-X relative transition moment variation

in the region 1.542-l -699 A in good agreement with the present result. They also concluded from their data that the B-A tranntron moment is constant in the region around 1.66 A. This is not quite in agree- ment with the present work, but the variation of the transition moment in this region is slow and would be difficult to determine experimentally. The electronic transition moments were vibrationally averaged with vibrational wavefunctions calculated numerically from the experimental Klein-Dunham potential curves for

. the A and X states and from the CI curve for the B

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Volume 117, number 4 CHEMICAL. PHYSICS LEITERS 21 June 1985

I I I I I I I

20 3o R(auJLo 50

Fig. 2. Calculated electronic transition moments as a function of intcmudear dktanoz for the A 2~--X 2E+, B *~;+c-_X~~~ and B 2Z+-A ‘II transitions of CS+.

state- The absorption oscillator strength and the transi- tion probability are related to the averaged transition moment through

f* vu . . = 3.038 X lO--%[(2 - &0,nn+,,r9/(2 - S,,,t.)]

x IWR,(r)lu”~ 12, (1)

A ’ rl= 2.026 X lC1%~[(2 - & VU O,*~+*M2 - ~,,,~~I x l(u’lR,(r) ILm*, (2)

where LJ IS the transition energy in cm-l, h’IR,(r) lu”)12 is the square of the vibratlonally averaged electronic transition moment, 8 is the Kronecker delta and A’ and A” are 0 and 1 for a IZ and lI state, respectively_ The radiative lifetime is ob- tained from summation of the transition probabilities over all lower vibronic states. The lifetime of the u’ = 0 level of the B 22’ state was calculated to be 222 ns, in FcZ?r agreement with the experimental re- sult of 425 ns obtzuned by Erman and Larsson [8] _ The dominant decay route for the B state is to the A state with a hfetime of 255 ns, while the lifetime to- wards the ground state is 1.7 w. This readily explains why the B-X system is weaker (or in some cases ab- sent, c-f. refs. [2,8]) than the B-A system. As pointed out in ref. [2] the isoelectionic molecule CP behaves differently since the B-X system in that case appears strongly III emission. Ab initio calculations on CF’ may shed some light on this problem- The large dis-

crepancy between calculated and measured B state hfetimes is probably due to three factors of different origin. In the first place there are indications that the U’ = 0 level of the B state is perturbed by high vibra- tional levels of the A state [2]. Such perturbations would lengthen the B state lifetime since the radiative lifetime of the A state is, as will be seen below, in the

mlcrosecond range. SecondIy the (0,O) band of the B-A system used in the hfetime measurements by Erman and Larsson [S] is partly overlapped by un- identified emission probably from neutral CS (c-f. ref. [2])_ If this emission has a hfetime longer than 222 ns it would tend to lengthen the measured B state life- time_ Thirdly it usually (though not always) found that ab initio calculations yield too large an electronic transition moment. The calculations on the nine-va-

lence-electrort molecule CN with the same methods as in the present work [21], gave results in excellent agreement with experiments borh for the B *2* and A *II states (see also ref. [26] for recent results for the A state). However, the presence of a second-row atom m the molecule m the present case might hrmt the value of a comparison between CS* and CN. It is in passing amusing to note that a very crude estimate of the B state lifetime [S] gave a result onLy slightly longer than the present ab initio value.

In order to deterrmne the abundance of a molecu.Ie in an astrophysical object it is essential to know the absorption oscillator strength of the particular transi- tion used to monitor it_ The oscillator strengths cal- culated according to eq- (1) for the strongest bands of the A-X transitlon are given in table 2. The radiative

Table 2

(m I, VU f I II vu

cl-o l-08 0-l 3 46 O-2 5.00 O-3 4-38 04 255 1-O 3.49 1-l 559 l-2 2.44 1-3 0.02 14 l-08 2-O 6.07 2-L 3.69

2-3 2-l 8 24 1.93 3-o 756 3-l 0.81 3-2 190 3-3 2.21 44 759 4-2 3.43 5-o 654 5-l 156 5-2 2-26

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Volume 117, number 4 CHEMICAL PHYSICS LETTERS 21 June 1985

Table 3 Radiative lifetimes of the A% state of CS*

0 22.3 3 120

: 17.1 14.0 4 5 105 9.4

hfetimes of the six Iowest vibrational levels of the A

state are listed in table 3_ No expeximental data exist for companson. The best method of measuring such long lifetimes of a molecule ion would be to use a radiofrequency ion trap in combination with a tunable laser as described by Mahan and O’Keefe [27]_

References

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[2] D. Gauyacq and M. Horam, Can 3. Phys. 56 (1978) 587. [3] M. TSUJX, H Obase, M. Matsuo, M. Endoh and

Y. Nishimura, Chem. Phys. 50 (1980) 195. [4] M. Tsuji, H. Obase and Y. Nishimum, J. Chem. Phys. 73

(1980) 2575. [5] J-A. Coxon, PJ_ Masmux and D W. Setser, Chem. Phys.

17 (1976) 403. [6] K-T. Wu and A-J. Yen&a, Chem. Phys. Letters 67

(1979) 134. [7] hf. Tsuji, M. Matsuo and Y. Nishimura. Intern. J. Mass.

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[12] G.H. King, H-W. Kroto and RJ. Suffolk, Chem. Phys Letters 13 (1972) 457.

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[14] M. Okuda and N. Jonathan, J. Eiectron Spectry. 3 (1974) 19

[15] W. Domcke, LS_ Ccderbaurn, W. van Niessen and WP. J&emer, Chem. Phys. Letters 43 (1976) 258.

j16] P-EM. Siegbahn, J_ Almiaf, A. Heiberg and B-0. Roos, J. Chem. Phys. 74 (1981) 2384.

[17] PB&t Siegbahn, Xntern. J. Quantum Chem. 23 (1983) 1869.

[18] A. Vedlard, Theorct Chim. Acta 12 (1968)405. [I91 T.H. Dunning, J. Chem. Phys. 55 (1971) 716.

1201 S. Hu&xaga, J. Chem. Phys. 42 (1965) 1293. [Zl] M. Jzusson. PEM. Sieghahn and H. Agren, Astrophys. J.

272 (1983) 369. [22] K9. Huber and G. Herr&erg, MoJecuJar spectra and

molecuJar structure, Vol. 4 Constants of diatomic mol- ecules (Van Nostrand, Prmcetoa. 1979).

[23] E.R. Davidson, in: The world of quantum chemistry, eds. R. Daudel and B. Pulhnan (Reidel, Dordrecht. 1974).

1241 L.G.M. Petterson and P-EM. Siegbahn, to be published. 1251 P.E hf. Siegbahn. Chem. Phys. Letters 109 (1984) 417. [26] M-R. Teherian and T-G. Slanger, J. Cbem. Phys. 81

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1209

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